SBMLBioModels: S - T

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S


MODEL1006230031 @ v0.0.1

This a model from the article: Distribution of a persistent sodium current across the ventricular wall in guinea pigs.…

A tetrodotoxin-sensitive persistent sodium current, I(pNa), was found in guinea pig ventricular myocytes by whole-cell patch clamping. This current was characterized in cells derived from the basal left ventricular subendocardium, midmyocardium, and subepicardium. Midmyocardial cells show a statistically significant (P<0.05) smaller I(pNa) than subendocardial and subepicardial myocytes. There was no significant difference in I(pNa) current density between subepicardial and subendocardial cells. Computer modeling studies support a role of this current in the dispersion of action potential duration across the ventricular wall. link: http://identifiers.org/pubmed/11073887

Parameters: none

States: none

Observables: none

MODEL1006230020 @ v0.0.1

This a model from the article: Distribution of a persistent sodium current across the ventricular wall in guinea pigs.…

A tetrodotoxin-sensitive persistent sodium current, I(pNa), was found in guinea pig ventricular myocytes by whole-cell patch clamping. This current was characterized in cells derived from the basal left ventricular subendocardium, midmyocardium, and subepicardium. Midmyocardial cells show a statistically significant (P<0.05) smaller I(pNa) than subendocardial and subepicardial myocytes. There was no significant difference in I(pNa) current density between subepicardial and subendocardial cells. Computer modeling studies support a role of this current in the dispersion of action potential duration across the ventricular wall. link: http://identifiers.org/pubmed/11073887

Parameters: none

States: none

Observables: none

MODEL1005050000 @ v0.0.1

This a model from the article: Prediction of photoperiodic regulators from quantitative gene circuit models. Salazar…

Photoperiod sensors allow physiological adaptation to the changing seasons. The prevalent hypothesis is that day length perception is mediated through coupling of an endogenous rhythm with an external light signal. Sufficient molecular data are available to test this quantitatively in plants, though not yet in mammals. In Arabidopsis, the clock-regulated genes CONSTANS (CO) and FLAVIN, KELCH, F-BOX (FKF1) and their light-sensitive proteins are thought to form an external coincidence sensor. Here, we model the integration of light and timing information by CO, its target gene FLOWERING LOCUS T (FT), and the circadian clock. Among other predictions, our models show that FKF1 activates FT. We demonstrate experimentally that this effect is independent of the known activation of CO by FKF1, thus we locate a major, novel controller of photoperiodism. External coincidence is part of a complex photoperiod sensor: modeling makes this complexity explicit and may thus contribute to crop improvement. link: http://identifiers.org/pubmed/20005809

Parameters: none

States: none

Observables: none

Salcedo-Sora2016 - Microbial folate biosynthesis and utilisationThis model is described in the article: [ A mathematica…

The metabolic biochemistry of folate biosynthesis and utilisation has evolved into a complex network of reactions. Although this complexity represents challenges to the field of folate research it has also provided a renewed source for antimetabolite targets. A range of improved folate chemotherapy continues to be developed and applied particularly to cancer and chronic inflammatory diseases. However, new or better antifolates against infectious diseases remain much more elusive. In this paper we describe the assembly of a generic deterministic mathematical model of microbial folate metabolism. Our aim is to explore how a mathematical model could be used to explore the dynamics of this inherently complex set of biochemical reactions. Using the model it was found that: (1) a particular small set of folate intermediates are overrepresented, (2) inhibitory profiles can be quantified by the level of key folate products, (3) using the model to scan for the most effective combinatorial inhibitions of folate enzymes we identified specific targets which could complement current antifolates, and (4) the model substantiates the case for a substrate cycle in the folinic acid biosynthesis reaction. Our model is coded in the systems biology markup language and has been deposited in the BioModels Database (MODEL1511020000), this makes it accessible to the community as a whole. link: http://identifiers.org/pubmed/26794619

Parameters:

Name Description
Km=7.4; V=792.064 Reaction: DHNTP => AHMDHP + HAD + Pi; DHNTP, Rate Law: compartment*V*DHNTP/(Km+DHNTP)
katp=15.0; vmax=382.2; kahmdhp=3.6 Reaction: AHMDHP + ATP => AHMDPP + AMP; AHMDHP, ATP, Rate Law: compartment*vmax*ATP*AHMDHP/(kahmdhp*katp+katp*ATP+kahmdhp*AHMDHP+ATP*AHMDHP)
kdlp=290.0; kgly=4505.0; vmax=751.66 Reaction: DLp + Gly => SAmDLp + COTwo; DLp, Gly, Rate Law: compartment*vmax*DLp*Gly/(kgly*kdlp+kgly*Gly+kdlp*DLp+DLp*Gly)
vmax=379.925; khcy=17.0; kmthfglu=30.0 Reaction: MTHFGlu + Hcy => THFGlu + Met; MTHFGlu, Hcy, Rate Law: compartment*vmax*MTHFGlu*Hcy/(kmthfglu*khcy+kmthfglu*Hcy+khcy*MTHFGlu+MTHFGlu*Hcy)
kffthfglu=5.0; katp=50.0; vmax=500.0 Reaction: ATP + ffTHFGlu => ADP + Pi + meTHFGlu; ATP, ffTHFGlu, Rate Law: compartment*vmax*ATP*ffTHFGlu/(katp*kffthfglu+katp*ffTHFGlu+kffthfglu*ATP+ATP*ffTHFGlu)
k1=0.08; k2=0.031 Reaction: meTHFGlu => fTHFGlu; meTHFGlu, fTHFGlu, Rate Law: compartment*(k1*meTHFGlu-k2*fTHFGlu)
kgln=1100.0; kcm=13.0; vmax=26.0 Reaction: CM + Gln => ADC + Glu; CM, Gln, Rate Law: compartment*vmax*CM*Gln/(kcm*kgln+kcm*Gln+kgln*CM+CM*Gln)
vmax=15315.3; kformyl=3190.0; kthfglu=134.0; katp=74.5 Reaction: fTHFGlu + ADP + Pi => THFGlu + ATP + Formyl; fTHFGlu, ADP, Pi, Rate Law: compartment*vmax*fTHFGlu*ADP*Pi/(kthfglu*kformyl*katp+kthfglu*(ADP+Pi)+kformyl*(fTHFGlu+Pi)+katp*(ADP+fTHFGlu)+fTHFGlu*ADP*Pi)
kep=285.0; kpep=36.0; vmax=578.76 Reaction: PEP + EP => DAHP + Pi; PEP, EP, Rate Law: compartment*vmax*EP*PEP/(kpep*kep+kpep*EP+kep*PEP+EP*PEP)
knadp=22.0; kidhf=0.428; vmax=1892.8; kmythfglu=25.0 Reaction: myTHFGlu + NADP => meTHFGlu + NADPH; DHF, myTHFGlu, NADP, Rate Law: compartment*vmax*myTHFGlu*NADP/(kmythfglu*(1+DHF/kidhf)*knadp+kmythfglu*NADP+knadp*myTHFGlu+myTHFGlu*NADP)
kthf=26.0; vmax=84.63; kglu=740.0; katp=128.0; kidhf=3.1 Reaction: THF + Glu + ATP => THFGlu + ADP + Pi; DHF, THF, Glu, ATP, Rate Law: compartment*vmax*THF*Glu*ATP/(kthf*(1+DHF/kidhf)*kglu*katp+kthf*(Glu+ATP)+kglu*(THF+ATP)+katp*(THF+Glu)+THF*Glu*ATP)
Km=4.7; V=7.462 Reaction: DAHP => DHQ + Pi; DAHP, Rate Law: compartment*V*DAHP/(Km+DAHP)
kthfglu=40.0; kithf=0.157; kser=700.0; vmax=682.5 Reaction: THFGlu + Ser => myTHFGlu + Gly; THF, THFGlu, Ser, Rate Law: compartment*vmax*THFGlu*Ser/(kthfglu*(1+THF/kithf)*kser+kthfglu*Ser+kser*THFGlu+THFGlu*Ser)
kfthfglu=7.85; vmax=59.332; knadp=0.9 Reaction: fTHFGlu + NADP => THFGlu + COTwo + NADPH; fTHFGlu, NADP, Rate Law: compartment*vmax*fTHFGlu*NADP/(kfthfglu*knadp+kfthfglu*NADP+knadp*fTHFGlu+fTHFGlu*NADP)
ksk=200.0; vmax=18200.0; katp=151.5 Reaction: SK + ATP => SKP + ADP + Pi; SK, ATP, Rate Law: compartment*vmax*SK*ATP/(ksk*katp+ksk*ATP+katp*SK+SK*ATP)
kdhsk=30.0; knadph=11.0; vmax=17290.0 Reaction: DHSK + NADPH => SK + NADP; DHSK, NADPH, Rate Law: compartment*vmax*DHSK*NADPH/(kdhsk*knadph+kdhsk*NADPH+knadph*DHSK+DHSK*NADPH)
kmythfglu=17.0; vmax=49.14; kidhf=0.428; kdump=5.4 Reaction: myTHFGlu + dUMP => dTMP + DHF; DHF, myTHFGlu, dUMP, Rate Law: compartment*vmax*myTHFGlu*dUMP/(kmythfglu*(1+DHF/kidhf)*kdump+kmythfglu*dUMP+kdump*myTHFGlu+myTHFGlu*dUMP)
Km=58.0; V=116.48 Reaction: DHQ => DHSK; DHQ, Rate Law: compartment*V*DHQ/(Km+DHQ)
kpaba=2.6; vmax=105.014; kahmdpp=3.15 Reaction: AHMDPP + pABA => DHP + Pi; AHMDPP, pABA, Rate Law: compartment*vmax*AHMDPP*pABA/(kahmdpp*kpaba+kpaba*AHMDPP+kahmdpp*pABA+AHMDPP*pABA)
kdhf=3.0; vmax=3000.0; knadph=6.12 Reaction: DHF + NADPH => THF + NADP; DHF, NADPH, Rate Law: compartment*vmax*DHF*NADPH/(kdhf*knadph+kdhf*NADPH+knadph*DHF+DHF*NADPH)
vmax=196.56; ksamdlp=290.0; kthfglu=67.7 Reaction: THFGlu + SAmDLp => myTHFGlu + Lp + Ammonia; THFGlu, SAmDLp, Rate Law: compartment*vmax*THFGlu*SAmDLp/(kthfglu*ksamdlp+kthfglu*SAmDLp+ksamdlp*THFGlu+THFGlu*SAmDLp)
V=2.2; Km=1.1 Reaction: ADC => pABA + Pyr; ADC, Rate Law: compartment*V*ADC/(Km+ADC)
vmax=2.821; kglu=1380.0; katp=100.0; kdhp=1.0 Reaction: DHP + Glu + ATP => DHF + ADP + Pi; DHP, Glu, ATP, Rate Law: compartment*vmax*DHP*Glu*ATP/(kdhp*kglu*katp+kdhp*(Glu+ATP)+kglu*(DHP+ATP)+katp*(Glu+ATP)+DHP*Glu*ATP)
vmax=738.92; knadph=19.0; kmythfglu=33.0; kidhf=0.428 Reaction: myTHFGlu + NADPH => MTHFGlu + NADP; DHF, myTHFGlu, NADPH, Rate Law: compartment*vmax*myTHFGlu*NADPH/(kmythfglu*(1+DHF/kidhf)*knadph+kmythfglu*NADPH+knadph*myTHFGlu+myTHFGlu*NADPH)
klp=1280.0; knadh=58.0; vmax=5432.7 Reaction: Lp + NADH => DLp + NAD; NADH, Lp, Rate Law: compartment*vmax*NADH*Lp/(knadh*klp+knadh*Lp+klp*NADH+NADH*Lp)
Km=12.7; V=728.0 Reaction: CVPSK => CM + Pi; CVPSK, Rate Law: compartment*V*CVPSK/(Km+CVPSK)
kmtrna=1.07; vmax=116.48; kfthfglu=12.15 Reaction: fTHFGlu + mtRNA => fmtRNA + THFGlu; fTHFGlu, mtRNA, Rate Law: compartment*vmax*fTHFGlu*mtRNA/(kfthfglu*kmtrna+kfthfglu*mtRNA+kmtrna*fTHFGlu+fTHFGlu*mtRNA)
Km=10.0; V=22.659 Reaction: DHNTP => PTHP + Pi; DHNTP, Rate Law: compartment*V*DHNTP/(Km+DHNTP)
kgtp=17.6; vmax=1515.15; kiTHF=0.157 Reaction: GTP => DHNTP + Formyl; THF, GTP, Rate Law: compartment*vmax*GTP/(kgtp*(1+THF/kiTHF)+GTP)
kpep=93.0; kskp=80.0; vmax=1547.0 Reaction: SKP + PEP => CVPSK + Pi; SKP, PEP, Rate Law: compartment*vmax*SKP*PEP/(kpep*kskp+kpep*PEP+kskp*SKP+PEP*SKP)
Km=67.0; V=200.0 Reaction: meTHFGlu => ffTHFGlu; meTHFGlu, Rate Law: compartment*V*meTHFGlu/(Km+meTHFGlu)

States:

Name Description
DHSK [3-Dehydroshikimate]
THF [Tetrahydrofolate]
DHF [Dihydrofolate]
NADPH [NADPH]
myTHFGlu [5,10-Methylenetetrahydrofolate]
fTHFGlu [10-Formyltetrahydrofolate]
Lp [Lipoylprotein]
NADP [NADP+]
EP [D-Erythrose 4-phosphate]
THFGlu [THF-polyglutamate]
mtRNA [L-Methionyl-tRNA]
ADC [4-Amino-4-deoxychorismate]
fmtRNA [N-Formylmethionyl-tRNA]
Formyl [Formate]
DLp [Dihydrolipoylprotein]
ADP [ADP]
NAD [NAD+]
HAD [Glycolaldehyde]
COTwo COTwo
ATP [ATP]
Gln [L-Glutamine]
DHNTP [7,8-Dihydroneopterin 3'-triphosphate]
CM [Chorismate]
Ammonia [Ammonia]
AHMDHP [6-(Hydroxymethyl)-7,8-dihydropterin]
AMP [AMP]
GTP [GTP]
DHP [Dihydropteroate]
ffTHFGlu [Folinic acid]
SKP [Shikimate 3-phosphate]
Glu [L-Glutamate]
meTHFGlu [5,10-Methenyltetrahydrofolate]
AHMDPP [6-Hydroxymethyl-7,8-dihydropterin diphosphate]
PTHP [6-Pyruvoyltetrahydropterin]
NADH [NADH]
SAmDLp [S-Aminomethyldihydrolipoylprotein]
pABA [4-Aminobenzoate]
CVPSK [5-O-(1-Carboxyvinyl)-3-phosphoshikimate]
DAHP [2-Dehydro-3-deoxy-D-arabino-heptonate 7-phosphate]
Pi [Orthophosphate]
SK [Shikimate]
DHQ [3-Dehydroquinate]
dUMP [dUMP]

Observables: none

Sanchez2017 - Inflammatory responses during acute hyperinsulinemia This model is described in the article: [The CD4+ T…

Obesity is frequently linked to insulin resistance, high insulin levels, chronic inflammation, and alterations in the behaviour of CD4+ T cells. Despite the biomedical importance of this condition, the system-level mechanisms that alter CD4+ T cell differentiation and plasticity are not well understood.

We model how hyperinsulinemia alters the dynamics of the CD4+ T regulatory network, and this, in turn, modulates cell differentiation and plasticity. Different polarizing microenvironments are simulated under basal and high levels of insulin to assess impacts on cell-fate attainment and robustness in response to transient perturbations. In the presence of high levels of insulin Th1 and Th17 become more stable to transient perturbations, and their basin sizes are augmented, Tr1 cells become less stable or disappear, while TGF? producing cells remain unaltered. Hence, the model provides a dynamic system-level framework and explanation to further understand the documented and apparently paradoxical role of TGF? in both inflammation and regulation of immune responses, as well as the emergence of the adipose Treg phenotype. Furthermore, our simulations provide new predictions on the impact of the microenvironment in the coexistence of the different cell types, suggesting that in pro-Th1, pro-Th2 and pro-Th17 environments effector and regulatory cells can coexist, but that high levels of insulin severely diminish regulatory cells, especially in a pro-Th17 environment.

This work provides a first step towards a system-level formal and dynamic framework to integrate further experimental data in the study of complex inflammatory diseases. link: http://identifiers.org/doi/10.1186/s12918-017-0436-y

Parameters: none

States: none

Observables: none

Modeling the dynamics of hepatitis C virus with combined antiviral drug therapy: interferon and ribavirin. Banerjee S1,…

A mathematical modeling of hepatitis C virus (HCV) dynamics and antiviral therapy has been presented in this paper. The proposed model, which involves four coupled ordinary differential equations, describes the interaction of target cells (hepatocytes), infected cells, infectious virions and non-infectious virions. The model takes into consideration the addition of ribavirin to interferon therapy and explains the dynamics regarding a biphasic and triphasic decline of viral load in the model. A critical drug efficacy parameter has been defined and it is shown that for an efficacy above this critical value, HCV is eradicated whereas for efficacy lower this critical value, a new steady state for infectious virions is reached, which is lower than the previous steady state value. link: http://identifiers.org/pubmed/23891586

Parameters: none

States: none

Observables: none

Modeling the dynamics of hepatitis C virus with combined antiviral drug therapy: interferon and ribavirin. Banerjee S1,…

A mathematical modeling of hepatitis C virus (HCV) dynamics and antiviral therapy has been presented in this paper. The proposed model, which involves four coupled ordinary differential equations, describes the interaction of target cells (hepatocytes), infected cells, infectious virions and non-infectious virions. The model takes into consideration the addition of ribavirin to interferon therapy and explains the dynamics regarding a biphasic and triphasic decline of viral load in the model. A critical drug efficacy parameter has been defined and it is shown that for an efficacy above this critical value, HCV is eradicated whereas for efficacy lower this critical value, a new steady state for infectious virions is reached, which is lower than the previous steady state value. link: http://identifiers.org/pubmed/23891586

Parameters:

Name Description
d2 = 1.0 Reaction: I =>, Rate Law: compartment*d2*I
n1 = 0.8; alpha = 2.25E-7; c = 0.5 Reaction: => I; VI, T, Rate Law: compartment*(1-c*n1)*alpha*VI*T
r = 1.99; s = 1.0; k = 3.6E7 Reaction: => T, Rate Law: compartment*(s+r*T*(1-(T+1)/k))
n1 = 0.8; alpha = 2.25E-7; d1 = 0.01; c = 0.5 Reaction: T => ; VI, Rate Law: compartment*(d1*T+(1-c*n1)*alpha*VI*T)
d3 = 6.0 Reaction: VI =>, Rate Law: compartment*d3*VI
n1 = 0.8; beta = 2.9; nr = 0.0 Reaction: => VI; I, Rate Law: compartment*(1-(nr+n1)/2)*beta*I

States:

Name Description
I [hepatocyte]
T [Neoplastic Cell]
VNI VNI
VI VI

Observables: none

Sanjuan2013 - Evolution of HIV T-cell epitope, control modelControl model in which the virus targets a nonimmune cell ty…

The immune system should constitute a strong selective pressure promoting viral genetic diversity and evolution. However, HIV shows lower sequence variability at T-cell epitopes than elsewhere in the genome, in contrast with other human RNA viruses. Here, we propose that epitope conservation is a consequence of the particular interactions established between HIV and the immune system. On one hand, epitope recognition triggers an anti-HIV response mediated by cytotoxic T-lymphocytes (CTLs), but on the other hand, activation of CD4(+) helper T lymphocytes (TH cells) promotes HIV replication. Mathematical modeling of these opposite selective forces revealed that selection at the intrapatient level can promote either T-cell epitope conservation or escape. We predict greater conservation for epitopes contributing significantly to total immune activation levels (immunodominance), and when TH cell infection is concomitant to epitope recognition (trans-infection). We suggest that HIV-driven immune activation in the lymph nodes during the chronic stage of the disease may offer a favorable scenario for epitope conservation. Our results also support the view that some pathogens draw benefits from the immune response and suggest that vaccination strategies based on conserved TH epitopes may be counterproductive. link: http://identifiers.org/pubmed/23565057

Parameters: none

States: none

Observables: none

Sanjuan2013 - Evolution of HIV T-cell epitope, immune activation modelModel of cellular immune response against HIV. Th…

The immune system should constitute a strong selective pressure promoting viral genetic diversity and evolution. However, HIV shows lower sequence variability at T-cell epitopes than elsewhere in the genome, in contrast with other human RNA viruses. Here, we propose that epitope conservation is a consequence of the particular interactions established between HIV and the immune system. On one hand, epitope recognition triggers an anti-HIV response mediated by cytotoxic T-lymphocytes (CTLs), but on the other hand, activation of CD4(+) helper T lymphocytes (TH cells) promotes HIV replication. Mathematical modeling of these opposite selective forces revealed that selection at the intrapatient level can promote either T-cell epitope conservation or escape. We predict greater conservation for epitopes contributing significantly to total immune activation levels (immunodominance), and when TH cell infection is concomitant to epitope recognition (trans-infection). We suggest that HIV-driven immune activation in the lymph nodes during the chronic stage of the disease may offer a favorable scenario for epitope conservation. Our results also support the view that some pathogens draw benefits from the immune response and suggest that vaccination strategies based on conserved TH epitopes may be counterproductive. link: http://identifiers.org/pubmed/23565057

Parameters: none

States: none

Observables: none

BIOMD0000000199 @ v0.0.1

This is a model of neuronal Nitric Oxide Synthase expressed in Escherichia coli based on [ Santolini J. et al. J B…

After initiating NO synthesis a majority of neuronal NO synthase (nNOS) quickly partitions into a ferrous heme-NO complex. This down-regulates activity and increases enzyme K(m,O(2)). To understand this process, we developed a 10-step kinetic model in which the ferric heme-NO enzyme forms as the immediate product of catalysis, and then partitions between NO dissociation versus reduction to a ferrous heme-NO complex. Rate constants used for the model were derived from recent literature or were determined here. Computer simulations of the model precisely described both pre-steady and steady-state features of nNOS catalysis, including NADPH consumption and NO production, buildup of a heme-NO complex, changes between pre-steady and steady-state rates, and the change in enzyme K(m,O(2)) in the presence or absence of NO synthesis. The model also correctly simulated the catalytic features of nNOS mutants W409F and W409Y, which are hyperactive and display less heme-NO complex formation in the steady state. Model simulations showed how the rate of heme reduction influences several features of nNOS catalysis, including populations of NO-bound versus NO-free enzyme in the steady state and the rate of NO synthesis. The simulation predicts that there is an optimum rate of heme reduction that is close to the measured rate in nNOS. Ratio between NADPH consumption and NO synthesis is also predicted to increase with faster heme reduction. Our kinetic model is an accurate and versatile tool for understanding catalytic behavior and will provide new perspectives on NOS regulation. link: http://identifiers.org/pubmed/11038356

Parameters:

Name Description
k9 = 1.0E-4 s^(-1) Reaction: FeII_NO => FeII + NO, Rate Law: cytosol*k9*FeII_NO
k1 = 2.6 s^(-1) Reaction: FeIII + NADPH => FeII + NADPplus, Rate Law: cytosol*k1*FeIII
k2 = 0.9 l*μmol^(-1)*s^(-1) Reaction: FeII + O2 => FeII_O2, Rate Law: cytosol*k2*FeII*O2
k8 = 2.6 s^(-1) Reaction: FeIII_NO + NADPH => FeII_NO + NADPplus, Rate Law: cytosol*k8*FeIII_NO
k7 = 5.0 s^(-1) Reaction: FeIII_NO => FeIII + NO, Rate Law: cytosol*k7*FeIII_NO
k6 = 26.0 s^(-1) Reaction: FeII_star_O2 => FeIII_NO + citrulline, Rate Law: cytosol*k6*FeII_star_O2
k4 = 2.6 s^(-1) Reaction: FeIII_star + NADPH => FeII_star + NADPplus, Rate Law: cytosol*k4*FeIII_star
k3 = 26.0 s^(-1) Reaction: FeII_O2 => FeIII_star, Rate Law: cytosol*k3*FeII_O2
k5 = 0.9 l*μmol^(-1)*s^(-1) Reaction: FeII_star + O2 => FeII_star_O2, Rate Law: cytosol*k5*FeII_star*O2
k10 = 0.0013 l*μmol^(-1)*s^(-1) Reaction: FeII_NO + O2 => FeIII + NO3, Rate Law: cytosol*k10*FeII_NO*O2

States:

Name Description
citrulline [L-citrulline; L-Citrulline]
NO [nitric oxide; Nitric oxide]
FeII [ferroheme b; iron(2+); Nitric oxide synthase, brain]
FeII star O2 [dioxygen; ferroheme b; iron(2+); Nitric oxide synthase, brain]
FeII NO [nitric oxide; ferroheme b; iron(2+); Nitric oxide synthase, brain]
FeIII [iron(3+); ferroheme b; Nitric oxide synthase, brain]
FeIII t [iron(3+); ferroheme b; Nitric oxide synthase, brain]
FeIII star [ferroheme b; iron(3+); Nitric oxide synthase, brain]
NADPH [NADPH; NADPH]
FeIII NO [nitric oxide; ferroheme b; iron(3+); Nitric oxide synthase, brain]
NO3 [nitrate; Nitrate]
FeII O2 [dioxygen; iron(2+); ferroheme b; Nitric oxide synthase, brain]
NADPplus [NADP(+); NADP+]
FeII star [ferroheme b; iron(2+); Nitric oxide synthase, brain]
O2 [dioxygen; Oxygen]

Observables: none

MODEL1006230108 @ v0.0.1

This a model from the article: Role of individual ionic current systems in the SA node hypothesized by a model study.…

This paper discusses the development of a cardiac sinoatrial (SA) node pacemaker model. The model successfully reconstructs the experimental action potentials at various concentrations of external Ca2+ and K+. Increasing the amplitude of L-type Ca2+ current (I(CaL)) prolongs the duration of the action potential and thereby slightly decreases the spontaneous rate. On the other hand, a negative voltage shift of I(CaL) gating by a few mV markedly increases the spontaneous rate. When the amplitude of sustained inward current (I(st)) is increased, the spontaneous rate is increased irrespective of the I(CaL) amplitude. Increasing Ca2+ shortens the action potential and increases the spontaneous rate. When the spontaneous activity is stopped by decreasing I(CaL) amplitude, the resting potential is nearly constant (-35 mV) over 1-15 mM K+ as observed in the experiment. This is because the conductance of the inward background non-selective cation current balances with the outward K+-dependent K+ conductance. The unique role of individual voltage- and time-dependent ion channels is clearly demonstrated and distinguished from that of the background current by calculating an instantaneous zero current potential ("lead potential") during the course of the spontaneous activity. link: http://identifiers.org/pubmed/12877768

Parameters: none

States: none

Observables: none

In India, 100,340 confirmed cases and 3155 confirmed deaths due to COVID-19 were reported as of May 18, 2020. Due to abs…

In India, 100,340 confirmed cases and 3155 confirmed deaths due to COVID-19 were reported as of May 18, 2020. Due to absence of specific vaccine or therapy, non-pharmacological interventions including social distancing, contact tracing are essential to end the worldwide COVID-19. We propose a mathematical model that predicts the dynamics of COVID-19 in 17 provinces of India and the overall India. A complete scenario is given to demonstrate the estimated pandemic life cycle along with the real data or history to date, which in turn divulges the predicted inflection point and ending phase of SARS-CoV-2. The proposed model monitors the dynamics of six compartments, namely susceptible (S), asymptomatic (A), recovered (R), infected (I), isolated infected (Iq ) and quarantined susceptible (Sq ), collectively expressed SARIIqSq . A sensitivity analysis is conducted to determine the robustness of model predictions to parameter values and the sensitive parameters are estimated from the real data on the COVID-19 pandemic in India. Our results reveal that achieving a reduction in the contact rate between uninfected and infected individuals by quarantined the susceptible individuals, can effectively reduce the basic reproduction number. Our model simulations demonstrate that the elimination of ongoing SARS-CoV-2 pandemic is possible by combining the restrictive social distancing and contact tracing. Our predictions are based on real data with reasonable assumptions, whereas the accurate course of epidemic heavily depends on how and when quarantine, isolation and precautionary measures are enforced. link: http://identifiers.org/pubmed/32834603

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M1_K1_PSEQ)The paper presents the various interaction topologies bet…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M1_K1_PSEQ_short_duration_signal)The paper presents the various inte…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M1_K1_USEQ)The paper presents the various interaction topologies bet…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M1_K1_USEQ_short_duration_signal)The paper presents the various inte…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M1_K2_PSEQ)The paper presents the various interaction topologies bet…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M1_K2_PSEQ_short_duration_signal)The paper presents the various inte…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M1_K2_QSS_PSEQ)The paper presents the various interaction topologies…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M1_K2_QSS_USEQ)The paper presents the various interaction topologies…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M1_K2_USEQ)The paper presents the various interaction topologies bet…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M1_K2_USEQ_short_duration_signal)The paper presents the various inte…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M2_K1_PSEQ)The paper presents the various interaction topologies bet…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M2_K1_PSEQ_short_duration_signal)The paper presents the various inte…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M2_K1_USEQ)The paper presents the various interaction topologies bet…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M2_K1_USEQ_short_duration_signal)The paper presents the various inte…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M2_K2_PSEQ)The paper presents the various interaction topologies bet…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M2_K2_PSEQ_short_duration_signal)The paper presents the various inte…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M2_K2_QSS_PSEQ)The paper presents the various interaction topologies…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M2_K2_QSS_USEQ)The paper presents the various interaction topologies…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M2_K2_USEQ)The paper presents the various interaction topologies bet…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M2_K2_USEQ_short_duration_signal)The paper presents the various inte…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M3_K1_PSEQ)The paper presents the various interaction topologies bet…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M3_K1_PSEQ_short_duration_signal)The paper presents the various inte…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M3_K1_USEQ)The paper presents the various interaction topologies bet…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M3_K1_USEQ_short_duration_signal)The paper presents the various inte…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M3_K2_PSEQ)The paper presents the various interaction topologies bet…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M3_K2_PSEQ_short_duration_signal)The paper presents the various inte…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M3_K2_QSS_PSEQ)The paper presents the various interaction topologies…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M3_K2_QSS_USEQ)The paper presents the various interaction topologies…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M3_K2_USEQ)The paper presents the various interaction topologies bet…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M3_K2_USEQ_short_duration_signal)The paper presents the various inte…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M4_K1_PSEQ)The paper presents the various interaction topologies bet…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M4_K1_PSEQ_short_duration_signal)The paper presents the various inte…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M4_K1_USEQ)The paper presents the various interaction topologies bet…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M4_K1_USEQ_short_duration_signal)The paper presents the various inte…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M4_K2_PSEQ)The paper presents the various interaction topologies bet…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters:

Name Description
k1=0.02; k2=1.0 Reaction: species_1 + species_2 => species_3; species_1, species_2, species_3, Rate Law: compartment_1*(k1*species_1*species_2-k2*species_3)
k1=1.0 Reaction: species_17 => species_8 + species_18; species_17, Rate Law: compartment_1*k1*species_17
k1=15.0 Reaction: species_11 => species_2 + species_8; species_11, Rate Law: compartment_1*k1*species_11
k1=0.092 Reaction: species_21 => species_4 + species_13; species_21, Rate Law: compartment_1*k1*species_21
k1=0.5 Reaction: species_14 => species_15; species_14, Rate Law: compartment_1*k1*species_14
k1=0.01 Reaction: species_3 => species_4 + species_2; species_3, Rate Law: compartment_1*k1*species_3
k1=0.032; k2=1.0 Reaction: species_4 + species_2 => species_5; species_4, species_2, species_5, Rate Law: compartment_1*(k1*species_4*species_2-k2*species_5)
k1=0.01; k2=1.0 Reaction: species_10 + species_13 => species_14; species_10, species_13, species_14, Rate Law: compartment_1*(k1*species_10*species_13-k2*species_14)
k2=0.005; k1=0.086 Reaction: species_23 => species_1 + species_13; species_23, species_1, species_13, Rate Law: compartment_1*(k1*species_23-k2*species_1*species_13)
k1=0.045; k2=1.0 Reaction: species_2 + species_13 => species_12; species_2, species_13, species_12, Rate Law: compartment_1*(k1*species_2*species_13-k2*species_12)

States:

Name Description
species 9 [RAF proto-oncogene serine/threonine-protein kinase; Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]
species 27 [RAF proto-oncogene serine/threonine-protein kinase; Dual specificity protein phosphatase 3]
species 1 [Mitogen-activated protein kinase 3]
species 18 [Ras-related protein Rap-2b]
species 4 [Mitogen-activated protein kinase 3; Phosphoprotein]
species 20 [Dual specificity protein phosphatase 3]
species 16 [RAF proto-oncogene serine/threonine-protein kinase]
species 21 [Mitogen-activated protein kinase 3; Dual specificity protein phosphatase 3; Phosphoprotein]
species 8 [RAF proto-oncogene serine/threonine-protein kinase; Phosphoprotein]
species 17 [RAF proto-oncogene serine/threonine-protein kinase; Ras-related protein Rap-2b]
species 12 [Dual specificity mitogen-activated protein kinase kinase 1; Dual specificity protein phosphatase 3; Phosphoprotein]
species 25 [Dual specificity mitogen-activated protein kinase kinase 1; Dual specificity protein phosphatase 3; Phosphoprotein]
species 5 [Mitogen-activated protein kinase 3; Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]
species 15 [Dual specificity mitogen-activated protein kinase kinase 1; Dual specificity protein phosphatase 3]
species 2 [Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]
species 6 [Mitogen-activated protein kinase 3; Phosphoprotein]
species 19 [RAF proto-oncogene serine/threonine-protein kinase; Dual specificity protein phosphatase 3; Phosphoprotein]
species 10 [Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]
species 11 [RAF proto-oncogene serine/threonine-protein kinase; Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]
species 24 [Dual specificity mitogen-activated protein kinase kinase 1; Dual specificity protein phosphatase 3; Phosphoprotein]
species 14 [Dual specificity mitogen-activated protein kinase kinase 1; Dual specificity protein phosphatase 3; Phosphoprotein]
species 22 [Mitogen-activated protein kinase 3; Dual specificity protein phosphatase 3; Phosphoprotein]
species 3 [Mitogen-activated protein kinase 3; Phosphoprotein]
species 23 [Mitogen-activated protein kinase 3; Dual specificity protein phosphatase 3]
species 7 [Dual specificity mitogen-activated protein kinase kinase 1]
species 26 [Dual specificity mitogen-activated protein kinase kinase 1; Dual specificity protein phosphatase 3]
species 13 [Dual specificity protein phosphatase 3]

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M4_K2_PSEQ_short_duration_signal)The paper presents the various inte…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M4_K2_QSS_PSEQ)The paper presents the various interaction topologies…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters:

Name Description
parameter_7 = 50.5; k7=0.01; parameter_8 = 500.0 Reaction: species_6 => species_7; species_5, species_7, species_5, species_6, species_7, Rate Law: compartment_1*k7*species_5*species_6/parameter_7/(1+species_6/parameter_7+species_7/parameter_8)
k4=15.0; parameter_4 = 500.0; parameter_3 = 50.5 Reaction: species_4 => species_5; species_2, species_3, species_2, species_4, species_3, Rate Law: compartment_1*k4*species_2*species_4/parameter_4/(1+species_3/parameter_3+species_4/parameter_4)
parameter_10 = 108.6; parameter_12 = 0.06; k10b=0.086; parameter_14 = 108.6; parameter_13 = 24.3; parameter_9 = 24.3 Reaction: species_7 => species_6; species_5, species_4, species_8, species_3, species_6, species_10, species_7, species_5, species_4, species_8, species_3, species_6, species_10, Rate Law: compartment_1*k10b*species_10*species_7/parameter_10/(1+species_5/parameter_13+species_4/parameter_14+species_3/parameter_12+species_6/parameter_12+species_7/parameter_10+species_8/parameter_9)
parameter_10 = 108.6; k6b=0.086; k6a=0.086; parameter_11 = 0.06; parameter_12 = 0.06; parameter_14 = 108.6; parameter_6 = 108.6; parameter_13 = 24.3; parameter_5 = 24.3; parameter_2 = 54.3; parameter_9 = 24.3 Reaction: species_4 => species_3; species_9, species_5, species_7, species_8, species_3, species_6, species_1, species_2, species_10, species_9, species_4, species_5, species_7, species_8, species_3, species_6, species_1, species_2, species_10, Rate Law: compartment_1*(k6a*species_9*species_4/parameter_6/(1+species_2/parameter_2+species_1/parameter_11+species_5/parameter_5+species_4/parameter_6+species_3/parameter_11)+k6b*species_10*species_4/parameter_14/(1+species_5/parameter_13+species_4/parameter_14+species_3/parameter_12+species_6/parameter_12+species_7/parameter_10+species_8/parameter_9))
k1=1.0; parameter_1 = 100.0 Reaction: species_1 => species_2; species_11, species_1, species_11, Rate Law: compartment_1*k1*species_11*species_1/(parameter_1+species_1)
parameter_11 = 0.06; parameter_6 = 108.6; parameter_5 = 24.3; parameter_2 = 54.3; k2a=0.086 Reaction: species_2 => species_1; species_1, species_9, species_5, species_4, species_3, species_2, species_1, species_9, species_5, species_4, species_3, Rate Law: compartment_1*k2a*species_2*species_9/parameter_2/(1+species_2/parameter_2+species_1/parameter_11+species_5/parameter_5+species_4/parameter_6+species_3/parameter_11)
parameter_10 = 108.6; k5a=0.092; k5b=0.092; parameter_11 = 0.06; parameter_12 = 0.06; parameter_14 = 108.6; parameter_6 = 108.6; parameter_13 = 24.3; parameter_5 = 24.3; parameter_2 = 54.3; parameter_9 = 24.3 Reaction: species_5 => species_4; species_4, species_7, species_8, species_9, species_3, species_6, species_1, species_2, species_10, species_5, species_4, species_7, species_8, species_9, species_3, species_6, species_1, species_2, species_10, Rate Law: compartment_1*(k5a*species_9*species_5/parameter_5/(1+species_2/parameter_2+species_1/parameter_11+species_5/parameter_5+species_4/parameter_6+species_3/parameter_11)+k5b*species_10*species_5/parameter_13/(1+species_5/parameter_13+species_4/parameter_14+species_3/parameter_12+species_6/parameter_12+species_7/parameter_10+species_8/parameter_9))
k7=15.0; parameter_7 = 50.5; parameter_8 = 500.0 Reaction: species_7 => species_8; species_5, species_6, species_5, species_7, species_6, Rate Law: compartment_1*k7*species_5*species_7/parameter_8/(1+species_6/parameter_7+species_7/parameter_8)
k3=0.01; parameter_4 = 500.0; parameter_3 = 50.5 Reaction: species_3 => species_4; species_2, species_4, species_2, species_3, species_4, Rate Law: compartment_1*k3*species_2*species_3/parameter_3/(1+species_3/parameter_3+species_4/parameter_4)
parameter_12 = 0.06; parameter_10 = 108.6; k9b=0.092; parameter_14 = 108.6; parameter_13 = 24.3; parameter_9 = 24.3 Reaction: species_8 => species_7; species_9, species_4, species_7, species_3, species_6, species_10, species_8, species_9, species_4, species_7, species_3, species_6, species_10, Rate Law: compartment_1*k9b*species_10*species_8/parameter_9/(1+species_9/parameter_13+species_4/parameter_14+species_3/parameter_12+species_6/parameter_12+species_7/parameter_10+species_8/parameter_9)

States:

Name Description
species 2 [RAF proto-oncogene serine/threonine-protein kinase; Phosphoprotein]
species 6 [Mitogen-activated protein kinase 3]
species 3 [Dual specificity mitogen-activated protein kinase kinase 1]
species 1 [RAF proto-oncogene serine/threonine-protein kinase]
species 8 [Mitogen-activated protein kinase 3; Phosphoprotein]
species 4 [Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]
species 7 [Mitogen-activated protein kinase 3; Phosphoprotein]
species 5 [Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M4_K2_QSS_USEQ)The paper presents the various interaction topologies…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters:

Name Description
parameter_10 = 108.6; k6b=0.086; k6a=0.086; parameter_12 = 3.0E51; parameter_11 = 3.0E51; parameter_14 = 108.6; parameter_6 = 108.6; parameter_13 = 24.3; parameter_5 = 24.3; parameter_2 = 54.3; parameter_9 = 24.3 Reaction: species_4 => species_3; species_9, species_5, species_7, species_8, species_3, species_6, species_1, species_2, species_10, species_9, species_4, species_5, species_7, species_8, species_3, species_6, species_1, species_2, species_10, Rate Law: compartment_1*(k6a*species_9*species_4/parameter_6/(1+species_2/parameter_2+species_1/parameter_11+species_5/parameter_5+species_4/parameter_6+species_3/parameter_11)+k6b*species_10*species_4/parameter_14/(1+species_5/parameter_13+species_4/parameter_14+species_3/parameter_12+species_6/parameter_12+species_7/parameter_10+species_8/parameter_9))
k4=15.0; parameter_4 = 500.0; parameter_3 = 50.5 Reaction: species_4 => species_5; species_2, species_3, species_2, species_4, species_3, Rate Law: compartment_1*k4*species_2*species_4/parameter_4/(1+species_3/parameter_3+species_4/parameter_4)
parameter_10 = 108.6; k10b=0.086; parameter_14 = 108.6; parameter_13 = 24.3; parameter_12 = 3.0E51; parameter_9 = 24.3 Reaction: species_7 => species_6; species_5, species_4, species_8, species_3, species_6, species_10, species_7, species_5, species_4, species_8, species_3, species_6, species_10, Rate Law: compartment_1*k10b*species_10*species_7/parameter_10/(1+species_5/parameter_13+species_4/parameter_14+species_3/parameter_12+species_6/parameter_12+species_7/parameter_10+species_8/parameter_9)
parameter_10 = 108.6; k5a=0.092; k5b=0.092; parameter_12 = 3.0E51; parameter_11 = 3.0E51; parameter_14 = 108.6; parameter_6 = 108.6; parameter_13 = 24.3; parameter_5 = 24.3; parameter_2 = 54.3; parameter_9 = 24.3 Reaction: species_5 => species_4; species_4, species_7, species_8, species_9, species_3, species_6, species_1, species_2, species_10, species_5, species_4, species_7, species_8, species_9, species_3, species_6, species_1, species_2, species_10, Rate Law: compartment_1*(k5a*species_9*species_5/parameter_5/(1+species_2/parameter_2+species_1/parameter_11+species_5/parameter_5+species_4/parameter_6+species_3/parameter_11)+k5b*species_10*species_5/parameter_13/(1+species_5/parameter_13+species_4/parameter_14+species_3/parameter_12+species_6/parameter_12+species_7/parameter_10+species_8/parameter_9))
parameter_7 = 50.5; k7=0.01; parameter_8 = 500.0 Reaction: species_6 => species_7; species_5, species_7, species_5, species_6, species_7, Rate Law: compartment_1*k7*species_5*species_6/parameter_7/(1+species_6/parameter_7+species_7/parameter_8)
parameter_10 = 108.6; k9b=0.092; parameter_14 = 108.6; parameter_13 = 24.3; parameter_9 = 24.3; parameter_12 = 3.0E51 Reaction: species_8 => species_7; species_9, species_4, species_7, species_3, species_6, species_10, species_8, species_9, species_4, species_7, species_3, species_6, species_10, Rate Law: compartment_1*k9b*species_10*species_8/parameter_9/(1+species_9/parameter_13+species_4/parameter_14+species_3/parameter_12+species_6/parameter_12+species_7/parameter_10+species_8/parameter_9)
k1=1.0; parameter_1 = 100.0 Reaction: species_1 => species_2; species_11, species_1, species_11, Rate Law: compartment_1*k1*species_11*species_1/(parameter_1+species_1)
k3=0.01; parameter_4 = 500.0; parameter_3 = 50.5 Reaction: species_3 => species_4; species_2, species_4, species_2, species_3, species_4, Rate Law: compartment_1*k3*species_2*species_3/parameter_3/(1+species_3/parameter_3+species_4/parameter_4)
parameter_11 = 3.0E51; parameter_6 = 108.6; parameter_5 = 24.3; parameter_2 = 54.3; k2a=0.086 Reaction: species_2 => species_1; species_1, species_9, species_5, species_4, species_3, species_2, species_1, species_9, species_5, species_4, species_3, Rate Law: compartment_1*k2a*species_2*species_9/parameter_2/(1+species_2/parameter_2+species_1/parameter_11+species_5/parameter_5+species_4/parameter_6+species_3/parameter_11)
k7=15.0; parameter_7 = 50.5; parameter_8 = 500.0 Reaction: species_7 => species_8; species_5, species_6, species_5, species_7, species_6, Rate Law: compartment_1*k7*species_5*species_7/parameter_8/(1+species_6/parameter_7+species_7/parameter_8)

States:

Name Description
species 2 [RAF proto-oncogene serine/threonine-protein kinase; Phosphoprotein]
species 6 [Mitogen-activated protein kinase 3]
species 3 [Dual specificity mitogen-activated protein kinase kinase 1]
species 1 [RAF proto-oncogene serine/threonine-protein kinase]
species 8 [Mitogen-activated protein kinase 3; Phosphoprotein]
species 4 [Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]
species 7 [Mitogen-activated protein kinase 3; Phosphoprotein]
species 5 [Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M4_K2_USEQ)The paper presents the various interaction topologies bet…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters:

Name Description
k1=0.02; k2=1.0 Reaction: species_7 + species_8 => species_9; species_7, species_8, species_9, Rate Law: compartment_1*(k1*species_7*species_8-k2*species_9)
k1=1.0 Reaction: species_17 => species_8 + species_18; species_17, Rate Law: compartment_1*k1*species_17
k1=15.0 Reaction: species_5 => species_6 + species_2; species_5, Rate Law: compartment_1*k1*species_5
k1=0.092 Reaction: species_12 => species_10 + species_13; species_12, Rate Law: compartment_1*k1*species_12
k1=0.032; k2=1.0 Reaction: species_10 + species_8 => species_11; species_10, species_8, species_11, Rate Law: compartment_1*(k1*species_10*species_8-k2*species_11)
k1=0.01 Reaction: species_3 => species_4 + species_2; species_3, Rate Law: compartment_1*k1*species_3
k1=0.086 Reaction: species_22 => species_1 + species_13; species_22, Rate Law: compartment_1*k1*species_22
k1=0.0; k2=0.0 Reaction: species_26 => species_7 + species_20; species_26, species_7, species_20, Rate Law: compartment_1*(k1*species_26-k2*species_7*species_20)
k1=0.01; k2=1.0 Reaction: species_10 + species_20 => species_25; species_10, species_20, species_25, Rate Law: compartment_1*(k1*species_10*species_20-k2*species_25)
k1=0.045; k2=1.0 Reaction: species_2 + species_20 => species_24; species_2, species_20, species_24, Rate Law: compartment_1*(k1*species_2*species_20-k2*species_24)

States:

Name Description
species 9 [Dual specificity mitogen-activated protein kinase kinase 1; Mitogen-activated protein kinase 3; Phosphoprotein]
species 27 [RAF proto-oncogene serine/threonine-protein kinase; Dual specificity protein phosphatase 3; Phosphoprotein]
species 1 [Mitogen-activated protein kinase 3]
species 18 [Ras-related protein Rap-2b]
species 20 [Dual specificity protein phosphatase 3]
species 16 [RAF proto-oncogene serine/threonine-protein kinase]
species 4 [Mitogen-activated protein kinase 3; Phosphoprotein]
species 21 [Mitogen-activated protein kinase 3; Dual specificity protein phosphatase 3; Phosphoprotein]
species 8 [RAF proto-oncogene serine/threonine-protein kinase; Phosphoprotein]
species 17 [Ras-related protein Rap-2b; RAF proto-oncogene serine/threonine-protein kinase]
species 12 [Dual specificity mitogen-activated protein kinase kinase 1; Dual specificity protein phosphatase 3; Phosphoprotein]
species 25 [Dual specificity protein phosphatase 3; Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]
species 5 [Mitogen-activated protein kinase 3; Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]
species 15 [Dual specificity mitogen-activated protein kinase kinase 1; Dual specificity protein phosphatase 3]
species 2 [Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]
species 6 [Mitogen-activated protein kinase 3; Phosphoprotein]
species 19 [RAF proto-oncogene serine/threonine-protein kinase; Phosphoprotein]
species 10 [Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]
species 11 [RAF proto-oncogene serine/threonine-protein kinase; Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]
species 24 [Dual specificity mitogen-activated protein kinase kinase 1; Dual specificity protein phosphatase 3; Phosphoprotein]
species 14 [Dual specificity mitogen-activated protein kinase kinase 1; Dual specificity protein phosphatase 3; Phosphoprotein]
species 22 [Mitogen-activated protein kinase 3; Dual specificity protein phosphatase 3]
species 3 [Mitogen-activated protein kinase 3; Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]
species 23 [Mitogen-activated protein kinase 3; Dual specificity protein phosphatase 3; Phosphoprotein]
species 7 [Dual specificity mitogen-activated protein kinase kinase 1]
species 26 [Dual specificity mitogen-activated protein kinase kinase 1; Dual specificity protein phosphatase 3; Phosphoprotein]
species 13 [Dual specificity protein phosphatase 3]

Observables: none

Sarma2012 - Interaction topologies of MAPK cascade (M4_K2_USEQ_short_duration_signal)The paper presents the various inte…

The three layer mitogen activated protein kinase (MAPK) signaling cascade exhibits different designs of interactions between its kinases and phosphatases. While the sequential interactions between the three kinases of the cascade are tightly preserved, the phosphatases of the cascade, such as MKP3 and PP2A, exhibit relatively diverse interactions with their substrate kinases. Additionally, the kinases of the MAPK cascade can also sequester their phosphatases. Thus, each topologically distinct interaction design of kinases and phosphatases could exhibit unique signal processing characteristics, and the presence of phosphatase sequestration may lead to further fine tuning of the propagated signal.We have built four architecturally distinct types of models of the MAPK cascade, each model with identical kinase-kinase interactions but unique kinases-phosphatases interactions. Our simulations unravelled that MAPK cascade's robustness to external perturbations is a function of nature of interaction between its kinases and phosphatases. The cascade's output robustness was enhanced when phosphatases were sequestrated by their target kinases. We uncovered a novel implicit/hidden negative feedback loop from the phosphatase MKP3 to its upstream kinase Raf-1, in a cascade resembling the B cell MAPK cascade. Notably, strength of the feedback loop was reciprocal to the strength of phosphatases' sequestration and stronger sequestration abolished the feedback loop completely. An experimental method to verify the presence of the feedback loop is also proposed. We further showed, when the models were activated by transient signal, memory (total time taken by the cascade output to reach its unstimulated level after removal of signal) of a cascade was determined by the specific designs of interaction among its kinases and phosphatases.Differences in interaction designs among the kinases and phosphatases can differentially shape the robustness and signal response behaviour of the MAPK cascade and phosphatase sequestration dramatically enhances the robustness to perturbations in each of the cascade. An implicit negative feedback loop was uncovered from our analysis and we found that strength of the negative feedback loop is reciprocally related to the strength of phosphatase sequestration. Duration of output phosphorylation in response to a transient signal was also found to be determined by the individual cascade's kinase-phosphatase interaction design. link: http://identifiers.org/pubmed/22748295

Parameters: none

States: none

Observables: none

Sarma2012 - Oscillations in MAPK cascade (S1)Two plausible designs (S1 and S2) of coupled positive and negative feedback…

BACKGROUND: Feedback loops, both positive and negative are embedded in the Mitogen Activated Protein Kinase (MAPK) cascade. In the three layer MAPK cascade, both feedback loops originate from the terminal layer and their sites of action are either of the two upstream layers. Recent studies have shown that the cascade uses coupled positive and negative feedback loops in generating oscillations. Two plausible designs of coupled positive and negative feedback loops can be elucidated from the literature; in one design the positive feedback precedes the negative feedback in the direction of signal flow and vice-versa in another. But it remains unexplored how the two designs contribute towards triggering oscillations in MAPK cascade. Thus it is also not known how amplitude, frequency, robustness or nature (analogous/digital) of the oscillations would be shaped by these two designs. RESULTS: We built two models of MAPK cascade that exhibited oscillations as function of two underlying designs of coupled positive and negative feedback loops. Frequency, amplitude and nature (digital/analogous) of oscillations were found to be differentially determined by each design. It was observed that the positive feedback emerging from an oscillating MAPK cascade and functional in an external signal processing module can trigger oscillations in the target module, provided that the target module satisfy certain parametric requirements. The augmentation of the two models was done to incorporate the nuclear-cytoplasmic shuttling of cascade components followed by induction of a nuclear phosphatase. It revealed that the fate of oscillations in the MAPK cascade is governed by the feedback designs. Oscillations were unaffected due to nuclear compartmentalization owing to one design but were completely abolished in the other case. CONCLUSION: The MAPK cascade can utilize two distinct designs of coupled positive and negative feedback loops to trigger oscillations. The amplitude, frequency and robustness of the oscillations in presence or absence of nuclear compartmentalization were differentially determined by two designs of coupled positive and negative feedback loops. A positive feedback from an oscillating MAPK cascade was shown to induce oscillations in an external signal processing module, uncovering a novel regulatory aspect of MAPK signal processing. link: http://identifiers.org/pubmed/22694947

Parameters:

Name Description
k9=0.1; K9=200.0 Reaction: species_7 => species_6; species_10, species_6, species_5, species_10, species_6, species_7, Rate Law: compartment_0*k9*species_10*species_7/K9/(1+species_7/K9+species_6/K9)
K6=200.0; k6=0.1 Reaction: species_3 => species_2; species_9, species_4, species_3, species_4, species_9, Rate Law: compartment_0*k6*species_9*species_3/K6/(1+species_4/K6+species_3/K6)
K5=200.0; k5=0.1 Reaction: species_4 => species_3; species_9, species_3, species_3, species_4, species_9, Rate Law: compartment_0*k5*species_9*species_4/K5/(1+species_4/K5+species_3/K5)
A=10.0; k4=0.1; K4=20.0; Ka=500.0 Reaction: species_3 => species_4; species_1, species_2, species_7, species_1, species_2, species_3, species_7, Rate Law: compartment_0*k4*species_1*species_3/K4/(1+species_3/K4+species_2/K4)*(1+A*species_7/Ka)/(1+species_7/Ka)
K8=20.0; k8=0.1 Reaction: species_6 => species_7; species_4, species_5, species_4, species_5, species_6, Rate Law: compartment_0*k8*species_4*species_6/K8/(1+species_5/K8+species_6/K8)
KI=9.0; K1=20.0; V1=2.5 Reaction: species_0 => species_1; species_7, species_0, species_7, Rate Law: compartment_0*V1*species_0/K1/((1+species_0/K1)*(1+species_7/KI))
K2=200.0; k2=0.025 Reaction: species_1 => species_0; species_8, species_1, species_8, Rate Law: compartment_0*k2*species_8*species_1/K2/(1+species_1/K2)
A=10.0; K3=20.0; Ka=500.0; k3=0.1 Reaction: species_2 => species_3; species_1, species_3, species_7, species_1, species_2, species_3, species_7, Rate Law: compartment_0*k3*species_1*species_2/K3/(1+species_2/K3+species_3/K3)*(1+A*species_7/Ka)/(1+species_7/Ka)
k10=0.1; K10=200.0 Reaction: species_6 => species_5; species_10, species_7, species_5, species_10, species_6, species_7, Rate Law: compartment_0*k10*species_10*species_6/K10/(1+species_7/K10+species_6/K10)
K7=20.0; k7=0.1 Reaction: species_5 => species_6; species_4, species_6, species_4, species_5, species_6, Rate Law: compartment_0*k7*species_4*species_5/K7/(1+species_5/K7+species_6/K7)

States:

Name Description
species 2 [Dual specificity mitogen-activated protein kinase kinase 1]
species 6 [Mitogen-activated protein kinase 1; Phosphoprotein]
species 3 [Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]
species 0 [RAF proto-oncogene serine/threonine-protein kinase]
species 1 [RAF proto-oncogene serine/threonine-protein kinase; Phosphoprotein]
species 4 [Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]
species 7 [Mitogen-activated protein kinase 1; Phosphoprotein]
species 5 [Mitogen-activated protein kinase 1]

Observables: none

Sarma2012 - Oscillations in MAPK cascade (S1n)Two plausible designs (S1 and S2) of coupled positive and negative feedbac…

BACKGROUND: Feedback loops, both positive and negative are embedded in the Mitogen Activated Protein Kinase (MAPK) cascade. In the three layer MAPK cascade, both feedback loops originate from the terminal layer and their sites of action are either of the two upstream layers. Recent studies have shown that the cascade uses coupled positive and negative feedback loops in generating oscillations. Two plausible designs of coupled positive and negative feedback loops can be elucidated from the literature; in one design the positive feedback precedes the negative feedback in the direction of signal flow and vice-versa in another. But it remains unexplored how the two designs contribute towards triggering oscillations in MAPK cascade. Thus it is also not known how amplitude, frequency, robustness or nature (analogous/digital) of the oscillations would be shaped by these two designs. RESULTS: We built two models of MAPK cascade that exhibited oscillations as function of two underlying designs of coupled positive and negative feedback loops. Frequency, amplitude and nature (digital/analogous) of oscillations were found to be differentially determined by each design. It was observed that the positive feedback emerging from an oscillating MAPK cascade and functional in an external signal processing module can trigger oscillations in the target module, provided that the target module satisfy certain parametric requirements. The augmentation of the two models was done to incorporate the nuclear-cytoplasmic shuttling of cascade components followed by induction of a nuclear phosphatase. It revealed that the fate of oscillations in the MAPK cascade is governed by the feedback designs. Oscillations were unaffected due to nuclear compartmentalization owing to one design but were completely abolished in the other case. CONCLUSION: The MAPK cascade can utilize two distinct designs of coupled positive and negative feedback loops to trigger oscillations. The amplitude, frequency and robustness of the oscillations in presence or absence of nuclear compartmentalization were differentially determined by two designs of coupled positive and negative feedback loops. A positive feedback from an oscillating MAPK cascade was shown to induce oscillations in an external signal processing module, uncovering a novel regulatory aspect of MAPK signal processing. link: http://identifiers.org/pubmed/22694947

Parameters:

Name Description
k1=22.56; k2=15.4 Reaction: species_14 => species_18; species_14, species_18, species_14, species_18, Rate Law: compartment_0*(k1*species_14-k2*species_18)
K22i=10300.0; K22=87.0; k22=0.31 Reaction: species_17 => species_16; species_18, species_11, species_18, species_17, species_11, species_18, species_17, species_11, Rate Law: compartment_0*k22*species_18*species_17/K22/(1+species_17/K22+species_11/K22i)
K5=200.0; k5=0.1 Reaction: species_4 => species_3; species_9, species_3, species_3, species_4, species_9, species_3, species_4, species_9, Rate Law: compartment_0*k5*species_9*species_4/K5/(1+species_4/K5+species_3/K5)
A=10.0; k4=0.1; K4=20.0; Ka=500.0 Reaction: species_3 => species_4; species_1, species_2, species_7, species_1, species_2, species_3, species_7, species_1, species_2, species_3, species_7, Rate Law: compartment_0*k4*species_1*species_3/K4/(1+species_3/K4+species_2/K4)*(1+A*species_7/Ka)/(1+species_7/Ka)
K6=200.0; k6=0.1 Reaction: species_3 => species_2; species_9, species_4, species_3, species_4, species_9, species_3, species_4, species_9, Rate Law: compartment_0*k6*species_9*species_3/K6/(1+species_4/K6+species_3/K6)
KI=9.0; K1=20.0; V1=2.5 Reaction: species_0 => species_1; species_7, species_0, species_7, species_0, species_7, Rate Law: compartment_0*V1*species_0/K1/((1+species_0/K1)*(1+species_7/KI))
K8=20.0; k8=0.1 Reaction: species_6 => species_7; species_4, species_5, species_4, species_5, species_6, species_4, species_5, species_6, Rate Law: compartment_0*k8*species_4*species_6/K8/(1+species_5/K8+species_6/K8)
k11b=2.86; k11f=10.34 Reaction: species_7 => species_11; species_7, species_11, species_7, species_11, Rate Law: compartment_0*(k11f*species_7-k11b*species_11)
A=10.0; K3=20.0; Ka=500.0; k3=0.1 Reaction: species_2 => species_3; species_1, species_3, species_7, species_1, species_2, species_3, species_7, species_1, species_2, species_3, species_7, Rate Law: compartment_0*k3*species_1*species_2/K3/(1+species_2/K3+species_3/K3)*(1+A*species_7/Ka)/(1+species_7/Ka)
K21i=87.0; k21=0.68; K21=10300.0 Reaction: species_11 => species_17; species_17, species_18, species_11, species_17, species_18, species_11, species_17, species_18, Rate Law: compartment_0*k21*species_18*species_11/K21/(1+species_11/K21+species_17/K21i)
V12=29.24; K12=169.0; n12=3.97 Reaction: => species_12; species_11, species_11, species_11, Rate Law: compartment_0*V12*species_11^n12/(K12^n12+species_11^n12)
k9=0.1; K9=200.0 Reaction: species_7 => species_6; species_10, species_6, species_5, species_10, species_6, species_7, species_10, species_6, species_7, Rate Law: compartment_0*k9*species_10*species_7/K9/(1+species_7/K9+species_6/K9)
k1=0.022 Reaction: species_12 => species_13; species_12, species_12, Rate Law: compartment_0*k1*species_12
k15=0.0012 Reaction: => species_14; species_13, species_13, species_13, Rate Law: compartment_0*k15*species_13
k1=0.0078 Reaction: species_13 => ; species_13, species_13, Rate Law: compartment_0*k1*species_13
K2=200.0; k2=0.025 Reaction: species_1 => species_0; species_8, species_1, species_8, species_1, species_8, Rate Law: compartment_0*k2*species_8*species_1/K2/(1+species_1/K2)
k2=2.86; k1=10.34 Reaction: species_5 => species_16; species_5, species_16, species_5, species_16, Rate Law: compartment_0*(k1*species_5-k2*species_16)
k1=2.5E-4 Reaction: species_14 => ; species_14, species_14, Rate Law: compartment_0*k1*species_14
k10=0.1; K10=200.0 Reaction: species_6 => species_5; species_10, species_7, species_5, species_10, species_6, species_7, species_10, species_6, species_7, Rate Law: compartment_0*k10*species_10*species_6/K10/(1+species_7/K10+species_6/K10)
K7=20.0; k7=0.1 Reaction: species_5 => species_6; species_4, species_6, species_4, species_5, species_6, species_4, species_5, species_6, Rate Law: compartment_0*k7*species_4*species_5/K7/(1+species_5/K7+species_6/K7)

States:

Name Description
species 2 [Dual specificity mitogen-activated protein kinase kinase 1]
species 6 [Mitogen-activated protein kinase 1; Phosphoprotein]
species 11 [Mitogen-activated protein kinase 1; Phosphoprotein; nucleus]
species 1 [RAF proto-oncogene serine/threonine-protein kinase; Phosphoprotein]
species 18 [Dual specificity protein phosphatase 3; nucleus]
species 4 [Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]
species 16 [Mitogen-activated protein kinase 1; nucleus]
species 14 [Dual specificity protein phosphatase 3; cytoplasm]
species 3 [Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]
species 0 [RAF proto-oncogene serine/threonine-protein kinase]
species 17 [Mitogen-activated protein kinase 1; Phosphoprotein; nucleus]
species 12 [Dual specificity protein phosphatase 3; nucleus]
species 7 [Mitogen-activated protein kinase 1; Phosphoprotein]
species 5 [Mitogen-activated protein kinase 1]
species 13 [Dual specificity protein phosphatase 3; nucleus]

Observables: none

Sarma2012 - Oscillations in MAPK cascade (S2)Two plausible designs (S1 and S2) of coupled positive and negative feedback…

BACKGROUND: Feedback loops, both positive and negative are embedded in the Mitogen Activated Protein Kinase (MAPK) cascade. In the three layer MAPK cascade, both feedback loops originate from the terminal layer and their sites of action are either of the two upstream layers. Recent studies have shown that the cascade uses coupled positive and negative feedback loops in generating oscillations. Two plausible designs of coupled positive and negative feedback loops can be elucidated from the literature; in one design the positive feedback precedes the negative feedback in the direction of signal flow and vice-versa in another. But it remains unexplored how the two designs contribute towards triggering oscillations in MAPK cascade. Thus it is also not known how amplitude, frequency, robustness or nature (analogous/digital) of the oscillations would be shaped by these two designs. RESULTS: We built two models of MAPK cascade that exhibited oscillations as function of two underlying designs of coupled positive and negative feedback loops. Frequency, amplitude and nature (digital/analogous) of oscillations were found to be differentially determined by each design. It was observed that the positive feedback emerging from an oscillating MAPK cascade and functional in an external signal processing module can trigger oscillations in the target module, provided that the target module satisfy certain parametric requirements. The augmentation of the two models was done to incorporate the nuclear-cytoplasmic shuttling of cascade components followed by induction of a nuclear phosphatase. It revealed that the fate of oscillations in the MAPK cascade is governed by the feedback designs. Oscillations were unaffected due to nuclear compartmentalization owing to one design but were completely abolished in the other case. CONCLUSION: The MAPK cascade can utilize two distinct designs of coupled positive and negative feedback loops to trigger oscillations. The amplitude, frequency and robustness of the oscillations in presence or absence of nuclear compartmentalization were differentially determined by two designs of coupled positive and negative feedback loops. A positive feedback from an oscillating MAPK cascade was shown to induce oscillations in an external signal processing module, uncovering a novel regulatory aspect of MAPK signal processing. link: http://identifiers.org/pubmed/22694947

Parameters:

Name Description
K2=100.0; k2=0.1 Reaction: species_1 => species_0; species_8, species_1, species_8, species_1, species_8, Rate Law: compartment_0*k2*species_8*species_1/K2/(1+species_1/K2)
K10=20.0; k10=0.02 Reaction: species_6 => species_5; species_10, species_7, species_5, species_10, species_6, species_7, species_10, species_6, species_7, Rate Law: compartment_0*k10*species_10*species_6/K10/(1+species_7/K10+species_6/K10)
KI=9.0; k4=0.1; K4=20.0 Reaction: species_3 => species_4; species_1, species_2, species_7, species_1, species_2, species_3, species_7, species_1, species_2, species_3, species_7, Rate Law: compartment_0*k4*species_1*species_3/K4/((1+species_2/K4+species_3/K4)*(1+species_7/KI))
K5=20.0; k5=0.02 Reaction: species_4 => species_3; species_9, species_3, species_3, species_4, species_9, species_3, species_4, species_9, Rate Law: compartment_0*k5*species_9*species_4/K5/(1+species_4/K5+species_3/K5)
K8=20.0; k8=0.1 Reaction: species_6 => species_7; species_4, species_5, species_4, species_5, species_6, species_4, species_5, species_6, Rate Law: compartment_0*k8*species_4*species_6/K8/(1+species_5/K8+species_6/K8)
K9=20.0; k9=0.02 Reaction: species_7 => species_6; species_10, species_6, species_5, species_10, species_6, species_7, species_10, species_6, species_7, Rate Law: compartment_0*k9*species_10*species_7/K9/(1+species_7/K9+species_6/K9)
A=100.0; V1=6.0; Ka=500.0; K1=15.0 Reaction: species_0 => species_1; species_7, species_0, species_7, species_0, species_7, Rate Law: compartment_0*V1*species_0/K1/(1+species_0/K1)*(1+A*species_7/Ka)/(1+species_7/Ka)
KI=9.0; K3=20.0; k3=0.1 Reaction: species_2 => species_3; species_1, species_3, species_7, species_1, species_2, species_3, species_7, species_1, species_2, species_3, species_7, Rate Law: compartment_0*k3*species_1*species_2/K3/((1+species_2/K3+species_3/K3)*(1+species_7/KI))
k6=0.02; K6=20.0 Reaction: species_3 => species_2; species_9, species_4, species_3, species_4, species_9, species_3, species_4, species_9, Rate Law: compartment_0*k6*species_9*species_3/K6/(1+species_4/K6+species_3/K6)
K7=20.0; k7=0.1 Reaction: species_5 => species_6; species_4, species_6, species_4, species_5, species_6, species_4, species_5, species_6, Rate Law: compartment_0*k7*species_4*species_5/K7/(1+species_5/K7+species_6/K7)

States:

Name Description
species 2 [Dual specificity mitogen-activated protein kinase kinase 1]
species 6 [Mitogen-activated protein kinase 1; Phosphoprotein]
species 3 [Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]
species 0 [RAF proto-oncogene serine/threonine-protein kinase]
species 1 [RAF proto-oncogene serine/threonine-protein kinase; Phosphoprotein]
species 4 [Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]
species 7 [Mitogen-activated protein kinase 1; Phosphoprotein]
species 5 [Mitogen-activated protein kinase 1]

Observables: none

Sarma2012 - Oscillations in MAPK cascade (S2), inclusion of external signalling moduleTwo plausible designs (S1 and S2)…

BACKGROUND: Feedback loops, both positive and negative are embedded in the Mitogen Activated Protein Kinase (MAPK) cascade. In the three layer MAPK cascade, both feedback loops originate from the terminal layer and their sites of action are either of the two upstream layers. Recent studies have shown that the cascade uses coupled positive and negative feedback loops in generating oscillations. Two plausible designs of coupled positive and negative feedback loops can be elucidated from the literature; in one design the positive feedback precedes the negative feedback in the direction of signal flow and vice-versa in another. But it remains unexplored how the two designs contribute towards triggering oscillations in MAPK cascade. Thus it is also not known how amplitude, frequency, robustness or nature (analogous/digital) of the oscillations would be shaped by these two designs. RESULTS: We built two models of MAPK cascade that exhibited oscillations as function of two underlying designs of coupled positive and negative feedback loops. Frequency, amplitude and nature (digital/analogous) of oscillations were found to be differentially determined by each design. It was observed that the positive feedback emerging from an oscillating MAPK cascade and functional in an external signal processing module can trigger oscillations in the target module, provided that the target module satisfy certain parametric requirements. The augmentation of the two models was done to incorporate the nuclear-cytoplasmic shuttling of cascade components followed by induction of a nuclear phosphatase. It revealed that the fate of oscillations in the MAPK cascade is governed by the feedback designs. Oscillations were unaffected due to nuclear compartmentalization owing to one design but were completely abolished in the other case. CONCLUSION: The MAPK cascade can utilize two distinct designs of coupled positive and negative feedback loops to trigger oscillations. The amplitude, frequency and robustness of the oscillations in presence or absence of nuclear compartmentalization were differentially determined by two designs of coupled positive and negative feedback loops. A positive feedback from an oscillating MAPK cascade was shown to induce oscillations in an external signal processing module, uncovering a novel regulatory aspect of MAPK signal processing. link: http://identifiers.org/pubmed/22694947

Parameters:

Name Description
K5=20.0; k5=0.02 Reaction: species_4 => species_3; species_9, species_3, species_3, species_4, species_9, species_3, species_4, species_9, Rate Law: compartment_0*k5*species_9*species_4/K5/(1+species_4/K5+species_3/K5)
K8=20.0; k8=0.1 Reaction: species_6 => species_7; species_4, species_5, species_4, species_5, species_6, species_4, species_5, species_6, Rate Law: compartment_0*k8*species_4*species_6/K8/(1+species_5/K8+species_6/K8)
K9=20.0; k9=0.02 Reaction: species_7 => species_6; species_10, species_6, species_5, species_10, species_6, species_7, species_10, species_6, species_7, Rate Law: compartment_0*k9*species_10*species_7/K9/(1+species_7/K9+species_6/K9)
A=100.0; V1=6.0; Ka=500.0; K1=15.0 Reaction: species_0 => species_1; species_7, species_0, species_7, species_0, species_7, Rate Law: compartment_0*V1*species_0/K1/(1+species_0/K1)*(1+A*species_7/Ka)/(1+species_7/Ka)
k6=0.02; K6=20.0 Reaction: species_3 => species_2; species_9, species_4, species_3, species_4, species_9, species_3, species_4, species_9, Rate Law: compartment_0*k6*species_9*species_3/K6/(1+species_4/K6+species_3/K6)
K10=20.0; k10=0.02 Reaction: species_6 => species_5; species_10, species_7, species_5, species_10, species_6, species_7, species_10, species_6, species_7, Rate Law: compartment_0*k10*species_10*species_6/K10/(1+species_7/K10+species_6/K10)
V12=0.5; K12=50.0 Reaction: species_12 => species_11; species_12, species_12, Rate Law: compartment_0*V12*species_12/(K12+species_12)
K2=100.0; k2=0.1 Reaction: species_1 => species_0; species_8, species_1, species_8, species_1, species_8, Rate Law: compartment_0*k2*species_8*species_1/K2/(1+species_1/K2)
A=100.0; K11=50.0; V11=0.1; Ka=500.0 Reaction: species_11 => species_12; species_7, species_11, species_7, species_11, species_7, Rate Law: compartment_0*V11*species_11/K11/(1+species_11/K11)*(1+A*species_7/Ka)/(1+species_7/Ka)
KI=9.0; k4=0.1; K4=20.0 Reaction: species_3 => species_4; species_1, species_2, species_7, species_1, species_2, species_3, species_7, species_1, species_2, species_3, species_7, Rate Law: compartment_0*k4*species_1*species_3/K4/((1+species_2/K4+species_3/K4)*(1+species_7/KI))
KI=9.0; K3=20.0; k3=0.1 Reaction: species_2 => species_3; species_1, species_3, species_7, species_1, species_2, species_3, species_7, species_1, species_2, species_3, species_7, Rate Law: compartment_0*k3*species_1*species_2/K3/((1+species_2/K3+species_3/K3)*(1+species_7/KI))
K7=20.0; k7=0.1 Reaction: species_5 => species_6; species_4, species_6, species_4, species_5, species_6, species_4, species_5, species_6, Rate Law: compartment_0*k7*species_4*species_5/K7/(1+species_5/K7+species_6/K7)

States:

Name Description
species 2 [Dual specificity mitogen-activated protein kinase kinase 1]
species 6 [Mitogen-activated protein kinase 1; Phosphoprotein]
species 3 [Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]
species 0 [RAF proto-oncogene serine/threonine-protein kinase]
species 1 [RAF proto-oncogene serine/threonine-protein kinase; Phosphoprotein]
species 11 [Mitogen-activated protein kinase 1]
species 4 [Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]
species 7 [Mitogen-activated protein kinase 1; Phosphoprotein]
species 12 [Mitogen-activated protein kinase 1; Phosphoprotein]
species 5 [Mitogen-activated protein kinase 1]

Observables: none

Sarma2012 - Oscillations in MAPK cascade (S2n)Two plausible designs (S1 and S2) of coupled positive and negative feedbac…

BACKGROUND: Feedback loops, both positive and negative are embedded in the Mitogen Activated Protein Kinase (MAPK) cascade. In the three layer MAPK cascade, both feedback loops originate from the terminal layer and their sites of action are either of the two upstream layers. Recent studies have shown that the cascade uses coupled positive and negative feedback loops in generating oscillations. Two plausible designs of coupled positive and negative feedback loops can be elucidated from the literature; in one design the positive feedback precedes the negative feedback in the direction of signal flow and vice-versa in another. But it remains unexplored how the two designs contribute towards triggering oscillations in MAPK cascade. Thus it is also not known how amplitude, frequency, robustness or nature (analogous/digital) of the oscillations would be shaped by these two designs. RESULTS: We built two models of MAPK cascade that exhibited oscillations as function of two underlying designs of coupled positive and negative feedback loops. Frequency, amplitude and nature (digital/analogous) of oscillations were found to be differentially determined by each design. It was observed that the positive feedback emerging from an oscillating MAPK cascade and functional in an external signal processing module can trigger oscillations in the target module, provided that the target module satisfy certain parametric requirements. The augmentation of the two models was done to incorporate the nuclear-cytoplasmic shuttling of cascade components followed by induction of a nuclear phosphatase. It revealed that the fate of oscillations in the MAPK cascade is governed by the feedback designs. Oscillations were unaffected due to nuclear compartmentalization owing to one design but were completely abolished in the other case. CONCLUSION: The MAPK cascade can utilize two distinct designs of coupled positive and negative feedback loops to trigger oscillations. The amplitude, frequency and robustness of the oscillations in presence or absence of nuclear compartmentalization were differentially determined by two designs of coupled positive and negative feedback loops. A positive feedback from an oscillating MAPK cascade was shown to induce oscillations in an external signal processing module, uncovering a novel regulatory aspect of MAPK signal processing. link: http://identifiers.org/pubmed/22694947

Parameters:

Name Description
k1=22.56; k2=15.4 Reaction: species_14 => species_15; species_14, species_15, species_14, species_15, Rate Law: compartment_0*(k1*species_14-k2*species_15)
K22i=10300.0; K22=87.0; k22=0.31 Reaction: species_17 => species_16; species_15, species_11, species_15, species_17, species_11, species_15, species_17, species_11, Rate Law: compartment_0*k22*species_15*species_17/K22/(1+species_17/K22+species_11/K22i)
K5=20.0; k5=0.02 Reaction: species_4 => species_3; species_9, species_3, species_3, species_4, species_9, species_3, species_4, species_9, Rate Law: compartment_0*k5*species_9*species_4/K5/(1+species_4/K5+species_3/K5)
K8=20.0; k8=0.1 Reaction: species_6 => species_7; species_4, species_5, species_4, species_5, species_6, species_4, species_5, species_6, Rate Law: compartment_0*k8*species_4*species_6/K8/(1+species_5/K8+species_6/K8)
A=100.0; V1=6.0; Ka=500.0; K1=15.0 Reaction: species_0 => species_1; species_7, species_0, species_7, species_0, species_7, Rate Law: compartment_0*V1*species_0/K1/(1+species_0/K1)*(1+A*species_7/Ka)/(1+species_7/Ka)
K9=20.0; k9=0.02 Reaction: species_7 => species_6; species_10, species_6, species_5, species_10, species_6, species_7, species_10, species_6, species_7, Rate Law: compartment_0*k9*species_10*species_7/K9/(1+species_7/K9+species_6/K9)
k11b=2.86; k11f=10.34 Reaction: species_7 => species_11; species_7, species_11, species_7, species_11, Rate Law: compartment_0*(k11f*species_7-k11b*species_11)
K21i=87.0; k21=0.68; K21=10300.0 Reaction: species_11 => species_17; species_15, species_17, species_15, species_11, species_17, species_15, species_11, species_17, Rate Law: compartment_0*k21*species_15*species_11/K21/(1+species_11/K21+species_17/K21i)
k6=0.02; K6=20.0 Reaction: species_3 => species_2; species_9, species_4, species_3, species_4, species_9, species_3, species_4, species_9, Rate Law: compartment_0*k6*species_9*species_3/K6/(1+species_4/K6+species_3/K6)
K10=20.0; k10=0.02 Reaction: species_6 => species_5; species_10, species_7, species_5, species_10, species_6, species_7, species_10, species_6, species_7, Rate Law: compartment_0*k10*species_10*species_6/K10/(1+species_7/K10+species_6/K10)
V12=29.24; K12=169.0; n12=3.97 Reaction: => species_12; species_11, species_11, species_11, Rate Law: compartment_0*V12*species_11^n12/(K12^n12+species_11^n12)
K2=100.0; k2=0.1 Reaction: species_1 => species_0; species_8, species_1, species_8, species_1, species_8, Rate Law: compartment_0*k2*species_8*species_1/K2/(1+species_1/K2)
k1=0.022 Reaction: species_12 => species_13; species_12, species_12, Rate Law: compartment_0*k1*species_12
k15=0.0012 Reaction: => species_14; species_13, species_13, species_13, Rate Law: compartment_0*k15*species_13
KI=9.0; k4=0.1; K4=20.0 Reaction: species_3 => species_4; species_1, species_2, species_7, species_1, species_2, species_3, species_7, species_1, species_2, species_3, species_7, Rate Law: compartment_0*k4*species_1*species_3/K4/((1+species_2/K4+species_3/K4)*(1+species_7/KI))
k1=0.0078 Reaction: species_13 => ; species_13, species_13, Rate Law: compartment_0*k1*species_13
KI=9.0; K3=20.0; k3=0.1 Reaction: species_2 => species_3; species_1, species_3, species_7, species_1, species_2, species_3, species_7, species_1, species_2, species_3, species_7, Rate Law: compartment_0*k3*species_1*species_2/K3/((1+species_2/K3+species_3/K3)*(1+species_7/KI))
k1=2.5E-4 Reaction: species_15 => ; species_15, species_15, Rate Law: compartment_0*k1*species_15
k2=2.86; k1=10.34 Reaction: species_5 => species_16; species_5, species_16, species_5, species_16, Rate Law: compartment_0*(k1*species_5-k2*species_16)
K7=20.0; k7=0.1 Reaction: species_5 => species_6; species_4, species_6, species_4, species_5, species_6, species_4, species_5, species_6, Rate Law: compartment_0*k7*species_4*species_5/K7/(1+species_5/K7+species_6/K7)

States:

Name Description
species 2 [Dual specificity mitogen-activated protein kinase kinase 1]
species 6 [Mitogen-activated protein kinase 1; Phosphoprotein]
species 11 [Mitogen-activated protein kinase 1; Phosphoprotein; nucleus]
species 1 [RAF proto-oncogene serine/threonine-protein kinase; Phosphoprotein]
species 4 [Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]
species 16 [Mitogen-activated protein kinase 1; nucleus]
species 14 [Dual specificity protein phosphatase 3; cytoplasm]
species 3 [Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]
species 0 [RAF proto-oncogene serine/threonine-protein kinase]
species 17 [Mitogen-activated protein kinase 1; Phosphoprotein; nucleus]
species 12 [Dual specificity protein phosphatase 3; nucleus]
species 7 [Mitogen-activated protein kinase 1; Phosphoprotein]
species 5 [Mitogen-activated protein kinase 1]
species 15 [Dual specificity protein phosphatase 3; nucleus]
species 13 [Dual specificity protein phosphatase 3; nucleus]

Observables: none

BIOMD0000000049 @ v0.0.1

This a model from the article: Prediction and validation of the distinct dynamics of transient and sustained ERK acti…

To elucidate the hidden dynamics of extracellular-signal-regulated kinase (ERK) signalling networks, we developed a simulation model of ERK signalling networks by constraining in silico dynamics based on in vivo dynamics in PC12 cells. We predicted and validated that transient ERK activation depends on rapid increases of epidermal growth factor and nerve growth factor (NGF) but not on their final concentrations, whereas sustained ERK activation depends on the final concentration of NGF but not on the temporal rate of increase. These ERK dynamics depend on Ras and Rap1 dynamics, the inactivation processes of which are growth-factor-dependent and -independent, respectively. Therefore, the Ras and Rap1 systems capture the temporal rate and concentration of growth factors, and encode these distinct physical properties into transient and sustained ERK activation, respectively. link: http://identifiers.org/pubmed/15793571

Parameters:

Name Description
J82_k=0.1 Reaction: Shc_pTrkA => pShc_pTrkA, Rate Law: c1*J82_k*Shc_pTrkA
J52_k1=60.0; J52_k2=0.5 Reaction: c_Raf + Ras_GTP => c_Raf_Ras_GTP, Rate Law: c1*(J52_k1*c_Raf*Ras_GTP-J52_k2*c_Raf_Ras_GTP)
J133_k2=0.6; J133_k1=16.304 Reaction: ERK + MEK => MEK_ERK, Rate Law: c1*(J133_k1*ERK*MEK-J133_k2*MEK_ERK)
J148_k1=9.375; J148_k2=1.2 Reaction: B_Raf_Rap1_GTP + MEK => B_Raf_Rap1_GTP_MEK, Rate Law: c1*(J148_k1*B_Raf_Rap1_GTP*MEK-J148_k2*B_Raf_Rap1_GTP_MEK)
J95_k1=10.0; J95_k2=0.2 Reaction: SOS_Grb2 + pShc_pTrkA_endo => Grb2_SOS_pShc_pTrkA_endo, Rate Law: c1*(J95_k1*SOS_Grb2*pShc_pTrkA_endo-J95_k2*Grb2_SOS_pShc_pTrkA_endo)
J47_k=0.001 Reaction: pFRS2_dpEGFR_c_Cbl_ubiq => proteosome + c_Cbl + pFRS2, Rate Law: c1*J47_k*pFRS2_dpEGFR_c_Cbl_ubiq
J12_k2=0.2; J12_k1=10.0 Reaction: L_dpEGFR + Shc => Shc_dpEGFR, Rate Law: c1*(J12_k1*L_dpEGFR*Shc-J12_k2*Shc_dpEGFR)
J11_k=0.002 Reaction: pSOS_Grb2 => SOS_Grb2, Rate Law: c1*J11_k*pSOS_Grb2
J90_k=0.0022 Reaction: pShc_pTrkA => degradation + pShc, Rate Law: c1*J90_k*pShc_pTrkA
J136_k=0.15 Reaction: ppMEK_ERK => ppERK + ppMEK, Rate Law: c1*J136_k*ppMEK_ERK
J121_Vmax=10.0; J121_Km1=1.0 Reaction: Ras_GTP => Ras_GDP; pDok_RasGAP, Rate Law: c1*J121_Vmax*Ras_GTP*pDok_RasGAP/(J121_Km1+Ras_GTP)
J25_k2=0.2; J25_k1=0.5 Reaction: c_Cbl + Grb2_SOS_pShc_dpEGFR => Grb2_SOS_pShc_dpEGFR_c_Cbl, Rate Law: c1*(J25_k1*c_Cbl*Grb2_SOS_pShc_dpEGFR-J25_k2*Grb2_SOS_pShc_dpEGFR_c_Cbl)
J21_k=1.0 Reaction: Shc_dpEGFR_c_Cbl => pShc_dpEGFR_c_Cbl, Rate Law: c1*J21_k*Shc_dpEGFR_c_Cbl
J163_k=0.3 Reaction: B_Raf_Rap1_GTP_pMEK_ERK => B_Raf_Rap1_GTP + ppMEK_ERK, Rate Law: c1*J163_k*B_Raf_Rap1_GTP_pMEK_ERK
re8_k2=0.02; re8_k1=10.0 Reaction: L_EGFR => L_EGFR_dimer, Rate Law: compartment*(re8_k1*L_EGFR*L_EGFR-re8_k2*L_EGFR_dimer)
J154_k=0.5 Reaction: c_Raf_Ras_GTP_MEK_ERK => c_Raf_Ras_GTP + pMEK_ERK, Rate Law: c1*J154_k*c_Raf_Ras_GTP_MEK_ERK
J100_k=6.3E-4 Reaction: FRS2_pTrkA => FRS2_pTrkA_endo, Rate Law: c1*J100_k*FRS2_pTrkA
J103_k1=1.0; J103_k2=0.2 Reaction: Crk_C3G + pFRS2_pTrkA => Crk_C3G_pFRS2_pTrkA, Rate Law: c1*(J103_k1*Crk_C3G*pFRS2_pTrkA-J103_k2*Crk_C3G_pFRS2_pTrkA)
J3_k2=0.0168; J3_k1=0.03 Reaction: SOS + Grb2 => SOS_Grb2, Rate Law: c1*(J3_k1*SOS*Grb2-J3_k2*SOS_Grb2)
J8_k2=1.0E-5; J8_k1=0.002 Reaction: pDok => Dok, Rate Law: c1*(J8_k1*pDok-J8_k2*Dok)
J149_k2=1.2; J149_k1=9.375 Reaction: B_Raf_Rap1_GTP + pMEK => B_Raf_Rap1_GTP_pMEK, Rate Law: c1*(J149_k1*B_Raf_Rap1_GTP*pMEK-J149_k2*B_Raf_Rap1_GTP_pMEK)
re1_k2=1.0E-4; re1_k1=1.0E-4 Reaction: pro_EGFR => EGFR, Rate Law: compartment*(re1_k1*pro_EGFR-re1_k2*EGFR)
J107_k=0.0022 Reaction: Crk_C3G_pFRS2_pTrkA => degradation + pFRS2 + Crk_C3G, Rate Law: c1*J107_k*Crk_C3G_pFRS2_pTrkA
J33_k=0.005 Reaction: pFRS2 => FRS2, Rate Law: c1*J33_k*pFRS2
J38_k1=1.0; J38_k2=0.2 Reaction: pFRS2_dpEGFR + Crk_C3G => Crk_C3G_pFRS2_dpEGFR, Rate Law: c1*(J38_k1*pFRS2_dpEGFR*Crk_C3G-J38_k2*Crk_C3G_pFRS2_dpEGFR)
J51_Km1=25.641; J51_Vmax=1.0 Reaction: SOS => pSOS; dppERK, Rate Law: c1*J51_Vmax*SOS*dppERK/(J51_Km1+SOS)
J37_k=1.0 Reaction: FRS2_dpEGFR => pFRS2_dpEGFR, Rate Law: c1*J37_k*FRS2_dpEGFR
J6_k2=0.2; J6_k1=0.5 Reaction: L_dpEGFR + c_Cbl => dpEGFR_c_Cbl, Rate Law: c1*(J6_k1*L_dpEGFR*c_Cbl-J6_k2*dpEGFR_c_Cbl)
J23_k1=10.0; J23_k2=0.2 Reaction: L_dpEGFR + Grb2_SOS_pShc => Grb2_SOS_pShc_dpEGFR, Rate Law: c1*(J23_k1*L_dpEGFR*Grb2_SOS_pShc-J23_k2*Grb2_SOS_pShc_dpEGFR)
J78_k1=5.0; J78_k2=0.1 Reaction: pFRS2 + pTrkA => pFRS2_pTrkA, Rate Law: c1*(J78_k1*pFRS2*pTrkA-J78_k2*pFRS2_pTrkA)
J120_k1=1.0; J120_k2=0.2 Reaction: dpEGFR_c_Cbl + pFRS2 => pFRS2_dpEGFR_c_Cbl, Rate Law: c1*(J120_k1*dpEGFR_c_Cbl*pFRS2-J120_k2*pFRS2_dpEGFR_c_Cbl)
J167_k=0.06 Reaction: ppERK_MKP3 => ERK + MKP3, Rate Law: c1*J167_k*ppERK_MKP3
J162_k=0.3 Reaction: B_Raf_Rap1_GTP_MEK_ERK => B_Raf_Rap1_GTP + pMEK_ERK, Rate Law: c1*J162_k*B_Raf_Rap1_GTP_MEK_ERK
J40_k1=0.5; J40_k2=0.2 Reaction: c_Cbl + pFRS2_dpEGFR => pFRS2_dpEGFR_c_Cbl, Rate Law: c1*(J40_k1*c_Cbl*pFRS2_dpEGFR-J40_k2*pFRS2_dpEGFR_c_Cbl)
J10_k=0.002 Reaction: pSOS => SOS, Rate Law: c1*J10_k*pSOS
J5_k1=4.0; J5_k2=0.001 Reaction: L_EGFR_dimer => L_dpEGFR, Rate Law: compartment*(J5_k1*L_EGFR_dimer-J5_k2*L_dpEGFR)
J72_k=6.3E-4 Reaction: pTrkA => pTrkA_endo, Rate Law: c1*J72_k*pTrkA
J143_k2=2.0; J143_k1=15.625 Reaction: c_Raf_Ras_GTP + pMEK_ERK => c_Raf_Ras_GTP_pMEK_ERK, Rate Law: c1*(J143_k1*c_Raf_Ras_GTP*pMEK_ERK-J143_k2*c_Raf_Ras_GTP_pMEK_ERK)
J102_k=6.3E-4 Reaction: Shc_pTrkA => Shc_pTrkA_endo, Rate Law: c1*J102_k*Shc_pTrkA
J112_k=4.2E-4 Reaction: pFRS2_pTrkA_endo => degradation + pFRS2, Rate Law: J112_k*pFRS2_pTrkA_endo
J63_k1=10.0; J63_k2=0.075 Reaction: ppERK => dppERK, Rate Law: c1*(J63_k1*ppERK*ppERK-J63_k2*dppERK)
J44_k1=1.0; J44_k2=0.2 Reaction: pFRS2_dpEGFR_c_Cbl + Crk_C3G => Crk_C3G_pFRS2_dpEGFR_c_Cbl, Rate Law: c1*(J44_k1*pFRS2_dpEGFR_c_Cbl*Crk_C3G-J44_k2*Crk_C3G_pFRS2_dpEGFR_c_Cbl)
J165_k1=15.0; J165_k2=0.24 Reaction: MKP3 + dppERK => dppERK_MKP3, Rate Law: c1*(J165_k1*MKP3*dppERK-J165_k2*dppERK_MKP3)
J77_k2=0.1; J77_k1=5.0 Reaction: FRS2 + pTrkA => FRS2_pTrkA, Rate Law: c1*(J77_k1*FRS2*pTrkA-J77_k2*FRS2_pTrkA)
J81_k=0.1 Reaction: Shc_pTrkA_endo => pShc_pTrkA_endo, Rate Law: c1*J81_k*Shc_pTrkA_endo
J108_k=4.2E-4 Reaction: Crk_C3G_pFRS2_pTrkA_endo => degradation + Crk_C3G + pFRS2, Rate Law: c1*J108_k*Crk_C3G_pFRS2_pTrkA_endo
J71_k=1.0 Reaction: L_NGFR => pTrkA, Rate Law: compartment*J71_k*L_NGFR
J164_k=0.001 Reaction: Crk_C3G_pFRS2_dpEGFR_c_Cbl_ubiq => c_Cbl + pFRS2 + Crk_C3G, Rate Law: c1*J164_k*Crk_C3G_pFRS2_dpEGFR_c_Cbl_ubiq
J168_k=0.06 Reaction: dppERK_MKP3 => ppERK + ERK + MKP3, Rate Law: c1*J168_k*dppERK_MKP3
J17_k=0.05 Reaction: Shc_dpEGFR_c_Cbl => Shc_dpEGFR_c_Cbl_ubiq, Rate Law: c1*J17_k*Shc_dpEGFR_c_Cbl
J138_Vmax=10.0; J138_Km1=1.0 Reaction: B_Raf_Ras_GTP => B_Raf + Ras_GDP; pDok_RasGAP, Rate Law: c1*J138_Vmax*B_Raf_Ras_GTP*pDok_RasGAP/(J138_Km1+B_Raf_Ras_GTP)
J135_k1=16.304; J135_k2=0.6 Reaction: ERK + ppMEK => ppMEK_ERK, Rate Law: c1*(J135_k1*ERK*ppMEK-J135_k2*ppMEK_ERK)
J46_k=0.001 Reaction: FRS2_dpEGFR_c_Cbl_ubiq => proteosome + c_Cbl + FRS2, Rate Law: c1*J46_k*FRS2_dpEGFR_c_Cbl_ubiq
J43_k=1.0 Reaction: FRS2_dpEGFR_c_Cbl => pFRS2_dpEGFR_c_Cbl, Rate Law: c1*J43_k*FRS2_dpEGFR_c_Cbl
J160_k=0.3 Reaction: B_Raf_Rap1_GTP_MEK => B_Raf_Rap1_GTP + pMEK, Rate Law: c1*J160_k*B_Raf_Rap1_GTP_MEK
J69_Km1=0.02; J69_Vmax=2.0 Reaction: Ras_GDP => Ras_GTP; Grb2_SOS_pShc_dpEGFR_c_Cbl, Grb2_SOS_pShc_dpEGFR, Grb2_SOS_pShc_pTrkA, Rate Law: c1*J69_Vmax*Ras_GDP*(Grb2_SOS_pShc_dpEGFR+Grb2_SOS_pShc_dpEGFR_c_Cbl+Grb2_SOS_pShc_pTrkA)/(J69_Km1+Ras_GDP)
J99_k=6.3E-4 Reaction: pFRS2_pTrkA => pFRS2_pTrkA_endo, Rate Law: c1*J99_k*pFRS2_pTrkA
re2_k2=0.0029666; re2_k1=2.2833 Reaction: EGF + EGFR => L_EGFR, Rate Law: compartment*(re2_k1*EGF*EGFR-re2_k2*L_EGFR)
J24_k1=10.0; J24_k2=0.2 Reaction: pShc_dpEGFR + SOS_Grb2 => Grb2_SOS_pShc_dpEGFR, Rate Law: c1*(J24_k1*pShc_dpEGFR*SOS_Grb2-J24_k2*Grb2_SOS_pShc_dpEGFR)
J50_Vmax=1.0; J50_Km1=25.641 Reaction: SOS_Grb2 => pSOS_Grb2; dppERK, Rate Law: c1*J50_Vmax*SOS_Grb2*dppERK/(J50_Km1+SOS_Grb2)
J85_k2=0.1; J85_k1=5.0 Reaction: pTrkA_endo + pFRS2 => pFRS2_pTrkA_endo, Rate Law: c1*(J85_k1*pTrkA_endo*pFRS2-J85_k2*pFRS2_pTrkA_endo)
J98_k=6.3E-4 Reaction: Crk_C3G_pFRS2_pTrkA => Crk_C3G_pFRS2_pTrkA_endo, Rate Law: c1*J98_k*Crk_C3G_pFRS2_pTrkA
J16_k1=0.5; J16_k2=0.2 Reaction: c_Cbl + Shc_dpEGFR => Shc_dpEGFR_c_Cbl, Rate Law: c1*(J16_k1*c_Cbl*Shc_dpEGFR-J16_k2*Shc_dpEGFR_c_Cbl)
J144_k1=6.25; J144_k2=0.8 Reaction: B_Raf_Ras_GTP + MEK => B_Raf_Ras_GTP_MEK, Rate Law: c1*(J144_k1*B_Raf_Ras_GTP*MEK-J144_k2*B_Raf_Ras_GTP_MEK)
J86_k=2.0 Reaction: FRS2_pTrkA_endo => pFRS2_pTrkA_endo, Rate Law: c1*J86_k*FRS2_pTrkA_endo
J4_k2=0.0168; J4_k1=0.03 Reaction: Grb2 + pSOS => pSOS_Grb2, Rate Law: c1*(J4_k1*Grb2*pSOS-J4_k2*pSOS_Grb2)
J49_k2=0.01; J49_k1=0.12 Reaction: pDok + RasGAP => pDok_RasGAP, Rate Law: c1*(J49_k1*pDok*RasGAP-J49_k2*pDok_RasGAP)
J155_k=0.5 Reaction: c_Raf_Ras_GTP_pMEK_ERK => c_Raf_Ras_GTP + ppMEK_ERK, Rate Law: c1*J155_k*c_Raf_Ras_GTP_pMEK_ERK
J145_k1=6.25; J145_k2=0.8 Reaction: B_Raf_Ras_GTP + pMEK => B_Raf_Ras_GTP_pMEK, Rate Law: c1*(J145_k1*B_Raf_Ras_GTP*pMEK-J145_k2*B_Raf_Ras_GTP_pMEK)
J76_k2=0.2; J76_k1=10.0 Reaction: pShc + pTrkA => pShc_pTrkA, Rate Law: c1*(J76_k1*pShc*pTrkA-J76_k2*pShc_pTrkA)
J115_k1=10.0; J115_k2=0.2 Reaction: Shc + dpEGFR_c_Cbl => Shc_dpEGFR_c_Cbl, Rate Law: c1*(J115_k1*Shc*dpEGFR_c_Cbl-J115_k2*Shc_dpEGFR_c_Cbl)
J156_k=0.2 Reaction: B_Raf_Ras_GTP_MEK => B_Raf_Ras_GTP + pMEK, Rate Law: c1*J156_k*B_Raf_Ras_GTP_MEK
J117_k2=0.2; J117_k1=10.0 Reaction: pShc_dpEGFR_c_Cbl + SOS_Grb2 => Grb2_SOS_pShc_dpEGFR_c_Cbl, Rate Law: c1*(J117_k1*pShc_dpEGFR_c_Cbl*SOS_Grb2-J117_k2*Grb2_SOS_pShc_dpEGFR_c_Cbl)
J36_k1=1.0; J36_k2=0.2 Reaction: L_dpEGFR + pFRS2 => pFRS2_dpEGFR, Rate Law: c1*(J36_k1*L_dpEGFR*pFRS2-J36_k2*pFRS2_dpEGFR)
J75_k2=0.2; J75_k1=10.0 Reaction: Shc + pTrkA => Shc_pTrkA, Rate Law: c1*(J75_k1*Shc*pTrkA-J75_k2*Shc_pTrkA)
J118_k1=1.0; J118_k2=0.2 Reaction: dpEGFR_c_Cbl + FRS2 => FRS2_dpEGFR_c_Cbl, Rate Law: c1*(J118_k1*dpEGFR_c_Cbl*FRS2-J118_k2*FRS2_dpEGFR_c_Cbl)
J41_k=0.05 Reaction: pFRS2_dpEGFR_c_Cbl => pFRS2_dpEGFR_c_Cbl_ubiq, Rate Law: c1*J41_k*pFRS2_dpEGFR_c_Cbl
J7_k2=0.2; J7_k1=10.0 Reaction: L_dpEGFR + pShc => pShc_dpEGFR, Rate Law: c1*(J7_k1*L_dpEGFR*pShc-J7_k2*pShc_dpEGFR)
J66_k=1.667E-4 Reaction: Ras_GTP => Ras_GDP, Rate Law: c1*J66_k*Ras_GTP

States:

Name Description
L EGFR dimer [Pro-epidermal growth factor; Receptor protein-tyrosine kinase]
RasGAP [IPR011575]
EGFR [Receptor protein-tyrosine kinase]
pFRS2 [Fibroblast growth factor receptor substrate 2Fibroblast growth factor receptor substrate 2 (Predicted), isoform CRA_b; Phosphoprotein]
pSOS [Son of sevenless 1]
Grb2 SOS pShc dpEGFR [Receptor protein-tyrosine kinase; Son of sevenless 1; SHC-transforming protein 1; Growth factor receptor-bound protein 2]
Shc dpEGFR [SHC-transforming protein 1; Pro-epidermal growth factor; Receptor protein-tyrosine kinase]
Shc dpEGFR c Cbl [SHC-transforming protein 1; E3 ubiquitin-protein ligase CBL-B; Receptor protein-tyrosine kinase]
pFRS2 dpEGFR c Cbl [Receptor protein-tyrosine kinase; Fibroblast growth factor receptor substrate 2Fibroblast growth factor receptor substrate 2 (Predicted), isoform CRA_b; E3 ubiquitin-protein ligase CBL-B]
c Cbl [E3 ubiquitin-protein ligase CBL-B]
L NGFR [High affinity nerve growth factor receptor; Beta-nerve growth factor]
ppMEK ERK [Dual specificity mitogen-activated protein kinase kinase 1; Mitogen-activated protein kinase 1]
SOS [Son of sevenless 1]
Crk C3G pFRS2 pTrkA endo [High affinity nerve growth factor receptor; C3G protein; Adapter molecule crk; Fibroblast growth factor receptor substrate 2Fibroblast growth factor receptor substrate 2 (Predicted), isoform CRA_b]
Crk C3G [Adapter molecule crk; C3G protein]
c Raf Ras GTP pMEK ERK [Mitogen-activated protein kinase 1; Dual specificity mitogen-activated protein kinase kinase 1; RAF proto-oncogene serine/threonine-protein kinase; IPR003577]
pFRS2 dpEGFR c Cbl ubiq [Fibroblast growth factor receptor substrate 2Fibroblast growth factor receptor substrate 2 (Predicted), isoform CRA_b; E3 ubiquitin-protein ligase CBL-B; Receptor protein-tyrosine kinase]
B Raf Rap1 GTP MEK [GTP; Dual specificity mitogen-activated protein kinase kinase 1; V-raf murine sarcoma viral oncogene B1-like protein; Ras-related protein Rap-1b]
Ras GDP [GDP; IPR003577]
pTrkA [High affinity nerve growth factor receptor]
SOS Grb2 [Son of sevenless 1; Growth factor receptor-bound protein 2]
Dok [Docking protein 1; IPR002404]
FRS2 dpEGFR c Cbl [Receptor protein-tyrosine kinase; Fibroblast growth factor receptor substrate 2Fibroblast growth factor receptor substrate 2 (Predicted), isoform CRA_b; E3 ubiquitin-protein ligase CBL-B]
B Raf Ras GTP pMEK [Dual specificity mitogen-activated protein kinase kinase 1; V-raf murine sarcoma viral oncogene B1-like protein; IPR003577]
L dpEGFR [Receptor protein-tyrosine kinase; Pro-epidermal growth factor]
B Raf Rap1 GTP [GTP; Ras-related protein Rap-1b; V-raf murine sarcoma viral oncogene B1-like protein]
pShc pTrkA [High affinity nerve growth factor receptor; SHC-transforming protein 1]
Shc pTrkA endo [High affinity nerve growth factor receptor; SHC-transforming protein 1]
B Raf [V-raf murine sarcoma viral oncogene B1-like protein]
L EGFR [Pro-epidermal growth factor; Receptor protein-tyrosine kinase]
c Raf Ras GTP MEK ERK [Mitogen-activated protein kinase 1; RAF proto-oncogene serine/threonine-protein kinase; Dual specificity mitogen-activated protein kinase kinase 1; IPR003577]
pMEK [Dual specificity mitogen-activated protein kinase kinase 1]
Shc pTrkA [High affinity nerve growth factor receptor; SHC-transforming protein 1]
pShc dpEGFR c Cbl [E3 ubiquitin-protein ligase CBL-B; SHC-transforming protein 1; Receptor protein-tyrosine kinase]
pFRS2 pTrkA endo [High affinity nerve growth factor receptor; Fibroblast growth factor receptor substrate 2Fibroblast growth factor receptor substrate 2 (Predicted), isoform CRA_b]
FRS2 pTrkA endo [Fibroblast growth factor receptor substrate 2Fibroblast growth factor receptor substrate 2 (Predicted), isoform CRA_b; High affinity nerve growth factor receptor]
Grb2 [Growth factor receptor-bound protein 2]
ppERK [Mitogen-activated protein kinase 1]
B Raf Rap1 GTP pMEK [GTP; Dual specificity mitogen-activated protein kinase kinase 1; Ras-related protein Rap-1b; V-raf murine sarcoma viral oncogene B1-like protein]
B Raf Ras GTP MEK [Dual specificity mitogen-activated protein kinase kinase 1; V-raf murine sarcoma viral oncogene B1-like protein; IPR003577]
FRS2 dpEGFR [Receptor protein-tyrosine kinase; Fibroblast growth factor receptor substrate 2Fibroblast growth factor receptor substrate 2 (Predicted), isoform CRA_b]
dppERK [Mitogen-activated protein kinase 1]
ERK [Mitogen-activated protein kinase 1]
c Raf [RAF proto-oncogene serine/threonine-protein kinase]

Observables: none

Sass2009 - Approach to an α-synuclein-based BST model of Parkinson's diseaseThis model is described in the article: [A…

This paper presents a detailed systems model of Parkinson's disease (PD), developed utilizing a pragmatic application of biochemical systems theory (BST) intended to assist experimentalists in the study of system behavior. This approach utilizes relative values as a reasonable initial estimate for BST and provides a theoretical means of applying numerical solutions to qualitative and semi-quantitative understandings of cellular pathways and mechanisms. The approach allows for the simulation of human disease through its ability to organize and integrate existing information about metabolic pathways without having a full quantitative description of those pathways, so that hypotheses about individual processes may be tested in a systems environment. Incorporating this method, the PD model describes alpha-synuclein aggregation as mediated by dopamine metabolism, the ubiquitin-proteasome system, and lysosomal degradation, allowing for the examination of dynamic pathway interactions and the evaluation of possible toxic mechanisms in the aggregation process. Four system perturbations: elevated alpha-synuclein aggregation, impaired dopamine packaging, increased neurotoxins, and alpha-synuclein overexpression, were analyzed for correlation to qualitative PD system hypotheses present in the literature, with the model demonstrating a high level of agreement with these hypotheses. Additionally, various PD treatment methods, including levadopa and monoamine oxidase inhibition (MAOI) therapy, were applied to the disease models to examine their effects on the system. Future additions and refinements to the model may further the understanding of the emergent behaviors of the disease, helping in the identification of system sensitivities and possible therapeutic targets. link: http://identifiers.org/pubmed/19136028

Parameters:

Name Description
g3679 = 1.0; k36 = 0.05; g3677 = 1.0 Reaction: Autophagosome_0 => Fragments; Lysosome_0, Autophagosome_0, Lysosome_0, Autophagosome_0, Lysosome_0, Autophagosome_0, Lysosome_0, Autophagosome_0, Lysosome_0, Autophagosome_0, Lysosome_0, Autophagosome_0, Lysosome_0, Autophagosome_0, Lysosome_0, Autophagosome_0, Lysosome_0, Autophagosome_0, Lysosome_0, Rate Law: k36*Autophagosome_0^g3679*Lysosome_0^g3677
g156 = 1.0; k15 = 0.2; g1545 = 1.0; g1544 = 1.0 Reaction: Dopamine + Vesicle_0 => V_DA; VMAT2, Dopamine, Vesicle_0, VMAT2, Dopamine, Vesicle_0, VMAT2, Dopamine, Vesicle_0, VMAT2, Dopamine, Vesicle_0, VMAT2, Dopamine, Vesicle_0, VMAT2, Dopamine, Vesicle_0, VMAT2, Dopamine, Vesicle_0, VMAT2, Dopamine, Vesicle_0, VMAT2, Dopamine, Vesicle_0, VMAT2, Rate Law: k15*Dopamine^g156*Vesicle_0^g1544*VMAT2^g1545
k27f = 0.05; g27f15 = 1.0; g27f68 = 1.0; g27f16 = 1.0 Reaction: Ub_E1 + UbcH8ub2 => E1 + UbcH8ub3; ATP, Ub_E1, UbcH8ub2, ATP, Ub_E1, UbcH8ub2, ATP, Ub_E1, UbcH8ub2, ATP, Ub_E1, UbcH8ub2, ATP, Ub_E1, UbcH8ub2, ATP, Ub_E1, UbcH8ub2, ATP, Ub_E1, UbcH8ub2, ATP, Ub_E1, UbcH8ub2, ATP, Ub_E1, UbcH8ub2, ATP, Rate Law: Neuronal_cytosol*k27f*Ub_E1^g27f16*UbcH8ub2^g27f68*ATP^g27f15
g3830 = 1.0; g3815 = 1.0; g3812 = 1.0; g3878 = 1.0; k38 = 0.7 Reaction: UCH_L1_asyn_ub4 => Fragments + UCH_L1 + Ubiquitin; Proteasome_0, ATP, UCH_L1, UCH_L1_asyn_ub4, Proteasome_0, ATP, UCH_L1, UCH_L1_asyn_ub4, Proteasome_0, ATP, UCH_L1, UCH_L1_asyn_ub4, Proteasome_0, ATP, UCH_L1, UCH_L1_asyn_ub4, Proteasome_0, ATP, UCH_L1, UCH_L1_asyn_ub4, Proteasome_0, ATP, UCH_L1, UCH_L1_asyn_ub4, Proteasome_0, ATP, UCH_L1, UCH_L1_asyn_ub4, Proteasome_0, ATP, UCH_L1, UCH_L1_asyn_ub4, Proteasome_0, ATP, UCH_L1, UCH_L1_asyn_ub4, Proteasome_0, ATP, UCH_L1, Rate Law: Neuronal_cytosol*k38*UCH_L1_asyn_ub4^g3878*Proteasome_0^g3812*ATP^g3815*UCH_L1^g3830
k24 = 1.0; g2463 = 1.0; g2464 = 1.0 Reaction: GSSG => GSH; Gluta_red, GSSG, Gluta_red, GSSG, Gluta_red, GSSG, Gluta_red, GSSG, Gluta_red, GSSG, Gluta_red, GSSG, Gluta_red, GSSG, Gluta_red, GSSG, Gluta_red, GSSG, Gluta_red, Rate Law: Neuronal_cytosol*k24*GSSG^g2463*Gluta_red^g2464
k37 = 0.05; g3773 = 1.0; g3770 = 1.0 Reaction: UbcH8ub4 + asyn_UCH_L1 => UCH_L1_asyn_ub4 + UbcH8; UbcH8ub4, asyn_UCH_L1, UbcH8ub4, asyn_UCH_L1, UbcH8ub4, asyn_UCH_L1, UbcH8ub4, asyn_UCH_L1, UbcH8ub4, asyn_UCH_L1, UbcH8ub4, asyn_UCH_L1, UbcH8ub4, asyn_UCH_L1, UbcH8ub4, asyn_UCH_L1, UbcH8ub4, asyn_UCH_L1, Rate Law: Neuronal_cytosol*k37*UbcH8ub4^g3770*asyn_UCH_L1^g3773
k57 = 0.005; g5762 = 1.0; g5710 = 1.0 Reaction: DA_quinone + GSH => DA_GSH; DA_quinone, GSH, DA_quinone, GSH, DA_quinone, GSH, DA_quinone, GSH, DA_quinone, GSH, DA_quinone, GSH, DA_quinone, GSH, DA_quinone, GSH, DA_quinone, GSH, Rate Law: Neuronal_cytosol*k57*DA_quinone^g5710*GSH^g5762
g4782 = 1.0; k47 = 0.03; g4777 = 1.0 Reaction: Hsc70_Protofibril => Hsc70 + Fragments; Lysosome_0, Hsc70_Protofibril, Lysosome_0, Hsc70_Protofibril, Lysosome_0, Hsc70_Protofibril, Lysosome_0, Hsc70_Protofibril, Lysosome_0, Hsc70_Protofibril, Lysosome_0, Hsc70_Protofibril, Lysosome_0, Hsc70_Protofibril, Lysosome_0, Hsc70_Protofibril, Lysosome_0, Hsc70_Protofibril, Lysosome_0, Rate Law: Neuronal_cytosol*k47*Hsc70_Protofibril^g4782*Lysosome_0^g4777
k116 = 0.5; g11642 = 1.0; g116118 = 1.0 Reaction: Neuromelanin + Neurotoxins => Neuromelanin_ntox_Fe3; Neuromelanin, Neurotoxins, Neuromelanin, Neurotoxins, Neuromelanin, Neurotoxins, Neuromelanin, Neurotoxins, Neuromelanin, Neurotoxins, Neuromelanin, Neurotoxins, Neuromelanin, Neurotoxins, Neuromelanin, Neurotoxins, Neuromelanin, Neurotoxins, Rate Law: Neuronal_cytosol*k116*Neuromelanin^g116118*Neurotoxins^g11642
g5280 = 1.0; g523 = 1.0; k52 = 0.05 Reaction: Fibril + Preautophagosome_membrane => Autophagosome_0; Fibril, Preautophagosome_membrane, Fibril, Preautophagosome_membrane, Fibril, Preautophagosome_membrane, Fibril, Preautophagosome_membrane, Fibril, Preautophagosome_membrane, Fibril, Preautophagosome_membrane, Fibril, Preautophagosome_membrane, Fibril, Preautophagosome_membrane, Fibril, Preautophagosome_membrane, Rate Law: k52*Fibril^g523*Preautophagosome_membrane^g5280
k2 = 0.01; g22 = 1.0 Reaction: Protofibril => Fibril; Protofibril, Protofibril, Protofibril, Protofibril, Protofibril, Protofibril, Protofibril, Protofibril, Protofibril, Rate Law: Neuronal_cytosol*k2*Protofibril^g22
g10051 = 1.0; g100115 = 1.0; g10037 = 1.0; k100 = 0.005 Reaction: L_Dopa + O2_0 + Cysteine => Neuromelanin + H2O2 + CO2; L_Dopa, O2_0, Cysteine, L_Dopa, O2_0, Cysteine, L_Dopa, O2_0, Cysteine, L_Dopa, O2_0, Cysteine, L_Dopa, O2_0, Cysteine, L_Dopa, O2_0, Cysteine, L_Dopa, O2_0, Cysteine, L_Dopa, O2_0, Cysteine, L_Dopa, O2_0, Cysteine, Rate Law: Neuronal_cytosol*k100*L_Dopa^g10037*O2_0^g10051*Cysteine^g100115
g919 = 1.0; g920 = 1.0; k9 = 0.001 Reaction: Parkin + Synphilin_1 => Parkin_synphilin_1; Parkin, Synphilin_1, Parkin, Synphilin_1, Parkin, Synphilin_1, Parkin, Synphilin_1, Parkin, Synphilin_1, Parkin, Synphilin_1, Parkin, Synphilin_1, Parkin, Synphilin_1, Parkin, Synphilin_1, Rate Law: Neuronal_cytosol*k9*Parkin^g919*Synphilin_1^g920
k26f = 0.05; g26f18 = 1.0; g26f16 = 1.0; g26f15 = 1.0 Reaction: Ub_E1 + UbcH8_Ub => E1 + UbcH8ub2; ATP, Ub_E1, UbcH8_Ub, ATP, Ub_E1, UbcH8_Ub, ATP, Ub_E1, UbcH8_Ub, ATP, Ub_E1, UbcH8_Ub, ATP, Ub_E1, UbcH8_Ub, ATP, Ub_E1, UbcH8_Ub, ATP, Ub_E1, UbcH8_Ub, ATP, Ub_E1, UbcH8_Ub, ATP, Ub_E1, UbcH8_Ub, ATP, Rate Law: Neuronal_cytosol*k26f*Ub_E1^g26f16*UbcH8_Ub^g26f18*ATP^g26f15
g3173 = 1.0; k31 = 0.05; g3172 = 1.0 Reaction: UbcH13_Uev1a_ub + asyn_UCH_L1 => UbcH13_Uev1a + UCH_L1 + asyn_ub; UbcH13_Uev1a_ub, asyn_UCH_L1, UbcH13_Uev1a_ub, asyn_UCH_L1, UbcH13_Uev1a_ub, asyn_UCH_L1, UbcH13_Uev1a_ub, asyn_UCH_L1, UbcH13_Uev1a_ub, asyn_UCH_L1, UbcH13_Uev1a_ub, asyn_UCH_L1, UbcH13_Uev1a_ub, asyn_UCH_L1, UbcH13_Uev1a_ub, asyn_UCH_L1, UbcH13_Uev1a_ub, asyn_UCH_L1, Rate Law: Neuronal_cytosol*k31*UbcH13_Uev1a_ub^g3172*asyn_UCH_L1^g3173
g5687 = 1.0; g5686 = 1.0; k56 = 0.05 Reaction: O2 => H2O2 + O2_0; SOD, O2, SOD, O2, SOD, O2, SOD, O2, SOD, O2, SOD, O2, SOD, O2, SOD, O2, SOD, O2, SOD, Rate Law: Neuronal_cytosol*k56*O2^g5686*SOD^g5687
g27r30 = 1.0; k27r = 0.005; g27r69 = 1.0 Reaction: UbcH8ub3 => UbcH8 + Ubiquitin; UCH_L1, UbcH8ub3, UCH_L1, UbcH8ub3, UCH_L1, UbcH8ub3, UCH_L1, UbcH8ub3, UCH_L1, UbcH8ub3, UCH_L1, UbcH8ub3, UCH_L1, UbcH8ub3, UCH_L1, UbcH8ub3, UCH_L1, UbcH8ub3, UCH_L1, Rate Law: Neuronal_cytosol*k27r*UbcH8ub3^g27r69*UCH_L1^g27r30
g26r68 = 1.0; g26r30 = 1.0; k26r = 0.005 Reaction: UbcH8ub2 => UbcH8 + Ubiquitin; UCH_L1, UbcH8ub2, UCH_L1, UbcH8ub2, UCH_L1, UbcH8ub2, UCH_L1, UbcH8ub2, UCH_L1, UbcH8ub2, UCH_L1, UbcH8ub2, UCH_L1, UbcH8ub2, UCH_L1, UbcH8ub2, UCH_L1, UbcH8ub2, UCH_L1, Rate Law: Neuronal_cytosol*k26r*UbcH8ub2^g26r68*UCH_L1^g26r30
k11 = 0.05; g1124 = 1.0; g1170 = 1.0 Reaction: Parkin_sub + UbcH8ub4 => Parkin_sub_ub4 + UbcH8; Parkin_sub, UbcH8ub4, Parkin_sub, UbcH8ub4, Parkin_sub, UbcH8ub4, Parkin_sub, UbcH8ub4, Parkin_sub, UbcH8ub4, Parkin_sub, UbcH8ub4, Parkin_sub, UbcH8ub4, Parkin_sub, UbcH8ub4, Parkin_sub, UbcH8ub4, Rate Law: Neuronal_cytosol*k11*Parkin_sub^g1124*UbcH8ub4^g1170
k1 = 0.03; g11 = 1.0 Reaction: Alpha_synuclein => Protofibril; Alpha_synuclein, Alpha_synuclein, Alpha_synuclein, Alpha_synuclein, Alpha_synuclein, Alpha_synuclein, Alpha_synuclein, Alpha_synuclein, Alpha_synuclein, Rate Law: Neuronal_cytosol*k1*Alpha_synuclein^g11
k3 = 0.007; g23 = 1.0; g326 = 1.0 Reaction: Fibril + Parkin_synphilin_1_ub => Lewy_body; Fibril, Parkin_synphilin_1_ub, Fibril, Parkin_synphilin_1_ub, Fibril, Parkin_synphilin_1_ub, Fibril, Parkin_synphilin_1_ub, Fibril, Parkin_synphilin_1_ub, Fibril, Parkin_synphilin_1_ub, Fibril, Parkin_synphilin_1_ub, Fibril, Parkin_synphilin_1_ub, Fibril, Parkin_synphilin_1_ub, Rate Law: Neuronal_cytosol*k3*Fibril^g23*Parkin_synphilin_1_ub^g326
g352 = 1.0; k35 = 0.001; g3576 = 1.0 Reaction: Protofibril + Protofibril_Ub => Fibril; Protofibril, Protofibril_Ub, Protofibril, Protofibril_Ub, Protofibril, Protofibril_Ub, Protofibril, Protofibril_Ub, Protofibril, Protofibril_Ub, Protofibril, Protofibril_Ub, Protofibril, Protofibril_Ub, Protofibril, Protofibril_Ub, Protofibril, Protofibril_Ub, Rate Law: Neuronal_cytosol*k35*Protofibril^g352*Protofibril_Ub^g3576
g1744 = 1.0; g1742 = 1.0; k17 = 1.0E-4 Reaction: Neurotoxins + Vesicle_0 => V_ntox_ba; Neurotoxins, Vesicle_0, Neurotoxins, Vesicle_0, Neurotoxins, Vesicle_0, Neurotoxins, Vesicle_0, Neurotoxins, Vesicle_0, Neurotoxins, Vesicle_0, Neurotoxins, Vesicle_0, Neurotoxins, Vesicle_0, Neurotoxins, Vesicle_0, Rate Law: k17*Neurotoxins^g1742*Vesicle_0^g1744
k43 = 0.05; g431 = 1.0; g4384 = 1.0 Reaction: Alpha_synuclein + Hsc70 => Hsc70_asyn; Alpha_synuclein, Hsc70, Alpha_synuclein, Hsc70, Alpha_synuclein, Hsc70, Alpha_synuclein, Hsc70, Alpha_synuclein, Hsc70, Alpha_synuclein, Hsc70, Alpha_synuclein, Hsc70, Alpha_synuclein, Hsc70, Alpha_synuclein, Hsc70, Rate Law: Neuronal_cytosol*k43*Alpha_synuclein^g431*Hsc70^g4384
g717 = 1.0; g716 = 1.0; k7 = 0.03; g715 = 1.0 Reaction: Ub_E1 + UbcH8 => E1 + UbcH8_Ub; ATP, Ub_E1, UbcH8, ATP, Ub_E1, UbcH8, ATP, Ub_E1, UbcH8, ATP, Ub_E1, UbcH8, ATP, Ub_E1, UbcH8, ATP, Ub_E1, UbcH8, ATP, Ub_E1, UbcH8, ATP, Ub_E1, UbcH8, ATP, Ub_E1, UbcH8, ATP, Rate Law: Neuronal_cytosol*k7*Ub_E1^g716*UbcH8^g717*ATP^g715
g2259 = 1.0; g229 = 1.0; k22 = 0.5 Reaction: H2O2 => H2O + O2_0; Catalase, H2O2, Catalase, H2O2, Catalase, H2O2, Catalase, H2O2, Catalase, H2O2, Catalase, H2O2, Catalase, H2O2, Catalase, H2O2, Catalase, H2O2, Catalase, Rate Law: Neuronal_cytosol*k22*H2O2^g229*Catalase^g2259
k13 = 0.1; g1336 = 1.0; g1335 = 1.0; g1351 = 1.0 Reaction: L_Tyr + O2_0 => L_Dopa; TH, L_Tyr, O2_0, TH, L_Tyr, O2_0, TH, L_Tyr, O2_0, TH, L_Tyr, O2_0, TH, L_Tyr, O2_0, TH, L_Tyr, O2_0, TH, L_Tyr, O2_0, TH, L_Tyr, O2_0, TH, L_Tyr, O2_0, TH, Rate Law: Neuronal_cytosol*k13*L_Tyr^g1336*O2_0^g1351*TH^g1335
k14 = 3.0; g1467 = 1.0; g1437 = 1.0 Reaction: L_Dopa => Dopamine + CO2; DDC, L_Dopa, DDC, L_Dopa, DDC, L_Dopa, DDC, L_Dopa, DDC, L_Dopa, DDC, L_Dopa, DDC, L_Dopa, DDC, L_Dopa, DDC, L_Dopa, DDC, Rate Law: Neuronal_cytosol*k14*L_Dopa^g1437*DDC^g1467
g301 = 1.0; g3030 = 1.0; k30 = 0.001 Reaction: Alpha_synuclein + UCH_L1 => asyn_UCH_L1; Alpha_synuclein, UCH_L1, Alpha_synuclein, UCH_L1, Alpha_synuclein, UCH_L1, Alpha_synuclein, UCH_L1, Alpha_synuclein, UCH_L1, Alpha_synuclein, UCH_L1, Alpha_synuclein, UCH_L1, Alpha_synuclein, UCH_L1, Alpha_synuclein, UCH_L1, Rate Law: Neuronal_cytosol*k30*Alpha_synuclein^g301*UCH_L1^g3030
k34 = 0.05; g3472 = 1.0; g3475 = 1.0 Reaction: UbcH13_Uev1a_ub + Protofibril_UCH_L1 => UbcH13_Uev1a + UCH_L1 + Protofibril_Ub; UbcH13_Uev1a_ub, Protofibril_UCH_L1, UbcH13_Uev1a_ub, Protofibril_UCH_L1, UbcH13_Uev1a_ub, Protofibril_UCH_L1, UbcH13_Uev1a_ub, Protofibril_UCH_L1, UbcH13_Uev1a_ub, Protofibril_UCH_L1, UbcH13_Uev1a_ub, Protofibril_UCH_L1, UbcH13_Uev1a_ub, Protofibril_UCH_L1, UbcH13_Uev1a_ub, Protofibril_UCH_L1, UbcH13_Uev1a_ub, Protofibril_UCH_L1, Rate Law: Neuronal_cytosol*k34*UbcH13_Uev1a_ub^g3472*Protofibril_UCH_L1^g3475
g2065 = 1.0; k20 = 0.1; g209 = 1.0 Reaction: H2O2 + Fe2 => Fe3 + OH_radical + OH; H2O2, Fe2, H2O2, Fe2, H2O2, Fe2, H2O2, Fe2, H2O2, Fe2, H2O2, Fe2, H2O2, Fe2, H2O2, Fe2, H2O2, Fe2, Rate Law: Neuronal_cytosol*k20*H2O2^g209*Fe2^g2065
g4677 = 1.0; g4681 = 1.0; k46 = 0.03 Reaction: Hsc70_asyn => Hsc70 + Fragments; Lysosome_0, Hsc70_asyn, Lysosome_0, Hsc70_asyn, Lysosome_0, Hsc70_asyn, Lysosome_0, Hsc70_asyn, Lysosome_0, Hsc70_asyn, Lysosome_0, Hsc70_asyn, Lysosome_0, Hsc70_asyn, Lysosome_0, Hsc70_asyn, Lysosome_0, Hsc70_asyn, Lysosome_0, Rate Law: Neuronal_cytosol*k46*Hsc70_asyn^g4681*Lysosome_0^g4677
g821 = 1.0; k8 = 0.001; g819 = 1.0 Reaction: Parkin + Substrate => Parkin_sub; Parkin, Substrate, Parkin, Substrate, Parkin, Substrate, Parkin, Substrate, Parkin, Substrate, Parkin, Substrate, Parkin, Substrate, Parkin, Substrate, Parkin, Substrate, Rate Law: Neuronal_cytosol*k8*Parkin^g819*Substrate^g821
k54 = 0.005; g5410 = 1.0; g5419 = 1.0 Reaction: DA_quinone + Parkin => DA_S_parkin; DA_quinone, Parkin, DA_quinone, Parkin, DA_quinone, Parkin, DA_quinone, Parkin, DA_quinone, Parkin, DA_quinone, Parkin, DA_quinone, Parkin, DA_quinone, Parkin, DA_quinone, Parkin, Rate Law: Neuronal_cytosol*k54*DA_quinone^g5410*Parkin^g5419
g1960 = 1.0; g196 = 1.0; k19 = 0.01; g1953 = 1.0; g1951 = 1.0 Reaction: Dopamine + O2_0 + H2O => NH3 + DOPAL + H2O2; MAO, Dopamine, O2_0, H2O, MAO, Dopamine, O2_0, H2O, MAO, Dopamine, O2_0, H2O, MAO, Dopamine, O2_0, H2O, MAO, Dopamine, O2_0, H2O, MAO, Dopamine, O2_0, H2O, MAO, Dopamine, O2_0, H2O, MAO, Dopamine, O2_0, H2O, MAO, Dopamine, O2_0, H2O, MAO, Rate Law: Neuronal_cytosol*k19*Dopamine^g196*O2_0^g1951*H2O^g1960*MAO^g1953
k28f = 0.05; g28f16 = 1.0; g28f69 = 1.0; g28f15 = 1.0 Reaction: Ub_E1 + UbcH8ub3 => E1 + UbcH8ub4; ATP, Ub_E1, UbcH8ub3, ATP, Ub_E1, UbcH8ub3, ATP, Ub_E1, UbcH8ub3, ATP, Ub_E1, UbcH8ub3, ATP, Ub_E1, UbcH8ub3, ATP, Ub_E1, UbcH8ub3, ATP, Ub_E1, UbcH8ub3, ATP, Ub_E1, UbcH8ub3, ATP, Ub_E1, UbcH8ub3, ATP, Rate Law: Neuronal_cytosol*k28f*Ub_E1^g28f16*UbcH8ub3^g28f69*ATP^g28f15
k101 = 0.005; g101115 = 1.0; g10151 = 1.0; g10136 = 1.0 Reaction: L_Tyr + O2_0 + Cysteine => Neuromelanin + H2O2 + CO2; L_Tyr, O2_0, Cysteine, L_Tyr, O2_0, Cysteine, L_Tyr, O2_0, Cysteine, L_Tyr, O2_0, Cysteine, L_Tyr, O2_0, Cysteine, L_Tyr, O2_0, Cysteine, L_Tyr, O2_0, Cysteine, L_Tyr, O2_0, Cysteine, L_Tyr, O2_0, Cysteine, Rate Law: Neuronal_cytosol*k101*L_Tyr^g10136*O2_0^g10151*Cysteine^g101115
g2915 = 1.0; g2971 = 1.0; g2916 = 1.0; k29 = 0.05 Reaction: Ub_E1 + UbcH13_Uev1a => E1 + UbcH13_Uev1a_ub; ATP, Ub_E1, UbcH13_Uev1a, ATP, Ub_E1, UbcH13_Uev1a, ATP, Ub_E1, UbcH13_Uev1a, ATP, Ub_E1, UbcH13_Uev1a, ATP, Ub_E1, UbcH13_Uev1a, ATP, Ub_E1, UbcH13_Uev1a, ATP, Ub_E1, UbcH13_Uev1a, ATP, Ub_E1, UbcH13_Uev1a, ATP, Ub_E1, UbcH13_Uev1a, ATP, Rate Law: Neuronal_cytosol*k29*Ub_E1^g2916*UbcH13_Uev1a^g2971*ATP^g2915
g115118 = 1.0; g11565 = 1.0; k115 = 0.5 Reaction: Fe3 + Neuromelanin => Neuromelanin_ntox_Fe3; Fe3, Neuromelanin, Fe3, Neuromelanin, Fe3, Neuromelanin, Fe3, Neuromelanin, Fe3, Neuromelanin, Fe3, Neuromelanin, Fe3, Neuromelanin, Fe3, Neuromelanin, Fe3, Neuromelanin, Rate Law: Neuronal_cytosol*k115*Fe3^g11565*Neuromelanin^g115118
k21 = 0.1; g2166 = 1.0 Reaction: Fe3 => Fe2; Fe3, Fe3, Fe3, Fe3, Fe3, Fe3, Fe3, Fe3, Fe3, Rate Law: Neuronal_cytosol*k21*Fe3^g2166
g615 = 1.0; g613 = 1.0; k6 = 0.5; g614 = 1.0 Reaction: Ubiquitin + E1 => Ub_E1; ATP, Ubiquitin, E1, ATP, Ubiquitin, E1, ATP, Ubiquitin, E1, ATP, Ubiquitin, E1, ATP, Ubiquitin, E1, ATP, Ubiquitin, E1, ATP, Ubiquitin, E1, ATP, Ubiquitin, E1, ATP, Ubiquitin, E1, ATP, Rate Law: Neuronal_cytosol*k6*Ubiquitin^g613*E1^g614*ATP^g615
k10 = 0.05; g1072 = 1.0; g1025 = 1.0 Reaction: Parkin_synphilin_1 + UbcH13_Uev1a_ub => Parkin_synphilin_1_ub + UbcH13_Uev1a; Parkin_synphilin_1, UbcH13_Uev1a_ub, Parkin_synphilin_1, UbcH13_Uev1a_ub, Parkin_synphilin_1, UbcH13_Uev1a_ub, Parkin_synphilin_1, UbcH13_Uev1a_ub, Parkin_synphilin_1, UbcH13_Uev1a_ub, Parkin_synphilin_1, UbcH13_Uev1a_ub, Parkin_synphilin_1, UbcH13_Uev1a_ub, Parkin_synphilin_1, UbcH13_Uev1a_ub, Parkin_synphilin_1, UbcH13_Uev1a_ub, Rate Law: Neuronal_cytosol*k10*Parkin_synphilin_1^g1025*UbcH13_Uev1a_ub^g1072
g4584 = 1.0; k45 = 0.04; g453 = 1.0 Reaction: Fibril + Hsc70 => Hsc70_fibril; Fibril, Hsc70, Fibril, Hsc70, Fibril, Hsc70, Fibril, Hsc70, Fibril, Hsc70, Fibril, Hsc70, Fibril, Hsc70, Fibril, Hsc70, Fibril, Hsc70, Rate Law: Neuronal_cytosol*k45*Fibril^g453*Hsc70^g4584
g412 = 1.0; k4 = 0.9; g427 = 1.0; g430 = 1.0; g415 = 1.0 Reaction: Parkin_sub_ub4 => Parkin + Fragments + Ubiquitin; Proteasome_0, ATP, UCH_L1, Parkin_sub_ub4, Proteasome_0, ATP, UCH_L1, Parkin_sub_ub4, Proteasome_0, ATP, UCH_L1, Parkin_sub_ub4, Proteasome_0, ATP, UCH_L1, Parkin_sub_ub4, Proteasome_0, ATP, UCH_L1, Parkin_sub_ub4, Proteasome_0, ATP, UCH_L1, Parkin_sub_ub4, Proteasome_0, ATP, UCH_L1, Parkin_sub_ub4, Proteasome_0, ATP, UCH_L1, Parkin_sub_ub4, Proteasome_0, ATP, UCH_L1, Parkin_sub_ub4, Proteasome_0, ATP, UCH_L1, Rate Law: Neuronal_cytosol*k4*Parkin_sub_ub4^g427*Proteasome_0^g412*ATP^g415*UCH_L1^g430
k32 = 0.001; g321 = 1.0; g3274 = 1.0 Reaction: Alpha_synuclein + asyn_ub => Protofibril; Alpha_synuclein, asyn_ub, Alpha_synuclein, asyn_ub, Alpha_synuclein, asyn_ub, Alpha_synuclein, asyn_ub, Alpha_synuclein, asyn_ub, Alpha_synuclein, asyn_ub, Alpha_synuclein, asyn_ub, Alpha_synuclein, asyn_ub, Alpha_synuclein, asyn_ub, Rate Law: Neuronal_cytosol*k32*Alpha_synuclein^g321*asyn_ub^g3274
g5380 = 1.0; g534 = 1.0; k53 = 0.05 Reaction: Lewy_body + Preautophagosome_membrane => Autophagosome_0; Lewy_body, Preautophagosome_membrane, Lewy_body, Preautophagosome_membrane, Lewy_body, Preautophagosome_membrane, Lewy_body, Preautophagosome_membrane, Lewy_body, Preautophagosome_membrane, Lewy_body, Preautophagosome_membrane, Lewy_body, Preautophagosome_membrane, Lewy_body, Preautophagosome_membrane, Lewy_body, Preautophagosome_membrane, Rate Law: k53*Lewy_body^g534*Preautophagosome_membrane^g5380
g556 = 1.0; g5586 = 1.0; k55 = 0.05 Reaction: Dopamine + O2 => H2O2 + DA_quinone; Dopamine, O2, Dopamine, O2, Dopamine, O2, Dopamine, O2, Dopamine, O2, Dopamine, O2, Dopamine, O2, Dopamine, O2, Dopamine, O2, Rate Law: Neuronal_cytosol*k55*Dopamine^g556*O2^g5586
g3330 = 1.0; g332 = 1.0; k33 = 0.001 Reaction: Protofibril + UCH_L1 => Protofibril_UCH_L1; Protofibril, UCH_L1, Protofibril, UCH_L1, Protofibril, UCH_L1, Protofibril, UCH_L1, Protofibril, UCH_L1, Protofibril, UCH_L1, Protofibril, UCH_L1, Protofibril, UCH_L1, Protofibril, UCH_L1, Rate Law: Neuronal_cytosol*k33*Protofibril^g332*UCH_L1^g3330
k48 = 0.03; g4883 = 1.0; g4877 = 1.0 Reaction: Hsc70_fibril => Hsc70 + Fragments; Lysosome_0, Hsc70_fibril, Lysosome_0, Hsc70_fibril, Lysosome_0, Hsc70_fibril, Lysosome_0, Hsc70_fibril, Lysosome_0, Hsc70_fibril, Lysosome_0, Hsc70_fibril, Lysosome_0, Hsc70_fibril, Lysosome_0, Hsc70_fibril, Lysosome_0, Hsc70_fibril, Lysosome_0, Rate Law: Neuronal_cytosol*k48*Hsc70_fibril^g4883*Lysosome_0^g4877
g10251 = 1.0; g10210 = 1.0; k102 = 0.005; g102115 = 1.0 Reaction: DA_quinone + O2_0 + Cysteine => Neuromelanin + CO2; DA_quinone, O2_0, Cysteine, DA_quinone, O2_0, Cysteine, DA_quinone, O2_0, Cysteine, DA_quinone, O2_0, Cysteine, DA_quinone, O2_0, Cysteine, DA_quinone, O2_0, Cysteine, DA_quinone, O2_0, Cysteine, DA_quinone, O2_0, Cysteine, DA_quinone, O2_0, Cysteine, Rate Law: Neuronal_cytosol*k102*DA_quinone^g10210*O2_0^g10251*Cysteine^g102115
k16 = 1.0E-4; g1644 = 1.0; g1643 = 1.0 Reaction: Bioamines + Vesicle_0 => V_ntox_ba; Bioamines, Vesicle_0, Bioamines, Vesicle_0, Bioamines, Vesicle_0, Bioamines, Vesicle_0, Bioamines, Vesicle_0, Bioamines, Vesicle_0, Bioamines, Vesicle_0, Bioamines, Vesicle_0, Bioamines, Vesicle_0, Rate Law: k16*Bioamines^g1643*Vesicle_0^g1644
k18 = 0.02; g186 = 1.0; g1851 = 1.0 Reaction: Dopamine + O2_0 => DA_quinone + O2; Dopamine, O2_0, Dopamine, O2_0, Dopamine, O2_0, Dopamine, O2_0, Dopamine, O2_0, Dopamine, O2_0, Dopamine, O2_0, Dopamine, O2_0, Dopamine, O2_0, Rate Law: Neuronal_cytosol*k18*Dopamine^g186*O2_0^g1851
g2556 = 0.25; g2552 = 1.0; g2555 = 0.3; k25 = 0.05 Reaction: DOPAL + NAD => DOPAC + NADH; ALDH, DOPAL, NAD, ALDH, DOPAL, NAD, ALDH, DOPAL, NAD, ALDH, DOPAL, NAD, ALDH, DOPAL, NAD, ALDH, DOPAL, NAD, ALDH, DOPAL, NAD, ALDH, DOPAL, NAD, ALDH, DOPAL, NAD, ALDH, Rate Law: Neuronal_cytosol*k25*DOPAL^g2552*NAD^g2556*ALDH^g2555
k51 = 0.05; g512 = 1.0; g5180 = 1.0 Reaction: Protofibril + Preautophagosome_membrane => Autophagosome_0; Protofibril, Preautophagosome_membrane, Protofibril, Preautophagosome_membrane, Protofibril, Preautophagosome_membrane, Protofibril, Preautophagosome_membrane, Protofibril, Preautophagosome_membrane, Protofibril, Preautophagosome_membrane, Protofibril, Preautophagosome_membrane, Protofibril, Preautophagosome_membrane, Protofibril, Preautophagosome_membrane, Rate Law: k51*Protofibril^g512*Preautophagosome_membrane^g5180
g501 = 1.0; g5080 = 1.0; k50 = 0.05 Reaction: Alpha_synuclein + Preautophagosome_membrane => Autophagosome_0; Alpha_synuclein, Preautophagosome_membrane, Alpha_synuclein, Preautophagosome_membrane, Alpha_synuclein, Preautophagosome_membrane, Alpha_synuclein, Preautophagosome_membrane, Alpha_synuclein, Preautophagosome_membrane, Alpha_synuclein, Preautophagosome_membrane, Alpha_synuclein, Preautophagosome_membrane, Alpha_synuclein, Preautophagosome_membrane, Alpha_synuclein, Preautophagosome_membrane, Rate Law: k50*Alpha_synuclein^g501*Preautophagosome_membrane^g5080
g2361 = 1.0; k23 = 0.5; g239 = 1.0; g2362 = 1.0 Reaction: H2O2 + GSH => H2O + GSSG; Gluta_per, H2O2, GSH, Gluta_per, H2O2, GSH, Gluta_per, H2O2, GSH, Gluta_per, H2O2, GSH, Gluta_per, H2O2, GSH, Gluta_per, H2O2, GSH, Gluta_per, H2O2, GSH, Gluta_per, H2O2, GSH, Gluta_per, H2O2, GSH, Gluta_per, Rate Law: Neuronal_cytosol*k23*H2O2^g239*GSH^g2362*Gluta_per^g2361
g4484 = 1.0; k44 = 0.045; g442 = 1.0 Reaction: Protofibril + Hsc70 => Hsc70_Protofibril; Protofibril, Hsc70, Protofibril, Hsc70, Protofibril, Hsc70, Protofibril, Hsc70, Protofibril, Hsc70, Protofibril, Hsc70, Protofibril, Hsc70, Protofibril, Hsc70, Protofibril, Hsc70, Rate Law: Neuronal_cytosol*k44*Protofibril^g442*Hsc70^g4484

States:

Name Description
Neuromelanin [5,6-dihydroxyindole; polymer]
Substrate [SBO:0000015]
UbcH13 Uev1a [Ubiquitin-conjugating enzyme E2 N; Ubiquitin-conjugating enzyme E2 variant 1]
UCH L1 asyn ub4 [Polyubiquitin-B; Ubiquitin carboxyl-terminal hydrolase isozyme L1; Alpha-synuclein]
Neurotoxins [neurotoxin]
asyn ub [Polyubiquitin-B; Alpha-synuclein]
Fragments [inactive; peptide]
Dopamine [dopamine]
Ub E1 [Polyubiquitin-B; Ubiquitin-like modifier-activating enzyme 1]
UbcH8ub3 [Polyubiquitin-B; Ubiquitin/ISG15-conjugating enzyme E2 L6]
Lewy body [Alpha-synuclein; Lewy body]
UbcH8 [Ubiquitin/ISG15-conjugating enzyme E2 L6]
DOPAC [(3,4-dihydroxyphenyl)acetic acid]
E1 [Ubiquitin-like modifier-activating enzyme 1]
Protofibril Ub [Polyubiquitin-B; Alpha-synuclein]
Ubiquitin [Polyubiquitin-B]
UbcH8ub2 [Polyubiquitin-B; Ubiquitin/ISG15-conjugating enzyme E2 L6]
DOPAL [3,4-dihydroxyphenylacetaldehyde]
GSH [glutathione]
Hsc70 asyn [Alpha-synuclein; Heat shock cognate 71 kDa protein]
Parkin sub [E3 ubiquitin-protein ligase parkin; SBO:0000015]
Bioamines [amine; biological role]
DA quinone [dopamine; quinone]
Parkin synphilin 1 [E3 ubiquitin-protein ligase parkin; Synphilin-1]
Protofibril [Alpha-synuclein]
UbcH8ub4 [Polyubiquitin-B; Ubiquitin/ISG15-conjugating enzyme E2 L6]
UCH L1 [Ubiquitin carboxyl-terminal hydrolase isozyme L1]
OH radical [hydroxyl]
DA GSH [dopamine; glutathione]
UbcH8 Ub [Polyubiquitin-B; Ubiquitin/ISG15-conjugating enzyme E2 L6]
Alpha synuclein [Alpha-synuclein]
Neuromelanin ntox Fe3 [polymer; 5,6-dihydroxyindole; iron(3+); neurotoxin]
L Tyr [L-tyrosine]
CO2 [carbon dioxide]
Parkin [E3 ubiquitin-protein ligase parkin]
Synphilin 1 [Synphilin-1]
H2O2 [hydrogen peroxide]
Fe3 [iron(3+)]
L Dopa [L-dopa]
Protofibril UCH L1 [Ubiquitin carboxyl-terminal hydrolase isozyme L1; Alpha-synuclein]
Fibril [Alpha-synuclein; supramolecular fiber]

Observables: none

This a model from the article: Modeling beta-adrenergic control of cardiac myocyte contractility in silico. Saucerma…

The beta-adrenergic signaling pathway regulates cardiac myocyte contractility through a combination of feedforward and feedback mechanisms. We used systems analysis to investigate how the components and topology of this signaling network permit neurohormonal control of excitation-contraction coupling in the rat ventricular myocyte. A kinetic model integrating beta-adrenergic signaling with excitation-contraction coupling was formulated, and each subsystem was validated with independent biochemical and physiological measurements. Model analysis was used to investigate quantitatively the effects of specific molecular perturbations. 3-Fold overexpression of adenylyl cyclase in the model allowed an 85% higher rate of cyclic AMP synthesis than an equivalent overexpression of beta 1-adrenergic receptor, and manipulating the affinity of Gs alpha for adenylyl cyclase was a more potent regulator of cyclic AMP production. The model predicted that less than 40% of adenylyl cyclase molecules may be stimulated under maximal receptor activation, and an experimental protocol is suggested for validating this prediction. The model also predicted that the endogenous heat-stable protein kinase inhibitor may enhance basal cyclic AMP buffering by 68% and increasing the apparent Hill coefficient of protein kinase A activation from 1.0 to 2.0. Finally, phosphorylation of the L-type calcium channel and phospholamban were found sufficient to predict the dominant changes in myocyte contractility, including a 2.6x increase in systolic calcium (inotropy) and a 28% decrease in calcium half-relaxation time (lusitropy). By performing systems analysis, the consequences of molecular perturbations in the beta-adrenergic signaling network may be understood within the context of integrative cellular physiology. link: http://identifiers.org/pubmed/12972422

Parameters: none

States: none

Observables: none

BIOMD0000000165 @ v0.0.1

The model reproduces Fig 2B of the paper. Model successfully tested on MathSBML To the extent possible under law, all c…

Compartmentation and dynamics of cAMP and PKA signaling are important determinants of specificity among cAMP's myriad cellular roles. Both cardiac inotropy and the progression of heart disease are affected by spatiotemporal variations in cAMP/PKA signaling, yet the dynamic patterns of PKA-mediated phosphorylation that influence differential responses to agonists have not been characterized. We performed live-cell imaging and systems modeling of PKA-mediated phosphorylation in neonatal cardiac myocytes in response to G-protein coupled receptor stimuli and UV photolysis of "caged" cAMP. cAMP accumulation was rate-limiting in PKA-mediated phosphorylation downstream of the beta-adrenergic receptor. Prostaglandin E1 stimulated higher PKA activity in the cytosol than at the sarcolemma, whereas isoproterenol triggered faster sarcolemmal responses than cytosolic, likely due to restricted cAMP diffusion from submembrane compartments. Localized UV photolysis of caged cAMP triggered gradients of PKA-mediated phosphorylation, enhanced by phosphodiesterase activity and PKA-mediated buffering of cAMP. These findings indicate that combining live-cell FRET imaging and mechanistic computational models can provide quantitative understanding of spatiotemporal signaling. link: http://identifiers.org/pubmed/16905651

Parameters:

Name Description
Kr=7000.0 s^(-1); Kf=1000.0 1000*dimensionless*m^3*mol^(-1)*s^(-1) Reaction: PP_cell + AKARp_cell => PP_AKARp_cell, Rate Law: (Kf*PP_cell*AKARp_cell+(-Kr*PP_AKARp_cell))*cell
k_reassoc=1210.0 1000*dimensionless*m^3*mol^(-1)*s^(-1) Reaction: Gsbg_cell + Gsa_gdp_cell => Gs_cell, Rate Law: k_reassoc*Gsa_gdp_cell*Gsbg_cell*cell
k_barkm=0.0022 s^(-1) Reaction: b1AR_S464_cell => L_b1AR_cell, Rate Law: k_barkm*b1AR_S464_cell*cell
kpka_akar=54.0 s^(-1) Reaction: PKAC_AKAR_cell => AKARp_cell + PKAC_cell, Rate Law: kpka_akar*PKAC_AKAR_cell*cell
Kd=0.535714 s^(-1); Kf=1000.0 1000*dimensionless*m^3*mol^(-1)*s^(-1) Reaction: b1AR_Gs_cell + L_cell => L_b1AR_Gs_cell, Rate Law: (Kf*b1AR_Gs_cell*L_cell+(-Kd*L_b1AR_Gs_cell))*cell
Kf=4375.0 s^(-1); Kr=1000.0 1000*dimensionless*m^3*mol^(-1)*s^(-1) Reaction: A2RC_cell => A2R_cell + PKAC_cell, Rate Law: (Kf*A2RC_cell+(-Kr*A2R_cell*PKAC_cell))*cell
Kr=9140.0 s^(-1); Kf=1000.0 1000*dimensionless*m^3*mol^(-1)*s^(-1) Reaction: RC_cell + cAMP_cell => ARC_cell, Rate Law: (Kf*RC_cell*cAMP_cell+(-Kr*ARC_cell))*cell
ar_for_add_propranolol = 0.0 Reaction: => Propranolol_cell, Rate Law: ar_for_add_propranolol*cell
kcat_PP_AKARp=8.5 s^(-1) Reaction: PP_AKARp_cell => PP_cell + AKAR_cell, Rate Law: kcat_PP_AKARp*PP_AKARp_cell*cell
ar_for_add_Ligand = 0.0 Reaction: => L_cell, Rate Law: ar_for_add_Ligand*cell
Kr=400.0 s^(-1); Kf=1000.0 1000*dimensionless*m^3*mol^(-1)*s^(-1) Reaction: Gsa_gtp_cell + AC_cell => GsAC_cell, Rate Law: (Kf*Gsa_gtp_cell*AC_cell+(-Kr*GsAC_cell))*cell
Vmax_cAMP_synthesis_FskAC = NaN 0.001*dimensionless*m^(-3)*mol*s^(-1); Km=860.0 0.001*dimensionless*m^(-3)*mol Reaction: ATP_cell => cAMP_cell; FskAC_cell, Rate Law: Vmax_cAMP_synthesis_FskAC*ATP_cell*1/(Km+ATP_cell)*cell
khyd=0.8 s^(-1) Reaction: Gsa_gtp_cell => Gsa_gdp_cell, Rate Law: khyd*Gsa_gtp_cell*cell
Kr=860000.0 s^(-1); Kf=1000.0 1000*dimensionless*m^3*mol^(-1)*s^(-1) Reaction: AC_cell + Fsk_cell => FskAC_cell, Rate Law: (Kf*AC_cell*Fsk_cell+(-Kr*FskAC_cell))*cell
kpde=5.0 s^(-1) Reaction: PDEcAMP_cell => PDE_cell, Rate Law: kpde*PDEcAMP_cell*cell
Kr=62.0 s^(-1); Kf=1000.0 1000*dimensionless*m^3*mol^(-1)*s^(-1) Reaction: Gs_cell + L_b1AR_cell => L_b1AR_Gs_cell, Rate Law: (Kf*Gs_cell*L_b1AR_cell+(-Kr*L_b1AR_Gs_cell))*cell
Kr=33000.0 s^(-1); Kf=1000.0 1000*dimensionless*m^3*mol^(-1)*s^(-1) Reaction: b1AR_cell + Gs_cell => b1AR_Gs_cell, Rate Law: (Kf*b1AR_cell*Gs_cell+(-Kr*b1AR_Gs_cell))*cell
k_gact=16.0 s^(-1) Reaction: L_b1AR_Gs_cell => Gsa_gtp_cell + Gsbg_cell + L_b1AR_cell, Rate Law: k_gact*L_b1AR_Gs_cell*cell
Kr=8.0 s^(-1); Kf=1000.0 1000*dimensionless*m^3*mol^(-1)*s^(-1) Reaction: Propranolol_cell + b1AR_cell => b1ARinhib_cell, Rate Law: (Kf*Propranolol_cell*b1AR_cell+(-Kr*b1ARinhib_cell))*cell
Kf=1000.0 1000*dimensionless*m^3*mol^(-1)*s^(-1); Kr=21000.0 s^(-1) Reaction: AKAR_cell + PKAC_cell => PKAC_AKAR_cell, Rate Law: (Kf*AKAR_cell*PKAC_cell+(-Kr*PKAC_AKAR_cell))*cell
kphot=0.1 1000*dimensionless*m^3*mol^(-1)*s^(-1); light_cAMP_photolysis = NaN 0.001*dimensionless*m^(-3)*mol Reaction: DMNB_cAMP_cell => cAMP_cell; light_spot_cell, Rate Law: kphot*light_cAMP_photolysis*DMNB_cAMP_cell*cell
Kr=0.2 s^(-1); Kf=1000.0 1000*dimensionless*m^3*mol^(-1)*s^(-1) Reaction: PKAC_cell + PKI_cell => PKAC_PKI_cell, Rate Law: (Kf*PKAC_cell*PKI_cell+(-Kr*PKAC_PKI_cell))*cell
Kf_inhibit_PDE = NaN 1000*dimensionless*m^3*mol^(-1)*s^(-1); Kr_inhibit_PDE = NaN s^(-1) Reaction: PDE_cell + IBMX_cell => PDE_IBMX_cell, Rate Law: (Kf_inhibit_PDE*PDE_cell*IBMX_cell+(-Kr_inhibit_PDE*PDE_IBMX_cell))*cell
Vmax_cAMP_synthesis_GsAC = NaN 0.001*dimensionless*m^(-3)*mol*s^(-1); Km=315.0 0.001*dimensionless*m^(-3)*mol Reaction: ATP_cell => cAMP_cell; GsAC_cell, Rate Law: Vmax_cAMP_synthesis_GsAC*ATP_cell*1/(Km+ATP_cell)*cell
Kr=285.0 s^(-1); Kf=1000.0 1000*dimensionless*m^3*mol^(-1)*s^(-1) Reaction: L_cell + b1AR_cell => L_b1AR_cell, Rate Law: (Kf*L_cell*b1AR_cell+(-Kr*L_b1AR_cell))*cell
k_barkp=0.0011 s^(-1) Reaction: L_b1AR_cell => b1AR_S464_cell; L_b1AR_Gs_cell, Rate Law: k_barkp*(L_b1AR_cell+L_b1AR_Gs_cell)*cell
Kr=1640.0 s^(-1); Kf=1000.0 1000*dimensionless*m^3*mol^(-1)*s^(-1) Reaction: ARC_cell + cAMP_cell => A2RC_cell, Rate Law: (Kf*ARC_cell*cAMP_cell+(-Kr*A2RC_cell))*cell
Kf=1000.0 1000*dimensionless*m^3*mol^(-1)*s^(-1); Kr=1300.0 s^(-1) Reaction: PDE_cell + cAMP_cell => PDEcAMP_cell, Rate Law: (Kf*PDE_cell*cAMP_cell+(-Kr*PDEcAMP_cell))*cell
kpkam=0.0022 s^(-1); kpkap=0.0036 1000*dimensionless*m^3*mol^(-1)*s^(-1) Reaction: b1AR_cell => b1AR_p_cell; PKAC_cell, L_b1AR_Gs_cell, L_b1AR_cell, Rate Law: (kpkap*PKAC_cell*(L_b1AR_Gs_cell+b1AR_cell+L_b1AR_cell)+(-kpkam*b1AR_p_cell))*cell

States:

Name Description
Gsbg cell [G-protein beta/gamma-subunit complex]
PDE IBMX cell PDE_IBMX
AC cell [Adenylate cyclase type 1]
ATP cell [ATP; ATP]
PKI cell PKI
AKAR cell AKAR
L b1AR cell [Beta-1 adrenergic receptor]
PP cell PP
ARC cell ARC
Propranolol cell Propranolol
b1AR p cell [Beta-1 adrenergic receptor]
PKAC PKI cell PKAC_PKI
GsAC cell [Adenylate cyclase type 1; Guanine nucleotide-binding protein G(s) subunit alpha isoforms short]
AKARp cell AKARp
PKAC cell PKAC
A2R cell A2R
PDE cell [Calcium/calmodulin-dependent 3',5'-cyclic nucleotide phosphodiesterase 1A]
IBMX cell IBMX
DMNB cAMP cell [3',5'-cyclic AMP; 3',5'-Cyclic AMP]
Gsa gdp cell [GDP; IPR001019; IPR001019; GDP]
RC cell RC
b1AR Gs cell [Guanine nucleotide-binding protein G(s) subunit alpha isoforms short; Beta-1 adrenergic receptor]
PKAC AKAR cell [cAMP-dependent protein kinase catalytic subunit alpha]
b1ARinhib cell b1ARinhib
cAMP cell [3',5'-cyclic AMP; 3',5'-Cyclic AMP]
Fsk cell Fsk
FskAC cell FskAC
b1AR cell [Beta-1 adrenergic receptor]
PP AKARp cell PP_AKARp
L cell L
Gsa gtp cell [GTP; IPR001019; IPR001019; GTP]
L b1AR Gs cell [Guanine nucleotide-binding protein G(s) subunit alpha isoforms short; Beta-1 adrenergic receptor]
A2RC cell A2RC
Gs cell [Guanine nucleotide-binding protein G(s) subunit alpha isoforms short]
PDEcAMP cell PDEcAMP
b1AR S464 cell [Beta-1 adrenergic receptor]

Observables: none

The two-receptor:one-transducerm odel (Leff, 1987) is here extended to analyze interactions between agonistsd isplaying…

The two-receptor:one-transducer model (Leff, 1987) is here extended to analyze interactions between agonists displaying E[A] curves of different shapes, by incorporating slope factors into the separate and common parts of the transduction pathway. Interactions were modelled as the effect of one agonist, at fixed concentration, on the curve to the other. A variety of patterns of position and slope changes are predicted. These do not depend on the shape of the control curve, rather, they depend on the slope factors in the separate and common pathways. The following specific predictions are made: (1) when the common pathway is steep, curves undergo potentiation and flattening; (2) when the common pathway is flat, curves undergo right-shift and steepening; (3) when the common pathway is hyperbolic, curves undergo right-shift, with no slope change; (4) when the slope depends on the separate pathways, curves only undergo right-shift with no change in slope. The model provides a sound basis for classifying agonist interactions and for detecting additional, synergistic or antagonistic properties. This analysis indicates that methods based on dose-additivity or independence are less reliable for these purposes. The model provides a practical test, based on slope changes, to detect and quantify additional properties. link: http://identifiers.org/pubmed/9253753

Parameters: none

States: none

Observables: none

This a model from the article: A modelling approach to quantify dynamic crosstalk between the pheromone and the star…

Cells must be able to process multiple information in parallel and, moreover, they must also be able to combine this information in order to trigger the appropriate response. This is achieved by wiring signalling pathways such that they can interact with each other, a phenomenon often called crosstalk. In this study, we employ mathematical modelling techniques to analyse dynamic mechanisms and measures of crosstalk. We present a dynamic mathematical model that compiles current knowledge about the wiring of the pheromone pathway and the filamentous growth pathway in yeast. We consider the main dynamic features and the interconnections between the two pathways in order to study dynamic crosstalk between these two pathways in haploid cells. We introduce two new measures of dynamic crosstalk, the intrinsic specificity and the extrinsic specificity. These two measures incorporate the combined signal of several stimuli being present simultaneously and seem to be more stable than previous measures. When both pathways are responsive and stimulated, the model predicts that (a) the filamentous growth pathway amplifies the response of the pheromone pathway, and (b) the pheromone pathway inhibits the response of filamentous growth pathway in terms of mitogen activated protein kinase activity and transcriptional activity, respectively. Among several mechanisms we identified leakage of activated Ste11 as the most influential source of crosstalk. Moreover, we propose new experiments and predict their outcomes in order to test hypotheses about the mechanisms of crosstalk between the two pathways. Studying signals that are transmitted in parallel gives us new insights about how pathways and signals interact in a dynamical way, e.g., whether they amplify, inhibit, delay or accelerate each other. link: http://identifiers.org/pubmed/16884493

Parameters:

Name Description
k8 = 0.1 Reaction: Ste11Ubi => p, Rate Law: compartment*k8*Ste11Ubi
k20 = 1.0 Reaction: s => PREP; Ste12P, Rate Law: compartment*k20*Ste12P
k31 = 1.0 Reaction: Ste12P => Ste12, Rate Law: compartment*k31*Ste12P
k7 = 10.0 Reaction: Ste5 + Ste5Ste11GbgP => Gbg + Ste11Ubi, Rate Law: compartment*k7*Ste5Ste11GbgP
k1 = 0.01 Reaction: Ste5 + Ste11 => Ste5Ste11, Rate Law: compartment*k1*Ste5*Ste11
k22 = 1.0 Reaction: Kss1 + Ste12TeSte5 => Ste12TeSte5Kss1, Rate Law: compartment*k22*Kss1*Ste12TeSte5
k26 = 0.1 Reaction: Fus3PP => Fus3, Rate Law: compartment*k26*Fus3PP
k3 = 1.0 Reaction: Ste5Ste11Gbg + Fus3 => Ste5Ste11GbgFus3, Rate Law: compartment*k3*Ste5Ste11Gbg*Fus3
k25 = 1.0 Reaction: s => FREP; Ste12TeSte5P, Rate Law: compartment*k25*Ste12TeSte5P
k12 = 1.0 Reaction: Ste5Ste11GbgP + Kss1 => Ste5Ste11GbgKss1P, Rate Law: compartment*k12*Ste5Ste11GbgP*Kss1
k15 = 0.1; k30 = 0.1 Reaction: Kss1 => Kss1PP; Ste11P, Ste11Ubi, Rate Law: compartment*(k15*Kss1*Ste11P+k30*Kss1*Ste11Ubi)
k5 = 1.0 Reaction: Ste5Ste11GbgFus3P => Fus3PP + Ste5Ste11GbgP, Rate Law: compartment*k5*Ste5Ste11GbgFus3P
k21 = 1.0 Reaction: Ste12TeSte5Kss1 => Kss1 + Ste12TeSte5, Rate Law: compartment*k21*Ste12TeSte5Kss1
k9 = 1.0 Reaction: Ste5Ste11Gbg + Kss1 => Ste5Ste11GbgKss1, Rate Law: compartment*k9*Ste5Ste11Gbg*Kss1
k6 = 1.0 Reaction: Fus3 + Ste5Ste11GbgP => Ste5Ste11GbgFus3P, Rate Law: compartment*k6*Fus3*Ste5Ste11GbgP
k32 = 1.0 Reaction: PREP => p, Rate Law: compartment*k32*PREP
k14 = 0.1 Reaction: Ste11P => Ste11, Rate Law: compartment*k14*Ste11P
k33 = 1.0 Reaction: Ste12TeSte5P => Ste12TeSte5, Rate Law: compartment*k33*Ste12TeSte5P
k11 = 1.0 Reaction: Ste5Ste11GbgKss1P => Ste5Ste11GbgP + Kss1PP, Rate Law: compartment*k11*Ste5Ste11GbgKss1P
k16 = 0.1; k28 = 0.01 Reaction: Kss1PP => Kss1; Fus3PP, Rate Law: compartment*(k16*Kss1PP+k28*Kss1PP*Fus3PP)
k23 = 1.0 Reaction: Ste12TeSte5 => Ste12TeSte5P; Kss1PP, Rate Law: compartment*k23*Ste12TeSte5*Kss1PP
k27 = 1.0 Reaction: Ste5Ste11 => Ste5 + Ste11, Rate Law: compartment*k27*Ste5Ste11
k10 = 1.0 Reaction: Ste5Ste11GbgKss1 => Ste5Ste11GbgKss1P, Rate Law: compartment*k10*Ste5Ste11GbgKss1
k4 = 1.0 Reaction: Ste5Ste11GbgFus3 => Ste5Ste11GbgFus3P, Rate Law: compartment*k4*Ste5Ste11GbgFus3
k29 = 0.01; k19 = 1.0 Reaction: Ste12 => Ste12P; Fus3PP, Kss1PP, Rate Law: compartment*(k19*Ste12*Fus3PP+k29*Ste12*Kss1PP)
k24 = 0.01 Reaction: Ste12TeSte5 => p; Fus3PP, Rate Law: compartment*k24*Ste12TeSte5*Fus3PP
k34 = 1.0 Reaction: FREP => p, Rate Law: compartment*k34*FREP
beta = NaN; k13 = 1.0 Reaction: Ste11 => Ste11P, Rate Law: compartment*k13*Ste11*beta
k18 = 10.0 Reaction: Kss1 + Ste12 => Ste12Kss1, Rate Law: compartment*k18*Kss1*Ste12
k17 = 1.0 Reaction: Ste12Kss1 => Kss1 + Ste12, Rate Law: compartment*k17*Ste12Kss1
k2 = 0.01; alpha = NaN Reaction: Ste5Ste11 + Gbg => Ste5Ste11Gbg, Rate Law: compartment*k2*Ste5Ste11*Gbg*alpha

States:

Name Description
Ste11Ubi [Serine/threonine-protein kinase STE11; Ubiquitin-60S ribosomal protein L40Ubiquitin-60S ribosomal protein L40Ubiquitin-40S ribosomal protein S31Polyubiquitin]
Ste5Ste11GbgFus3P [Protein STE5; Serine/threonine-protein kinase STE11; G protein beta subunit; Heterotrimeric G protein gamma subunit GPG1; Mitogen-activated protein kinase FUS3]
Ste12Kss1 [Mitogen-activated protein kinase KSS1; Protein STE12]
Ste5Ste11GbgP [Protein STE5; Serine/threonine-protein kinase STE11; G protein beta subunit; Heterotrimeric G protein gamma subunit GPG1]
Kss1 [Mitogen-activated protein kinase KSS1]
Ste5Ste11GbgKss1P [Protein STE5; Serine/threonine-protein kinase STE11; G protein beta subunit; Heterotrimeric G protein gamma subunit GPG1; Mitogen-activated protein kinase KSS1]
Fus3 [Mitogen-activated protein kinase FUS3]
Ste12TeSte5 [Protein STE5; Protein STE12]
Ste5 [Protein STE5; MAP-kinase scaffold activity]
Ste12 [Protein STE12]
Ste12P [Protein STE12]
Ste5Ste11 [Serine/threonine-protein kinase STE11; Protein STE5]
PREP [response to pheromone]
s s
Ste11 [Serine/threonine-protein kinase STE11; MAP kinase kinase kinase activity]
Ste12TeSte5Kss1 [Protein STE5; Mitogen-activated protein kinase KSS1; Protein STE12]
Fus3PP [Mitogen-activated protein kinase FUS3; MAP kinase activity]
Ste5Ste11Gbg [Heterotrimeric G protein gamma subunit GPG1; G protein beta subunit; Protein STE5; Serine/threonine-protein kinase STE11]
Gbg [G protein beta subunit; Heterotrimeric G protein gamma subunit GPG1]
Ste12TeSte5P [Protein STE5; Protein STE12]
Ste5Ste11GbgFus3 [Protein STE5; Serine/threonine-protein kinase STE11; G protein beta subunit; Heterotrimeric G protein gamma subunit GPG1; Mitogen-activated protein kinase FUS3]
Kss1PP [Mitogen-activated protein kinase KSS1]
FREP [invasive growth in response to pheromone]
Ste11P [Serine/threonine-protein kinase STE11]
Ste5Ste11GbgKss1 [Protein STE5; Serine/threonine-protein kinase STE11; G protein beta subunit; Heterotrimeric G protein gamma subunit GPG1; Mitogen-activated protein kinase KSS1]
p p

Observables: none

BIOMD0000000429 @ v0.0.1

Schaber2012 - Hog pathway in yeastThe high osmolarity glycerol (HOG) pathway in the yeast Saccharomyces cerevisiae is on…

The high osmolarity glycerol (HOG) pathway in yeast serves as a prototype signalling system for eukaryotes. We used an unprecedented amount of data to parameterise 192 models capturing different hypotheses about molecular mechanisms underlying osmo-adaptation and selected a best approximating model. This model implied novel mechanisms regulating osmo-adaptation in yeast. The model suggested that (i) the main mechanism for osmo-adaptation is a fast and transient non-transcriptional Hog1-mediated activation of glycerol production, (ii) the transcriptional response serves to maintain an increased steady-state glycerol production with low steady-state Hog1 activity, and (iii) fast negative feedbacks of activated Hog1 on upstream signalling branches serves to stabilise adaptation response. The best approximating model also indicated that homoeostatic adaptive systems with two parallel redundant signalling branches show a more robust and faster response than single-branch systems. We corroborated this notion to a large extent by dedicated measurements of volume recovery in single cells. Our study also demonstrates that systematically testing a model ensemble against data has the potential to achieve a better and unbiased understanding of molecular mechanisms. link: http://identifiers.org/pubmed/23149687

Parameters:

Name Description
parameter_79 = 0.00226722 Reaction: species_11 => species_10 + species_4; species_11, Rate Law: parameter_79*species_11
parameter_82 = 0.00459138; parameter_56 = 0.0036065403549782; parameter_81 = 2.0793; parameter_80 = 0.297524; parameter_57 = 1.0 Reaction: species_4 + species_10 => species_11; species_12, species_4, species_10, species_12, Rate Law: compartment_1*parameter_57*parameter_82*parameter_56*species_4/compartment_1*species_10/compartment_1/(1+(species_12/compartment_1/parameter_80)^parameter_81)
parameter_39 = 7.09644965005112 Reaction: species_8 => ; species_8, Rate Law: parameter_39*species_8
parameter_87 = 46.8363; parameter_88 = 0.420741; parameter_86 = 680.818 Reaction: => species_1; species_7, species_12, species_7, species_12, Rate Law: compartment_1*parameter_86*species_7/compartment_1*(1+parameter_87*species_12/compartment_1)/(parameter_88+species_7/compartment_1*(1+parameter_87*species_12/compartment_1))
parameter_63 = 0.500000000000001; parameter_71 = 1.0; parameter_83 = 0.00529124 Reaction: species_14 => species_15; species_14, Rate Law: compartment_4*parameter_71*parameter_83*parameter_63*species_14/compartment_4
parameter_78 = 0.506878; parameter_77 = 18.1824 Reaction: => species_8; species_12, species_12, Rate Law: compartment_1*parameter_77*species_12/compartment_1/(parameter_78+species_12/compartment_1)
parameter_69 = 1.0 Reaction: species_12 = parameter_69*species_3/compartment_1*compartment_1, Rate Law: missing
parameter_35 = 6.78688610600496E-5 Reaction: species_7 => ; species_7, Rate Law: parameter_35*species_7
parameter_75 = 0.075474; parameter_73 = 0.00940584; parameter_58 = 1.0; parameter_74 = 0.345701; parameter_22 = 7.10539561053171E-4 Reaction: species_4 => species_5; species_12, species_4, species_12, Rate Law: compartment_1*parameter_58*parameter_75*parameter_22*species_4/compartment_1/(1+(species_12/compartment_1/parameter_73)^parameter_74)
parameter_26 = 1.78587 Reaction: species_3 => species_9; species_6, species_6, species_3, Rate Law: compartment_1*parameter_26*species_6/compartment_1*species_3/compartment_1
parameter_71 = 1.0; parameter_84 = 0.0811033; parameter_65 = 0.00320327093093651; parameter_85 = 0.628719 Reaction: species_15 => species_14; species_12, species_15, species_12, Rate Law: compartment_4*parameter_71*parameter_65*species_15/compartment_4/(1+(species_12/compartment_1/parameter_84)^parameter_85)
parameter_72 = 0.607124 Reaction: species_5 => species_4; species_6, species_6, species_5, Rate Law: compartment_1*parameter_72*species_6/compartment_1*species_5/compartment_1
parameter_27 = 4.28194136809108E-4; parameter_28 = 0.5; parameter_16 = 65.6342903668733 Reaction: species_1 => species_13; species_13, species_1, Rate Law: parameter_28*parameter_27*parameter_16*(species_1/compartment_1-species_13/compartment_2)
parameter_25 = 42.6396538263077; parameter_41 = 48.0003902091319 Reaction: species_2 => species_9; species_5, species_11, species_5, species_2, species_11, Rate Law: compartment_1*(parameter_25*species_5/compartment_1*species_2/compartment_1+parameter_41*species_11/compartment_1*species_2/compartment_1)
parameter_76 = 9.06781E-5 Reaction: => species_7; species_8, species_8, Rate Law: compartment_1*parameter_76*species_8/compartment_1

States:

Name Description
species 9 [Mitogen-activated protein kinase HOG1; Phosphoprotein]
species 2 [Mitogen-activated protein kinase HOG1; S000004103]
species 10 [High osmolarity signaling protein SHO1; S000000920]
species 11 [High osmolarity signaling protein SHO1; MAP kinase kinase PBS2]
species 1 [glycerol]
species 4 [S000003664]
species 14 [Glycerol uptake/efflux facilitator protein; S000003966]
species 3 [Mitogen-activated protein kinase HOG1; Phosphoprotein]
species 8 [messenger RNA]
species 12 [Mitogen-activated protein kinase HOG1]
species 7 [protein]
species 5 [MAP kinase kinase PBS2]
species 15 [Glycerol uptake/efflux facilitator protein; S000003966]
species 13 [glycerol]

Observables: none

A minimally parameterized mathematical model for low-dose metronomic chemotherapy is formulated that takes into account…

A minimally parameterized mathematical model for low-dose metronomic chemotherapy is formulated that takes into account angiogenic signaling between the tumor and its vasculature and tumor inhibiting effects of tumor-immune system interactions. The dynamical equations combine a model for tumor development under angiogenic signaling formulated by Hahnfeldt et al. with a model for tumor-immune system interactions by Stepanova. The dynamical properties of the model are analyzed. Depending on the parameter values, the system encompasses a variety of medically realistic scenarios that range from cases when (i) low-dose metronomic chemotherapy is able to eradicate the tumor (all trajectories converge to a tumor-free equilibrium point) to situations when (ii) tumor dormancy is induced (a unique, globally asymptotically stable benign equilibrium point exists) to (iii) multi-stable situations that have both persistent benign and malignant behaviors separated by the stable manifold of an unstable equilibrium point and finally to (iv) situations when tumor growth cannot be overcome by low-dose metronomic chemotherapy. The model forms a basis for a more general study of chemotherapy when the main components of a tumor's microenvironment are taken into account. link: http://identifiers.org/pubmed/26089097

Parameters: none

States: none

Observables: none

Xenophagy, also known as antibacterial autophagy, is a process of capturing and eliminating cytosolic pathogens, like Sa…

The degradation of cytosol-invading pathogens by autophagy, a process known as xenophagy, is an important mechanism of the innate immune system. Inside the host, Salmonella Typhimurium invades epithelial cells and resides within a specialized intracellular compartment, the Salmonella-containing vacuole. A fraction of these bacteria does not persist inside the vacuole and enters the host cytosol. Salmonella Typhimurium that invades the host cytosol becomes a target of the autophagy machinery for degradation. The xenophagy pathway has recently been discovered, and the exact molecular processes are not entirely characterized. Complete kinetic data for each molecular process is not available, so far. We developed a mathematical model of the xenophagy pathway to investigate this key defense mechanism. In this paper, we present a Petri net model of Salmonella xenophagy in epithelial cells. The model is based on functional information derived from literature data. It comprises the molecular mechanism of galectin-8-dependent and ubiquitin-dependent autophagy, including regulatory processes, like nutrient-dependent regulation of autophagy and TBK1-dependent activation of the autophagy receptor, OPTN. To model the activation of TBK1, we proposed a new mechanism of TBK1 activation, suggesting a spatial and temporal regulation of this process. Using standard Petri net analysis techniques, we found basic functional modules, which describe different pathways of the autophagic capture of Salmonella and reflect the basic dynamics of the system. To verify the model, we performed in silico knockout experiments. We introduced a new concept of knockout analysis to systematically compute and visualize the results, using an in silico knockout matrix. The results of the in silico knockout analyses were consistent with published experimental results and provide a basis for future investigations of the Salmonella xenophagy pathway. link: http://identifiers.org/pubmed/27906974

Parameters: none

States: none

Observables: none

BIOMD0000000024 @ v0.0.1

To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedic…

A mathematical model for the intracellular circadian rhythm generator has been studied, based on a negative feedback of protein products on the transcription rate of their genes. The study is an attempt at examining minimal but biologically realistic requirements for a negative molecular feedback loop involving considerably faster reactions, to produce (slow) circadian oscillations. The model included mRNA and protein production and degradation, along with a negative feedback of the proteins upon mRNA production. The protein production process was described solely by its total duration and a nonlinear term, whereas also the feedback included nonlinear interactions among protein molecules. This system was found to produce robust oscillations in protein and mRNA levels over a wide range of parameter values. Oscillations were slow, with periods much longer than the time constants of any of the individual system parameters. Circadian oscillations were obtained for realistic values of the parameters. The system was readily entrainable to external periodic perturbations. Two distinct classes of phase response curves were found, viz. with or without a time domain within the circadian cycle in which external perturbations fail to induce a phase shift ("dead zone"). The delay and nonlinearity in the protein production and the cooperativity in the negative feedback (Hill coefficient) were for this model found to be necessary and sufficient to generate robust circadian oscillations. The similarities between model outcomes and empirical findings establish that circadian rhythmicity at the cellular level can plausibly emerge from interactions among molecular systems which are not in themselves rhythmic. link: http://identifiers.org/pubmed/9870936

Parameters:

Name Description
k=1.0; rM=1.0; n=2.0 Reaction: EmptySet => M; P, Rate Law: compartment_0000004*rM/(1+(P/k)^n)
qP=0.21 Reaction: P => EmptySet, Rate Law: compartment_0000004*qP*P
qM=0.21 Reaction: M => EmptySet, Rate Law: compartment_0000004*qM*M
parameter_0000009=4.0; rP=1.0; m=3.0 Reaction: EmptySet => P; M, Rate Law: compartment_0000004*rP*delay(M, parameter_0000009)^m

States:

Name Description
M [messenger RNA; RNA]
P [Protein; protein polypeptide chain]

Observables: none

Schilling2000- Genome-scale metabolic network of Haemophilus influenzae (iCS400)This model is described in the article:…

The annotated full DNA sequence is becoming available for a growing number of organisms. This information along with additional biochemical and strain-specific data can be used to define metabolic genotypes and reconstruct cellular metabolic networks. The first free-living organism for which the entire genomic sequence was established was Haemophilus influenzae. Its metabolic network is reconstructed herein and contains 461 reactions operating on 367 intracellular and 84 extracellular metabolites. With the metabolic reaction network established, it becomes necessary to determine its underlying pathway structure as defined by the set of extreme pathways. The H. influenzae metabolic network was subdivided into six subsystems and the extreme pathways determined for each subsystem based on stoichiometric, thermodynamic, and systems-specific constraints. Positive linear combinations of these pathways can be taken to determine the extreme pathways for the complete system. Since these pathways span the capabilities of the full system, they could be used to address a number of important physiological questions. First, they were used to reconcile and curate the sequence annotation by identifying reactions whose function was not supported in any of the extreme pathways. Second, they were used to predict gene products that should be co-regulated and perhaps co-expressed. Third, they were used to determine the composition of the minimal substrate requirements needed to support the production of 51 required metabolic products such as amino acids, nucleotides, phospholipids, etc. Fourth, sets of critical gene deletions from core metabolism were determined in the presence of the minimal substrate conditions and in more complete conditions reflecting the environmental niche of H. influenzae in the human host. In the former case, 11 genes were determined to be critical while six remained critical under the latter conditions. This study represents an important milestone in theoretical biology, namely the establishment of the first extreme pathway structure of a whole genome. link: http://identifiers.org/pubmed/10716908

Parameters: none

States: none

Observables: none

Schilling2002 - Genome-scale metabolic network of Helicobacter pylori (iCS291)This model is described in the article: […

A genome-scale metabolic model of Helicobacter pylori 26695 was constructed from genome sequence annotation, biochemical, and physiological data. This represents an in silico model largely derived from genomic information for an organism for which there is substantially less biochemical information available relative to previously modeled organisms such as Escherichia coli. The reconstructed metabolic network contains 388 enzymatic and transport reactions and accounts for 291 open reading frames. Within the paradigm of constraint-based modeling, extreme-pathway analysis and flux balance analysis were used to explore the metabolic capabilities of the in silico model. General network properties were analyzed and compared to similar results previously generated for Haemophilus influenzae. A minimal medium required by the model to generate required biomass constituents was calculated, indicating the requirement of eight amino acids, six of which correspond to essential human amino acids. In addition a list of potential substrates capable of fulfilling the bulk carbon requirements of H. pylori were identified. A deletion study was performed wherein reactions and associated genes in central metabolism were deleted and their effects were simulated under a variety of substrate availability conditions, yielding a number of reactions that are deemed essential. Deletion results were compared to recently published in vitro essentiality determinations for 17 genes. The in silico model accurately predicted 10 of 17 deletion cases, with partial support for additional cases. Collectively, the results presented herein suggest an effective strategy of combining in silico modeling with experimental technologies to enhance biological discovery for less characterized organisms and their genomes. link: http://identifiers.org/pubmed/12142428

Parameters: none

States: none

Observables: none

BIOMD0000000270 @ v0.0.1

Schilling2009 - ERK distributive This model has been exported from [PottersWheel](http://www.potterswheel.de) on 200…

Cell fate decisions are regulated by the coordinated activation of signalling pathways such as the extracellular signal-regulated kinase (ERK) cascade, but contributions of individual kinase isoforms are mostly unknown. By combining quantitative data from erythropoietin-induced pathway activation in primary erythroid progenitor (colony-forming unit erythroid stage, CFU-E) cells with mathematical modelling, we predicted and experimentally confirmed a distributive ERK phosphorylation mechanism in CFU-E cells. Model analysis showed bow-tie-shaped signal processing and inherently transient signalling for cytokine-induced ERK signalling. Sensitivity analysis predicted that, through a feedback-mediated process, increasing one ERK isoform reduces activation of the other isoform, which was verified by protein over-expression. We calculated ERK activation for biochemically not addressable but physiologically relevant ligand concentrations showing that double-phosphorylated ERK1 attenuates proliferation beyond a certain activation level, whereas activated ERK2 enhances proliferation with saturation kinetics. Thus, we provide a quantitative link between earlier unobservable signalling dynamics and cell fate decisions. link: http://identifiers.org/pubmed/20029368

Parameters:

Name Description
SOS_recruitment_by_pEpoR = 0.10271 second order rate constant Reaction: SOS => mSOS; pEpoR, Rate Law: SOS_recruitment_by_pEpoR*SOS*pEpoR*cell
First_MEK1_phosphorylation_by_pRaf = 0.687193 second order rate constant Reaction: MEK1 => pMEK1; pRaf, Rate Law: First_MEK1_phosphorylation_by_pRaf*MEK1*pRaf*cell
EpoR_phosphorylation_by_pJAK2 = 3.15714 second order rate constant Reaction: EpoR => pEpoR; pJAK2, Rate Law: EpoR_phosphorylation_by_pJAK2*EpoR*pJAK2*cell
Second_MEK1_phosphorylation_by_pRaf = 667.957 second order rate constant Reaction: pMEK1 => ppMEK1; pRaf, Rate Law: Second_MEK1_phosphorylation_by_pRaf*pMEK1*pRaf*cell
SHP1_activation_by_pEpoR = 0.408408 second order rate constant Reaction: SHP1 => mSHP1; pEpoR, Rate Law: SHP1_activation_by_pEpoR*SHP1*pEpoR*cell
Second_ERK2_phosphorylation_by_ppMEK = 53.0816 second order rate constant Reaction: pERK2 => ppERK2; ppMEK2, Rate Law: Second_ERK2_phosphorylation_by_ppMEK*pERK2*ppMEK2*cell
Second_ERK_dephosphorylation = 3.00453 per minute Reaction: pERK2 => ERK2, Rate Law: Second_ERK_dephosphorylation*pERK2*cell
First_ERK2_phosphorylation_by_ppMEK = 2.44361 second order rate constant Reaction: ERK2 => pERK2; ppMEK1, Rate Law: First_ERK2_phosphorylation_by_ppMEK*ERK2*ppMEK1*cell
Second_MEK_dephosphorylation = 0.0732724 per minute Reaction: pMEK2 => MEK2, Rate Law: Second_MEK_dephosphorylation*pMEK2*cell
pRaf_dephosphorylation = 0.374228 per minute Reaction: pRaf => Raf, Rate Law: pRaf_dephosphorylation*pRaf*cell
actSHP1_deactivation = 0.0248773 per minute Reaction: actSHP1 => SHP1, Rate Law: actSHP1_deactivation*actSHP1*cell
pJAK2_dephosphorylation_by_actSHP1 = 0.368384 second order rate constant Reaction: pJAK2 => JAK2; actSHP1, Rate Law: pJAK2_dephosphorylation_by_actSHP1*pJAK2*actSHP1*cell
mSOS_induced_Raf_phosphorylation = 0.144515 second order rate constant Reaction: Raf => pRaf; mSOS, Rate Law: mSOS_induced_Raf_phosphorylation*Raf*mSOS*cell
SHP1_delay = 0.408408 per minute Reaction: Delay01_mSHP1 => Delay02_mSHP1, Rate Law: SHP1_delay*Delay01_mSHP1*cell
pSOS_dephosphorylation = 0.124944 per minute Reaction: pSOS => SOS, Rate Law: pSOS_dephosphorylation*pSOS*cell
First_MEK_dephosphorylation = 0.130937 per minute Reaction: ppMEK1 => pMEK1, Rate Law: First_MEK_dephosphorylation*ppMEK1*cell
First_ERK1_phosphorylation_by_ppMEK = 2.4927 second order rate constant Reaction: ERK1 => pERK1; ppMEK2, Rate Law: First_ERK1_phosphorylation_by_ppMEK*ERK1*ppMEK2*cell
mSOS_release_from_membrane = 15.5956 per minute Reaction: mSOS => SOS, Rate Law: mSOS_release_from_membrane*mSOS*cell
pEpoR_dephosphorylation_by_actSHP1 = 1.19995 second order rate constant Reaction: pEpoR => EpoR; actSHP1, Rate Law: pEpoR_dephosphorylation_by_actSHP1*pEpoR*actSHP1*cell
ppERK_neg_feedback_on_mSOS = 5122.68 second order rate constant Reaction: mSOS => pSOS; ppERK1, Rate Law: ppERK_neg_feedback_on_mSOS*mSOS*ppERK1*cell
JAK2_phosphorylation_by_Epo = 0.0122149 per min per (Uml) Reaction: JAK2 => pJAK2; Epo, Rate Law: JAK2_phosphorylation_by_Epo*JAK2*Epo*cell
First_ERK_dephosphorylation = 39.0886 per minute Reaction: ppERK1 => pERK1, Rate Law: First_ERK_dephosphorylation*ppERK1*cell
First_MEK2_phosphorylation_by_pRaf = 3.11919 second order rate constant Reaction: MEK2 => pMEK2; pRaf, Rate Law: First_MEK2_phosphorylation_by_pRaf*MEK2*pRaf*cell
Second_ERK1_phosphorylation_by_ppMEK = 59.5251 second order rate constant Reaction: pERK1 => ppERK1; ppMEK2, Rate Law: Second_ERK1_phosphorylation_by_ppMEK*pERK1*ppMEK2*cell
Second_MEK2_phosphorylation_by_pRaf = 215.158 second order rate constant Reaction: pMEK2 => ppMEK2; pRaf, Rate Law: Second_MEK2_phosphorylation_by_pRaf*pMEK2*pRaf*cell

States:

Name Description
mSHP1 [Tyrosine-protein phosphatase non-receptor type 6; extrinsic component of plasma membrane]
Delay04 mSHP1 [Tyrosine-protein phosphatase non-receptor type 6]
ppMEK1 [urn:miriam:mod:MOD%3A00048; urn:miriam:mod:MOD%3A00047; MAP kinase kinase kinase activity; Phosphoprotein; Dual specificity mitogen-activated protein kinase kinase 1]
Delay01 mSHP1 [Tyrosine-protein phosphatase non-receptor type 6]
pERK1 [urn:miriam:mod:MOD%3A00048; Mitogen-activated protein kinase 3; Phosphoprotein]
Delay05 mSHP1 [Tyrosine-protein phosphatase non-receptor type 6]
pSOS [Son of sevenless homolog 1; Phosphoprotein]
Delay06 mSHP1 [Tyrosine-protein phosphatase non-receptor type 6]
SHP1 [IPR000387; Tyrosine-protein phosphatase non-receptor type 6]
MEK2 [Dual specificity mitogen-activated protein kinase kinase 2]
pJAK2 [urn:miriam:mod:MOD%3A00048; Phosphoprotein; REACT_24029; protein tyrosine kinase activity; Tyrosine-protein kinase JAK2]
MEK1 [Dual specificity mitogen-activated protein kinase kinase 1]
Delay03 mSHP1 [Tyrosine-protein phosphatase non-receptor type 6]
mSOS [Son of sevenless homolog 1; extrinsic component of plasma membrane; guanyl-nucleotide exchange factor activity]
JAK2 [Tyrosine-protein kinase JAK2]
Delay08 mSHP1 [Tyrosine-protein phosphatase non-receptor type 6]
Delay02 mSHP1 [Tyrosine-protein phosphatase non-receptor type 6]
EpoR [Erythropoietin receptor]
ppERK1 [urn:miriam:mod:MOD%3A00047; urn:miriam:mod:MOD%3A00048; Phosphoprotein; MAP kinase activity; Mitogen-activated protein kinase 3]
pMEK1 [Phosphoprotein; Dual specificity mitogen-activated protein kinase kinase 1]
ppERK2 [urn:miriam:mod:MOD%3A00047; urn:miriam:mod:MOD%3A00048; Mitogen-activated protein kinase 1; MAP kinase activity; Phosphoprotein]
pMEK2 [Phosphoprotein; Dual specificity mitogen-activated protein kinase kinase 2]
SOS [Son of sevenless homolog 1]
actSHP1 [Tyrosine-protein phosphatase non-receptor type 6; protein tyrosine phosphatase activity]
ppMEK2 [Phosphoprotein; Dual specificity mitogen-activated protein kinase kinase 2; urn:miriam:mod:MOD%3A00048; urn:miriam:mod:MOD%3A00047; MAP kinase kinase kinase activity]
pERK2 [urn:miriam:mod:MOD%3A00048; Phosphoprotein; Mitogen-activated protein kinase 1]
Delay07 mSHP1 [Tyrosine-protein phosphatase non-receptor type 6]
ERK1 [Mitogen-activated protein kinase 3]
Raf [RAF proto-oncogene serine/threonine-protein kinase]
pEpoR [Phosphoprotein; Erythropoietin receptor; urn:miriam:mod:MOD%3A00048]
ERK2 [Mitogen-activated protein kinase 1]
pRaf [RAF proto-oncogene serine/threonine-protein kinase; Phosphoprotein; urn:miriam:mod:MOD%3A00046; p-S259,S621-RAF1 [cytosol]; MAP kinase kinase kinase activity]

Observables: none

Schittler2010 - Cell fate of progenitor cells, osteoblasts or chondrocytesMathematical model describing the mechanism of…

Mesenchymal stem cells can give rise to bone and other tissue cells, but their differentiation still escapes full control. In this paper we address this issue by mathematical modeling. We present a model for a genetic switch determining the cell fate of progenitor cells which can differentiate into osteoblasts (bone cells) or chondrocytes (cartilage cells). The model consists of two switch mechanisms and reproduces the experimentally observed three stable equilibrium states: a progenitor, an osteogenic, and a chondrogenic state. Conventionally, the loss of an intermediate (progenitor) state and the entailed attraction to one of two opposite (differentiated) states is modeled as a result of changing parameters. In our model in contrast, we achieve this by distributing the differentiation process to two functional switch parts acting in concert: one triggering differentiation and the other determining cell fate. Via stability and bifurcation analysis, we investigate the effects of biochemical stimuli associated with different system inputs. We employ our model to generate differentiation scenarios on the single cell as well as on the cell population level. The single cell scenarios allow to reconstruct the switching upon extrinsic signals, whereas the cell population scenarios provide a framework to identify the impact of intrinsic properties and the limiting factors for successful differentiation. link: http://identifiers.org/pubmed/21198133

Parameters:

Name Description
kP = 0.1 Reaction: P =>, Rate Law: kP*P
kC = 0.1 Reaction: C =>, Rate Law: kC*C
mO = 1.0; cOP = 0.5; zO = 0.0; cOO = 0.1; bO = 1.0; aO = 0.1; n = 2.0; cOC = 0.1 Reaction: => O; P, C, Rate Law: (aO*O^n+bO+zO)/(mO+cOC*C^n+cOP*P^n+cOO*O^n)
kO = 0.1 Reaction: O =>, Rate Law: kO*O
mC = 1.0; cCO = 0.1; cCP = 0.5; aC = 0.1; bC = 1.0; n = 2.0; zC = 0.0; cCC = 0.1 Reaction: => C; P, O, Rate Law: (aC*C^n+bC+zC)/(mC+cCO*O^n+cCP*P^n+cCC*C^n)
zD = 0.0; bP = 0.5; aP = 0.2; mP = 10.0; n = 2.0; cPP = 0.1 Reaction: => P, Rate Law: (aP*P^n+bP)/(mP+zD+cPP*P^n)

States:

Name Description
C [chondrogenic cell]
P [hematopoietic stem cell]
O [osteogenic cell]

Observables: none

BIOMD0000000407 @ v0.0.1

This model is from the article: Heterogeneity Reduces Sensitivity of Cell Death for TNF-Stimuli Schliemann M, Bullin…

BACKGROUND: Apoptosis is a form of programmed cell death essential for the maintenance of homeostasis and the removal of potentially damaged cells in multicellular organisms. By binding its cognate membrane receptor, TNF receptor type 1 (TNF-R1), the proinflammatory cytokine Tumor Necrosis Factor (TNF) activates pro-apoptotic signaling via caspase activation, but at the same time also stimulates nuclear factor κB (NF-κB)-mediated survival pathways. Differential dose-response relationships of these two major TNF signaling pathways have been described experimentally and using mathematical modeling. However, the quantitative analysis of the complex interplay between pro- and anti-apoptotic signaling pathways is an open question as it is challenging for several reasons: the overall signaling network is complex, various time scales are present, and cells respond quantitatively and qualitatively in a heterogeneous manner. RESULTS: This study analyzes the complex interplay of the crosstalk of TNF-R1 induced pro- and anti-apoptotic signaling pathways based on an experimentally validated mathematical model. The mathematical model describes the temporal responses on both the single cell level as well as the level of a heterogeneous cell population, as observed in the respective quantitative experiments using TNF-R1 stimuli of different strengths and durations. Global sensitivity of the heterogeneous population was quantified by measuring the average gradient of time of death versus each population parameter. This global sensitivity analysis uncovers the concentrations of Caspase-8 and Caspase-3, and their respective inhibitors BAR and XIAP, as key elements for deciding the cell's fate. A simulated knockout of the NF-κB-mediated anti-apoptotic signaling reveals the importance of this pathway for delaying the time of death, reducing the death rate in the case of pulse stimulation and significantly increasing cell-to-cell variability. CONCLUSIONS: Cell ensemble modeling of a heterogeneous cell population including a global sensitivity analysis presented here allowed us to illuminate the role of the different elements and parameters on apoptotic signaling. The receptors serve to transmit the external stimulus; procaspases and their inhibitors control the switching from life to death, while NF-κB enhances the heterogeneity of the cell population. The global sensitivity analysis of the cell population model further revealed an unexpected impact of heterogeneity, i.e. the reduction of parametric sensitivity. link: http://identifiers.org/pubmed/22204418

Parameters:

Name Description
ka_84=5.0E-5 s^(-1) Reaction: XIAP_Casp3 => XIAP, Rate Law: ka_84*XIAP_Casp3
ka_23=0.0118534 amol^(-2)*s^(-1) Reaction: FADD + TNFRCint2 => TNFRCint3, Rate Law: ka_23*FADD^2*TNFRCint2
kd_88=0.001 s^(-1); ka_88=0.520833 amol^(-1)*s^(-1) Reaction: BAR + Casp8 => BAR_Casp8, Rate Law: ka_88*BAR*Casp8-kd_88*BAR_Casp8
ka_82=0.625 amol^(-1)*s^(-1); kd_82=0.001 s^(-1) Reaction: XIAP + Casp3 => XIAP_Casp3, Rate Law: ka_82*XIAP*Casp3-kd_82*XIAP_Casp3
ka_48=4.70498E-4 s^(-1) Reaction: A20_mRNA =>, Rate Law: ka_48*A20_mRNA
ka_42=1.0E-4 s^(-1) Reaction: NFkB_N =>, Rate Law: ka_42*NFkB_N
ka_41=1.0E-4 s^(-1) Reaction: IkBa_NFkB =>, Rate Law: ka_41*IkBa_NFkB
ka_66=3.33333E-5 s^(-1) Reaction: => FLIP_mRNA; NFkB_N, Rate Law: ka_66*NFkB_N
ka_33=0.00976562 amol^(-2)*s^(-1) Reaction: RIP + TRAF2 + TNFRC2_FLIP_pCasp8 => TNFRC2_FLIP_pCasp8_RIP_TRAF2, Rate Law: ka_33*RIP*TRAF2*TNFRC2_FLIP_pCasp8
ka_25=0.3125 amol^(-1)*s^(-1) Reaction: TNFRC2 + FLIP => TNFRC2_FLIP, Rate Law: ka_25*TNFRC2*FLIP
ka_62=3.78788E-5 s^(-1) Reaction: => A20_mRNA; NFkB_N, Rate Law: ka_62*NFkB_N
kd_69=6.17284E-5 s^(-1); ka_69=4.93827E-5 amol*s^(-1) Reaction: => pCasp3, Rate Law: ka_69-kd_69*pCasp3
ka_80=0.009375 amol^(-1)*s^(-1) Reaction: pCasp6 => Casp6; Casp3, Rate Law: ka_80*pCasp6*Casp3
ka_18=0.00953471 amol^(-1)*s^(-1); kd_18=6.60377E-5 s^(-1) Reaction: TNFR_E + TNF_E => TNF_TNFR_E, Rate Law: ka_18*TNFR_E*TNF_E-kd_18*TNF_TNFR_E
ka_7=3.0944E-5 amol*s^(-1); kd_7=1.0E-4 s^(-1) Reaction: => FADD, Rate Law: ka_7-kd_7*FADD
ka_24=0.1135 s^(-1) Reaction: TNFRCint3 => TNFRC2, Rate Law: ka_24*TNFRCint3
ka_53=0.00625 amol^(-1)*s^(-1) Reaction: TNFRC1 => TRAF2 + TNF_TNFR_TRADD; A20, Rate Law: ka_53*TNFRC1*A20
ka_22=0.001135 s^(-1) Reaction: TNFRCint1 => RIP + TRAF2 + TNFRCint2, Rate Law: ka_22*TNFRCint1
ka_9=0.02352 s^(-1) Reaction: TNF_TNFR_TRADD =>, Rate Law: ka_9*TNF_TNFR_TRADD
ka_30=0.3125 amol^(-1)*s^(-1) Reaction: FLIP + TNFRC2_pCasp8 => TNFRC2_FLIP_pCasp8, Rate Law: ka_30*FLIP*TNFRC2_pCasp8
ka_12=5.6E-5 s^(-1) Reaction: TNFRC2_FLIP =>, Rate Law: ka_12*TNFRC2_FLIP
ka_87=0.1875 amol^(-1)*s^(-1) Reaction: PARP => cPARP; Casp3, Rate Law: ka_87*Casp3*PARP
ka_19=0.00427827 amol^(-1)*s^(-1) Reaction: TNF_TNFR_E + TRADD => TNF_TNFR_TRADD, Rate Law: ka_19*TNF_TNFR_E*TRADD
ka_47=0.0115517 s^(-1) Reaction: PIkBa =>, Rate Law: ka_47*PIkBa
ka_79=0.015625 amol^(-1)*s^(-1) Reaction: pCasp3 => Casp3; Casp8, Rate Law: ka_79*pCasp3*Casp8
ka_64=3.33333E-5 s^(-1) Reaction: => XIAP_mRNA; NFkB_N, Rate Law: ka_64*NFkB_N
ka_26=0.3125 amol^(-1)*s^(-1) Reaction: FLIP + TNFRC2_FLIP => TNFRC2_FLIP_FLIP, Rate Law: ka_26*FLIP*TNFRC2_FLIP
ka_43=3.94201E-4 s^(-1) Reaction: IkBa_mRNA =>, Rate Law: ka_43*IkBa_mRNA
ka_16=5.6E-5 s^(-1) Reaction: TNFRC2_FLIP_pCasp8 =>, Rate Law: ka_16*TNFRC2_FLIP_pCasp8
ka_31=0.3125 amol^(-1)*s^(-1) Reaction: TNFRC2_FLIP + pCasp8 => TNFRC2_FLIP_pCasp8, Rate Law: ka_31*TNFRC2_FLIP*pCasp8
ka_63=0.0151515 s^(-1) Reaction: => A20; A20_mRNA, Rate Law: ka_63*A20_mRNA
ka_59=0.005 s^(-1); kd_59=0.00257576 s^(-1) Reaction: IkBa => IkBa_N, Rate Law: ka_59*IkBa-kd_59*IkBa_N
kd_75=5.78704E-6 s^(-1); ka_75=1.66603E-6 amol*s^(-1) Reaction: => BAR, Rate Law: ka_75-kd_75*BAR
ka_46=1.0E-4 s^(-1) Reaction: IkBa_NFkB_N =>, Rate Law: ka_46*IkBa_NFkB_N
ka_3=5.6E-5 s^(-1) Reaction: TNFR_E =>, Rate Law: ka_3*TNFR_E
ka_65=0.0506061 s^(-1) Reaction: => XIAP; XIAP_mRNA, Rate Law: ka_65*XIAP_mRNA
ka_70=3.95062E-6 amol*s^(-1); kd_70=6.17284E-5 s^(-1) Reaction: => pCasp6, Rate Law: ka_70-kd_70*pCasp6
ka_27=0.03125 amol^(-1)*s^(-1) Reaction: TNFRC2 + pCasp8 => TNFRC2_pCasp8, Rate Law: ka_27*TNFRC2*pCasp8
ka_35=6.4E-5 amol*s^(-1); kd_35=1.0E-4 s^(-1) Reaction: => IKK, Rate Law: ka_35-kd_35*IKK
ka_28=0.03125 amol^(-1)*s^(-1) Reaction: TNFRC2_pCasp8 + pCasp8 => TNFRC2_pCasp8_pCasp8, Rate Law: ka_28*TNFRC2_pCasp8*pCasp8
kd_36=1.0E-4 s^(-1); ka_36=1.6E-6 amol*s^(-1) Reaction: => NFkB, Rate Law: ka_36-kd_36*NFkB
ka_29=0.45 s^(-1) Reaction: TNFRC2_pCasp8_pCasp8 => TNFRC2 + Casp8, Rate Law: ka_29*TNFRC2_pCasp8_pCasp8
ka_1=0.001 s^(-1) Reaction: TNFR => TNFR_E, Rate Law: ka_1*TNFR
ka_11=5.6E-5 s^(-1) Reaction: TNFRC2 =>, Rate Law: ka_11*TNFRC2
ka_5=2.9344E-5 amol*s^(-1); kd_5=1.0E-4 s^(-1) Reaction: => TRADD, Rate Law: ka_5-kd_5*TRADD
ka_55=0.104167 amol^(-1)*s^(-1) Reaction: IkBa_NFkB => NFkB + PIkBa; IKKa, Rate Law: ka_55*IKKa*IkBa_NFkB
ka_49=1.04931E-4 s^(-1) Reaction: XIAP_mRNA =>, Rate Law: ka_49*XIAP_mRNA
ka_54=1.25 amol^(-1)*s^(-1) Reaction: NFkB + IkBa => IkBa_NFkB, Rate Law: ka_54*NFkB*IkBa
ka_56=0.0125 s^(-1) Reaction: NFkB => NFkB_N, Rate Law: ka_56*NFkB
ka_52=0.1 s^(-1) Reaction: IKKa => IKK, Rate Law: ka_52*IKKa
ka_32=0.3 s^(-1) Reaction: TNFRC2_FLIP_pCasp8 => TNFRC2 + Casp8, Rate Law: ka_32*TNFRC2_FLIP_pCasp8
ka_38=7.72256E-4 amol*s^(-1); kd_38=1.0E-4 s^(-1) Reaction: => XIAP, Rate Law: ka_38-kd_38*XIAP
ka_86=0.15625 amol^(-1)*s^(-1) Reaction: FLIP => ; Casp3, Rate Law: ka_86*FLIP*Casp3
ka_71=5.78704E-5 s^(-1) Reaction: Casp8 =>, Rate Law: ka_71*Casp8
ka_58=0.0606061 s^(-1) Reaction: => IkBa; IkBa_mRNA, Rate Law: ka_58*IkBa_mRNA
ka_61=0.0151515 s^(-1) Reaction: IkBa_NFkB_N => IkBa_NFkB, Rate Law: ka_61*IkBa_NFkB_N
ka_44=0.00154022 s^(-1) Reaction: IkBa =>, Rate Law: ka_44*IkBa
ka_83=1.875 amol^(-1)*s^(-1) Reaction: XIAP => ; Casp3, Rate Law: ka_83*XIAP*Casp3
ka_34=0.03125 amol^(-1)*s^(-1) Reaction: IKK => IKKa; TNFRC2_FLIP_pCasp8_RIP_TRAF2, Rate Law: ka_34*TNFRC2_FLIP_pCasp8_RIP_TRAF2*IKK
ka_68=1.97531E-4 amol*s^(-1); kd_68=6.17284E-5 s^(-1) Reaction: => pCasp8, Rate Law: ka_68-kd_68*pCasp8
ka_81=0.0015625 amol^(-1)*s^(-1) Reaction: pCasp8 => Casp8; Casp6, Rate Law: ka_81*pCasp8*Casp6
ka_50=1.65744E-4 s^(-1) Reaction: FLIP_mRNA =>, Rate Law: ka_50*FLIP_mRNA
ka_21=0.001135 s^(-1) Reaction: TNFRC1 => TNFRCint1, Rate Law: ka_21*TNFRC1
ka_17=5.6E-5 s^(-1) Reaction: TNFRC2_FLIP_pCasp8_RIP_TRAF2 =>, Rate Law: ka_17*TNFRC2_FLIP_pCasp8_RIP_TRAF2
ka_51=93.75 amol^(-1)*s^(-1) Reaction: IKK => IKKa; TNFRC1, Rate Law: ka_51*TNFRC1*IKK
ka_20=0.0976562 amol^(-2)*s^(-1) Reaction: RIP + TRAF2 + TNF_TNFR_TRADD => TNFRC1, Rate Law: ka_20*RIP*TRAF2*TNF_TNFR_TRADD
ka_15=5.6E-5 s^(-1) Reaction: TNFRC2_pCasp8_pCasp8 =>, Rate Law: ka_15*TNFRC2_pCasp8_pCasp8
ka_67=0.00687273 s^(-1) Reaction: => FLIP; FLIP_mRNA, Rate Law: ka_67*FLIP_mRNA
kd_37=1.0E-4 s^(-1); ka_37=2.24902E-6 amol*s^(-1) Reaction: => FLIP, Rate Law: ka_37-kd_37*FLIP
ka_40=1.0E-4 s^(-1) Reaction: IKKa =>, Rate Law: ka_40*IKKa
ka_39=9.6E-6 amol*s^(-1); kd_39=1.0E-4 s^(-1) Reaction: => A20, Rate Law: ka_39-kd_39*A20
ka_14=5.6E-5 s^(-1) Reaction: TNFRC2_pCasp8 =>, Rate Law: ka_14*TNFRC2_pCasp8

States:

Name Description
TNFR [Tumor necrosis factor receptor superfamily member 1A]
NFkB N [Nuclear factor NF-kappa-B p105 subunit]
TNFRC2 [Tumor necrosis factor receptor superfamily member 1A; Tumor necrosis factor; Tumor necrosis factor receptor type 1-associated DEATH domain protein; FAS-associated death domain protein]
TRAF2 [TNF receptor-associated factor 2]
XIAP [E3 ubiquitin-protein ligase XIAP]
FLIP mRNA [CFLAR-201]
FADD [FAS-associated death domain protein]
TNFRC2 FLIP [Tumor necrosis factor receptor superfamily member 1A; Tumor necrosis factor; Tumor necrosis factor receptor type 1-associated DEATH domain protein; FAS-associated death domain protein; CASP8 and FADD-like apoptosis regulator]
IkBa NFkB [NF-kappa-B inhibitor alpha; Nuclear factor NF-kappa-B p105 subunit]
TNFRC2 FLIP pCasp8 [Tumor necrosis factor receptor superfamily member 1A; Tumor necrosis factor; Tumor necrosis factor receptor type 1-associated DEATH domain protein; FAS-associated death domain protein; CASP8 and FADD-like apoptosis regulator; Caspase-8]
A20 [Tumor necrosis factor alpha-induced protein 3]
IkBa NFkB N [NF-kappa-B inhibitor alpha; Nuclear factor NF-kappa-B p105 subunit]
TNFRC1 [Tumor necrosis factor receptor superfamily member 1A; Tumor necrosis factor; Tumor necrosis factor receptor type 1-associated DEATH domain protein; TNF receptor-associated factor 2; Receptor-interacting serine/threonine-protein kinase 1]
IKK [Inhibitor of nuclear factor kappa-B kinase subunit alpha]
TRADD [Tumor necrosis factor receptor type 1-associated DEATH domain protein]
pCasp8 [Caspase-8]
IkBa mRNA [NFKBIA-201]
FLIP [CASP8 and FADD-like apoptosis regulator]
TNFRC2 FLIP FLIP [Tumor necrosis factor receptor superfamily member 1A; Tumor necrosis factor; Tumor necrosis factor receptor type 1-associated DEATH domain protein; FAS-associated death domain protein; CASP8 and FADD-like apoptosis regulator]
PARP [Poly [ADP-ribose] polymerase 1]
TNF TNFR E [Tumor necrosis factor receptor superfamily member 1A; Tumor necrosis factor]
BAR [Bifunctional apoptosis regulator]
pCasp3 [Caspase-3]
A20 mRNA [TNFAIP3-201]
XIAP mRNA [XIAP-202]
TNF E [Tumor necrosis factor]
TNFRCint3 [Tumor necrosis factor receptor superfamily member 1A; Tumor necrosis factor; Tumor necrosis factor receptor type 1-associated DEATH domain protein; FAS-associated death domain protein]
IKKa [Inhibitor of nuclear factor kappa-B kinase subunit alpha]
TNFRC2 FLIP pCasp8 RIP TRAF2 [Tumor necrosis factor receptor superfamily member 1A; Tumor necrosis factor; Tumor necrosis factor receptor type 1-associated DEATH domain protein; FAS-associated death domain protein; CASP8 and FADD-like apoptosis regulator; Caspase-8; Receptor-interacting serine/threonine-protein kinase 1; TNF receptor-associated factor 2]
PIkBa [NF-kappa-B inhibitor alpha]
IkBa [NF-kappa-B inhibitor alpha]
TNFR E [Tumor necrosis factor receptor superfamily member 1A]
TNFRCint2 [Tumor necrosis factor receptor superfamily member 1A; Tumor necrosis factor; Tumor necrosis factor receptor type 1-associated DEATH domain protein]
TNFRCint1 [Tumor necrosis factor receptor superfamily member 1A; Tumor necrosis factor; Tumor necrosis factor receptor type 1-associated DEATH domain protein; TNF receptor-associated factor 2; Receptor-interacting serine/threonine-protein kinase 1]
NFkB [Nuclear factor NF-kappa-B p105 subunit]
cPARP [Poly [ADP-ribose] polymerase 1]
TNFRC2 pCasp8 pCasp8 [Tumor necrosis factor receptor superfamily member 1A; Tumor necrosis factor; Tumor necrosis factor receptor type 1-associated DEATH domain protein; FAS-associated death domain protein; Caspase-8]
TNFRC2 pCasp8 [Tumor necrosis factor receptor superfamily member 1A; Tumor necrosis factor; Tumor necrosis factor receptor type 1-associated DEATH domain protein; FAS-associated death domain protein; Caspase-8]
pCasp6 [Caspase-6]
TNF TNFR TRADD [Tumor necrosis factor receptor superfamily member 1A; Tumor necrosis factor; Tumor necrosis factor receptor type 1-associated DEATH domain protein]
Casp8 [Caspase-8]

Observables: none

This a model from the article: Modeling insulin kinetics: responses to a single oral glucose administration or ambulat…

Increasing concerns that environmental contaminants may disrupt the endocrine system require development of mathematical tools to predict the potential for such compounds to significantly alter human endocrine function. The endocrine system is largely self-regulating, compensating for moderate changes in dietary phytoestrogens (e.g., in soy products) and normal variations in physiology. However, severe changes in dietary or oral exposures or in health status (e.g., anorexia), can completely disrupt the menstrual cycle in women. Thus, risk assessment tools should account for normal regulation and its limits. We present a mathematical model for the synthesis and release of luteinizing hormone (LH) and follicle-stimulating hormone (FSH) in women as a function of estrogen, progesterone, and inhibin blood levels. The model reproduces the time courses of LH and FSH during the menstrual cycle and correctly predicts observed effects of administered estrogen and progesterone on LH and FSH during clinical studies. The model should be useful for predicting effects of hormonally active substances, both in the pharmaceutical sciences and in toxicology and risk assessment. link: http://identifiers.org/pubmed/11035997

Parameters: none

States: none

Observables: none

BIOMD0000000300 @ v0.0.1

This a model from the article: Hypoxia-dependent sequestration of an oxygen sensor by a widespread structural motif…

The activity of the heterodimeric transcription factor hypoxia inducible factor (HIF) is regulated by the post-translational, oxygen-dependent hydroxylation of its α-subunit by members of the prolyl hydroxylase domain (PHD or EGLN)-family and by factor inhibiting HIF (FIH). PHD-dependent hydroxylation targets HIFα for rapid proteasomal degradation; FIH-catalysed asparaginyl-hydroxylation of the C-terminal transactivation domain (CAD) of HIFα suppresses the CAD-dependent subset of the extensive transcriptional responses induced by HIF. FIH can also hydroxylate ankyrin-repeat domain (ARD) proteins, a large group of proteins which are functionally unrelated but share common structural features. Competition by ARD proteins for FIH is hypothesised to affect FIH activity towards HIFα; however the extent of this competition and its effect on the HIF-dependent hypoxic response are unknown.To analyse if and in which way the FIH/ARD protein interaction affects HIF-activity, we created a rate equation model. Our model predicts that an oxygen-regulated sequestration of FIH by ARD proteins significantly shapes the input/output characteristics of the HIF system. The FIH/ARD protein interaction is predicted to create an oxygen threshold for HIFα CAD-hydroxylation and to significantly sharpen the signal/response curves, which not only focuses HIFα CAD-hydroxylation into a defined range of oxygen tensions, but also makes the response ultrasensitive to varying oxygen tensions. Our model further suggests that the hydroxylation status of the ARD protein pool can encode the strength and the duration of a hypoxic episode, which may allow cells to memorise these features for a certain time period after reoxygenation.The FIH/ARD protein interaction has the potential to contribute to oxygen-range finding, can sensitise the response to changes in oxygen levels, and can provide a memory of the strength and the duration of a hypoxic episode. These emergent properties are predicted to significantly shape the characteristics of HIF activity in animal cells. We argue that the FIH/ARD interaction should be taken into account in studies of the effect of pharmacological inhibition of the HIF-hydroxylases and propose that the interaction of a signalling sensor with a large group of proteins might be a general mechanism for the regulation of signalling pathways. link: http://identifiers.org/pubmed/20955552

Parameters:

Name Description
parameter_14 = 0.2 dimensionless Reaction: species_3 =>, Rate Law: compartment_1*parameter_14*species_3
parameter_17 = 1.0 dimensionless Reaction: species_1 =>, Rate Law: compartment_1*parameter_17*species_1
parameter_4 = 1.0 dimensionless Reaction: species_10 = 0.5*(((species_1-species_8)-parameter_4)+(((parameter_4-species_1)+species_8)^2+4*species_1*parameter_4)^(0.5)), Rate Law: missing
parameter_7 = 101.0 dimensionless; parameter_1 = 0.33 dimensionless; parameter_13 = 500.0 dimensionless Reaction: species_2 => ; species_7, species_11, species_9, Rate Law: compartment_1*species_2*parameter_13*species_7*species_11/(parameter_1+species_11)/(parameter_7+species_7+species_9)
parameter_7 = 101.0 dimensionless Reaction: species_9 = 0.5*(((species_2-species_7)-parameter_7)+(((parameter_7-species_2)+species_7)^2+4*species_2*parameter_7)^(0.5)), Rate Law: missing
parameter_5 = 0.3 dimensionless Reaction: species_14 = species_1/(parameter_5+species_1), Rate Law: missing
parameter_16 = 20.0 dimensionless Reaction: => species_3, Rate Law: compartment_1*parameter_16
parameter_7 = 101.0 dimensionless; parameter_2 = 1.0 dimensionless Reaction: species_12 = (parameter_2+species_9)/(parameter_7+species_9), Rate Law: missing
parameter_1 = 0.33 dimensionless; parameter_9 = 1.0 dimensionless; parameter_13 = 500.0 dimensionless; parameter_6 = 0.0 dimensionless Reaction: species_3 => ; species_7, species_11, species_5, Rate Law: compartment_1*species_3*parameter_13*species_7*species_11/(parameter_1+species_11)/(parameter_9+species_3+parameter_6*(species_5-species_3))
parameter_8 = 500.0 dimensionless; parameter_4 = 1.0 dimensionless Reaction: species_2 => ; species_8, species_11, species_10, Rate Law: compartment_1*species_2*parameter_8*species_8*species_11/(1+species_11)/(parameter_4+species_8+species_10)
parameter_18 = 1.0 dimensionless Reaction: => species_1, Rate Law: compartment_1*parameter_18

States:

Name Description
species 9 HF
species 2 [Endothelial PAS domain-containing protein 1; Hypoxia-inducible factor 1-alpha; Hypoxia-inducible factor 3-alpha]
species 6 [Ankyrin-1]
species 10 HP
species 1 [Endothelial PAS domain-containing protein 1; Hypoxia-inducible factor 1-alpha; Hypoxia-inducible factor 3-alpha]
species 4 [Hypoxia-inducible factor 1-alpha; Endothelial PAS domain-containing protein 1; Hypoxia-inducible factor 3-alpha]
species 16 A for plotting
species 14 NAD
species 3 [Ankyrin-1]
species 12 FIHfree
species 15 CADOH
species 13 CAD

Observables: none

BIOMD0000000173 @ v0.0.1

This sbml file describes the RECI model from: "Mathematical modeling identifies Smad nucleocytoplasmic…

TGF-beta-induced Smad signal transduction from the membrane into the nucleus is not linear and unidirectional, but rather a dynamic network that couples Smad phosphorylation and dephosphorylation through continuous nucleocytoplasmic shuttling of Smads. To understand the quantitative behavior of this network, we have developed a tightly constrained computational model, exploiting the interplay between mathematical modeling and experimental strategies. The model simultaneously reproduces four distinct datasets with excellent accuracy and provides mechanistic insights into how the network operates. We use the model to make predictions about the outcome of fluorescence recovery after photobleaching experiments and the behavior of a functionally impaired Smad2 mutant, which we then verify experimentally. Successful model performance strongly supports the hypothesis of a dynamic maintenance of Smad nuclear accumulation during active signaling. The presented work establishes Smad nucleocytoplasmic shuttling as a dynamic network that flexibly transmits quantitative features of the extracellular TGF-beta signal, such as its duration and intensity, into the nucleus. link: http://identifiers.org/pubmed/18443295

Parameters:

Name Description
k_TGFb = 0.07423555020288 pernMpersecond Reaction: R + TGFb_c => R_act, Rate Law: cytosol*k_TGFb*R*TGFb_c
kon = 0.00183925592901392 pernMpersecond; koff = 0.016 persecond Reaction: pS2_n + S4_n => S24_n, Rate Law: nucleus*(kon*pS2_n*S4_n-koff*S24_n)
koff_SB = 100.0 persecond; kon_SB = 0.146422317103884 pernMpersecond Reaction: R_act + SB => R_inact, Rate Law: cytosol*(kon_SB*R_act*SB-koff_SB*R_inact)
kin_CIF = 3.36347821E-14 litrepersecond Reaction: S24_c => S24_n, Rate Law: kin_CIF*S24_c
kin = 5.93E-15 litrepersecond Reaction: S4_c => S4_n, Rate Law: kin*S4_c-kin*S4_n
kdephos = 0.00656639 pernMpersecond Reaction: pS2_n + PPase => S2_n + PPase, Rate Law: nucleus*kdephos*pS2_n*PPase
kphos = 4.037081673984E-4 pernMpersecond Reaction: R_act + S2_c => R_act + pS2_c, Rate Law: cytosol*kphos*R_act*S2_c
SB_add = 10000.0 nM; t_SB = 2700.0 Predefined unit time; SB_0 = 0.0 nM Reaction: SB = piecewise(SB_add, time > t_SB, SB_0), Rate Law: missing
kex = 1.26E-14 litrepersecond; kin = 5.93E-15 litrepersecond Reaction: pG_c => pG_n, Rate Law: kin*pG_c-kex*pG_n

States:

Name Description
G4 c [protein complex; Mothers against decapentaplegic homolog 2; Mothers against decapentaplegic homolog 4; IPR000786; Phosphoprotein]
G n [Mothers against decapentaplegic homolog 2; IPR000786]
S22 n [protein complex; Mothers against decapentaplegic homolog 2; Phosphoprotein]
G4 n [Mothers against decapentaplegic homolog 2; Mothers against decapentaplegic homolog 4; protein complex; IPR000786; Phosphoprotein]
PPase [Protein phosphatase 1A; phosphoprotein phosphatase activity]
S2 c [Mothers against decapentaplegic homolog 2]
TGFb c [Transforming growth factor beta-1; Transforming growth factor beta-2; Transforming growth factor beta-3]
pS2 c [Mothers against decapentaplegic homolog 2; Phosphoprotein]
pG c [Mothers against decapentaplegic homolog 2; Phosphoprotein; IPR000786]
R inact [TGF-beta receptor type-1; Receptor protein serine/threonine kinase; Activin receptor type-1C; TGF-beta receptor type-2]
G c [Mothers against decapentaplegic homolog 2; IPR000786]
pG n [Mothers against decapentaplegic homolog 2; Phosphoprotein; IPR000786]
SB [protein serine/threonine kinase inhibitor activity]
G2 n [protein complex; Mothers against decapentaplegic homolog 2; IPR000786; Phosphoprotein]
S22 c [protein complex; Mothers against decapentaplegic homolog 2; Phosphoprotein]
S24 c [protein complex; Mothers against decapentaplegic homolog 2; Mothers against decapentaplegic homolog 4; Phosphoprotein]
S4 c [Mothers against decapentaplegic homolog 4]
GG n [Mothers against decapentaplegic homolog 2; protein complex; IPR000786; Phosphoprotein]
pS2 n [Mothers against decapentaplegic homolog 2; Phosphoprotein]
G2 c [protein complex; Mothers against decapentaplegic homolog 2; IPR000786; Phosphoprotein]
R act [TGF-beta receptor type-1; Activin receptor type-1C; Receptor protein serine/threonine kinase; TGF-beta receptor type-2]
GG c [protein complex; Mothers against decapentaplegic homolog 2; IPR000786; Phosphoprotein]
S24 n [protein complex; Mothers against decapentaplegic homolog 2; Mothers against decapentaplegic homolog 4; Phosphoprotein]
S2 n [Mothers against decapentaplegic homolog 2]
S4 n [Mothers against decapentaplegic homolog 4]
R [TGF-beta receptor type-1; Receptor protein serine/threonine kinase; Activin receptor type-1C; TGF-beta receptor type-2]

Observables: none

BIOMD0000000530 @ v0.0.1

Schmitz2014 - RNA triplex formationThe model is parameterized using the parameters for gene CCDC3 from Supplementary Tab…

MicroRNAs (miRNAs) are an integral part of gene regulation at the post-transcriptional level. Recently, it has been shown that pairs of miRNAs can repress the translation of a target mRNA in a cooperative manner, which leads to an enhanced effectiveness and specificity in target repression. However, it remains unclear which miRNA pairs can synergize and which genes are target of cooperative miRNA regulation. In this paper, we present a computational workflow for the prediction and analysis of cooperating miRNAs and their mutual target genes, which we refer to as RNA triplexes. The workflow integrates methods of miRNA target prediction; triplex structure analysis; molecular dynamics simulations and mathematical modeling for a reliable prediction of functional RNA triplexes and target repression efficiency. In a case study we analyzed the human genome and identified several thousand targets of cooperative gene regulation. Our results suggest that miRNA cooperativity is a frequent mechanism for an enhanced target repression by pairs of miRNAs facilitating distinctive and fine-tuned target gene expression patterns. Human RNA triplexes predicted and characterized in this study are organized in a web resource at www.sbi.uni-rostock.de/triplexrna/. link: http://identifiers.org/pubmed/24875477

Parameters:

Name Description
k1=1.0 Reaction: species_2 => ; species_2, Rate Law: compartment_1*k1*species_2
k1=4.5298E-4 Reaction: species_1 + species_2 => species_4; species_1, species_2, Rate Law: compartment_1*k1*species_1*species_2
k_syn_miRNA_1=1.0 Reaction: => species_2; species_8, species_8, Rate Law: compartment_1*k_syn_miRNA_1*species_8
k_syn_mRNA=1.0 Reaction: => species_1; species_7, species_7, Rate Law: compartment_1*k_syn_mRNA*species_7
k1=0.187796 Reaction: species_6 => species_2 + species_3 + species_1; species_6, Rate Law: compartment_1*k1*species_6
k_syn_prot=1.0 Reaction: => species_10; species_1, species_1, Rate Law: compartment_1*k_syn_prot*species_1
k1=0.241033 Reaction: species_5 => species_3 + species_1; species_5, Rate Law: compartment_1*k1*species_5
k1=1.30837E-5 Reaction: species_1 + species_3 => species_5; species_1, species_3, Rate Law: compartment_1*k1*species_1*species_3
k1=0.249955 Reaction: species_4 => species_2 + species_1; species_4, Rate Law: compartment_1*k1*species_4
k1=0.999534 Reaction: species_1 + species_2 + species_3 => species_6; species_1, species_2, species_3, Rate Law: compartment_1*k1*species_1*species_2*species_3
k_syn_miRNA_2=1.0 Reaction: => species_3; species_9, species_9, Rate Law: compartment_1*k_syn_miRNA_2*species_9

States:

Name Description
species 2 [MI0003575; SBO:0000316]
species 6 [CCDC3; MI0003575; MI0000476]
species 10 [CCDC3]
species 3 [MI0000476; SBO:0000316]
species 1 [CCDC3; messenger RNA]
species 4 [CCDC3; MI0003575]
species 5 [CCDC3; MI0000476]

Observables: none

MODEL7907879432 @ v0.0.1

This a model from the article: Mechanism of the Frank-Starling law--a simulation study with a novel cardiac muscle con…

A stretch-induced increase of active tension is one of the most important properties of the heart, known as the Frank-Starling law. Although a variation of myofilament Ca(2+) sensitivity with sarcomere length (SL) change was found to be involved, the underlying molecular mechanisms are not fully clarified. Some recent experimental studies indicate that a reduction of the lattice spacing between thin and thick filaments, through the increase of passive tension caused by the sarcomeric protein titin with an increase in SL within the physiological range, promotes formation of force-generating crossbridges (Xbs). However, the mechanism by which the Xb concentration determines the degree of cooperativity for a given SL has so far evaded experimental elucidation. In this simulation study, a novel, rather simple molecular-based cardiac contraction model, appropriate for integration into a ventricular cell model, was designed, being the first model to introduce experimental data on titin-based radial tension to account for the SL-dependent modulation of the interfilament lattice spacing and to include a conformational change of troponin I (TnI). Simulation results for the isometric twitch contraction time course, the length-tension and the force-[Ca(2+)] relationships are comparable to experimental data. A complete potential Frank-Starling mechanism was analyzed by this simulation study. The SL-dependent modulation of the myosin binding rate through titin's passive tension determines the Xb concentration which then alters the degree of positive cooperativity affecting the rate of the TnI conformation change and causing the Hill coefficient to be SL-dependent. link: http://identifiers.org/pubmed/16860336

Parameters: none

States: none

Observables: none

BIOMD0000000019 @ v0.0.1

Schoeberl2002 - EGF MAPK Computational model that offers an integrated quantitative, dynamic, and topological represent…

We present a computational model that offers an integrated quantitative, dynamic, and topological representation of intracellular signal networks, based on known components of epidermal growth factor (EGF) receptor signal pathways. The model provides insight into signal-response relationships between the binding of EGF to its receptor at the cell surface and the activation of downstream proteins in the signaling cascade. It shows that EGF-induced responses are remarkably stable over a 100-fold range of ligand concentration and that the critical parameter in determining signal efficacy is the initial velocity of receptor activation. The predictions of the model agree well with experimental analysis of the effect of EGF on two downstream responses, phosphorylation of ERK-1/2 and expression of the target gene, c-fos. link: http://identifiers.org/pubmed/11923843

Parameters:

Name Description
kr56 = 36.0 permin; k56 = 0.00145 peritempermin Reaction: x59 + x60 => x61, Rate Law: k56*x59*x60-kr56*x61
k50 = 2.5E-5 peritempermin; kr50 = 30.0 permin Reaction: x53 + x75 => x79, Rate Law: k50*x53*x75-kr50*x79
k18 = 0.0015 peritempermin; kr18 = 78.0 permin Reaction: x26 + x66 => x67, Rate Law: k18*x26*x66-kr18*x67
k25 = 0.001 peritempermin; kr25 = 1.284 permin Reaction: x24 + x65 => x66, Rate Law: k25*x24*x65-kr25*x66
k48 = 0.00143 peritempermin; kr48 = 48.0 permin Reaction: x77 + x53 => x78, Rate Law: k48*x77*x53-kr48*x78
k59 = 18.0 permin Reaction: x85 => x55 + x60, Rate Law: k59*x85
kr32 = 2.4E-5 peritempermin; k32 = 6.0 permin Reaction: x66 => x17 + x38, Rate Law: k32*x66-kr32*x17*x38
kr41 = 2.574 permin; k41 = 0.003 peritempermin Reaction: x30 + x33 => x35, Rate Law: k41*x30*x33-kr41*x35
k20 = 2.1E-4 peritempermin; kr20 = 24.0 permin Reaction: x35 + x43 => x37, Rate Law: k20*x35*x43-kr20*x37
kr4 = 0.0996 permin; k4 = 1.038E-5 peritempermin Reaction: x36 + x12 => x93, Rate Law: k4*x36*x12-kr4*x93
k5 = NaN permin Reaction: x93 => x9 + x67, Rate Law: k5*x93
k29 = 60.0 permin; kr29 = 7.0E-5 peritempermin Reaction: x70 => x71 + x72, Rate Law: k29*x70-kr29*x71*x72
k57 = 16.2 permin Reaction: x84 => x81 + x60, Rate Law: k57*x84
k47 = 174.0 permin Reaction: x76 => x72 + x77, Rate Law: k47*x76
kr58 = 30.0 permin; k58 = 5.0E-4 peritempermin Reaction: x60 + x81 => x85, Rate Law: k58*x60*x81-kr58*x85
k6 = 0.003 permin; kr6 = 0.3 permin Reaction: x2 => x6, Rate Law: k6*x2-kr6*x6
kr2 = 6.0 permin; k2 = 0.001 peritempermin Reaction: x10 => x11, Rate Law: k2*x10*x10-kr2*x11
k15 = 600000.0 permin Reaction: x9 => x12, Rate Law: k15*x9
k10 = 3.25581 peritempermin; kr10 = 0.66 permin Reaction: x6 + x16 => x10, Rate Law: k10*x6*x16-kr10*x10
k44 = 0.00111 peritempermin; kr44 = 1.0998 permin Reaction: x47 + x72 => x74, Rate Law: k44*x47*x72-kr44*x74
k45 = 210.0 permin Reaction: x74 => x75 + x72, Rate Law: k45*x74
kr3 = 0.6 permin; k3 = 60.0 permin Reaction: x11 => x8, Rate Law: k3*x11-kr3*x8
k49 = 3.48 permin Reaction: x78 => x75 + x53, Rate Law: k49*x78
k55 = 342.0 permin Reaction: x82 => x83 + x77, Rate Law: k55*x82
k60 = 0.04002 permin Reaction: x6 => x86, Rate Law: k60*x6
k19 = 30.0 permin; kr19 = 1.0E-5 peritempermin Reaction: x36 => x35 + x28, Rate Law: k19*x36-kr19*x35*x28
k42 = 0.0071 peritempermin; kr42 = 12.0 permin Reaction: x44 + x72 => x73, Rate Law: k42*x44*x72-kr42*x73
k53 = 960.0 permin Reaction: x80 => x81 + x77, Rate Law: k53*x80
k52 = 0.00534 peritempermin; kr52 = 1.98 permin Reaction: x77 + x81 => x82, Rate Law: k52*x77*x81-kr52*x82
k21 = 1.38 permin; kr21 = 2.2E-5 peritempermin Reaction: x37 => x35 + x26, Rate Law: k21*x37-kr21*x35*x26

States:

Name Description
x72 Rafi*
x85 ERKi-P-P'ase3i
x80 ERKi-MEKi-PP
x67 EGF-EGFRi*^2-GAP-Shc*-Grb2-Sos-Ras-GDP
x89 EGF-EGFR*^2-GAP-Grb2-Sos-Ras-GDP-Prot
x86 EGFRideg
x79 MEKi-P-P'ase2i
x62 ERK-P-P'ase3
Ras GTP t_Ras_GTP
x45 Raf*
x66 EGF-EGFRi*^2-GAP-Shc*-Grb2-Sos
x78 MEKi-PP-P'ase2i
x75 MEKi-P
x91 EGF-EGFR*^2-GAP-Shc*-Grb2-Prot
x56 ERK-MEK-PP
x59 ERK-PP
x77 MEKi-PP
x12 Prot
x74 MEKi-Rafi*
x44 Phosphotase1
x61 ERK-PP-P'ase3
Raf act t_Raf*
x47 [Dual specificity mitogen-activated protein kinase kinase 1; Mitogen-activated protein kinase kinase 1Mitogen-activated protein kinase kinase 1, isoform CRA_acDNA FLJ76051, highly similar to Homo sapiens mitogen-activated protein kinase kinase 1 (MAP2K1), mRNA; 176872]
x9 [AP-type membrane coat adaptor complex]
x8 [Epidermal growth factor receptor; Pro-epidermal growth factor]
x69 Rasi-GTP
x81 ERKi-P
x35 EGF-EGFR*^2-GAP-Shc*-Grb2-Sos
x43 Ras-GTP*
x71 Rasi-GTP*
x36 EGF-EGFR*^2-GAP-Shc*-Grb2-Sos-Ras-GDP
x54 MEK-P-P'ase2
x6 [Epidermal growth factor receptor]
x87 EGF-EGFRi*^2deg
x60 Phosphotase3
x58 ERK-P-MEK-PP
x84 ERKi-PP-P'ase3i
SHC P t t_SHC_P_t
x88 EGF-EGFR*^2-GAP-Grb2-Sos-Prot
x51 MEK-PP
x11 EGF-EGFRi^2
x94 EGF-EGFR*^2-GAP-Shc*-Grb2-Sos-Ras-GTP-Prot
x53 Phosphatase2
x37 EGF-EGFR*^2-GAP-Shc*-Grb2-Sos-Ras-GTP
x63 EGF-EGFRi*^2-GAP-Shc
x57 ERK-P
x55 [Mitogen-activated protein kinase 1; 176948]
x48 MEK-Raf*
x82 ERKi-P-MEKi-PP
x73 Rafi*-P'ase
x52 MEK-PP-P'ase2
x70 Rafi-Rasi-GTP
x7 [Ras GTPase-activating protein 1; Growth factor receptor-bound protein 2; Epidermal growth factor receptor; Pro-epidermal growth factor; AP-type membrane coat adaptor complex]
x49 [Dual specificity mitogen-activated protein kinase kinase 1; Mitogen-activated protein kinase kinase 1Mitogen-activated protein kinase kinase 1, isoform CRA_acDNA FLJ76051, highly similar to Homo sapiens mitogen-activated protein kinase kinase 1 (MAP2K1), mRNA; Phosphoprotein; 176872]
x10 [Pro-epidermal growth factor; Epidermal growth factor receptor]
x65 EGF-EGFRi*^2-GAP-Shc*-Grb2
x76 MEKi-P-Rafi*

Observables: none

This is a dynamic mathematical model describing the development of the cellular branch of the intestinal immune system o…

The aim of this study was to create a dynamic mathematical model of the development of the cellular branch of the intestinal immune system of poultry during the first 42 days of life and of its response towards an oral infection with Salmonella enterica serovar Enteritidis. The system elements were grouped in five important classes consisting of intra- and extracellular S. Enteritidis bacteria, macrophages, CD4+, and CD8+ cells. Twelve model variables were described by ordinary differential equations, including 50 parameters. Parameter values were estimated from literature or from own immunohistochemistry data. The model described the immune development in non-infected birds with an average R² of 0.87. The model showed less accuracy in reproducing the immune response to S. Enteritidis infection, with an average R² of 0.51, although model response did follow observed trends in time. Evaluation of the model against independent data derived from several infection trials showed strong/significant deviations from observed values. Nevertheless, it was shown that the model could be used to simulate the effect of varying input parameters on system elements response, such as the number of immune cells at hatch. Model simulations allowed one to study the sensitivity of the model outcome for varying model inputs. The initial number of immune cells at hatch was shown to have a profound impact on the predicted development in the number of systemic S. Enteritidis bacteria after infection. The theoretical contribution of this work is the identification of responses in system elements of the developing intestinal immune system of poultry obtaining a mathematical representation which allows one to explore the relationships between these elements under contrasting environmental conditions during different stages of intestinal development. link: http://identifiers.org/pubmed/23603730

Parameters:

Name Description
iMr = 0.1; cSeMr = 1.0 Reaction: => Si; Mr, Rate Law: compartment*iMr*Mr*Si/(Si+cSeMr)
vrecMr = 1.0; kmrecMr = 1000.0 Reaction: Mrrec => Mr; Se, Rate Law: compartment*Mrrec*vrecMr*Se/(Se+kmrecMr)
kSedCD4 = 4200.0; CD4n = 0.4; ndCD4 = 8.0 Reaction: CD4 => ; Se, Rate Law: compartment*CD4n*CD4*Se^ndCD4/(Se^ndCD4+kSedCD4^ndCD4)
cc1CD8 = 1.3E7; gbCD8 = 1.44; k2CD8 = 4.7E7 Reaction: => CD8, Rate Law: compartment*gbCD8*CD8*(1-CD8/cc1CD8)*CD8/(CD8+k2CD8)
drCD4 = 0.016 Reaction: CD4 =>, Rate Law: compartment*drCD4*CD4
kSeMa = 2.6E-7 Reaction: Ma + Se =>, Rate Law: compartment*kSeMa*Ma*Se
sCD8 = 430000.0 Reaction: => CD8, Rate Law: compartment*sCD8
drSe = 27.8 Reaction: Se =>, Rate Law: compartment*drSe*Se
lMi = 0.8; cCD4CD8 = 10.0 Reaction: Si => ; CD4, CD8, Mi, Rate Law: compartment*lMi*(CD4+CD8/Mi)/(CD4+CD8/Mi+cCD4CD8)
sCD4 = 490000.0 Reaction: => CD4, Rate Law: compartment*sCD4
aMr = 100.0; cSeMr = 1.0 Reaction: Mr => Ma; Se, Rate Law: compartment*aMr*Mr*Se/(Se+cSeMr)
pSe = 35.0; ccSe = 500000.0 Reaction: => Se, Rate Law: compartment*pSe*Se*(1-Se/ccSe)
drMi = 0.011 Reaction: Mi =>, Rate Law: compartment*drMi*Mi
sMr = 300000.0 Reaction: => Mr, Rate Law: compartment*sMr
apop = 0.7; N = 30.0; lMi = 0.8; cCD4CD8 = 10.0 Reaction: Mi => ; CD4, CD8, Si, Rate Law: compartment*(1-apop*Si/(Si+N+Mi))*lMi*(CD4+CD8/Mi)/(CD4+CD8/Mi+cCD4CD8)
cdaMa = 3.0E7; daMa = 40.0 Reaction: Ma => Mr; CD4, Rate Law: compartment*daMa*Ma*CD4/(CD4+cdaMa)
kSeCD4 = 1.0E-9 Reaction: CD4 + Se =>, Rate Law: compartment*kSeCD4*CD4*Se
kmrecCD4 = 1.0; vrecCD4 = 100.0 Reaction: CD4rec => CD4; Se, Rate Law: compartment*CD4rec*vrecCD4*Se/(Se+kmrecCD4)
gbCD4 = 0.19; cc1CD4 = 8.2E7; ngbCD4 = 2.0; k2CD4 = 8700000.0 Reaction: => CD4, Rate Law: compartment*gbCD4*CD4*(1-CD4/cc1CD4)*CD4^ngbCD4/(CD4^ngbCD4+k2CD4^ngbCD4)
iMr = 0.1; cSeMri = 600000.0 Reaction: Mr + Se => Mi, Rate Law: compartment*iMr*Mr*Se/(Se+cSeMri)
N = 30.0; pSi = 4.1 Reaction: => Si; Mi, Rate Law: compartment*pSi*Si*(1-Si/(Si+N*Mi))
gbMr = 1.2; ccMr = 2.5E7; p1 = 0.65 Reaction: => Mr, Rate Law: compartment*gbMr*Mr*(1-Mr/(ccMr-ccMr*p1))
drSi = 0.05 Reaction: Si =>, Rate Law: compartment*drSi*Si
bMi = 0.4; N = 30.0; mMi = 2.0 Reaction: Si + Mi => Se, Rate Law: compartment*bMi*Mi*Si^mMi/(Si^mMi+(N*Mi)^mMi)
drMr = 0.011 Reaction: Mr =>, Rate Law: compartment*drMr*Mr
drMa = 0.08 Reaction: Ma =>, Rate Law: compartment*drMa*Ma
drCD8 = 0.001 Reaction: CD8 =>, Rate Law: compartment*drCD8*CD8
kSeMr = 5.0E-8 Reaction: Mr + Se =>, Rate Law: compartment*kSeMr*Mr*Se
compCD8 = 0.85; kcompCD4 = 3.4E7; w1 = 1.0E-25; ncompCD4 = 0.5 Reaction: CD8 => ; Se, CD4, Rate Law: compartment*compCD8*CD8*Se/(Se+w1)*CD4^ncompCD4/(CD4^ncompCD4+kcompCD4^ncompCD4)

States:

Name Description
CD4 [CD4-positive helper T cell]
Mrrec [C12558]
CD8 [CD8-Positive T-Lymphocyte]
Si [C76380; C28217]
Ma [inflammatory macrophage]
Mi [C12558; infected cell]
Se [C76380; extracellular region]
Mr [CL:0000864]
CD4rec [CD4-positive helper T cell]

Observables: none

This model presents a general target-mediated drug disposition (TMDD) model for bispecific antibodies (BsAbs), which bin…

Bispecific antibodies (BsAbs) bind to two different targets, and create two binary and one ternary complex (TC). These molecules have shown promise as immuno-oncology drugs, and the TC is considered the pharmacologically active species that drives their pharmacodynamic effect. Here, we have presented a general target-mediated drug disposition (TMDD) model for these BsAbs, which bind to two different targets on different cell membranes. The model includes four different binding events for BsAbs, turnover of the targets, and internalization of the complexes. In addition, a quasi-equilibrium (QE) approximation with decreased number of binding parameters and, if necessary, reduced internalization parameters is presented. The model is further used to investigate the kinetics of BsAb and TC concentrations. Our analysis shows that larger doses of BsAbs may delay the build-up of the TC. Consequently, a method to compute the optimal dosing strategy of BsAbs, which will immediately create and maintain maximal possible TC concentration, is presented. link: http://identifiers.org/pubmed/30480383

Parameters:

Name Description
k_deg_A = 0.1 1/ms Reaction: R_A =>, Rate Law: Central*k_deg_A*R_A
k_on_2 = 1.0 ml/(mol*s) Reaction: C_free + R_B => RC_B, Rate Law: Central*k_on_2*C_free*R_B
k_21 = 0.03 1/ms; V = 3.0 l Reaction: => C_free; AP, Rate Law: k_21*AP/V
k_on_3 = 1.0 ml/(mol*s) Reaction: RC_A + R_B => RC_AB, Rate Law: Central*k_on_3*RC_A*R_B
k_off_3 = 0.01 1/ms Reaction: => RC_B + R_B; RC_AB, Rate Law: Central*k_off_3*RC_AB
k_12 = 0.1 1/ms Reaction: C_free =>, Rate Law: Central*k_12*C_free
k_el = 0.1 1/ms Reaction: C_free =>, Rate Law: Central*k_el*C_free
k_off_3 = 0.01 1/ms; k_off_4 = 0.01 1/ms; k_int_AB = 0.1 1/ms Reaction: RC_AB =>, Rate Law: Central*(k_off_3+k_off_4+k_int_AB)*RC_AB
k_int_B = 0.05 1/ms; k_off_2 = 0.01 1/ms Reaction: RC_B =>, Rate Law: Central*(k_off_2+k_int_B)*RC_B
k_12 = 0.1 1/ms; V = 3.0 l Reaction: => AP; C_free, Rate Law: k_12*C_free*V
k_syn_A = 1.0 ml/(mol*s) Reaction: => R_A, Rate Law: Central*k_syn_A
k_off_1 = 0.01 1/ms Reaction: => C_free + R_A; RC_A, Rate Law: Central*k_off_1*RC_A
k_off_1 = 0.01 1/ms; k_int_A = 0.05 1/ms Reaction: RC_A =>, Rate Law: Central*(k_off_1+k_int_A)*RC_A
V = 3.0 l; k_a = 0.2 1/ms Reaction: => C_free; AD, Rate Law: k_a*AD*V
k_syn_B = 10.0 ml/(mol*s) Reaction: => R_B, Rate Law: Central*k_syn_B
k_21 = 0.03 1/ms Reaction: AP =>, Rate Law: Peripheral*k_21*AP
k_deg_B = 0.1 1/ms Reaction: R_B =>, Rate Law: Central*k_deg_B*R_B
k_off_2 = 0.01 1/ms Reaction: => C_free + R_B; RC_B, Rate Law: Central*k_off_2*RC_B
k_off_4 = 0.01 1/ms Reaction: => RC_A + R_A; RC_AB, Rate Law: Central*k_off_4*RC_AB
k_on_1 = 10.0 ml/(mol*s) Reaction: C_free + R_A => RC_A, Rate Law: Central*k_on_1*C_free*R_A
k_a = 0.2 1/ms Reaction: AD =>, Rate Law: Peripheral*k_a*AD
k_on_4 = 10.0 ml/(mol*s) Reaction: RC_B + R_A => RC_AB, Rate Law: Central*k_on_4*RC_B*R_A

States:

Name Description
RC A [Receptor; Bispecific Monoclonal Antibody; macromolecular complex]
AP [Bispecific Antibody; Bispecific Monoclonal Antibody; peripheral blood]
C free [Bispecific Monoclonal Antibody]
RC AB [Receptor; Bispecific Monoclonal Antibody; macromolecular complex]
RC B [Receptor; Bispecific Monoclonal Antibody; macromolecular complex]
AD [Bispecific Antibody; Bispecific Monoclonal Antibody; Subcutaneous Route of Administration]
R B [Receptor]
R A [Receptor]

Observables: none

MODEL4665428627 @ v0.0.1

This is a stoichiometric map from the supplement of the publication: **Systematic evaluation of objective functions fo…

To which extent can optimality principles describe the operation of metabolic networks? By explicitly considering experimental errors and in silico alternate optima in flux balance analysis, we systematically evaluate the capacity of 11 objective functions combined with eight adjustable constraints to predict (13)C-determined in vivo fluxes in Escherichia coli under six environmental conditions. While no single objective describes the flux states under all conditions, we identified two sets of objectives for biologically meaningful predictions without the need for further, potentially artificial constraints. Unlimited growth on glucose in oxygen or nitrate respiring batch cultures is best described by nonlinear maximization of the ATP yield per flux unit. Under nutrient scarcity in continuous cultures, in contrast, linear maximization of the overall ATP or biomass yields achieved the highest predictive accuracy. Since these particular objectives predict the system behavior without preconditioning of the network structure, the identified optimality principles reflect, to some extent, the evolutionary selection of metabolic network regulation that realizes the various flux states. link: http://identifiers.org/pubmed/17625511

Parameters: none

States: none

Observables: none

BIOMD0000000215 @ v0.0.1

This a model from the article: Sequential polarization and imprinting of type 1 T helper lymphocytes by interferon-g…

Differentiation of naive T lymphocytes into type I T helper (Th1) cells requires interferon-gamma and interleukin-12. It is puzzling that interferon-gamma induces the Th1 transcription factor T-bet, whereas interleukin-12 mediates Th1 cell lineage differentiation. We use mathematical modeling to analyze the expression kinetics of T-bet, interferon-gamma, and the IL-12 receptor beta2 chain (IL-12Rbeta2) during Th1 cell differentiation, in the presence or absence of interleukin-12 or interferon-gamma signaling. We show that interferon-gamma induced initial T-bet expression, whereas IL-12Rbeta2 was repressed by T cell receptor (TCR) signaling. The termination of TCR signaling permitted upregulation of IL-12Rbeta2 by T-bet and interleukin-12 signaling that maintained T-bet expression. This late expression of T-bet, accompanied by the upregulation of the transcription factors Runx3 and Hlx, was required to imprint the Th cell for interferon-gamma re-expression. Thus initial polarization and subsequent imprinting of Th1 cells are mediated by interlinked, sequentially acting positive feedback loops of TCR-interferon-gamma-Stat1-T-bet and interleukin-12-Stat4-T-bet signaling. link: http://identifiers.org/pubmed/19409816

Parameters:

Name Description
gamma_Tbet=1.0 Reaction: Tbet_mRNA =>, Rate Law: compartment*gamma_Tbet*Tbet_mRNA
delta_Tbet=0.1 Reaction: Tbet_Prot =>, Rate Law: compartment*delta_Tbet*Tbet_Prot
gamma_Rec=1.0 Reaction: Rec_mRNA =>, Rate Law: compartment*gamma_Rec*Rec_mRNA
a1=0.044 Reaction: => Tbet_mRNA, Rate Law: compartment*a1
gamma_IFN=1.0 Reaction: Ifn_mRNA =>, Rate Law: compartment*gamma_IFN*Ifn_mRNA
b=100.0 Reaction: => Tbet_Prot; Tbet_mRNA, Rate Law: compartment*b*Tbet_mRNA
K5=0.029; K7=0.014; K6=66.0; a5=3.7 Reaction: => Ifn_mRNA; Tbet_Prot, Rec_Prot, Ag, Rate Law: compartment*a5*Tbet_Prot/(K5+Tbet_Prot)*Rec_Prot/(K6+Rec_Prot)*Ag/(K7+Ag)
delta_IFN=1.0 Reaction: Ifn_Prot =>, Rate Law: compartment*delta_IFN*Ifn_Prot
a4=0.0028; K4=0.013 Reaction: => Rec_mRNA; Tbet_Prot, Ag, Rate Law: compartment*a4*Tbet_Prot*K4/(K4+Ag)
K1=0.46; K2=2.1; a2=0.42 Reaction: => Tbet_mRNA; Ag, Ifn_Prot, Rate Law: compartment*a2*Ag/(K1+Ag)*Ifn_Prot/(K2+Ifn_Prot)
a3=5.1E-4 Reaction: => Tbet_mRNA; Rec_Prot, Rate Law: compartment*a3*Rec_Prot
delta_Rec=0.1 Reaction: Rec_Prot =>, Rate Law: compartment*delta_Rec*Rec_Prot

States:

Name Description
Ifn Prot [Interferon gamma]
Tbet Prot [T-box transcription factor TBX21]
Ag [positive regulation of T cell receptor signaling pathway]
Ifn mRNA [messenger RNA; RNA; Interferon gamma]
Rec mRNA [Interleukin-12 receptor subunit beta-2; messenger RNA; RNA]
Tbet mRNA [messenger RNA; RNA; T-box transcription factor TBX21]
Rec Prot [Interleukin-12 receptor subunit beta-2]

Observables: none

At the restriction point (R), mammalian cells irreversibly commit to divide. R has been viewed as a point in G1 that is…

At the restriction point (R), mammalian cells irreversibly commit to divide. R has been viewed as a point in G1 that is passed when growth factor signaling initiates a positive feedback loop of Cdk activity. However, recent studies have cast doubt on this model by claiming R occurs prior to positive feedback activation in G1 or even before completion of the previous cell cycle. Here we reconcile these results and show that whereas many commonly used cell lines do not exhibit a G1 R, primary fibroblasts have a G1 R that is defined by a precise Cdk activity threshold and the activation of cell-cycle-dependent transcription. A simple threshold model, based solely on Cdk activity, predicted with more than 95% accuracy whether individual cells had passed R. That a single measurement accurately predicted cell fate shows that the state of complex regulatory networks can be assessed using a few critical protein activities. link: http://identifiers.org/pubmed/29351845

Parameters:

Name Description
kR = 0.18; kP1 = 18.0; kP2 = 18.0; KCD = 0.92; KCE = 0.92; kDP = 3.6; dR = 0.06; kRE = 180.0; KRP = 0.01 Reaction: => Rb; Phosphorylated_Rb, E2F, CycD, CycE, Rate Law: Cell*(((((kR+kDP*Phosphorylated_Rb/(KRP+Phosphorylated_Rb))-kRE*Rb*E2F)-kP1*CycD*Rb/(KCD+Rb))-kP2*CycE*Rb/(KCE+Rb))-dR*Rb)
kP1 = 18.0; kP2 = 18.0; dRP = 0.06; KCD = 0.92; KCE = 0.92 Reaction: => Phosphorylated_Rb; CycD, Rb, CycE, Rb_E2F_complex, Rate Law: Cell*((kP1*CycD*Rb/(KCD+Rb)+kP2*CycE*Rb/(KCE+Rb_E2F_complex)+kP1*CycD*Rb_E2F_complex/(KCD+Rb_E2F_complex)+kP2*CycE*Rb_E2F_complex/(KCE+Rb_E2F_complex))-dRP*Phosphorylated_Rb)
kP1 = 18.0; dE = 0.25; kb = 0.003; kpfb = 4.0; kP2 = 18.0; KCD = 0.92; KCE = 0.92; kE = 0.4; KM = 0.15; KE = 0.15; kRE = 180.0 Reaction: => E2F; Myc, CycD, Rb_E2F_complex, CycE, Rb, Rate Law: Cell*(((kE*(kpfb+Myc/(KM+Myc))*E2F/(KE+E2F)+kb*Myc/(KM+Myc)+kP1*CycD*Rb_E2F_complex/(KCD+Rb_E2F_complex)+kP2*CycE*Rb_E2F_complex/(KCE+Rb_E2F_complex))-dE*E2F)-kRE*Rb*E2F)
kP1 = 18.0; kP2 = 18.0; dRE = 0.03; KCD = 0.92; KCE = 0.92; kRE = 180.0 Reaction: => Rb_E2F_complex; CycD, CycE, Rate Law: Cell*(((kRE-kP1*CycD*Rb_E2F_complex/(KCD+Rb_E2F_complex))+kP2*CycE*Rb_E2F_complex/(KCE+Rb_E2F_complex))-dRE*Rb_E2F_complex)
kM = 1.0; dM = 0.7; KS = 0.5 Reaction: => Myc; serum, Rate Law: Cell*(kM*Myc/(KS+serum)-dM*Myc)
kCD = 0.03; KM = 0.15; kCDS = 0.45; dCD = 1.5; KS = 0.5 Reaction: => CycD; Myc, serum, Rate Law: Cell*((kCD*Myc/(KM+Myc)+kCDS*serum/(KS+serum))-dCD*CycD)
kCE = 0.35; dCE = 1.5; KE = 0.15 Reaction: => CycE; E2F, Rate Law: Cell*(kCE*E2F/(KE+E2F)-dCE*CycE)

States:

Name Description
E2F [C129647]
CycE [C104197]
CycD [C104194]
Myc [C18538]
Rb [0016708]
Phosphorylated Rb [0016708; phosphorylated]
Rb E2F complex [Rb-E2F complex]

Observables: none

This project contains a reusable, reproducible, understandable, and extensible reimplementation of the one-dimensional m…

One should assume that in silico experiments in systems biology are less susceptible to reproducibility issues than their wet-lab counterparts, because they are free from natural biological variations and their environment can be fully controlled. However, recent studies show that only half of the published mathematical models of biological systems can be reproduced without substantial effort. In this article we examine the potential causes for failed or cumbersome reproductions in a case study of a one-dimensional mathematical model of the atrioventricular node, which took us four months to reproduce. The model demonstrates that even otherwise rigorous studies can be hard to reproduce due to missing information, errors in equations and parameters, a lack in available data files, non-executable code, missing or incomplete experiment protocols, and missing rationales behind equations. Many of these issues seem similar to problems that have been solved in software engineering using techniques such as unit testing, regression tests, continuous integration, version control, archival services, and a thorough modular design with extensive documentation. Applying these techniques, we reimplement the examined model using the modeling language Modelica. The resulting workflow is independent of the model and can be translated to SBML, CellML, and other languages. It guarantees methods reproducibility by executing automated tests in a virtual machine on a server that is physically separated from the development environment. Additionally, it facilitates results reproducibility, because the model is more understandable and because the complete model code, experiment protocols, and simulation data are published and can be accessed in the exact version that was used in this article. We found the additional design and documentation effort well justified, even just considering the immediate benefits during development such as easier and faster debugging, increased understandability of equations, and a reduced requirement for looking up details from the literature. link: http://identifiers.org/doi/10.1371/journal.pone.0254749

Parameters: none

States: none

Observables: none

Model reproduces the various plots in Figure 6 and 7 of the paper. It was successfully tested on MathSBML. To the exten…

We develop a mathematical model that explicitly represents many of the known signaling components mediating translocation of the insulin-responsive glucose transporter GLUT4 to gain insight into the complexities of metabolic insulin signaling pathways. A novel mechanistic model of postreceptor events including phosphorylation of insulin receptor substrate-1, activation of phosphatidylinositol 3-kinase, and subsequent activation of downstream kinases Akt and protein kinase C-zeta is coupled with previously validated subsystem models of insulin receptor binding, receptor recycling, and GLUT4 translocation. A system of differential equations is defined by the structure of the model. Rate constants and model parameters are constrained by published experimental data. Model simulations of insulin dose-response experiments agree with published experimental data and also generate expected qualitative behaviors such as sequential signal amplification and increased sensitivity of downstream components. We examined the consequences of incorporating feedback pathways as well as representing pathological conditions, such as increased levels of protein tyrosine phosphatases, to illustrate the utility of our model for exploring molecular mechanisms. We conclude that mathematical modeling of signal transduction pathways is a useful approach for gaining insight into the complexities of metabolic insulin signaling. link: http://identifiers.org/pubmed/12376338

Parameters:

Name Description
kminus4prime = 2.1E-4; k4prime = 0.0021 Reaction: x5 => x8, Rate Law: CellSurface*(k4prime*x5-kminus4prime*x8)
k6 = 0.461; PTP = 1.0 Reaction: x8 => x6, Rate Law: Intracellular*k6*PTP*x8
k13 = 0.00696; kminus13 = 0.167; k13prime = 0.0 Reaction: x20 => x21, Rate Law: Intracellular*((k13+k13prime)*x20-kminus13*x21)
k8 = 7.06E-4; kminus8 = 10.0 Reaction: x11 + x10 => x12, Rate Law: Intracellular*(k8*x10*x11-kminus8*x12)
kminus14 = 0.001155 Reaction: x20 =>, Rate Law: Intracellular*kminus14*x20
k14 = 0.11088 Reaction: => x20, Rate Law: Intracellular*k14
kminus7 = 1.396; PTP = 1.0; k7 = 4.16; IRp = 897.0 Reaction: x9 => x10; x4, x5, Rate Law: Intracellular*(k7*x9*(x4+x5)/IRp-kminus7*PTP*x10)
SHIP = 1.0; k10 = 2.961; kminus10 = 2.77 Reaction: x15 => x13, Rate Law: Intracellular*(k10*x15-kminus10*SHIP*x13)
k3 = 2500.0 Reaction: x3 => x5, Rate Law: CellSurface*k3*x3
k2 = 6.0E-8; kminus2 = 20.0 Reaction: x5 => x4; x1, Rate Law: CellSurface*k2*x1*x5-kminus2*x4
kminus5 = 1.67E-18 Reaction: x6 =>, Rate Law: Intracellular*kminus5*x6
k1 = 6.0E-8; kminus1 = 0.2 Reaction: x2 => x3; x1, Rate Law: CellSurface*(k1*x1*x2-kminus1*x3)
PTP = 1.0; kminus3 = 0.2 Reaction: x5 => x2, Rate Law: CellSurface*kminus3*PTP*x5
k12 = 0.0; kminus12 = 6.9315 Reaction: x18 => x19, Rate Law: Intracellular*(k12*x18-kminus12*x19)
PTEN = 1.0; k9 = 0.0; kminus9 = 42.15 Reaction: x14 => x13, Rate Law: Intracellular*(k9*x14-kminus9*PTEN*x13)
k11 = 0.0; kminus11 = 6.9315 Reaction: x16 => x17, Rate Law: Intracellular*(k11*x16-kminus11*x17)
k5 = 0.0 Reaction: => x6, Rate Law: Intracellular*k5
k4 = 3.3333334E-4; kminus4 = 0.003 Reaction: x2 => x6, Rate Law: CellSurface*(k4*x2-kminus4*x6)

States:

Name Description
x5 [Insulin receptor]
x19 [Protein kinase C iota type]
x16 [RAC-gamma serine/threonine-protein kinase]
x4 [Insulin receptor]
x6 [Insulin receptor]
x2 [Insulin receptor]
x14 [1-phosphatidyl-1D-myo-inositol 4,5-bisphosphate; 1-Phosphatidyl-D-myo-inositol 4,5-bisphosphate]
x20 [Solute carrier family 2, facilitated glucose transporter member 4]
x17 [RAC-gamma serine/threonine-protein kinase]
x3 [Insulin receptor]
x18 [Protein kinase C iota type]
x15 [1-phosphatidyl-1D-myo-inositol 3,4-bisphosphate; 1-Phosphatidyl-1D-myo-inositol 3,4-bisphosphate]
x9 [Insulin receptor substrate 1]
x8 [Insulin receptor]
x7 [Insulin receptor]
x13 [1-phosphatidyl-1D-myo-inositol 3,4,5-trisphosphate; Phosphatidylinositol-3,4,5-trisphosphate]
x11 [Phosphoinositide 3-kinase regulatory subunit 5]
x21 [Solute carrier family 2, facilitated glucose transporter member 4]
x10 [Insulin receptor substrate 1]
x12 [Insulin receptor substrate 1; Phosphoinositide 3-kinase regulatory subunit 5]

Observables: none

&lt;notes xmlns=&quot;http://www.sbml.org/sbml/level2/version4&quot;&gt; &lt;body xmlns=&quot;http://www.w3.org/1…

In this paper, a mathematical model of breast cancer governed by a system of ordinary differential equations in the presence of chemotherapy treatment and ketogenic diet is discussed. Several comprehensive mathematical analyses were carried out using a variety of analytical methods to study the stability of the breast cancer model. Also, sufficient conditions on parameter values to ensure cancer persistence in the absence of anti-cancer drugs, ketogenic diet, and cancer emission when anti-cancer drugs, immune-booster, and ketogenic diet are included were established. Furthermore, optimal control theory is applied to discover the optimal drug adjustment as an input control of the system therapies in order to minimize the number of cancerous cells by considering different controlled combinations of administering the chemotherapy agent and ketogenic diet using the popular Pontryagin’s maximum principle. Numerical simulations are presented to validate our theoretical results link: http://identifiers.org/doi/10.20944/preprints201802.0004.v1

Parameters: none

States: none

Observables: none

Epithelial to Mesenchymal Transition (EMT) has been associated with cancer cell heterogeneity, plasticity and metastasis…

Epithelial-to-mesenchymal transition (EMT) has been associated with cancer cell heterogeneity, plasticity, and metastasis. However, the extrinsic signals supervising these phenotypic transitions remain elusive. To assess how selected microenvironmental signals control cancer-associated phenotypes along the EMT continuum, we defined a logical model of the EMT cellular network that yields qualitative degrees of cell adhesions by adherens junctions and focal adhesions, two features affected during EMT. The model attractors recovered epithelial, mesenchymal, and hybrid phenotypes. Simulations showed that hybrid phenotypes may arise through independent molecular paths involving stringent extrinsic signals. Of particular interest, model predictions and their experimental validations indicated that: 1) stiffening of the ExtraCellular Matrix (ECM) was a prerequisite for cells overactivating FAKSRC to upregulate SNAIL and acquire a mesenchymal phenotype, and 2) FAKSRC inhibition of cell-cell contacts through the Receptor-type tyrosine-protein phosphatases kappa led to acquisition of a full mesenchymal, rather than a hybrid, phenotype. Altogether, these computational and experimental approaches allow assessment of critical microenvironmental signals controlling hybrid EMT phenotypes and indicate that EMT involves multiple molecular programs. link: http://identifiers.org/doi/10.1158/0008-5472.CAN-19-3147

Parameters: none

States: none

Observables: none

Selvarasu2009 - Genome-scale metabolic network of Mus Musculus (iSS724)This model is described in the article: [Genome-…

Genome-scale metabolic modeling has been successfully applied to a multitude of microbial systems, thus improving our understanding of their cellular metabolisms. Nevertheless, only a handful of works have been done for describing mammalian cells, particularly mouse, which is one of the important model organisms, providing various opportunities for both biomedical research and biotechnological applications. Presented herein is a genome-scale mouse metabolic model that was systematically reconstructed by improving and expanding the previous generic model based on integrated biochemical and genomic data of Mus musculus. The key features of the updated model include additional information on gene-protein-reaction association, and improved network connectivity through lipid, amino acid, carbohydrate and nucleotide biosynthetic pathways. After examining the model predictability both quantitatively and qualitatively using constraints-based flux analysis, the structural and functional characteristics of the mouse metabolism were investigated by evaluating network statistics/centrality, gene/metabolite essentiality and their correlation. The results revealed that overall mouse metabolic network is topologically dominated by highly connected and bridging metabolites, and functionally by lipid metabolism that most of essential genes and metabolites are from. The current in silico mouse model can be exploited for understanding and characterizing the cellular physiology, identifying potential cell engineering targets for the enhanced production of recombinant proteins and developing diseased state models for drug targeting. link: http://identifiers.org/pubmed/20024077

Parameters: none

States: none

Observables: none

Sen2013 - Phospholipid Synthesis in P.knowlesiThe model describes the multiple phospholipid synthetic pathways in Plasmo…

BACKGROUND: Plasmodium is the causal parasite of malaria, infectious disease responsible for the death of up to one million people each year. Glycerophospholipid and consequently membrane biosynthesis are essential for the survival of the parasite and are targeted by a new class of antimalarial drugs developed in our lab. In order to understand the highly redundant phospholipid synthethic pathways and eventual mechanism of resistance to various drugs, an organism specific kinetic model of these metabolic pathways need to be developed in Plasmodium species. RESULTS: Fluxomic data were used to build a quantitative kinetic model of glycerophospholipid pathways in Plasmodium knowlesi. In vitro incorporation dynamics of phospholipids unravels multiple synthetic pathways. A detailed metabolic network with values of the kinetic parameters (maximum rates and Michaelis constants) has been built. In order to obtain a global search in the parameter space, we have designed a hybrid, discrete and continuous, optimization method. Discrete parameters were used to sample the cone of admissible fluxes, whereas the continuous Michaelis and maximum rates constants were obtained by local minimization of an objective function.The model was used to predict the distribution of fluxes within the network of various metabolic precursors.The quantitative analysis was used to understand eventual links between different pathways. The major source of phosphatidylcholine (PC) is the CDP-choline Kennedy pathway.In silico knock-out experiments showed comparable importance of phosphoethanolamine-N-methyltransferase (PMT) and phosphatidylethanolamine-N-methyltransferase (PEMT) for PC synthesis.The flux values indicate that, major part of serine derived phosphatidylethanolamine (PE) is formed via serine decarboxylation, whereas major part of phosphatidylserine (PS) is formed by base-exchange reactions.Sensitivity analysis of CDP-choline pathway shows that the carrier-mediated choline entry into the parasite and the phosphocholine cytidylyltransferase reaction have the largest sensitivity coefficients in this pathway, but does not distinguish a reaction as an unique rate-limiting step. CONCLUSION: We provide a fully parametrized kinetic model for the multiple phospholipid synthetic pathways in P. knowlesi. This model has been used to clarify the relative importance of the various reactions in these metabolic pathways. Future work extensions of this modelling strategy will serve to elucidate the regulatory mechanisms governing the development of Plasmodium during its blood stages, as well as the mechanisms of action of drugs on membrane biosynthetic pathways and eventual mechanisms of resistance. link: http://identifiers.org/pubmed/24209716

Parameters:

Name Description
mw961dacfa_f443_4814_ad6c_a27c04e74268 = 1.0780611108133E-6 mole/liter/minute; mw15ba24b5_7a87_479e_9be7_261b12cbdb63 = 1.22223738254533E-4 mole/liter Reaction: mw849ed3fd_87d9_44d2_9f3e_4d631b900d41 => mwcb834e43_dc57_45ae_9452_f4c10955caf1; mw849ed3fd_87d9_44d2_9f3e_4d631b900d41, mw849ed3fd_87d9_44d2_9f3e_4d631b900d41, Rate Law: mw961dacfa_f443_4814_ad6c_a27c04e74268*mw849ed3fd_87d9_44d2_9f3e_4d631b900d41/(mw15ba24b5_7a87_479e_9be7_261b12cbdb63+mw849ed3fd_87d9_44d2_9f3e_4d631b900d41)
mw284c519a_cc2b_4a98_99ce_5a4471af99e1 = 3.04072645117622E-5 mole/liter; mwff26437c_166b_4946_ad35_f13df6145780 = 5.55658410000431E-7 mole/liter/minute Reaction: mw812f63db_4cb0_40ad_b92b_9874be969dfe => mwcb834e43_dc57_45ae_9452_f4c10955caf1; mw812f63db_4cb0_40ad_b92b_9874be969dfe, mw812f63db_4cb0_40ad_b92b_9874be969dfe, Rate Law: mwff26437c_166b_4946_ad35_f13df6145780*mw812f63db_4cb0_40ad_b92b_9874be969dfe/(mw284c519a_cc2b_4a98_99ce_5a4471af99e1+mw812f63db_4cb0_40ad_b92b_9874be969dfe)
mw1a53a2cb_a3a7_40d7_ae07_4d93ad1123a3 = 0.00141678261342411 mole/liter/minute; mw4035a2c9_3cda_467c_83cc_8f9c2902abaf = 0.321125432799976 mole/liter Reaction: mwf166ad55_4ff0_49fb_95d2_b657ad7653d5 => mwee54b5b4_b8c0_41df_8dda_5b160c5e10a5; mwf166ad55_4ff0_49fb_95d2_b657ad7653d5, mwf166ad55_4ff0_49fb_95d2_b657ad7653d5, Rate Law: mw1a53a2cb_a3a7_40d7_ae07_4d93ad1123a3*mwf166ad55_4ff0_49fb_95d2_b657ad7653d5/(mw4035a2c9_3cda_467c_83cc_8f9c2902abaf+mwf166ad55_4ff0_49fb_95d2_b657ad7653d5)
mw3046ca21_42a2_4a4b_89c4_9d6ca3d927c5 = 0.171122974053956 mole/liter; mw5ffad843_5f02_419d_ba99_6e1f9b7e6b7b = 8.99054709659885E-5 mole/liter/minute Reaction: mwf166ad55_4ff0_49fb_95d2_b657ad7653d5 => mwfcfaf604_14d4_47a6_b021_226d1fb5497c; mwf166ad55_4ff0_49fb_95d2_b657ad7653d5, mwf166ad55_4ff0_49fb_95d2_b657ad7653d5, Rate Law: mw5ffad843_5f02_419d_ba99_6e1f9b7e6b7b*mwf166ad55_4ff0_49fb_95d2_b657ad7653d5/(mw3046ca21_42a2_4a4b_89c4_9d6ca3d927c5+mwf166ad55_4ff0_49fb_95d2_b657ad7653d5)
mw231a5907_d1ee_4a43_83ab_abb72f19502c = 4.12788404046025E-7 mole/liter/minute; mwaf289d12_4291_4651_8bd1_82e321e476a4 = 3.10498877738431E-5 mole/liter Reaction: mwcb834e43_dc57_45ae_9452_f4c10955caf1 => mwee54b5b4_b8c0_41df_8dda_5b160c5e10a5; mwcb834e43_dc57_45ae_9452_f4c10955caf1, mwcb834e43_dc57_45ae_9452_f4c10955caf1, Rate Law: mw231a5907_d1ee_4a43_83ab_abb72f19502c*mwcb834e43_dc57_45ae_9452_f4c10955caf1/(mwaf289d12_4291_4651_8bd1_82e321e476a4+mwcb834e43_dc57_45ae_9452_f4c10955caf1)
mw798d0b02_925e_471b_a372_526d681cc370 = 2.620389955953E-6 mole/liter/minute; mwd3807289_133c_4621_8087_366621f553d3 = 2.39591245105385E-5 mole/liter Reaction: mw15abaa48_d7d0_4845_ae04_c573d289d495 => mw8796c919_9251_4970_8f87_0bca9ecfeb5c; mw15abaa48_d7d0_4845_ae04_c573d289d495, mw15abaa48_d7d0_4845_ae04_c573d289d495, Rate Law: mw798d0b02_925e_471b_a372_526d681cc370*mw15abaa48_d7d0_4845_ae04_c573d289d495/(mwd3807289_133c_4621_8087_366621f553d3+mw15abaa48_d7d0_4845_ae04_c573d289d495)
mw5c4edb54_cfd9_43af_b70b_e9ff1b44dc55 = 1.08608492867695E-4 mole/liter; mw2439178f_a48f_4425_82f9_13267b917b85 = 8.62083015294042E-6 mole/liter/minute Reaction: mw8796c919_9251_4970_8f87_0bca9ecfeb5c => mw849ed3fd_87d9_44d2_9f3e_4d631b900d41; mw8796c919_9251_4970_8f87_0bca9ecfeb5c, mw8796c919_9251_4970_8f87_0bca9ecfeb5c, Rate Law: mw2439178f_a48f_4425_82f9_13267b917b85*mw8796c919_9251_4970_8f87_0bca9ecfeb5c/(mw5c4edb54_cfd9_43af_b70b_e9ff1b44dc55+mw8796c919_9251_4970_8f87_0bca9ecfeb5c)
mw7ce1b6a3_e65e_4aaa_9c32_aeefb420f0ea = 1.30568052867489E-6 mole/liter/minute; mw85485398_9f97_408c_bca6_90f0a8377eae = 7.96722533770371E-4 mole/liter Reaction: mw15abaa48_d7d0_4845_ae04_c573d289d495 => mwfcfaf604_14d4_47a6_b021_226d1fb5497c; mw15abaa48_d7d0_4845_ae04_c573d289d495, mw15abaa48_d7d0_4845_ae04_c573d289d495, Rate Law: mw7ce1b6a3_e65e_4aaa_9c32_aeefb420f0ea*mw15abaa48_d7d0_4845_ae04_c573d289d495/(mw85485398_9f97_408c_bca6_90f0a8377eae+mw15abaa48_d7d0_4845_ae04_c573d289d495)
mwff99ad6c_8951_4d58_a836_cf2d3d08ac86 = 1.32810241970949E-4 1/minute; mw2cd81e51_eb11_4e2c_b609_b2f802438a6b = 5.0E-4 1/minute Reaction: mw08818dfe_fb12_45cc_8c1d_d965f142d0ce => mw8796c919_9251_4970_8f87_0bca9ecfeb5c; mw08818dfe_fb12_45cc_8c1d_d965f142d0ce, mw8796c919_9251_4970_8f87_0bca9ecfeb5c, mw08818dfe_fb12_45cc_8c1d_d965f142d0ce, mw8796c919_9251_4970_8f87_0bca9ecfeb5c, Rate Law: mw2cd81e51_eb11_4e2c_b609_b2f802438a6b*mw08818dfe_fb12_45cc_8c1d_d965f142d0ce-mwff99ad6c_8951_4d58_a836_cf2d3d08ac86*mw8796c919_9251_4970_8f87_0bca9ecfeb5c
mwba0debe9_c575_4f5a_a980_e2b6857ff053 = 5.61352652271706E-6 mole/liter/minute; mwffba86ff_a560_401a_93d6_c0e30bf42c87 = 2.27368268903121E-4 mole/liter Reaction: mw849ed3fd_87d9_44d2_9f3e_4d631b900d41 => mwf166ad55_4ff0_49fb_95d2_b657ad7653d5; mw849ed3fd_87d9_44d2_9f3e_4d631b900d41, mw849ed3fd_87d9_44d2_9f3e_4d631b900d41, Rate Law: mwba0debe9_c575_4f5a_a980_e2b6857ff053*mw849ed3fd_87d9_44d2_9f3e_4d631b900d41/(mwffba86ff_a560_401a_93d6_c0e30bf42c87+mw849ed3fd_87d9_44d2_9f3e_4d631b900d41)
mwf7d1ff9f_1734_4232_9a96_037b31b193b0 = 6.97333029651601E-7 mole/liter/minute; mw7d57aa6b_1bfb_4472_b555_919263d9eaf9 = 3.76085190209901E-6 mole/liter Reaction: mwee54b5b4_b8c0_41df_8dda_5b160c5e10a5 => mwfcfaf604_14d4_47a6_b021_226d1fb5497c; mwee54b5b4_b8c0_41df_8dda_5b160c5e10a5, mwee54b5b4_b8c0_41df_8dda_5b160c5e10a5, Rate Law: mwf7d1ff9f_1734_4232_9a96_037b31b193b0*mwee54b5b4_b8c0_41df_8dda_5b160c5e10a5/(mw7d57aa6b_1bfb_4472_b555_919263d9eaf9+mwee54b5b4_b8c0_41df_8dda_5b160c5e10a5)
mw9f56ecc5_c22b_4f8c_8b82_90e2a6d9e364 = 2.24518521682572E-6 mole/liter/minute; mw18bbabcb_d229_4d91_99f1_484f2ba8f020 = 2.03868171233541E-4 mole/liter Reaction: mwfcfaf604_14d4_47a6_b021_226d1fb5497c => mwf166ad55_4ff0_49fb_95d2_b657ad7653d5; mwfcfaf604_14d4_47a6_b021_226d1fb5497c, mwfcfaf604_14d4_47a6_b021_226d1fb5497c, Rate Law: mw9f56ecc5_c22b_4f8c_8b82_90e2a6d9e364*mwfcfaf604_14d4_47a6_b021_226d1fb5497c/(mw18bbabcb_d229_4d91_99f1_484f2ba8f020+mwfcfaf604_14d4_47a6_b021_226d1fb5497c)
mw371071cd_ec20_4517_acc1_08dfdc871e87 = 2.41308392167819E-5 mole/liter; mw87bb1238_3292_467e_bfe3_ff7f1e64a351 = 1.5662833197895E-6 mole/liter/minute Reaction: mwee54b5b4_b8c0_41df_8dda_5b160c5e10a5 => ; mwee54b5b4_b8c0_41df_8dda_5b160c5e10a5, mwee54b5b4_b8c0_41df_8dda_5b160c5e10a5, Rate Law: mw87bb1238_3292_467e_bfe3_ff7f1e64a351*mwee54b5b4_b8c0_41df_8dda_5b160c5e10a5/(mw371071cd_ec20_4517_acc1_08dfdc871e87+mwee54b5b4_b8c0_41df_8dda_5b160c5e10a5)
mw5b225cdc_783f_4a15_93db_e960a2398b8e = 1.53754224136353E-6 mole/liter/minute; mw27f524cb_75b3_401c_8533_99d6f27af654 = 2.03777063277265E-4 mole/liter Reaction: mwfcfaf604_14d4_47a6_b021_226d1fb5497c => ; mwfcfaf604_14d4_47a6_b021_226d1fb5497c, mwfcfaf604_14d4_47a6_b021_226d1fb5497c, Rate Law: mw5b225cdc_783f_4a15_93db_e960a2398b8e*mwfcfaf604_14d4_47a6_b021_226d1fb5497c/(mw27f524cb_75b3_401c_8533_99d6f27af654+mwfcfaf604_14d4_47a6_b021_226d1fb5497c)
mwee07eca4_0806_4cc3_a6ab_9226ee79be6c = 3.40936490738966E-6 mole/liter/minute; mw8f20c25d_9700_4822_b5f9_fe243e001091 = 3.62894258752347E-4 mole/liter Reaction: mw73259e20_240e_4f3a_b2e0_9ca248658898 => mw15abaa48_d7d0_4845_ae04_c573d289d495; mw73259e20_240e_4f3a_b2e0_9ca248658898, mw73259e20_240e_4f3a_b2e0_9ca248658898, Rate Law: mwee07eca4_0806_4cc3_a6ab_9226ee79be6c*mw73259e20_240e_4f3a_b2e0_9ca248658898/(mw8f20c25d_9700_4822_b5f9_fe243e001091+mw73259e20_240e_4f3a_b2e0_9ca248658898)
mwbf296afc_5e4f_4819_8028_06b20d7af7ca = 0.155164586398126 mole/liter; mwc623d82f_a94e_4460_9aed_444597a728c2 = 7.7375270429582E-4 mole/liter/minute Reaction: mwf166ad55_4ff0_49fb_95d2_b657ad7653d5 => ; mwfcfaf604_14d4_47a6_b021_226d1fb5497c, mwfcfaf604_14d4_47a6_b021_226d1fb5497c, Rate Law: mwc623d82f_a94e_4460_9aed_444597a728c2*mwfcfaf604_14d4_47a6_b021_226d1fb5497c/(mwbf296afc_5e4f_4819_8028_06b20d7af7ca+mwfcfaf604_14d4_47a6_b021_226d1fb5497c)
mwf5cecb8f_89f8_4fba_b39b_b517d0bef2ce = 1.02326862282225E-4 mole/liter; mw91e15e1e_c73e_4866_ab2b_8225a32b7610 = 2.32432741134546E-7 mole/liter/minute Reaction: mw919f8a86_e702_4b24_9cd7_adad694fcf9b => mw812f63db_4cb0_40ad_b92b_9874be969dfe; mw919f8a86_e702_4b24_9cd7_adad694fcf9b, mw919f8a86_e702_4b24_9cd7_adad694fcf9b, Rate Law: mw91e15e1e_c73e_4866_ab2b_8225a32b7610*mw919f8a86_e702_4b24_9cd7_adad694fcf9b/(mwf5cecb8f_89f8_4fba_b39b_b517d0bef2ce+mw919f8a86_e702_4b24_9cd7_adad694fcf9b)

States:

Name Description
mw08818dfe fb12 45cc 8c1d d965f142d0ce [ethanolamine]
mw73259e20 240e 4f3a b2e0 9ca248658898 [serine]
mw849ed3fd 87d9 44d2 9f3e 4d631b900d41 [O-phosphoethanolamine]
mw812f63db 4cb0 40ad b92b 9874be969dfe [choline]
mwfcfaf604 14d4 47a6 b021 226d1fb5497c [phosphatidylserine O-18:0/0:0]
mw15abaa48 d7d0 4845 ae04 c573d289d495 [serine]
mwee54b5b4 b8c0 41df 8dda 5b160c5e10a5 [phosphatidylcholine(1+)]
mwcb834e43 dc57 45ae 9452 f4c10955caf1 [phosphocholine]
mw8796c919 9251 4970 8f87 0bca9ecfeb5c [ethanolamine]
mw919f8a86 e702 4b24 9cd7 adad694fcf9b [choline]
mwf166ad55 4ff0 49fb 95d2 b657ad7653d5 [phosphatidylethanolamine]

Observables: none

&lt;notes xmlns=&quot;http://www.sbml.org/sbml/level2&quot;&gt; &lt;body xmlns=&quot;http://www.w3.org/1999/xhtml…

AIMS/HYPOTHESIS:Previous metabolomics studies suggest that type 1 diabetes is preceded by specific metabolic disturbances. The aim of this study was to investigate whether distinct metabolic patterns occur in peripheral blood mononuclear cells (PBMCs) of children who later develop pancreatic beta cell autoimmunity or overt type 1 diabetes. METHODS:In a longitudinal cohort setting, PBMC metabolomic analysis was applied in children who (1) progressed to type 1 diabetes (PT1D, n = 34), (2) seroconverted to ≥1 islet autoantibody without progressing to type 1 diabetes (P1Ab, n = 27) or (3) remained autoantibody negative during follow-up (CTRL, n = 10). RESULTS:During the first year of life, levels of most lipids and polar metabolites were lower in the PT1D and P1Ab groups compared with the CTRL group. Pathway over-representation analysis suggested alanine, aspartate, glutamate, glycerophospholipid and sphingolipid metabolism were over-represented in PT1D. Genome-scale metabolic models of PBMCs during type 1 diabetes progression were developed by using publicly available transcriptomics data and constrained with metabolomics data from our study. Metabolic modelling confirmed altered ceramide pathways, known to play an important role in immune regulation, as specifically associated with type 1 diabetes progression. CONCLUSIONS/INTERPRETATION:Our data suggest that systemic dysregulation of lipid metabolism, as observed in plasma, may impact the metabolism and function of immune cells during progression to overt type 1 diabetes. DATA AVAILABILITY:The GEMs for PBMCs have been submitted to BioModels (www.ebi.ac.uk/biomodels/), under accession number MODEL1905270001. The metabolomics datasets and the clinical metadata generated in this study were submitted to MetaboLights (https://www.ebi.ac.uk/metabolights/), under accession number MTBLS1015. link: http://identifiers.org/pubmed/32043185

Parameters: none

States: none

Observables: none

Senger2008 - Genome-scale metabolic network of Clostridium acetobutylicum (iCac802)This model is described in the articl…

A genome-scale metabolic network reconstruction for Clostridium acetobutylicum (ATCC 824) was carried out using a new semi-automated reverse engineering algorithm. The network consists of 422 intracellular metabolites involved in 552 reactions and includes 80 membrane transport reactions. The metabolic network illustrates the reliance of clostridia on the urea cycle, intracellular L-glutamate solute pools, and the acetylornithine transaminase for amino acid biosynthesis from the 2-oxoglutarate precursor. The semi-automated reverse engineering algorithm identified discrepancies in reaction network databases that are major obstacles for fully automated network-building algorithms. The proposed semi-automated approach allowed for the conservation of unique clostridial metabolic pathways, such as an incomplete TCA cycle. A thermodynamic analysis was used to determine the physiological conditions under which proposed pathways (e.g., reverse partial TCA cycle and reverse arginine biosynthesis pathway) are feasible. The reconstructed metabolic network was used to create a genome-scale model that correctly characterized the butyrate kinase knock-out and the asolventogenic M5 pSOL1 megaplasmid degenerate strains. Systematic gene knock-out simulations were performed to identify a set of genes encoding clostridial enzymes essential for growth in silico. link: http://identifiers.org/pubmed/18767192

Parameters: none

States: none

Observables: none

Sengupta2015 - Knowledge base model of human energy pool network (HEPNet)This model is described in the article: [HEPNe…

HEPNet is an electronic representation of metabolic reactions occurring within human cellular organization focusing on inflow and outflow of the energy currency ATP, GTP and other energy associated moieties. The backbone of HEPNet consists of primary bio-molecules such as carbohydrates, proteins and fats which ultimately constitute the chief source for the synthesis and obliteration of energy currencies in a cell. A series of biochemical pathways and reactions constituting the catabolism and anabolism of various metabolites are portrayed through cellular compartmentalization. The depicted pathways function synchronously toward an overarching goal of producing ATP and other energy associated moieties to bring into play a variety of cellular functions. HEPNet is manually curated with raw data from experiments and is also connected to KEGG and Reactome databases. This model has been validated by simulating it with physiological states like fasting, starvation, exercise and disease conditions like glycaemia, uremia and dihydrolipoamide dehydrogenase deficiency (DLDD). The results clearly indicate that ATP is the master regulator under different metabolic conditions and physiological states. The results also highlight that energy currencies play a minor role. However, the moiety creatine phosphate has a unique character, since it is a ready-made source of phosphoryl groups for the rapid synthesis of ATP from ADP. HEPNet provides a framework for further expanding the network diverse age groups of both the sexes, followed by the understanding of energetics in more complex metabolic pathways that are related to human disorders. link: http://identifiers.org/pubmed/26053019

Parameters:

Name Description
v1=1.0 substance; k1=0.157 substance Reaction: s182 + s334 => s183 + s190 + s329 + s237; s192, s182, Rate Law: v1*s182/(k1+s182)
k1=1.3 substance; v1=1.0 substance Reaction: s73 + s64 => s3 + s44; s31, s73, Rate Law: v1*s73/(k1+s73)
k1=34.5 substance; v1=1.0 substance Reaction: s72 + s355 => s80 + s351 + s361; s366, s72, Rate Law: v1*s72/(k1+s72)
k1=3.8E-4 substance; v1=1.0 substance Reaction: s9 + s355 => s50 + s351 + s361; s28, s9, Rate Law: v1*s9/(k1+s9)
k1=1.37 substance; v1=1.0 substance Reaction: s297 + s64 => s71; s298, s297, Rate Law: v1*s297/(k1+s297)
k1=0.04 substance; v1=1.0 substance Reaction: s234 + s334 => s181 + s185; s186, s333, s234, Rate Law: v1*s234/(k1+s234)
k1=100.0 substance; v1=1.0 substance Reaction: s70 + s347 => s72; s365, s70, Rate Law: v1*s70/(k1+s70)
k1=294.0 substance; v1=1.0 substance Reaction: s321 + s326 + s347 => s322 + s350; s327, s321, Rate Law: v1*s321/(k1+s321)
v1=1.0 substance; k1=18.2 substance Reaction: s181 + s64 => s182; s189, s333, s181, Rate Law: v1*s181/(k1+s181)
k1=0.1 substance; v1=1.0 substance Reaction: s253 + s63 => s195 + s46; s255, s253, Rate Law: v1*s253/(k1+s253)
k1=0.31 substance; v1=1.0 substance Reaction: s293 + s63 => s35 + s46; s294, s293, Rate Law: v1*s293/(k1+s293)
k1=0.09 substance; v1=1.0 substance Reaction: s6 + s352 => s7 + s345 + s350; s58, s6, Rate Law: v1*s6/(k1+s6)
k1=5.8 substance; v1=1.0 substance Reaction: s10 + s46 => s11 + s63; s45, s10, Rate Law: v1*s10/(k1+s10)
k1=16.0 substance; v1=1.0 substance Reaction: s66 + s350 => s65; s362, s66, Rate Law: v1*s66/(k1+s66)
v1=1.0 substance; k1=2900.0 substance Reaction: s4 + s347 => s52; s354, s4, Rate Law: v1*s4/(k1+s4)
k1=3.0 substance; v1=1.0 substance Reaction: s65 + s356 => s70 + s353; s364, s65, Rate Law: v1*s65/(k1+s65)
k1=0.069 substance; v1=1.0 substance Reaction: s302 + s301 => s335 + s300 + s329; s13, s302, Rate Law: v1*s302/(k1+s302)
k1=970.0 substance; v1=1.0 substance Reaction: s306 + s63 => s302 + s46; s305, s333, s306, Rate Law: v1*s306/(k1+s306)
k1=73.0 substance; v1=1.0 substance Reaction: s52 + s355 => s5 + s349 + s351 + s361; s56, s52, Rate Law: v1*s52/(k1+s52)
k1=0.58 substance; v1=1.0 substance Reaction: s286 + s63 => s285 + s46; s287, s286, Rate Law: v1*s286/(k1+s286)
v1=1.0 substance; k1=13.0 substance Reaction: s25 + s29 => s33 + s30; s41, s25, Rate Law: v1*s25/(k1+s25)
v1=1.0 substance; k1=0.08 substance Reaction: s197 => s198; s336, s203, s336, s250, s197, Rate Law: v1*s197/(k1+s197)
k1=300.0 substance; v1=1.0 substance Reaction: s74 + s46 => s8 + s63; s86, s333, s74, Rate Law: v1*s74/(k1+s74)
k1=33.0 substance; v1=1.0 substance Reaction: s74 + s67 + s329 => s35 + s44 + s93; s85, s74, Rate Law: v1*s74/(k1+s74)
k1=1.0 substance Reaction: s125 + s126 => s127 + s238; s123, s125, s126, Rate Law: s125*s126*k1
k1=10.0 substance; v1=1.0 substance Reaction: s284 + s64 => s71 + s286; s283, s284, Rate Law: v1*s284/(k1+s284)
k1=0.11 substance; v1=1.0 substance Reaction: s11 + s63 => s81 + s46; s90, s11, Rate Law: v1*s11/(k1+s11)
k1=0.013 substance; v1=1.0 substance Reaction: s40 + s347 => s9; s27, s40, Rate Law: v1*s40/(k1+s40)
v1=1.0 substance; k1=1.16 substance Reaction: s124 + s345 => s123; s400, s124, Rate Law: v1*s124/(k1+s124)
k1=9.6 substance; v1=1.0 substance Reaction: s123 => s124 + s47; s123, Rate Law: v1*s123/(k1+s123)
v1=1.0 substance; k1=0.048 substance Reaction: s71 + s63 => s234 + s46; s16, s71, Rate Law: v1*s71/(k1+s71)

States:

Name Description
s351 [NADH; NADH]
s297 [alpha,alpha-Trehalose; alpha,alpha-trehalose]
s100 C14 Ketoacyl-CoA
s105 [2-trans-Dodecenoyl-CoA; trans-dodec-2-enoyl-CoA]
s197 Glycogen Primer
s72 [(3S)-3-Hydroxyacyl-CoA; (S)-3-hydroxyacyl-CoA]
s46 [ADP; ADP]
s70 [2-trans-Dodecenoyl-CoA; trans-dodec-2-enoyl-CoA]
s345 [ATP; ATP]
s134 C14 AcylCoA_cyt
s129 C20car_ims
s292 [Triacylglycerol; triglyceride]
s25 [HCO3-; hydrogencarbonate; NH4+; ammonium]
s131 C18car_ims
s348 [ADP; ADP]
s182 [6-Phospho-D-gluconate; 6-phospho-D-gluconic acid]
s101 [Acyl-CoA; acyl-CoA]
s334 [NADP+; NADP(+)]
s347 [H2O; water]
s300 [NADH; NADH]
s358 [H+; hydron]
s381 [NADH; NADH]
s125 C22 AcylCoA_cyt
s8 3-PGA
s93 [NAD+; NAD(+)]
s361 [H+; hydron]
s47 [AMP; AMP]
s104 [(3S)-3-Hydroxyacyl-CoA; (S)-3-hydroxyacyl-CoA]
s370 C18car_ims
s103 C12 Ketoacyl-CoA
s136 car_mat
s185 NADPH
s355 [NAD+; NAD(+)]
s98 [2-trans-Dodecenoyl-CoA; trans-dodec-2-enoyl-CoA]
s389 [H+; hydron]
s67 [NADH; NADH]
s63 [ATP; ATP]
s80 C18 Ketoacyl-CoA
s4 [cis-Aconitate; cis-aconitic acid]
s64 [H2O; water]
s346 [ADP; ADP]
s259 [SPRR2E; Small proline-rich protein 2E]
s190 [NADPH; NADPH]
s65 [Acyl-CoA; acyl-CoA]
s322 [(S)-3-Hydroxy-3-methylglutaryl-CoA; (3S)-3-hydroxy-3-methylglutaryl-CoA]

Observables: none

MODEL7914464799 @ v0.0.1

This a model from the article: A mathematical treatment of integrated Ca dynamics within the ventricular myocyte. Sh…

We have developed a detailed mathematical model for Ca2+ handling and ionic currents in the rabbit ventricular myocyte. The objective was to develop a model that: 1), accurately reflects Ca-dependent Ca release; 2), uses realistic parameters, particularly those that concern Ca transport from the cytosol; 3), comes to steady state; 4), simulates basic excitation-contraction coupling phenomena; and 5), runs on a normal desktop computer. The model includes the following novel features: 1), the addition of a subsarcolemmal compartment to the other two commonly formulated cytosolic compartments (junctional and bulk) because ion channels in the membrane sense ion concentrations that differ from bulk; 2), the use of realistic cytosolic Ca buffering parameters; 3), a reversible sarcoplasmic reticulum (SR) Ca pump; 4), a scheme for Na-Ca exchange transport that is [Na]i dependent and allosterically regulated by [Ca]i; and 5), a practical model of SR Ca release including both inactivation/adaptation and SR Ca load dependence. The data describe normal electrical activity and Ca handling characteristics of the cardiac myocyte and the SR Ca load dependence of these processes. The model includes a realistic balance of Ca removal mechanisms (e.g., SR Ca pump versus Na-Ca exchange), and the phenomena of rest decay and frequency-dependent inotropy. A particular emphasis is placed upon reproducing the nonlinear dependence of gain and fractional SR Ca release upon SR Ca load. We conclude that this model is more robust than many previously existing models and reproduces many experimental results using parameters based largely on experimental measurements in myocytes. link: http://identifiers.org/pubmed/15347581

Parameters: none

States: none

Observables: none

This is a ODE-based mathematical model featuring equations describing the dynamics of tumor cells, cytotoxic T cells, na…

Myeloid-derived suppressor cells (MDSCs) belong to immature myeloid cells that are generated and accumulated during the tumor development. MDSCs strongly suppress the anti-tumor immunity and provide conditions for tumor progression and metastasis. In this study, we present a mathematical model based on ordinary differential equations (ODE) to describe tumor-induced immunosuppression caused by MDSCs. The model consists of four equations and incorporates tumor cells, cytotoxic T cells (CTLs), natural killer (NK) cells and MDSCs. We also provide simulation models that evaluate or predict the effects of anti-MDSC drugs (e.g., l-arginine and 5-Fluorouracil (5-FU)) on the tumor growth and the restoration of anti-tumor immunity. The simulated results obtained using our model were in good agreement with the corresponding experimental findings on the expansion of splenic MDSCs, immunosuppressive effects of these cells at the tumor site and effectiveness of l-arginine and 5-FU on the re-establishment of antitumor immunity. Regarding this latter issue, our predictive simulation results demonstrated that intermittent therapy with low-dose 5-FU alone could eradicate the tumors irrespective of their origins and types. Furthermore, at the time of tumor eradication, the number of CTLs prevailed over that of cancer cells and the number of splenic MDSCs returned to the normal levels. Finally, our predictive simulation results also showed that the addition of l-arginine supplementation to the intermittent 5-FU therapy reduced the time of the tumor eradication and the number of iterations for 5-FU treatment. Thus, the present mathematical model provides important implications for designing new therapeutic strategies that aim to restore antitumor immunity by targeting MDSCs. link: http://identifiers.org/pubmed/29337259

Parameters: none

States: none

Observables: none

BIOMD0000000798 @ v0.0.1

The paper describes a model of acute myeloid leukaemia. Created by COPASI 4.26 (Build 213) This model is described…

Acute myeloid leukaemia (AML) is a blood cancer affecting haematopoietic stem cells. AML is routinely treated with chemotherapy, and so it is of great interest to develop optimal chemotherapy treatment strategies. In this work, we incorporate an immune response into a stem cell model of AML, since we find that previous models lacking an immune response are inappropriate for deriving optimal control strategies. Using optimal control theory, we produce continuous controls and bang-bang controls, corresponding to a range of objectives and parameter choices. Through example calculations, we provide a practical approach to applying optimal control using Pontryagin's Maximum Principle. In particular, we describe and explore factors that have a profound influence on numerical convergence. We find that the convergence behaviour is sensitive to the method of control updating, the nature of the control, and to the relative weighting of terms in the objective function. All codes we use to implement optimal control are made available. link: http://identifiers.org/pubmed/30853393

Parameters:

Name Description
y = 0.01 1; a = 0.015 1 Reaction: L =>, Rate Law: bone_marrow*a*L/(y+L)
ut = 0.3 1 Reaction: T =>, Rate Law: bone_marrow*ut*T
da = 0.44 1 Reaction: A => D, Rate Law: bone_marrow*da*A
dl = 0.05 1 Reaction: L => T, Rate Law: bone_marrow*dl*L
pl = 0.27 1; k2 = 1.0 1; Z2 = 0.1 1 Reaction: => L, Rate Law: bone_marrow*pl*L*(k2-Z2)
k1 = 1.0 1; Z1 = 0.1 1; ps = 0.5 1 Reaction: => S, Rate Law: bone_marrow*ps*S*(k1-Z1)
pa = 0.43 1; k2 = 1.0 1; Z2 = 0.1 1 Reaction: => A, Rate Law: bone_marrow*pa*A*(k2-Z2)
ud = 0.275 1 Reaction: D =>, Rate Law: bone_marrow*ud*D
ds = 0.14 1 Reaction: S => A, Rate Law: bone_marrow*ds*S

States:

Name Description
S [hematopoietic stem cell]
A [common myeloid progenitor]
T [lymphoma or leukaemia cell line]
D [cell]
L [stem cell]

Observables: none

SBML model exported from PottersWheel on 2019-01-17 12:49:15. This model was created via Matlab and automatically conve…

G protein-coupled receptor (GPCR) signaling is the primary method eukaryotes use to respond to specific cues in their environment. However, the relationship between stimulus and response for each GPCR is difficult to predict due to diversity in natural signal transduction architecture and expression. Using genome engineering in yeast, we constructed an insulated, modular GPCR signal transduction system to study how the response to stimuli can be predictably tuned using synthetic tools. We delineated the contributions of a minimal set of key components via computational and experimental refactoring, identifying simple design principles for rationally tuning the dose response. Using five different GPCRs, we demonstrate how this enables cells and consortia to be engineered to respond to desired concentrations of peptides, metabolites, and hormones relevant to human health. This work enables rational tuning of cell sensing while providing a framework to guide reprogramming of GPCR-based signaling in other systems. link: http://identifiers.org/pubmed/30955892

Parameters: none

States: none

Observables: none

SBML model exported from PottersWheel on 2018-06-29 21:50:11.

G protein-coupled receptor (GPCR) signaling is the primary method eukaryotes use to respond to specific cues in their environment. However, the relationship between stimulus and response for each GPCR is difficult to predict due to diversity in natural signal transduction architecture and expression. Using genome engineering in yeast, we constructed an insulated, modular GPCR signal transduction system to study how the response to stimuli can be predictably tuned using synthetic tools. We delineated the contributions of a minimal set of key components via computational and experimental refactoring, identifying simple design principles for rationally tuning the dose response. Using five different GPCRs, we demonstrate how this enables cells and consortia to be engineered to respond to desired concentrations of peptides, metabolites, and hormones relevant to human health. This work enables rational tuning of cell sensing while providing a framework to guide reprogramming of GPCR-based signaling in other systems. link: http://identifiers.org/pubmed/30955892

Parameters: none

States: none

Observables: none

BIOMD0000000316 @ v0.0.1

This is the coherent feed forward loop with an AND-gate like control of the response operon described in the article:…

Little is known about the design principles of transcriptional regulation networks that control gene expression in cells. Recent advances in data collection and analysis, however, are generating unprecedented amounts of information about gene regulation networks. To understand these complex wiring diagrams, we sought to break down such networks into basic building blocks. We generalize the notion of motifs, widely used for sequence analysis, to the level of networks. We define 'network motifs' as patterns of interconnections that recur in many different parts of a network at frequencies much higher than those found in randomized networks. We applied new algorithms for systematically detecting network motifs to one of the best-characterized regulation networks, that of direct transcriptional interactions in Escherichia coli. We find that much of the network is composed of repeated appearances of three highly significant motifs. Each network motif has a specific function in determining gene expression, such as generating temporal expression programs and governing the responses to fluctuating external signals. The motif structure also allows an easily interpretable view of the entire known transcriptional network of the organism. This approach may help define the basic computational elements of other biological networks. link: http://identifiers.org/pubmed/11967538

Parameters:

Name Description
Ty=0.5 dimensionless; Tz=0.5 dimensionless Reaction: => Z; X, Y, Rate Law: piecewise(1, X >= Ty, 0)*piecewise(1, Y >= Tz, 0)
a=1.0 dimensionless Reaction: Z =>, Rate Law: a*Z
Ty=0.5 dimensionless Reaction: => Y; X, Rate Law: piecewise(1, X >= Ty, 0)

States:

Name Description
Y [protein; obsolete transcription activator activity]
Z [protein]

Observables: none

BIOMD0000000317 @ v0.0.1

This is the single input module, SIM, described in the article: **Network motifs in the transcriptional regulation netw…

Little is known about the design principles of transcriptional regulation networks that control gene expression in cells. Recent advances in data collection and analysis, however, are generating unprecedented amounts of information about gene regulation networks. To understand these complex wiring diagrams, we sought to break down such networks into basic building blocks. We generalize the notion of motifs, widely used for sequence analysis, to the level of networks. We define 'network motifs' as patterns of interconnections that recur in many different parts of a network at frequencies much higher than those found in randomized networks. We applied new algorithms for systematically detecting network motifs to one of the best-characterized regulation networks, that of direct transcriptional interactions in Escherichia coli. We find that much of the network is composed of repeated appearances of three highly significant motifs. Each network motif has a specific function in determining gene expression, such as generating temporal expression programs and governing the responses to fluctuating external signals. The motif structure also allows an easily interpretable view of the entire known transcriptional network of the organism. This approach may help define the basic computational elements of other biological networks. link: http://identifiers.org/pubmed/11967538

Parameters:

Name Description
T2=0.5 dimensionless Reaction: => Z2; X, Rate Law: piecewise(1, X >= T2, 0)
FX = 0.0 dimensionless Reaction: X = FX-X, Rate Law: FX-X
T3=0.8 dimensionless Reaction: => Z3; X, Rate Law: piecewise(1, X >= T3, 0)
a=1.0 dimensionless Reaction: Z3 =>, Rate Law: a*Z3
T1=0.1 dimensionless Reaction: => Z1; X, Rate Law: piecewise(1, X >= T1, 0)

States:

Name Description
X [protein; obsolete transcription activator activity]
Z2 [protein]
Z3 [protein]
Z1 [protein]

Observables: none

BIOMD0000000241 @ v0.0.1

described in: **Pharmacokinetic-pharmacodynamic modeling of caffeine: Tolerance to pressor effects** Shi J, Benowit…

We propose a parametric pharmacokinetic-pharmacodynamic model for caffeine that quantifies the development of tolerance to the pressor effect of the drug and characterizes the mean behavior and inter-individual variation of both pharmacokinetics and pressor effect. Our study in a small group of subjects indicates that acute tolerance develops to the pressor effect of caffeine and that both the pressor effect and tolerance occur after some time delay relative to changes in plasma caffeine concentration. The half-life of equilibration of effect with plasma caffeine concentration is about 20 minutes. The half-life of development and regression of tolerance is estimated to be about 1 hour, and the model suggests that tolerance, at its fullest, causes more than a 90% reduction of initial (nontolerant) effect. Whereas tolerance to the pressor effect of caffeine develops in habitual coffee drinkers, the pressor response is regained after relatively brief periods of abstinence. Because of the rapid development and regression of tolerance, the pressor response to caffeine depends on how much caffeine is consumed, the schedule of consumption, and the elimination half-life of caffeine. link: http://identifiers.org/pubmed/8422743

Parameters:

Name Description
k_tol = 0.75 per_hour Reaction: C_t = k_tol*(C_p-C_t), Rate Law: k_tol*(C_p-C_t)
k12 = 1.64 per_hour; k21 = 1.19 per_hour Reaction: C_per = k12*C_p-k21*C_per, Rate Law: k12*C_p-k21*C_per
k10 = 0.34 per_hour; k12 = 1.64 per_hour; F = 0.984; k21 = 1.19 per_hour; V_C = 0.32 liter_per_kg; k_a = 12.0 per_hour Reaction: C_p = ((k_a*F*X_gut/V_C-k12*C_p)+k21*C_per)-k10*C_p, Rate Law: ((k_a*F*X_gut/V_C-k12*C_p)+k21*C_per)-k10*C_p
k_eo = 2.03 per_hour Reaction: C_e = k_eo*(C_p-C_e), Rate Law: k_eo*(C_p-C_e)
k_a = 12.0 per_hour Reaction: X_gut = (-k_a)*X_gut, Rate Law: (-k_a)*X_gut

States:

Name Description
C t [caffeine]
X gut [Caffeine; caffeine]
C p [caffeine; Caffeine]
C per [caffeine; Caffeine]
C e [caffeine]

Observables: none

MODEL1808150001 @ v0.0.1

Mathematical model of blood coagulation investigating the effects of varied rFVIIa and TF concentration.

Recombinant factor VIIa (rFVIIa) is used for treatment of hemophilia patients with inhibitors, as well for off-label treatment of severe bleeding in trauma and surgery. Effective bleeding control requires supraphysiological doses of rFVIIa, posing both high expense and uncertain thrombotic risk. Two major competing theories offer different explanations for the supraphysiological rFVIIa dosing requirement: (1) the need to overcome competition between FVIIa and FVII zymogen for tissue factor (TF) binding, and (2) a high-dose-requiring phospholipid-related pathway of FVIIa action. In the present study, we found experimental conditions in which both mechanisms contribute simultaneously and independently to rFVIIa-driven thrombin generation in FVII-deficient human plasma. From mathematical simulations of our model of FX activation, which were confirmed by thrombin-generation experiments, we conclude that the action of rFVIIa at pharmacologic doses is dominated by the TF-dependent pathway with a minor contribution from a phospholipid-dependent mechanism. We established a dose-response curve for rFVIIa that is useful to explain dosing strategies. In the present study, we present a pathway to reconcile the 2 major mechanisms of rFVIIa action, a necessary step to understanding future dose optimization and evaluation of new rFVIIa analogs currently under development. link: http://identifiers.org/pubmed/22563088

Parameters: none

States: none

Observables: none

MODEL2937159804 @ v0.0.1

Shimoni2009 - Escherichia Coli SOS Simple model, involving only the basic components of the circuit, sufficient to expl…

BACKGROUND: DNA damage in Escherichia coli evokes a response mechanism called the SOS response. The genetic circuit of this mechanism includes the genes recA and lexA, which regulate each other via a mixed feedback loop involving transcriptional regulation and protein-protein interaction. Under normal conditions, recA is transcriptionally repressed by LexA, which also functions as an auto-repressor. In presence of DNA damage, RecA proteins recognize stalled replication forks and participate in the DNA repair process. Under these conditions, RecA marks LexA for fast degradation. Generally, such mixed feedback loops are known to exhibit either bi-stability or a single steady state. However, when the dynamics of the SOS system following DNA damage was recently studied in single cells, ordered peaks were observed in the promoter activity of both genes (Friedman et al., 2005, PLoS Biol. 3(7):e238). This surprising phenomenon was masked in previous studies of cell populations. Previous attempts to explain these results harnessed additional genes to the system and deployed complex deterministic mathematical models that were only partially successful in explaining the results. METHODOLOGY/PRINCIPAL FINDINGS: Here we apply stochastic methods, which are better suited for dynamic simulations of single cells. We show that a simple model, involving only the basic components of the circuit, is sufficient to explain the peaks in the promoter activities of recA and lexA. Notably, deterministic simulations of the same model do not produce peaks in the promoter activities. CONCLUSION/SIGNIFICANCE: We conclude that the double negative mixed feedback loop with auto-repression accounts for the experimentally observed peaks in the promoter activities. In addition to explaining the experimental results, this result shows that including additional regulations in a mixed feedback loop may dramatically change the dynamic functionality of this regulatory module. Furthermore, our results suggests that stochastic fluctuations strongly affect the qualitative behavior of important regulatory modules even under biologically relevant conditions, thus emphasizing the importance of stochastic analysis of regulatory circuits. link: http://identifiers.org/pubmed/19424504

Parameters: none

States: none

Observables: none

This is a mathematical model describing Hippo signalling pathway activity. It includes descriptions of crosstalk with th…

The Hippo signalling pathway has recently emerged as an important regulator of cell apoptosis and proliferation with significant implications in human diseases. In mammals, the pathway contains the core kinases MST1/2, which phosphorylate and activate LATS1/2 kinases. The pro-apoptotic function of the MST/LATS signalling axis was previously linked to the Akt and ERK MAPK pathways, demonstrating that the Hippo pathway does not act alone but crosstalks with other signalling pathways to coordinate network dynamics and cellular outcomes. These crosstalks were characterised by a multitude of complex regulatory mechanisms involving competitive protein-protein interactions and phosphorylation mediated feedback loops. However, how these different mechanisms interplay in different cellular contexts to drive the context-specific network dynamics of Hippo-ERK signalling remains elusive. Using mathematical modelling and computational analysis, we uncovered that the Hippo-ERK network can generate highly diverse dynamical profiles that can be clustered into distinct dose-response patterns. For each pattern, we offered mechanistic explanation that defines when and how the observed phenomenon can arise. We demonstrated that Akt displays opposing, dose-dependent functions towards ERK, which are mediated by the balance between the Raf-1/MST2 protein interaction module and the LATS1 mediated feedback regulation. Moreover, Ras displays a multi-functional role and drives biphasic responses of both MST2 and ERK activities; which are critically governed by the competitive protein interaction between MST2 and Raf-1. Our study represents the first in-depth and systematic analysis of the Hippo-ERK network dynamics and provides a concrete foundation for future studies. link: http://identifiers.org/pubmed/27527217

Parameters:

Name Description
Km_93 = 0.9015; kc_92 = 0.9203 Reaction: iRaf1 => Raf1; RasGTP, Rate Law: compartment*kc_92*iRaf1*RasGTP/(Km_93+iRaf1)
Km_122 = 297.2; V_121 = 1027.0 Reaction: RasGTP => RasGDP, Rate Law: compartment*V_121*RasGTP/(Km_122+RasGTP)
ka_41 = 0.4237; kd_41 = 1.226 Reaction: aMST2 + RASSF1A => aMST2uRASSF1A, Rate Law: compartment*(ka_41*aMST2*RASSF1A-kd_41*aMST2uRASSF1A)
kd_31 = 0.6117 Reaction: dMST2 => aMST2, Rate Law: compartment*kd_31*dMST2
Km_91 = 0.8821; V_91 = 2.071 Reaction: Raf1 => iRaf1, Rate Law: compartment*V_91*Raf1/(Km_91+Raf1)
V_22 = 7511.0; Km_22 = 816.2 Reaction: iMST2 => MST2, Rate Law: compartment*V_22*iMST2/(Km_22+iMST2)
V_81 = 2261.0; Km_81 = 0.08503 Reaction: aLATS1 => LATS1, Rate Law: compartment*V_81*aLATS1/(Km_81+aLATS1)
Km_92 = 10.68; kc_91 = 0.1177 Reaction: Raf1 => iRaf1; aLATS1, Rate Law: compartment*kc_91*aLATS1*Raf1/(Km_92+Raf1)
aEGFR = 500.0; Km_11 = 51.21; kc_11 = 0.001149 Reaction: Akt => pAkt, Rate Law: compartment*kc_11*aEGFR*Akt/(Km_11+Akt)
Km_13 = 0.744; kc_12 = 0.717 Reaction: Akt => pAkt; RasGTP, Rate Law: compartment*kc_12*Akt*RasGTP/(Km_13+Akt)
Km_101 = 457.5; V_101 = 994.8 Reaction: aRaf1 => Raf1, Rate Law: compartment*V_101*aRaf1/(Km_101+aRaf1)
V_11 = 0.08687; Km_12 = 0.01497 Reaction: pAkt => Akt, Rate Law: compartment*V_11*pAkt/(Km_12+pAkt)
Km_21 = 427.3; V_21 = 1414.0 Reaction: aMST2 => MST2, Rate Law: compartment*V_21*aMST2/(Km_21+aMST2)
V_131 = 995.3; Km_132 = 151.0 Reaction: ppERK => ERK, Rate Law: compartment*V_131*ppERK/(Km_132+ppERK)
ka_22 = 0.0684; kd_21 = 0.113 Reaction: MST2 + RASSF1A => MST2uRASSF1A, Rate Law: compartment*(ka_22*MST2*RASSF1A-kd_21*MST2uRASSF1A)
Km_111 = 0.07678; V_111 = 254.7 Reaction: ipRaf1 => aRaf1, Rate Law: compartment*V_111*ipRaf1/(Km_111+ipRaf1)
ka_71 = 28.12; kd_71 = 4.886E-4 Reaction: iMST2 + iRaf1 => iRaf1uiMST2, Rate Law: compartment*(ka_71*iMST2*iRaf1-kd_71*iRaf1uiMST2)
V_102 = 317.3; Km_102 = 3.197 Reaction: Raf1 => aRaf1, Rate Law: compartment*V_102*Raf1/(Km_102+Raf1)
kc_112 = 0.002742; Km_112 = 207.1 Reaction: aRaf1 => ipRaf1; ppERK, Rate Law: compartment*kc_112*aRaf1*ppERK/(Km_112+aRaf1)
kc_131 = 5.342; Km_131 = 0.03676 Reaction: ERK => ppERK; aRaf1, Rate Law: compartment*kc_131*aRaf1*ERK/(Km_131+ERK)
kc_21 = 6684.0; Km_23 = 8.313E-4 Reaction: MST2 => iMST2; pAkt, Rate Law: compartment*kc_21*MST2*pAkt/(Km_23+MST2)
kc_82 = 2.93E-4; Km_83 = 22.26 Reaction: LATS1 => aLATS1; aMST2uRASSF1A, Rate Law: compartment*kc_82*aMST2uRASSF1A*LATS1/(Km_83+LATS1)
aEGFR = 500.0; kc_121 = 0.2061; Km_121 = 120.5 Reaction: RasGDP => RasGTP, Rate Law: compartment*kc_121*aEGFR*RasGDP/(Km_121+RasGDP)
ka_21 = 4472.0 Reaction: MST2 => dMST2, Rate Law: compartment*ka_21*MST2^2
Km_51 = 6.708; V_51 = 5.688E-4 Reaction: MST2uRASSF1A => aMST2uRASSF1A, Rate Law: compartment*V_51*MST2uRASSF1A/(Km_51+MST2uRASSF1A)
kc_81 = 6189.0; Km_82 = 3961.0 Reaction: LATS1 => aLATS1; aMST2, Rate Law: compartment*kc_81*aMST2*LATS1/(Km_82+LATS1)

States:

Name Description
MST2uRASSF1A [Ras Association Domain-Containing Protein 1; STE20-Like Serine/Threonine-Protein Kinase]
aMST2uRASSF1A [STE20-Like Serine/Threonine-Protein Kinase; Ras Association Domain-Containing Protein 1]
MST2 [STE20-Like Serine/Threonine-Protein Kinase]
aMST2 [STE20-Like Serine/Threonine-Protein Kinase]
Akt [AKT kinase]
iRaf1 [RAF proto-oncogene serine/threonine-protein kinase]
ipRaf1 [RAF proto-oncogene serine/threonine-protein kinase]
Raf1 [RAF proto-oncogene serine/threonine-protein kinase]
aLATS1 [serine/threonine-protein kinase LATS1]
LATS1 [serine/threonine-protein kinase LATS1]
RasGDP [RAS Family Gene]
ppERK [Mitogen-activated protein kinase 3]
pAkt [AKT kinase]
dMST2 [STE20-Like Serine/Threonine-Protein Kinase]
aRaf1 [RAF proto-oncogene serine/threonine-protein kinase]
RasGTP [RAS Family Gene]
RASSF1A [Ras Association Domain-Containing Protein 1]
iMST2 [STE20-Like Serine/Threonine-Protein Kinase]
ERK [Mitogen-activated protein kinase 3]
iRaf1uiMST2 [RAF proto-oncogene serine/threonine-protein kinase; STE20-Like Serine/Threonine-Protein Kinase]

Observables: none

A properly functioning immune system is vital for an organism's wellbeing. Immune tolerance is a critical feature of the…

Dendritic cells are a promising immunotherapy tool for boosting an individual's antigen-specific immune response to cancer. We develop a mathematical model using differential and delay-differential equations to describe the interactions between dendritic cells, effector-immune cells, and tumor cells. We account for the trafficking of immune cells between lymph, blood, and tumor compartments. Our model reflects experimental results both for dendritic cell trafficking and for immune suppression of tumor growth in mice. In addition, in silico experiments suggest more effective immunotherapy treatment protocols can be achieved by modifying dose location and schedule. A sensitivity analysis of the model reveals which patient-specific parameters have the greatest impact on treatment efficacy. link: http://identifiers.org/pubmed/23516248

Parameters: none

States: none

Observables: none

A properly functioning immune system is vital for an organism's wellbeing. Immune tolerance is a critical feature of the…

A properly functioning immune system is vital for an organism's wellbeing. Immune tolerance is a critical feature of the immune system that allows immune cells to mount effective responses against exogenous pathogens such as viruses and bacteria, while preventing attack to self-tissues. Activation-induced cell death (AICD) in T lymphocytes, in which repeated stimulations of the T-cell receptor (TCR) lead to activation and then apoptosis of T cells, is a major mechanism for T cell homeostasis and helps maintain peripheral immune tolerance. Defects in AICD can lead to development of autoimmune diseases. Despite its importance, the regulatory mechanisms that underlie AICD remain poorly understood, particularly at an integrative network level. Here, we develop a dynamic multi-pathway model of the integrated TCR signalling network and perform model-based analysis to characterize the network-level properties of AICD. Model simulation and analysis show that amplified activation of the transcriptional factor NFAT in response to repeated TCR stimulations, a phenomenon central to AICD, is tightly modulated by a coupled positive-negative feedback mechanism. NFAT amplification is predominantly enabled by a positive feedback self-regulated by NFAT, while opposed by a NFAT-induced negative feedback via Carabin. Furthermore, model analysis predicts an optimal therapeutic window for drugs that help minimize proliferation while maximize AICD of T cells. Overall, our study provides a comprehensive mathematical model of TCR signalling and model-based analysis offers new network-level insights into the regulation of activation-induced cell death in T cells. link: http://identifiers.org/pubmed/31337782

Parameters: none

States: none

Observables: none

Systems modelling of the EGFR-PYK2-c-Met interaction network predicted and prioritized synergistic drug combinations for…

Prediction of drug combinations that effectively target cancer cells is a critical challenge for cancer therapy, in particular for triple-negative breast cancer (TNBC), a highly aggressive breast cancer subtype with no effective targeted treatment. As signalling pathway networks critically control cancer cell behaviour, analysis of signalling network activity and crosstalk can help predict potent drug combinations and rational stratification of patients, thus bringing therapeutic and prognostic values. We have previously showed that the non-receptor tyrosine kinase PYK2 is a downstream effector of EGFR and c-Met and demonstrated their crosstalk signalling in basal-like TNBC. Here we applied a systems modelling approach and developed a mechanistic model of the integrated EGFR-PYK2-c-Met signalling network to identify and prioritize potent drug combinations for TNBC. Model predictions validated by experimental data revealed that among six potential combinations of drug pairs targeting the central nodes of the network, including EGFR, c-Met, PYK2 and STAT3, co-targeting of EGFR and PYK2 and to a lesser extent of EGFR and c-Met yielded strongest synergistic effect. Importantly, the synergy in co-targeting EGFR and PYK2 was linked to switch-like cell proliferation-associated responses. Moreover, simulations of patient-specific models using public gene expression data of TNBC patients led to predictive stratification of patients into subgroups displaying distinct susceptibility to specific drug combinations. These results suggest that mechanistic systems modelling is a powerful approach for the rational design, prediction and prioritization of potent combination therapies for individual patients, thus providing a concrete step towards personalized treatment for TNBC and other tumour types. link: http://identifiers.org/pubmed/29920512

Parameters:

Name Description
PF396 = 0.0; kc11 = 0.321366; STAT3tot = 144.212; Ki3b = 1.0; Km11 = 20.6063 Reaction: => pSTAT3; STAT3uStattic, pPYK2, Rate Law: rootCompartment*kc11*pPYK2*rootCompartment/(1+PF396/Ki3b)*((STAT3tot-pSTAT3*rootCompartment)-STAT3uStattic*rootCompartment)/(Km11+((STAT3tot-pSTAT3*rootCompartment)-STAT3uStattic*rootCompartment))/rootCompartment
Vmax24 = 4.39542E9; Km24 = 0.156675 Reaction: pERK =>, Rate Law: rootCompartment*Vmax24*pERK*rootCompartment/(Km24+pERK*rootCompartment)/rootCompartment
Km17 = 9.81748; HGF = 0.0; kc17 = 8.10961E-4; caHGF = 0.0090365 Reaction: cMET => pcMET, Rate Law: rootCompartment*(kc17*HGF+caHGF)*cMET*rootCompartment/(Km17+cMET*rootCompartment)/rootCompartment
Vmax22 = 0.034914; Km22 = 46.4515 Reaction: aPTP =>, Rate Law: rootCompartment*Vmax22*aPTP*rootCompartment/(Km22+aPTP*rootCompartment)/rootCompartment
Stattictot = 0.0; ka25 = 127.35; STAT3tot = 144.212; kd25 = 11.749 Reaction: => STAT3uStattic; pSTAT3, Rate Law: rootCompartment*(ka25*((STAT3tot-pSTAT3*rootCompartment)-STAT3uStattic*rootCompartment)*(Stattictot-STAT3uStattic*rootCompartment)-kd25*STAT3uStattic*rootCompartment)/rootCompartment
Vs13 = 0.0937562; Vmax13 = 0.354813; Km13 = 38.7258 Reaction: => cMETm; pSTAT3, Rate Law: rootCompartment*(Vs13+Vmax13*pSTAT3*rootCompartment/(Km13+pSTAT3*rootCompartment))/rootCompartment
kdeg6 = 53.5797 Reaction: PYK2m =>, Rate Law: rootCompartment*kdeg6*PYK2m*rootCompartment/rootCompartment
kdeg14 = 4.56037 Reaction: cMETm =>, Rate Law: rootCompartment*kdeg14*cMETm*rootCompartment/rootCompartment
kc10 = 0.00610942; Vmax10 = 0.530884; Km10 = 9.14113 Reaction: pPYK2 => PYK2; aPTP, Rate Law: rootCompartment*(Vmax10+kc10*aPTP*rootCompartment)*pPYK2*rootCompartment/(Km10+pPYK2*rootCompartment)/rootCompartment
EGF = 10.0; caEGF = 0.0891251; kc1 = 413.048; Km1 = 248.886; Gefitinib = 0.0; EGFRtot = 398.107; Ki1 = 1.0 Reaction: => pEGFR; EGFRub, Rate Law: rootCompartment*kc1*(EGF/(1+Gefitinib/Ki1)+caEGF)*((EGFRtot-pEGFR*rootCompartment)-EGFRub*rootCompartment)/(Km1+((EGFRtot-pEGFR*rootCompartment)-EGFRub*rootCompartment))/rootCompartment
Vs5 = 26.5461; Km5 = 4.74242; Vmax5 = 34.0408 Reaction: => PYK2m; pSTAT3, Rate Law: rootCompartment*(Vs5+Vmax5*pSTAT3*rootCompartment/(Km5+pSTAT3*rootCompartment))/rootCompartment
Vmax4 = 11.1173; Km4 = 90.7821 Reaction: EGFRub =>, Rate Law: rootCompartment*Vmax4*EGFRub*rootCompartment/(Km4+EGFRub*rootCompartment)/rootCompartment
Km20 = 24.322; Vmax20 = 0.0483059; kc20 = 35.6451 Reaction: pCbl => ; aPTP, Rate Law: rootCompartment*(Vmax20+kc20*aPTP*rootCompartment)*pCbl*rootCompartment/(Km20+pCbl*rootCompartment)/rootCompartment
Km7 = 3.33426; Vmax7 = 3.34965 Reaction: => PYK2; PYK2m, Rate Law: rootCompartment*Vmax7*PYK2m*rootCompartment/(Km7+PYK2m*rootCompartment)/rootCompartment
EMD = 0.0; Km9 = 34.914; kc9a = 0.463447; kc9b = 0.988553; Ki9 = 1.65577 Reaction: PYK2 => pPYK2; pEGFR, pcMET, Rate Law: rootCompartment*(kc9a*pEGFR*rootCompartment+kc9b*pcMET*rootCompartment/(1+EMD/Ki9))*PYK2*rootCompartment/(Km9+PYK2*rootCompartment)/rootCompartment
Km2 = 3.80189; Vmax2 = 112.202; kc2 = 1406.05 Reaction: pEGFR => ; aPTP, Rate Law: rootCompartment*(Vmax2+kc2*aPTP*rootCompartment)*pEGFR*rootCompartment/(Km2+pEGFR*rootCompartment)/rootCompartment
kc16 = 1.1749; Km16 = 528.445; kdeg16 = 24.4906 Reaction: cMET => ; pCbl, Rate Law: rootCompartment*(kdeg16+kc16*pCbl*rootCompartment)*cMET*rootCompartment/(Km16+cMET*rootCompartment)/rootCompartment
Km18 = 9.95405; Vmax18 = 0.0606736 Reaction: pcMET => cMET, Rate Law: rootCompartment*Vmax18*pcMET*rootCompartment/(Km18+pcMET*rootCompartment)/rootCompartment
kc19 = 52.723; Km19 = 13.3045; Cbltot = 174.985 Reaction: => pCbl; pEGFR, Rate Law: rootCompartment*kc19*pEGFR*rootCompartment*(Cbltot-pCbl*rootCompartment)/(Km19+(Cbltot-pCbl*rootCompartment))/rootCompartment
Km12 = 11.5878; kc12 = 2.89734E-4; Vmax12 = 7.63836 Reaction: pSTAT3 => ; aPTP, Rate Law: rootCompartment*(Vmax12+kc12*aPTP*rootCompartment)*pSTAT3*rootCompartment/(Km12+pSTAT3*rootCompartment)/rootCompartment
kdeg8 = 0.0566239 Reaction: PYK2 =>, Rate Law: rootCompartment*kdeg8*PYK2*rootCompartment/rootCompartment
EMD = 0.0; ERKtot = 166.725; kc23b = 8.43335E8; kc23a = 7.03072E9; Km23 = 2.83139; Ki23 = 13.4896 Reaction: => pERK; pEGFR, pcMET, Rate Law: rootCompartment*(kc23a*pcMET*rootCompartment/(1+EMD/Ki23)+kc23b*pEGFR*rootCompartment)*(ERKtot-pERK*rootCompartment)/(Km23+(ERKtot-pERK*rootCompartment))/rootCompartment
Vmax15 = 91.4113; Km15 = 6.45654 Reaction: => cMET; cMETm, Rate Law: rootCompartment*Vmax15*cMETm*rootCompartment/(Km15+cMETm*rootCompartment)/rootCompartment
kc3 = 10.7895; PF396 = 0.0; Ki3a = 0.0835603; Ki3b = 1.0; Vmax3 = 1.03753E-4; EGFRtot = 398.107; Km3 = 2.2856 Reaction: => EGFRub; PYK2, pCbl, pEGFR, pPYK2, Rate Law: rootCompartment*(Vmax3+kc3*pCbl*rootCompartment)*((EGFRtot-pEGFR*rootCompartment)-EGFRub*rootCompartment)/(Km3+((EGFRtot-pEGFR*rootCompartment)-EGFRub*rootCompartment))*Ki3a/(Ki3a+(PYK2*rootCompartment+pPYK2*rootCompartment)/(1+PF396/Ki3b))/rootCompartment
kc21 = 0.00397192; PTPtot = 296.483; Km21 = 52.723 Reaction: => aPTP; pEGFR, Rate Law: rootCompartment*kc21*pEGFR*rootCompartment*(PTPtot-aPTP*rootCompartment)/(Km21+(PTPtot-aPTP*rootCompartment))/rootCompartment

States:

Name Description
pcMET [PR:P08581]
STAT3uStattic [signal transducer and activator of transcription 3; stattic]
pCbl [E3 Ubiquitin-Protein Ligase CBL]
pPYK2 [Protein Tyrosine Kinase]
aPTP [Protein Tyrosine Phosphatase]
pSTAT3 [signal transducer and activator of transcription 3]
cMET [PR:P08581]
PYK2m [Protein Tyrosine Kinase; messenger RNA]
PYK2 [Protein Tyrosine Kinase]
pERK [mitogen-activated protein kinase]
pEGFR [epidermal growth factor receptor]
cMETm [PR:P08581; messenger RNA]
EGFRub [epidermal growth factor receptor; ubiquinated]

Observables: none

Shlomi2011 - Warburg effect, metabolic modelUsing a genome-scale human metabolic network model accounting for stoichiome…

The Warburg effect–a classical hallmark of cancer metabolism–is a counter-intuitive phenomenon in which rapidly proliferating cancer cells resort to inefficient ATP production via glycolysis leading to lactate secretion, instead of relying primarily on more efficient energy production through mitochondrial oxidative phosphorylation, as most normal cells do. The causes for the Warburg effect have remained a subject of considerable controversy since its discovery over 80 years ago, with several competing hypotheses. Here, utilizing a genome-scale human metabolic network model accounting for stoichiometric and enzyme solvent capacity considerations, we show that the Warburg effect is a direct consequence of the metabolic adaptation of cancer cells to increase biomass production rate. The analysis is shown to accurately capture a three phase metabolic behavior that is observed experimentally during oncogenic progression, as well as a prominent characteristic of cancer cells involving their preference for glutamine uptake over other amino acids. link: http://identifiers.org/pubmed/21423717

Parameters: none

States: none

Observables: none

MODEL0912160004 @ v0.0.1

This a model from the article: A mathematical model of fatigue in skeletal muscle force contraction. Shorten PR, O'C…

The ability for muscle to repeatedly generate force is limited by fatigue. The cellular mechanisms behind muscle fatigue are complex and potentially include breakdown at many points along the excitation-contraction pathway. In this paper we construct a mathematical model of the skeletal muscle excitation-contraction pathway based on the cellular biochemical events that link excitation to contraction. The model includes descriptions of membrane voltage, calcium cycling and crossbridge dynamics and was parameterised and validated using the response characteristics of mouse skeletal muscle to a range of electrical stimuli. This model was used to uncover the complexities of skeletal muscle fatigue. We also parameterised our model to describe force kinetics in fast and slow twitch fibre types, which have a number of biochemical and biophysical differences. How these differences interact to generate different force/fatigue responses in fast- and slow- twitch fibres is not well understood and we used our modelling approach to bring new insights to this relationship. link: http://identifiers.org/pubmed/18080210

Parameters: none

States: none

Observables: none

BIOMD0000000277 @ v0.0.1

This a model from the article: A mathematical model of parathyroid hormone response to acute changes in plasma ioniz…

A complex bio-mechanism, commonly referred to as calcium homeostasis, regulates plasma ionized calcium (Ca(2+)) concentration in the human body within a narrow range which is crucial for maintaining normal physiology and metabolism. Taking a step towards creating a complete mathematical model of calcium homeostasis, we focus on the short-term dynamics of calcium homeostasis and consider the response of the parathyroid glands to acute changes in plasma Ca(2+) concentration. We review available models, discuss their limitations, then present a two-pool, linear, time-varying model to describe the dynamics of this calcium homeostasis subsystem, the Ca-PTH axis. We propose that plasma PTH concentration and plasma Ca(2+) concentration bear an asymmetric reverse sigmoid relation. The parameters of our model are successfully estimated based on clinical data corresponding to three healthy subjects that have undergone induced hypocalcemic clamp tests. In the first validation of this kind, with parameters estimated separately for each subject we test the model's ability to predict the same subject's induced hypercalcemic clamp test responses. Our results demonstrate that a two-pool, linear, time-varying model with an asymmetric reverse sigmoid relation characterizes the short-term dynamics of the Ca-PTH axis. link: http://identifiers.org/pubmed/20406649

Parameters:

Name Description
alpha = 0.0569; t0 = 575.0; Ca0 = 1.22; Ca1 = 0.2624 Reaction: Ca = piecewise(Ca0, time < t0, Ca0+Ca1*(1-exp((-alpha)*(time-t0)))), Rate Law: missing
lambda_Ca = 170.0; k = 9.8436755; lambda_1 = 0.0125 Reaction: x1 = (k-lambda_Ca*x1)-lambda_1*x1, Rate Law: (k-lambda_Ca*x1)-lambda_1*x1
lambda_Ca = 170.0; lambda_2 = 0.5595 Reaction: x2 = lambda_Ca*x1-lambda_2*x2, Rate Law: lambda_Ca*x1-lambda_2*x2

States:

Name Description
x1 [Parathyroid hormone]
x2 [Parathyroid hormone]
Ca [calcium(2+); Calcium cation]

Observables: none

BIOMD0000000276 @ v0.0.1

This a model from the article: A mathematical model of parathyroid hormone response to acute changes in plasma ioniz…

A complex bio-mechanism, commonly referred to as calcium homeostasis, regulates plasma ionized calcium (Ca(2+)) concentration in the human body within a narrow range which is crucial for maintaining normal physiology and metabolism. Taking a step towards creating a complete mathematical model of calcium homeostasis, we focus on the short-term dynamics of calcium homeostasis and consider the response of the parathyroid glands to acute changes in plasma Ca(2+) concentration. We review available models, discuss their limitations, then present a two-pool, linear, time-varying model to describe the dynamics of this calcium homeostasis subsystem, the Ca-PTH axis. We propose that plasma PTH concentration and plasma Ca(2+) concentration bear an asymmetric reverse sigmoid relation. The parameters of our model are successfully estimated based on clinical data corresponding to three healthy subjects that have undergone induced hypocalcemic clamp tests. In the first validation of this kind, with parameters estimated separately for each subject we test the model's ability to predict the same subject's induced hypercalcemic clamp test responses. Our results demonstrate that a two-pool, linear, time-varying model with an asymmetric reverse sigmoid relation characterizes the short-term dynamics of the Ca-PTH axis. link: http://identifiers.org/pubmed/20406649

Parameters:

Name Description
Ca1 = 0.1817; t0 = 575.0; Ca0 = 1.255; alpha = 0.0442 Reaction: Ca = piecewise(Ca0, time < t0, Ca0-Ca1*(1-exp((-alpha)*(time-t0)))), Rate Law: missing
lambda_Ca = 170.0; k = 9.8436755; lambda_1 = 0.0125 Reaction: x1 = (k-lambda_Ca*x1)-lambda_1*x1, Rate Law: (k-lambda_Ca*x1)-lambda_1*x1
lambda_Ca = 170.0; lambda_2 = 0.5595 Reaction: x2 = lambda_Ca*x1-lambda_2*x2, Rate Law: lambda_Ca*x1-lambda_2*x2

States:

Name Description
x1 [Parathyroid hormone]
x2 [Parathyroid hormone]
Ca [calcium(2+); Calcium cation]

Observables: none

Although not a traditional experimental "method," mathematical modeling can provide a powerful approach for investigatin…

Although not a traditional experimental "method," mathematical modeling can provide a powerful approach for investigating complex cell signaling networks, such as those that regulate the eukaryotic cell division cycle. We describe here one modeling approach based on expressing the rates of biochemical reactions in terms of nonlinear ordinary differential equations. We discuss the steps and challenges in assigning numerical values to model parameters and the importance of experimental testing of a mathematical model. We illustrate this approach throughout with the simple and well-characterized example of mitotic cell cycles in frog egg extracts. To facilitate new modeling efforts, we describe several publicly available modeling environments, each with a collection of integrated programs for mathematical modeling. This review is intended to justify the place of mathematical modeling as a standard method for studying molecular regulatory networks and to guide the non-expert to initiate modeling projects in order to gain a systems-level perspective for complex control systems. link: http://identifiers.org/pubmed/17189866

Parameters:

Name Description
KKa = 0.1; ka = 0.02 Reaction: => Cdc25_phosphorylated; Cyclin_Cdk1_MPF, Cdc25_total, Rate Law: nuclear*ka*Cyclin_Cdk1_MPF*(Cdc25_total-Cdc25_phosphorylated)/((KKa+Cdc25_total)-Cdc25_phosphorylated)
k2 = 0.25 Reaction: Cyclin_Cdk1_MPF =>, Rate Law: nuclear*k2*Cyclin_Cdk1_MPF
kh = 0.15; KKh = 0.01 Reaction: IE_phosphorylated => ; ppase, Rate Law: nuclear*kh*ppase*IE_phosphorylated/(KKh+IE_phosphorylated)
kd = 0.13; KKd = 1.0 Reaction: APC_active => ; ppase, Rate Law: nuclear*kd*ppase*APC_active/(KKd+APC_active)
KKc = 0.01; kc = 0.13 Reaction: => APC_active; IE_phosphorylated, APC_total, Rate Law: nuclear*kc*IE_phosphorylated*(APC_total-APC_active)/((KKc+APC_total)-APC_active)
kwee = 1.0 Reaction: Cyclin_Cdk1_MPF => Cyclin_Cdk1_preMPF; Wee1, Rate Law: nuclear*kwee*Cyclin_Cdk1_MPF
k3 = 0.005 Reaction: Cyclin => Cyclin_Cdk1_MPF; Cdk1, Rate Law: nuclear*k3*Cdk1*Cyclin
k1 = 1.0 Reaction: => Cyclin, Rate Law: nuclear*k1
k25 = 0.017 Reaction: Cyclin_Cdk1_preMPF => Cyclin_Cdk1_MPF; Cdc25_phosphorylated, Rate Law: nuclear*k25*Cyclin_Cdk1_preMPF
kb = 0.1; KKb = 1.0 Reaction: Cdc25_phosphorylated => ; ppase, Rate Law: nuclear*kb*ppase*Cdc25_phosphorylated/(KKb+Cdc25_phosphorylated)
ke = 0.02; KKe = 0.1 Reaction: => Wee1_phosphorylated; Cyclin_Cdk1_MPF, Wee1_total, Rate Law: nuclear*ke*Cyclin_Cdk1_MPF*(Wee1_total-Wee1_phosphorylated)/((KKe+Wee1_total)-Wee1_phosphorylated)
KKf = 1.0; kf = 0.1 Reaction: Wee1_phosphorylated => ; ppase, Rate Law: nuclear*kf*ppase*Wee1_phosphorylated/(KKf+Wee1_phosphorylated)
KKg = 0.01; kg = 0.02 Reaction: => IE_phosphorylated; Cyclin_Cdk1_MPF, IE_total, Rate Law: nuclear*kg*Cyclin_Cdk1_MPF*(IE_total-IE_phosphorylated)/((KKg+IE_total)-IE_phosphorylated)

States:

Name Description
Wee1 [Wee1-like protein kinase 1-B]
APC active [Adenomatous polyposis coli homolog; active]
Cyclin Cdk1 MPF [G2/mitotic-specific cyclin-B1; Cyclin-dependent kinase 1-A]
Wee1 phosphorylated [Wee1-like protein kinase 1-B; phosphorylated]
IE IE
Cdc25 [M-phase inducer phosphatase 1-B]
Cdc25 phosphorylated [M-phase inducer phosphatase 1-B; phosphorylated]
Cyclin [G2/mitotic-specific cyclin-B1]
Cyclin total [G2/mitotic-specific cyclin-B1]
IE phosphorylated [phosphorylated]
Cdk1 [Cyclin-dependent kinase 1-A]
Cyclin Cdk1 preMPF [G2/mitotic-specific cyclin-B1; Cyclin-dependent kinase 1-A; phosphorylated]

Observables: none

MODEL1006230119 @ v0.0.1

This a model from the article: Nonlinearities make a difference: comparison of two common Hill-type models with real m…

Compared to complex structural Huxley-type models, Hill-type models phenomenologically describe muscle contraction using only few state variables. The Hill-type models dominate in the ever expanding field of musculoskeletal simulations for simplicity and low computational cost. Reasonable parameters are required to gain insight into mechanics of movement. The two most common Hill-type muscle models used contain three components. The series elastic component is connected in series to the contractile component. A parallel elastic component is either connected in parallel to both the contractile and the series elastic component (model [CC+SEC]), or is connected in parallel only with the contractile component (model [CC]). As soon as at least one of the components exhibits substantial nonlinearities, as, e.g., the contractile component by the ability to turn on and off, the two models are mechanically different. We tested which model ([CC+SEC] or [CC]) represents the cat soleus better. Ramp experiments consisting of an isometric and an isokinetic part were performed with an in situ cat soleus preparation using supramaximal nerve stimulation. Hill-type models containing force-length and force-velocity relationship, excitation-contraction coupling and series and parallel elastic force-elongation relations were fitted to the data. To test which model might represent the muscle better, the obtained parameters were compared with experimentally determined parameters. Determined in situations with negligible passive force, the force-velocity relation and the series elastic component relation are independent of the chosen model. In contrast to model [CC+SEC], these relations predicted by model [CC] were in accordance with experimental relations. In conclusion model [CC] seemed to better represent the cat soleus contraction dynamics and should be preferred in the nonlinear regression of muscle parameters and in musculoskeletal modeling. link: http://identifiers.org/pubmed/18049823

Parameters: none

States: none

Observables: none

MODEL1006230120 @ v0.0.1

This a model from the article: Nonlinearities make a difference: comparison of two common Hill-type models with real m…

Compared to complex structural Huxley-type models, Hill-type models phenomenologically describe muscle contraction using only few state variables. The Hill-type models dominate in the ever expanding field of musculoskeletal simulations for simplicity and low computational cost. Reasonable parameters are required to gain insight into mechanics of movement. The two most common Hill-type muscle models used contain three components. The series elastic component is connected in series to the contractile component. A parallel elastic component is either connected in parallel to both the contractile and the series elastic component (model [CC+SEC]), or is connected in parallel only with the contractile component (model [CC]). As soon as at least one of the components exhibits substantial nonlinearities, as, e.g., the contractile component by the ability to turn on and off, the two models are mechanically different. We tested which model ([CC+SEC] or [CC]) represents the cat soleus better. Ramp experiments consisting of an isometric and an isokinetic part were performed with an in situ cat soleus preparation using supramaximal nerve stimulation. Hill-type models containing force-length and force-velocity relationship, excitation-contraction coupling and series and parallel elastic force-elongation relations were fitted to the data. To test which model might represent the muscle better, the obtained parameters were compared with experimentally determined parameters. Determined in situations with negligible passive force, the force-velocity relation and the series elastic component relation are independent of the chosen model. In contrast to model [CC+SEC], these relations predicted by model [CC] were in accordance with experimental relations. In conclusion model [CC] seemed to better represent the cat soleus contraction dynamics and should be preferred in the nonlinear regression of muscle parameters and in musculoskeletal modeling. link: http://identifiers.org/pubmed/18049823

Parameters: none

States: none

Observables: none

MODEL1711210002 @ v0.0.1

Using scaling from PhysB model Blood flow in L/hr Compartments in Kg Baseline as ~0.003nM Free E2 in Blood_venous E2 bi…

Estrogen is a vital hormone that regulates many biological functions within the body. These include roles in the development of the secondary sexual organs in both sexes, plus uterine angiogenesis and proliferation during the menstrual cycle and pregnancy in women. The varied biological roles of estrogens in human health also make them a therapeutic target for contraception, mitigation of the adverse effects of the menopause, and treatment of estrogen-responsive tumours. In addition, endogenous (e.g. genetic variation) and external (e.g. exposure to estrogen-like chemicals) factors are known to impact estrogen biology. To understand how these multiple factors interact to determine an individual's response to therapy is complex, and may be best approached through a systems approach.We present a physiologically-based pharmacokinetic model (PBPK) of estradiol, and validate it against plasma kinetics in humans following intravenous and oral exposure. We extend this model by replacing the intrinsic clearance term with: a detailed kinetic model of estrogen metabolism in the liver; or, a genome-scale model of liver metabolism. Both models were validated by their ability to reproduce clinical data on estradiol exposure. We hypothesise that the enhanced mechanistic information contained within these models will lead to more robust predictions of the biological phenotype that emerges from the complex interactions between estrogens and the body.To demonstrate the utility of these models we examine the known drug-drug interactions between phenytoin and oral estradiol. We are able to reproduce the approximate 50% reduction in area under the concentration-time curve for estradiol associated with this interaction. Importantly, the inclusion of a genome-scale metabolic model allows the prediction of this interaction without directly specifying it within the model. In addition, we predict that PXR activation by drugs results in an enhanced ability of the liver to excrete glucose. This has important implications for the relationship between drug treatment and metabolic syndrome.We demonstrate how the novel coupling of PBPK models with genome-scale metabolic networks has the potential to aid prediction of drug action, including both drug-drug interactions and changes to the metabolic landscape that may predispose an individual to disease development. link: http://identifiers.org/pubmed/29246152

Parameters: none

States: none

Observables: none

MODEL1711210003 @ v0.0.1

Physiologically-based Pharmacokinetic (PBPK) model of estradiol disposition in humans. Based on Sier et al_2017_estroge…

Estrogen is a vital hormone that regulates many biological functions within the body. These include roles in the development of the secondary sexual organs in both sexes, plus uterine angiogenesis and proliferation during the menstrual cycle and pregnancy in women. The varied biological roles of estrogens in human health also make them a therapeutic target for contraception, mitigation of the adverse effects of the menopause, and treatment of estrogen-responsive tumours. In addition, endogenous (e.g. genetic variation) and external (e.g. exposure to estrogen-like chemicals) factors are known to impact estrogen biology. To understand how these multiple factors interact to determine an individual's response to therapy is complex, and may be best approached through a systems approach.We present a physiologically-based pharmacokinetic model (PBPK) of estradiol, and validate it against plasma kinetics in humans following intravenous and oral exposure. We extend this model by replacing the intrinsic clearance term with: a detailed kinetic model of estrogen metabolism in the liver; or, a genome-scale model of liver metabolism. Both models were validated by their ability to reproduce clinical data on estradiol exposure. We hypothesise that the enhanced mechanistic information contained within these models will lead to more robust predictions of the biological phenotype that emerges from the complex interactions between estrogens and the body.To demonstrate the utility of these models we examine the known drug-drug interactions between phenytoin and oral estradiol. We are able to reproduce the approximate 50% reduction in area under the concentration-time curve for estradiol associated with this interaction. Importantly, the inclusion of a genome-scale metabolic model allows the prediction of this interaction without directly specifying it within the model. In addition, we predict that PXR activation by drugs results in an enhanced ability of the liver to excrete glucose. This has important implications for the relationship between drug treatment and metabolic syndrome.We demonstrate how the novel coupling of PBPK models with genome-scale metabolic networks has the potential to aid prediction of drug action, including both drug-drug interactions and changes to the metabolic landscape that may predispose an individual to disease development. link: http://identifiers.org/pubmed/29246152

Parameters: none

States: none

Observables: none

This is a mathematical model studies how specific immune system components, namely dendritic cells and cytotoxic T-cells…

The cancer stem cell hypothesis states that tumors are heterogeneous and comprised of several different cell types that have a range of reproductive potentials. Cancer stem cells (CSCs), represent one class of cells that has both reproductive potential and the ability to differentiate. These cells are thought to drive the progression of aggressive and recurring cancers since they give rise to all other constituent cells within a tumor. With the development of immunotherapy in the last decade, the specific targeting of CSCs has become feasible and presents a novel therapeutic approach. In this paper, we construct a mathematical model to study how specific components of the immune system, namely dendritic cells and cytotoxic T-cells interact with different cancer cell types (CSCs and non-CSCs). Using a system of ordinary differential equations, we model the effects of immunotherapy, specifically dendritic cell vaccines and T-cell adoptive therapy, on tumor growth, with and without chemotherapy. The model reproduces several results observed in the literature, including temporal measurements of tumor size from in vivo experiments, and it is used to predict the optimal treatment schedule when combining different treatment modalities. Importantly, the model also demonstrates that chemotherapy increases tumorigenicity whereas CSC-targeted immunotherapy decreases it. link: http://identifiers.org/pubmed/31622595

Parameters: none

States: none

Observables: none

Sigurdsson2010 - Genome-scale metabolic model of Mus Musculus (iMM1415)This model is described in the article: [A detai…

BACKGROUND: Well-curated and validated network reconstructions are extremely valuable tools in systems biology. Detailed metabolic reconstructions of mammals have recently emerged, including human reconstructions. They raise the question if the various successful applications of microbial reconstructions can be replicated in complex organisms. RESULTS: We mapped the published, detailed reconstruction of human metabolism (Recon 1) to other mammals. By searching for genes homologous to Recon 1 genes within mammalian genomes, we were able to create draft metabolic reconstructions of five mammals, including the mouse. Each draft reconstruction was created in compartmentalized and non-compartmentalized version via two different approaches. Using gap-filling algorithms, we were able to produce all cellular components with three out of four versions of the mouse metabolic reconstruction. We finalized a functional model by iterative testing until it passed a predefined set of 260 validation tests. The reconstruction is the largest, most comprehensive mouse reconstruction to-date, accounting for 1,415 genes coding for 2,212 gene-associated reactions and 1,514 non-gene-associated reactions.We tested the mouse model for phenotype prediction capabilities. The majority of predicted essential genes were also essential in vivo. However, our non-tissue specific model was unable to predict gene essentiality for many of the metabolic genes shown to be essential in vivo. Our knockout simulation of the lipoprotein lipase gene correlated well with experimental results, suggesting that softer phenotypes can also be simulated. CONCLUSIONS: We have created a high-quality mouse genome-scale metabolic reconstruction, iMM1415 (Mus Musculus, 1415 genes). We demonstrate that the mouse model can be used to perform phenotype simulations, similar to models of microbe metabolism. Since the mouse is an important experimental organism, this model should become an essential tool for studying metabolic phenotypes in mice, including outcomes from drug screening. link: http://identifiers.org/pubmed/20959003

Parameters: none

States: none

Observables: none

This a model from the article: An integrated model for glucose and insulin regulation in healthy volunteers and type 2…

An integrated model for the regulation of glucose and insulin concentrations following intravenous glucose provocations in healthy volunteers and type 2 diabetic patients was developed. Data from 72 individuals were included. Total glucose, labeled glucose, and insulin concentrations were determined. Simultaneous analysis of all data by nonlinear mixed effect modeling was performed in NONMEM. Integrated models for glucose, labeled glucose, and insulin were developed. Control mechanisms for regulation of glucose production, insulin secretion, and glucose uptake were incorporated. Physiologically relevant differences between healthy volunteers and patients were identified in the regulation of glucose production, elimination rate of glucose, and secretion of insulin. The model was able to describe the insulin and glucose profiles well and also showed a good ability to simulate data. The features of the present model are likely to be of interest for analysis of data collected in antidiabetic drug development and for optimization of study design. link: http://identifiers.org/pubmed/17766701

Parameters: none

States: none

Observables: none

This model represents NIK-dependent p100 processing into p52 and NIK-dependent IkBd degradation with mass action kinetic…

Signaling pathways often share molecular components, tying the activity of one pathway to the functioning of another. In the NFκB signaling system, distinct kinases mediate inflammatory and developmental signaling via RelA and RelB, respectively. Although the substrates of the developmental, so-called noncanonical, pathway are induced by inflammatory/canonical signaling, crosstalk is limited. Through dynamical systems modeling, we identified the underlying regulatory mechanism. We found that as the substrate of the noncanonical kinase NIK, the nfkb2 gene product p100, transitions from a monomer to a multimeric complex, it may compete with and inhibit p100 processing to the active p52. Although multimeric complexes of p100 (IκBδ) are known to inhibit preexisting RelA:p50 through sequestration, here we report that p100 complexes can inhibit the enzymatic formation of RelB:p52. We show that the dose–response systems properties of this complex substrate competition motif are poorly accounted for by standard Michaelis–Menten kinetics, but require more detailed mass action formulations. In sum, although tonic inflammatory signaling is required for adequate expression of the noncanonical pathway precursors, the substrate complex competition motif identified here can prevent amplification of the active RelB:p52 dimer in elevated inflammatory conditions to ensure reliable RelB-dependent developmental signaling independent of inflammatory context. link: http://identifiers.org/doi/10.1073/pnas.1816000116

Parameters:

Name Description
k1=0.05 Reaction: p100_NIK => p52 + NIK, Rate Law: compartment*k1*p100_NIK
k1=1.6E-5; k2=2.4E-4 Reaction: p100 => IkBd, Rate Law: compartment*(k1*p100^2-k2*IkBd)
k1=3.8E-4 Reaction: p52 =>, Rate Law: compartment*k1*p52
k1=0.005; k2=2.4E-4 Reaction: p100 + NIK => p100_NIK, Rate Law: compartment*(k1*p100*NIK-k2*p100_NIK)
k1=0.2 Reaction: p100t => p100, Rate Law: compartment*k1*p100t

States:

Name Description
IkBd [Nuclear factor NF-kappa-B p100 subunit]
p100t [ENSG00000077150]
p52 [Nuclear factor NF-kappa-B p100 subunit]
NIK [Mitogen-activated protein kinase kinase kinase 14]
IkBd NIK [Mitogen-activated protein kinase kinase kinase 14; Nuclear factor NF-kappa-B p100 subunit]
p100 NIK [Mitogen-activated protein kinase kinase kinase 14; Nuclear factor NF-kappa-B p100 subunit]
p100 [Nuclear factor NF-kappa-B p100 subunit]

Observables: none

This model represents NIK-dependent p100 processing into p52 and NIK-dependent IkBd degradation with Michaelis-Menten ki…

Signaling pathways often share molecular components, tying the activity of one pathway to the functioning of another. In the NFκB signaling system, distinct kinases mediate inflammatory and developmental signaling via RelA and RelB, respectively. Although the substrates of the developmental, so-called noncanonical, pathway are induced by inflammatory/canonical signaling, crosstalk is limited. Through dynamical systems modeling, we identified the underlying regulatory mechanism. We found that as the substrate of the noncanonical kinase NIK, the nfkb2 gene product p100, transitions from a monomer to a multimeric complex, it may compete with and inhibit p100 processing to the active p52. Although multimeric complexes of p100 (IκBδ) are known to inhibit preexisting RelA:p50 through sequestration, here we report that p100 complexes can inhibit the enzymatic formation of RelB:p52. We show that the dose–response systems properties of this complex substrate competition motif are poorly accounted for by standard Michaelis–Menten kinetics, but require more detailed mass action formulations. In sum, although tonic inflammatory signaling is required for adequate expression of the noncanonical pathway precursors, the substrate complex competition motif identified here can prevent amplification of the active RelB:p52 dimer in elevated inflammatory conditions to ensure reliable RelB-dependent developmental signaling independent of inflammatory context. link: http://identifiers.org/doi/10.1073/pnas.1816000116

Parameters:

Name Description
k1=1.6E-5; k2=2.4E-4 Reaction: p100 => IkBd, Rate Law: compartment*(k1*p100^2-k2*IkBd)
Km=10.0; kcat=0.05 Reaction: IkBd => ; NIK, Rate Law: compartment*NIK*kcat*IkBd/(Km+IkBd)
k1=3.8E-4 Reaction: p100 =>, Rate Law: compartment*k1*p100
k1=0.2 Reaction: p100t => p100, Rate Law: compartment*k1*p100t

States:

Name Description
IkBd [Nuclear factor NF-kappa-B p100 subunit]
p100t [ENSG00000077150]
p52 [Nuclear factor NF-kappa-B p100 subunit]
p100 [Nuclear factor NF-kappa-B p100 subunit]

Observables: none

This model represents NIK-dependent p100 processing into p52 with mass action kinetics. While this model shows identical…

Signaling pathways often share molecular components, tying the activity of one pathway to the functioning of another. In the NFκB signaling system, distinct kinases mediate inflammatory and developmental signaling via RelA and RelB, respectively. Although the substrates of the developmental, so-called noncanonical, pathway are induced by inflammatory/canonical signaling, crosstalk is limited. Through dynamical systems modeling, we identified the underlying regulatory mechanism. We found that as the substrate of the noncanonical kinase NIK, the nfkb2 gene product p100, transitions from a monomer to a multimeric complex, it may compete with and inhibit p100 processing to the active p52. Although multimeric complexes of p100 (IκBδ) are known to inhibit preexisting RelA:p50 through sequestration, here we report that p100 complexes can inhibit the enzymatic formation of RelB:p52. We show that the dose–response systems properties of this complex substrate competition motif are poorly accounted for by standard Michaelis–Menten kinetics, but require more detailed mass action formulations. In sum, although tonic inflammatory signaling is required for adequate expression of the noncanonical pathway precursors, the substrate complex competition motif identified here can prevent amplification of the active RelB:p52 dimer in elevated inflammatory conditions to ensure reliable RelB-dependent developmental signaling independent of inflammatory context. link: http://identifiers.org/doi/10.1073/pnas.1816000116

Parameters:

Name Description
k1=0.05 Reaction: p100_NIK => p52 + NIK, Rate Law: compartment*k1*p100_NIK
k1=0.005; k2=2.4E-4 Reaction: p100 + NIK => p100_NIK, Rate Law: compartment*(k1*p100*NIK-k2*p100_NIK)
k1=3.8E-4 Reaction: p100 =>, Rate Law: compartment*k1*p100
k1=0.2 Reaction: p100t => p100, Rate Law: compartment*k1*p100t

States:

Name Description
p100 NIK [Mitogen-activated protein kinase kinase kinase 14; Nuclear factor NF-kappa-B p100 subunit]
NIK [Mitogen-activated protein kinase kinase kinase 14]
p52 [Nuclear factor NF-kappa-B p100 subunit]
p100t [ENSG00000077150]
p100 [Nuclear factor NF-kappa-B p100 subunit]

Observables: none

This model represents NIK-dependent p100 processing into p52 with Michaelis-Menten kinetics. While this model shows iden…

Signaling pathways often share molecular components, tying the activity of one pathway to the functioning of another. In the NFκB signaling system, distinct kinases mediate inflammatory and developmental signaling via RelA and RelB, respectively. Although the substrates of the developmental, so-called noncanonical, pathway are induced by inflammatory/canonical signaling, crosstalk is limited. Through dynamical systems modeling, we identified the underlying regulatory mechanism. We found that as the substrate of the noncanonical kinase NIK, the nfkb2 gene product p100, transitions from a monomer to a multimeric complex, it may compete with and inhibit p100 processing to the active p52. Although multimeric complexes of p100 (IκBδ) are known to inhibit preexisting RelA:p50 through sequestration, here we report that p100 complexes can inhibit the enzymatic formation of RelB:p52. We show that the dose–response systems properties of this complex substrate competition motif are poorly accounted for by standard Michaelis–Menten kinetics, but require more detailed mass action formulations. In sum, although tonic inflammatory signaling is required for adequate expression of the noncanonical pathway precursors, the substrate complex competition motif identified here can prevent amplification of the active RelB:p52 dimer in elevated inflammatory conditions to ensure reliable RelB-dependent developmental signaling independent of inflammatory context. link: http://identifiers.org/doi/10.1073/pnas.1816000116

Parameters:

Name Description
k1=3.8E-4 Reaction: p100 =>, Rate Law: compartment*k1*p100
Km=10.0; kcat=0.05 Reaction: p100 => p52; NIK, Rate Law: compartment*NIK*kcat*p100/(Km+p100)
k1=0.2 Reaction: p100t => p100, Rate Law: compartment*k1*p100t

States:

Name Description
p100t [ENSG00000077150]
p52 [Nuclear factor NF-kappa-B p100 subunit]
p100 [Nuclear factor NF-kappa-B p100 subunit]

Observables: none

BIOMD0000000151 @ v0.0.1

Cytokines like interleukin-6 (IL-6) play an important role in triggering the acute phase response of the body to injury…

The model reproduces Fig 2, Fig3A and Fig 3B of the paper. The ODE for x1(gp180) and x3 (gp 130) is wrong and the authors have communicated to the curator that the species ought to have a constant value. There are a few other differences from the paper and these were made in consultation with the authors. Model was successfully tested on MathSBML

To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. Please refer to CC0 Public Domain Dedication for more information.

In summary, you are entitled to use this encoded model in absolutely any manner you deem suitable, verbatim, or with modification, alone or embedded it in a larger context, redistribute it, commercially or not, in a restricted way or not.

To cite BioModels Database, please use:

Li C, Donizelli M, Rodriguez N, Dharuri H, Endler L, Chelliah V, Li L, He E, Henry A, Stefan MI, Snoep JL, Hucka M, Le Novère N, Laibe C (2010) BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol., 4:92.

Parameters:

Name Description
kf13 = 2.0E-7; kr13 = 0.2 Reaction: x10 + x9 => x14, Rate Law: cytosol*(kf13*x9*x10-kr13*x14)
k49 = 0.058 Reaction: x58 => x59 + x55, Rate Law: cytosol*k49*x58
kr46 = 0.001833; kf46 = 0.011 Reaction: x55 + x51 => x56, Rate Law: cytosol*(kf46*x55*x51-kr46*x56)
kr44 = 0.001833; kf44 = 0.011 Reaction: x53 + x51 => x54, Rate Law: cytosol*(kf44*x51*x53-kr44*x54)
kf39 = 0.3; kr39 = 9.0E-4 Reaction: x40 => x45 + x8, Rate Law: cytosol*(kf39*x40-kr39*x45*x8)
k23 = 5.0E-4 Reaction: x32 => x33 + x29, Rate Law: cytosol*k23*x32
kr11 = 0.2; kf11 = 0.001 Reaction: x17 + x10 => x18, Rate Law: cytosol*(kf11*x10*x17-kr11*x18)
k6 = 0.4 Reaction: x11 => x10 + x8, Rate Law: cytosol*k6*x11
kr29 = 7.0E-4; kf29 = 1.0 Reaction: x48 => x51 + x49, Rate Law: cytosol*(kf29*x48-kr29*x49*x51)
kf34 = 6.0; kr34 = 0.06 Reaction: x16 => x39, Rate Law: cytosol*(kf34*x16-kr34*x39)
kr42 = 0.2; kf42 = 0.0717 Reaction: x51 + x50 => x52, Rate Law: cytosol*(kf42*x50*x51-kr42*x52)
kf25 = 0.01; kr25 = 0.0214 Reaction: x40 + x35 => x41, Rate Law: cytosol*(kf25*x35*x40-kr25*x41)
kr38 = 0.55; kf38 = 0.01 Reaction: x46 + x34 => x45, Rate Law: cytosol*(kf38*x34*x46-kr38*x45)
k43 = 1.0 Reaction: x52 => x47 + x50, Rate Law: cytosol*k43*x52
kf40 = 0.03; kr40 = 0.064 Reaction: x45 + x35 => x44, Rate Law: cytosol*(kf40*x35*x45-kr40*x44)
kf2 = 0.02; kr2 = 0.02 Reaction: x6 => x5 + x2, Rate Law: cytosol*(kr2*x6-kf2*x2*x5)
kr52 = 0.033; kf52 = 1.1E-4 Reaction: x61 + x57 => x62, Rate Law: cytosol*(kf52*x57*x61-kr52*x62)
kf56 = 0.014; kr56 = 0.6 Reaction: x66 + x65 => x67, Rate Law: cytosol*(kf56*x65*x66-kr56*x67)
k53 = 16.0 Reaction: x62 => x63 + x57, Rate Law: cytosol*k53*x62
Km = 340.0; Vm = 1.7 Reaction: x46 => x15, Rate Law: cytosol*Vm*x46/(Km+x46)
kf50 = 2.5E-4; kr50 = 0.5 Reaction: x59 + x55 => x60, Rate Law: cytosol*(kf50*x55*x59-kr50*x60)
kr24 = 0.55; kf24 = 0.01 Reaction: x39 + x34 => x40, Rate Law: cytosol*(kf24*x39*x34-kr24*x40)
k51 = 0.058 Reaction: x60 => x59 + x53, Rate Law: cytosol*k51*x60
kf3 = 0.04 Reaction: x6 => x7, Rate Law: cytosol*kf3*x6^2
k12 = 0.003 Reaction: x18 => x17 + x9, Rate Law: cytosol*k12*x18
kr8 = 0.1; kf8 = 0.02 Reaction: x10 => x13, Rate Law: cytosol*(2*kf8*x10^2-2*kr8*x13)
k45 = 3.5 Reaction: x54 => x55 + x51, Rate Law: cytosol*k45*x54
kr26 = 1.3; kf26 = 0.015 Reaction: x41 + x36 => x42, Rate Law: cytosol*(kf26*x36*x41-kr26*x42)
kf48 = 0.0143; kr48 = 0.8 Reaction: x59 + x57 => x58, Rate Law: cytosol*(kf48*x57*x59-kr48*x58)
kf54 = 1.1E-4; kr54 = 0.033 Reaction: x64 => x63 + x57, Rate Law: cytosol*(kr54*x64-kf54*x57*x63)
k14 = 0.005 Reaction: x13 => x20, Rate Law: cytosol*k14*x13
k20 = 0.01 Reaction: => x29; x26, Rate Law: nucleus*k20*x26
kf32 = 0.1; kr32 = 2.45E-4 Reaction: x41 => x44 + x8, Rate Law: cytosol*(kf32*x41-kr32*x44*x8)
kr1 = 0.05; kf1 = 0.1 Reaction: x4 => x5; x3, Rate Law: cytosol*(kf1*x3*x4-kr1*x5)
kf37 = 0.3; kr37 = 9.0E-4 Reaction: x39 => x46 + x8, Rate Law: cytosol*(kf37*x39-kr37*x8*x46)
kf58 = 0.005; kr58 = 0.5 Reaction: x66 + x63 => x68, Rate Law: cytosol*(kf58*x63*x66-kr58*x68)
kr3 = 0.2 Reaction: x7 => x6, Rate Law: cytosol*kr3*x7
k4 = 0.005 Reaction: x7 => x8, Rate Law: cytosol*k4*x7
k10 = 0.003 Reaction: x32 => x29 + x15 + x9 + x7, Rate Law: cytosol*k10*x32
kf7 = 0.005; kr7 = 0.5 Reaction: x10 + x8 => x12, Rate Law: cytosol*(kf7*x8*x10-kr7*x12)
kf21 = 0.02; kr21 = 0.1 Reaction: x29 + x8 => x30, Rate Law: cytosol*(kf21*x29*x8-kr21*x30)
kf9 = 0.001; kr9 = 0.2 Reaction: x15 + x8 => x16, Rate Law: cytosol*(kf9*x8*x15-kr9*x16)
kr5 = 0.8; kf5 = 0.008 Reaction: x30 + x9 => x31, Rate Law: cytosol*(kf5*x9*x30-kr5*x31)
k17 = 0.05 Reaction: x22 => x9, Rate Law: nucleus*k17*x22
k47 = 2.9 Reaction: x56 => x51 + x57, Rate Law: cytosol*k47*x56
k55 = 6.7 Reaction: x64 => x65 + x57, Rate Law: cytosol*k55*x64
kf15 = 0.001; kr15 = 0.2 Reaction: x23 + x20 => x27, Rate Law: nucleus*(kf15*x23*x20-kr15*x27)
kr33 = 0.021; kf33 = 0.3 Reaction: x44 => x46 + x38, Rate Law: cytosol*(kf33*x44-kr33*x38*x46)
k59 = 0.3 Reaction: x68 => x66 + x61, Rate Law: cytosol*k59*x68

States:

Name Description
x16 [Tyrosine-protein phosphatase non-receptor type 11; Tyrosine-protein kinase JAK1; Interleukin 6 signal transducer; Interleukin-6; Interleukin-6 receptor subunit alpha]
x54 [Mitogen activated protein kinase kinase 1Putative uncharacterized protein; RAF proto-oncogene serine/threonine-protein kinase]
x32 [Suppressor of cytokine signaling 3; Signal transducer and activator of transcription 3; Tyrosine-protein phosphatase non-receptor type 11; Tyrosine-protein kinase JAK1; Interleukin 6 signal transducer; Interleukin-6; Interleukin-6 receptor subunit alpha]
x60 [Mitogen activated protein kinase kinase 1Putative uncharacterized protein]
x62 [Mitogen-activated protein kinase 1; Mitogen activated protein kinase kinase 1Putative uncharacterized protein]
x38 [Son of sevenless homolog 1; Growth factor receptor-bound protein 2]
x45 [Growth factor receptor-bound protein 2; Tyrosine-protein phosphatase non-receptor type 11]
x23 PP2
x66 Phosp3
x51 [RAF proto-oncogene serine/threonine-protein kinase]
x46 [Tyrosine-protein phosphatase non-receptor type 11]
x11 [Signal transducer and activator of transcription 3; Tyrosine-protein kinase JAK1; Interleukin 6 signal transducer; Interleukin-6; Interleukin-6 receptor subunit alpha]
x29 [Suppressor of cytokine signaling 3]
x53 [Mitogen activated protein kinase kinase 1Putative uncharacterized protein]
x59 Phosp2
x12 [Signal transducer and activator of transcription 3; Tyrosine-protein kinase JAK1; Interleukin 6 signal transducer; Interleukin-6; Interleukin-6 receptor subunit alpha]
x5 [Interleukin 6 signal transducer; Tyrosine-protein kinase JAK1]
x40 [Growth factor receptor-bound protein 2; Tyrosine-protein phosphatase non-receptor type 11; Tyrosine-protein kinase JAK1; Interleukin 6 signal transducer; Interleukin-6; Interleukin-6 receptor subunit alpha]
x19 [Signal transducer and activator of transcription 3]
x63 [Mitogen-activated protein kinase 1]
x57 [Mitogen activated protein kinase kinase 1Putative uncharacterized protein]
x55 [Mitogen activated protein kinase kinase 1Putative uncharacterized protein]
x20 [Signal transducer and activator of transcription 3]
x41 [Growth factor receptor-bound protein 2; Tyrosine-protein phosphatase non-receptor type 11; Tyrosine-protein kinase JAK1; Interleukin 6 signal transducer; Interleukin-6; Interleukin-6 receptor subunit alpha]
x39 [Tyrosine-protein phosphatase non-receptor type 11; Tyrosine-protein kinase JAK1; Interleukin 6 signal transducer; Interleukin-6; Interleukin-6 receptor subunit alpha]
x50 Phosp1
x61 [Mitogen-activated protein kinase 1]
x9 [Signal transducer and activator of transcription 3]
x15 [Tyrosine-protein phosphatase non-receptor type 11]
x8 [Tyrosine-protein kinase JAK1; Interleukin 6 signal transducer; Interleukin-6; Interleukin-6 receptor subunit alpha]
x7 [Tyrosine-protein kinase JAK1; Interleukin 6 signal transducer; Interleukin-6; Interleukin-6 receptor subunit alpha]
x13 [Signal transducer and activator of transcription 3]
x52 [RAF proto-oncogene serine/threonine-protein kinase]
x21 [Signal transducer and activator of transcription 3]
x10 [Signal transducer and activator of transcription 3]
x64 [Mitogen-activated protein kinase 1; Mitogen activated protein kinase kinase 1Putative uncharacterized protein]

Observables: none

BIOMD0000000221 @ v0.0.1

This a model from the article: Kinetic modeling of tricarboxylic acid cycle and glyoxylate bypass in Mycobacterium tub…

BACKGROUND: Targeting persistent tubercule bacilli has become an important challenge in the development of anti-tuberculous drugs. As the glyoxylate bypass is essential for persistent bacilli, interference with it holds the potential for designing new antibacterial drugs. We have developed kinetic models of the tricarboxylic acid cycle and glyoxylate bypass in Escherichia coli and Mycobacterium tuberculosis, and studied the effects of inhibition of various enzymes in the M. tuberculosis model. RESULTS: We used E. coli to validate the pathway-modeling protocol and showed that changes in metabolic flux can be estimated from gene expression data. The M. tuberculosis model reproduced the observation that deletion of one of the two isocitrate lyase genes has little effect on bacterial growth in macrophages, but deletion of both genes leads to the elimination of the bacilli from the lungs. It also substantiated the inhibition of isocitrate lyases by 3-nitropropionate. On the basis of our simulation studies, we propose that: (i) fractional inactivation of both isocitrate dehydrogenase 1 and isocitrate dehydrogenase 2 is required for a flux through the glyoxylate bypass in persistent mycobacteria; and (ii) increasing the amount of active isocitrate dehydrogenases can stop the flux through the glyoxylate bypass, so the kinase that inactivates isocitrate dehydrogenase 1 and/or the proposed inactivator of isocitrate dehydrogenase 2 is a potential target for drugs against persistent mycobacteria. In addition, competitive inhibition of isocitrate lyases along with a reduction in the inactivation of isocitrate dehydrogenases appears to be a feasible strategy for targeting persistent mycobacteria. CONCLUSION: We used kinetic modeling of biochemical pathways to assess various potential anti-tuberculous drug targets that interfere with the glyoxylate bypass flux, and indicated the type of inhibition needed to eliminate the pathogen. The advantage of such an approach to the assessment of drug targets is that it facilitates the study of systemic effect(s) of the modulation of the target enzyme(s) in the cellular environment. link: http://identifiers.org/pubmed/16887020

Parameters:

Name Description
Kgly_ms=2.0 mmol*l^(-1); Vr_ms=0.285 mmol*l^(-1)*(60*s)^(-1); Kmal_ms=1.0 mmol*l^(-1); Kaca_ms=0.01 mmol*l^(-1); Vf_ms=28.5 mmol*l^(-1)*(60*s)^(-1); Kcoa_ms=0.1 mmol*l^(-1) Reaction: gly + aca => mal + coa, Rate Law: cell*(Vf_ms*gly/Kgly_ms*aca/Kaca_ms-Vr_ms*mal/Kmal_ms*coa/Kcoa_ms)/((1+gly/Kgly_ms+mal/Kmal_ms)*(1+aca/Kaca_ms+coa/Kcoa_ms))
Vr_icl=0.285 mmol*l^(-1)*(60*s)^(-1); Vf_icl=28.5 mmol*l^(-1)*(60*s)^(-1); Kicit_icl=0.604 mmol*l^(-1); Kgly_icl=0.13 mmol*l^(-1); Ksuc_icl=0.59 mmol*l^(-1) Reaction: icit => suc + gly, Rate Law: cell*(Vf_icl*icit/Kicit_icl-Vr_icl*suc/Ksuc_icl*gly/Kgly_icl)/(1+icit/Kicit_icl+suc/Ksuc_icl+gly/Kgly_icl+icit/Kicit_icl*suc/Ksuc_icl+suc/Ksuc_icl*gly/Kgly_icl)
Vr_fum=144.67 mmol*l^(-1)*(60*s)^(-1); Kmal_fum=0.04 mmol*l^(-1); Vf_fum=156.24 mmol*l^(-1)*(60*s)^(-1); Kfa_fum=0.15 mmol*l^(-1) Reaction: fa => mal, Rate Law: cell*(Vf_fum*fa/Kfa_fum-Vr_fum*mal/Kmal_fum)/(1+fa/Kfa_fum+mal/Kmal_fum)
Vf_scas=8.96 mmol*l^(-1)*(60*s)^(-1); Ksca_scas=0.02 mmol*l^(-1); Ksuc_scas=5.0 mmol*l^(-1); Vr_scas=0.0896 mmol*l^(-1)*(60*s)^(-1) Reaction: sca => suc, Rate Law: cell*(Vf_scas*sca/Ksca_scas-Vr_scas*suc/Ksuc_scas)/(1+sca/Ksca_scas+suc/Ksuc_scas)
Kaca_cs=0.03 mmol*l^(-1); Kcit_cs=0.7 mmol*l^(-1); Vf_cs=446.88 mmol*l^(-1)*(60*s)^(-1); Koaa_cs=0.07 mmol*l^(-1); Vr_cs=4.4688 mmol*l^(-1)*(60*s)^(-1); Kcoa_cs=0.3 mmol*l^(-1) Reaction: aca + oaa => coa + cit, Rate Law: cell*(Vf_cs*aca/Kaca_cs*oaa/Koaa_cs-Vr_cs*coa/Kcoa_cs*cit/Kcit_cs)/((1+aca/Kaca_cs+coa/Kcoa_cs)*(1+oaa/Koaa_cs+cit/Kcit_cs))
Vr_acn=6.2928 mmol*l^(-1)*(60*s)^(-1); Kcit_acn=1.7 mmol*l^(-1); Kicit_acn=3.33 mmol*l^(-1); Vf_acn=629.28 mmol*l^(-1)*(60*s)^(-1) Reaction: cit => icit, Rate Law: cell*(Vf_acn*cit/Kcit_acn-Vr_acn*icit/Kicit_acn)/(1+cit/Kcit_acn+icit/Kicit_acn)
Ksca_kdh=1.0 mmol*l^(-1); Kakg_kdh=0.1 mmol*l^(-1); Vr_kdh=0.57344 mmol*l^(-1)*(60*s)^(-1); Vf_kdh=57.344 mmol*l^(-1)*(60*s)^(-1) Reaction: akg => sca, Rate Law: cell*(Vf_kdh*akg/Kakg_kdh-Vr_kdh*sca/Ksca_kdh)/(1+akg/Kakg_kdh+sca/Ksca_kdh)
Vf_icd=6.625 mmol*l^(-1)*(60*s)^(-1); Vr_icd=0.06625 mmol*l^(-1)*(60*s)^(-1); Kakg_icd=0.13 mmol*l^(-1); Kicit_icd=0.008 mmol*l^(-1) Reaction: icit => akg, Rate Law: cell*(Vf_icd*icit/Kicit_icd-Vr_icd*akg/Kakg_icd)/(1+icit/Kicit_icd+akg/Kakg_icd)
Vf_mdh=1390.9 mmol*l^(-1)*(60*s)^(-1); Koaa_mdh=0.04 mmol*l^(-1); Kmal_mdh=2.6 mmol*l^(-1); Vr_mdh=1276.06 mmol*l^(-1)*(60*s)^(-1) Reaction: mal => oaa, Rate Law: cell*(Vf_mdh*mal/Kmal_mdh-Vr_mdh*oaa/Koaa_mdh)/(1+mal/Kmal_mdh+oaa/Koaa_mdh)
Vr_sdh=16.24 mmol*l^(-1)*(60*s)^(-1); Vf_sdh=17.7 mmol*l^(-1)*(60*s)^(-1); Ksuc_sdh=0.02 mmol*l^(-1); Kfa_sdh=0.4 mmol*l^(-1) Reaction: suc => fa, Rate Law: cell*(Vf_sdh*suc/Ksuc_sdh-Vr_sdh*fa/Kfa_sdh)/(1+suc/Ksuc_sdh+fa/Kfa_sdh)

States:

Name Description
gly [glyoxylic acid; Glyoxylate]
icit [isocitric acid; Isocitrate]
coa [coenzyme A; CoA]
mal [malic acid; Malate]
akg [2-oxoglutaric acid; 2-Oxoglutarate]
aca [acetyl-CoA; Acetyl-CoA]
cit [citric acid; Citrate]
oaa [oxaloacetic acid; Oxaloacetate]
biosyn biosyn
fa [fumaric acid; Fumarate]
suc [succinic acid; Succinate]
sca [succinyl-CoA; Succinyl-CoA]

Observables: none

BIOMD0000000222 @ v0.0.1

This a model from the article: Kinetic modeling of tricarboxylic acid cycle and glyoxylate bypass in Mycobacterium tub…

BACKGROUND: Targeting persistent tubercule bacilli has become an important challenge in the development of anti-tuberculous drugs. As the glyoxylate bypass is essential for persistent bacilli, interference with it holds the potential for designing new antibacterial drugs. We have developed kinetic models of the tricarboxylic acid cycle and glyoxylate bypass in Escherichia coli and Mycobacterium tuberculosis, and studied the effects of inhibition of various enzymes in the M. tuberculosis model. RESULTS: We used E. coli to validate the pathway-modeling protocol and showed that changes in metabolic flux can be estimated from gene expression data. The M. tuberculosis model reproduced the observation that deletion of one of the two isocitrate lyase genes has little effect on bacterial growth in macrophages, but deletion of both genes leads to the elimination of the bacilli from the lungs. It also substantiated the inhibition of isocitrate lyases by 3-nitropropionate. On the basis of our simulation studies, we propose that: (i) fractional inactivation of both isocitrate dehydrogenase 1 and isocitrate dehydrogenase 2 is required for a flux through the glyoxylate bypass in persistent mycobacteria; and (ii) increasing the amount of active isocitrate dehydrogenases can stop the flux through the glyoxylate bypass, so the kinase that inactivates isocitrate dehydrogenase 1 and/or the proposed inactivator of isocitrate dehydrogenase 2 is a potential target for drugs against persistent mycobacteria. In addition, competitive inhibition of isocitrate lyases along with a reduction in the inactivation of isocitrate dehydrogenases appears to be a feasible strategy for targeting persistent mycobacteria. CONCLUSION: We used kinetic modeling of biochemical pathways to assess various potential anti-tuberculous drug targets that interfere with the glyoxylate bypass flux, and indicated the type of inhibition needed to eliminate the pathogen. The advantage of such an approach to the assessment of drug targets is that it facilitates the study of systemic effect(s) of the modulation of the target enzyme(s) in the cellular environment. link: http://identifiers.org/pubmed/16887020

Parameters:

Name Description
Vf_scas=3.5 mM_per_min; Ksca_scas=0.02 mM; Vr_scas=0.035 mM_per_min; Ksuc_scas=5.0 mM Reaction: sca => suc, Rate Law: cell*(Vf_scas*sca/Ksca_scas-Vr_scas*suc/Ksuc_scas)/(1+sca/Ksca_scas+suc/Ksuc_scas)
Kaca_cs=0.03 mM; Kcit_cs=0.7 mM; Vf_cs=91.2 mM_per_min; Koaa_cs=0.07 mM; Kcoa_cs=0.3 mM; Vr_cs=0.912 mM_per_min Reaction: aca + oaa => coa + cit, Rate Law: cell*(Vf_cs*aca/Kaca_cs*oaa/Koaa_cs-Vr_cs*coa/Kcoa_cs*cit/Kcit_cs)/((1+aca/Kaca_cs+coa/Kcoa_cs)*(1+oaa/Koaa_cs+cit/Kcit_cs))
Vr_sdh=7.31 mM_per_min; Vf_sdh=7.38 mM_per_min; Ksuc_sdh=0.02 mM; Kfa_sdh=0.4 mM Reaction: suc => fa, Rate Law: cell*(Vf_sdh*suc/Ksuc_sdh-Vr_sdh*fa/Kfa_sdh)/(1+suc/Ksuc_sdh+fa/Kfa_sdh)
Koaa_mdh=0.04 mM; Kmal_mdh=2.6 mM; Vr_mdh=353.11 mM_per_min; Vf_mdh=356.64 mM_per_min Reaction: mal => oaa, Rate Law: cell*(Vf_mdh*mal/Kmal_mdh-Vr_mdh*oaa/Koaa_mdh)/(1+mal/Kmal_mdh+oaa/Koaa_mdh)
Ksuc_icl=0.59 mM; Kgly_icl=0.13 mM; Vf_icl=1.9 mM_per_min; Vr_icl=0.019 mM_per_min; Kicit_icl=0.604 mM Reaction: icit => suc + gly, Rate Law: cell*(Vf_icl*icit/Kicit_icl-Vr_icl*suc/Ksuc_icl*gly/Kgly_icl)/(1+icit/Kicit_icl+suc/Ksuc_icl+gly/Kgly_icl+icit/Kicit_icl*suc/Ksuc_icl+suc/Ksuc_icl*gly/Kgly_icl)
Vf_fum=44.64 mM_per_min; Vr_fum=37.2 mM_per_min; Kmal_fum=0.04 mM; Kfa_fum=0.15 mM Reaction: fa => mal, Rate Law: cell*(Vf_fum*fa/Kfa_fum-Vr_fum*mal/Kmal_fum)/(1+fa/Kfa_fum+mal/Kmal_fum)
Kicit_acn=3.33 mM; Vr_acn=0.912 mM_per_min; Kcit_acn=1.7 mM; Vf_acn=91.2 mM_per_min Reaction: cit => icit, Rate Law: cell*(Vf_acn*cit/Kcit_acn-Vr_acn*icit/Kicit_acn)/(1+cit/Kcit_acn+icit/Kicit_acn)
Kakg_kdh=0.1 mM; Vr_kdh=0.3584 mM_per_min; Vf_kdh=35.84 mM_per_min; Ksca_kdh=1.0 mM Reaction: akg => sca, Rate Law: cell*(Vf_kdh*akg/Kakg_kdh-Vr_kdh*sca/Ksca_kdh)/(1+akg/Kakg_kdh+sca/Ksca_kdh)
Kakg_icd=0.13 mM; Kicit_icd=0.008 mM; Vr_icd=0.1472 mM_per_min; Vf_icd=14.72 mM_per_min Reaction: icit => akg, Rate Law: cell*(Vf_icd*icit/Kicit_icd-Vr_icd*akg/Kakg_icd)/(1+icit/Kicit_icd+akg/Kakg_icd)
Kmal_ms=1.0 mM; Vf_ms=1.9 mM_per_min; Vr_ms=0.019 mM_per_min; Kgly_ms=2.0 mM; Kcoa_ms=0.1 mM; Kaca_ms=0.01 mM Reaction: gly + aca => mal + coa, Rate Law: cell*(Vf_ms*gly/Kgly_ms*aca/Kaca_ms-Vr_ms*mal/Kmal_ms*coa/Kcoa_ms)/((1+gly/Kgly_ms+mal/Kmal_ms)*(1+aca/Kaca_ms+coa/Kcoa_ms))

States:

Name Description
gly [glyoxylic acid; Glyoxylate]
icit [isocitric acid; Isocitrate]
coa [coenzyme A; C000010]
mal [malic acid; Malate]
akg [2-oxoglutaric acid; 2-Oxoglutarate]
aca [acetyl-CoA; Acetyl-CoA]
cit [citric acid; Citrate]
fa [fumaric acid; Fumarate]
biosyn biosyn
oaa [oxaloacetic acid; Oxaloacetate]
suc [succinic acid; Succinate]
sca [succinyl-CoA; Succinyl-CoA]

Observables: none

BIOMD0000000219 @ v0.0.1

This a model from the article: Kinetic modeling of tricarboxylic acid cycle and glyoxylate bypass in Mycobacterium tub…

BACKGROUND: Targeting persistent tubercule bacilli has become an important challenge in the development of anti-tuberculous drugs. As the glyoxylate bypass is essential for persistent bacilli, interference with it holds the potential for designing new antibacterial drugs. We have developed kinetic models of the tricarboxylic acid cycle and glyoxylate bypass in Escherichia coli and Mycobacterium tuberculosis, and studied the effects of inhibition of various enzymes in the M. tuberculosis model. RESULTS: We used E. coli to validate the pathway-modeling protocol and showed that changes in metabolic flux can be estimated from gene expression data. The M. tuberculosis model reproduced the observation that deletion of one of the two isocitrate lyase genes has little effect on bacterial growth in macrophages, but deletion of both genes leads to the elimination of the bacilli from the lungs. It also substantiated the inhibition of isocitrate lyases by 3-nitropropionate. On the basis of our simulation studies, we propose that: (i) fractional inactivation of both isocitrate dehydrogenase 1 and isocitrate dehydrogenase 2 is required for a flux through the glyoxylate bypass in persistent mycobacteria; and (ii) increasing the amount of active isocitrate dehydrogenases can stop the flux through the glyoxylate bypass, so the kinase that inactivates isocitrate dehydrogenase 1 and/or the proposed inactivator of isocitrate dehydrogenase 2 is a potential target for drugs against persistent mycobacteria. In addition, competitive inhibition of isocitrate lyases along with a reduction in the inactivation of isocitrate dehydrogenases appears to be a feasible strategy for targeting persistent mycobacteria. CONCLUSION: We used kinetic modeling of biochemical pathways to assess various potential anti-tuberculous drug targets that interfere with the glyoxylate bypass flux, and indicated the type of inhibition needed to eliminate the pathogen. The advantage of such an approach to the assessment of drug targets is that it facilitates the study of systemic effect(s) of the modulation of the target enzyme(s) in the cellular environment. link: http://identifiers.org/pubmed/16887020

Parameters:

Name Description
Ksuc_ssadh=0.15 mM; Vr_ssadh=0.0651 mM_per_min; Vf_ssadh=6.51 mM_per_min; Kssa_ssadh=0.015 mM Reaction: ssa => suc, Rate Law: cell*(Vf_ssadh*ssa/Kssa_ssadh-Vr_ssadh*suc/Ksuc_ssadh)/(1+ssa/Kssa_ssadh+suc/Ksuc_ssadh)
Vr_scas=0.012 mM_per_min; Ksca_scas=0.02 mM; Vf_scas=1.2 mM_per_min; Ksuc_scas=5.0 mM Reaction: sca => suc, Rate Law: cell*(Vf_scas*sca/Ksca_scas-Vr_scas*suc/Ksuc_scas)/(1+sca/Ksca_scas+suc/Ksuc_scas)
Kakg_kgd=0.48 mM; Vr_kgd=0.483 mM_per_min; Vf_kgd=48.3 mM_per_min; Kssa_kgd=4.8 mM Reaction: akg => ssa, Rate Law: cell*(Vf_kgd*akg/Kakg_kgd-Vr_kgd*ssa/Kssa_kgd)/(1+akg/Kakg_kgd+ssa/Kssa_kgd)
Vr_icl1=0.01172 mM_per_min; Kicit_icl1=0.145 mM; Ksuc_icl1=0.59 mM; Vf_icl1=1.172 mM_per_min; Kgly_icl1=0.13 mM Reaction: icit => suc + gly, Rate Law: cell*(Vf_icl1*icit/Kicit_icl1-Vr_icl1*suc/Ksuc_icl1*gly/Kgly_icl1)/(1+icit/Kicit_icl1+suc/Ksuc_icl1+gly/Kgly_icl1+icit/Kicit_icl1*suc/Ksuc_icl1+suc/Ksuc_icl1*gly/Kgly_icl1)
Kfa_sdh=0.15 mM; Ksuc_sdh=0.12 mM; Vf_sdh=1.02 mM_per_min; Vr_sdh=1.02 mM_per_min Reaction: suc => fa, Rate Law: cell*(Vf_sdh*suc/Ksuc_sdh-Vr_sdh*fa/Kfa_sdh)/(1+suc/Ksuc_sdh+fa/Kfa_sdh)
Kakg_icd1=0.3 mM; Vf_icd1=10.2 mM_per_min; Vr_icd1=0.102 mM_per_min; Kicit_icd1=0.03 mM Reaction: icit => akg, Rate Law: cell*(Vf_icd1*icit/Kicit_icd1-Vr_icd1*akg/Kakg_icd1)/(1+icit/Kicit_icd1+akg/Kakg_icd1)
Vr_icd2=0.09965 mM_per_min; Kakg_icd2=0.6 mM; Vf_icd2=9.965 mM_per_min; Kicit_icd2=0.06 mM Reaction: icit => akg, Rate Law: cell*(Vf_icd2*icit/Kicit_icd2-Vr_icd2*akg/Kakg_icd2)/(1+icit/Kicit_icd2+akg/Kakg_icd2)
Kakg_kdh=0.1 mM; Ksca_kdh=1.0 mM; Vr_kdh=0.57344 mM_per_min; Vf_kdh=57.344 mM_per_min Reaction: akg => sca, Rate Law: cell*(Vf_kdh*akg/Kakg_kdh-Vr_kdh*sca/Ksca_kdh)/(1+akg/Kakg_kdh+sca/Ksca_kdh)
Kakg_icd1=0.3 mM; Vf_icd1=10.2 mM_per_min; Vr_icd2=0.09965 mM_per_min; Kakg_icd2=0.6 mM; Vr_icd1=0.102 mM_per_min; Vf_icd2=9.965 mM_per_min; Kicit_icd1=0.03 mM; Kicit_icd2=0.06 mM Reaction: akg => biosyn; icit, Rate Law: cell*0.0341*((Vf_icd1*icit/Kicit_icd1-Vr_icd1*akg/Kakg_icd1)/(1+icit/Kicit_icd1+akg/Kakg_icd1)+(Vf_icd2*icit/Kicit_icd2-Vr_icd2*akg/Kakg_icd2)/(1+icit/Kicit_icd2+akg/Kakg_icd2))
Vr_cs=0.648 mM_per_min; Kaca_cs=0.05 mM; Kcit_cs=0.12 mM; Kcoa_cs=0.5 mM; Vf_cs=64.8 mM_per_min; Koaa_cs=0.012 mM Reaction: aca + oaa => coa + cit, Rate Law: cell*(Vf_cs*aca/Kaca_cs*oaa/Koaa_cs-Vr_cs*coa/Kcoa_cs*cit/Kcit_cs)/((1+aca/Kaca_cs+coa/Kcoa_cs)*(1+oaa/Koaa_cs+cit/Kcit_cs))
Vr_acn=0.312 mM_per_min; Kicit_acn=0.7 mM; Vf_acn=31.2 mM_per_min; Kcit_acn=1.7 mM Reaction: cit => icit, Rate Law: cell*(Vf_acn*cit/Kcit_acn-Vr_acn*icit/Kicit_acn)/(1+cit/Kcit_acn+icit/Kicit_acn)
Kmal_fum=2.38 mM; Kfa_fum=0.25 mM; Vr_fum=87.7 mM_per_min; Vf_fum=87.7 mM_per_min Reaction: fa => mal, Rate Law: cell*(Vf_fum*fa/Kfa_fum-Vr_fum*mal/Kmal_fum)/(1+fa/Kfa_fum+mal/Kmal_fum)
Kicit_icl2=1.3 mM; Kgly_icl2=1.3 mM; Vr_icl2=0.00391 mM_per_min; Ksuc_icl2=5.9 mM; Vf_icl2=0.391 mM_per_min Reaction: icit => suc + gly, Rate Law: cell*(Vf_icl2*icit/Kicit_icl2-Vr_icl2*suc/Ksuc_icl2*gly/Kgly_icl2)/(1+icit/Kicit_icl2+suc/Ksuc_icl2+gly/Kgly_icl2+icit/Kicit_icl2*suc/Ksuc_icl2+suc/Ksuc_icl2*gly/Kgly_icl2)
Koaa_mdh=0.0443 mM; Vr_mdh=184.0 mM_per_min; Kmal_mdh=0.833 mM; Vf_mdh=184.0 mM_per_min Reaction: mal => oaa, Rate Law: cell*(Vf_mdh*mal/Kmal_mdh-Vr_mdh*oaa/Koaa_mdh)/(1+mal/Kmal_mdh+oaa/Koaa_mdh)
Kmal_ms=1.0 mM; Vf_ms=20.0 mM_per_min; Kgly_ms=0.057 mM; Kaca_ms=0.03 mM; Vr_ms=0.2 mM_per_min; Kcoa_ms=0.1 mM Reaction: gly + aca => mal + coa, Rate Law: cell*(Vf_ms*gly/Kgly_ms*aca/Kaca_ms-Vr_ms*mal/Kmal_ms*coa/Kcoa_ms)/((1+gly/Kgly_ms+mal/Kmal_ms)*(1+aca/Kaca_ms+coa/Kcoa_ms))

States:

Name Description
gly [glyoxylic acid; Glyoxylate]
icit [isocitric acid; Isocitrate]
coa [coenzyme A; CoA]
mal [malic acid; Malate]
ssa [succinic semialdehyde; Succinate semialdehyde]
akg [2-oxoglutaric acid; 2-Oxoglutarate]
aca [acetyl-CoA; Acetyl-CoA]
cit [citric acid; Citrate]
oaa [oxaloacetic acid; Oxaloacetate]
biosyn biosyn
fa [fumaric acid; Fumarate]
suc [succinic acid; Succinate]
sca [succinyl-CoA; Succinyl-CoA]

Observables: none

BIOMD0000000218 @ v0.0.1

This a model from the article: Kinetic modeling of tricarboxylic acid cycle and glyoxylate bypass in Mycobacterium tub…

BACKGROUND: Targeting persistent tubercule bacilli has become an important challenge in the development of anti-tuberculous drugs. As the glyoxylate bypass is essential for persistent bacilli, interference with it holds the potential for designing new antibacterial drugs. We have developed kinetic models of the tricarboxylic acid cycle and glyoxylate bypass in Escherichia coli and Mycobacterium tuberculosis, and studied the effects of inhibition of various enzymes in the M. tuberculosis model. RESULTS: We used E. coli to validate the pathway-modeling protocol and showed that changes in metabolic flux can be estimated from gene expression data. The M. tuberculosis model reproduced the observation that deletion of one of the two isocitrate lyase genes has little effect on bacterial growth in macrophages, but deletion of both genes leads to the elimination of the bacilli from the lungs. It also substantiated the inhibition of isocitrate lyases by 3-nitropropionate. On the basis of our simulation studies, we propose that: (i) fractional inactivation of both isocitrate dehydrogenase 1 and isocitrate dehydrogenase 2 is required for a flux through the glyoxylate bypass in persistent mycobacteria; and (ii) increasing the amount of active isocitrate dehydrogenases can stop the flux through the glyoxylate bypass, so the kinase that inactivates isocitrate dehydrogenase 1 and/or the proposed inactivator of isocitrate dehydrogenase 2 is a potential target for drugs against persistent mycobacteria. In addition, competitive inhibition of isocitrate lyases along with a reduction in the inactivation of isocitrate dehydrogenases appears to be a feasible strategy for targeting persistent mycobacteria. CONCLUSION: We used kinetic modeling of biochemical pathways to assess various potential anti-tuberculous drug targets that interfere with the glyoxylate bypass flux, and indicated the type of inhibition needed to eliminate the pathogen. The advantage of such an approach to the assessment of drug targets is that it facilitates the study of systemic effect(s) of the modulation of the target enzyme(s) in the cellular environment. link: http://identifiers.org/pubmed/16887020

Parameters:

Name Description
Ksuc_ssadh=0.15 mM; Vr_ssadh=0.0651 mM_per_min; Vf_ssadh=6.51 mM_per_min; Kssa_ssadh=0.015 mM Reaction: ssa => suc, Rate Law: cell*(Vf_ssadh*ssa/Kssa_ssadh-Vr_ssadh*suc/Ksuc_ssadh)/(1+ssa/Kssa_ssadh+suc/Ksuc_ssadh)
Vr_scas=0.012 mM_per_min; Ksca_scas=0.02 mM; Vf_scas=1.2 mM_per_min; Ksuc_scas=5.0 mM Reaction: sca => suc, Rate Law: cell*(Vf_scas*sca/Ksca_scas-Vr_scas*suc/Ksuc_scas)/(1+sca/Ksca_scas+suc/Ksuc_scas)
Kakg_kgd=0.48 mM; Vr_kgd=0.483 mM_per_min; Vf_kgd=48.3 mM_per_min; Kssa_kgd=4.8 mM Reaction: akg => ssa, Rate Law: cell*(Vf_kgd*akg/Kakg_kgd-Vr_kgd*ssa/Kssa_kgd)/(1+akg/Kakg_kgd+ssa/Kssa_kgd)
Vr_icl1=0.01172 mM_per_min; Kicit_icl1=0.145 mM; Ksuc_icl1=0.59 mM; Vf_icl1=1.172 mM_per_min; Kgly_icl1=0.13 mM Reaction: icit => suc + gly, Rate Law: cell*(Vf_icl1*icit/Kicit_icl1-Vr_icl1*suc/Ksuc_icl1*gly/Kgly_icl1)/(1+icit/Kicit_icl1+suc/Ksuc_icl1+gly/Kgly_icl1+icit/Kicit_icl1*suc/Ksuc_icl1+suc/Ksuc_icl1*gly/Kgly_icl1)
Kfa_sdh=0.15 mM; Ksuc_sdh=0.12 mM; Vf_sdh=1.02 mM_per_min; Vr_sdh=1.02 mM_per_min Reaction: suc => fa, Rate Law: cell*(Vf_sdh*suc/Ksuc_sdh-Vr_sdh*fa/Kfa_sdh)/(1+suc/Ksuc_sdh+fa/Kfa_sdh)
Kakg_icd1=0.3 mM; Vf_icd1=10.2 mM_per_min; Vr_icd1=0.102 mM_per_min; Kicit_icd1=0.03 mM Reaction: icit => akg, Rate Law: cell*(Vf_icd1*icit/Kicit_icd1-Vr_icd1*akg/Kakg_icd1)/(1+icit/Kicit_icd1+akg/Kakg_icd1)
Vr_icd2=0.09965 mM_per_min; Kakg_icd2=0.6 mM; Vf_icd2=9.965 mM_per_min; Kicit_icd2=0.06 mM Reaction: icit => akg, Rate Law: cell*(Vf_icd2*icit/Kicit_icd2-Vr_icd2*akg/Kakg_icd2)/(1+icit/Kicit_icd2+akg/Kakg_icd2)
Kakg_icd1=0.3 mM; Vf_icd1=10.2 mM_per_min; Vr_icd2=0.09965 mM_per_min; Kakg_icd2=0.6 mM; Vr_icd1=0.102 mM_per_min; Vf_icd2=9.965 mM_per_min; Kicit_icd1=0.03 mM; Kicit_icd2=0.06 mM Reaction: akg => biosyn; icit, Rate Law: cell*0.0341*((Vf_icd1*icit/Kicit_icd1-Vr_icd1*akg/Kakg_icd1)/(1+icit/Kicit_icd1+akg/Kakg_icd1)+(Vf_icd2*icit/Kicit_icd2-Vr_icd2*akg/Kakg_icd2)/(1+icit/Kicit_icd2+akg/Kakg_icd2))
Vr_cs=0.648 mM_per_min; Kaca_cs=0.05 mM; Kcit_cs=0.12 mM; Kcoa_cs=0.5 mM; Vf_cs=64.8 mM_per_min; Koaa_cs=0.012 mM Reaction: aca + oaa => coa + cit, Rate Law: cell*(Vf_cs*aca/Kaca_cs*oaa/Koaa_cs-Vr_cs*coa/Kcoa_cs*cit/Kcit_cs)/((1+aca/Kaca_cs+coa/Kcoa_cs)*(1+oaa/Koaa_cs+cit/Kcit_cs))
Vr_acn=0.312 mM_per_min; Kicit_acn=0.7 mM; Vf_acn=31.2 mM_per_min; Kcit_acn=1.7 mM Reaction: cit => icit, Rate Law: cell*(Vf_acn*cit/Kcit_acn-Vr_acn*icit/Kicit_acn)/(1+cit/Kcit_acn+icit/Kicit_acn)
Kmal_fum=2.38 mM; Kfa_fum=0.25 mM; Vr_fum=87.7 mM_per_min; Vf_fum=87.7 mM_per_min Reaction: fa => mal, Rate Law: cell*(Vf_fum*fa/Kfa_fum-Vr_fum*mal/Kmal_fum)/(1+fa/Kfa_fum+mal/Kmal_fum)
Kicit_icl2=1.3 mM; Kgly_icl2=1.3 mM; Vr_icl2=0.00391 mM_per_min; Ksuc_icl2=5.9 mM; Vf_icl2=0.391 mM_per_min Reaction: icit => suc + gly, Rate Law: cell*(Vf_icl2*icit/Kicit_icl2-Vr_icl2*suc/Ksuc_icl2*gly/Kgly_icl2)/(1+icit/Kicit_icl2+suc/Ksuc_icl2+gly/Kgly_icl2+icit/Kicit_icl2*suc/Ksuc_icl2+suc/Ksuc_icl2*gly/Kgly_icl2)
Koaa_mdh=0.0443 mM; Vr_mdh=184.0 mM_per_min; Kmal_mdh=0.833 mM; Vf_mdh=184.0 mM_per_min Reaction: mal => oaa, Rate Law: cell*(Vf_mdh*mal/Kmal_mdh-Vr_mdh*oaa/Koaa_mdh)/(1+mal/Kmal_mdh+oaa/Koaa_mdh)
Kmal_ms=1.0 mM; Vf_ms=20.0 mM_per_min; Kgly_ms=0.057 mM; Kaca_ms=0.03 mM; Vr_ms=0.2 mM_per_min; Kcoa_ms=0.1 mM Reaction: gly + aca => mal + coa, Rate Law: cell*(Vf_ms*gly/Kgly_ms*aca/Kaca_ms-Vr_ms*mal/Kmal_ms*coa/Kcoa_ms)/((1+gly/Kgly_ms+mal/Kmal_ms)*(1+aca/Kaca_ms+coa/Kcoa_ms))

States:

Name Description
gly [glyoxylic acid; Glyoxylate]
icit [isocitric acid; Isocitrate]
coa [coenzyme A; CoA]
mal [malic acid; Malate]
ssa [succinic semialdehyde; Succinate semialdehyde]
akg [2-oxoglutaric acid; 2-Oxoglutarate]
aca [acetyl-CoA; Acetyl-CoA]
cit [citric acid; Citrate]
oaa [oxaloacetic acid; Oxaloacetate]
biosyn biosyn
fa [fumaric acid; Fumarate]
suc [succinic acid; Succinate]
sca [succinyl-CoA; Succinyl-CoA]

Observables: none

This a model from the article: Model-Based Quantification of the Systemic Interplay between Glucose and Fatty Acids…

In metabolic diseases such as Type 2 Diabetes and Non-Alcoholic Fatty Liver Disease, the systemic regulation of postprandial metabolite concentrations is disturbed. To understand this dysregulation, a quantitative and temporal understanding of systemic postprandial metabolite handling is needed. Of particular interest is the intertwined regulation of glucose and non-esterified fatty acids (NEFA), due to the association between disturbed NEFA metabolism and insulin resistance. However, postprandial glucose metabolism is characterized by a dynamic interplay of simultaneously responding regulatory mechanisms, which have proven difficult to measure directly. Therefore, we propose a mathematical modelling approach to untangle the systemic interplay between glucose and NEFA in the postprandial period. The developed model integrates data of both the perturbation of glucose metabolism by NEFA as measured under clamp conditions, and postprandial time-series of glucose, insulin, and NEFA. The model can describe independent data not used for fitting, and perturbations of NEFA metabolism result in an increased insulin, but not glucose, response, demonstrating that glucose homeostasis is maintained. Finally, the model is used to show that NEFA may mediate up to 30-45% of the postprandial increase in insulin-dependent glucose uptake at two hours after a glucose meal. In conclusion, the presented model can quantify the systemic interactions of glucose and NEFA in the postprandial state, and may therefore provide a new method to evaluate the disturbance of this interplay in metabolic disease. link: http://identifiers.org/pubmed/26356502

Parameters: none

States: none

Observables: none

Sivakumar2011 - EGF Receptor Signaling Pathway EGFR belongs to the human epidermal receptor (HER) family of receptor ty…

The Notch, Sonic Hedgehog (Shh), Wnt, and EGF pathways have long been known to influence cell fate specification in the developing nervous system. Here we attempted to evaluate the contemporary knowledge about neural stem cell differentiation promoted by various drug-based regulations through a systems biology approach. Our model showed the phenomenon of DAPT-mediated antagonism of Enhancer of split [E(spl)] genes and enhancement of Shh target genes by a SAG agonist that were effectively demonstrated computationally and were consistent with experimental studies. However, in the case of model simulation of Wnt and EGF pathways, the model network did not supply any concurrent results with experimental data despite the fact that drugs were added at the appropriate positions. This paves insight into the potential of crosstalks between pathways considered in our study. Therefore, we manually developed a map of signaling crosstalk, which included the species connected by representatives from Notch, Shh, Wnt, and EGF pathways and highlighted the regulation of a single target gene, Hes-1, based on drug-induced simulations. These simulations provided results that matched with experimental studies. Therefore, these signaling crosstalk models complement as a tool toward the discovery of novel regulatory processes involved in neural stem cell maintenance, proliferation, and differentiation during mammalian central nervous system development. To our knowledge, this is the first report of a simple crosstalk map that highlights the differential regulation of neural stem cell differentiation and underscores the flow of positive and negative regulatory signals modulated by drugs. link: http://identifiers.org/pubmed/21978399

Parameters:

Name Description
kdiss_r6_s144 = 1.0; kass_r6_s144 = 1.0 Reaction: s127 => s127; s144, Rate Law: s144*(kass_r6_s144*s127-kdiss_r6_s144*s127)
kM_r14_s27 = 0.038; kM_r14_s28 = 1.65; kcatn_r14 = 0.725; kcatp_r14 = 0.558 Reaction: s27 => s28; s26, Rate Law: s26*(kcatp_r14/kM_r14_s27*s27-kcatn_r14/kM_r14_s28*s28)/(1+s27/kM_r14_s27+s28/kM_r14_s28)
kcatp_r8_s31 = 0.727; kM_r8_s124_s23 = 0.47; kcatn_r8_s31 = 0.636; kM_r8_s31_s23 = 0.614; kI_r8_s29 = 1.219; kM_r8_s31_s24 = 1.367; kI_r8_s22 = 0.583; kcatp_r8_s124 = 0.511; kI_r8_s33 = 0.293; kcatn_r8_s124 = 1.083; kM_r8_s124_s24 = 0.786 Reaction: s23 => s24; s22, s29, s124, s33, s31, Rate Law: kI_r8_s22/(kI_r8_s22+s22)*kI_r8_s29/(kI_r8_s29+s29)*kI_r8_s33/(kI_r8_s33+s33)*(s124*(kcatp_r8_s124/kM_r8_s124_s23*s23-kcatn_r8_s124/kM_r8_s124_s24*s24)/(1+s23/kM_r8_s124_s23+s24/kM_r8_s124_s24)+s31*(kcatp_r8_s31/kM_r8_s31_s23*s23-kcatn_r8_s31/kM_r8_s31_s24*s24)/(1+s23/kM_r8_s31_s23+s24/kM_r8_s31_s24))
kcatp_r9 = 2.0; kcatn_r9 = 0.693; kM_r9_s25 = 0.626; kM_r9_s26 = 0.463 Reaction: s25 => s26; s24, Rate Law: s24*(kcatp_r9/kM_r9_s25*s25-kcatn_r9/kM_r9_s26*s26)/(1+s25/kM_r9_s25+s26/kM_r9_s26)
kass_r15 = 2.0; kdiss_r15 = 0.074 Reaction: s28 => s34, Rate Law: kass_r15*s28-kdiss_r15*s34
kdiss_r4_s144 = 1.0; kass_r4_s144 = 1.0 Reaction: s124 + s125 => s124 + s126; s144, Rate Law: s144*(kass_r4_s144*s124*s125-kdiss_r4_s144*s124*s126)
kI_re11_s142 = 1.0; kM_re11_s129 = 1.0; Vp_re11 = 1.0; ki_re11_s129 = 1.0; kM_re11_s147 = 1.0 Reaction: s129 + s147 => s144; s142, Rate Law: kI_re11_s142/(kI_re11_s142+s142)*Vp_re11*s129*s147/(ki_re11_s129*kM_re11_s147+kM_re11_s147*s129+kM_re11_s129*s147+s129*s147)
kcatn_r11 = 0.566; kM_r11_s30 = 1.021; kM_r11_s29 = 1.459; kcatp_r11 = 0.787 Reaction: s29 => s30; s127, Rate Law: s127*(kcatp_r11/kM_r11_s29*s29-kcatn_r11/kM_r11_s30*s30)/(1+s29/kM_r11_s29+s30/kM_r11_s30)
kass_r17_s3 = 0.73; kdiss_r17_s3 = 1.13 Reaction: s123 => s129; s3, Rate Law: s3*(kass_r17_s3*s123^2-kdiss_r17_s3*s129)
kass_r7_s144 = 1.0; kdiss_r7_s144 = 1.0 Reaction: s21 => s22; s144, Rate Law: s144*(kass_r7_s144*s21-kdiss_r7_s144*s22)

States:

Name Description
s29 [Phosphatidylethanolamine-binding protein 1]
s27 [MAP kinase activity]
s23 [RAF proto-oncogene serine/threonine-protein kinase]
s124 [Ras-like protein 1]
s24 [RAF proto-oncogene serine/threonine-protein kinase]
s25 [Dual specificity mitogen-activated protein kinase kinase 1]
s34 Mitogenesis_br_Differentiation
s30 [Phosphatidylethanolamine-binding protein 1]
s147 [protein complex]
s123 [Receptor protein-tyrosine kinase]
s26 [Dual specificity mitogen-activated protein kinase kinase 1]
s21 [RAC-alpha serine/threonine-protein kinase]
s22 [RAC-alpha serine/threonine-protein kinase]
s28 [MAP kinase activity]
s127 [Protein kinase C alpha type]
s129 [Receptor protein-tyrosine kinase]
s144 [protein complex]
s126 [GTP]
s125 [GDP]

Observables: none

Sivakumar2011 - Hedgehog Signaling Pathway This is the current model for the Hedgehog signaling pathway. The best data…

The Notch, Sonic Hedgehog (Shh), Wnt, and EGF pathways have long been known to influence cell fate specification in the developing nervous system. Here we attempted to evaluate the contemporary knowledge about neural stem cell differentiation promoted by various drug-based regulations through a systems biology approach. Our model showed the phenomenon of DAPT-mediated antagonism of Enhancer of split [E(spl)] genes and enhancement of Shh target genes by a SAG agonist that were effectively demonstrated computationally and were consistent with experimental studies. However, in the case of model simulation of Wnt and EGF pathways, the model network did not supply any concurrent results with experimental data despite the fact that drugs were added at the appropriate positions. This paves insight into the potential of crosstalks between pathways considered in our study. Therefore, we manually developed a map of signaling crosstalk, which included the species connected by representatives from Notch, Shh, Wnt, and EGF pathways and highlighted the regulation of a single target gene, Hes-1, based on drug-induced simulations. These simulations provided results that matched with experimental studies. Therefore, these signaling crosstalk models complement as a tool toward the discovery of novel regulatory processes involved in neural stem cell maintenance, proliferation, and differentiation during mammalian central nervous system development. To our knowledge, this is the first report of a simple crosstalk map that highlights the differential regulation of neural stem cell differentiation and underscores the flow of positive and negative regulatory signals modulated by drugs. link: http://identifiers.org/pubmed/21978399

Parameters:

Name Description
kass_r55 = 1.56 Reaction: s158 => s75, Rate Law: kass_r55*s158
kdiss_r25 = 0.73; kass_r25 = 1.27 Reaction: s160 => s161 + s69, Rate Law: kass_r25*s160-kdiss_r25*s161*s69
kdiss_r23_s21 = 1.0; kass_r23_s21 = 1.0 Reaction: s159 => s68 + s160; s21, Rate Law: s21*(kass_r23_s21*s159-kdiss_r23_s21*s68*s160)
kass_r52 = 0.6; kdiss_r52 = 1.67 Reaction: s140 => s75, Rate Law: kass_r52*s140-kdiss_r52*s75
kass_re24_s157 = 1.0 Reaction: s148 + s150 => s159; s157, Rate Law: s157*kass_re24_s157*s148*s150
kcatp_r53 = 1.29; kM_r53_s70 = 0.79; kcatn_r53 = 1.62 Reaction: s70 => s70; s48, Rate Law: s48*(kcatp_r53/kM_r53_s70*s70-kcatn_r53/kM_r53_s70*s70)/(1+s70/kM_r53_s70+s70/kM_r53_s70)
kass_r54 = 1.28; kdiss_r54 = 0.71 Reaction: s70 + s71 => s158, Rate Law: kass_r54*s70*s71-kdiss_r54*s158
kass_r7 = 1.13; kdiss_r7 = 1.122 Reaction: s7 + s1 => s21, Rate Law: kass_r7*s7*s1-kdiss_r7*s21
kass_r51 = 1.23; kdiss_r51 = 0.46 Reaction: s135 + s128 => s140, Rate Law: kass_r51*s135*s128-kdiss_r51*s140
kass_r15_s21 = 1.53; kdiss_r15_s21 = 0.89 Reaction: s46 + s9 => s48 + s10; s21, Rate Law: s21*(kass_r15_s21*s46*s9-kdiss_r15_s21*s48*s10)
kass_r26 = 1.33; kdiss_r26 = 0.61 Reaction: s161 => s70, Rate Law: kass_r26*s161-kdiss_r26*s70
kM_r14_s46 = 0.215; kcatp_r14 = 1.146; kcatn_r14 = 1.75; kM_r14_s69 = 1.03 Reaction: s69 => s46; s21, Rate Law: s21*(kcatp_r14/kM_r14_s69*s69-kcatn_r14/kM_r14_s46*s46)/(1+s69/kM_r14_s69+s46/kM_r14_s46)

States:

Name Description
s150 [protein complex]
s1 [Protein patched homolog 1]
s48 [protein complex]
s159 [protein complex]
s135 [Sin3-associated polypeptide 18]
s7 [Sonic hedgehog protein]
s68 [microtubule]
s75 [positive regulation of hh target transcription factor activity]
s71 [CREB-binding protein]
s128 [protein complex]
s9 [ATP]
s161 Complex_br_(Su(fu)/Cubitus)
s10 [ADP]
s21 [protein complex]
s148 smoothened
s46 [protein complex]
s70 [Cubitus interruptusCubitus interruptus, isoform A]
s140 [protein complex]
s160 [protein complex]
s69 [protein complex]
s158 [protein complex]

Observables: none

BIOMD0000000396 @ v0.0.1

Sivakumar2011 - Notch Signaling Pathway Notch is a transmembrane receptor that mediates local cell-cell communication a…

The Notch, Sonic Hedgehog (Shh), Wnt, and EGF pathways have long been known to influence cell fate specification in the developing nervous system. Here we attempted to evaluate the contemporary knowledge about neural stem cell differentiation promoted by various drug-based regulations through a systems biology approach. Our model showed the phenomenon of DAPT-mediated antagonism of Enhancer of split [E(spl)] genes and enhancement of Shh target genes by a SAG agonist that were effectively demonstrated computationally and were consistent with experimental studies. However, in the case of model simulation of Wnt and EGF pathways, the model network did not supply any concurrent results with experimental data despite the fact that drugs were added at the appropriate positions. This paves insight into the potential of crosstalks between pathways considered in our study. Therefore, we manually developed a map of signaling crosstalk, which included the species connected by representatives from Notch, Shh, Wnt, and EGF pathways and highlighted the regulation of a single target gene, Hes-1, based on drug-induced simulations. These simulations provided results that matched with experimental studies. Therefore, these signaling crosstalk models complement as a tool toward the discovery of novel regulatory processes involved in neural stem cell maintenance, proliferation, and differentiation during mammalian central nervous system development. To our knowledge, this is the first report of a simple crosstalk map that highlights the differential regulation of neural stem cell differentiation and underscores the flow of positive and negative regulatory signals modulated by drugs. link: http://identifiers.org/pubmed/21978399

Parameters:

Name Description
kdiss_r13 = 2.0; kass_r13 = 0.5 Reaction: s24 + s26 + s27 + s29 => s35, Rate Law: kass_r13*s24*s26*s27*s29-kdiss_r13*s35
kcatn_r16 = 1.0; kcatp_r16 = 1.0; kM_r16_s39 = 1.0; ki_r16_s39 = 1.0 Reaction: s24 + s39 => s37; s38, Rate Law: (kcatp_r16/(ki_r16_s39*kM_r16_s39)*s38*s24*s39-kcatn_r16/kM_r16_s39*s38*s37)/(1+s24/ki_r16_s39+s39/ki_r16_s39+s24*s39/(ki_r16_s39*kM_r16_s39)+s37/kM_r16_s39)
kcatp_r9 = 1.5; kM_r9_s22 = 0.05; kcatn_r9 = 0.04; kM_r9_s7 = 1.0 Reaction: s7 => s22; s23, Rate Law: s23*(kcatp_r9/kM_r9_s7*s7-kcatn_r9/kM_r9_s22*s22)/(1+s7/kM_r9_s7+s22/kM_r9_s22)
kM_r18_s4 = 1.0; ki_r18_s4 = 1.5; kcatn_r18 = 1.5; kcatp_r18 = 1.0 Reaction: s1 + s4 => s41; s42, Rate Law: (kcatp_r18/(ki_r18_s4*kM_r18_s4)*s42*s1*s4-kcatn_r18/kM_r18_s4*s42*s41)/(1+s1/ki_r18_s4+s4/ki_r18_s4+s1*s4/(ki_r18_s4*kM_r18_s4)+s41/kM_r18_s4)
kcatp_r28 = 1.71; ki_r28_s41 = 1.28; kcatn_r28 = 1.48; kM_r28_s41 = 1.64 Reaction: s7 + s41 => s67; s2, Rate Law: (kcatp_r28/(ki_r28_s41*kM_r28_s41)*s2*s7*s41-kcatn_r28/kM_r28_s41*s2*s67)/(1+s7/ki_r28_s41+s41/ki_r28_s41+s7*s41/(ki_r28_s41*kM_r28_s41)+s67/kM_r28_s41)
kI_r21_s2 = 1.5; kass_r21 = 1.5; kdiss_r21 = 1.5 Reaction: s41 + s48 => s53; s2, Rate Law: kI_r21_s2/(kI_r21_s2+s2)*(kass_r21*s41*s48-kdiss_r21*s53)
kM_r26_s25 = 1.7; kM_r26_s64 = 1.61; kcatn_r26 = 1.0; kcatp_r26 = 0.5 Reaction: s25 => s64; s65, Rate Law: s65*(kcatp_r26/kM_r26_s25*s25-kcatn_r26/kM_r26_s64*s64)/(1+s25/kM_r26_s25+s64/kM_r26_s64)
kM_r25_s15 = 1.5; kM_r25_s53 = 1.5; kcatn_r25 = 1.5; kM_r25_s60 = 1.25; kcatp_r25 = 1.0 Reaction: s53 => s60 + s15; s21, Rate Law: s21*(kcatp_r25*s53/kM_r25_s53-kcatn_r25*s60/kM_r25_s60*s15/kM_r25_s15)/(s53/kM_r25_s53+(1+s60/kM_r25_s60)*(1+s15/kM_r25_s15))
kcatp_r29 = 1.86; kM_r29_s67 = 1.61; kM_r29_s18 = 0.15; kM_r29_s15 = 1.87; kcatn_r29 = 1.78 Reaction: s67 => s18 + s15; s21, Rate Law: s21*(kcatp_r29*s67/kM_r29_s67-kcatn_r29*s18/kM_r29_s18*s15/kM_r29_s15)/(s67/kM_r29_s67+(1+s18/kM_r29_s18)*(1+s15/kM_r29_s15))
kM_r8_s63 = 1.5; kcatp_r8 = 0.5; kcatn_r8 = 1.5; kM_r8_s15 = 1.0; kM_r8_s19 = 2.0 Reaction: s15 => s19 + s63; s82, Rate Law: s82*(kcatp_r8*s15/kM_r8_s15-kcatn_r8*s19/kM_r8_s19*s63/kM_r8_s63)/(s15/kM_r8_s15+(1+s19/kM_r8_s19)*(1+s63/kM_r8_s63))
kI_re16_s81 = 0.00594; kass_re16 = 0.004; kdiss_re16 = 2.0 Reaction: s76 + s77 => s82; s81, Rate Law: kI_re16_s81/(kI_re16_s81+s81)*(kass_re16*s76*s77-kdiss_re16*s82)
kass_r31 = 0.055; kdiss_r31 = 2.0 Reaction: s35 => s75, Rate Law: kass_r31*s35-kdiss_r31*s75
kdiss_r10 = 0.01; kI_r10_s25 = 1.0; kass_r10 = 2.0 Reaction: s63 => s24; s25, Rate Law: kI_r10_s25/(kI_r10_s25+s25)*(kass_r10*s63-kdiss_r10*s24)
kass_r30 = 1.95 Reaction: s32 => s75, Rate Law: kass_r30*s32
kcatp_r11 = 0.5; kM_r11_s32 = 1.0; kcatn_r11 = 0.5; kM_r11_s26 = 1.5; kM_r11_s28 = 1.0 Reaction: s32 => s26 + s28; s24, Rate Law: s24*(kcatp_r11*s32/kM_r11_s32-kcatn_r11*s26/kM_r11_s26*s28/kM_r11_s28)/(s32/kM_r11_s32+(1+s26/kM_r11_s26)*(1+s28/kM_r11_s28))
kass_r17 = 1.5; kdiss_r17 = 1.5 Reaction: s37 => s40, Rate Law: kass_r17*s37-kdiss_r17*s40

States:

Name Description
s76 [CCO:U0000005]
s7 [Delta-like protein 1]
s24 [protein complex]
s35 [protein complex]
s18 [protein complex]
s37 [protein complex]
s40 [protein]
s53 [protein complex]
s19 [protein complex]
s32 [protein complex]
s22 [protein]
s77 [CCO:U0000005]
s15 [protein complex]
s1 [NOTCH1 protein]
s48 [Serrate]
s67 [protein complex]
s63 [protein complex]
s41 [NOTCH1 protein]
s25 [Protein numb homolog]
s75 [Basic helix-loop-helix transcription factorE(Spl)]
s4 [L-fucose]
s82 [Gamma-secretase subunit PEN-2; Gamma-secretase subunit APH-1A]
s26 [Suppressor of hairless protein]
s64 a25_degraded
s28 CoR
s39 [CCO:F0004655]
s60 [protein complex]
s29 [protein]
s27 [Mastermind-like protein 1]

Observables: none

Sivakumar2011_NeuralStemCellDifferentiation_CrosstalkThis model is generated by integrating [BIOMD0000000394](http://ww…

The Notch, Sonic Hedgehog (Shh), Wnt, and EGF pathways have long been known to influence cell fate specification in the developing nervous system. Here we attempted to evaluate the contemporary knowledge about neural stem cell differentiation promoted by various drug-based regulations through a systems biology approach. Our model showed the phenomenon of DAPT-mediated antagonism of Enhancer of split [E(spl)] genes and enhancement of Shh target genes by a SAG agonist that were effectively demonstrated computationally and were consistent with experimental studies. However, in the case of model simulation of Wnt and EGF pathways, the model network did not supply any concurrent results with experimental data despite the fact that drugs were added at the appropriate positions. This paves insight into the potential of crosstalks between pathways considered in our study. Therefore, we manually developed a map of signaling crosstalk, which included the species connected by representatives from Notch, Shh, Wnt, and EGF pathways and highlighted the regulation of a single target gene, Hes-1, based on drug-induced simulations. These simulations provided results that matched with experimental studies. Therefore, these signaling crosstalk models complement as a tool toward the discovery of novel regulatory processes involved in neural stem cell maintenance, proliferation, and differentiation during mammalian central nervous system development. To our knowledge, this is the first report of a simple crosstalk map that highlights the differential regulation of neural stem cell differentiation and underscores the flow of positive and negative regulatory signals modulated by drugs. link: http://identifiers.org/pubmed/21978399

Parameters:

Name Description
kass_re35_s89 = 1.0; kdiss_re35_s89 = 1.0 Reaction: s88 => s73; s89, Rate Law: s89*(kass_re35_s89*s88-kdiss_re35_s89*s73)
kass_re36 = 1.0; kdiss_re36 = 1.0; kI_re36_s101 = 1.0 Reaction: s96 + s98 => s100; s101, Rate Law: kI_re36_s101/(kI_re36_s101+s101)*(kass_re36*s96*s98-kdiss_re36*s100)
kdiss_re33 = 1.0; kass_re33 = 1.0 Reaction: s81 + s83 => s85, Rate Law: kass_re33*s81*s83-kdiss_re33*s85
kdiss_re31 = 1.0; kass_re31 = 1.0 Reaction: s53 + s68 => s72, Rate Law: kass_re31*s53*s68-kdiss_re31*s72
kcatn_re40 = 1.0; kcatp_re40 = 1.0; ki_re40_s124 = 1.0; kM_re40_s124 = 1.0 Reaction: s122 + s124 => s135; s111, Rate Law: (kcatp_re40/(ki_re40_s124*kM_re40_s124)*s111*s122*s124-kcatn_re40/kM_re40_s124*s111*s135)/(1+s122/ki_re40_s124+s124/ki_re40_s124+s122*s124/(ki_re40_s124*kM_re40_s124)+s135/kM_re40_s124)
kass_re34_s85 = 1.0; kass_re34_s89 = 1.0; kdiss_re34_s89 = 1.0; kdiss_re34_s85 = 1.0 Reaction: s88 => s88; s85, s89, Rate Law: s85*(kass_re34_s85*s88-kdiss_re34_s85*s88)+s89*(kass_re34_s89*s88-kdiss_re34_s89*s88)
kM_re29_s60_s58 = 1.0; kV_re29_s60 = 1.0; kG_s57 = 1.0; kM_re29_s60_s53 = 1.0; kM_re29_s60_s57 = 1.0; kG_s58 = 1.0; kG_s53 = 1.0; kI_re29_s61 = 1.0 Reaction: s57 => s53 + s58; s60, s61, Rate Law: kI_re29_s61/(kI_re29_s61+s61)*s60*kV_re29_s60*(s57/kM_re29_s60_s57*(kG_s57*kM_re29_s60_s57/(kG_s53*kM_re29_s60_s53*kG_s58*kM_re29_s60_s58))^(0.5)-s53/kM_re29_s60_s53*s58/kM_re29_s60_s58*(kG_s53*kM_re29_s60_s53*kG_s58*kM_re29_s60_s58/(kG_s57*kM_re29_s60_s57))^(0.5))/(s57/kM_re29_s60_s57+(1+s53/kM_re29_s60_s53)*(1+s58/kM_re29_s60_s58))
kass_re32 = 1.0; kdiss_re32 = 1.0 Reaction: s72 => s73, Rate Law: kass_re32*s72-kdiss_re32*s73
kI_re42_s147 = 1.0; kdiss_re42 = 1.0; kI_re42_s135 = 1.0; kass_re42 = 1.0 Reaction: s142 + s144 => s146; s147, s135, Rate Law: kI_re42_s147/(kI_re42_s147+s147)*kI_re42_s135/(kI_re42_s135+s135)*(kass_re42*s142*s144-kdiss_re42*s146)
kass_re37 = 1.0; kdiss_re37 = 1.0 Reaction: s100 => s73, Rate Law: kass_re37*s100-kdiss_re37*s73
kass_re38 = 1.0; kdiss_re38 = 1.0 Reaction: s107 + s109 => s111, Rate Law: kass_re38*s107*s109-kdiss_re38*s111
kass_re43 = 1.0; kdiss_re43 = 1.0 Reaction: s144 => s73, Rate Law: kass_re43*s144-kdiss_re43*s73

States:

Name Description
s146 [protein complex]
s107 [Protein Wnt-3a]
s111 Complex Wnt-Frzzl
s124 [protein complex]
s135 [protein complex]
s142 [Glycogen synthase kinase-3 beta]
s109 [Frizzled]
s57 [Neurogenic locus Notch protein]
s58 [protein]
s53 [Neurogenic locus notch homolog protein 1]
s122 [Dishevelled, dsh homolog 1 (Drosophila)]
s100 [protein complex]
s81 [Sonic hedgehog protein]
s72 [protein complex]
s96 [Pro-epidermal growth factor]
s98 [EGFR protein]
s144 [Catenin beta-1]
s68 [Recombining binding protein suppressor of hairless]
s73 [139605]
s88 [Smoothened homolog]
s85 [protein complex]
s83 [Protein patched homolog 1]

Observables: none

BIOMD0000000397 @ v0.0.1

Sivakumar2011_WntSignalingPathwayThe secreted protein Wnt activates the heptahelical receptor Frizzled on nieghboring ce…

The Notch, Sonic Hedgehog (Shh), Wnt, and EGF pathways have long been known to influence cell fate specification in the developing nervous system. Here we attempted to evaluate the contemporary knowledge about neural stem cell differentiation promoted by various drug-based regulations through a systems biology approach. Our model showed the phenomenon of DAPT-mediated antagonism of Enhancer of split [E(spl)] genes and enhancement of Shh target genes by a SAG agonist that were effectively demonstrated computationally and were consistent with experimental studies. However, in the case of model simulation of Wnt and EGF pathways, the model network did not supply any concurrent results with experimental data despite the fact that drugs were added at the appropriate positions. This paves insight into the potential of crosstalks between pathways considered in our study. Therefore, we manually developed a map of signaling crosstalk, which included the species connected by representatives from Notch, Shh, Wnt, and EGF pathways and highlighted the regulation of a single target gene, Hes-1, based on drug-induced simulations. These simulations provided results that matched with experimental studies. Therefore, these signaling crosstalk models complement as a tool toward the discovery of novel regulatory processes involved in neural stem cell maintenance, proliferation, and differentiation during mammalian central nervous system development. To our knowledge, this is the first report of a simple crosstalk map that highlights the differential regulation of neural stem cell differentiation and underscores the flow of positive and negative regulatory signals modulated by drugs. link: http://identifiers.org/pubmed/21978399

Parameters:

Name Description
kass_r107 = 0.91; kdiss_r107 = 1.056 Reaction: s239 => s5, Rate Law: kass_r107*s239-kdiss_r107*s5
kass_r67 = 0.86; kdiss_r67 = 0.7 Reaction: s188 + s172 => s305, Rate Law: kass_r67*s188*s172-kdiss_r67*s305
kass_r66 = 1.99; kdiss_r66 = 0.036 Reaction: s183 + s173 => s188, Rate Law: kass_r66*s183*s173-kdiss_r66*s188
kass_re65 = 1.68 Reaction: s260 => s232, Rate Law: kass_re65*s260
kdiss_r105 = 1.62; kass_r105 = 0.48 Reaction: s292 => s37, Rate Law: kass_r105*s292-kdiss_r105*s37
kass_r91 = 0.36; kdiss_r91 = 1.16 Reaction: s266 => s155 + s267, Rate Law: kass_r91*s266-kdiss_r91*s155*s267
kass_r54 = 0.8; kdiss_r54 = 1.7 Reaction: s123 + s75 => s159, Rate Law: kass_r54*s123*s75-kdiss_r54*s159
kass_r58 = 1.74; kdiss_r58 = 0.25 Reaction: s36 => s232, Rate Law: kass_r58*s36-kdiss_r58*s232
kass_r48 = 0.85; kdiss_r48 = 1.36 Reaction: s123 + s46 => s129, Rate Law: kass_r48*s123*s46-kdiss_r48*s129
kass_r1 = 0.784; kdiss_r1 = 0.82 Reaction: s5 + s1 => s16, Rate Law: kass_r1*s5*s1-kdiss_r1*s16
kass_r103 = 0.45; kdiss_r103 = 1.277 Reaction: s288 + s102 => s292, Rate Law: kass_r103*s288*s102-kdiss_r103*s292
kass_r98 = 1.97; kdiss_r98 = 1.09 Reaction: s275 => s101 + s278, Rate Law: kass_r98*s275-kdiss_r98*s101*s278
kass_r63 = 1.77; kdiss_r63 = 0.61 Reaction: s174 + s232 => s176, Rate Law: kass_r63*s174*s232-kdiss_r63*s176
kass_r64 = 1.29; kdiss_r64 = 0.72 Reaction: s176 + s170 => s179, Rate Law: kass_r64*s176*s170-kdiss_r64*s179
kass_r68 = 2.0 Reaction: s305 => s195, Rate Law: kass_r68*s305
kass_r65 = 1.8; kdiss_r65 = 0.004 Reaction: s179 + s171 => s183, Rate Law: kass_r65*s179*s171-kdiss_r65*s183
kdiss_r5 = 0.92; kass_r5 = 1.15 Reaction: s28 + s16 => s27, Rate Law: kass_r5*s28*s16-kdiss_r5*s27
kass_re64 = 0.83 Reaction: s270 => s232, Rate Law: kass_re64*s270
kdiss_r47 = 0.81; kass_r47 = 1.31 Reaction: s121 + s36 => s123, Rate Law: kass_r47*s121*s36-kdiss_r47*s123
kdiss_r106 = 1.13; kass_r106 = 0.05 Reaction: s286 => s30, Rate Law: kass_r106*s286-kdiss_r106*s30
kass_r102 = 0.163; kdiss_r102 = 1.65 Reaction: s286 + s31 => s288, Rate Law: kass_r102*s286*s31-kdiss_r102*s288
kdiss_r96 = 0.183; kass_r96 = 1.45 Reaction: s159 + s268 => s275, Rate Law: kass_r96*s159*s268-kdiss_r96*s275
kass_r92 = 0.58; kdiss_r92 = 0.92 Reaction: s267 => s61 + s260, Rate Law: kass_r92*s267-kdiss_r92*s61*s260
kdiss_r88 = 1.09; kass_r88 = 0.2 Reaction: s252 + s61 => s259, Rate Law: kass_r88*s252*s61-kdiss_r88*s259
kass_r90 = 0.27; kdiss_r90 = 1.028 Reaction: s259 + s268 => s266, Rate Law: kass_r90*s259*s268-kdiss_r90*s266
kass_r85_s30 = 0.7; kdiss_r85_s30 = 0.649 Reaction: s129 + s32 => s245 + s33; s30, Rate Law: s30*(kass_r85_s30*s129*s32-kdiss_r85_s30*s245*s33)
kass_r104_s30 = 0.39; kdiss_r104_s30 = 1.278 Reaction: s107 + s32 => s286 + s33; s27, s30, Rate Law: s30*(kass_r104_s30*s107*s32-kdiss_r104_s30*s286*s33)
kdiss_r99 = 0.854; kass_r99 = 0.51 Reaction: s278 => s164 + s270, Rate Law: kass_r99*s278-kdiss_r99*s164*s270
kI_r86_s304 = 1.43; kass_r86_s37 = 0.87; kdiss_r86_s37 = 1.32 Reaction: s245 + s32 + s32 + s32 => s252 + s33 + s33 + s33; s37, s304, Rate Law: kI_r86_s304/(kI_r86_s304+s304)*s37*(kass_r86_s37*s245*s32*s32*s32-kdiss_r86_s37*s252*s33*s33*s33)

States:

Name Description
s107 Complex_br_(Dishevelled/Beta-Arrestin/_br_Frodo)
s260 [Catenin beta-1]
s159 Complex_br_(Adenomatous Polyposis Coli/Axin/_br_PP2A/_Beta_-Catenin/_br_Siah-1/Ebi)
s172 [CREB-binding protein]
s232 [Catenin beta-1]
s5 [Protein Wnt-3a]
s121 Complex_br_(Axin/PP2A/_br_Adenomatous Polyposis Coli)
s278 Complex_br_(Adenomatous Polyposis Coli/_Beta_-Catenin/_br_Axin/PP2A)
s61 [Beta-TrCP]
s37 [Glycogen synthase kinase-3 beta]
s36 [Catenin beta-1]
s183 Complex_br_(Bcl9/_Beta_-Catenin/_br_TCF/Smad4/_br_Pygo)
s31 [Casein kinase II subunit beta; Casein kinase II subunit alpha]
s266 Complex_br_(Adenomatous Polyposis Coli/Axin/_br_PP2A/Diversin/_br_Casein Kinase 1/_Beta_-Catenin/_br__beta_TrCP/Glycogen Synthase Kinase-3_Beta_)
s46 [Diversin]
s268 Ubiquitin
s129 Complex_br_(Adenomatous Polyposis Coli/Axin/_br_Diversin/_Beta_-Catenin/_br_PP2A)
s1 [Frizzled]
s292 Complex_br_(Dishevelled/Casein Kinase 2/_br_Beta-Arrestin/Frodo/_br_FRAT)
s267 Complex_br_(_beta_TrCP/_Beta_-Catenin)
s75 Complex_br_(Ebi/Siah-1)
s33 [ADP]
s101 Complex_br_(Siah-1/Ebi)
s16 Complex_br_(Wnt/Frizzled)
s179 Complex_br_(TCF/_Beta_-Catenin/_br_Smad4/Bcl9)
s155 Complex_br_(Adenomatous Polyposis Coli/Axin/_br_Diversin/Casein Kinase 1/_br_Glycogen Synthase Kinase-3_Beta_/PP2A)
s28 [Low-density lipoprotein receptor-related protein 6; Low-density lipoprotein receptor-related protein 5]
s174 Complex_br_(TCF/Smad4)
s270 [Catenin beta-1]
s245 Complex_br_(Adenomatous Polyposis Coli/_Beta_-Catenin/_br_Axin/PP2A/_br_Diversin/Casein Kinase 1)
s252 Complex_br_(Adenomatous Polyposis Coli/_Beta_-Catenin/_br_Glycogen Synthase Kinase-3_Beta_/Axin/_br_PP2A/Diversin/_br_Casein Kinase 1)
s239 [Wingless-type MMTV integration site family member 3a]
s32 [ATP]
s170 [B-cell CLL/lymphoma 9 protein]
s195 Wnt Target Genes
s305 Complex_br_(Bcl9/Pygo/../Smad4)
s275 Complex_br_(Adenomatous Polyposis Coli/_Beta_-Catenin/_br_Siah-1/Ebi/_br_Axin/PP2A)
s164 Complex_br_(Adenomatous Polyposis Coli/Axin/_br_PP2A)
s176 Complex_br_(TCF/Smad4/_br__Beta_-Catenin)
s188 Complex_br_(_Beta_-Catenin/TCF/_br_Smad4/Bcl9/_br_Pygo/SWI/_br_SNF)
s30 [Casein kinase I isoform alpha]
s171 [Protein pygopus]
s123 Complex_br_(Adenomatous Polyposis Coli/Axin/_br__Beta_-Catenin/PP2A)
s288 Complex_br_(Dishevelled/Beta-Arrestin/_br_Frodo/Casein Kinase 2)
s173 [SWI/SNF-related matrix-associated actin-dependent regulator of chromatin subfamily A member 5]
s286 Complex_br_(Dishevelled/Beta-Arrestin/_br_Frodo)
s259 Complex_br_(Adenomatous Polyposis Coli/Axin/_br_PP2A/Diversin/_br_Casein Kinase 1/_Beta_-Catenin/_br__beta_TrCP/Glycogen Synthase Kinase-3_Beta_)
s102 [Proto-oncogene FRAT1]
s27 Complex_br_(Frizzled/Wnt/_br_LRP5/6)

Observables: none

This 89-node Boolean model of mammalian growth factor signaling can reproduce oscillations in PI3K signaling in cycling…

The PI3K/AKT signaling pathway plays a role in most cellular functions linked to cancer progression, including cell growth, proliferation, cell survival, tissue invasion and angiogenesis. It is generally recognized that hyperactive PI3K/AKT1 are oncogenic due to their boost to cell survival, cell cycle entry and growth-promoting metabolism. That said, the dynamics of PI3K and AKT1 during cell cycle progression are highly nonlinear. In addition to negative feedback that curtails their activity, protein expression of PI3K subunits has been shown to oscillate in dividing cells. The low-PI3K/low-AKT1 phase of these oscillations is required for cytokinesis, indicating that oncogenic PI3K may directly contribute to genome duplication. To explore this, we construct a Boolean model of growth factor signaling that can reproduce PI3K oscillations and link them to cell cycle progression and apoptosis. The resulting modular model reproduces hyperactive PI3K-driven cytokinesis failure and genome duplication and predicts the molecular drivers responsible for these failures by linking hyperactive PI3K to mis-regulation of Polo-like kinase 1 (Plk1) expression late in G2. To do this, our model captures the role of Plk1 in cell cycle progression and accurately reproduces multiple effects of its loss: G2 arrest, mitotic catastrophe, chromosome mis-segregation / aneuploidy due to premature anaphase, and cytokinesis failure leading to genome duplication, depending on the timing of Plk1 inhibition along the cell cycle. Finally, we offer testable predictions on the molecular drivers of PI3K oscillations, the timing of these oscillations with respect to division, and the role of altered Plk1 and FoxO activity in genome-level defects caused by hyperactive PI3K. Our model is an important starting point for the predictive modeling of cell fate decisions that include AKT1-driven senescence, as well as the non-intuitive effects of drugs that interfere with mitosis. link: http://identifiers.org/pubmed/30875364

Parameters: none

States: none

Observables: none

BIOMD0000000619 @ v0.0.1

# Basic PBPK (Physiologically Based PharmacoKinetic) model of Acetaminophen. This is a basic model of Acetaminophen (APA…

We describe a multi-scale, liver-centric in silico modeling framework for acetaminophen pharmacology and metabolism. We focus on a computational model to characterize whole body uptake and clearance, liver transport and phase I and phase II metabolism. We do this by incorporating sub-models that span three scales; Physiologically Based Pharmacokinetic (PBPK) modeling of acetaminophen uptake and distribution at the whole body level, cell and blood flow modeling at the tissue/organ level and metabolism at the sub-cellular level. We have used standard modeling modalities at each of the three scales. In particular, we have used the Systems Biology Markup Language (SBML) to create both the whole-body and sub-cellular scales. Our modeling approach allows us to run the individual sub-models separately and allows us to easily exchange models at a particular scale without the need to extensively rework the sub-models at other scales. In addition, the use of SBML greatly facilitates the inclusion of biological annotations directly in the model code. The model was calibrated using human in vivo data for acetaminophen and its sulfate and glucuronate metabolites. We then carried out extensive parameter sensitivity studies including the pairwise interaction of parameters. We also simulated population variation of exposure and sensitivity to acetaminophen. Our modeling framework can be extended to the prediction of liver toxicity following acetaminophen overdose, or used as a general purpose pharmacokinetic model for xenobiotics. link: http://identifiers.org/pubmed/27636091

Parameters:

Name Description
QRest = 188.8 Volumetric_Flow Reaction: CArt => CRest, Rate Law: QRest*CArt/VArt
kGutabs = 1.5 first_order_rate_constant Reaction: AGutlumen => CGut, Rate Law: kGutabs*AGutlumen
Kkidney2plasma = 1.0 dimensionless; Qgfr = 0.9438 Volumetric_Flow Reaction: CKidney => CTubules, Rate Law: Qgfr/VKidney*CKidney/Kkidney2plasma
QGut = 74.42 Volumetric_Flow Reaction: CArt => CGut, Rate Law: QGut/VArt*CArt
CLmetabolism = 9.5 first_order_rate_constant; Kliver2plasma = 1.0 dimensionless; Fraction_unbound_plasma = 0.8 dimensionless Reaction: CLiver => CMetabolized, Rate Law: CLmetabolism*CLiver/(Kliver2plasma*Fraction_unbound_plasma)
Ratioblood2plasma = 1.09 dimensionless; Fraction_unbound_plasma = 0.8 dimensionless; KRest2plasma = 1.6 dimensionless; QRest = 188.8 Volumetric_Flow Reaction: CRest => CVen, Rate Law: QRest/VRest*CRest*Ratioblood2plasma/(KRest2plasma*Fraction_unbound_plasma)
QGut = 74.42 Volumetric_Flow; Kliver2plasma = 1.0 dimensionless; QLiver = 19.42 Volumetric_Flow; Ratioblood2plasma = 1.09 dimensionless; Fraction_unbound_plasma = 0.8 dimensionless Reaction: CLiver => CVen, Rate Law: (QLiver+QGut)/VLiver*CLiver*Ratioblood2plasma/(Kliver2plasma*Fraction_unbound_plasma)
QCardiac = 363.0 Volumetric_Flow Reaction: CLung => CArt, Rate Law: QCardiac/VLung*CLung
QLiver = 19.42 Volumetric_Flow Reaction: CArt => CLiver, Rate Law: QLiver/VArt*CArt
QKidney = 80.37 Volumetric_Flow Reaction: CArt => CKidney, Rate Law: QKidney/VArt*CArt
Kkidney2plasma = 1.0 dimensionless; QKidney = 80.37 Volumetric_Flow; Ratioblood2plasma = 1.09 dimensionless; Fraction_unbound_plasma = 0.8 dimensionless Reaction: CKidney => CVen, Rate Law: QKidney/VKidney*CKidney*Ratioblood2plasma/(Kkidney2plasma*Fraction_unbound_plasma)

States:

Name Description
CVen CVen
CArt CArt
CKidney CKidney
CMetabolized CMetabolized
CGut CGut
AGutlumen AGutlumen
CTubules CTubules
CLung CLung
CLiver CLiver
CRest CRest

Observables: none

BIOMD0000000624 @ v0.0.1

Sluka2016 - Acetaminophen metabolism**Liver metabolism of Acetaminophen:** Acetaminophen (APAP) is metabolized in the li…

We describe a multi-scale, liver-centric in silico modeling framework for acetaminophen pharmacology and metabolism. We focus on a computational model to characterize whole body uptake and clearance, liver transport and phase I and phase II metabolism. We do this by incorporating sub-models that span three scales; Physiologically Based Pharmacokinetic (PBPK) modeling of acetaminophen uptake and distribution at the whole body level, cell and blood flow modeling at the tissue/organ level and metabolism at the sub-cellular level. We have used standard modeling modalities at each of the three scales. In particular, we have used the Systems Biology Markup Language (SBML) to create both the whole-body and sub-cellular scales. Our modeling approach allows us to run the individual sub-models separately and allows us to easily exchange models at a particular scale without the need to extensively rework the sub-models at other scales. In addition, the use of SBML greatly facilitates the inclusion of biological annotations directly in the model code. The model was calibrated using human in vivo data for acetaminophen and its sulfate and glucuronate metabolites. We then carried out extensive parameter sensitivity studies including the pairwise interaction of parameters. We also simulated population variation of exposure and sensitivity to acetaminophen. Our modeling framework can be extended to the prediction of liver toxicity following acetaminophen overdose, or used as a general purpose pharmacokinetic model for xenobiotics. link: http://identifiers.org/pubmed/27636091

Parameters:

Name Description
Vmax_2E1_APAP = 2.0E-5 flux; Km_2E1_APAP = 1.29 millimolar Reaction: APAP => NAPQI, Rate Law: Vmax_2E1_APAP*APAP/(Km_2E1_APAP+APAP)
kGsh = 1.0E-4 first_order_rate_constant; GSHmax = 10.0 millimolar Reaction: X1 => GSH, Rate Law: kGsh*(GSHmax-GSH)*compartment
Km_PhaseIIEnzGlu_APAP = 1.0 millimolar; Vmax_PhaseIIEnzGlu_APAP = 0.001 flux Reaction: APAP => APAPconj_Glu, Rate Law: Vmax_PhaseIIEnzGlu_APAP*APAP/(Km_PhaseIIEnzGlu_APAP+APAP)
kNapqiGsh = 0.1 second_order_rate_constant Reaction: GSH + NAPQI => NAPQIGSH, Rate Law: kNapqiGsh*NAPQI*GSH*compartment*compartment
Km_PhaseIIEnzSul_APAP = 0.2 millimolar; Vmax_PhaseIIEnzSul_APAP = 1.75E-4 flux Reaction: APAP => APAPconj_Sul, Rate Law: Vmax_PhaseIIEnzSul_APAP*APAP/(Km_PhaseIIEnzSul_APAP+APAP)

States:

Name Description
APAPconj Sul [paracetamol sulfate]
APAP [paracetamol]
NAPQI [N-acetyl-1,4-benzoquinone imine]
NAPQIGSH [acetaminophen glutathione conjugate]
APAPconj Glu [acetaminophen O-beta-D-glucosiduronic acid]
X1 X1
GSH [glutathione]

Observables: none

This model is from the article: Flux balance analysis: a geometric perspective. Smallbone K, Simeonidis E. J Theor B…

Advances in the field of bioinformatics have led to reconstruction of genome-scale networks for a number of key organisms. The application of physicochemical constraints to these stoichiometric networks allows researchers, through methods such as flux balance analysis, to highlight key sets of reactions necessary to achieve particular objectives. The key benefits of constraint-based analysis lie in the minimal knowledge required to infer systemic properties. However, network degeneracy leads to a large number of flux distributions that satisfy any objective; moreover, these distributions may be dominated by biologically irrelevant internal cycles. By examining the geometry underlying the problem, we define two methods for finding a unique solution within the space of all possible flux distributions; such a solution contains no internal cycles, and is representative of the space as a whole. The first method draws on typical geometric knowledge, but cannot be applied to large networks because of the high computational complexity of the problem. Thus a second method, an iteration of linear programs which scales easily to the genome scale, is defined. The algorithm is run on four recent genome-scale models, and unique flux solutions are found. The algorithm set out here will allow researchers in flux balance analysis to exchange typical solutions to their models in a reproducible format. Moreover, having found a single solution, statistical analyses such as correlations may be performed. link: http://identifiers.org/pubmed/19490860

Parameters: none

States: none

Observables: none

This is the model described in the article: Towards a genome-scale kinetic model of cellular metabolism Smallbone K,…

Advances in bioinformatic techniques and analyses have led to the availability of genome-scale metabolic reconstructions. The size and complexity of such networks often means that their potential behaviour can only be analysed with constraint-based methods. Whilst requiring minimal experimental data, such methods are unable to give insight into cellular substrate concentrations. Instead, the long-term goal of systems biology is to use kinetic modelling to characterize fully the mechanics of each enzymatic reaction, and to combine such knowledge to predict system behaviour.We describe a method for building a parameterized genome-scale kinetic model of a metabolic network. Simplified linlog kinetics are used and the parameters are extracted from a kinetic model repository. We demonstrate our methodology by applying it to yeast metabolism. The resultant model has 956 metabolic reactions involving 820 metabolites, and, whilst approximative, has considerably broader remit than any existing models of its type. Control analysis is used to identify key steps within the system.Our modelling framework may be considered a stepping-stone toward the long-term goal of a fully-parameterized model of yeast metabolism. The model is available in SBML format from the BioModels database (BioModels ID: MODEL1001200000) and at http://www.mcisb.org/resources/genomescale/. link: http://identifiers.org/pubmed/20109182

Parameters: none

States: none

Observables: none

BIOMD0000000380 @ v0.0.1

This model is from the article: Building a Kinetic Model of Trehalose Biosynthesis in Saccharomyces cerevisiae. Smal…

In this chapter, we describe the steps needed to create a kinetic model of a metabolic pathway based on kinetic data from experimental measurements and literature review. Our methodology is presented by utilizing the example of trehalose metabolism in yeast. The biology of the trehalose cycle is briefly reviewed and discussed. link: http://identifiers.org/pubmed/21943906

Parameters:

Name Description
Keq=0.3 dimensionless; Kf6p=0.29 mM; shock=1.0 dimensionless; heat = 0.0 dimensionless; Kg6p=1.4 mM; Vmax=1071.0 mM per min Reaction: g6p => f6p, Rate Law: cell*shock^heat*Vmax/Kg6p*(g6p-f6p/Keq)/(1+g6p/Kg6p+f6p/Kf6p)
Kudg=0.886 mM; activity=1.0 dimensionless; heat = 0.0 dimensionless; Vmax=1.371 mM per min; shock=12.0 dimensionless; Kg6p=3.8 mM Reaction: g6p + udg => t6p + udp + h, Rate Law: cell*activity*shock^heat*Vmax*g6p*udg/(Kg6p*Kudg)/((1+g6p/Kg6p)*(1+udg/Kudg))
Kg1p=0.023 mM; heat = 0.0 dimensionless; Vmax=0.3545 mM per min; Kg6p=0.05 mM; shock=16.0 dimensionless; Keq=0.1667 dimensionless Reaction: g6p => g1p, Rate Law: cell*shock^heat*Vmax/Kg6p*(g6p-g1p/Keq)/(1+g6p/Kg6p+g1p/Kg1p)
Kt6p=0.5 mM; heat = 0.0 dimensionless; Vmax=6.5 mM per min; shock=18.0 dimensionless Reaction: t6p + h2o => trh + pho, Rate Law: cell*shock^heat*Vmax*t6p/Kt6p/(1+t6p/Kt6p)
Kg6p=30.0 mM; Kglc=0.08 mM; Katp=0.15 mM; heat = 0.0 dimensionless; Keq=2000.0 dimensionless; shock=8.0 dimensionless; Vmax=289.6 mM per min; Kadp=0.23 mM; Kit6p=0.04 mM Reaction: glc + atp => g6p + adp + h; t6p, Rate Law: cell*shock^heat*Vmax/(Kglc*Katp)*(glc*atp-g6p*adp/Keq)/((1+glc/Kglc+g6p/Kg6p+t6p/Kit6p)*(1+atp/Katp+adp/Kadp))
Vmax=15.2 mM per min; heat = 0.0 dimensionless; shock=6.0 dimensionless; Ktrh=2.99 mM Reaction: trh + h2o => glc, Rate Law: cell*shock^heat*Vmax*trh/Ktrh/(1+trh/Ktrh)
heat = 0.0 dimensionless; Vmax=97.24 mM per min; shock=8.0 dimensionless; Ki=0.91 dimensionless; Kglc=1.1918 mM Reaction: glx => glc, Rate Law: cell*shock^heat*Vmax*(glx-glc)/Kglc/(1+(glx+glc)/Kglc+Ki*glx*glc/Kglc^2)
Kiutp=0.11 mM; heat = 0.0 dimensionless; Kg1p=0.32 mM; Kutp=0.11 mM; Vmax=36.82 mM per min; shock=16.0 dimensionless; Kiudg=0.0035 mM Reaction: g1p + utp + h => udg + ppi, Rate Law: cell*shock^heat*Vmax*utp*g1p/(Kutp*Kg1p)/(Kiutp/Kutp+utp/Kutp+g1p/Kg1p+utp*g1p/(Kutp*Kg1p)+Kiutp/Kutp*udg/Kiudg+g1p*udg/(Kg1p*Kiudg))

States:

Name Description
ppi [diphosphate(4-)]
glx [alpha-D-glucose]
trh [alpha,alpha-trehalose]
pho [hydrogenphosphate]
glc [alpha-D-glucose]
h2o [water]
h [proton]
udp [UDP]
atp [ATP]
utp [UTP(4-)]
g6p [alpha-D-glucose 6-phosphate]
adp [ADP]
t6p [alpha,alpha-trehalose 6-phosphate]
f6p [beta-D-fructofuranose 6-phosphate]
udg [UDP-D-glucose]
g1p [D-glucopyranose 1-phosphate]

Observables: none

Smallbone2013 - Colon Crypt cycle - Version 0This model is described in the article: [A mathematical model of the colon…

Models of the development and early progression of colorectal cancer are based upon understanding the cycle of stem cell turnover, proliferation, differentiation and death. Existing crypt compartmental models feature a linear pathway of cell types, with little regulatory mechanism. Previous work has shown that there are perturbations in the enteroendocrine cell population of macroscopically normal crypts, a compartment not included in existing models. We show that existing models do not adequately recapitulate the dynamics of cell fate pathways in the crypt. We report the progressive development, iterative testing and fitting of a developed compartmental model with additional cell types, and which includes feedback mechanisms and cross-regulatory mechanisms between cell types. The fitting of the model to existing data sets suggests a need to invoke cross-talk between cell types as a feature of colon crypt cycle models. link: http://identifiers.org/pubmed/24354351

Parameters:

Name Description
d2 = 1.83 per day Reaction: N2 => ; N2, Rate Law: d2*N2
d1 = 0.263 per day Reaction: N1 => ; N1, Rate Law: d1*N1
b1 = 0.547 per day; m1 = 29.2408052354609 cell; c1 = 1.0 per day Reaction: N1 => N1 + N2; N1, Rate Law: (b1+c1*N1/(N1+m1))*N1
a0 = 0.0999999999999998 per day Reaction: N0 => N0; N0, Rate Law: a0*N0
b0 = 0.218 per day; c0 = 1.0 per day; m0 = 2.92408052354609 cell Reaction: N0 => N0 + N1; N0, Rate Law: (b0+c0*N0/(N0+m0))*N0
a1 = 0.239254806051979 per day Reaction: N1 => N1; N1, Rate Law: a1*N1
d0 = 0.1 per day Reaction: N0 => ; N0, Rate Law: d0*N0

States:

Name Description
N1 [stem cell]
N0 [stem cell]
N2 [stem cell]

Observables: none

Smallbone2013 - Colon Crypt cycle - Version 1This model is described in the article: [A mathematical model of the colon…

Models of the development and early progression of colorectal cancer are based upon understanding the cycle of stem cell turnover, proliferation, differentiation and death. Existing crypt compartmental models feature a linear pathway of cell types, with little regulatory mechanism. Previous work has shown that there are perturbations in the enteroendocrine cell population of macroscopically normal crypts, a compartment not included in existing models. We show that existing models do not adequately recapitulate the dynamics of cell fate pathways in the crypt. We report the progressive development, iterative testing and fitting of a developed compartmental model with additional cell types, and which includes feedback mechanisms and cross-regulatory mechanisms between cell types. The fitting of the model to existing data sets suggests a need to invoke cross-talk between cell types as a feature of colon crypt cycle models. link: http://identifiers.org/pubmed/24354351

Parameters:

Name Description
p01 = 0.855699855699856 dimensionless; f0 = NaN cell per_day Reaction: N0 => N0 + N1, Rate Law: p01*f0
d1 = 0.420467092599869 per day Reaction: N1 => ; N1, Rate Law: d1*N1
p12 = 0.827377484810943 dimensionless; f1 = NaN cell per_day Reaction: N1 => N1 + N2, Rate Law: p12*f1
d2 = 1.10138534772246 per day Reaction: N2 => ; N2, Rate Law: d2*N2
d0 = 0.1 per day Reaction: N0 => ; N0, Rate Law: d0*N0
f0 = NaN cell per_day; p00 = NaN dimensionless Reaction: N0 => N0, Rate Law: p00*f0
f1 = NaN cell per_day; p11 = NaN dimensionless Reaction: N1 => N1, Rate Law: p11*f1

States:

Name Description
N1 [stem cell]
N0 [stem cell]
N2 [stem cell]

Observables: none

Smallbone2013 - Colon Crypt cycle - Version 2This model is described in the article: [A mathematical model of the colon…

Models of the development and early progression of colorectal cancer are based upon understanding the cycle of stem cell turnover, proliferation, differentiation and death. Existing crypt compartmental models feature a linear pathway of cell types, with little regulatory mechanism. Previous work has shown that there are perturbations in the enteroendocrine cell population of macroscopically normal crypts, a compartment not included in existing models. We show that existing models do not adequately recapitulate the dynamics of cell fate pathways in the crypt. We report the progressive development, iterative testing and fitting of a developed compartmental model with additional cell types, and which includes feedback mechanisms and cross-regulatory mechanisms between cell types. The fitting of the model to existing data sets suggests a need to invoke cross-talk between cell types as a feature of colon crypt cycle models. link: http://identifiers.org/pubmed/24354351

Parameters:

Name Description
p01 = 0.815689334807208 dimensionless; f0 = NaN cell per_day Reaction: N0 => N0 + N1, Rate Law: p01*f0
p12 = 0.827377484810943 dimensionless; f1 = NaN cell per_day Reaction: N1 => N1 + N2, Rate Law: p12*f1
f0 = NaN cell per_day; p03 = NaN dimensionless Reaction: N0 => N0 + N3, Rate Law: p03*f0
d2 = 2.20277069544492 per day; K2X = 1.5709821429 cell Reaction: N2 => ; N3, N2, N3, Rate Law: d2*N2*K2X/(N3+K2X)
K1X = 1.5709821429 cell; d1 = 0.840934185199738 per day Reaction: N1 => ; N3, N1, N3, Rate Law: d1*N1*K1X/(N3+K1X)
d3 = 0.0379622536021846 per day Reaction: N3 => ; N3, Rate Law: d3*N3
d0 = 0.2 per day; K0X = 1.5709821429 cell Reaction: N0 => ; N3, N0, N3, Rate Law: d0*N0*K0X/(N3+K0X)
f1 = NaN cell per_day; p11 = NaN dimensionless Reaction: N1 => N1, Rate Law: p11*f1
f0 = NaN cell per_day; p00 = NaN dimensionless Reaction: N0 => N0, Rate Law: p00*f0

States:

Name Description
N2 [stem cell]
N1 [stem cell]
N0 [stem cell]
N3 N3

Observables: none

Smallbone2013 - Colon Crypt cycle - Version 3This model is described in the article: [A mathematical model of the colon…

Models of the development and early progression of colorectal cancer are based upon understanding the cycle of stem cell turnover, proliferation, differentiation and death. Existing crypt compartmental models feature a linear pathway of cell types, with little regulatory mechanism. Previous work has shown that there are perturbations in the enteroendocrine cell population of macroscopically normal crypts, a compartment not included in existing models. We show that existing models do not adequately recapitulate the dynamics of cell fate pathways in the crypt. We report the progressive development, iterative testing and fitting of a developed compartmental model with additional cell types, and which includes feedback mechanisms and cross-regulatory mechanisms between cell types. The fitting of the model to existing data sets suggests a need to invoke cross-talk between cell types as a feature of colon crypt cycle models. link: http://identifiers.org/pubmed/24354351

Parameters:

Name Description
d2 = 1.888676618 per day; K2X = 2.70405837954268 cell Reaction: N2 => ; N3, N2, N3, Rate Law: d2*N2*K2X/(N3+K2X)
f0 = NaN cell per_day; p03 = NaN dimensionless Reaction: N0 => N0 + N3, Rate Law: p03*f0
d3 = 0.1677359306 per day Reaction: N3 => ; N3, Rate Law: d3*N3
d0 = 0.02 per day; K0X = 0.153646265911768 cell Reaction: N0 => ; N3, N0, N3, Rate Law: d0*N0*K0X/(N3+K0X)
p12 = 0.8050459589 dimensionless; f1 = NaN cell per_day Reaction: N1 => N1 + N2, Rate Law: p12*f1
K1X = 15.3645644864404 cell; d1 = 0.5480597115 per day Reaction: N1 => ; N3, N1, N3, Rate Law: d1*N1*K1X/(N3+K1X)
p01 = 0.6313780928 dimensionless; f0 = NaN cell per_day Reaction: N0 => N0 + N1, Rate Law: p01*f0
f0 = NaN cell per_day; p00 = NaN dimensionless Reaction: N0 => N0, Rate Law: p00*f0
f1 = NaN cell per_day; p11 = NaN dimensionless Reaction: N1 => N1, Rate Law: p11*f1

States:

Name Description
N3 N3
N1 [stem cell]
N0 [stem cell]
N2 [stem cell]

Observables: none

Smallbone2013 - Glycolysis in S.cerevisiae - Iteration 00This model is described in the article: [A model of yeast glyc…

We present an experimental and computational pipeline for the generation of kinetic models of metabolism, and demonstrate its application to glycolysis in Saccharomyces cerevisiae. Starting from an approximate mathematical model, we employ a "cycle of knowledge" strategy, identifying the steps with most control over flux. Kinetic parameters of the individual isoenzymes within these steps are measured experimentally under a standardised set of conditions. Experimental strategies are applied to establish a set of in vivo concentrations for isoenzymes and metabolites. The data are integrated into a mathematical model that is used to predict a new set of metabolite concentrations and reevaluate the control properties of the system. This bottom-up modelling study reveals that control over the metabolic network most directly involved in yeast glycolysis is more widely distributed than previously thought. link: http://identifiers.org/pubmed/23831062

Parameters: none

States: none

Observables: none

Smallbone2013 - Glycolysis in S.cerevisiae - Iteration 01This model is described in the article: [A model of yeast glyc…

We present an experimental and computational pipeline for the generation of kinetic models of metabolism, and demonstrate its application to glycolysis in Saccharomyces cerevisiae. Starting from an approximate mathematical model, we employ a "cycle of knowledge" strategy, identifying the steps with most control over flux. Kinetic parameters of the individual isoenzymes within these steps are measured experimentally under a standardised set of conditions. Experimental strategies are applied to establish a set of in vivo concentrations for isoenzymes and metabolites. The data are integrated into a mathematical model that is used to predict a new set of metabolite concentrations and reevaluate the control properties of the system. This bottom-up modelling study reveals that control over the metabolic network most directly involved in yeast glycolysis is more widely distributed than previously thought. link: http://identifiers.org/pubmed/23831062

Parameters: none

States: none

Observables: none

Smallbone2013 - Glycolysis in S.cerevisiae - Iteration 02This model is described in the article: [A model of yeast glyc…

We present an experimental and computational pipeline for the generation of kinetic models of metabolism, and demonstrate its application to glycolysis in Saccharomyces cerevisiae. Starting from an approximate mathematical model, we employ a "cycle of knowledge" strategy, identifying the steps with most control over flux. Kinetic parameters of the individual isoenzymes within these steps are measured experimentally under a standardised set of conditions. Experimental strategies are applied to establish a set of in vivo concentrations for isoenzymes and metabolites. The data are integrated into a mathematical model that is used to predict a new set of metabolite concentrations and reevaluate the control properties of the system. This bottom-up modelling study reveals that control over the metabolic network most directly involved in yeast glycolysis is more widely distributed than previously thought. link: http://identifiers.org/pubmed/23831062

Parameters: none

States: none

Observables: none

Smallbone2013 - Glycolysis in S.cerevisiae - Iteration 03This model is described in the article: [A model of yeast glyc…

We present an experimental and computational pipeline for the generation of kinetic models of metabolism, and demonstrate its application to glycolysis in Saccharomyces cerevisiae. Starting from an approximate mathematical model, we employ a "cycle of knowledge" strategy, identifying the steps with most control over flux. Kinetic parameters of the individual isoenzymes within these steps are measured experimentally under a standardised set of conditions. Experimental strategies are applied to establish a set of in vivo concentrations for isoenzymes and metabolites. The data are integrated into a mathematical model that is used to predict a new set of metabolite concentrations and reevaluate the control properties of the system. This bottom-up modelling study reveals that control over the metabolic network most directly involved in yeast glycolysis is more widely distributed than previously thought. link: http://identifiers.org/pubmed/23831062

Parameters: none

States: none

Observables: none

Smallbone2013 - Glycolysis in S.cerevisiae - Iteration 04This model is described in the article: [A model of yeast glyc…

We present an experimental and computational pipeline for the generation of kinetic models of metabolism, and demonstrate its application to glycolysis in Saccharomyces cerevisiae. Starting from an approximate mathematical model, we employ a "cycle of knowledge" strategy, identifying the steps with most control over flux. Kinetic parameters of the individual isoenzymes within these steps are measured experimentally under a standardised set of conditions. Experimental strategies are applied to establish a set of in vivo concentrations for isoenzymes and metabolites. The data are integrated into a mathematical model that is used to predict a new set of metabolite concentrations and reevaluate the control properties of the system. This bottom-up modelling study reveals that control over the metabolic network most directly involved in yeast glycolysis is more widely distributed than previously thought. link: http://identifiers.org/pubmed/23831062

Parameters: none

States: none

Observables: none

Smallbone2013 - Glycolysis in S.cerevisiae - Iteration 05This model is described in the article: [A model of yeast glyc…

We present an experimental and computational pipeline for the generation of kinetic models of metabolism, and demonstrate its application to glycolysis in Saccharomyces cerevisiae. Starting from an approximate mathematical model, we employ a "cycle of knowledge" strategy, identifying the steps with most control over flux. Kinetic parameters of the individual isoenzymes within these steps are measured experimentally under a standardised set of conditions. Experimental strategies are applied to establish a set of in vivo concentrations for isoenzymes and metabolites. The data are integrated into a mathematical model that is used to predict a new set of metabolite concentrations and reevaluate the control properties of the system. This bottom-up modelling study reveals that control over the metabolic network most directly involved in yeast glycolysis is more widely distributed than previously thought. link: http://identifiers.org/pubmed/23831062

Parameters: none

States: none

Observables: none

Smallbone2013 - Glycolysis in S.cerevisiae - Iteration 06This model is described in the article: [A model of yeast glyc…

We present an experimental and computational pipeline for the generation of kinetic models of metabolism, and demonstrate its application to glycolysis in Saccharomyces cerevisiae. Starting from an approximate mathematical model, we employ a "cycle of knowledge" strategy, identifying the steps with most control over flux. Kinetic parameters of the individual isoenzymes within these steps are measured experimentally under a standardised set of conditions. Experimental strategies are applied to establish a set of in vivo concentrations for isoenzymes and metabolites. The data are integrated into a mathematical model that is used to predict a new set of metabolite concentrations and reevaluate the control properties of the system. This bottom-up modelling study reveals that control over the metabolic network most directly involved in yeast glycolysis is more widely distributed than previously thought. link: http://identifiers.org/pubmed/23831062

Parameters: none

States: none

Observables: none

Smallbone2013 - Glycolysis in S.cerevisiae - Iteration 07This model is described in the article: [A model of yeast glyc…

We present an experimental and computational pipeline for the generation of kinetic models of metabolism, and demonstrate its application to glycolysis in Saccharomyces cerevisiae. Starting from an approximate mathematical model, we employ a "cycle of knowledge" strategy, identifying the steps with most control over flux. Kinetic parameters of the individual isoenzymes within these steps are measured experimentally under a standardised set of conditions. Experimental strategies are applied to establish a set of in vivo concentrations for isoenzymes and metabolites. The data are integrated into a mathematical model that is used to predict a new set of metabolite concentrations and reevaluate the control properties of the system. This bottom-up modelling study reveals that control over the metabolic network most directly involved in yeast glycolysis is more widely distributed than previously thought. link: http://identifiers.org/pubmed/23831062

Parameters: none

States: none

Observables: none

Smallbone2013 - Glycolysis in S.cerevisiae - Iteration 08This model is described in the article: [A model of yeast glyc…

We present an experimental and computational pipeline for the generation of kinetic models of metabolism, and demonstrate its application to glycolysis in Saccharomyces cerevisiae. Starting from an approximate mathematical model, we employ a "cycle of knowledge" strategy, identifying the steps with most control over flux. Kinetic parameters of the individual isoenzymes within these steps are measured experimentally under a standardised set of conditions. Experimental strategies are applied to establish a set of in vivo concentrations for isoenzymes and metabolites. The data are integrated into a mathematical model that is used to predict a new set of metabolite concentrations and reevaluate the control properties of the system. This bottom-up modelling study reveals that control over the metabolic network most directly involved in yeast glycolysis is more widely distributed than previously thought. link: http://identifiers.org/pubmed/23831062

Parameters: none

States: none

Observables: none

Smallbone2013 - Glycolysis in S.cerevisiae - Iteration 09This model is described in the article: [A model of yeast glyc…

We present an experimental and computational pipeline for the generation of kinetic models of metabolism, and demonstrate its application to glycolysis in Saccharomyces cerevisiae. Starting from an approximate mathematical model, we employ a "cycle of knowledge" strategy, identifying the steps with most control over flux. Kinetic parameters of the individual isoenzymes within these steps are measured experimentally under a standardised set of conditions. Experimental strategies are applied to establish a set of in vivo concentrations for isoenzymes and metabolites. The data are integrated into a mathematical model that is used to predict a new set of metabolite concentrations and reevaluate the control properties of the system. This bottom-up modelling study reveals that control over the metabolic network most directly involved in yeast glycolysis is more widely distributed than previously thought. link: http://identifiers.org/pubmed/23831062

Parameters: none

States: none

Observables: none

Smallbone2013 - Glycolysis in S.cerevisiae - Iteration 10This model is described in the article: [A model of yeast glyc…

We present an experimental and computational pipeline for the generation of kinetic models of metabolism, and demonstrate its application to glycolysis in Saccharomyces cerevisiae. Starting from an approximate mathematical model, we employ a "cycle of knowledge" strategy, identifying the steps with most control over flux. Kinetic parameters of the individual isoenzymes within these steps are measured experimentally under a standardised set of conditions. Experimental strategies are applied to establish a set of in vivo concentrations for isoenzymes and metabolites. The data are integrated into a mathematical model that is used to predict a new set of metabolite concentrations and reevaluate the control properties of the system. This bottom-up modelling study reveals that control over the metabolic network most directly involved in yeast glycolysis is more widely distributed than previously thought. link: http://identifiers.org/pubmed/23831062

Parameters: none

States: none

Observables: none

Smallbone2013 - Glycolysis in S.cerevisiae - Iteration 11This model is described in the article: [A model of yeast glyc…

We present an experimental and computational pipeline for the generation of kinetic models of metabolism, and demonstrate its application to glycolysis in Saccharomyces cerevisiae. Starting from an approximate mathematical model, we employ a "cycle of knowledge" strategy, identifying the steps with most control over flux. Kinetic parameters of the individual isoenzymes within these steps are measured experimentally under a standardised set of conditions. Experimental strategies are applied to establish a set of in vivo concentrations for isoenzymes and metabolites. The data are integrated into a mathematical model that is used to predict a new set of metabolite concentrations and reevaluate the control properties of the system. This bottom-up modelling study reveals that control over the metabolic network most directly involved in yeast glycolysis is more widely distributed than previously thought. link: http://identifiers.org/pubmed/23831062

Parameters: none

States: none

Observables: none

Smallbone2013 - Glycolysis in S.cerevisiae - Iteration 12This model is described in the article: [A model of yeast glyc…

We present an experimental and computational pipeline for the generation of kinetic models of metabolism, and demonstrate its application to glycolysis in Saccharomyces cerevisiae. Starting from an approximate mathematical model, we employ a "cycle of knowledge" strategy, identifying the steps with most control over flux. Kinetic parameters of the individual isoenzymes within these steps are measured experimentally under a standardised set of conditions. Experimental strategies are applied to establish a set of in vivo concentrations for isoenzymes and metabolites. The data are integrated into a mathematical model that is used to predict a new set of metabolite concentrations and reevaluate the control properties of the system. This bottom-up modelling study reveals that control over the metabolic network most directly involved in yeast glycolysis is more widely distributed than previously thought. link: http://identifiers.org/pubmed/23831062

Parameters: none

States: none

Observables: none

Smallbone2013 - Glycolysis in S.cerevisiae - Iteration 13This model is described in the article: [A model of yeast glyc…

We present an experimental and computational pipeline for the generation of kinetic models of metabolism, and demonstrate its application to glycolysis in Saccharomyces cerevisiae. Starting from an approximate mathematical model, we employ a "cycle of knowledge" strategy, identifying the steps with most control over flux. Kinetic parameters of the individual isoenzymes within these steps are measured experimentally under a standardised set of conditions. Experimental strategies are applied to establish a set of in vivo concentrations for isoenzymes and metabolites. The data are integrated into a mathematical model that is used to predict a new set of metabolite concentrations and reevaluate the control properties of the system. This bottom-up modelling study reveals that control over the metabolic network most directly involved in yeast glycolysis is more widely distributed than previously thought. link: http://identifiers.org/pubmed/23831062

Parameters: none

States: none

Observables: none

Smallbone2013 - Glycolysis in S.cerevisiae - Iteration 14This model is described in the article: [A model of yeast glyc…

We present an experimental and computational pipeline for the generation of kinetic models of metabolism, and demonstrate its application to glycolysis in Saccharomyces cerevisiae. Starting from an approximate mathematical model, we employ a "cycle of knowledge" strategy, identifying the steps with most control over flux. Kinetic parameters of the individual isoenzymes within these steps are measured experimentally under a standardised set of conditions. Experimental strategies are applied to establish a set of in vivo concentrations for isoenzymes and metabolites. The data are integrated into a mathematical model that is used to predict a new set of metabolite concentrations and reevaluate the control properties of the system. This bottom-up modelling study reveals that control over the metabolic network most directly involved in yeast glycolysis is more widely distributed than previously thought. link: http://identifiers.org/pubmed/23831062

Parameters: none

States: none

Observables: none

Smallbone2013 - Glycolysis in S.cerevisiae - Iteration 15This model is described in the article: [A model of yeast glyc…

We present an experimental and computational pipeline for the generation of kinetic models of metabolism, and demonstrate its application to glycolysis in Saccharomyces cerevisiae. Starting from an approximate mathematical model, we employ a "cycle of knowledge" strategy, identifying the steps with most control over flux. Kinetic parameters of the individual isoenzymes within these steps are measured experimentally under a standardised set of conditions. Experimental strategies are applied to establish a set of in vivo concentrations for isoenzymes and metabolites. The data are integrated into a mathematical model that is used to predict a new set of metabolite concentrations and reevaluate the control properties of the system. This bottom-up modelling study reveals that control over the metabolic network most directly involved in yeast glycolysis is more widely distributed than previously thought. link: http://identifiers.org/pubmed/23831062

Parameters: none

States: none

Observables: none

Smallbone2013 - Glycolysis in S.cerevisiae - Iteration 16This model is described in the article: [A model of yeast glyc…

We present an experimental and computational pipeline for the generation of kinetic models of metabolism, and demonstrate its application to glycolysis in Saccharomyces cerevisiae. Starting from an approximate mathematical model, we employ a "cycle of knowledge" strategy, identifying the steps with most control over flux. Kinetic parameters of the individual isoenzymes within these steps are measured experimentally under a standardised set of conditions. Experimental strategies are applied to establish a set of in vivo concentrations for isoenzymes and metabolites. The data are integrated into a mathematical model that is used to predict a new set of metabolite concentrations and reevaluate the control properties of the system. This bottom-up modelling study reveals that control over the metabolic network most directly involved in yeast glycolysis is more widely distributed than previously thought. link: http://identifiers.org/pubmed/23831062

Parameters: none

States: none

Observables: none

Smallbone2013 - Glycolysis in S.cerevisiae - Iteration 17This model is described in the article: [A model of yeast glyc…

We present an experimental and computational pipeline for the generation of kinetic models of metabolism, and demonstrate its application to glycolysis in Saccharomyces cerevisiae. Starting from an approximate mathematical model, we employ a "cycle of knowledge" strategy, identifying the steps with most control over flux. Kinetic parameters of the individual isoenzymes within these steps are measured experimentally under a standardised set of conditions. Experimental strategies are applied to establish a set of in vivo concentrations for isoenzymes and metabolites. The data are integrated into a mathematical model that is used to predict a new set of metabolite concentrations and reevaluate the control properties of the system. This bottom-up modelling study reveals that control over the metabolic network most directly involved in yeast glycolysis is more widely distributed than previously thought. link: http://identifiers.org/pubmed/23831062

Parameters: none

States: none

Observables: none

Smallbone2013 - Glycolysis in S.cerevisiae - Iteration 18This model is described in the article: [A model of yeast glyc…

We present an experimental and computational pipeline for the generation of kinetic models of metabolism, and demonstrate its application to glycolysis in Saccharomyces cerevisiae. Starting from an approximate mathematical model, we employ a "cycle of knowledge" strategy, identifying the steps with most control over flux. Kinetic parameters of the individual isoenzymes within these steps are measured experimentally under a standardised set of conditions. Experimental strategies are applied to establish a set of in vivo concentrations for isoenzymes and metabolites. The data are integrated into a mathematical model that is used to predict a new set of metabolite concentrations and reevaluate the control properties of the system. This bottom-up modelling study reveals that control over the metabolic network most directly involved in yeast glycolysis is more widely distributed than previously thought. link: http://identifiers.org/pubmed/23831062

Parameters: none

States: none

Observables: none

Smallbone2013 - Human metabolism global reconstruction (recon 2.1)Recon 2.1. This model is described in the article: […

Recon 2 is a highly curated reconstruction of the human metabolic network. Whilst the network is state of the art, it has shortcomings, including the presence of unbalanced reactions involving generic metabolites. By replacing these generic molecules with each of their specific instances, we can ensure full elemental balancing, in turn allowing constraint-based analyses to be performed. The resultant model, called Recon 2.1, is an order of magnitude larger than the original. link: http://arxiv.org/abs/1311.5696

Parameters: none

States: none

Observables: none

Smallbone2013 - Human metabolism global reconstruction (recon 2.1x)Recon 2.1x. This model is described in the article:…

Recon 2 is a highly curated reconstruction of the human metabolic network. Whilst the network is state of the art, it has shortcomings, including the presence of unbalanced reactions involving generic metabolites. By replacing these generic molecules with each of their specific instances, we can ensure full elemental balancing, in turn allowing constraint-based analyses to be performed. The resultant model, called Recon 2.1, is an order of magnitude larger than the original. link: http://arxiv.org/abs/1311.5696

Parameters: none

States: none

Observables: none

Smallbone2013 - Metabolic Control Analysis - Example 1Metabolic control analysis (MCA) is a biochemical formalism, defin…

Metabolic control analysis is a biochemical formalism defined by Kacser and Burns in 1973, and given firm mathematical basis by Reder in 1988. The algorithm defined by Reder for calculating the control matrices is still used by software programs today, but is only valid for some biochemical models. We show that, with slight modification, the algorithm may be applied to all models. link: http://arxiv.org/pdf/1305.6449v1.pdf

Parameters:

Name Description
p1=10.0 dimensionless; e1=1.0 dimensionless Reaction: y1 + x2 => x1 + x3; y1, x2, x1, x3, Rate Law: e1*(p1*y1*x2-x1*x3)/(1+y1+x2+x1+x3+y1*x2+x1*x3)
e3=1.0 dimensionless; p3=50.0 dimensionless Reaction: x1 => y2; x1, y2, Rate Law: e3*(p3*x1-y2)/(1+x1+y2)
e2=1.0 dimensionless; p2=10.0 dimensionless Reaction: y4 + x3 => y5 + x2; y4, x3, y5, x2, Rate Law: e2*(p2*y4*x3-y5*x2)/(1+x3+x2+y4+y5+x3*y4+x2*y5)
p4=10.0 dimensionless; e4=1.0 dimensionless Reaction: x1 => y3; x1, y3, Rate Law: e4*(p4*x1-y3)/(1+x1+y3)

States:

Name Description
y3 y3
x1 x1
y4 y4
y1 y1
x2 x2
y2 y2
x3 x3
y5 y5

Observables: none

Smallbone2013 - Metabolic Control Analysis - Example 2Metabolic control analysis (MCA) is a biochemical formalism, defin…

Metabolic control analysis is a biochemical formalism defined by Kacser and Burns in 1973, and given firm mathematical basis by Reder in 1988. The algorithm defined by Reder for calculating the control matrices is still used by software programs today, but is only valid for some biochemical models. We show that, with slight modification, the algorithm may be applied to all models. link: http://arxiv.org/pdf/1305.6449v1.pdf

Parameters:

Name Description
p1=10.0 dimensionless; e1=1.0 dimensionless Reaction: y1 + x2 => x1 + x3; y1, x2, x1, x3, Rate Law: e1*(p1*y1*x2-x1*x3)/(1+y1+x2+x1+x3+y1*x2+x1*x3)
e3=1.0 dimensionless; p3=50.0 dimensionless Reaction: x1 => y2; x1, y2, Rate Law: e3*(p3*x1-y2)/(1+x1+y2)
p4=10.0 dimensionless; e4=1.0 dimensionless Reaction: x1 => y3; x1, y3, Rate Law: e4*(p4*x1-y3)/(1+x1+y3)
e2=1.0 dimensionless; p2=10.0 dimensionless Reaction: y4 + x3 => y5 + x2; y4, x3, y5, x2, Rate Law: e2*(p2*y4*x3-y5*x2)/(1+x3+x2+y4+y5+x3*y4+x2*y5)
e5=1.0 dimensionless; p5=0.0 dimensionless Reaction: x3 => y6; x3, Rate Law: e5*p5*x3

States:

Name Description
y3 y3
x1 x1
y1 y1
y4 y4
x2 x2
y2 y2
y6 y6
x3 x3
y5 y5

Observables: none

Smallbone2013 - Metabolic Control Analysis - Example 3Metabolic control analysis (MCA) is a biochemical formalism, defin…

Metabolic control analysis is a biochemical formalism defined by Kacser and Burns in 1973, and given firm mathematical basis by Reder in 1988. The algorithm defined by Reder for calculating the control matrices is still used by software programs today, but is only valid for some biochemical models. We show that, with slight modification, the algorithm may be applied to all models. link: http://arxiv.org/pdf/1305.6449v1.pdf

Parameters:

Name Description
e6=1.0 dimensionless; p6=1.0 dimensionless Reaction: y7 => x4; y7, Rate Law: e6*p6*y7
p1=10.0 dimensionless; e1=1.0 dimensionless Reaction: y1 + x2 => x1 + x3; y1, x2, x1, x3, Rate Law: e1*(p1*y1*x2-x1*x3)/(1+y1+x2+x1+x3+y1*x2+x1*x3)
e3=1.0 dimensionless; p3=50.0 dimensionless Reaction: x1 => y2; x1, y2, Rate Law: e3*(p3*x1-y2)/(1+x1+y2)
e2=1.0 dimensionless; p2=10.0 dimensionless Reaction: y4 + x3 => y5 + x2; y4, x3, y5, x2, Rate Law: e2*(p2*y4*x3-y5*x2)/(1+x3+x2+y4+y5+x3*y4+x2*y5)
p4=10.0 dimensionless; e4=1.0 dimensionless Reaction: x1 => y3; x1, y3, Rate Law: e4*(p4*x1-y3)/(1+x1+y3)
p7=1.0 dimensionless; e7=1.0 dimensionless Reaction: x4 => y8, Rate Law: e7*p7

States:

Name Description
y3 y3
x4 x4
x2 x2
x3 x3
y8 y8
x1 x1
y4 y4
y1 y1
y7 y7
y2 y2
y5 y5

Observables: none

BIOMD0000000458 @ v0.0.1

Smallbone2013 - Serine biosynthesisKinetic modelling of metabolic pathways in application to Serine biosynthesis. This…

In this chapter, we describe the steps needed to create a kinetic model of a metabolic pathway using kinetic data from both experimental measurements and literature review. Our methodology is presented by using the example of serine biosynthesis in E. coli. link: http://identifiers.org/pubmed/23417802

Parameters:

Name Description
KAphp=0.0032 mM; KiAser=0.0038 mM; kcatA=0.55 per s; KAp3g=1.2 mM Reaction: p3g => php; serA, ser, serA, p3g, php, ser, Rate Law: cell*serA*kcatA*p3g/KAp3g/(1+p3g/KAp3g+php/KAphp)/(1+ser/KiAser)
kcatC=1.75 per s; KCpser=0.0017 mM; KCphp=0.0015 mM Reaction: php => pser; serC, serC, php, pser, Rate Law: cell*serC*kcatC*php/KCphp/(1+php/KCphp+pser/KCpser)
KBpser=0.0015 mM; KBser=0.15 mM; kcatB=1.43 per s Reaction: pser => ser; serB, serB, pser, ser, Rate Law: cell*serB*kcatB*pser/KBpser/(1+pser/KBpser+ser/KBser)

States:

Name Description
p3g [3-phosphonato-D-glycerate(3-)]
ser [L-serine]
php [3-phosphonatooxypyruvate(3-)]
pser [O-phosphonato-L-serine(2-)]

Observables: none

BIOMD0000000831 @ v0.0.1

This a model from the article: Hypothalamic regulation of pituitary secretion of luteinizing hormone.II. Feedback cont…

A general mathematical model describing the biochemical interactions of the hormones luteinizing hormone releasing hormone (LHRH), luteinizing hormone (LH) and testosterone (T) in the male is presented. The model structure consists of a negative feedback system of three ordinary differential equations, in which the quali]ative behavior is either a stable constant equilibrium solution or oscillatory solutions. A specific realization of the model is used to describe the experimental observations of pulsatile hormone release, its experimental suppression, the onset of puberty, the effects of castration, and several other qualitative and quantitative results. This model is presented as a first step in understanding the physi- cochemical interactions of the hypothalamic pituitary gonadal axis. link: http://identifiers.org/pubmed/6986927

Parameters:

Name Description
g1 = 10.0 1/h Reaction: => L; R, Rate Law: Compartment*g1*R
h = 12.0 1/h; H = 1.0 1; c = 100.0 ng/(l*h) Reaction: => R; T, Rate Law: Compartment*(c-h*T)*(1-H)
b1 = 1.29 1/h Reaction: R =>, Rate Law: Compartment*b1*R
g2 = 0.7 1/h Reaction: => T; L, Rate Law: Compartment*g2*L
b3 = 1.39 1/h Reaction: T =>, Rate Law: Compartment*b3*T
b2 = 0.97 1/h Reaction: L =>, Rate Law: Compartment*b2*L

States:

Name Description
T [Thyroxine 5-deiodinase]
L [Luteinizing hormone]
R [Luteinizing hormone receptor]

Observables: none

MODEL1006230000 @ v0.0.1

This a model from the article: Minimal haemodynamic system model including ventricular interaction and valve dynamics.…

Characterising circulatory dysfunction and choosing a suitable treatment is often difficult and time consuming, and can result in a deterioration in patient condition, or unsuitable therapy choices. A stable minimal model of the human cardiovascular system (CVS) is developed with the ultimate specific aim of assisting medical staff for rapid, on site modelling to assist in diagnosis and treatment. Models found in the literature simulate specific areas of the CVS with limited direct usefulness to medical staff. Others model the full CVS as a closed loop system, but they were found to be very complex, difficult to solve, or unstable. This paper develops a model that uses a minimal number of governing equations with the primary goal of accurately capturing trends in the CVS dynamics in a simple, easily solved, robust model. The model is shown to have long term stability and consistency with non-specific initial conditions as a result. An "open on pressure close on flow" valve law is created to capture the effects of inertia and the resulting dynamics of blood flow through the cardiac valves. An accurate, stable solution is performed using a method that varies the number of states in the model depending on the specific phase of the cardiac cycle, better matching the real physiological conditions. Examples of results include a 9% drop in cardiac output when increasing the thoracic pressure from -4 to 0 mmHg, and an increase in blood pressure from 120/80 to 165/130 mmHg when the systemic resistance is doubled. These results show that the model adequately provides appropriate magnitudes and trends that are in agreement with existing data for a variety of physiologically verified test cases simulating human CVS function. link: http://identifiers.org/pubmed/15036180

Parameters: none

States: none

Observables: none

BIOMD0000000439 @ v0.0.1

Smith2009 - RGS mediated GTP hydrolysisThis model is described in the article: [Dual positive and negative regulation o…

G protein-coupled receptors (GPCRs) regulate a variety of intracellular pathways through their ability to promote the binding of GTP to heterotrimeric G proteins. Regulator of G protein signaling (RGS) proteins increases the intrinsic GTPase activity of Galpha-subunits and are widely regarded as negative regulators of G protein signaling. Using yeast we demonstrate that GTP hydrolysis is not only required for desensitization, but is essential for achieving a high maximal (saturated level) response. Thus RGS-mediated GTP hydrolysis acts as both a negative (low stimulation) and positive (high stimulation) regulator of signaling. To account for this we generated a new kinetic model of the G protein cycle where Galpha(GTP) enters an inactive GTP-bound state following effector activation. Furthermore, in vivo and in silico experimentation demonstrates that maximum signaling output first increases and then decreases with RGS concentration. This unimodal, non-monotone dependence on RGS concentration is novel. Analysis of the kinetic model has revealed a dynamic network motif that shows precisely how inclusion of the inactive GTP-bound state for the Galpha produces this unimodal relationship. link: http://identifiers.org/pubmed/19285552

Parameters:

Name Description
k1=0.0025 1/(nM*hr) Reaction: R + L => RL; R, L, Rate Law: compartment*R*L*k1
k8=2.5 1/hr Reaction: RGSGaGTP => GaGDPP + RGS; RGSGaGTP, Rate Law: compartment*RGSGaGTP*k8
k7=500.0 1/(nM*hr) Reaction: GaGTP + RGS => RGSGaGTP; GaGTP, RGS, Rate Law: compartment*GaGTP*RGS*k7
k9=0.005 1/hr Reaction: GaGTP => GaGDPP; GaGTP, Rate Law: compartment*GaGTP*k9
k16=1000.0 1/(nM*hr) Reaction: GaGDP + Gbg => Gabg; GaGDP, Gbg, Rate Law: compartment*GaGDP*Gbg*k16
k15=1000.0 1/hr Reaction: GaGDPP => GaGDP + P; GaGDPP, Rate Law: compartment*GaGDPP*k15
k4=0.005 1/(nM*hr) Reaction: RGabg + L => RGabgL; RGabg, L, Rate Law: compartment*RGabg*L*k4
k11=1.0 1/hr Reaction: GaGTPEffector => inertGaGTP + Effector; GaGTPEffector, Rate Law: compartment*GaGTPEffector*k11
k5=50.0 1/hr Reaction: RGabgL => RL + GaGTP + Gbg; RGabgL, Rate Law: compartment*RGabgL*k5
k17=10.0 1/hr Reaction: P => ; P, Rate Law: compartment*P*k17
k13=0.3 1/hr Reaction: RGSinertGaGTP => GaGDPP + RGS; RGSinertGaGTP, Rate Law: compartment*RGSinertGaGTP*k13
k6=0.2 1/hr Reaction: Gabg => GaGTP + Gbg; Gabg, Rate Law: compartment*Gabg*k6
k12=50.0 1/(nM*hr) Reaction: inertGaGTP + RGS => RGSinertGaGTP; inertGaGTP, RGS, Rate Law: compartment*inertGaGTP*RGS*k12
k14=0.005 1/hr Reaction: inertGaGTP => GaGDPP; inertGaGTP, Rate Law: compartment*inertGaGTP*k14
k3=0.02 1/(nM*hr) Reaction: RL + Gabg => RGabgL; RL, Gabg, Rate Law: compartment*RL*Gabg*k3
k2=0.005 1/(nM*hr) Reaction: R + Gabg => RGabg; R, Gabg, Rate Law: compartment*R*Gabg*k2
k10=10.0 1/(nM*hr) Reaction: Effector + GaGTP => GaGTPEffector; Effector, GaGTP, Rate Law: compartment*Effector*GaGTP*k10
ka = 1.5 1/hr Reaction: => z1; GaGTPEffector, GaGTPEffector, Rate Law: compartment*GaGTPEffector*ka

States:

Name Description
RGabg [IPR000276; heterotrimeric G-protein complex]
GaGTP [GTP; Guanine nucleotide-binding protein G(t) subunit alpha-1]
GaGDPP [GDP; Guanine nucleotide-binding protein G(t) subunit alpha-1]
inertGaGTP [GTP; Guanine nucleotide-binding protein G(t) subunit alpha-1; inactive]
RGS [IPR000342]
P [phosphate(3-)]
z1 [SBO:0000347]
RL [receptor complex]
L L
Gabg [heterotrimeric G-protein complex]
Gbg [Guanine nucleotide-binding protein G(I)/G(S)/G(T) subunit beta-1; Guanine nucleotide-binding protein G(T) subunit gamma-T1]
z3 [SBO:0000347]
GaGDP [GDP; Guanine nucleotide-binding protein G(t) subunit alpha-1]
GaGTPEffector [GTP; Guanine nucleotide-binding protein G(t) subunit alpha-1; SBO:0000459]
RGSGaGTP [GTP; Guanine nucleotide-binding protein G(t) subunit alpha-1; IPR000342]
RGSinertGaGTP [GTP; Guanine nucleotide-binding protein G(t) subunit alpha-1; IPR000342; inactive]
Effector [SBO:0000459]
RGabgL [IPR000276; heterotrimeric G-protein complex; SBO:0000280]
z2 [SBO:0000347]
R [IPR000276]

Observables: none

This a model from the article: Modelling the response of FOXO transcription factors to multiple post-translational mod…

FOXO transcription factors are an important, conserved family of regulators of cellular processes including metabolism, cell-cycle progression, apoptosis and stress resistance. They are required for the efficacy of several of the genetic interventions that modulate lifespan. FOXO activity is regulated by multiple post-translational modifications (PTMs) that affect its subcellular localization, half-life, DNA binding and transcriptional activity. Here, we show how a mathematical modelling approach can be used to simulate the effects, singly and in combination, of these PTMs. Our model is implemented using the Systems Biology Markup Language (SBML), generated by an ancillary program and simulated in a stochastic framework. The use of the ancillary program to generate the SBML is necessary because the possibility that many regulatory PTMs may be added, each independently of the others, means that a large number of chemically distinct forms of the FOXO molecule must be taken into account, and the program is used to generate them. Although the model does not yet include detailed representations of events upstream and downstream of FOXO, we show how it can qualitatively, and in some cases quantitatively, reproduce the known effects of certain treatments that induce various single and multiple PTMs, and allows for a complex spatiotemporal interplay of effects due to the activation of multiple PTM-inducing treatments. Thus, it provides an important framework to integrate current knowledge about the behaviour of FOXO. The approach should be generally applicable to other proteins experiencing multiple regulations. link: http://identifiers.org/pubmed/20567500

Parameters: none

States: none

Observables: none

Pneumococcal pneumonia is a leading cause of death and a major source of human morbidity. The initial immune response pl…

Pneumococcal pneumonia is a leading cause of death and a major source of human morbidity. The initial immune response plays a central role in determining the course and outcome of pneumococcal disease. We combine bacterial titer measurements from mice infected with Streptococcus pneumoniae with mathematical modeling to investigate the coordination of immune responses and the effects of initial inoculum on outcome. To evaluate the contributions of individual components, we systematically build a mathematical model from three subsystems that describe the succession of defensive cells in the lung: resident alveolar macrophages, neutrophils and monocyte-derived macrophages. The alveolar macrophage response, which can be modeled by a single differential equation, can by itself rapidly clear small initial numbers of pneumococci. Extending the model to include the neutrophil response required additional equations for recruitment cytokines and host cell status and damage. With these dynamics, two outcomes can be predicted: bacterial clearance or sustained bacterial growth. Finally, a model including monocyte-derived macrophage recruitment by neutrophils suggests that sustained bacterial growth is possible even in their presence. Our model quantifies the contributions of cytotoxicity and immune-mediated damage in pneumococcal pathogenesis. link: http://identifiers.org/pubmed/21300073

Parameters:

Name Description
eta = 1.33; N_max = 180000.0 Reaction: => Neutrophils__N; proinflammatory_cytokine__C, Rate Law: compartment*eta*proinflammatory_cytokine__C*(1-Neutrophils__N/N_max)
theta_M = 4.2E-8; d = 0.001; k_n = 1.4E-5; M_Astar = 1000000.0; alpha = 0.021; v = 0.029; kappa = 0.042 Reaction: => proinflammatory_cytokine__C; Epithelial_cells_with_bacteria_attached__Ea, Neutrophils__N, Pneumococci___P, Rate Law: compartment*(alpha*Epithelial_cells_with_bacteria_attached__Ea/(1+k_n*Neutrophils__N)+v*theta_M*Pneumococci___P*M_Astar/(d+kappa+theta_M*Pneumococci___P*(1+k_n*Neutrophils__N)))
d_E = 0.167 Reaction: Epithelial_cells_with_bacteria_attached__Ea =>, Rate Law: compartment*d_E*Epithelial_cells_with_bacteria_attached__Ea
d_C = 0.83 Reaction: proinflammatory_cytokine__C =>, Rate Law: compartment*d_C*proinflammatory_cytokine__C
d_NP = 1.76E-7; d_E = 0.167; rho1 = 0.15; d_N = 0.063; rho2 = 0.001; rho3 = 1.0E-5 Reaction: => Debris__D; Neutrophils__N, Pneumococci___P, Epithelial_cells_with_bacteria_attached__Ea, Rate Law: compartment*(rho1*d_NP*Neutrophils__N*Pneumococci___P+rho2*d_N*Neutrophils__N+rho3*d_E*Epithelial_cells_with_bacteria_attached__Ea)
d_D = 1.4E-7; M_Astar = 1000000.0 Reaction: Debris__D =>, Rate Law: compartment*d_D*Debris__D*M_Astar
f_P_M_A = 0.00249376558603491; gamma_N = 1.0E-5; k_d = 5.0E-9; M_Astar = 1000000.0; gamma_M_A = 5.6E-6 Reaction: Pneumococci___P => ; Debris__D, Neutrophils__N, Rate Law: compartment*(gamma_M_A*f_P_M_A/(1+k_d*Debris__D*M_Astar)*M_Astar*Pneumococci___P+gamma_N*Neutrophils__N*Pneumococci___P)
K_P = 3.41765197726012E8; r = 1.13 Reaction: => Pneumococci___P, Rate Law: compartment*r*Pneumococci___P*(1-Pneumococci___P/K_P)
omega = 2.1E-8 Reaction: Susceptible_epithelial_cells__EU => ; Pneumococci___P, Rate Law: compartment*omega*Pneumococci___P*Susceptible_epithelial_cells__EU
d_NP = 1.76E-7; d_N = 0.063 Reaction: Neutrophils__N => ; Pneumococci___P, Rate Law: compartment*(d_NP*Neutrophils__N*Pneumococci___P+d_N*Neutrophils__N)

States:

Name Description
Pneumococci P [C76384]
Epithelial cells with bacteria attached Ea [infected cell]
Susceptible epithelial cells EU [0006083]
Neutrophils N [0010527]
proinflammatory cytokine C [Cytokine]
Debris D [C120869]

Observables: none

This model is from the article: A metabolic model of the mitochondrion and its use in modelling diseases of the tricar…

Mitochondria are a vital component of eukaryotic cells and their dysfunction is implicated in a large number of metabolic, degenerative and age-related human diseases. The mechanism or these disorders can be difficult to elucidate due to the inherent complexity of mitochondrial metabolism. To understand how mitochondrial metabolic dysfunction contributes to these diseases, a metabolic model of a human heart mitochondrion was created.A new model of mitochondrial metabolism was built on the principle of metabolite availability using MitoMiner, a mitochondrial proteomics database, to evaluate the subcellular localisation of reactions that have evidence for mitochondrial localisation. Extensive curation and manual refinement was used to create a model called iAS253, containing 253 reactions, 245 metabolites and 89 transport steps across the inner mitochondrial membrane. To demonstrate the predictive abilities of the model, flux balance analysis was used to calculate metabolite fluxes under normal conditions and to simulate three metabolic disorders that affect the TCA cycle: fumarase deficiency, succinate dehydrogenase deficiency and α-ketoglutarate dehydrogenase deficiency.The results of simulations using the new model corresponded closely with phenotypic data under normal conditions and provided insight into the complicated and unintuitive phenotypes of the three disorders, including the effect of interventions that may be of therapeutic benefit, such as low glucose diets or amino acid supplements. The model offers the ability to investigate other mitochondrial disorders and can provide the framework for the integration of experimental data in future studies. link: http://identifiers.org/pubmed/21714867

Parameters: none

States: none

Observables: none

Smith2013 - Regulation of Insulin Signalling by Oxidative StressThe model describes insulin signalling (in rodent adipoc…

Existing models of insulin signalling focus on short term dynamics, rather than the longer term dynamics necessary to understand many physiologically relevant behaviours. We have developed a model of insulin signalling in rodent adipocytes that includes both transcriptional feedback through the Forkhead box type O (FOXO) transcription factor, and interaction with oxidative stress, in addition to the core pathway. In the model Reactive Oxygen Species are both generated endogenously and can be applied externally. They regulate signalling though inhibition of phosphatases and induction of the activity of Stress Activated Protein Kinases, which themselves modulate feedbacks to insulin signalling and FOXO.Insulin and oxidative stress combined produce a lower degree of activation of insulin signalling than insulin alone. Fasting (nutrient withdrawal) and weak oxidative stress upregulate antioxidant defences while stronger oxidative stress leads to a short term activation of insulin signalling but if prolonged can have other effects including degradation of the insulin receptor substrate (IRS1) and FOXO. At high insulin the protective effect of moderate oxidative stress may disappear.Our model is consistent with a wide range of experimental data, some of which is difficult to explain. Oxidative stress can have effects that are both up- and down-regulatory on insulin signalling. Our model therefore shows the complexity of the interaction between the two pathways and highlights the need for such integrated computational models to give insight into the dysregulation of insulin signalling along with more data at the individual level.A complete SBML model file can be downloaded from BIOMODELS (https://www.ebi.ac.uk/biomodels-main) with unique identifier MODEL1212210000.Other files and scripts are available as additional files with this journal article and can be downloaded from https://github.com/graham1034/Smith2012insulinsignalling. link: http://identifiers.org/pubmed/23705851

Parameters:

Name Description
k1 = 2.0E-5 Reaction: Ins + InR => Ins_InR; InR, Ins, Rate Law: k1*Ins*extracellular*InR*cellsurface
kminusr16a = 1.0E-6 Reaction: AS160_P => AS160; PP2A, AS160_P, PP2A, Rate Law: cytoplasm*kminusr16a*PP2A*cytoplasm*AS160_P*cytoplasm/cytoplasm
kminus9 = 0.0014; kminus9_basal = 2.7 Reaction: PI345P3 => PIP2; PTEN, PI345P3, PTEN, Rate Law: cytoplasm*(kminus9_basal+kminus9*PTEN*cytoplasm)*PI345P3*cytoplasm/cytoplasm
ktr=0.125 Reaction: nucleus_Foxo1_Pa1_Pd0_Pe1_pUb0 => dnabound_Foxo1_Pa1_Pd0_Pe1_pUb0; nucleus_Foxo1_Pa1_Pd0_Pe1_pUb0, Rate Law: nucleus_Foxo1_Pa1_Pd0_Pe1_pUb0*nucleus*ktr
kdeg=1.0E-4 Reaction: cytoplasm_Foxo1_Pa1_Pd1_Pe1_pUb1 => degr_Foxo1; Proteasome, Proteasome, cytoplasm_Foxo1_Pa1_Pd1_Pe1_pUb1, Rate Law: cytoplasm*cytoplasm_Foxo1_Pa1_Pd1_Pe1_pUb1*cytoplasm*Proteasome*cytoplasm*kdeg/cytoplasm
kkin=3.0E-4 Reaction: cytoplasm_Foxo1_Pa0_Pd1_Pe1_pUb1 => cytoplasm_Foxo1_Pa1_Pd1_Pe1_pUb1; SGK, SGK, cytoplasm_Foxo1_Pa0_Pd1_Pe1_pUb1, Rate Law: cytoplasm*cytoplasm_Foxo1_Pa0_Pd1_Pe1_pUb1*cytoplasm*SGK*cytoplasm*kkin/cytoplasm
k36f = 180.0 Reaction: Mt => Mt + ROS; Mt, Rate Law: cytoplasm*k36f*Mt*cytoplasm/cytoplasm
kub=6.6E-5 Reaction: dnabound_Foxo1_Pa1_Pd1_Pe0_pUb0 => dnabound_Foxo1_Pa1_Pd1_Pe0_pUb1; SCF, SCF, dnabound_Foxo1_Pa1_Pd1_Pe0_pUb0, Rate Law: dnabound*dnabound_Foxo1_Pa1_Pd1_Pe0_pUb0*dnabound*SCF*cytoplasm*kub/dnabound
ktr=0.055 Reaction: nucleus_Foxo1_Pa0_Pd1_Pe1_pUb1 => cytoplasm_Foxo1_Pa0_Pd1_Pe1_pUb1; nucleus_Foxo1_Pa0_Pd1_Pe1_pUb1, Rate Law: nucleus_Foxo1_Pa0_Pd1_Pe1_pUb1*nucleus*ktr
kub=1.0E-6 Reaction: dnabound_Foxo1_Pa0_Pd0_Pe1_pUb0 => dnabound_Foxo1_Pa0_Pd0_Pe1_pUb1; SCF, SCF, dnabound_Foxo1_Pa0_Pd0_Pe1_pUb0, Rate Law: dnabound*dnabound_Foxo1_Pa0_Pd0_Pe1_pUb0*dnabound*SCF*cytoplasm*kub/dnabound
k35f = 450.0 Reaction: NOX => ROS + NOX; NOX, Rate Law: cytoplasm*k35f*NOX*cytoplasm/cytoplasm
kub=3.0E-6 Reaction: nucleus_Foxo1_Pa1_Pd0_Pe0_pUb0 => nucleus_Foxo1_Pa1_Pd0_Pe0_pUb1; SCF, SCF, nucleus_Foxo1_Pa1_Pd0_Pe0_pUb0, Rate Law: nucleus*nucleus_Foxo1_Pa1_Pd0_Pe0_pUb0*nucleus*SCF*cytoplasm*kub/nucleus
kpdeg=0.0044 Reaction: cytoplasm_InR => null; cytoplasm_InR, Rate Law: cytoplasm*cytoplasm_InR*cytoplasm*kpdeg/cytoplasm
kminus12 = 1.25E-6 Reaction: PKC_P => PKC; PP2A, PKC_P, PP2A, Rate Law: cytoplasm*kminus12*PP2A*cytoplasm*PKC_P*cytoplasm/cytoplasm
kminus13 = 0.167 Reaction: cellsurface_GLUT4 => cytoplasm_GLUT4; cellsurface_GLUT4, Rate Law: kminus13*cellsurface_GLUT4*cellsurface
k_ros_perm = 4.81 Reaction: ROS => extracellular_ROS; ROS, Rate Law: k_ros_perm*extracellular/cytoplasm*ROS*cytoplasm
ktr=0.55 Reaction: nucleus_Foxo1_Pa0_Pd1_Pe0_pUb0 => cytoplasm_Foxo1_Pa0_Pd1_Pe0_pUb0; nucleus_Foxo1_Pa0_Pd1_Pe0_pUb0, Rate Law: nucleus_Foxo1_Pa0_Pd1_Pe0_pUb0*nucleus*ktr
ktr=0.0909090909091 Reaction: cytoplasm_Foxo1_Pa0_Pd1_Pe0_pUb0 => nucleus_Foxo1_Pa0_Pd1_Pe0_pUb0; cytoplasm_Foxo1_Pa0_Pd1_Pe0_pUb0, Rate Law: cytoplasm_Foxo1_Pa0_Pd1_Pe0_pUb0*cytoplasm*ktr
k30r = 0.005 Reaction: PTP1B_ox + GSH => PTP1B + GSH; GSH, PTP1B_ox, Rate Law: cytoplasm*k30r*PTP1B_ox*cytoplasm*GSH*cytoplasm/cytoplasm
k13 = 7.5E-6; k13_basal = 0.015 Reaction: cytoplasm_GLUT4 => cellsurface_GLUT4; AS160_P, AS160_P, cytoplasm_GLUT4, Rate Law: (k13_basal+k13*AS160_P*cytoplasm)*cytoplasm_GLUT4*cytoplasm
k32f = 6.0E-4 Reaction: DUSP + ROS => DUSP_ox + ROS; DUSP, ROS, Rate Law: cytoplasm*k32f*DUSP*cytoplasm*ROS*cytoplasm/cytoplasm
k31r = 0.002 Reaction: PTEN_ox + GSH => PTEN + GSH; GSH, PTEN_ox, Rate Law: cytoplasm*k31r*PTEN_ox*cytoplasm*GSH*cytoplasm/cytoplasm
by_jnk_phos_factor = 2.0; kkin=5.0E-5 Reaction: dnabound_Foxo1_Pa0_Pd0_Pe0_pUb1 => dnabound_Foxo1_Pa0_Pd0_Pe1_pUb1; JNK_P, JNK_P, dnabound_Foxo1_Pa0_Pd0_Pe0_pUb1, Rate Law: dnabound*dnabound_Foxo1_Pa0_Pd0_Pe0_pUb1*dnabound*JNK_P*cytoplasm*by_jnk_phos_factor*kkin/dnabound
kminus11 = 1.1878E-6 Reaction: Akt_P2 => Akt; PP2A, Akt_P2, PP2A, Rate Law: cytoplasm*kminus11*PP2A*cytoplasm*Akt_P2*cytoplasm/cytoplasm
k9 = 0.0055; k9_basal = 0.13145 Reaction: PIP2 => PI345P3; IRS1_TyrP_PI3K, IRS1_TyrP_PI3K, PIP2, Rate Law: cytoplasm*(k9_basal+k9*IRS1_TyrP_PI3K*cytoplasm)*PIP2*cytoplasm/cytoplasm
by_ikk_phos_factor = 3.0; kkin=5.0E-5 Reaction: dnabound_Foxo1_Pa0_Pd0_Pe1_pUb1 => dnabound_Foxo1_Pa0_Pd1_Pe1_pUb1; IKK_P, IKK_P, dnabound_Foxo1_Pa0_Pd0_Pe1_pUb1, Rate Law: dnabound*dnabound_Foxo1_Pa0_Pd0_Pe1_pUb1*dnabound*IKK_P*cytoplasm*by_ikk_phos_factor*kkin/dnabound
ktr=0.181818181818 Reaction: cytoplasm_Foxo1_Pa0_Pd0_Pe0_pUb1 => nucleus_Foxo1_Pa0_Pd0_Pe0_pUb1; cytoplasm_Foxo1_Pa0_Pd0_Pe0_pUb1, Rate Law: cytoplasm_Foxo1_Pa0_Pd0_Pe0_pUb1*cytoplasm*ktr
pip3_basal = 200.0; k12 = 3.5E-5 Reaction: PKC => PKC_P; PI345P3, PI345P3, PKC, Rate Law: cytoplasm*k12*PKC*cytoplasm*piecewise(PI345P3*cytoplasm-pip3_basal, (PI345P3*cytoplasm) > pip3_basal, 0)/cytoplasm
k31f = 2.7E-4 Reaction: PTEN + ROS => PTEN_ox + ROS; PTEN, ROS, Rate Law: cytoplasm*k31f*PTEN*cytoplasm*ROS*cytoplasm/cytoplasm
pip3_basal = 200.0; k11 = 2.5E-5 Reaction: Akt => Akt_P2; PI345P3, Akt, PI345P3, Rate Law: cytoplasm*k11*Akt*cytoplasm*piecewise(PI345P3*cytoplasm-pip3_basal, (PI345P3*cytoplasm) > pip3_basal, 0)/cytoplasm
ktranscr=0.24 Reaction: null => nucleus_RNA_InR; dnabound_Foxo1_Pa1_Pd0_Pe0_pUb0, dnabound_Foxo1_Pa1_Pd0_Pe0_pUb0, Rate Law: dnabound_Foxo1_Pa1_Pd0_Pe0_pUb0*dnabound*ktranscr
k_irs1_basal_degr = 0.001 Reaction: IRS1 => NULL; IRS1, Rate Law: cytoplasm*IRS1*cytoplasm*k_irs1_basal_degr/cytoplasm
kdephos=1.0E-6 Reaction: dnabound_Foxo1_Pa1_Pd0_Pe1_pUb1 => dnabound_Foxo1_Pa0_Pd0_Pe1_pUb1; PP2A, PP2A, dnabound_Foxo1_Pa1_Pd0_Pe1_pUb1, Rate Law: dnabound*dnabound_Foxo1_Pa1_Pd0_Pe1_pUb1*dnabound*PP2A*cytoplasm*kdephos/dnabound

States:

Name Description
dnabound Foxo1 Pa1 Pd1 Pe1 pUb1 [double-stranded DNA; Forkhead box protein O1]
dnabound Foxo1 Pa1 Pd1 Pe1 pUb0 [double-stranded DNA; Forkhead box protein O1]
PIP2 [phosphatidylinositol bisphosphate]
PKC P [phosphorylated; Atypical protein kinase C]
PTEN [Phosphatase and tensin homologPhosphatase and tensin homolog, isoform CRA_aProtein tyrosine phosphatase and tensin homolog/mutated in multiple advanced cancers proteinProtein tyrosine phosphatase and tensin-like protein]
cytoplasm Foxo1 Pa0 Pd1 Pe0 pUb0 [Forkhead box protein O1]
Akt [RAC-alpha serine/threonine-protein kinase]
cytoplasm Foxo1 Pa1 Pd0 Pe1 pUb1 [Forkhead box protein O1]
cytoplasm Foxo1 Pa0 Pd0 Pe0 pUb1 [Forkhead box protein O1]
nucleus Foxo1 Pa1 Pd1 Pe1 pUb0 [Forkhead box protein O1]
nucleus Foxo1 Pa1 Pd0 Pe0 pUb0 [Forkhead box protein O1]
dnabound Foxo1 Pa1 Pd0 Pe1 pUb0 [double-stranded DNA; Forkhead box protein O1]
PTP1B ox PTP1B_ox
nucleus Foxo1 Pa1 Pd1 Pe1 pUb1 [Forkhead box protein O1]
cytoplasm InR [Insulin receptor]
cellsurface GLUT4 [Solute carrier family 2, facilitated glucose transporter member 4]
dnabound Foxo1 Pa0 Pd0 Pe1 pUb1 [double-stranded DNA; Forkhead box protein O1]
ROS [reactive oxygen species]
cytoplasm Foxo1 Pa0 Pd1 Pe1 pUb1 [Forkhead box protein O1]
NULL NULL
dnabound Foxo1 Pa0 Pd0 Pe0 pUb0 [double-stranded DNA; Forkhead box protein O1]
nucleus Foxo1 Pa1 Pd0 Pe1 pUb0 [Forkhead box protein O1]
PTEN ox [oxidized; Phosphatase and tensin homologPhosphatase and tensin homolog, isoform CRA_aProtein tyrosine phosphatase and tensin homolog/mutated in multiple advanced cancers proteinProtein tyrosine phosphatase and tensin-like protein]
nucleus RNA InR [ribonucleic acid; Insulin receptor]
dnabound Foxo1 Pa1 Pd1 Pe0 pUb0 [double-stranded DNA; Forkhead box protein O1]
Akt P2 [phosphorylated; RAC-alpha serine/threonine-protein kinase]
AS160 [TBC1 domain family member 4]
cytoplasm GLUT4 [Solute carrier family 2, facilitated glucose transporter member 4]
Ins [Insulin-1]
dnabound Foxo1 Pa1 Pd0 Pe0 pUb0 [double-stranded DNA; Forkhead box protein O1]
cytoplasm Foxo1 Pa1 Pd1 Pe0 pUb1 [Forkhead box protein O1]
cytoplasm Foxo1 Pa1 Pd1 Pe1 pUb1 [Forkhead box protein O1]
PKC [Atypical protein kinase C]
extracellular ROS [extracellular region; reactive oxygen species]

Observables: none

Secondary bacterial infections (SBIs) exacerbate influenza-associated disease and mortality. Antimicrobial agents can re…

Secondary bacterial infections (SBIs) exacerbate influenza-associated disease and mortality. Antimicrobial agents can reduce the severity of SBIs, but many have limited efficacy or cause adverse effects. Thus, new treatment strategies are needed. Kinetic models describing the infection process can help determine optimal therapeutic targets, the time scale on which a drug will be most effective, and how infection dynamics will change under therapy. To understand how different therapies perturb the dynamics of influenza infection and bacterial coinfection and to quantify the benefit of increasing a drug's efficacy or targeting a different infection process, I analyzed data from mice treated with an antiviral, an antibiotic, or an immune modulatory agent with kinetic models. The results suggest that antivirals targeting the viral life cycle are most efficacious in the first 2 days of infection, potentially because of an improved immune response, and that increasing the clearance of infected cells is important for treatment later in the infection. For a coinfection, immunotherapy could control low bacterial loads with as little as 20 % efficacy, but more effective drugs would be necessary for high bacterial loads. Antibiotics targeting bacterial replication and administered 10 h after infection would require 100 % efficacy, which could be reduced to 40 % with prophylaxis. Combining immunotherapy with antibiotics could substantially increase treatment success. Taken together, the results suggest when and why some therapies fail, determine the efficacy needed for successful treatment, identify potential immune effects, and show how the regulation of underlying mechanisms can be used to design new therapeutic strategies. link: http://identifiers.org/pubmed/27679506

Parameters: none

States: none

Observables: none

BIOMD0000000164 @ v0.0.1

The model reproduces the compartmental model for Ran transport as depicted in Fig 3 of the paper. Model reproduced using…

The separate components of nucleocytoplasmic transport have been well characterized, including the key regulatory role of Ran, a guanine nucleotide triphosphatase. However, the overall system behavior in intact cells is difficult to analyze because the dynamics of these components are interdependent. We used a combined experimental and computational approach to study Ran transport in vivo. The resulting model provides the first quantitative picture of Ran flux between the nuclear and cytoplasmic compartments in eukaryotic cells. The model predicts that the Ran exchange factor RCC1, and not the flux capacity of the nuclear pore complex (NPC), is the crucial regulator of steady-state flux across the NPC. Moreover, it provides the first estimate of the total in vivo flux (520 molecules per NPC per second and predicts that the transport system is robust. link: http://identifiers.org/pubmed/11799242

Parameters:

Name Description
RCC1Kcat=8.5 s^(-1); RCC1Km=1.1 0.001*dimensionless*m^(-3)*mol Reaction: RanGDP_Nucleus => RanGTP_Nucleus; RCC1_Nucleus, NTF2_RanGDP_Nucleus, Rate Law: 0.75*RCC1Kcat*RCC1_Nucleus*RanGDP_Nucleus*1/(RCC1Km+RanGDP_Nucleus+NTF2_RanGDP_Nucleus)*Nucleus
I=0.0 dimensionless*A*m^(-2); NTF2_RanGDP_Kperm=3.73333 1E-6*dimensionless*m*s^(-1) Reaction: FNTF2_RanGDP_Cytosol => FNTF2_RanGDP_Nucleus, Rate Law: NTF2_RanGDP_Kperm*(FNTF2_RanGDP_Cytosol+(-FNTF2_RanGDP_Nucleus))*Nuc_membrane
Koff_RanBP1_binding=0.5 s^(-1); Kon_RanBP1_binding=100.0 1000*dimensionless*m^3*mol^(-1)*s^(-1) Reaction: FCarrier_RanGTP_Cytosol + RanBP1_Cytosol => FRanBP1_Carrier_RanGTP_Cytosol, Rate Law: (Kon_RanBP1_binding*FCarrier_RanGTP_Cytosol*RanBP1_Cytosol+(-Koff_RanBP1_binding*FRanBP1_Carrier_RanGTP_Cytosol))*Cytosol
I=0.0 dimensionless*A*m^(-2); Carrier_RanGTP_Kperm=0.173333 1E-6*dimensionless*m*s^(-1) Reaction: Carrier_RanGTP_Cytosol => Carrier_RanGTP_Nucleus, Rate Law: Carrier_RanGTP_Kperm*(Carrier_RanGTP_Cytosol+(-Carrier_RanGTP_Nucleus))*Nuc_membrane
Kon_RanGTP_Carrier_binding=100.0 1000*dimensionless*m^3*mol^(-1)*s^(-1); Koff_RanGTP_Carrier_binding=1.0 s^(-1) Reaction: Carrier_Nucleus + FRanGTP_Nucleus => FCarrier_RanGTP_Nucleus, Rate Law: (Kon_RanGTP_Carrier_binding*Carrier_Nucleus*FRanGTP_Nucleus+(-Koff_RanGTP_Carrier_binding*FCarrier_RanGTP_Nucleus))*Nucleus
Vmax_RanGTP_dephosphorylation_RanGTP_dephosphorylation = NaN 0.001*dimensionless*m^(-3)*mol*s^(-1); Km_RanGTP_dephosphorylation=0.43 0.001*dimensionless*m^(-3)*mol Reaction: RanGTP_Cytosol => RanGDP_Cytosol; RanGAP_Cytosol, Rate Law: Vmax_RanGTP_dephosphorylation_RanGTP_dephosphorylation*RanGTP_Cytosol*1/(Km_RanGTP_dephosphorylation+RanGTP_Cytosol)*Cytosol
Km_dephosphorylation=0.43 0.001*dimensionless*m^(-3)*mol; Vmax_dephosphorylation_dephosphorylationF = NaN 0.001*dimensionless*m^(-3)*mol*s^(-1) Reaction: FRanBP1_Carrier_RanGTP_Cytosol => FRanGDP_Cytosol + RanBP1_Cytosol + Carrier_Cytosol; RanGAP_Cytosol, Rate Law: Vmax_dephosphorylation_dephosphorylationF*FRanBP1_Carrier_RanGTP_Cytosol*1/(Km_dephosphorylation+FRanBP1_Carrier_RanGTP_Cytosol)*Cytosol
Koff_NTF2_RanGDP_unbinding=2.5 s^(-1); Kon_NTF2_RanGDP_unbinding=100.0 1000*dimensionless*m^3*mol^(-1)*s^(-1) Reaction: NTF2_RanGDP_Nucleus => RanGDP_Nucleus + NTF2_Nucleus, Rate Law: (Koff_NTF2_RanGDP_unbinding*NTF2_RanGDP_Nucleus+(-Kon_NTF2_RanGDP_unbinding*RanGDP_Nucleus*NTF2_Nucleus))*Nucleus
I=0.0 dimensionless*A*m^(-2); Carrier_Kperm=1.86667 1E-6*dimensionless*m*s^(-1) Reaction: Carrier_Cytosol => Carrier_Nucleus, Rate Law: Carrier_Kperm*(Carrier_Cytosol+(-Carrier_Nucleus))*Nuc_membrane
RanGDP_Kperm=0.0 1E-6*dimensionless*m*s^(-1); I=0.0 dimensionless*A*m^(-2) Reaction: FRanGDP_Cytosol => FRanGDP_Nucleus, Rate Law: RanGDP_Kperm*(FRanGDP_Cytosol+(-FRanGDP_Nucleus))*Nuc_membrane
I=0.0 dimensionless*A*m^(-2); NTF2_Kperm=3.73333 1E-6*dimensionless*m*s^(-1) Reaction: NTF2_Cytosol => NTF2_Nucleus, Rate Law: NTF2_Kperm*(NTF2_Cytosol+(-NTF2_Nucleus))*Nuc_membrane
Koff_NTF2_RanGDP_binding=2.5 s^(-1); Kon_NTF2_RanGDP_binding=100.0 1000*dimensionless*m^3*mol^(-1)*s^(-1) Reaction: NTF2_Cytosol + FRanGDP_Cytosol => FNTF2_RanGDP_Cytosol, Rate Law: (Kon_NTF2_RanGDP_binding*NTF2_Cytosol*FRanGDP_Cytosol+(-Koff_NTF2_RanGDP_binding*FNTF2_RanGDP_Cytosol))*Cytosol
RanGTP_Kperm=0.0 1E-6*dimensionless*m*s^(-1); I=0.0 dimensionless*A*m^(-2) Reaction: RanGTP_Cytosol => RanGTP_Nucleus, Rate Law: RanGTP_Kperm*(RanGTP_Cytosol+(-RanGTP_Nucleus))*Nuc_membrane
Vmax_RanGTP_dephosphorylation_FRanGTP_dephosphorylation = NaN 0.001*dimensionless*m^(-3)*mol*s^(-1); Km_RanGTP_dephosphorylation=0.43 0.001*dimensionless*m^(-3)*mol Reaction: FRanGTP_Cytosol => FRanGDP_Cytosol; RanGAP_Cytosol, Rate Law: Vmax_RanGTP_dephosphorylation_FRanGTP_dephosphorylation*FRanGTP_Cytosol*1/(Km_RanGTP_dephosphorylation+FRanGTP_Cytosol)*Cytosol
ar_for_Microinj = 0.0 Reaction: => FRanGDP_Cytosol; Pipet_Cytosol, Rate Law: ar_for_Microinj*Cytosol*1
Koff_Carrier_RanGTP_binding=0.0 s^(-1); Kon_Carrier_RanGTP_binding=0.0 1000*dimensionless*m^3*mol^(-1)*s^(-1) Reaction: Carrier_Cytosol + FRanGTP_Cytosol => FCarrier_RanGTP_Cytosol, Rate Law: (Kon_Carrier_RanGTP_binding*Carrier_Cytosol*FRanGTP_Cytosol+(-Koff_Carrier_RanGTP_binding*FCarrier_RanGTP_Cytosol))*Cytosol
Km_dephosphorylation=0.43 0.001*dimensionless*m^(-3)*mol; Vmax_dephosphorylation_dephosphorylation = NaN 0.001*dimensionless*m^(-3)*mol*s^(-1) Reaction: RanBP1_Carrier_RanGTP_Cytosol => RanGDP_Cytosol + Carrier_Cytosol + RanBP1_Cytosol; RanGAP_Cytosol, Rate Law: Vmax_dephosphorylation_dephosphorylation*RanBP1_Carrier_RanGTP_Cytosol*1/(Km_dephosphorylation+RanBP1_Carrier_RanGTP_Cytosol)*Cytosol

States:

Name Description
Carrier Cytosol Carrier_Cytosol
FNTF2 RanGDP Cytosol [Nuclear transport factor 2; GTP-binding nuclear protein Ran; GDP; GDP]
RanGTP Nucleus [GTP; GTP-binding nuclear protein Ran; GTP-binding nuclear protein Ran; GTP; GTP]
FRanGDP Cytosol [GTP-binding nuclear protein Ran; GDP; GDP]
Carrier RanGTP Nucleus [GTP; GTP-binding nuclear protein Ran; GTP-binding nuclear protein Ran; GTP; GTP]
RanGDP Nucleus [GTP-binding nuclear protein Ran; GDP; GDP]
FRanGDP Nucleus [GTP-binding nuclear protein Ran; GDP; GDP]
NTF2 Nucleus [Nuclear transport factor 2]
NTF2 Cytosol [Nuclear transport factor 2]
Carrier RanGTP Cytosol [GTP; GTP-binding nuclear protein Ran; GTP-binding nuclear protein Ran; GTP; GTP]
RanGTP Cytosol [GTP; GTP-binding nuclear protein Ran; GTP-binding nuclear protein Ran; GTP; GTP]
NTF2 RanGDP Nucleus [GTP-binding nuclear protein Ran; Nuclear transport factor 2; GDP; GDP]
RanBP1 Carrier RanGTP Cytosol [GTP; GTP-binding nuclear protein Ran; GTP]
FNTF2 RanGDP Nucleus [Nuclear transport factor 2; GTP-binding nuclear protein Ran; GDP; GDP]
RanGDP Cytosol [GTP-binding nuclear protein Ran; GDP; GDP]
NTF2 RanGDP Cytosol [Nuclear transport factor 2; GTP-binding nuclear protein Ran; GDP; GDP]
FCarrier RanGTP Cytosol [GTP; GTP-binding nuclear protein Ran; GTP-binding nuclear protein Ran; GTP; GTP]
FRanGTP Cytosol [GTP; GTP-binding nuclear protein Ran; GTP-binding nuclear protein Ran; GTP; GTP]
FCarrier RanGTP Nucleus [GTP; GTP-binding nuclear protein Ran; GTP-binding nuclear protein Ran; GTP; GTP]
FRanBP1 Carrier RanGTP Cytosol [GTP; GTP-binding nuclear protein Ran; GTP-binding nuclear protein Ran; GTP; GTP]
FRanGTP Nucleus [GTP; GTP-binding nuclear protein Ran; GTP-binding nuclear protein Ran; GTP; GTP]
RanBP1 Cytosol RanBP1_Cytosol
Carrier Nucleus Carrier_Nucleus

Observables: none

BIOMD0000000025 @ v0.0.1

This model originates from BioModels Database: A Database of Annotated Published Models. It is copyright (c) 2005-2010 T…

Although several detailed models of molecular processes essential for circadian oscillations have been developed, their complexity makes intuitive understanding of the oscillation mechanism difficult. The goal of the present study was to reduce a previously developed, detailed model to a minimal representation of the transcriptional regulation essential for circadian rhythmicity in Drosophila. The reduced model contains only two differential equations, each with time delays. A negative feedback loop is included, in which PER protein represses per transcription by binding the dCLOCK transcription factor. A positive feedback loop is also included, in which dCLOCK indirectly enhances its own formation. The model simulated circadian oscillations, light entrainment, and a phase-response curve with qualitative similarities to experiment. Time delays were found to be essential for simulation of circadian oscillations with this model. To examine the robustness of the simplified model to fluctuations in molecule numbers, a stochastic variant was constructed. Robust circadian oscillations and entrainment to light pulses were simulated with fewer than 80 molecules of each gene product present on average. Circadian oscillations persisted when the positive feedback loop was removed. Moreover, elimination of positive feedback did not decrease the robustness of oscillations to stochastic fluctuations or to variations in parameter values. Such reduced models can aid understanding of the oscillation mechanisms in Drosophila and in other organisms in which feedback regulation of transcription may play an important role. link: http://identifiers.org/pubmed/12414672

Parameters:

Name Description
kdp = 0.5 per_hr Reaction: dClk => EmptySet, Rate Law: kdp*dClk*CELL
K1 = 0.3 nM; dClkF_tau1 = NaN nM; Vsp = 0.5 nM_per_hr Reaction: EmptySet => Per; dClkF, Rate Law: Vsp*dClkF_tau1/(K1+dClkF_tau1)*CELL
kdc = 0.5 per_hr Reaction: Per => EmptySet, Rate Law: kdc*Per*CELL
K2 = 0.1 nM; Vsc = 0.25 nM_per_hr; dClkF_tau2 = NaN nM Reaction: EmptySet => dClk; dClkF, Rate Law: CELL*Vsc*K2/(K2+dClkF_tau2)

States:

Name Description
dClkF [Circadian locomoter output cycles protein kaput]
dClk [Period circadian protein; Circadian locomoter output cycles protein kaput]
Per [Period circadian protein]

Observables: none

BIOMD0000000034 @ v0.0.1

No inititial conditions are specified in the paper. Because there is a basal rate of transcription for each gene, it doe…

A model of Drosophila circadian rhythm generation was developed to represent feedback loops based on transcriptional regulation of per, Clk (dclock), Pdp-1, and vri (vrille). The model postulates that histone acetylation kinetics make transcriptional activation a nonlinear function of [CLK]. Such a nonlinearity is essential to simulate robust circadian oscillations of transcription in our model and in previous models. Simulations suggest that two positive feedback loops involving Clk are not essential for oscillations, because oscillations of [PER] were preserved when Clk, vri, or Pdp-1 expression was fixed. However, eliminating positive feedback by fixing vri expression altered the oscillation period. Eliminating the negative feedback loop in which PER represses per expression abolished oscillations. Simulations of per or Clk null mutations, of per overexpression, and of vri, Clk, or Pdp-1 heterozygous null mutations altered model behavior in ways similar to experimental data. The model simulated a photic phase-response curve resembling experimental curves, and oscillations entrained to simulated light-dark cycles. Temperature compensation of oscillation period could be simulated if temperature elevation slowed PER nuclear entry or PER phosphorylation. The model makes experimental predictions, some of which could be tested in transgenic Drosophila. link: http://identifiers.org/pubmed/15111397

Parameters:

Name Description
parameter_0000048 = 0.00531 Reaction: species_0000001 =>, Rate Law: compartment_0000001*parameter_0000048*species_0000001
parameter_0000043 = 0.001; parameter_0000042 = 0.3186 Reaction: species_0000001 => species_0000002, Rate Law: compartment_0000001*parameter_0000042*species_0000001/(parameter_0000043+species_0000001)
parameter_0000010 = 0.54; parameter_0000008 = 0.54; parameter_0000030 = 1.062; parameter_0000033 = 0.001062 Reaction: => species_0000008; species_0000009, species_0000007, Rate Law: compartment_0000001*(parameter_0000030*species_0000009^2/(species_0000009^2+parameter_0000010^2)*parameter_0000008^2/(species_0000007^2+parameter_0000008^2)+parameter_0000033)
parameter_0000040 = 1.6992; parameter_0000041 = 0.25 Reaction: species_0000004 => species_0000005, Rate Law: compartment_0000002*parameter_0000040*species_0000004/(parameter_0000041+species_0000004)
parameter_0000027 = 10.62; parameter_0000031 = 0.02124; parameter_0000021 = NaN Reaction: => species_0000004, Rate Law: compartment_0000002*(parameter_0000027*parameter_0000021+parameter_0000031)
parameter_0000037 = 0.7434 Reaction: species_0000007 =>, Rate Law: compartment_0000001*parameter_0000037*species_0000007
parameter_0000038 = 0.6903 Reaction: species_0000009 =>, Rate Law: compartment_0000001*parameter_0000038*species_0000009
parameter_0000046 = 5.31; parameter_0000047 = 0.01 Reaction: species_0000003 =>, Rate Law: compartment_0000001*parameter_0000046*species_0000003/(parameter_0000047+species_0000003)
parameter_0000044 = 1.6992; parameter_0000045 = 0.25 Reaction: species_0000006 => species_0000001, Rate Law: compartment_0000002*parameter_0000044*species_0000006/(parameter_0000045+species_0000006)
parameter_0000020 = NaN; parameter_0000028 = 76.464; parameter_0000032 = 0.19116 Reaction: => species_0000007, Rate Law: compartment_0000001*(parameter_0000028*parameter_0000020+parameter_0000032)
parameter_0000036 = 0.2124 Reaction: species_0000008 =>, Rate Law: compartment_0000001*parameter_0000036*species_0000008
parameter_0000029 = 344.09; parameter_0000022 = NaN; parameter_0000034 = 0.38232; parameter_0000039 = 2.8249 Reaction: => species_0000009, Rate Law: compartment_0000001*delay(parameter_0000029*parameter_0000022+parameter_0000034, parameter_0000039)

States:

Name Description
species 0000008 [Circadian locomoter output cycles protein kaput; Period circadian protein]
species 0000005 [Period circadian protein]
species 0000002 [Period circadian protein]
species 0000003 [Period circadian protein]
species 0000001 [Period circadian protein]
species 0000007 [BZIP transcription factor]
species 0000004 [Period circadian protein]
species 0000009 [PAR domain protein 1-epislonPAR domain protein 1-epsilon]
species 0000006 [Period circadian protein]

Observables: none

This is a mathematical model describing the formation of long-term potentiation (LTP) at the Schaffer collateral of CA1…

The transition from early long-term potentiation (E-LTP) to late long-term potentiation (L-LTP) is a multistep process that involves both protein synthesis and degradation. The ways in which these two opposing processes interact to establish L-LTP are not well understood, however. For example, L-LTP is attenuated by inhibiting either protein synthesis or proteasome-dependent degradation prior to and during a tetanic stimulus (e.g., Huang et al., 1996; Karpova et al., 2006), but paradoxically, L-LTP is not attenuated when synthesis and degradation are inhibited simultaneously (Fonseca et al., 2006). These paradoxical results suggest that counter-acting 'positive' and 'negative' proteins regulate L-LTP. To investigate the basis of this paradox, we developed a model of LTP at the Schaffer collateral to CA1 pyramidal cell synapse. The model consists of nine ordinary differential equations that describe the levels of both positive- and negative-regulator proteins (PP and NP, respectively) and the transitions among five discrete synaptic states, including a basal state (BAS), three states corresponding to E-LTP (EP1, EP2, and ED), and a L-LTP state (LP). An LTP-inducing stimulus: 1) initiates the transition from BAS to EP1 and from EP1 to EP2; 2) initiates the synthesis of PP and NP; and finally; 3) activates the ubiquitin-proteasome system (UPS), which in turn, mediates transitions of EP1 and EP2 to ED and the degradation of NP. The conversion of E-LTP to L-LTP is mediated by the PP-dependent transition from ED to LP, whereas NP mediates reversal of EP2 to BAS. We found that the inclusion of the five discrete synaptic states was necessary to simulate key empirical observations: 1) normal L-LTP, 2) block of L-LTP by either proteasome inhibitor or protein synthesis inhibitor alone, and 3) preservation of L-LTP when both inhibitors are applied together. Although our model is abstract, elements of the model can be correlated with specific molecular processes. Moreover, the model correctly captures the dynamics of protein synthesis- and degradation-dependent phases of LTP, and it makes testable predictions, such as a unique synaptic state (ED) that precedes the transition from E-LTP to L-LTP, and a well-defined time window for the action of the UPS (i.e., during the transitions from EP1 and EP2 to ED). Tests of these predictions will provide new insights into the processes and dynamics of long-term synaptic plasticity. link: http://identifiers.org/pubmed/30138630

Parameters:

Name Description
kdeg2 = 0.01; LAC = 0.0 Reaction: NP => ; UPS, Rate Law: compartment*kdeg2*UPS*NP*(1-LAC)
PSI = 0.0; STIM = 1.0; ksyn2 = 2.0; ksyn2bas = 0.0014 Reaction: => NP, Rate Law: compartment*(1-PSI)*(ksyn2*STIM+ksyn2bas)
kdeg3 = 0.02 Reaction: STAB =>, Rate Law: compartment*kdeg3*STAB
kb3 = 0.02 Reaction: ED => BAS, Rate Law: compartment*kb3*ED
kf4 = 0.02; LAC = 0.0 Reaction: EP2 => ED; UPS, Rate Law: compartment*kf4*UPS*(1-LAC)*EP2
ksyn1 = 1.0; PSI = 0.0; ksyn1bas = 0.0035; STIM = 1.0 Reaction: => PP, Rate Law: compartment*(1-PSI)*(ksyn1*STIM+ksyn1bas)
ksyn3 = 1.0; STIM = 1.0 Reaction: => STAB, Rate Law: compartment*ksyn3*STIM
kf1bas = 0.0; STIM = 1.0 Reaction: BAS => EP1, Rate Law: compartment*kf1bas*(1-STIM)*BAS
kb1 = 0.005 Reaction: EP1 => BAS, Rate Law: compartment*kb1*EP1
kdeact = 0.0143 Reaction: UPS =>, Rate Law: compartment*kdeact*UPS
kactbas = 0.00214 Reaction: => UPS, Rate Law: compartment*kactbas
kf3 = 0.01 Reaction: EP1 => EP2; STAB, Rate Law: compartment*kf3*STAB*EP1
kact = 0.2; STIM = 1.0 Reaction: => UPS, Rate Law: compartment*kact*STIM
kf2 = 0.02; LAC = 0.0 Reaction: EP1 => ED; UPS, Rate Law: compartment*kf2*UPS*(1-LAC)*EP1
STIM = 1.0; kf1 = 0.1 Reaction: BAS => EP1, Rate Law: compartment*kf1*STIM*BAS
ksyn3bas = 0.008 Reaction: => STAB, Rate Law: compartment*ksyn3bas
kb4 = 0.001 Reaction: LP => BAS, Rate Law: compartment*kb4*LP
kf5 = 5.0E-4 Reaction: ED => LP; PP, Rate Law: compartment*kf5*PP^2*ED
kb2 = 7.0E-4 Reaction: EP2 => BAS; NP, Rate Law: compartment*kb2*EP2*NP
kdeg1 = 0.005 Reaction: PP =>, Rate Law: compartment*kdeg1*PP
kdeg2bas = 0.002 Reaction: NP =>, Rate Law: compartment*kdeg2bas*NP

States:

Name Description
ED [C13281; C61589]
NP [Protein; Inhibitor]
EP1 [C13281; C61589]
PP [Protein; SBO:0000459]
UPS [PW:0000144]
LP [C13281; C25322]
BAS [C13281; C90067]
EP2 [C13281; C61589]
STAB [PR:000009238]

Observables: none

Sneppen2009 - Modeling proteasome dynamics in Parkinson's diseaseThis model is described in the article: [Modeling prot…

In Parkinson's disease (PD), there is evidence that alpha-synuclein (alphaSN) aggregation is coupled to dysfunctional or overburdened protein quality control systems, in particular the ubiquitin-proteasome system. Here, we develop a simple dynamical model for the on-going conflict between alphaSN aggregation and the maintenance of a functional proteasome in the healthy cell, based on the premise that proteasomal activity can be titrated out by mature alphaSN fibrils and their protofilament precursors. In the presence of excess proteasomes the cell easily maintains homeostasis. However, when the ratio between the available proteasome and the alphaSN protofilaments is reduced below a threshold level, we predict a collapse of homeostasis and onset of oscillations in the proteasome concentration. Depleted proteasome opens for accumulation of oligomers. Our analysis suggests that the onset of PD is associated with a proteasome population that becomes occupied in periodic degradation of aggregates. This behavior is found to be the general state of a proteasome/chaperone system under pressure, and suggests new interpretations of other diseases where protein aggregation could stress elements of the protein quality control system. link: http://identifiers.org/pubmed/19411740

Parameters:

Name Description
m = 25.0; gamma = 1.0 Reaction: F = m/(1+P)-gamma*F*P, Rate Law: m/(1+P)-gamma*F*P
sigma = 1.0; nu = 1.0; gamma = 1.0 Reaction: P = ((sigma-P)-gamma*F*P)+nu*C, Rate Law: ((sigma-P)-gamma*F*P)+nu*C
nu = 1.0; gamma = 1.0 Reaction: C = gamma*F*P-nu*C, Rate Law: gamma*F*P-nu*C

States:

Name Description
P [proteasome complex]
C [Alpha-synuclein; proteasome complex; supramolecular fiber]
F [supramolecular fiber; Alpha-synuclein]

Observables: none

MODEL1006230107 @ v0.0.1

This a model from the article: Intercellular calcium waves mediated by diffusion of inositol trisphosphate: a two-dime…

In response to mechanical stimulation of a single cell, airway epithelial cells in culture exhibit a wave of increased intracellular free Ca2+ concentration that spreads from cell to cell over a limited distance through the culture. We present a detailed analysis of the intercellular wave in a two-dimensional sheet of cells. The model is based on the hypothesis that the wave is the result of diffusion of inositol trisphosphate (IP3) from the stimulated cell. The two-dimensional model agrees well with experimental data and makes the following quantitative predictions: as the distance from the stimulated cells increases, 1) the intercellular delay increases exponentially, 2) the intracellular wave speed decreases exponentially, and 3) the arrival time increases exponentially. Furthermore, 4) a proportion of the cells at the periphery of the response will exhibit waves of decreased amplitude, 5) the intercellular membrane permeability to IP3 must be approximately 2 microns/s or greater, and 6) the ratio of the maximum concentration of IP3 in the stimulated cell to the Km of the IP3 receptor (with respect to IP3) must be approximately 300 or greater. These predictions constitute a rigorous test of the hypothesis that the intercellular Ca2+ waves are mediated by IP3 diffusion. link: http://identifiers.org/pubmed/7611375

Parameters: none

States: none

Observables: none

BIOMD0000000057 @ v0.0.1

This model was successfully tested on Jarnac and MathSBML. The model reproduces the time profile of "Open Probability" o…

The dynamic properties of the inositol (1,4,5)-trisphosphate (IP(3)) receptor are crucial for the control of intracellular Ca(2+), including the generation of Ca(2+) oscillations and waves. However, many models of this receptor do not agree with recent experimental data on the dynamic responses of the receptor. We construct a model of the IP(3) receptor and fit the model to dynamic and steady-state experimental data from type-2 IP(3) receptors. Our results indicate that, (i) Ca(2+) binds to the receptor using saturating, not mass-action, kinetics; (ii) Ca(2+) decreases the rate of IP(3) binding while simultaneously increasing the steady-state sensitivity of the receptor to IP(3); (iii) the rate of Ca(2+)-induced receptor activation increases with Ca(2+) and is faster than Ca(2+)-induced receptor inactivation; and (iv) IP(3) receptors are sequentially activated and inactivated by Ca(2+) even when IP(3) is bound. Our results emphasize that measurement of steady-state properties alone is insufficient to characterize the functional properties of the receptor. link: http://identifiers.org/pubmed/11842185

Parameters:

Name Description
lminus2 = 0.8; kminus1 = 0.04; lminus2=0.8; kminus1=0.04; Phi5 = 0.0 Reaction: A => I2, Rate Law: compartment*(Phi5*A-(kminus1+lminus2)*I2)
kminus3 = 29.8; kminus3=29.8; Phi3 = 0.0 Reaction: O => S, Rate Law: compartment*(Phi3*O-kminus3*S)
Phi4 = 0.0; Phi_minus4 = 0.0 Reaction: O => A, Rate Law: compartment*(Phi4*O-Phi_minus4*A)
lminus2 = 0.8; kminus1 = 0.04; Phi1 = 0.0; lminus2=0.8; kminus1=0.04 Reaction: R => I1, Rate Law: compartment*(Phi1*R-(kminus1+lminus2)*I1)
IP3=10.0; IP3 = 10.0; Phi_minus2 = 0.0; Phi2 = 0.0 Reaction: R => O, Rate Law: compartment*(Phi2*IP3*R-Phi_minus2*O)

States:

Name Description
I1 [IPR000493]
I2 [IPR000493]
S [IPR000493]
A [IPR000493]
R [IPR000493]
O [IPR000493]

Observables: none

MODEL7896869925 @ v0.0.1

This a model from the article: Mathematical modelling of prolactin-receptor interaction and the corollary for prolacti…

A mathematical model of prolactin regulating its own receptors was developed, and compared with experimental data on a qualitative level. The model incorporates the kinetics of prolactin-receptor interactions and subsequent signalling by prolactin-receptor dimers to regulate the production of receptor mRNA and hence the receptor population. The model relates changes in plasma prolactin concentration to prolactin receptor (PRLR) gene expression, and can be used for predictive purposes. The cell signalling that leads to the activation of target genes, and the mechanisms for regulation of transcription, were treated empirically in the model. The model's parameters were adjusted so that model simulations agreed with experimentally observed responses to administration of prolactin in sheep. In particular, the model correctly predicts insensitivity of receptor mRNA regulation to a series of subcutaneous injections of prolactin, versus sensitivity to prolonged infusion of prolactin. In the latter case, response was an acute down-regulation followed by a prolonged up-regulation of mRNA, with the magnitude of the up-regulation increasing with the duration of infusion period. The model demonstrates the feasibility of predicting the in vivo response of prolactin target genes to external manipulation of plasma prolactin, and could provide a useful tool for identifying optimal prolactin treatments for desirable outcomes. link: http://identifiers.org/pubmed/15757685

Parameters: none

States: none

Observables: none

Sohn2010 - Genome-scale metabolic network of Pichia pastoris (PpaMBEL1254)This model is described in the article: [Geno…

The methylotrophic yeast Pichia pastoris has gained much attention during the last decade as a platform for producing heterologous recombinant proteins of pharmaceutical importance, due to its ability to reproduce post-translational modification similar to higher eukaryotes. With the recent release of the full genome sequence for P. pastoris, in-depth study of its functions has become feasible. Here we present the first reconstruction of the genome-scale metabolic model of the eukaryote P. pastoris type strain DSMZ 70382, PpaMBEL1254, consisting of 1254 metabolic reactions and 1147 metabolites compartmentalized into eight different regions to represent organelles. Additionally, equations describing the production of two heterologous proteins, human serum albumin and human superoxide dismutase, were incorporated. The protein-producing model versions of PpaMBEL1254 were then analyzed to examine the impact on oxygen limitation on protein production. link: http://identifiers.org/pubmed/20503221

Parameters: none

States: none

Observables: none

Sohn2010 - Genome-scale metabolic network of Pseudomonas putida (PpuMBEL1071)This model is described in the article: [I…

Genome-scale metabolic models have been appearing with increasing frequency and have been employed in a wide range of biotechnological applications as well as in biological studies. With the metabolic model as a platform, engineering strategies have become more systematic and focused, unlike the random shotgun approach used in the past. Here we present the genome-scale metabolic model of the versatile Gram-negative bacterium Pseudomonas putida, which has gained widespread interest for various biotechnological applications. With the construction of the genome-scale metabolic model of P. putida KT2440, PpuMBEL1071, we investigated various characteristics of P. putida, such as its capacity for synthesizing polyhydroxyalkanoates (PHA) and degrading aromatics. Although P. putida has been characterized as a strict aerobic bacterium, the physiological characteristics required to achieve anaerobic survival were investigated. Through analysis of PpuMBEL1071, extended survival of P. putida under anaerobic stress was achieved by introducing the ackA gene from Pseudomonas aeruginosa and Escherichia coli. link: http://identifiers.org/pubmed/20540110

Parameters: none

States: none

Observables: none

Sohn2012 - Genome-scale metabolic network of Schizosaccharomyces pombe (SpoMBEL1693)This model is described in the artic…

BACKGROUND: Over the last decade, the genome-scale metabolic models have been playing increasingly important roles in elucidating metabolic characteristics of biological systems for a wide range of applications including, but not limited to, system-wide identification of drug targets and production of high value biochemical compounds. However, these genome-scale metabolic models must be able to first predict known in vivo phenotypes before it is applied towards these applications with high confidence. One benchmark for measuring the in silico capability in predicting in vivo phenotypes is the use of single-gene mutant libraries to measure the accuracy of knockout simulations in predicting mutant growth phenotypes. RESULTS: Here we employed a systematic and iterative process, designated as Reconciling In silico/in vivo mutaNt Growth (RING), to settle discrepancies between in silico prediction and in vivo observations to a newly reconstructed genome-scale metabolic model of the fission yeast, Schizosaccharomyces pombe, SpoMBEL1693. The predictive capabilities of the genome-scale metabolic model in predicting single-gene mutant growth phenotypes were measured against the single-gene mutant library of S. pombe. The use of RING resulted in improving the overall predictive capability of SpoMBEL1693 by 21.5%, from 61.2% to 82.7% (92.5% of the negative predictions matched the observed growth phenotype and 79.7% the positive predictions matched the observed growth phenotype). CONCLUSION: This study presents validation and refinement of a newly reconstructed metabolic model of the yeast S. pombe, through improving the metabolic model's predictive capabilities by reconciling the in silico predicted growth phenotypes of single-gene knockout mutants, with experimental in vivo growth data. link: http://identifiers.org/pubmed/22631437

Parameters: none

States: none

Observables: none

A fractional mathematical model of breast cancer competition model Author links open overlay panelJ.E.Solís-PérezaJ.F.Gó…

In this paper, a mathematical model which considers population dynamics among cancer stem cells, tumor cells, healthy cells, the effects of excess estrogen and the body’s natural immune response on the cell populations was considered. Fractional derivatives with power law and exponential decay law in Liouville–Caputo sense were considered. Special solutions using an iterative scheme via Laplace transform were obtained. Furthermore, numerical simulations of the model considering both derivatives were obtained using the Atangana–Toufik numerical method. Also, random model described by a system of random differential equations was presented. The use of fractional derivatives provides more useful information about the complexity of the dynamics of the breast cancer competition model.

Volume 127, October 2019, Pages 38-54 link: http://identifiers.org/doi/10.1016/j.chaos.2019.06.027

Parameters:

Name Description
a3 = 1250000.0; p3 = 100.0; delta = 6.0E-8 Reaction: H => ; T, E, Rate Law: compartment*(delta*H*T+p3*H*E/(a3+H))
gamma1 = 3.0E-7 Reaction: C => ; I, Rate Law: compartment*gamma1*I*C
tau = 2700.0 Reaction: => E, Rate Law: compartment*tau
q = 0.7; M3 = 2.5E7 Reaction: => H, Rate Law: compartment*q*H*(1-H/M3)
a2 = 1.135E7; mu = 0.97; a3 = 1250000.0; a1 = 1135000.0; d1 = 0.01; d2 = 0.01; d3 = 0.01 Reaction: E => ; C, T, H, Rate Law: compartment*(mu+d1*C/(a1+C)+d2*T/(a2+T)+d3*H/(a3+H))*E
gamma2 = 3.0E-6; n1 = 0.01 Reaction: T => ; I, Rate Law: compartment*(n1*T+gamma2*I*T)
s = 13000.0; w = 300000.0; p = 0.2 Reaction: => I; T, Rate Law: compartment*(s+p*I*T/(w+T))
p1 = 600.0; M1 = 2270000.0; k1 = 0.75; a1 = 1135000.0 Reaction: => C; E, Rate Law: compartment*(k1*C*(1-C/M1)+p1*C*E/(a1+C))
p2 = 0.0; M2 = 2.27E7; a2 = 1.135E7; M1 = 2270000.0; k2 = 0.514 Reaction: => T; C, E, Rate Law: compartment*(k2*C*C/M1*(1-T/M2)+p2*T*E/(a2+T))
gamma3 = 1.0E-7; v = 400.0; u = 0.2; n2 = 0.29 Reaction: I => ; T, E, Rate Law: compartment*(gamma3*I*T+n2*I+u*I*E/(v+E))

States:

Name Description
I [Immune Cell]
T [Neoplastic Cell]
C [BTO:0006293]
E E
H [Healthy]

Observables: none

BIOMD0000000114 @ v0.0.1

This model encoded according to the paper *Hormone induced Calcium Oscillations in Liver Cells Can Be Explained by a Sim…

Hormone-induced oscillations of the free intracellular calcium concentration are thought to be relevant for frequency encoding of hormone signals. In liver cells, such Ca2+ oscillations occur in response to stimulation by hormones acting via phosphoinositide breakdown. This observation may be explained by cooperative, positive feedback of Ca2+ on its own release from one inositol 1,4,5-trisphosphate-sensitive pool, obviating oscillations of inositol 1,4,5-trisphosphate. The kinetic rate laws of the associated model have a mathematical structure reminiscent of the Brusselator, a hypothetical chemical model involving a rather improbable trimolecular reaction step, thus giving a realistic biological interpretation to this hallmark of dissipative structures. We propose that calmodulin is involved in mediating this cooperativity and positive feedback, as suggested by the presented experiments. For one, hormone-induced calcium oscillations can be inhibited by the (nonphenothiazine) calmodulin antagonists calmidazolium or CGS 9343 B. Alternatively, in cells overstimulated by hormone, as characterized by a non-oscillatory elevated Ca2+ concentration, these antagonists could again restore sustained calcium oscillations. The experimental observations, including modulation of the oscillations by extracellular calcium, were in qualitative agreement with the predictions of our mathematical model. link: http://identifiers.org/pubmed/1904060

Parameters:

Name Description
alpha = 5.0; fy = NaN Reaction: x => y, Rate Law: alpha*fy*x*cytoplasm
k = 0.01; k1 = 2.0 Reaction: x => y, Rate Law: k*x*cytoplasm-k1*y*ER
beta = 1.0 Reaction: y =>, Rate Law: beta*y*extracellular
gamma = 1.0 Reaction: => y, Rate Law: gamma*cytoplasm

States:

Name Description
x [calcium(2+); Calcium cation]
y [calcium(2+); Calcium cation]