SBMLBioModels: F - I

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F


MODEL5662398146 @ v0.0.1

This model originates from BioModels Database: A Database of Annotated Published Models (http://www.ebi.ac.uk/biomodels/…

We present a genome-scale metabolic model for the archaeal methanogen Methanosarcina barkeri. We characterize the metabolic network and compare it to reconstructions from the prokaryotic, eukaryotic and archaeal domains. Using the model in conjunction with constraint-based methods, we simulate the metabolic fluxes and resulting phenotypes induced by different environmental and genetic conditions. This represents the first large-scale simulation of either a methanogen or an archaeal species. Model predictions are validated by comparison to experimental growth measurements and phenotypes of M. barkeri on different substrates. The predicted growth phenotypes for wild type and mutants of the methanogenic pathway have a high level of agreement with experimental findings. We further examine the efficiency of the energy-conserving reactions in the methanogenic pathway, specifically the Ech hydrogenase reaction, and determine a stoichiometry for the nitrogenase reaction. This work demonstrates that a reconstructed metabolic network can serve as an analysis platform to predict cellular phenotypes, characterize methanogenic growth, improve the genome annotation and further uncover the metabolic characteristics of methanogenesis. link: http://identifiers.org/pubmed/16738551

Parameters: none

States: none

Observables: none

MODEL5662324959 @ v0.0.1

This model originates from BioModels Database: A Database of Annotated Published Models (http://www.ebi.ac.uk/biomodels/…

We present a genome-scale metabolic model for the archaeal methanogen Methanosarcina barkeri. We characterize the metabolic network and compare it to reconstructions from the prokaryotic, eukaryotic and archaeal domains. Using the model in conjunction with constraint-based methods, we simulate the metabolic fluxes and resulting phenotypes induced by different environmental and genetic conditions. This represents the first large-scale simulation of either a methanogen or an archaeal species. Model predictions are validated by comparison to experimental growth measurements and phenotypes of M. barkeri on different substrates. The predicted growth phenotypes for wild type and mutants of the methanogenic pathway have a high level of agreement with experimental findings. We further examine the efficiency of the energy-conserving reactions in the methanogenic pathway, specifically the Ech hydrogenase reaction, and determine a stoichiometry for the nitrogenase reaction. This work demonstrates that a reconstructed metabolic network can serve as an analysis platform to predict cellular phenotypes, characterize methanogenic growth, improve the genome annotation and further uncover the metabolic characteristics of methanogenesis. link: http://identifiers.org/pubmed/16738551

Parameters: none

States: none

Observables: none

MODEL5662425708 @ v0.0.1

This model originates from BioModels Database: A Database of Annotated Published Models (http://www.ebi.ac.uk/biomodels/…

We present a genome-scale metabolic model for the archaeal methanogen Methanosarcina barkeri. We characterize the metabolic network and compare it to reconstructions from the prokaryotic, eukaryotic and archaeal domains. Using the model in conjunction with constraint-based methods, we simulate the metabolic fluxes and resulting phenotypes induced by different environmental and genetic conditions. This represents the first large-scale simulation of either a methanogen or an archaeal species. Model predictions are validated by comparison to experimental growth measurements and phenotypes of M. barkeri on different substrates. The predicted growth phenotypes for wild type and mutants of the methanogenic pathway have a high level of agreement with experimental findings. We further examine the efficiency of the energy-conserving reactions in the methanogenic pathway, specifically the Ech hydrogenase reaction, and determine a stoichiometry for the nitrogenase reaction. This work demonstrates that a reconstructed metabolic network can serve as an analysis platform to predict cellular phenotypes, characterize methanogenic growth, improve the genome annotation and further uncover the metabolic characteristics of methanogenesis. link: http://identifiers.org/pubmed/16738551

Parameters: none

States: none

Observables: none

MODEL3023609334 @ v0.0.1

organism E. coli K-12 MG1655 model iAF1260 Biomass Objective Function (BOF) Ec_biomass_iAF1260_core_59p81M (E. coli biom…

An updated genome-scale reconstruction of the metabolic network in Escherichia coli K-12 MG1655 is presented. This updated metabolic reconstruction includes: (1) an alignment with the latest genome annotation and the metabolic content of EcoCyc leading to the inclusion of the activities of 1260 ORFs, (2) characterization and quantification of the biomass components and maintenance requirements associated with growth of E. coli and (3) thermodynamic information for the included chemical reactions. The conversion of this metabolic network reconstruction into an in silico model is detailed. A new step in the metabolic reconstruction process, termed thermodynamic consistency analysis, is introduced, in which reactions were checked for consistency with thermodynamic reversibility estimates. Applications demonstrating the capabilities of the genome-scale metabolic model to predict high-throughput experimental growth and gene deletion phenotypic screens are presented. The increased scope and computational capability using this new reconstruction is expected to broaden the spectrum of both basic biology and applied systems biology studies of E. coli metabolism. link: http://identifiers.org/pubmed/17593909

Parameters: none

States: none

Observables: none

MODEL3023641273 @ v0.0.1

organism E. coli K-12 MG1655 model iAF1260 Biomass Objective Function (BOF) Ec_biomass_iAF1260_core_59p81M (E. coli biom…

An updated genome-scale reconstruction of the metabolic network in Escherichia coli K-12 MG1655 is presented. This updated metabolic reconstruction includes: (1) an alignment with the latest genome annotation and the metabolic content of EcoCyc leading to the inclusion of the activities of 1260 ORFs, (2) characterization and quantification of the biomass components and maintenance requirements associated with growth of E. coli and (3) thermodynamic information for the included chemical reactions. The conversion of this metabolic network reconstruction into an in silico model is detailed. A new step in the metabolic reconstruction process, termed thermodynamic consistency analysis, is introduced, in which reactions were checked for consistency with thermodynamic reversibility estimates. Applications demonstrating the capabilities of the genome-scale metabolic model to predict high-throughput experimental growth and gene deletion phenotypic screens are presented. The increased scope and computational capability using this new reconstruction is expected to broaden the spectrum of both basic biology and applied systems biology studies of E. coli metabolism. link: http://identifiers.org/pubmed/17593909

Parameters: none

States: none

Observables: none

The paper describes a basic model of immune-cancer interaction. Created by COPASI 4.25 (Build 207) This model is desc…

In this paper, we develop a theoretical contribution towards the understanding of the complex behavior of conjoint tumor-normal cell growth under the influence of immuno-chemotherapeutic agents under simple immune system response. In particular, we consider a core model for the interaction of tumor cells with the surrounding normal cells. We then add the effects of a simple immune system, and both immune-suppression factors and immuno-chemotherapeutic agents as well. Through a series of numerical simulations, we illustrate that the interdependency of tumor-normal cells, together with choice of drug and the nature of the immunodeficiency, leads to a variety of interesting patterns in the evolution of both the tumor and the normal cell populations. link: http://identifiers.org/pubmed/21647303

Parameters:

Name Description
t = 300000.0 1; k = 0.028 1 Reaction: => N; T, Rate Law: tumor_microenvironment*k*T*(1-T/t)
r0 = 1.0 1; r1 = 1000.0 1; b = 1.0 1 Reaction: T => ; N, Rate Law: tumor_microenvironment*b*r0*N/(r1+N)
rt = 0.3 1; kt = 1200000.0 1 Reaction: => T, Rate Law: tumor_microenvironment*rt*T*(1-T/kt)
rn = 0.4 1; kn = 1000000.0 1 Reaction: => N, Rate Law: tumor_microenvironment*rn*N*(1-N/kn)

States:

Name Description
T [malignant cell]
N [cell]

Observables: none

FelixGarza2017 - Blue Light Treatment of Psoriasis (simplified)This model is described in the article: [A Dynamic Model…

Clinical investigations prove that blue light irradiation reduces the severity of psoriasis vulgaris. Nevertheless, the mechanisms involved in the management of this condition remain poorly defined. Despite the encouraging results of the clinical studies, no clear guidelines are specified in the literature for the irradiation scheme regime of blue light-based therapy for psoriasis. We investigated the underlying mechanism of blue light irradiation of psoriatic skin, and tested the hypothesis that regulation of proliferation is a key process. We implemented a mechanistic model of cellular epidermal dynamics to analyze whether a temporary decrease of keratinocytes hyper-proliferation can explain the outcome of phototherapy with blue light. Our results suggest that the main effect of blue light on keratinocytes impacts the proliferative cells. They show that the decrease in the keratinocytes proliferative capacity is sufficient to induce a transient decrease in the severity of psoriasis. To study the impact of the therapeutic regime on the efficacy of psoriasis treatment, we performed simulations for different combinations of the treatment parameters, i.e., length of treatment, fluence (also referred to as dose), and intensity. These simulations indicate that high efficacy is achieved by regimes with long duration and high fluence levels, regardless of the chosen intensity. Our modeling approach constitutes a framework for testing diverse hypotheses on the underlying mechanism of blue light-based phototherapy, and for designing effective strategies for the treatment of psoriasis. link: http://identifiers.org/pubmed/28184200

Parameters:

Name Description
k4 = 0.0556 Reaction: xFinal_4 => xFinal_5, Rate Law: compartmentOne*k4*xFinal_4/compartmentOne
apopFBL = 0.0; k3 = 0.216; AIh = 0.0012 Reaction: xFinal_3 =>, Rate Law: compartmentOne*(k3*xFinal_3*AIh/(1-AIh)+apopFBL*xFinal_3)/compartmentOne
apopFBL = 0.0; alpha = 0.0714 Reaction: xFinal_6 =>, Rate Law: compartmentOne*(alpha*xFinal_6+apopFBL*xFinal_6)/compartmentOne
rhoTA = 4.0; k2s = 0.0173 Reaction: xFinal_8 => xFinal_9, Rate Law: Psoriatic*k2s*rhoTA*xFinal_8/compartmentOne
Pscmax = 4500.0; lambda = 3.5; bProl = -0.003404; doseBL = 52.11; aProl = 1.0; rhoSC = 4.0; gamma1h = 0.0033 Reaction: xFinal_6 + xFinal_7 => xFinal_6, Rate Law: aProl*gamma1h*rhoSC*exp(bProl*doseBL)*xFinal_7*xFinal_6/(lambda*Pscmax)/compartmentOne
apopFBL = 0.0; alpha = 0.0714; rhoDe = 4.0 Reaction: xFinal_12 =>, Rate Law: Psoriatic*(alpha*rhoDe*xFinal_12+apopFBL*xFinal_12)/compartmentOne
apopFBL = 0.0; k4 = 0.0556; AIh = 0.0012 Reaction: xFinal_4 =>, Rate Law: compartmentOne*(k4*xFinal_4*AIh/(1-AIh)+apopFBL*xFinal_4)/compartmentOne
k2a = 0.138 Reaction: xFinal_2 => xFinal_2 + xFinal_3, Rate Law: compartmentOne*k2a*xFinal_2/compartmentOne
k2a = 0.138; rhoTA = 4.0 Reaction: xFinal_8 => xFinal_8 + xFinal_9, Rate Law: Psoriatic*k2a*rhoTA*xFinal_8/compartmentOne
apopFBL = 0.0; AId = 3.5E-4; rhoTA = 4.0; k2s = 0.0173 Reaction: xFinal_8 =>, Rate Law: Psoriatic*(AId*k2s*xFinal_8*rhoTA/(1-AId)+apopFBL*xFinal_8)/compartmentOne
apopFBL = 0.0; k1sh = 0.00164; AIh = 0.0012 Reaction: xFinal_1 =>, Rate Law: compartmentOne*(k1sh*xFinal_1*AIh/(1-AIh)+apopFBL*xFinal_1)/compartmentOne
k5 = 0.111 Reaction: xFinal_5 => xFinal_6, Rate Law: compartmentOne*k5*xFinal_5/compartmentOne
bProl = -0.003404; doseBL = 52.11; Ptah = 11184.7844353585; aProl = 1.0; k1sh = 0.00164; Pscmax = 4500.0; n = 3.0; gamma1h = 0.0033; omega = 100.0 Reaction: xFinal_1 + xFinal_2 + xFinal_8 => xFinal_2 + xFinal_8, Rate Law: (gamma1h*aProl*exp(bProl*doseBL)*xFinal_1*omega*xFinal_1/(1+(omega-1)*((xFinal_2+xFinal_8)/Ptah)^n)/Pscmax+k1sh*xFinal_1*omega/(1+(omega-1)*((xFinal_2+xFinal_8)/Ptah)^n))/compartmentOne
k1sh = 0.00164; rhoSC = 4.0 Reaction: xFinal_7 => xFinal_8, Rate Law: Psoriatic*k1sh*rhoSC*xFinal_7/compartmentOne
n = 3.0; Ptah = 11184.7844353585; k1sh = 0.00164; omega = 100.0 Reaction: xFinal_1 + xFinal_2 + xFinal_8 => xFinal_1 + xFinal_2 + xFinal_8, Rate Law: omega*xFinal_1*k1sh/(1+(omega-1)*((xFinal_2+xFinal_8)/Ptah)^n)/compartmentOne
rhoTr = 5.0; apopFBL = 0.0; k4 = 0.0556; AId = 3.5E-4 Reaction: xFinal_10 =>, Rate Law: Psoriatic*(AId*k4*xFinal_10*rhoTr/(1-AId)+apopFBL*xFinal_10)/compartmentOne
rhoTr = 5.0; apopFBL = 0.0; k3 = 0.216; AId = 3.5E-4 Reaction: xFinal_9 =>, Rate Law: Psoriatic*(AId*k3*xFinal_9*rhoTr/(1-AId)+apopFBL*xFinal_9)/compartmentOne
k1ah = 0.0131; rhoSC = 4.0 Reaction: xFinal_7 => xFinal_7 + xFinal_8, Rate Law: Psoriatic*k1ah*rhoSC*xFinal_7/compartmentOne
gamma2 = 0.014; bProl = -0.003404; doseBL = 52.11; aProl = 1.0 Reaction: xFinal_2 => xFinal_2, Rate Law: compartmentOne*aProl*gamma2*exp(bProl*doseBL)*xFinal_2/compartmentOne
apopFBL = 0.0; k5 = 0.111; AIh = 0.0012 Reaction: xFinal_5 =>, Rate Law: compartmentOne*(k5*xFinal_5*AIh/(1-AIh)+apopFBL*xFinal_5)/compartmentOne
gamma2 = 0.014; bProl = -0.003404; doseBL = 52.11; aProl = 1.0; rhoTA = 4.0 Reaction: xFinal_8 => xFinal_8, Rate Law: Psoriatic*aProl*aProl*gamma2*rhoTA*exp(bProl*doseBL)*exp(bProl*doseBL)*xFinal_8/compartmentOne
n = 3.0; bProl = -0.003404; doseBL = 52.11; Ptah = 11184.7844353585; aProl = 1.0; gamma1h = 0.0033; omega = 100.0 Reaction: xFinal_1 + xFinal_2 + xFinal_8 => xFinal_1 + xFinal_2 + xFinal_8, Rate Law: aProl*gamma1h*exp(bProl*doseBL)*xFinal_1*omega/(1+(omega-1)*((xFinal_2+xFinal_8)/Ptah)^n)/compartmentOne
k2s = 0.0173 Reaction: xFinal_2 => xFinal_3, Rate Law: compartmentOne*k2s*xFinal_2/compartmentOne
Pscmax = 4500.0; n = 3.0; lambda = 3.5; bProl = -0.003404; doseBL = 52.11; Ptah = 11184.7844353585; aProl = 1.0; gamma1h = 0.0033; omega = 100.0 Reaction: xFinal_1 + xFinal_2 + xFinal_7 + xFinal_8 => xFinal_2 + xFinal_7 + xFinal_8, Rate Law: gamma1h*aProl*exp(bProl*doseBL)*xFinal_1*omega*xFinal_7/(1+(omega-1)*((xFinal_2+xFinal_8)/Ptah)^n)/lambda/Pscmax/compartmentOne
bProl = -0.003404; doseBL = 52.11; aProl = 1.0; rhoSC = 4.0; gamma1h = 0.0033 Reaction: xFinal_7 => xFinal_7, Rate Law: Psoriatic*aProl*gamma1h*rhoSC*exp(bProl*doseBL)*xFinal_7/compartmentOne
n = 3.0; k1ah = 0.0131; Ptah = 11184.7844353585; omega = 100.0 Reaction: xFinal_1 + xFinal_2 + xFinal_8 => xFinal_1 + xFinal_2 + xFinal_8, Rate Law: omega*xFinal_1*k1ah/(1+(omega-1)*((xFinal_2+xFinal_8)/Ptah)^n)/compartmentOne
rhoTr = 5.0; k3 = 0.216 Reaction: xFinal_9 => xFinal_10, Rate Law: Psoriatic*k3*rhoTr*xFinal_9/compartmentOne
rhoTr = 5.0; k4 = 0.0556 Reaction: xFinal_10 => xFinal_12, Rate Law: Psoriatic*k4*rhoTr*xFinal_10/compartmentOne
Kp = 6.0; apopFBL = 0.0; bProl = -0.003404; doseBL = 52.11; aProl = 1.0; k1sh = 0.00164; Pscmax = 4500.0; Ka = 392.772887665773; lambda = 3.5; rhoSC = 4.0; AId = 3.5E-4; gamma1h = 0.0033 Reaction: xFinal_7 =>, Rate Law: Psoriatic*(aProl*gamma1h*rhoSC*exp(bProl*doseBL)*xFinal_7*xFinal_7/(lambda*Pscmax)+AId*k1sh*xFinal_7*rhoSC/(1-AId)+apopFBL*xFinal_7+Kp*1/(Ka^2+xFinal_7^2)*xFinal_7^2)/compartmentOne
km1 = 1.0E-6 Reaction: xFinal_2 => xFinal_1, Rate Law: compartmentOne*km1*xFinal_2/compartmentOne
apopFBL = 0.0; AIh = 0.0012; k2s = 0.0173 Reaction: xFinal_2 =>, Rate Law: compartmentOne*(k2s*xFinal_2*AIh/(1-AIh)+apopFBL*xFinal_2)/compartmentOne
km2 = 1.0E-6 Reaction: xFinal_3 => xFinal_2, Rate Law: compartmentOne*km2*xFinal_3/compartmentOne
k3 = 0.216 Reaction: xFinal_3 => xFinal_4, Rate Law: compartmentOne*k3*xFinal_3/compartmentOne

States:

Name Description
xFinal 3 [keratinocyte; cell cycle arrest]
xFinal 5 [keratinocyte; granular cell of epidermis]
xFinal 4 [keratinocyte]
xFinal 12 [keratinocyte; corneocyte]
xFinal 9 [keratinocyte; cell cycle arrest]
xFinal 1 [keratinocyte; stem cell]
xFinal 8 [keratinocyte]
xFinal 7 [keratinocyte; stem cell]
xFinal 2 [keratinocyte]
xFinal 10 [keratinocyte]
xFinal 6 [keratinocyte; corneocyte]

Observables: none

MODEL0911989198 @ v0.0.1

This a model from the article: Vortex dynamics in three-dimensional continuous myocardium with fiber rotation: Filamen…

Wave propagation in ventricular muscle is rendered highly anisotropic by the intramural rotation of the fiber. This rotational anisotropy is especially important because it can produce a twist of electrical vortices, which measures the rate of rotation (in degree/mm) of activation wavefronts in successive planes perpendicular to a line of phase singularity, or filament. This twist can then significantly alter the dynamics of the filament. This paper explores this dynamics via numerical simulation. After a review of the literature, we present modeling tools that include: (i) a simplified ionic model with three membrane currents that approximates well the restitution properties and spiral wave behavior of more complex ionic models of cardiac action potential (Beeler-Reuter and others), and (ii) a semi-implicit algorithm for the fast solution of monodomain cable equations with rotational anisotropy. We then discuss selected results of a simulation study of vortex dynamics in a parallelepipedal slab of ventricular muscle of varying wall thickness (S) and fiber rotation rate (theta(z)). The main finding is that rotational anisotropy generates a sufficiently large twist to destabilize a single transmural filament and cause a transition to a wave turbulent state characterized by a high density of chaotically moving filaments. This instability is manifested by the propagation of localized disturbances along the filament and has no previously known analog in isotropic excitable media. These disturbances correspond to highly twisted and distorted regions of filament, or "twistons," that create vortex rings when colliding with the natural boundaries of the ventricle. Moreover, when sufficiently twisted, these rings expand and create additional filaments by further colliding with boundaries. This instability mechanism is distinct from the commonly invoked patchy failure or wave breakup that is not observed here during the initial instability. For modified Beeler-Reuter-like kinetics with stable reentry in two dimensions, decay into turbulence occurs in the left ventricle in about one second above a critical wall thickness in the range of 4-6 mm that matches experiment. However this decay is suppressed by uniformly decreasing excitability. Specific experiments to test these results, and a method to characterize the filament density during fibrillation are discussed. Results are contrasted with other mechanisms of fibrillation and future prospects are summarized. (c)1998 American Institute of Physics. link: http://identifiers.org/pubmed/12779708

Parameters: none

States: none

Observables: none

BIOMD0000000152 @ v0.0.1

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

Integration of neurotransmitter and neuromodulator signals in the striatum plays a central role in the functions and dysfunctions of the basal ganglia. DARPP-32 is a key actor of this integration in the GABAergic medium-size spiny neurons, in particular in response to dopamine and glutamate. When phosphorylated by cAMP-dependent protein kinase (PKA), DARPP-32 inhibits protein phosphatase-1 (PP1), whereas when phosphorylated by cyclin-dependent kinase 5 (CDK5) it inhibits PKA. DARPP-32 is also regulated by casein kinases and by several protein phosphatases. These complex and intricate regulations make simple predictions of DARPP-32 dynamic behaviour virtually impossible. We used detailed quantitative modelling of the regulation of DARPP-32 phosphorylation to improve our understanding of its function. The models included all the combinations of the three best-characterized phosphorylation sites of DARPP-32, their regulation by kinases and phosphatases, and the regulation of those enzymes by cAMP and Ca(2+) signals. Dynamic simulations allowed us to observe the temporal relationships between cAMP and Ca(2+) signals. We confirmed that the proposed regulation of protein phosphatase-2A (PP2A) by calcium can account for the observed decrease of Threonine 75 phosphorylation upon glutamate receptor activation. DARPP-32 is not simply a switch between PP1-inhibiting and PKA-inhibiting states. Sensitivity analysis showed that CDK5 activity is a major regulator of the response, as previously suggested. Conversely, the strength of the regulation of PP2A by PKA or by calcium had little effect on the PP1-inhibiting function of DARPP-32 in these conditions. The simulations showed that DARPP-32 is not only a robust signal integrator, but that its response also depends on the delay between cAMP and calcium signals affecting the response to the latter. This integration did not depend on the concentration of DARPP-32, while the absolute effect on PP1 varied linearly. In silico mutants showed that Ser137 phosphorylation affects the influence of the delay between dopamine and glutamate, and that constitutive phosphorylation in Ser137 transforms DARPP-32 in a quasi-irreversible switch. This work is a first attempt to better understand the complex interactions between cAMP and Ca(2+) regulation of DARPP-32. Progressive inclusion of additional components should lead to a realistic model of signalling networks underlying the function of striatal neurons. link: http://identifiers.org/pubmed/17194217

Parameters:

Name Description
kcat28=3.0 Reaction: D34_75_137_PP2C => D34_75 + PP2C, Rate Law: Spine*D34_75_137_PP2C*kcat28
kcat44=10.0 Reaction: cAMP_PDE => AMP + PDE, Rate Law: Spine*cAMP_PDE*kcat44
kon29=3.0E7 Reaction: CK1P + PP2B => CK1P_PP2B, Rate Law: Spine*CK1P*PP2B*kon29
kon7=4400000.0 Reaction: D75 + CK1 => D75CK1, Rate Law: Spine*D75*CK1*kon7
kon36=3.0E15 Reaction: PP2BinactiveCa2 + Ca => PP2B, Rate Law: Spine*PP2BinactiveCa2*Ca*Ca*kon36
kon38=5.4E7 Reaction: cAMP_R2C2 + cAMP => cAMP2_R2C2, Rate Law: Spine*cAMP_R2C2*cAMP*kon38
kon4=5600000.0 Reaction: D34 + CDK5 => D34_CDK5, Rate Law: Spine*D34*CDK5*kon4
kcat17=4.0 Reaction: D34_75_PP2B => D75 + PP2B, Rate Law: Spine*D34_75_PP2B*kcat17
koff39=110.0 Reaction: cAMP3_R2C2 => cAMP2_R2C2 + cAMP, Rate Law: Spine*cAMP3_R2C2*koff39
koff37=33.0 Reaction: cAMP_R2C2 => R2C2 + cAMP, Rate Law: Spine*cAMP_R2C2*koff37
kon43=60.0 Reaction: cAMP4_R2C => cAMP4_R2 + PKA, Rate Law: Spine*cAMP4_R2C*kon43
koff9=24.0 Reaction: D75_PP2A => D75 + PP2A, Rate Law: Spine*D75_PP2A*koff9
koff5=12.0 Reaction: D34_CK1 => D34 + CK1, Rate Law: Spine*D34_CK1*koff5
kcat34=5.0 Reaction: PP2AP => PP2A, Rate Law: Spine*PP2AP*kcat34
kcat6=4.0 Reaction: D34_PP2B => D + PP2B, Rate Law: Spine*D34_PP2B*kcat6
kcat5=3.0 Reaction: D34_CK1 => D34_137 + CK1, Rate Law: Spine*D34_CK1*kcat5
kcat29=6.0 Reaction: CK1P_PP2B => CK1 + PP2B, Rate Law: Spine*CK1P_PP2B*kcat29
koff36=1.0 Reaction: PP2B => PP2BinactiveCa2 + Ca, Rate Law: Spine*PP2B*koff36
kon27=75000.0 Reaction: D34_75_137 + PP2B => D34_75_137_PP2B, Rate Law: Spine*D34_75_137*PP2B*kon27
kon39=7.5E7 Reaction: cAMP2_R2C2 + cAMP => cAMP3_R2C2, Rate Law: Spine*cAMP2_R2C2*cAMP*kon39
kcat14=3.0 Reaction: D34_75_CK1 => D34_75_137 + CK1, Rate Law: Spine*D34_75_CK1*kcat14
kon14=4400000.0 Reaction: D34_75 + CK1 => D34_75_CK1, Rate Law: Spine*D34_75*CK1*kon14
kcat15=10.0 Reaction: D34_75_PP2A => D34 + PP2A, Rate Law: Spine*D34_75_PP2A*kcat15
kon3=5600000.0 Reaction: D + PKA => D_PKA, Rate Law: Spine*D*PKA*kon3
koff4=12.0 Reaction: D34_CDK5 => D34 + CDK5, Rate Law: Spine*D34_CDK5*koff4
koff27=120.0 Reaction: D34_75_137_PP2B => D34_75_137 + PP2B, Rate Law: Spine*D34_75_137_PP2B*koff27
kon19=75000.0 Reaction: D34_137 + PP2B => D34_137_PP2B, Rate Law: Spine*D34_137*PP2B*kon19
kon45=5040000.0 Reaction: cAMP + PDEP => cAMP_PDEP, Rate Law: Spine*cAMP*PDEP*kon45
kon24=7500000.0 Reaction: D75_137 + PP2C => D75_137_PP2C, Rate Law: Spine*D75_137*PP2C*kon24
koff40=32.5 Reaction: cAMP4_R2C2 => cAMP3_R2C2 + cAMP, Rate Law: Spine*cAMP4_R2C2*koff40
koff20=12.0 Reaction: D34_137_PP2C => D34_137 + PP2C, Rate Law: Spine*D34_137_PP2C*koff20
kcat20=3.0 Reaction: D34_137_PP2C => D34 + PP2C, Rate Law: Spine*D34_137_PP2C*kcat20
koff14=12.0 Reaction: D34_75_CK1 => D34_75 + CK1, Rate Law: Spine*D34_75_CK1*koff14
koff45=80.0 Reaction: cAMP_PDEP => cAMP + PDEP, Rate Law: Spine*cAMP_PDEP*koff45
kcat26=24.0 Reaction: D34_75_137_PP2AP => D34_137 + PP2AP, Rate Law: Spine*D34_75_137_PP2AP*kcat26
koff16=40.0 Reaction: D34_75_PP2AP => D34_75 + PP2AP, Rate Law: Spine*D34_75_PP2AP*koff16
koff24=12.0 Reaction: D75_137_PP2C => D75_137 + PP2C, Rate Law: Spine*D75_137_PP2C*koff24
kcat8=0.0 Reaction: D75_PKA => D34_75 + PKA, Rate Law: Spine*D75_PKA*kcat8
kon5=4400000.0 Reaction: D34 + CK1 => D34_CK1, Rate Law: Spine*D34*CK1*kon5
kon10=1.7E7 Reaction: D75 + PP2AP => D75_PP2AP, Rate Law: Spine*D75*PP2AP*kon10
kon23=1.7E7 Reaction: D75_137 + PP2AP => D75_137_PP2AP, Rate Law: Spine*D75_137*PP2AP*kon23
kon15=3800000.0 Reaction: D34_75 + PP2A => D34_75_PP2A, Rate Law: Spine*D34_75*PP2A*kon15
kon28=7500000.0 Reaction: D34_75_137 + PP2C => D34_75_137_PP2C, Rate Law: Spine*D34_75_137*PP2C*kon28
k57 = 2.5E-8 Reaction: Empty => Ca, Rate Law: Spine*k57
kon9=3800000.0 Reaction: D75 + PP2A => D75_PP2A, Rate Law: Spine*D75*PP2A*kon9
kcat23=24.0 Reaction: D75_137_PP2AP => D137 + PP2AP, Rate Law: Spine*D75_137_PP2AP*kcat23
kcat4=3.0 Reaction: D34_CDK5 => D34_75 + CDK5, Rate Law: Spine*D34_CDK5*kcat4
kon17=1.0E7 Reaction: D34_75 + PP2B => D34_75_PP2B, Rate Law: Spine*D34_75*PP2B*kon17
kcat16=24.0 Reaction: D34_75_PP2AP => D34 + PP2AP, Rate Law: Spine*D34_75_PP2AP*kcat16
koff28=12.0 Reaction: D34_75_137_PP2C => D34_75_137 + PP2C, Rate Law: Spine*D34_75_137_PP2C*koff28
kcat10=24.0 Reaction: D75_PP2AP => D + PP2AP, Rate Law: Spine*D75_PP2AP*kcat10
kon42=1.8E7 Reaction: cAMP4_R2 + PKA => cAMP4_R2C, Rate Law: Spine*cAMP4_R2*PKA*kon42
kcat33=4.0 Reaction: PP2A_PKA => PP2AP + PKA, Rate Law: Spine*PP2A_PKA*kcat33
kon1=5600000.0 Reaction: D + CDK5 => D_CDK5, Rate Law: Spine*kon1*D*CDK5
k58=1.7 Reaction: Ca => Empty, Rate Law: Spine*Ca*k58
koff15=24.0 Reaction: D34_75_PP2A => D34_75 + PP2A, Rate Law: Spine*D34_75_PP2A*koff15
kcat24=3.0 Reaction: D75_137_PP2C => D75 + PP2C, Rate Law: Spine*D75_137_PP2C*kcat24
koff19=0.12 Reaction: D34_137_PP2B => D34_137 + PP2B, Rate Law: Spine*D34_137_PP2B*koff19
koff17=1600.0 Reaction: D34_75_PP2B => D34_75 + PP2B, Rate Law: Spine*D34_75_PP2B*koff17
koff26=40.0 Reaction: D34_75_137_PP2AP => D34_75_137 + PP2AP, Rate Law: Spine*D34_75_137_PP2AP*koff26
koff1=12.0 Reaction: D_CDK5 => D + CDK5, Rate Law: Spine*D_CDK5*koff1
koff29=24.0 Reaction: CK1P_PP2B => CK1P + PP2B, Rate Law: Spine*CK1P_PP2B*koff29
koff6=16.0 Reaction: D34_PP2B => D34 + PP2B, Rate Law: Spine*D34_PP2B*koff6
kcat1=3.0 Reaction: D_CDK5 => D75 + CDK5, Rate Law: Spine*D_CDK5*kcat1
koff44=40.0 Reaction: cAMP_PDE => cAMP + PDE, Rate Law: Spine*cAMP_PDE*koff44
kon6=1.0E7 Reaction: D34 + PP2B => D34_PP2B, Rate Law: Spine*D34*PP2B*kon6
kcat27=0.03 Reaction: D34_75_137_PP2B => D75_137 + PP2B, Rate Law: Spine*D34_75_137_PP2B*kcat27
kcat19=0.03 Reaction: D34_137_PP2B => D137 + PP2B, Rate Law: Spine*D34_137_PP2B*kcat19
koff38=33.0 Reaction: cAMP2_R2C2 => cAMP_R2C2 + cAMP, Rate Law: Spine*cAMP2_R2C2*koff38
kon11=5600000.0 Reaction: D137 + CDK5 => D137_CDK5, Rate Law: Spine*D137*CDK5*kon11
kcat45=20.0 Reaction: cAMP_PDEP => AMP + PDEP, Rate Law: Spine*cAMP_PDEP*kcat45
koff41=60.0 Reaction: cAMP4_R2C2 => cAMP4_R2C + PKA, Rate Law: Spine*cAMP4_R2C2*koff41

States:

Name Description
D34 CDK5 [Cyclin-dependent-like kinase 5; Protein phosphatase 1 regulatory subunit 1B]
D34 75 CK1 [Casein kinase 1, epsilonCasein kinase1 epsilon-2; Protein phosphatase 1 regulatory subunit 1B]
D75 [Protein phosphatase 1 regulatory subunit 1B]
D PKA [Protein phosphatase 1 regulatory subunit 1B; PIRSF000582]
cAMP4 R2 [protein complex; 3',5'-cyclic AMP; PIRSF000548]
AMP [AMP]
cAMP PDEP [3',5'-cyclic AMP; IPR000396]
cAMP [3',5'-cyclic AMP]
cAMP4 R2C2 [3',5'-cyclic AMP; PIRSF000548; PIRSF000582; protein complex]
cAMP4 R2C [3',5'-cyclic AMP; PIRSF000548; PIRSF000582; protein complex]
PP2B [PIRSF000911]
PP2C [IPR015655]
D34 75 [Protein phosphatase 1 regulatory subunit 1B]
D75 PP2A [Protein phosphatase 1 regulatory subunit 1B; IPR006186]
cAMP R2C2 [protein complex; 3',5'-cyclic AMP; PIRSF000582; PIRSF000548]
cAMP PDE [3',5'-cyclic AMP; IPR000396]
cAMP2 R2C2 [3',5'-cyclic AMP; PIRSF000582; PIRSF000548; protein complex]
D34 PP2B [Protein phosphatase 1 regulatory subunit 1B; PIRSF000911]
PKA [PIRSF000582]
D75 PP2AP [Protein phosphatase 1 regulatory subunit 1B; IPR006186]
CDK5 [Cyclin-dependent-like kinase 5]
Empty Empty
D34 CK1 [Casein kinase 1, epsilonCasein kinase1 epsilon-2; Protein phosphatase 1 regulatory subunit 1B]
PP2AP [IPR006186]
D CDK5 [Cyclin-dependent-like kinase 5; Protein phosphatase 1 regulatory subunit 1B]
D34 [Protein phosphatase 1 regulatory subunit 1B]

Observables: none

BIOMD0000000153 @ v0.0.1

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

Integration of neurotransmitter and neuromodulator signals in the striatum plays a central role in the functions and dysfunctions of the basal ganglia. DARPP-32 is a key actor of this integration in the GABAergic medium-size spiny neurons, in particular in response to dopamine and glutamate. When phosphorylated by cAMP-dependent protein kinase (PKA), DARPP-32 inhibits protein phosphatase-1 (PP1), whereas when phosphorylated by cyclin-dependent kinase 5 (CDK5) it inhibits PKA. DARPP-32 is also regulated by casein kinases and by several protein phosphatases. These complex and intricate regulations make simple predictions of DARPP-32 dynamic behaviour virtually impossible. We used detailed quantitative modelling of the regulation of DARPP-32 phosphorylation to improve our understanding of its function. The models included all the combinations of the three best-characterized phosphorylation sites of DARPP-32, their regulation by kinases and phosphatases, and the regulation of those enzymes by cAMP and Ca(2+) signals. Dynamic simulations allowed us to observe the temporal relationships between cAMP and Ca(2+) signals. We confirmed that the proposed regulation of protein phosphatase-2A (PP2A) by calcium can account for the observed decrease of Threonine 75 phosphorylation upon glutamate receptor activation. DARPP-32 is not simply a switch between PP1-inhibiting and PKA-inhibiting states. Sensitivity analysis showed that CDK5 activity is a major regulator of the response, as previously suggested. Conversely, the strength of the regulation of PP2A by PKA or by calcium had little effect on the PP1-inhibiting function of DARPP-32 in these conditions. The simulations showed that DARPP-32 is not only a robust signal integrator, but that its response also depends on the delay between cAMP and calcium signals affecting the response to the latter. This integration did not depend on the concentration of DARPP-32, while the absolute effect on PP1 varied linearly. In silico mutants showed that Ser137 phosphorylation affects the influence of the delay between dopamine and glutamate, and that constitutive phosphorylation in Ser137 transforms DARPP-32 in a quasi-irreversible switch. This work is a first attempt to better understand the complex interactions between cAMP and Ca(2+) regulation of DARPP-32. Progressive inclusion of additional components should lead to a realistic model of signalling networks underlying the function of striatal neurons. link: http://identifiers.org/pubmed/17194217

Parameters:

Name Description
kon25=3800000.0 Reaction: D34_75_137 + PP2A => D34_75_137_PP2A, Rate Law: Spine*D34_75_137*PP2A*kon25
kcat3=2.7 Reaction: D_PKA => D34 + PKA, Rate Law: Spine*D_PKA*kcat3
kon7=4400000.0 Reaction: D75 + CK1 => D75CK1, Rate Law: Spine*D75*CK1*kon7
koff2=12.0 Reaction: D_CK1 => D + CK1, Rate Law: Spine*koff2*D_CK1
kcat50=24.0 Reaction: D34_75_PP2APCa => D34 + PP2APCa, Rate Law: Spine*D34_75_PP2APCa*kcat50
kon2=4400000.0 Reaction: D + CK1 => D_CK1, Rate Law: Spine*D*CK1*kon2
kon4=5600000.0 Reaction: D34 + CDK5 => D34_CDK5, Rate Law: Spine*D34*CDK5*kon4
kon56=200000.0 Reaction: PP2AP + Ca => PP2APCa, Rate Law: Spine*PP2AP*Ca*kon56
kcat55=4.0 Reaction: PP2ACa_PKA => PP2APCa + PKA, Rate Law: Spine*PP2ACa_PKA*kcat55
kon43=60.0 Reaction: cAMP4_R2C => cAMP4_R2 + PKA, Rate Law: Spine*cAMP4_R2C*kon43
koff9=24.0 Reaction: D75_PP2A => D75 + PP2A, Rate Law: Spine*D75_PP2A*koff9
kcat34=5.0 Reaction: PP2AP => PP2A, Rate Law: Spine*PP2AP*kcat34
koff5=12.0 Reaction: D34_CK1 => D34 + CK1, Rate Law: Spine*D34_CK1*koff5
kcat48=10.0 Reaction: D75_PP2ACa => D + PP2ACa, Rate Law: Spine*D75_PP2ACa*kcat48
kcat6=4.0 Reaction: D34_PP2B => D + PP2B, Rate Law: Spine*D34_PP2B*kcat6
kcat29=6.0 Reaction: CK1P_PP2B => CK1 + PP2B, Rate Law: Spine*CK1P_PP2B*kcat29
koff47=6.0 Reaction: D34_75_137_PP2ACa => D34_75_137 + PP2ACa, Rate Law: Spine*D34_75_137_PP2ACa*koff47
kcat5=3.0 Reaction: D34_CK1 => D34_137 + CK1, Rate Law: Spine*D34_CK1*kcat5
kon54=200000.0 Reaction: Ca + PP2A => PP2ACa, Rate Law: Spine*PP2A*Ca*kon54
koff55=16.0 Reaction: PP2ACa_PKA => PP2ACa + PKA, Rate Law: Spine*PP2ACa_PKA*koff55
kon26=1.7E7 Reaction: D34_75_137 + PP2AP => D34_75_137_PP2AP, Rate Law: Spine*D34_75_137*PP2AP*kon26
kon8=5600000.0 Reaction: D75 + PKA => D75_PKA, Rate Law: Spine*D75*PKA*kon8
kcat14=3.0 Reaction: D34_75_CK1 => D34_75_137 + CK1, Rate Law: Spine*D34_75_CK1*kcat14
kon3=5600000.0 Reaction: D + PKA => D_PKA, Rate Law: Spine*D*PKA*kon3
kcat18=3.0 Reaction: D34_137_CDK5 => D34_75_137 + CDK5, Rate Law: Spine*D34_137_CDK5*kcat18
koff4=12.0 Reaction: D34_CDK5 => D34 + CDK5, Rate Law: Spine*D34_CDK5*koff4
kon45=5040000.0 Reaction: cAMP + PDEP => cAMP_PDEP, Rate Law: Spine*cAMP*PDEP*kon45
kcat22=10.0 Reaction: D75_137_PP2A => D137 + PP2A, Rate Law: Spine*D75_137_PP2A*kcat22
kcat26=24.0 Reaction: D34_75_137_PP2AP => D34_137 + PP2AP, Rate Law: Spine*D34_75_137_PP2AP*kcat26
koff14=12.0 Reaction: D34_75_CK1 => D34_75 + CK1, Rate Law: Spine*D34_75_CK1*koff14
koff45=80.0 Reaction: cAMP_PDEP => cAMP + PDEP, Rate Law: Spine*cAMP_PDEP*koff45
koff16=40.0 Reaction: D34_75_PP2AP => D34_75 + PP2AP, Rate Law: Spine*D34_75_PP2AP*koff16
koff23=40.0 Reaction: D75_137_PP2AP => D75_137 + PP2AP, Rate Law: Spine*D75_137_PP2AP*koff23
kcat47=10.0 Reaction: D34_75_137_PP2ACa => D34_137 + PP2ACa, Rate Law: Spine*D34_75_137_PP2ACa*kcat47
kcat2=3.0 Reaction: D_CK1 => D137 + CK1, Rate Law: Spine*kcat2*D_CK1
kon5=4400000.0 Reaction: D34 + CK1 => D34_CK1, Rate Law: Spine*D34*CK1*kon5
kcat52=24.0 Reaction: D75_PP2APCa => D + PP2APCa, Rate Law: Spine*D75_PP2APCa*kcat52
kcat46=10.0 Reaction: D34_75_PP2ACa => D34 + PP2ACa, Rate Law: Spine*D34_75_PP2ACa*kcat46
kon10=1.7E7 Reaction: D75 + PP2AP => D75_PP2AP, Rate Law: Spine*D75*PP2AP*kon10
koff31=36.0 Reaction: PDE_PKA => PDE + PKA, Rate Law: Spine*PDE_PKA*koff31
kcat53=24.0 Reaction: D75_137_PP2APCa => D137 + PP2APCa, Rate Law: Spine*D75_137_PP2APCa*kcat53
kon33=1.0E7 Reaction: PP2A + PKA => PP2A_PKA, Rate Law: Spine*PP2A*PKA*kon33
kon48=3800000.0 Reaction: D75 + PP2ACa => D75_PP2ACa, Rate Law: Spine*D75*PP2ACa*kon48
kcat49=10.0 Reaction: D75_137_PP2ACa => D137 + PP2ACa, Rate Law: Spine*D75_137_PP2ACa*kcat49
koff7=12.0 Reaction: D75CK1 => D75 + CK1, Rate Law: Spine*D75CK1*koff7
koff11=12.0 Reaction: D137_CDK5 => D137 + CDK5, Rate Law: Spine*D137_CDK5*koff11
koff54=1.0 Reaction: PP2ACa => PP2A + Ca, Rate Law: Spine*PP2ACa*koff54
kon18=5600000.0 Reaction: D34_137 + CDK5 => D34_137_CDK5, Rate Law: Spine*D34_137*CDK5*kon18
kcat13=3.0 Reaction: D137_PP2C => D + PP2C, Rate Law: Spine*D137_PP2C*kcat13
koff56=1.0 Reaction: PP2APCa => PP2AP + Ca, Rate Law: Spine*PP2APCa*koff56
kcat23=24.0 Reaction: D75_137_PP2AP => D137 + PP2AP, Rate Law: Spine*D75_137_PP2AP*kcat23
kcat4=3.0 Reaction: D34_CDK5 => D34_75 + CDK5, Rate Law: Spine*D34_CDK5*kcat4
kon12=5600000.0 Reaction: D137 + PKA => D137_PKA, Rate Law: Spine*D137*PKA*kon12
kcat16=24.0 Reaction: D34_75_PP2AP => D34 + PP2AP, Rate Law: Spine*D34_75_PP2AP*kcat16
koff3=10.8 Reaction: D_PKA => D + PKA, Rate Law: Spine*D_PKA*koff3
koff49=6.0 Reaction: D75_137_PP2ACa => D75_137 + PP2ACa, Rate Law: Spine*D75_137_PP2ACa*koff49
kcat10=24.0 Reaction: D75_PP2AP => D + PP2AP, Rate Law: Spine*D75_PP2AP*kcat10
kon42=1.8E7 Reaction: cAMP4_R2 + PKA => cAMP4_R2C, Rate Law: Spine*cAMP4_R2*PKA*kon42
kon1=5600000.0 Reaction: D + CDK5 => D_CDK5, Rate Law: Spine*kon1*D*CDK5
koff25=24.0 Reaction: D34_75_137_PP2A => D34_75_137 + PP2A, Rate Law: Spine*D34_75_137_PP2A*koff25
koff26=40.0 Reaction: D34_75_137_PP2AP => D34_75_137 + PP2AP, Rate Law: Spine*D34_75_137_PP2AP*koff26
kon49=3800000.0 Reaction: D75_137 + PP2ACa => D75_137_PP2ACa, Rate Law: Spine*D75_137*PP2ACa*kon49
koff17=1600.0 Reaction: D34_75_PP2B => D34_75 + PP2B, Rate Law: Spine*D34_75_PP2B*koff17
koff52=10.0 Reaction: D75_PP2APCa => D75 + PP2APCa, Rate Law: Spine*D75_PP2APCa*koff52
koff1=12.0 Reaction: D_CDK5 => D + CDK5, Rate Law: Spine*D_CDK5*koff1
koff46=6.0 Reaction: D34_75_PP2ACa => D34_75 + PP2ACa, Rate Law: Spine*D34_75_PP2ACa*koff46
kcat1=3.0 Reaction: D_CDK5 => D75 + CDK5, Rate Law: Spine*D_CDK5*kcat1
kcat9=10.0 Reaction: D75_PP2A => D + PP2A, Rate Law: Spine*D75_PP2A*kcat9
kon52=1.7E7 Reaction: D75 + PP2APCa => D75_PP2APCa, Rate Law: Spine*D75*PP2APCa*kon52
kcat30=1.0 Reaction: CK1 => CK1P, Rate Law: Spine*CK1*kcat30
kon6=1.0E7 Reaction: D34 + PP2B => D34_PP2B, Rate Law: Spine*D34*PP2B*kon6
koff53=10.0 Reaction: D75_137_PP2APCa => D75_137 + PP2APCa, Rate Law: Spine*D75_137_PP2APCa*koff53

States:

Name Description
D137 [Protein phosphatase 1 regulatory subunit 1B]
D34 CDK5 [Cyclin-dependent-like kinase 5; Protein phosphatase 1 regulatory subunit 1B]
D75 137 PP2ACa [calcium(2+); Protein phosphatase 1 regulatory subunit 1B; IPR006186]
D75 [Protein phosphatase 1 regulatory subunit 1B]
D34 75 CK1 [Casein kinase 1, epsilonCasein kinase1 epsilon-2; Protein phosphatase 1 regulatory subunit 1B]
cAMP PDEP [3',5'-cyclic AMP; IPR000396]
PP2ACa [IPR006186]
cAMP4 R2 [3',5'-cyclic AMP; PIRSF000548]
PP2B [calcium(2+); PIRSF000911]
D75 PP2ACa [calcium(2+); Protein phosphatase 1 regulatory subunit 1B; IPR006186]
D34 75 137 PP2AP [Protein phosphatase 1 regulatory subunit 1B; IPR006186]
D75 PP2A [Protein phosphatase 1 regulatory subunit 1B; IPR006186]
D CK1 [Casein kinase 1, epsilonCasein kinase1 epsilon-2; Protein phosphatase 1 regulatory subunit 1B]
D75 PP2AP [Protein phosphatase 1 regulatory subunit 1B; IPR006186]
PKA [PIRSF000582]
D [Protein phosphatase 1 regulatory subunit 1B]
CDK5 [Cyclin-dependent-like kinase 5]
D34 75 137 PP2ACa [calcium(2+); Protein phosphatase 1 regulatory subunit 1B; IPR006186]
PP2A [IPR006186]
PP2AP [IPR006186]
D34 CK1 [Casein kinase 1, epsilonCasein kinase1 epsilon-2; Protein phosphatase 1 regulatory subunit 1B]
CK1 [Casein kinase 1, epsilonCasein kinase1 epsilon-2]
PP2APCa [calcium(2+); IPR006186]
D75 137 PP2AP [Protein phosphatase 1 regulatory subunit 1B; IPR006186]
D CDK5 [Cyclin-dependent-like kinase 5; Protein phosphatase 1 regulatory subunit 1B]
D34 [Protein phosphatase 1 regulatory subunit 1B]

Observables: none

BIOMD0000000053 @ v0.0.1

The model should reproduce the figure 2F of the article. The equation 7 has been split into equations 7a-7c, in order t…

The Maillard reaction between reducing sugars and amino groups of biomolecules generates complex structures known as AGEs (advanced glycation endproducts). These have been linked to protein modifications found during aging, diabetes and various amyloidoses. To investigate the contribution of alternative routes to the formation of AGEs, we developed a mathematical model that describes the generation of CML [ N(epsilon)-(carboxymethyl)lysine] in the Maillard reaction between glucose and collagen. Parameter values were obtained by fitting published data from kinetic experiments of Amadori compound decomposition and glycoxidation of collagen by glucose. These raw parameter values were subsequently fine-tuned with adjustment factors that were deduced from dynamic experiments taking into account the glucose and phosphate buffer concentrations. The fine-tuned model was used to assess the relative contributions of the reaction between glyoxal and lysine, the Namiki pathway, and Amadori compound degradation to the generation of CML. The model suggests that the glyoxal route dominates, except at low phosphate and high glucose concentrations. The contribution of Amadori oxidation is generally the least significant at low glucose concentrations. Simulations of the inhibition of CML generation by aminoguanidine show that this compound effectively blocks the glyoxal route at low glucose concentrations (5 mM). Model results are compared with literature estimates of the contributions to CML generation by the three pathways. The significance of the dominance of the glyoxal route is discussed in the context of possible natural defensive mechanisms and pharmacological interventions with the goal of inhibiting the Maillard reaction in vivo. link: http://identifiers.org/pubmed/12911334

Parameters:

Name Description
k5b=0.0017 Reaction: Glyoxal =>, Rate Law: compartment*k5b*Glyoxal
k2b=0.0012; p2=0.75 Reaction: Amadori => Schiff, Rate Law: compartment*p2*k2b*Amadori
k3=7.92E-7; p7=60.0; ox=1.0 Reaction: Schiff =>, Rate Law: compartment*ox*p7*k3*(Schiff/0.25)^0.36
k1b=0.36 Reaction: Schiff => Lysine + Glucose, Rate Law: compartment*k1b*Schiff
p4=1.0; k4=8.6E-5; ox=1.0 Reaction: Amadori => CML, Rate Law: compartment*ox*p4*k4*Amadori
p5=1.0; ox=1.0; k5=0.019 Reaction: Lysine + Glyoxal => CML, Rate Law: compartment*ox*p5*k5*Glyoxal*Lysine
p6=2.7; k3=7.92E-7; ox=1.0 Reaction: Schiff => CML, Rate Law: compartment*ox*p6*k3*(Schiff/0.25)^0.36
p1=0.115; k1a=0.09 Reaction: Lysine + Glucose => Schiff, Rate Law: compartment*p1*k1a*Glucose*Lysine
p2=0.75; k2a=0.033 Reaction: Schiff => Amadori, Rate Law: compartment*p2*k2a*Schiff
p3=1.0; k3=7.92E-7; ox=1.0 Reaction: Glucose => Glyoxal, Rate Law: compartment*ox*p3*k3*(Glucose/0.25)^0.36

States:

Name Description
Glucose [glucose; C00293]
Schiff Schiff
CML CML
Lysine [lysine]
Amadori Amadori
Glyoxal [Glyoxal; glyoxal]

Observables: none

Computational modeling and the theory of nonlinear dynamical systems allow one to not simply describe the events of the…

Computational modeling and the theory of nonlinear dynamical systems allow one to not simply describe the events of the cell cycle, but also to understand why these events occur, just as the theory of gravitation allows one to understand why cannonballs fly in parabolic arcs. The simplest examples of the eukaryotic cell cycle operate like autonomous oscillators. Here, we present the basic theory of oscillatory biochemical circuits in the context of the Xenopus embryonic cell cycle. We examine Boolean models, delay differential equation models, and especially ordinary differential equation (ODE) models. For ODE models, we explore what it takes to get oscillations out of two simple types of circuits (negative feedback loops and coupled positive and negative feedback loops). Finally, we review the procedures of linear stability analysis, which allow one to determine whether a given ODE model and a particular set of kinetic parameters will produce oscillations. link: http://identifiers.org/pubmed/21414480

Parameters:

Name Description
n1 = 8.0; b1 = 1.0; k1 = 0.5 Reaction: CDK1_active =>, Rate Law: compartment*b1*CDK1_active^(n1+1)/(k1^n1+CDK1_active^n1)
a1 = 0.1 Reaction: => CDK1_active, Rate Law: compartment*a1

States:

Name Description
CDK1 active [Cyclin-dependent kinase 1-A; active]

Observables: none

Computational modeling and the theory of nonlinear dynamical systems allow one to not simply describe the events of the…

Computational modeling and the theory of nonlinear dynamical systems allow one to not simply describe the events of the cell cycle, but also to understand why these events occur, just as the theory of gravitation allows one to understand why cannonballs fly in parabolic arcs. The simplest examples of the eukaryotic cell cycle operate like autonomous oscillators. Here, we present the basic theory of oscillatory biochemical circuits in the context of the Xenopus embryonic cell cycle. We examine Boolean models, delay differential equation models, and especially ordinary differential equation (ODE) models. For ODE models, we explore what it takes to get oscillations out of two simple types of circuits (negative feedback loops and coupled positive and negative feedback loops). Finally, we review the procedures of linear stability analysis, which allow one to determine whether a given ODE model and a particular set of kinetic parameters will produce oscillations. link: http://identifiers.org/pubmed/21414480

Parameters:

Name Description
n1 = 8.0; b1 = 3.0; k1 = 0.5 Reaction: CDK1_active => ; APC_active, Rate Law: compartment*b1*CDK1_active*APC_active^n1/(k1^n1+APC_active^n1)
a3 = 3.0; n3 = 8.0; k3 = 0.5 Reaction: => APC_active; Plk1_active, Rate Law: compartment*a3*(1-APC_active)*Plk1_active^n3/(k3^n3+Plk1_active^n3)
k2 = 0.5; n2 = 8.0; a2 = 3.0 Reaction: => Plk1_active; CDK1_active, Rate Law: compartment*a2*(1-Plk1_active)*CDK1_active^n2/(k2^n2+CDK1_active^n2)
b2 = 1.0 Reaction: Plk1_active =>, Rate Law: compartment*b2*Plk1_active
a1 = 0.1 Reaction: => CDK1_active, Rate Law: compartment*a1
b3 = 1.0 Reaction: APC_active =>, Rate Law: compartment*b3*APC_active

States:

Name Description
APC active [Adenomatous polyposis coli homolog; active]
Plk1 active [Serine/threonine-protein kinase PLK1; active]
CDK1 active [Cyclin-dependent kinase 1-A; active]

Observables: none

Mathematical model of the regulation of Cdk1 and APC in cell cycle in Xenopus Laevis

Computational modeling and the theory of nonlinear dynamical systems allow one to not simply describe the events of the cell cycle, but also to understand why these events occur, just as the theory of gravitation allows one to understand why cannonballs fly in parabolic arcs. The simplest examples of the eukaryotic cell cycle operate like autonomous oscillators. Here, we present the basic theory of oscillatory biochemical circuits in the context of the Xenopus embryonic cell cycle. We examine Boolean models, delay differential equation models, and especially ordinary differential equation (ODE) models. For ODE models, we explore what it takes to get oscillations out of two simple types of circuits (negative feedback loops and coupled positive and negative feedback loops). Finally, we review the procedures of linear stability analysis, which allow one to determine whether a given ODE model and a particular set of kinetic parameters will produce oscillations. link: http://identifiers.org/pubmed/21414480

Parameters:

Name Description
n1 = 8.0; b1 = 3.0; k1 = 0.5 Reaction: CDK1_active => ; APC_active, Rate Law: nuclear*b1*CDK1_active*APC_active^n1/(k1^n1+APC_active^n1)
k2 = 0.5; n2 = 8.0; a2 = 3.0 Reaction: => APC_active; CDK1_active, Rate Law: nuclear*a2*(1-APC_active)*CDK1_active^n2/(k2^n2+CDK1_active^n2)
a1 = 0.1 Reaction: => CDK1_active, Rate Law: nuclear*a1
b2 = 1.0 Reaction: APC_active =>, Rate Law: nuclear*b2*APC_active

States:

Name Description
APC active [Adenomatous polyposis coli homolog; active]
CDK1 active [Cyclin-dependent kinase 1-A; active]

Observables: none

BIOMD0000000040 @ v0.0.1

# Field-Noyes Model of BZ Reaction CitationR.J.Field and R.M.Noyes,J.Chem.Phys.60,1877 (1974)DescriptionField Noyes Vers…

The chemical mechanism of Field, Körös, and Noyes for the oscillatory Belousov reaction has been generalized by a model composed of five steps involving three independent chemical intermediates. The behavior of the resulting differential equations has been examined numerically, and it has been shown that the system traces a stable closed trajectory in three dimensional phase space. The same trajectory is attained from other phase points and even from the point corresponding to steady state solution of the differential equations. The model appears to exhibit limit cycle behavior. By stiffly coupling the concentrations of two of the intermediates, the limit cycle model can be simplified to a system described by two independent variables; this coupled system is amenable to analysis by theoretical techniques already developed for such systems. ©1974 American Institute of Physics link: http://identifiers.org/doi/10.1063/1.1681288

Parameters:

Name Description
k5=1.0 Reaction: Ce => Br, Rate Law: Ce*k5*BZ
k3=8000.0 Reaction: BrO3 + HBrO2 => Ce + HBrO2, Rate Law: BrO3*HBrO2*k3*BZ
k2=1.6E9 Reaction: Br + HBrO2 => HOBr, Rate Law: Br*HBrO2*k2*BZ
k4=4.0E7 Reaction: HBrO2 => BrO3 + HOBr, Rate Law: HBrO2^2*k4*BZ
k1=1.34 Reaction: Br + BrO3 => HBrO2 + HOBr, Rate Law: Br*BrO3*k1*BZ

States:

Name Description
Ce Ce4+
Br [bromide]
BrO3 [bromate]
HOBr Ce4+
HBrO2 Ce4+

Observables: none

The paper describes a basic model of immune-itumor interaction. Created by COPASI 4.25 (Build 207) This model is de…

Many advances in research regarding immuno-interactions with cancer were developed with the help of ordinary differential equation (ODE) models. These models, however, are not effectively capable of representing problems involving individual localisation, memory and emerging properties, which are common characteristics of cells and molecules of the immune system. Agent-based modelling and simulation is an alternative paradigm to ODE models that overcomes these limitations. In this paper we investigate the potential contribution of agent-based modelling and simulation when compared to ODE modelling and simulation. We seek answers to the following questions: Is it possible to obtain an equivalent agent-based model from the ODE formulation? Do the outcomes differ? Are there any benefits of using one method compared to the other? To answer these questions, we have considered three case studies using established mathematical models of immune interactions with early-stage cancer. These case studies were re-conceptualised under an agent-based perspective and the simulation results were then compared with those from the ODE models. Our results show that it is possible to obtain equivalent agent-based models (i.e. implementing the same mechanisms); the simulation output of both types of models however might differ depending on the attributes of the system to be modelled. In some cases, additional insight from using agent-based modelling was obtained. Overall, we can confirm that agent-based modelling is a useful addition to the tool set of immunologists, as it has extra features that allow for simulations with characteristics that are closer to the biological phenomena. link: http://identifiers.org/pubmed/23734575

Parameters:

Name Description
m = 0.00311 1 Reaction: E => ; T, Rate Law: tumor_microenvironment*m*E*T
d = 2.0 1 Reaction: E =>, Rate Law: tumor_microenvironment*d*E
a = 1.636 1 Reaction: => T, Rate Law: tumor_microenvironment*a*T
a = 1.636 1; b = 0.004 1 Reaction: T =>, Rate Law: tumor_microenvironment*a*b*T*T
n = 1.0 1 Reaction: T => ; E, Rate Law: tumor_microenvironment*n*T*E
s = 0.318 1 Reaction: => E, Rate Law: tumor_microenvironment*s
g = 20.19 1; p = 1.131 1 Reaction: => E; T, Rate Law: tumor_microenvironment*p*T*E/(g+T)

States:

Name Description
T [malignant cell]
E [Effector Immune Cell]

Observables: none

The paper describes a model of immune-itumor interaction with IL2. Created by COPASI 4.25 (Build 207) This model is…

Many advances in research regarding immuno-interactions with cancer were developed with the help of ordinary differential equation (ODE) models. These models, however, are not effectively capable of representing problems involving individual localisation, memory and emerging properties, which are common characteristics of cells and molecules of the immune system. Agent-based modelling and simulation is an alternative paradigm to ODE models that overcomes these limitations. In this paper we investigate the potential contribution of agent-based modelling and simulation when compared to ODE modelling and simulation. We seek answers to the following questions: Is it possible to obtain an equivalent agent-based model from the ODE formulation? Do the outcomes differ? Are there any benefits of using one method compared to the other? To answer these questions, we have considered three case studies using established mathematical models of immune interactions with early-stage cancer. These case studies were re-conceptualised under an agent-based perspective and the simulation results were then compared with those from the ODE models. Our results show that it is possible to obtain equivalent agent-based models (i.e. implementing the same mechanisms); the simulation output of both types of models however might differ depending on the attributes of the system to be modelled. In some cases, additional insight from using agent-based modelling was obtained. Overall, we can confirm that agent-based modelling is a useful addition to the tool set of immunologists, as it has extra features that allow for simulations with characteristics that are closer to the biological phenomena. link: http://identifiers.org/pubmed/23734575

Parameters:

Name Description
g2 = 100000.0 1; aa = 1.0 1 Reaction: T => ; E, Rate Law: tumor_microenvironment*aa*E*T/(g2+T)
u2 = 0.03 1 Reaction: E =>, Rate Law: tumor_microenvironment*u2*E
p2 = 5.0 1; g3 = 1000.0 1 Reaction: => I; E, T, Rate Law: tumor_microenvironment*p2*E*T/(g3+T)
s2 = 0.0 1 Reaction: => I, Rate Law: tumor_microenvironment*s2
a = 0.18 1 Reaction: => T, Rate Law: tumor_microenvironment*a*T
c = 0.05 1 Reaction: => E; T, Rate Law: tumor_microenvironment*c*T
s1 = 0.0 1 Reaction: => E, Rate Law: tumor_microenvironment*s1
g1 = 2.0E7 1; p1 = 0.1245 1 Reaction: => E; I, Rate Law: tumor_microenvironment*p1*E*I/(g1+I)
a = 0.18 1; b = 1.0E-9 1 Reaction: T =>, Rate Law: tumor_microenvironment*a*b*T*T
u3 = 10.0 1 Reaction: I =>, Rate Law: tumor_microenvironment*u3*I

States:

Name Description
I [Interleukin-2]
T [malignant cell]
E [Effector Immune Cell]

Observables: none

The paper describes a full model of immune-itumor interaction. Created by COPASI 4.25 (Build 207) This model is des…

Many advances in research regarding immuno-interactions with cancer were developed with the help of ordinary differential equation (ODE) models. These models, however, are not effectively capable of representing problems involving individual localisation, memory and emerging properties, which are common characteristics of cells and molecules of the immune system. Agent-based modelling and simulation is an alternative paradigm to ODE models that overcomes these limitations. In this paper we investigate the potential contribution of agent-based modelling and simulation when compared to ODE modelling and simulation. We seek answers to the following questions: Is it possible to obtain an equivalent agent-based model from the ODE formulation? Do the outcomes differ? Are there any benefits of using one method compared to the other? To answer these questions, we have considered three case studies using established mathematical models of immune interactions with early-stage cancer. These case studies were re-conceptualised under an agent-based perspective and the simulation results were then compared with those from the ODE models. Our results show that it is possible to obtain equivalent agent-based models (i.e. implementing the same mechanisms); the simulation output of both types of models however might differ depending on the attributes of the system to be modelled. In some cases, additional insight from using agent-based modelling was obtained. Overall, we can confirm that agent-based modelling is a useful addition to the tool set of immunologists, as it has extra features that allow for simulations with characteristics that are closer to the biological phenomena. link: http://identifiers.org/pubmed/23734575

Parameters:

Name Description
g4 = 1000.0 1; p3 = 5.0 1; alpha = 0.001 1 Reaction: => I; E, T, S, Rate Law: tumor_microenvironment*p3*E*T/((g4+T)*(1+alpha*S))
a = 0.18 1; k = 1.0E10 1 Reaction: T =>, Rate Law: tumor_microenvironment*a*T^2/k
g3 = 2.0E7 1; p2 = 0.27 1 Reaction: => T; S, Rate Law: tumor_microenvironment*p2*S*T/(g3+S)
g2 = 100000.0 1; aa = 1.0 1 Reaction: T => ; E, Rate Law: tumor_microenvironment*aa*E*T/(g2+T)
p4 = 2.84 1; theta = 1000000.0 1 Reaction: => S; T, Rate Law: tumor_microenvironment*p4*T^2/(theta^2+T^2)
a = 0.18 1 Reaction: => T, Rate Law: tumor_microenvironment*a*T
u2 = 10.0 1 Reaction: I =>, Rate Law: tumor_microenvironment*u2*I
gamma = 10.0 1; c = 0.035 1 Reaction: => E; T, S, Rate Law: tumor_microenvironment*c*T/(1+gamma*S)
g1 = 2.0E7 1; q1 = 10.0 1; p1 = 0.1245 1; q2 = 0.1121 1 Reaction: => E; I, S, Rate Law: tumor_microenvironment*p1*E*I/(g1+I)*(p1-q1*S/(q2+S))
u3 = 10.0 1 Reaction: S =>, Rate Law: tumor_microenvironment*u3*S
u1 = 0.03 1 Reaction: E =>, Rate Law: tumor_microenvironment*u1*E

States:

Name Description
I [Interleukin-2]
S [Transforming growth factor beta-1]
T [malignant cell]
E [Effector Immune Cell]

Observables: none

MODEL1006230009 @ v0.0.1

This a model from the article: Contributions of HERG K+ current to repolarization of the human ventricular action pote…

Action potential repolarization in the mammalian heart is governed by interactions of a number of time- and voltage-dependent channel-mediated currents, as well as contributions from the Na+/Ca2+ exchanger and the Na+/K+ pump. Recent work has shown that one of the K+ currents (HERG) which contributes to repolarization in mammalian ventricle is a locus at which a number of point mutations can have significant functional consequences. In addition, the remarkable sensitivity of this K+ channel isoform to inhibition by a variety of pharmacological agents and clinical drugs has resulted in HERG being a major focus for Safety Pharmacology requirements. For these reasons we and others have attempted to define the functional role for HERG-mediated K+ currents in repolarization of the action potential in the human ventricle. Here, we describe and evaluate changes in the formulations for two K+ currents, IK1 and HERG (or IK,r), within the framework of ten Tusscher model of the human ventricular action potential. In this computational study, new mathematical formulations for the two nonlinear K+ conductances, IK1 and HERG, have been developed based upon experimental data obtained from electrophysiological studies of excised human ventricular tissue and/or myocytes. The resulting mathematical model provides much improved simulations of the relative sizes and time courses of the K+ currents which modulate repolarization. Our new formulation represents an important first step in defining the mechanism(s) of repolarization of the membrane action potential in the human ventricle. Our overall goal is to understand the genesis of the T-wave of the human electrocardiogram. link: http://identifiers.org/pubmed/17919688

Parameters: none

States: none

Observables: none

Firczuk2013 - Eukaryotic mRNA translation machineryThis is a model of *Saccharomyces cerevisiae* mRNA translation which…

Rate control analysis defines the in vivo control map governing yeast protein synthesis and generates an extensively parameterized digital model of the translation pathway. Among other non-intuitive outcomes, translation demonstrates a high degree of functional modularity and comprises a non-stoichiometric combination of proteins manifesting functional convergence on a shared maximal translation rate. In exponentially growing cells, polypeptide elongation (eEF1A, eEF2, and eEF3) exerts the strongest control. The two other strong control points are recruitment of mRNA and tRNA(i) to the 40S ribosomal subunit (eIF4F and eIF2) and termination (eRF1; Dbp5). In contrast, factors that are found to promote mRNA scanning efficiency on a longer than-average 5'untranslated region (eIF1, eIF1A, Ded1, eIF2B, eIF3, and eIF5) exceed the levels required for maximal control. This is expected to allow the cell to minimize scanning transition times, particularly for longer 5'UTRs. The analysis reveals these and other collective adaptations of control shared across the factors, as well as features that reflect functional modularity and system robustness. Remarkably, gene duplication is implicated in the fine control of cellular protein synthesis. link: http://identifiers.org/pubmed/23340841

Parameters:

Name Description
k=1.3072E13; parameter_1 = 7.16464328895E-7 Reaction: species_34 + species_33 => species_46 + species_11 + species_14 + species_1 + species_7 + species_24 + species_25 + species_17 + species_18 + species_8 + species_31 + species_21 + species_20 + species_29; species_46, species_47, species_48, species_49, species_50, species_51, species_52, species_53, species_54, species_55, species_56, species_57, species_58, species_59, species_60, species_61, species_62, species_63, species_64, species_65, species_66, species_67, species_68, species_69, species_70, species_71, species_72, species_73, species_74, species_75, species_76, species_77, species_78, species_79, species_80, species_81, species_82, species_83, species_84, species_85, species_86, species_87, species_88, species_89, species_90, species_91, species_92, species_93, species_94, species_95, species_96, species_97, species_98, species_99, species_100, species_101, species_102, species_103, species_104, species_105, species_106, species_107, species_108, species_109, species_110, species_111, species_112, species_113, species_114, species_115, species_116, species_117, species_118, species_119, species_120, species_121, species_122, species_123, species_124, species_125, species_126, species_127, species_128, species_129, species_130, species_131, species_132, species_133, species_34, species_33, species_46, species_47, species_48, species_49, species_50, species_51, species_52, species_53, species_54, species_55, species_56, species_57, species_58, species_59, species_60, species_61, species_62, species_63, species_64, species_65, species_66, species_67, species_68, species_69, species_70, species_71, species_72, species_73, species_74, species_75, species_76, species_77, species_78, species_79, species_80, species_81, species_82, species_83, species_84, species_85, species_86, species_87, species_88, species_89, species_90, species_91, species_92, species_93, species_94, species_95, species_96, species_97, species_98, species_99, species_100, species_101, species_102, species_103, species_104, species_105, species_106, species_107, species_108, species_109, species_110, species_111, species_112, species_113, species_114, species_115, species_116, species_117, species_118, species_119, species_120, species_121, species_122, species_123, species_124, species_125, species_126, species_127, species_128, species_129, species_130, species_131, species_132, species_133, Rate Law: compartment_1*k*species_34*species_33*(parameter_1-(species_46+species_47+species_48+species_49+species_50+species_51+species_52+species_53+species_54+species_55+species_56+species_57+species_58+species_59+species_60+species_61+species_62+species_63+species_64+species_65+species_66+species_67+species_68+species_69+species_70+species_71+species_72+species_73+species_74+species_75+species_76+species_77+species_78+species_79+species_80+species_81+species_82+species_83+species_84+species_85+species_86+species_87+species_88+species_89+species_90+species_91+species_92+species_93+species_94+species_95+species_96+species_97+species_98+species_99+species_100+species_101+species_102+species_103+species_104+species_105+species_106+species_107+species_108+species_109+species_110+species_111+species_112+species_113+species_114+species_115+species_116+species_117+species_118+species_119+species_120+species_121+species_122+species_123+species_124+species_125+species_126+species_127+species_128+species_129+species_130+species_131+species_132+species_133))
parameter_2 = 8.10035535716195E9; parameter_3 = 0.284007213965168 Reaction: species_40 + species_98 => species_99; species_40, species_98, species_99, Rate Law: compartment_1*(parameter_2*species_40*species_98-parameter_3*species_99)
parameter_6 = 0.00322599; parameter_5 = 3.10377169466493E9 Reaction: species_42 + species_94 => species_95; species_42, species_94, species_95, Rate Law: compartment_1*(parameter_5*species_42*species_94-parameter_6*species_95)
k1=1.06204E9 Reaction: species_16 + species_27 => species_28; species_16, species_27, Rate Law: compartment_1*k1*species_16*species_27
k1=3.5208E14; k2=0.785013 Reaction: species_25 + species_166 => species_27; species_25, species_166, species_27, Rate Law: compartment_1*(k1*species_25*species_166-k2*species_27)
k2=47.8215; k1=5.61005E8 Reaction: species_30 + species_32 => species_33; species_30, species_32, species_33, Rate Law: compartment_1*(k1*species_30*species_32-k2*species_33)
k1=1.80542; k2=1.29513 Reaction: species_41 => species_42; species_41, species_42, Rate Law: compartment_1*(k1*species_41-k2*species_42)
parameter_7 = 2306950.0; parameter_1 = 7.16464328895E-7 Reaction: species_53 => species_60 + species_41; species_56, species_57, species_58, species_59, species_60, species_61, species_62, species_63, species_64, species_65, species_66, species_67, species_68, species_69, species_70, species_71, species_72, species_73, species_74, species_75, species_76, species_77, species_78, species_79, species_80, species_81, species_82, species_83, species_84, species_85, species_86, species_87, species_88, species_89, species_90, species_91, species_92, species_93, species_94, species_95, species_96, species_97, species_98, species_99, species_100, species_101, species_102, species_103, species_104, species_105, species_106, species_107, species_108, species_109, species_110, species_111, species_112, species_113, species_114, species_115, species_116, species_117, species_118, species_119, species_120, species_121, species_122, species_123, species_124, species_125, species_126, species_127, species_128, species_129, species_130, species_131, species_132, species_133, species_134, species_135, species_136, species_137, species_138, species_139, species_140, species_141, species_142, species_143, species_144, species_145, species_53, species_56, species_57, species_58, species_59, species_60, species_61, species_62, species_63, species_64, species_65, species_66, species_67, species_68, species_69, species_70, species_71, species_72, species_73, species_74, species_75, species_76, species_77, species_78, species_79, species_80, species_81, species_82, species_83, species_84, species_85, species_86, species_87, species_88, species_89, species_90, species_91, species_92, species_93, species_94, species_95, species_96, species_97, species_98, species_99, species_100, species_101, species_102, species_103, species_104, species_105, species_106, species_107, species_108, species_109, species_110, species_111, species_112, species_113, species_114, species_115, species_116, species_117, species_118, species_119, species_120, species_121, species_122, species_123, species_124, species_125, species_126, species_127, species_128, species_129, species_130, species_131, species_132, species_133, species_134, species_135, species_136, species_137, species_138, species_139, species_140, species_141, species_142, species_143, species_144, species_145, Rate Law: compartment_1*parameter_7*species_53*(parameter_1-(species_56+species_57+species_58+species_59+species_60+species_61+species_62+species_63+species_64+species_65+species_66+species_67+species_68+species_69+species_70+species_71+species_72+species_73+species_74+species_75+species_76+species_77+species_78+species_79+species_80+species_81+species_82+species_83+species_84+species_85+species_86+species_87+species_88+species_89+species_90+species_91+species_92+species_93+species_94+species_95+species_96+species_97+species_98+species_99+species_100+species_101+species_102+species_103+species_104+species_105+species_106+species_107+species_108+species_109+species_110+species_111+species_112+species_113+species_114+species_115+species_116+species_117+species_118+species_119+species_120+species_121+species_122+species_123+species_124+species_125+species_126+species_127+species_128+species_129+species_130+species_131+species_132+species_133+species_134+species_135+species_136+species_137+species_138+species_139+species_140+species_141+species_142+species_143+species_144+species_145))/(parameter_1-(species_56+species_57+species_58+species_59+species_60+species_61+species_62+species_63+species_64+species_65+species_66+species_67+species_68+species_69+species_70+species_71+species_72+species_73+species_74+species_75+species_76+species_77+species_78+species_79+species_80+species_81+species_82+species_83+species_84+species_85+species_86+species_87+species_88+species_89+species_90+species_91+species_92+species_93+species_94+species_95+species_96+species_97+species_98+species_99+species_100+species_101+species_102+species_103+species_104+species_105+species_106+species_107+species_108+species_109+species_110+species_111+species_112+species_113+species_114+species_115+species_116+species_117+species_118+species_119+species_120+species_121+species_122+species_123+species_124+species_125+species_126+species_127+species_128+species_129+species_130+species_131+species_132+species_133+species_134+species_135+species_136+species_137+species_138+species_139))
parameter_9 = 72911.6740026381 Reaction: species_97 => species_92 + species_43 + species_45; species_97, Rate Law: compartment_1*parameter_9*species_97
k1=8.7134E10; k2=1.2395 Reaction: species_28 + species_29 => species_30; species_28, species_29, species_30, Rate Law: compartment_1*(k1*species_28*species_29-k2*species_30)
k1=93.5995; k2=43714.4 Reaction: species_43 => species_44; species_43, species_44, Rate Law: compartment_1*(k1*species_43-k2*species_44)
k2=45.4082; k1=304.768 Reaction: species_31 => species_32; species_31, species_32, Rate Law: compartment_1*(k1*species_31-k2*species_32)
k2=2.70026; k1=5.79912E7 Reaction: species_19 + species_22 => species_23; species_19, species_22, species_23, Rate Law: compartment_1*(k1*species_19*species_22-k2*species_23)
k1=4.33274E7; k2=1977.92 Reaction: species_17 + species_18 => species_19; species_17, species_18, species_19, Rate Law: compartment_1*(k1*species_17*species_18-k2*species_19)
parameter_8 = 2.24052E9 Reaction: species_96 + species_44 => species_97; species_96, species_44, Rate Law: compartment_1*parameter_8*species_96*species_44
k2=0.00774034; k1=5026500.0 Reaction: species_20 + species_21 => species_22; species_20, species_21, species_22, Rate Law: compartment_1*(k1*species_20*species_21-k2*species_22)
parameter_4 = 28324.3562938545 Reaction: species_99 => species_100 + species_35; species_99, Rate Law: compartment_1*parameter_4*species_99
parameter_7 = 2306950.0 Reaction: species_101 => species_108 + species_41; species_101, Rate Law: compartment_1*parameter_7*species_101
k1=1.97254E7 Reaction: species_12 + species_15 => species_16; species_12, species_15, Rate Law: compartment_1*k1*species_12*species_15
k1=3865650.0; k2=31.1969 Reaction: species_11 + species_10 => species_12; species_11, species_10, species_12, Rate Law: compartment_1*(k1*species_11*species_10-k2*species_12)

States:

Name Description
species 50 [cytosolic ribosome]
species 101 [alpha-aminoacyl-tRNA; GTP; Elongation factor 2]
species 27 [messenger RNA; ATP-dependent RNA helicase eIF4A; Eukaryotic initiation factor 4F subunit p150; Eukaryotic translation initiation factor 4B; Eukaryotic initiation factor 4F subunit p130]
species 100 [alpha-aminoacyl-tRNA; cytosolic ribosome]
species 31 [GDP; Eukaryotic translation initiation factor 5B]
species 45 [transfer RNA]
species 98 [cytosolic ribosome]
species 51 [alpha-aminoacyl-tRNA; GTP; Elongation factor 1-alpha; cytosolic ribosome]
species 20 [messenger RNA; capped_mRNA]
species 28 [eukaryotic 48S preinitiation complex]
species 97 [GTP; alpha-aminoacyl-tRNA; Elongation factor 3A; cytosolic ribosome]
species 16 [eukaryotic 43S preinitiation complex]
species 61 [alpha-aminoacyl-tRNA; GTP; Elongation factor 3A; cytosolic ribosome]
species 60 [transfer RNA; cytosolic ribosome]
species 102 [transfer RNA; cytosolic ribosome]
species 25 [Eukaryotic translation initiation factor 4B]
species 29 [ATP-dependent RNA helicase DED1]
species 32 [GTP; Eukaryotic translation initiation factor 5B]
species 30 [ATP-dependent RNA helicase DED1; eukaryotic 48S preinitiation complex]
species 12 [tRNA(Met); GTP; Eukaryotic translation initiation factor 3 subunit C; Eukaryotic translation initiation factor 2 subunit alpha; Eukaryotic translation initiation factor 3 subunit G; Eukaryotic translation initiation factor 3 subunit A; Eukaryotic translation initiation factor 5; Eukaryotic translation initiation factor eIF-1; Eukaryotic translation initiation factor 2 subunit gamma; Eukaryotic translation initiation factor 3 subunit B; Eukaryotic translation initiation factor 3 subunit I; Eukaryotic translation initiation factor 2 subunit beta; multi-eIF complex]
species 17 [Eukaryotic translation initiation factor 4E]
species 21 [Polyadenylate-binding protein, cytoplasmic and nuclear]
species 94 [alpha-aminoacyl-tRNA; cytosolic ribosome]
species 42 [GTP; Elongation factor 2]
species 44 [GTP; Elongation factor 3A]
species 123 [alpha-aminoacyl-tRNA; GTP; Elongation factor 1-alpha; cytosolic ribosome]
species 19 [Eukaryotic initiation factor 4F subunit p150; Eukaryotic initiation factor 4F subunit p130; Eukaryotic translation initiation factor 4E]
species 129 [alpha-aminoacyl-tRNA; GTP; Elongation factor 1-alpha; cytosolic ribosome]
species 11 [Eukaryotic translation initiation factor eIF-1]
species 96 [transfer RNA; cytosolic ribosome]
species 24 [ATP-dependent RNA helicase eIF4A]
species 77 [alpha-aminoacyl-tRNA; GTP; Elongation factor 2]
species 95 [GTP; alpha-aminoacyl-tRNA; Elongation factor 2]
species 43 [GDP; Elongation factor 3A]
species 130 [alpha-aminoacyl-tRNA; cytosolic ribosome]
species 122 [cytosolic ribosome]
species 41 [GDP; Elongation factor 2]
species 99 [GTP; alpha-aminoacyl-tRNA; Elongation factor 1-alpha; cytosolic ribosome]
species 46 [cytosolic ribosome; translation initiation complex]
species 40 [GTP; alpha-aminoacyl-tRNA; Elongation factor 1-alpha]
species 65 [GTP; alpha-aminoacyl-tRNA; Elongation factor 2]

Observables: none

The model reproduces the calcium oscillation dependent activation-deactivation kinetics of nuclear factor of activated T…

Mathematical models for the regulation of the Ca(2+)-dependent transcription factors NFAT and NFkappaB that are involved in the activation of the immune and inflammatory responses in T lymphocytes have been developed. These pathways are important targets for drugs, which act as powerful immunosuppressants by suppressing activation of NFAT and NFkappaB in T cells. The models simulate activation and deactivation over physiological concentrations of Ca(2+), diacyl glycerol (DAG), and PKCtheta using single and periodic step increases. The model suggests the following: (1) the activation NFAT does not occur at low frequencies as NFAT requires calcineurin activated by Ca(2+) to remain dephosphorylated and in the nucleus; (2) NFkappaB is activated at lower Ca(2+) oscillation frequencies than NFAT as IkappaB is degraded in response to elevations in Ca(2+) allowing free NFkappaB to translocate into the nucleus; and (3) the degradation of IkappaB is essential for efficient translocation of NFkappaB to the nucleus. Through sensitivity analysis, the model also suggests that the largest controlling factor for NFAT activation is the dissociation/reassociation rate of the NFAT:calcineurin complex and the translocation rate of the complex into the nucleus and for NFkappaB is the degradation/resynthesis rate of IkappaB and the import rate of IkappaB into the nucleus. link: http://identifiers.org/pubmed/17031595

Parameters:

Name Description
k19 = 1.0; k20 = 1.0 Reaction: Ca_Nuc + Inact_C_Nuc => Act_C_Nuc, Rate Law: nucleus*(k19*Inact_C_Nuc*Ca_Nuc^3-k20*Act_C_Nuc)
k8 = 0.5; k7 = 0.005 Reaction: NFAT_Pi_Act_C_Cyt => NFAT_Pi_Act_C_Nuc, Rate Law: cytosol*k7*NFAT_Pi_Act_C_Cyt-nucleus*k8*NFAT_Pi_Act_C_Nuc
k1 = 2.56E-5; k2 = 0.00256 Reaction: NFAT_Pi_Nuc + Act_C_Nuc => Act_C_Nuc + NFAT_Nuc, Rate Law: nucleus*(k1*NFAT_Pi_Nuc-k2*NFAT_Nuc)
k17 = 0.0015; k18 = 9.6E-4 Reaction: NFAT_Nuc => NFAT_Cyt, Rate Law: nucleus*k18*NFAT_Nuc-cytosol*k17*NFAT_Cyt
k5 = 0.0019; k6 = 9.2E-4 Reaction: Inact_C_Cyt => Inact_C_Nuc, Rate Law: cytosol*k5*Inact_C_Cyt-nucleus*k6*Inact_C_Nuc
k12 = 0.00168; k11 = 6.63 Reaction: NFAT_Pi_Act_C_Cyt => Act_C_Cyt + NFAT_Pi_Cyt, Rate Law: cytosol*(k12*NFAT_Pi_Act_C_Cyt-k11*NFAT_Pi_Cyt*Act_C_Cyt)
k9 = 0.5; k10 = 0.005 Reaction: NFAT_Act_C_Nuc => NFAT_Act_C_Cyt, Rate Law: nucleus*k10*NFAT_Act_C_Nuc-cytosol*k9*NFAT_Act_C_Cyt
k3 = 0.005; k4 = 0.5 Reaction: NFAT_Pi_Cyt => NFAT_Pi_Nuc, Rate Law: cytosol*k3*NFAT_Pi_Cyt-nucleus*k4*NFAT_Pi_Nuc
k21 = 0.21; k22 = 0.5 Reaction: Ca_Cyt => Ca_Nuc, Rate Law: cytosol*k21*Ca_Cyt-nucleus*k22*Ca_Nuc
k15 = 0.00168; k16 = 6.63 Reaction: Act_C_Nuc + NFAT_Nuc => NFAT_Act_C_Nuc, Rate Law: nucleus*(k16*NFAT_Nuc*Act_C_Nuc-k15*NFAT_Act_C_Nuc)
k13 = 0.5; k14 = 0.00256 Reaction: NFAT_Act_C_Cyt => NFAT_Pi_Act_C_Cyt, Rate Law: cytosol*(k14*NFAT_Act_C_Cyt-k13*NFAT_Pi_Act_C_Cyt)

States:

Name Description
Act C Cyt [Calcineurin B homologous protein 1]
NFAT Act C Nuc [Calcineurin B homologous protein 1; Nuclear factor of activated T-cells 5]
NFAT Pi Act C Nuc [Calcineurin B homologous protein 1; Nuclear factor of activated T-cells 5]
Inact C Cyt [Calcineurin B homologous protein 1]
NFAT Act C Cyt [Calcineurin B homologous protein 1; Nuclear factor of activated T-cells 5]
NFAT Pi Nuc [Nuclear factor of activated T-cells 5]
NFAT Pi Act C Cyt [Calcineurin B homologous protein 1; Nuclear factor of activated T-cells 5]
Inact C Nuc [Calcineurin B homologous protein 1]
NFAT Pi Cyt [Nuclear factor of activated T-cells 5]
Ca Nuc [calcium(2+); Calcium cation]
NFAT Cyt [Nuclear factor of activated T-cells 5]
Act C Nuc [Calcineurin B homologous protein 1]
NFAT Nuc [Nuclear factor of activated T-cells 5]
Ca Cyt [calcium(2+); Calcium cation]

Observables: none

BIOMD0000000123 @ v0.0.1

The model reproduces the kinetics of the nuclear factor of activated cells (NFAT) as depicted in Figure 3a of the paper.…

Mathematical models for the regulation of the Ca(2+)-dependent transcription factors NFAT and NFkappaB that are involved in the activation of the immune and inflammatory responses in T lymphocytes have been developed. These pathways are important targets for drugs, which act as powerful immunosuppressants by suppressing activation of NFAT and NFkappaB in T cells. The models simulate activation and deactivation over physiological concentrations of Ca(2+), diacyl glycerol (DAG), and PKCtheta using single and periodic step increases. The model suggests the following: (1) the activation NFAT does not occur at low frequencies as NFAT requires calcineurin activated by Ca(2+) to remain dephosphorylated and in the nucleus; (2) NFkappaB is activated at lower Ca(2+) oscillation frequencies than NFAT as IkappaB is degraded in response to elevations in Ca(2+) allowing free NFkappaB to translocate into the nucleus; and (3) the degradation of IkappaB is essential for efficient translocation of NFkappaB to the nucleus. Through sensitivity analysis, the model also suggests that the largest controlling factor for NFAT activation is the dissociation/reassociation rate of the NFAT:calcineurin complex and the translocation rate of the complex into the nucleus and for NFkappaB is the degradation/resynthesis rate of IkappaB and the import rate of IkappaB into the nucleus. link: http://identifiers.org/pubmed/17031595

Parameters:

Name Description
k19 = 1.0; k20 = 1.0 Reaction: Ca_Nuc + Inact_C_Nuc => Act_C_Nuc, Rate Law: nucleus*(k19*Inact_C_Nuc*Ca_Nuc^3-k20*Act_C_Nuc)
k8 = 0.5; k7 = 0.005 Reaction: NFAT_Pi_Act_C_Cyt => NFAT_Pi_Act_C_Nuc, Rate Law: cytosol*k7*NFAT_Pi_Act_C_Cyt-nucleus*k8*NFAT_Pi_Act_C_Nuc
k1 = 2.56E-5; k2 = 0.00256 Reaction: NFAT_Pi_Cyt + Act_C_Cyt => Act_C_Cyt + NFAT_Cyt, Rate Law: cytosol*(k1*NFAT_Pi_Cyt-k2*NFAT_Cyt)
k17 = 0.0015; k18 = 9.6E-4 Reaction: NFAT_Nuc => NFAT_Cyt, Rate Law: nucleus*k18*NFAT_Nuc-cytosol*k17*NFAT_Cyt
k5 = 0.0019; k6 = 9.2E-4 Reaction: Act_C_Nuc => Act_C_Cyt, Rate Law: nucleus*k6*Act_C_Nuc-cytosol*k5*Act_C_Cyt
k12 = 0.00168; k11 = 6.63 Reaction: NFAT_Pi_Act_C_Cyt => Act_C_Cyt + NFAT_Pi_Cyt, Rate Law: cytosol*(k12*NFAT_Pi_Act_C_Cyt-k11*NFAT_Pi_Cyt*Act_C_Cyt)
k9 = 0.5; k10 = 0.005 Reaction: NFAT_Act_C_Nuc => NFAT_Act_C_Cyt, Rate Law: nucleus*k10*NFAT_Act_C_Nuc-cytosol*k9*NFAT_Act_C_Cyt
k3 = 0.005; k4 = 0.5 Reaction: NFAT_Pi_Cyt => NFAT_Pi_Nuc, Rate Law: cytosol*k3*NFAT_Pi_Cyt-nucleus*k4*NFAT_Pi_Nuc
k21 = 0.21; k22 = 0.5 Reaction: Ca_Cyt => Ca_Nuc, Rate Law: cytosol*k21*Ca_Cyt-nucleus*k22*Ca_Nuc
k15 = 0.00168; k16 = 6.63 Reaction: NFAT_Act_C_Cyt => Act_C_Cyt + NFAT_Cyt, Rate Law: cytosol*(k15*NFAT_Act_C_Cyt-k16*NFAT_Cyt*Act_C_Cyt)
k13 = 0.5; k14 = 0.00256 Reaction: NFAT_Act_C_Cyt => NFAT_Pi_Act_C_Cyt, Rate Law: cytosol*(k14*NFAT_Act_C_Cyt-k13*NFAT_Pi_Act_C_Cyt)

States:

Name Description
Act C Cyt [calcineurin complex; Serine/threonine-protein phosphatase 2B catalytic subunit beta isoform]
NFAT Act C Nuc [Nuclear factor of activated T-cells 5; Serine/threonine-protein phosphatase 2B catalytic subunit beta isoform; calcineurin complex]
Inact C Cyt [calcineurin complex; Serine/threonine-protein phosphatase 2B catalytic subunit beta isoform]
NFAT Pi Act C Nuc [Nuclear factor of activated T-cells 5; Serine/threonine-protein phosphatase 2B catalytic subunit beta isoform; calcineurin complex]
NFAT Act C Cyt [Nuclear factor of activated T-cells 5; Serine/threonine-protein phosphatase 2B catalytic subunit beta isoform; calcineurin complex]
NFAT Pi Nuc [Nuclear factor of activated T-cells 5]
NFAT Pi Act C Cyt [Nuclear factor of activated T-cells 5; Serine/threonine-protein phosphatase 2B catalytic subunit beta isoform; calcineurin complex]
Inact C Nuc [calcineurin complex; Serine/threonine-protein phosphatase 2B catalytic subunit beta isoform]
NFAT Pi Cyt [Nuclear factor of activated T-cells 5]
Ca Nuc [calcium(2+); Calcium cation]
NFAT Cyt [Nuclear factor of activated T-cells 5]
Act C Nuc [calcineurin complex; Serine/threonine-protein phosphatase 2B catalytic subunit beta isoform]
NFAT Nuc [Nuclear factor of activated T-cells 5]
Ca Cyt [calcium(2+); Calcium cation]

Observables: none

BIOMD0000000346 @ v0.0.1

This is the original model from Richard FitzHugh, which led the famous FitzHugh–Nagumo model, still used for instance in…

Van der Pol's equation for a relaxation oscillator is generalized by the addition of terms to produce a pair of non-linear differential equations with either a stable singular point or a limit cycle. The resulting "BVP model" has two variables of state, representing excitability and refractoriness, and qualitatively resembles Bonhoeffer's theoretical model for the iron wire model of nerve. This BVP model serves as a simple representative of a class of excitable-oscillatory systems including the Hodgkin-Huxley (HH) model of the squid giant axon. The BVP phase plane can be divided into regions corresponding to the physiological states of nerve fiber (resting, active, refractory, enhanced, depressed, etc.) to form a "physiological state diagram," with the help of which many physiological phenomena can be summarized. A properly chosen projection from the 4-dimensional HH phase space onto a plane produces a similar diagram which shows the underlying relationship between the two models. Impulse trains occur in the BVP and HH models for a range of constant applied currents which make the singular point representing the resting state unstable. link: http://identifiers.org/pubmed/19431309

Parameters:

Name Description
a = 0.7 dimensionless; c = 3.0 dimensionless; b = 0.8 dimensionless Reaction: y = (-1/c)*(x+(-a)+b*y), Rate Law: (-1/c)*(x+(-a)+b*y)
z = -0.4 dimensionless; c = 3.0 dimensionless Reaction: x = c*(x+(-x^3/3)+y+z), Rate Law: c*(x+(-x^3/3)+y+z)

States:

Name Description
x x
y y

Observables: none

Flahaut2013 - Genome-scale metabolic model of L.lactis (MG1363)Genome-scale metabolic model for *Lactococcus lactis* MG…

Lactococcus lactis subsp. cremoris MG1363 is a paradigm strain for lactococci used in industrial dairy fermentations. However, despite of its importance for process development, no genome-scale metabolic model has been reported thus far. Moreover, current models for other lactococci only focus on growth and sugar degradation. A metabolic model that includes nitrogen metabolism and flavor-forming pathways is instrumental for the understanding and designing new industrial applications of these lactic acid bacteria. A genome-scale, constraint-based model of the metabolism and transport in L. lactis MG1363, accounting for 518 genes, 754 reactions, and 650 metabolites, was developed and experimentally validated. Fifty-nine reactions are directly or indirectly involved in flavor formation. Flux Balance Analysis and Flux Variability Analysis were used to investigate flux distributions within the whole metabolic network. Anaerobic carbon-limited continuous cultures were used for estimating the energetic parameters. A thorough model-driven analysis showing a highly flexible nitrogen metabolism, e.g., branched-chain amino acid catabolism which coupled with the redox balance, is pivotal for the prediction of the formation of different flavor compounds. Furthermore, the model predicted the formation of volatile sulfur compounds as a result of the fermentation. These products were subsequently identified in the experimental fermentations carried out. Thus, the genome-scale metabolic model couples the carbon and nitrogen metabolism in L. lactis MG1363 with complete known catabolic pathways leading to flavor formation. The model provided valuable insights into the metabolic networks underlying flavor formation and has the potential to contribute to new developments in dairy industries and cheese-flavor research. link: http://identifiers.org/pubmed/23974365

Parameters: none

States: none

Observables: none

Flis2015 - Plant clock gene circuit (P2011.1.2 PLM_71 ver 1)This model is described in the article: [Defining the robus…

Our understanding of the complex, transcriptional feedback loops in the circadian clock mechanism has depended upon quantitative, timeseries data from disparate sources. We measure clock gene RNA profiles in Arabidopsis thaliana seedlings, grown with or without exogenous sucrose, or in soil-grown plants and in wild-type and mutant backgrounds. The RNA profiles were strikingly robust across the experimental conditions, so current mathematical models are likely to be broadly applicable in leaf tissue. In addition to providing reference data, unexpected behaviours included co-expression of PRR9 and ELF4, and regulation of PRR5 by GI. Absolute RNA quantification revealed low levels of PRR9 transcripts (peak approx. 50 copies cell(-1)) compared with other clock genes, and threefold higher levels of LHY RNA (more than 1500 copies cell(-1)) than of its close relative CCA1. The data are disseminated from BioDare, an online repository for focused timeseries data, which is expected to benefit mechanistic modelling. One data subset successfully constrained clock gene expression in a complex model, using publicly available software on parallel computers, without expert tuning or programming. We outline the empirical and mathematical justification for data aggregation in understanding highly interconnected, dynamic networks such as the clock, and the observed design constraints on the resources required to make this approach widely accessible. link: http://identifiers.org/pubmed/26468131

Parameters:

Name Description
p16 = 0.62 Reaction: => cE3; cE3_m, cE3_m, Rate Law: def*p16*cE3_m/def
m16 = 0.5 Reaction: cNI_m => ; cNI_m, Rate Law: def*m16*cNI_m/def
m11 = 1.0; L = 0.5 Reaction: cP => ; cP, Rate Law: def*m11*cP*L/def
p8 = 0.6 Reaction: => cP9; cP9_m, cP9_m, Rate Law: def*p8*cP9_m/def
n2 = 0.64; g5 = 0.15; g4 = 0.01; e = 2.0 Reaction: => cT_m; cEC, cL, cEC, cL, Rate Law: def*n2*g4/(cEC+g4)*g5^e/(cL^e+g5^e)/def
p6 = 0.6 Reaction: cCOP1c => cCOP1n; cCOP1c, Rate Law: def*p6*cCOP1c/def
a = 2.0; n1 = 2.6; g1 = 0.1; q1 = 1.2; L = 0.5 Reaction: => cL_m; cNI, cP, cP7, cP9, cT, cNI, cP, cP7, cP9, cT, Rate Law: def*(L*q1*cP+n1*g1^a/((cP9+cP7+cNI+cT)^a+g1^a))/def
g16 = 0.3; e = 2.0; n3 = 0.29 Reaction: => cE3_m; cL, cL, Rate Law: def*n3*g16^e/(cL^e+g16^e)/def
p23 = 0.37 Reaction: => cE4; cE4_m, cE4_m, Rate Law: def*p23*cE4_m/def
p3 = 0.1; c = 2.0; g3 = 0.6 Reaction: => cLm; cL, cL, Rate Law: def*p3*cL^c/(cL^c+g3^c)/def
n5 = 0.23 Reaction: => cCOP1c, Rate Law: def*n5/def
p11 = 0.51 Reaction: => cG; cG_m, cG_m, Rate Law: def*p11*cG_m/def
p17 = 4.8 Reaction: cE3 + cG => cEG; cE3, cG, Rate Law: def*p17*cE3*cG/def
p27 = 0.8 Reaction: => cLUX; cLUX_m, cLUX_m, Rate Law: def*p27*cLUX_m/def
m20 = 0.6 Reaction: cZTL => ; cZTL, Rate Law: def*m20*cZTL/def
m14 = 0.4 Reaction: cP7_m => ; cP7_m, Rate Law: def*m14*cP7_m/def
p9 = 0.8 Reaction: => cP7; cP7_m, cP7_m, Rate Law: def*p9*cP7_m/def
m12 = 1.0 Reaction: cP9_m => ; cP9_m, Rate Law: def*m12*cP9_m/def
g14 = 0.004; n12 = 12.5; q2 = 1.56; g15 = 0.4; e = 2.0; L = 0.5 Reaction: => cG_m; cEC, cL, cP, cEC, cL, cP, Rate Law: def*(L*q2*cP+n12*g14/(cEC+g14)*g15^e/(cL^e+g15^e))/def
m19 = 0.2; p26 = 0.3; p28 = 2.0; m30 = 3.0; m29 = 5.0; p25 = 8.0; m37 = 0.8; p29 = 0.1; m36 = 0.1; p17 = 4.8; p21 = 1.0 Reaction: cE3n => ; cCOP1d, cCOP1n, cE4, cG, cLUX, cCOP1d, cCOP1n, cE3n, cE4, cG, cLUX, Rate Law: def*(((m29*cE3n*cCOP1n+m30*cE3n*cCOP1d+p25*cE4*cE3n)-p21*p25*cE4*cE3n/(p26*cLUX+p21+m37*cCOP1d+m36*cCOP1n))+p17*cE3n*p28*cG/(p29+m19+p17*cE3n))/def
m5 = 0.3 Reaction: cT_m => ; cT_m, Rate Law: def*m5*cT_m/def
m21 = 0.08 Reaction: cZG => ; cZG, Rate Law: def*m21*cZG/def
m13 = 0.32; D = 0.5; m22 = 0.1 Reaction: cP9 => ; cP9, Rate Law: def*(m13+m22*D)*cP9/def
p1 = 0.13; p2 = 0.27; L = 0.5 Reaction: => cL; cL_m, cL_m, Rate Law: def*cL_m*(p1*L+p2)/def
m1 = 0.3; m2 = 0.24; L = 0.5 Reaction: cL_m => ; cL_m, Rate Law: def*(m1*L+m2)*cL_m/def
m26 = 0.5 Reaction: cE3_m => ; cE3_m, Rate Law: def*m26*cE3_m/def
m3 = 0.2; p3 = 0.1; c = 2.0; g3 = 0.6 Reaction: cL => ; cL, Rate Law: def*(m3*cL+p3*cL^c/(cL^c+g3^c))/def
p4 = 0.56 Reaction: => cT; cT_m, cT_m, Rate Law: def*p4*cT_m/def
p25 = 8.0; m37 = 0.8; m36 = 0.1; p26 = 0.3; m39 = 0.3; p21 = 1.0 Reaction: cLUX => ; cCOP1d, cCOP1n, cE3n, cE4, cCOP1d, cCOP1n, cE3n, cE4, cLUX, Rate Law: def*(m39*cLUX+p26*cLUX*p25*cE4*cE3n/(p26*cLUX+p21+m37*cCOP1d+m36*cCOP1n))/def
m4 = 0.2 Reaction: cLm => ; cLm, Rate Law: def*m4*cLm/def
p14 = 0.14 Reaction: => cZTL, Rate Law: def*p14/def
m34 = 0.6 Reaction: cE4_m => ; cE4_m, Rate Law: def*m34*cE4_m/def
D = 0.5; m33 = 13.0; m31 = 0.3 Reaction: cCOP1d => ; cCOP1d, Rate Law: def*m31*(1+m33*D)*cCOP1d/def
m32 = 0.2; m19 = 0.2; m10 = 1.0; p29 = 0.1; m36 = 0.1; p17 = 4.8; p31 = 0.1; L = 0.5; d = 2.0; p24 = 10.0; p18 = 4.0; p28 = 2.0; g7 = 0.6; m37 = 0.8; m9 = 1.1 Reaction: cEC => ; cCOP1d, cCOP1n, cE3n, cEG, cG, cCOP1d, cCOP1n, cE3n, cEC, cEG, cG, Rate Law: def*(m36*cCOP1n*cEC+m37*cCOP1d*cEC+m32*cEC*(1+p24*L*(p28*cG/(p29+m19+p17*cE3n)+(p18*cEG+p17*cE3n*p28*cG/(p29+m19+p17*cE3n))/(m9*cCOP1n+m10*cCOP1d+p31))^d/((p28*cG/(p29+m19+p17*cE3n)+(p18*cEG+p17*cE3n*p28*cG/(p29+m19+p17*cE3n))/(m9*cCOP1n+m10*cCOP1d+p31))^d+g7^d)))/def
p25 = 8.0; m37 = 0.8; m36 = 0.1; p26 = 0.3; p21 = 1.0; m35 = 0.3 Reaction: cE4 => ; cCOP1d, cCOP1n, cE3n, cLUX, cCOP1d, cCOP1n, cE3n, cE4, cLUX, Rate Law: def*((m35*cE4+p25*cE4*cE3n)-p21*p25*cE4*cE3n/(p26*cLUX+p21+m37*cCOP1d+m36*cCOP1n))/def
q3 = 2.8; g8 = 0.01; g9 = 0.3; n7 = 0.2; e = 2.0; L = 0.5; n4 = 0.07 Reaction: => cP9_m; cEC, cL, cP, cEC, cL, cP, Rate Law: def*(L*q3*cP+(n4+n7*cL^e/(cL^e+g9^e))*g8/(cEC+g8))/def
n10 = 0.4; g12 = 0.2; n11 = 0.6; b = 2.0; e = 2.0; g13 = 1.0 Reaction: => cNI_m; cLm, cP7, cLm, cP7, Rate Law: def*(n10*cLm^e/(cLm^e+g12^e)+n11*cP7^b/(cP7^b+g13^b))/def
m18 = 3.4 Reaction: cG_m => ; cG_m, Rate Law: def*m18*cG_m/def
m19 = 0.2; p29 = 0.1; p17 = 4.8; p28 = 2.0 Reaction: cG => ; cE3n, cE3n, cG, Rate Law: def*((m19*cG+p28*cG)-p29*p28*cG/(p29+m19+p17*cE3n))/def
D = 0.5; p7 = 0.3 Reaction: => cP; cP, Rate Law: def*p7*D*(1-cP)/def
D = 0.5; m23 = 1.8; m15 = 0.7 Reaction: cP7 => ; cP7, Rate Law: def*(m15+m23*D)*cP7/def
p12 = 3.4; D = 0.5; L = 0.5; p13 = 0.1 Reaction: cG + cZTL => cZG; cG, cZG, cZTL, Rate Law: def*(p12*L*cZTL*cG-p13*D*cZG)/def
m9 = 1.1 Reaction: cE3 => ; cCOP1c, cCOP1c, cE3, Rate Law: def*m9*cE3*cCOP1c/def
m27 = 0.1; p15 = 3.0; L = 0.5 Reaction: cCOP1c => ; cCOP1c, Rate Law: def*m27*cCOP1c*(1+p15*L)/def
n14 = 0.1; n6 = 20.0; L = 0.5 Reaction: cCOP1n => cCOP1d; cP, cCOP1n, cP, Rate Law: def*(n6*L*cP*cCOP1n+n14*cCOP1n)/def
D = 0.5; m24 = 0.1; m17 = 0.5 Reaction: cNI => ; cNI, Rate Law: def*(m17+m24*D)*cNI/def
m19 = 0.2; p18 = 4.0; p28 = 2.0; m10 = 1.0; p29 = 0.1; m9 = 1.1; p17 = 4.8; p31 = 0.1 Reaction: cEG => ; cCOP1c, cCOP1d, cCOP1n, cE3n, cG, cCOP1c, cCOP1d, cCOP1n, cE3n, cEG, cG, Rate Law: def*((m9*cEG*cCOP1c+p18*cEG)-p31*(p18*cEG+p17*cE3n*p28*cG/(p29+m19+p17*cE3n))/(m9*cCOP1n+m10*cCOP1d+p31))/def
p20 = 0.1; p19 = 1.0 Reaction: cE3 => cE3n; cE3, cE3n, Rate Law: def*(p19*cE3-p20*cE3n)/def
p10 = 0.54 Reaction: => cNI; cNI_m, cNI_m, Rate Law: def*p10*cNI_m/def
p25 = 8.0; m37 = 0.8; m36 = 0.1; p26 = 0.3; p21 = 1.0 Reaction: => cEC; cCOP1d, cCOP1n, cE3n, cE4, cLUX, cCOP1d, cCOP1n, cE3n, cE4, cLUX, Rate Law: def*p26*cLUX*p25*cE4*cE3n/(p26*cLUX+p21+m37*cCOP1d+m36*cCOP1n)/def
g11 = 0.7; n9 = 0.2; f = 2.0; g10 = 0.5; n8 = 0.5; e = 2.0 Reaction: => cP7_m; cL, cLm, cP9, cL, cLm, cP9, Rate Law: def*(n8*(cLm+cL)^e/((cLm+cL)^e+g10^e)+n9*cP9^f/(cP9^f+g11^f))/def
n13 = 1.3; g2 = 0.01; e = 2.0; g6 = 0.3 Reaction: => cE4_m; cEC, cL, cEC, cL, Rate Law: def*n13*g2/(cEC+g2)*g6^e/(cL^e+g6^e)/def
D = 0.5; p5 = 4.0; m7 = 0.7; m6 = 0.3; m8 = 0.4 Reaction: cT => ; cZG, cZTL, cT, cZG, cZTL, Rate Law: def*((m6+m7*D)*cT*(p5*cZTL+cZG)+m8*cT)/def

States:

Name Description
cE4 cE4
cNI cNI
cLUX cLUX
cP9 cP9
cP9 m cP9_m
cZTL cZTL
cCOP1n cCOP1n
cNI m cNI_m
cE4 m cE4_m
cG m cG_m
cEG cEG
cCOP1d cCOP1d
cE3n cE3n
cP cP
cP7 cP7
cZG cZG
cE3 m cE3_m
cEC cEC
cG cG
cE3 cE3
cL m cL_m
cP7 m cP7_m
cCOP1c cCOP1c
cLUX m cLUX_m
cT m cT_m
cLm cLm
cT cT
cL cL

Observables: none

cL_m_degr, param m1, modified to ensure light rate > dark rate. Parameter set from PLM_67v2_LDLLLDs_newFFT_1, with modif…

Our understanding of the complex, transcriptional feedback loops in the circadian clock mechanism has depended upon quantitative, timeseries data from disparate sources. We measure clock gene RNA profiles in Arabidopsis thaliana seedlings, grown with or without exogenous sucrose, or in soil-grown plants and in wild-type and mutant backgrounds. The RNA profiles were strikingly robust across the experimental conditions, so current mathematical models are likely to be broadly applicable in leaf tissue. In addition to providing reference data, unexpected behaviours included co-expression of PRR9 and ELF4, and regulation of PRR5 by GI. Absolute RNA quantification revealed low levels of PRR9 transcripts (peak approx. 50 copies cell(-1)) compared with other clock genes, and threefold higher levels of LHY RNA (more than 1500 copies cell(-1)) than of its close relative CCA1. The data are disseminated from BioDare, an online repository for focused timeseries data, which is expected to benefit mechanistic modelling. One data subset successfully constrained clock gene expression in a complex model, using publicly available software on parallel computers, without expert tuning or programming. We outline the empirical and mathematical justification for data aggregation in understanding highly interconnected, dynamic networks such as the clock, and the observed design constraints on the resources required to make this approach widely accessible. link: http://identifiers.org/pubmed/26468131

Parameters:

Name Description
n8 = 0.46468005656595; f = 2.0; n9 = 0.12054287502747; g10 = 0.59800649651902; e = 2.0; g11 = 0.97065591755812 Reaction: => cP7_m; cL, cLm, cP9, cL, cLm, cP9, Rate Law: def*(n8*(cLm+cL)^e/((cLm+cL)^e+g10^e)+n9*cP9^f/(cP9^f+g11^f))/def
p3 = 0.0738150022314; c = 2.0; g3 = 0.6; m3 = 0.17565464903571 Reaction: cL => ; cL, Rate Law: def*(m3*cL+p3*cL^c/(cL^c+g3^c))/def
p11 = 0.49350029121361 Reaction: => cG; cG_m, cG_m, Rate Law: def*p11*cG_m/def
p17 = 4.32998167851186; m29 = 6.5829611214384; m19 = 0.47083189258762; p26 = 0.3; m30 = 3.12936002914913; m37 = 0.43830433763055; p28 = 2.0; p25 = 8.0; m36 = 0.09362464249722; p29 = 0.1; p21 = 1.0 Reaction: cE3n => ; cCOP1d, cCOP1n, cE4, cG, cLUX, cCOP1d, cCOP1n, cE3n, cE4, cG, cLUX, Rate Law: def*(((m29*cE3n*cCOP1n+m30*cE3n*cCOP1d+p25*cE4*cE3n)-p21*p25*cE4*cE3n/(p26*cLUX+p21+m37*cCOP1d+m36*cCOP1n))+p17*cE3n*p28*cG/(p29+m19+p17*cE3n))/def
g8 = 0.02785533720284; q3 = 2.91645248092752; n4 = 0.04557059014918; n7 = 0.14205317472212; g9 = 0.32642600662781; e = 2.0; L = 0.5 Reaction: => cP9_m; cEC, cL, cP, cEC, cL, cP, Rate Law: def*(L*q3*cP+(n4+n7*cL^e/(cL^e+g9^e))*g8/(cEC+g8))/def
m14 = 0.58317183194053 Reaction: cP7_m => ; cP7_m, Rate Law: def*m14*cP7_m/def
m11 = 1.0; L = 0.5 Reaction: cP => ; cP, Rate Law: def*m11*cP*L/def
p6 = 0.6 Reaction: cCOP1c => cCOP1n; cCOP1c, Rate Law: def*p6*cCOP1c/def
m18 = 2.38992856366188 Reaction: cG_m => ; cG_m, Rate Law: def*m18*cG_m/def
p17 = 4.32998167851186 Reaction: cE3 + cG => cEG; cE3, cG, Rate Law: def*p17*cE3*cG/def
p27 = 1.04800925749369 Reaction: => cLUX; cLUX_m, cLUX_m, Rate Law: def*p27*cLUX_m/def
a = 2.0; g1 = 0.08672864809113; q1 = 0.6; n1 = 1.99252254640817; L = 0.5 Reaction: => cL_m; cNI, cP, cP7, cP9, cT, cNI, cP, cP7, cP9, cT, Rate Law: def*(L*q1*cP+n1*g1^a/((cP9+cP7+cNI+cT)^a+g1^a))/def
n3 = 0.16472770747976; g16 = 0.21835306363087; e = 2.0 Reaction: => cE3_m; cL, cL, Rate Law: def*n3*g16^e/(cL^e+g16^e)/def
n5 = 0.23 Reaction: => cCOP1c, Rate Law: def*n5/def
p2 = 0.20262717003844; p1 = 0.07150399789214; L = 0.5 Reaction: => cL; cL_m, cL_m, Rate Law: def*cL_m*(p1*L+p2)/def
p9 = 0.85704792589418 Reaction: => cP7; cP7_m, cP7_m, Rate Law: def*p9*cP7_m/def
p14 = 0.10935964554573 Reaction: => cZTL, Rate Law: def*p14/def
m20 = 0.6 Reaction: cZTL => ; cZTL, Rate Law: def*m20*cZTL/def
p25 = 8.0; m36 = 0.09362464249722; p26 = 0.3; m37 = 0.43830433763055; p21 = 1.0 Reaction: => cEC; cCOP1d, cCOP1n, cE3n, cE4, cLUX, cCOP1d, cCOP1n, cE3n, cE4, cLUX, Rate Law: def*p26*cLUX*p25*cE4*cE3n/(p26*cLUX+p21+m37*cCOP1d+m36*cCOP1n)/def
g4 = 0.00503234997631; n2 = 0.68148116717556; g5 = 0.20247194961847; e = 2.0 Reaction: => cT_m; cEC, cL, cEC, cL, Rate Law: def*n2*g4/(cEC+g4)*g5^e/(cL^e+g5^e)/def
m9 = 1.42873823342205; m32 = 0.2; p17 = 4.32998167851186; m37 = 0.43830433763055; p24 = 14.5984045217467; m10 = 1.0; m36 = 0.09362464249722; p29 = 0.1; p31 = 0.1; L = 0.5; d = 2.0; g7 = 0.45632674147836; m19 = 0.47083189258762; p18 = 3.48112987474967; p28 = 2.0 Reaction: cEC => ; cCOP1d, cCOP1n, cE3n, cEG, cG, cCOP1d, cCOP1n, cE3n, cEC, cEG, cG, Rate Law: def*(m36*cCOP1n*cEC+m37*cCOP1d*cEC+m32*cEC*(1+p24*L*(p28*cG/(p29+m19+p17*cE3n)+(p18*cEG+p17*cE3n*p28*cG/(p29+m19+p17*cE3n))/(m9*cCOP1n+m10*cCOP1d+p31))^d/((p28*cG/(p29+m19+p17*cE3n)+(p18*cEG+p17*cE3n*p28*cG/(p29+m19+p17*cE3n))/(m9*cCOP1n+m10*cCOP1d+p31))^d+g7^d)))/def
m12 = 1.0 Reaction: cP9_m => ; cP9_m, Rate Law: def*m12*cP9_m/def
p25 = 8.0; m36 = 0.09362464249722; m35 = 0.18382557500265; p26 = 0.3; m37 = 0.43830433763055; p21 = 1.0 Reaction: cE4 => ; cCOP1d, cCOP1n, cE3n, cLUX, cCOP1d, cCOP1n, cE3n, cE4, cLUX, Rate Law: def*((m35*cE4+p25*cE4*cE3n)-p21*p25*cE4*cE3n/(p26*cLUX+p21+m37*cCOP1d+m36*cCOP1n))/def
n13 = 1.18471991918001; g6 = 0.28604744186645; e = 2.0; g2 = 0.01109625947768 Reaction: => cE4_m; cEC, cL, cEC, cL, Rate Law: def*n13*g2/(cEC+g2)*g6^e/(cL^e+g6^e)/def
m9 = 1.42873823342205 Reaction: cE3 => ; cCOP1c, cCOP1c, cE3, Rate Law: def*m9*cE3*cCOP1c/def
p16 = 0.9855875650128 Reaction: => cE3; cE3_m, cE3_m, Rate Law: def*p16*cE3_m/def
m5 = 0.3 Reaction: cT_m => ; cT_m, Rate Law: def*m5*cT_m/def
p3 = 0.0738150022314; c = 2.0; g3 = 0.6 Reaction: => cLm; cL, cL, Rate Law: def*p3*cL^c/(cL^c+g3^c)/def
m21 = 0.08 Reaction: cZG => ; cZG, Rate Law: def*m21*cZG/def
m24 = 0.11119364985807; D = 0.5; m17 = 0.5 Reaction: cNI => ; cNI, Rate Law: def*(m17+m24*D)*cNI/def
p10 = 0.88102987349092 Reaction: => cNI; cNI_m, cNI_m, Rate Law: def*p10*cNI_m/def
m26 = 0.5 Reaction: cE3_m => ; cE3_m, Rate Law: def*m26*cE3_m/def
g14 = 0.00518249003042; q2 = 0.57336977424479; g15 = 0.49185301792787; e = 2.0; L = 0.5; n12 = 8.43921672276903 Reaction: => cG_m; cEC, cL, cP, cEC, cL, cP, Rate Law: def*(L*q2*cP+n12*g14/(cEC+g14)*g15^e/(cL^e+g15^e))/def
p29 = 0.1; p17 = 4.32998167851186; m19 = 0.47083189258762; p28 = 2.0 Reaction: cG => ; cE3n, cE3n, cG, Rate Law: def*((m19*cG+p28*cG)-p29*p28*cG/(p29+m19+p17*cE3n))/def
p8 = 0.4098375626616 Reaction: => cP9; cP9_m, cP9_m, Rate Law: def*p8*cP9_m/def
p4 = 0.51783935402389 Reaction: => cT; cT_m, cT_m, Rate Law: def*p4*cT_m/def
p12 = 2.43270583452351; D = 0.5; p13 = 0.16471437958494; L = 0.5 Reaction: cG + cZTL => cZG; cG, cZG, cZTL, Rate Law: def*(p12*L*cZTL*cG-p13*D*cZG)/def
p20 = 0.1940717319972; p19 = 1.74107843497564 Reaction: cE3 => cE3n; cE3, cE3n, Rate Law: def*(p19*cE3-p20*cE3n)/def
m2 = 0.45186541768694; m1 = 0.04813458231306; L = 0.5 Reaction: cL_m => ; cL_m, Rate Law: def*(m1*L+m2)*cL_m/def
m23 = 0.54491969619247; D = 0.5; m15 = 0.7 Reaction: cP7 => ; cP7, Rate Law: def*(m15+m23*D)*cP7/def
m4 = 0.2 Reaction: cLm => ; cLm, Rate Law: def*m4*cLm/def
m34 = 0.74619776125315 Reaction: cE4_m => ; cE4_m, Rate Law: def*m34*cE4_m/def
D = 0.5; m33 = 13.0; m31 = 0.3 Reaction: cCOP1d => ; cCOP1d, Rate Law: def*m31*(1+m33*D)*cCOP1d/def
p25 = 8.0; m36 = 0.09362464249722; p26 = 0.3; m37 = 0.43830433763055; p21 = 1.0; m39 = 0.36610515263739 Reaction: cLUX => ; cCOP1d, cCOP1n, cE3n, cE4, cCOP1d, cCOP1n, cE3n, cE4, cLUX, Rate Law: def*(m39*cLUX+p26*cLUX*p25*cE4*cE3n/(p26*cLUX+p21+m37*cCOP1d+m36*cCOP1n))/def
p23 = 0.74 Reaction: => cE4; cE4_m, cE4_m, Rate Law: def*p23*cE4_m/def
m7 = 0.49132441826399; D = 0.5; m6 = 0.1718885396183; m8 = 0.33013479704789; p5 = 3.69349002161811 Reaction: cT => ; cZG, cZTL, cT, cZG, cZTL, Rate Law: def*((m6+m7*D)*cT*(p5*cZTL+cZG)+m8*cT)/def
m16 = 0.54342221617699 Reaction: cNI_m => ; cNI_m, Rate Law: def*m16*cNI_m/def
D = 0.5; p7 = 0.3 Reaction: => cP; cP, Rate Law: def*p7*D*(1-cP)/def
m27 = 0.1; p15 = 3.0; L = 0.5 Reaction: cCOP1n => ; cCOP1n, Rate Law: def*m27*cCOP1n*(1+p15*L)/def
n14 = 0.1; n6 = 20.0; L = 0.5 Reaction: cCOP1n => cCOP1d; cP, cCOP1n, cP, Rate Law: def*(n6*L*cP*cCOP1n+n14*cCOP1n)/def
g12 = 0.2; n11 = 1.04887048285294; n10 = 0.53104365301892; b = 2.0; e = 2.0; g13 = 1.0 Reaction: => cNI_m; cLm, cP7, cLm, cP7, Rate Law: def*(n10*cLm^e/(cLm^e+g12^e)+n11*cP7^b/(cP7^b+g13^b))/def
m13 = 0.32; D = 0.5; m22 = 0.09605427710298 Reaction: cP9 => ; cP9, Rate Law: def*(m13+m22*D)*cP9/def
m9 = 1.42873823342205; p17 = 4.32998167851186; p18 = 3.48112987474967; m19 = 0.47083189258762; p28 = 2.0; m10 = 1.0; p29 = 0.1; p31 = 0.1 Reaction: cEG => ; cCOP1c, cCOP1d, cCOP1n, cE3n, cG, cCOP1c, cCOP1d, cCOP1n, cE3n, cEG, cG, Rate Law: def*((m9*cEG*cCOP1c+p18*cEG)-p31*(p18*cEG+p17*cE3n*p28*cG/(p29+m19+p17*cE3n))/(m9*cCOP1n+m10*cCOP1d+p31))/def

States:

Name Description
cE4 cE4
cNI cNI
cLUX cLUX
cP9 cP9
cP9 m cP9_m
cZTL cZTL
cCOP1n cCOP1n
cE4 m cE4_m
cNI m cNI_m
cEG cEG
cG m cG_m
cCOP1d cCOP1d
cP cP
cE3n cE3n
cP7 cP7
cZG cZG
cE3 m cE3_m
cEC cEC
cG cG
cE3 cE3
cL m cL_m
cP7 m cP7_m
cCOP1c cCOP1c
cT m cT_m
cLUX m cLUX_m
cLm cLm
cT cT
cL cL

Observables: none

cL_m_degr, param m1, modified to ensure light rate > dark rate.

Our understanding of the complex, transcriptional feedback loops in the circadian clock mechanism has depended upon quantitative, timeseries data from disparate sources. We measure clock gene RNA profiles in Arabidopsis thaliana seedlings, grown with or without exogenous sucrose, or in soil-grown plants and in wild-type and mutant backgrounds. The RNA profiles were strikingly robust across the experimental conditions, so current mathematical models are likely to be broadly applicable in leaf tissue. In addition to providing reference data, unexpected behaviours included co-expression of PRR9 and ELF4, and regulation of PRR5 by GI. Absolute RNA quantification revealed low levels of PRR9 transcripts (peak approx. 50 copies cell(-1)) compared with other clock genes, and threefold higher levels of LHY RNA (more than 1500 copies cell(-1)) than of its close relative CCA1. The data are disseminated from BioDare, an online repository for focused timeseries data, which is expected to benefit mechanistic modelling. One data subset successfully constrained clock gene expression in a complex model, using publicly available software on parallel computers, without expert tuning or programming. We outline the empirical and mathematical justification for data aggregation in understanding highly interconnected, dynamic networks such as the clock, and the observed design constraints on the resources required to make this approach widely accessible. link: http://identifiers.org/pubmed/26468131

Parameters: none

States: none

Observables: none

cL_m_degr, param m1, modified to ensure light rate > dark rate.

Our understanding of the complex, transcriptional feedback loops in the circadian clock mechanism has depended upon quantitative, timeseries data from disparate sources. We measure clock gene RNA profiles in Arabidopsis thaliana seedlings, grown with or without exogenous sucrose, or in soil-grown plants and in wild-type and mutant backgrounds. The RNA profiles were strikingly robust across the experimental conditions, so current mathematical models are likely to be broadly applicable in leaf tissue. In addition to providing reference data, unexpected behaviours included co-expression of PRR9 and ELF4, and regulation of PRR5 by GI. Absolute RNA quantification revealed low levels of PRR9 transcripts (peak approx. 50 copies cell(-1)) compared with other clock genes, and threefold higher levels of LHY RNA (more than 1500 copies cell(-1)) than of its close relative CCA1. The data are disseminated from BioDare, an online repository for focused timeseries data, which is expected to benefit mechanistic modelling. One data subset successfully constrained clock gene expression in a complex model, using publicly available software on parallel computers, without expert tuning or programming. We outline the empirical and mathematical justification for data aggregation in understanding highly interconnected, dynamic networks such as the clock, and the observed design constraints on the resources required to make this approach widely accessible. link: http://identifiers.org/pubmed/26468131

Parameters: none

States: none

Observables: none

cL_m_degr, param m1, modified to ensure light rate > dark rate.

Our understanding of the complex, transcriptional feedback loops in the circadian clock mechanism has depended upon quantitative, timeseries data from disparate sources. We measure clock gene RNA profiles in Arabidopsis thaliana seedlings, grown with or without exogenous sucrose, or in soil-grown plants and in wild-type and mutant backgrounds. The RNA profiles were strikingly robust across the experimental conditions, so current mathematical models are likely to be broadly applicable in leaf tissue. In addition to providing reference data, unexpected behaviours included co-expression of PRR9 and ELF4, and regulation of PRR5 by GI. Absolute RNA quantification revealed low levels of PRR9 transcripts (peak approx. 50 copies cell(-1)) compared with other clock genes, and threefold higher levels of LHY RNA (more than 1500 copies cell(-1)) than of its close relative CCA1. The data are disseminated from BioDare, an online repository for focused timeseries data, which is expected to benefit mechanistic modelling. One data subset successfully constrained clock gene expression in a complex model, using publicly available software on parallel computers, without expert tuning or programming. We outline the empirical and mathematical justification for data aggregation in understanding highly interconnected, dynamic networks such as the clock, and the observed design constraints on the resources required to make this approach widely accessible. link: http://identifiers.org/pubmed/26468131

Parameters: none

States: none

Observables: none

cL_m_degr, param m1, modified to ensure light rate > dark rate.

Our understanding of the complex, transcriptional feedback loops in the circadian clock mechanism has depended upon quantitative, timeseries data from disparate sources. We measure clock gene RNA profiles in Arabidopsis thaliana seedlings, grown with or without exogenous sucrose, or in soil-grown plants and in wild-type and mutant backgrounds. The RNA profiles were strikingly robust across the experimental conditions, so current mathematical models are likely to be broadly applicable in leaf tissue. In addition to providing reference data, unexpected behaviours included co-expression of PRR9 and ELF4, and regulation of PRR5 by GI. Absolute RNA quantification revealed low levels of PRR9 transcripts (peak approx. 50 copies cell(-1)) compared with other clock genes, and threefold higher levels of LHY RNA (more than 1500 copies cell(-1)) than of its close relative CCA1. The data are disseminated from BioDare, an online repository for focused timeseries data, which is expected to benefit mechanistic modelling. One data subset successfully constrained clock gene expression in a complex model, using publicly available software on parallel computers, without expert tuning or programming. We outline the empirical and mathematical justification for data aggregation in understanding highly interconnected, dynamic networks such as the clock, and the observed design constraints on the resources required to make this approach widely accessible. link: http://identifiers.org/pubmed/26468131

Parameters: none

States: none

Observables: none

Multilevel logical model encompassing the Nodal and BMP pathways together with key transcription factors setting the dor…

During sea urchin development, secretion of Nodal and BMP2/4 ligands and their antagonists Lefty and Chordin from a ventral organizer region specifies the ventral and dorsal territories. This process relies on a complex interplay between the Nodal and BMP pathways through numerous regulatory circuits. To decipher the interplay between these pathways, we used a combination of treatments with recombinant Nodal and BMP2/4 proteins and a computational modelling approach. We assembled a logical model focusing on cell responses to signalling inputs along the dorsal-ventral axis, which was extended to cover ligand diffusion and enable multicellular simulations. Our model simulations accurately recapitulate gene expression in wild type embryos, accounting for the specification of ventral ectoderm, ciliary band and dorsal ectoderm. Our model simulations further recapitulate various morphant phenotypes, reveals a dominance of the BMP pathway over the Nodal pathway, and stresses the crucial impact of the rate of Smad activation in D/V patterning. These results emphasise the key role of the mutual antagonism between the Nodal and BMP2/4 pathways in driving early dorsal-ventral patterning of the sea urchin embryo. link: http://identifiers.org/pubmed/33298464

Parameters: none

States: none

Observables: none

MODEL0911665321 @ v0.0.1

This a model from the article: Ionic mechanism of electrical alternans. Fox JJ, McHarg JL, Gilmour RF Jr. Am J Physi…

Although alternans of action potential duration (APD) is a robust feature of the rapidly paced canine ventricle, currently available ionic models of cardiac myocytes do not recreate this phenomenon. To address this problem, we developed a new ionic model using formulations of currents based on previous models and recent experimental data. Compared with existing models, the inward rectifier K(+) current (I(K1)) was decreased at depolarized potentials, the maximum conductance and rectification of the rapid component of the delayed rectifier K(+) current (I(Kr)) were increased, and I(Kr) activation kinetics were slowed. The slow component of the delayed rectifier K(+) current (I(Ks)) was increased in magnitude and activation shifted to less positive voltages, and the L-type Ca(2+) current (I(Ca)) was modified to produce a smaller, more rapidly inactivating current. Finally, a simplified form of intracellular calcium dynamics was adopted. In this model, APD alternans occurred at cycle lengths = 150-210 ms, with a maximum alternans amplitude of 39 ms. APD alternans was suppressed by decreasing I(Ca) magnitude or calcium-induced inactivation and by increasing the magnitude of I(K1), I(Kr), or I(Ks). These results establish an ionic basis for APD alternans, which should facilitate the development of pharmacological approaches to eliminating alternans. link: http://identifiers.org/pubmed/11788399

Parameters: none

States: none

Observables: none

This is a coupled ordinary differential equation model of tumour-immune dynamics, accounting for biological and clinical…

A coupled ordinary differential equation model of tumour-immune dynamics is presented and analysed. The model accounts for biological and clinical factors which regulate the interaction rates of cytotoxic T lymphocytes on the surface of the tumour mass. A phase plane analysis demonstrates that competition between tumour cells and lymphocytes can result in tumour eradication, perpetual oscillations, or unbounded solutions. To investigate the dependence of the dynamic behaviour on model parameters, the equations are solved analytically and conditions for unbounded versus bounded solutions are discussed. An analytic characterisation of the basin of attraction for oscillatory orbits is given. It is also shown that the tumour shape, characterised by a surface area to volume scaling factor, influences the size of the basin, with significant consequences for therapy design. The findings reveal that the tumour volume must surpass a threshold size that depends on lymphocyte parameters for the cancer to be completely eliminated. A semi-analytic procedure to calculate oscillation periods and determine their sensitivity to model parameters is also presented. Numerical results show that the period of oscillations exhibits notable nonlinear dependence on biologically relevant conditions. link: http://identifiers.org/pubmed/24759513

Parameters:

Name Description
rho = 4.83597586204941; min_C = 0.1; k = 0.2 Reaction: V_Tumor_Volume => ; C_Cytotoxic_T_Lymphocytes_Coverage, Rate Law: compartment*rho*k*V_Tumor_Volume^(2/3)*min_C
d_c = 0.2 Reaction: C_Cytotoxic_T_Lymphocytes_Coverage =>, Rate Law: compartment*d_c*C_Cytotoxic_T_Lymphocytes_Coverage
rho = 4.83597586204941; r_t = 0.1 Reaction: => V_Tumor_Volume, Rate Law: compartment*rho*r_t*V_Tumor_Volume^(2/3)
r_c = 0.001; rho = 4.83597586204941 Reaction: => C_Cytotoxic_T_Lymphocytes_Coverage; V_Tumor_Volume, Rate Law: compartment*rho*r_c*V_Tumor_Volume^(2/3)*C_Cytotoxic_T_Lymphocytes_Coverage

States:

Name Description
C Cytotoxic T Lymphocytes Coverage [cytotoxic T cell; T cell mediated cytotoxicity directed against tumor cell target]
V Tumor Volume [Tumor Volume]

Observables: none

Fribourg2014 - Dynamics of viral antagonism and innate immune response (H1N1 influenza A virus - Cal/09) The dynamics o…

Viral antagonism of host responses is an essential component of virus pathogenicity. The study of the interplay between immune response and viral antagonism is challenging due to the involvement of many processes acting at multiple time scales. Here we develop an ordinary differential equation model to investigate the early, experimentally measured, responses of human monocyte-derived dendritic cells to infection by two H1N1 influenza A viruses of different clinical outcomes: pandemic A/California/4/2009 and seasonal A/New Caledonia/20/1999. Our results reveal how the strength of virus antagonism, and the time scale over which it acts to thwart the innate immune response, differs significantly between the two viruses, as is made clear by their impact on the temporal behavior of a number of measured genes. The model thus sheds light on the mechanisms that underlie the variability of innate immune responses to different H1N1 viruses. link: http://identifiers.org/pubmed/24594370

Parameters:

Name Description
k26 = 0.360085 substance; tao12 = 1.0 substance; r4 = 1.0E-5 substance; IC2 = 0.0; IC1 = 0.0 Reaction: w => STATm; STATP2n, Rate Law: (r4*IC1+k26*STATP2n)*IC2-STATm*ln(2)/tao12
C = 500000.0 substance; K19 = 0.004 substance; vmax19 = 154800.0 substance; NA = 6.023E23 substance Reaction: w => TNFenv; TNFam, Rate Law: 1000000000*C*vmax19/NA*TNFam/(K19+TNFam)
TJ = 0.0; tao3 = 0.56 substance; K5 = 0.01 substance Reaction: w => STATP2n; STAT, Rate Law: K5*TJ*STAT/2/(K5+STAT)-STATP2n*ln(2)/tao3
tao1 = 2.5 substance; IC2 = 0.0; k15 = 3.6E-8 substance; r0 = 0.001 substance; IC1 = 0.0 Reaction: w => IFNb_mRNA; IRF7Pn, Rate Law: (r0*IC1+k15*IRF7Pn)*IC2-IFNb_mRNA*ln(2)/tao1
tao8 = 2.0 substance; IC2ifa = 0.0; k16 = 0.36 substance Reaction: w => IFNa_mRNA; IRF7Pn, Rate Law: k16*IRF7Pn*IC2ifa-IFNa_mRNA*ln(2)/tao8
k28 = 360.0 substance; tao13 = 15.0 substance Reaction: w => STAT; STATm, Rate Law: k28*STATm-STAT*ln(2)/tao13
C = 500000.0 substance; K17 = 0.002 substance; vmax17 = 72000.0 substance; NA = 6.023E23 substance Reaction: w => IFNa_env; IFNa_mRNA, Rate Law: 1000000000*C*vmax17/NA*IFNa_mRNA/(K17+IFNa_mRNA)
C = 500000.0 substance; K2 = 0.002 substance; vmax2 = 72000.0 substance; NA = 6.023E23 substance Reaction: w => IFNb_env; IFNb_mRNA, Rate Law: 1000000000*C*vmax2/NA*IFNb_mRNA/(K2+IFNb_mRNA)
K20 = 6.0E-4 substance; tao9 = 2.0 substance; r1 = 1.0E-4 substance; IC2 = 0.0; rmax20 = 0.001 substance; IC1 = 0.0 Reaction: w => TNFam; TNFenv, Rate Law: (r1*IC1+rmax20*TNFenv/(K20+TNFenv))*IC2-TNFam*ln(2)/tao9
k8 = 0.0036 substance; IC2 = 0.0; r3 = 1.0E-7 substance; tao4 = 0.46 substance; IC1 = 0.0 Reaction: w => SOCS1m; STATP2n, Rate Law: (r3*IC1+k8*STATP2n)*IC2-SOCS1m*ln(2)/tao4
k12 = 360.0 substance; IC1 = 0.0 Reaction: w => IRF7Pn; IRF7m, Rate Law: k12*IC1*IRF7m
k11 = 3.6E-4 substance; k14 = 3.204E-7 substance; IC2 = 0.0; tao6 = 1.0 Reaction: w => IRF7m; STATP2n, IRF7Pn, Rate Law: (k11*STATP2n+k14*IRF7Pn)*IC2-IRF7m*ln(2)/tao6

States:

Name Description
SOCS1m [IPR028411]
IFNa mRNA [IPR015589]
IFNa env [IPR015589]
IRF7Pn [Interferon regulatory factor 7]
IRF7m [Interferon regulatory factor 7]
TNFam [Tumor necrosis factor]
w w
STATm [IPR001217]
IFNb env [Interferon beta]
IFNb mRNA [Interferon beta]
TNFenv [Tumor necrosis factor]
STATP2n [IPR001217]
STAT [IPR001217]

Observables: none

Fribourg2014 - Dynamics of viral antagonism and innate immune response (H1N1 influenza A virus - NC/99) The dynamics of…

Viral antagonism of host responses is an essential component of virus pathogenicity. The study of the interplay between immune response and viral antagonism is challenging due to the involvement of many processes acting at multiple time scales. Here we develop an ordinary differential equation model to investigate the early, experimentally measured, responses of human monocyte-derived dendritic cells to infection by two H1N1 influenza A viruses of different clinical outcomes: pandemic A/California/4/2009 and seasonal A/New Caledonia/20/1999. Our results reveal how the strength of virus antagonism, and the time scale over which it acts to thwart the innate immune response, differs significantly between the two viruses, as is made clear by their impact on the temporal behavior of a number of measured genes. The model thus sheds light on the mechanisms that underlie the variability of innate immune responses to different H1N1 viruses. link: http://identifiers.org/pubmed/24594370

Parameters:

Name Description
C = 500000.0 substance; K19 = 0.004 substance; vmax19 = 154800.0 substance; NA = 6.023E23 substance Reaction: w => TNFenv; TNFam, Rate Law: 1000000000*C*vmax19/NA*TNFam/(K19+TNFam)
C = 500000.0 substance; K2 = 72000.0 substance; vmax2 = 72000.0 substance; NA = 6.023E23 substance Reaction: w => IFNb_env; IFNb_mRNA, Rate Law: 1000000000*C*vmax2/NA*IFNb_mRNA/(K2+IFNb_mRNA)
tao8 = 2.0 substance; k16 = 3600.0 substance; IC2ifa = 0.0 Reaction: w => IFNa_mRNA; IRF7Pn, Rate Law: k16*IRF7Pn*IC2ifa-IFNa_mRNA*ln(2)/tao8
k15 = 3.6E-5 substance; tao1 = 2.5 substance; IC2 = 0.0; r0 = 0.003 substance; IC1 = 0.0 Reaction: w => IFNb_mRNA; IRF7Pn, Rate Law: (r0*IC1+k15*IRF7Pn)*IC2-IFNb_mRNA*ln(2)/tao1
TJ = 0.0; tao3 = 0.56 substance; K5 = 0.01 substance Reaction: w => STATP2n; STAT, Rate Law: K5*TJ*STAT/2/(K5+STAT)-STATP2n*ln(2)/tao3
k28 = 360.0 substance; tao13 = 15.0 substance Reaction: w => STAT; STATm, Rate Law: k28*STATm-STAT*ln(2)/tao13
k26 = 0.360085 substance; tao12 = 1.0 substance; r4 = 1.0E-6 substance; IC2 = 0.0; IC1 = 0.0 Reaction: w => STATm; STATP2n, Rate Law: (r4*IC1+k26*STATP2n)*IC2-STATm*ln(2)/tao12
K20 = 6.0E-4 substance; tao9 = 2.0 substance; IC2 = 0.0; rmax20 = 0.001 substance; r1 = 2.5E-4 substance; IC1 = 0.0 Reaction: w => TNFam; TNFenv, Rate Law: (r1*IC1+rmax20*TNFenv/(K20+TNFenv))*IC2-TNFam*ln(2)/tao9
C = 500000.0 substance; K17 = 0.002 substance; vmax17 = 72000.0 substance; NA = 6.023E23 substance Reaction: w => IFNa_env; IFNa_mRNA, Rate Law: 1000000000*C*vmax17/NA*IFNa_mRNA/(K17+IFNa_mRNA)
k8 = 0.0036 substance; IC2 = 0.0; r3 = 1.0E-7 substance; tao4 = 0.46 substance; IC1 = 0.0 Reaction: w => SOCS1m; STATP2n, Rate Law: (r3*IC1+k8*STATP2n)*IC2-SOCS1m*ln(2)/tao4
k12 = 3600.0 substance; IC1 = 0.0 Reaction: w => IRF7Pn; IRF7m, Rate Law: k12*IC1*IRF7m
k11 = 3.6E-4 substance; k14 = 3.204E-7 substance; IC2 = 0.0; tao6 = 1.0 Reaction: w => IRF7m; STATP2n, IRF7Pn, Rate Law: (k11*STATP2n+k14*IRF7Pn)*IC2-IRF7m*ln(2)/tao6

States:

Name Description
SOCS1m [IPR028411]
IFNa mRNA [IPR015589]
IFNa env [IPR015589]
IRF7m [Interferon regulatory factor 7]
IRF7Pn [Interferon regulatory factor 7]
TNFam [Tumor necrosis factor]
w w
STATm [IPR001217]
IFNb env [IPR015588]
IFNb mRNA [IPR015588]
TNFenv [Tumor necrosis factor]
STATP2n [IPR001217]
STAT [IPR001217]

Observables: none

This is an ordinary differential equation mathematical model investigating the early responses of human monocyte-derived…

Viral antagonism of host responses is an essential component of virus pathogenicity. The study of the interplay between immune response and viral antagonism is challenging due to the involvement of many processes acting at multiple time scales. Here we develop an ordinary differential equation model to investigate the early, experimentally measured, responses of human monocyte-derived dendritic cells to infection by two H1N1 influenza A viruses of different clinical outcomes: pandemic A/California/4/2009 and seasonal A/New Caledonia/20/1999. Our results reveal how the strength of virus antagonism, and the time scale over which it acts to thwart the innate immune response, differs significantly between the two viruses, as is made clear by their impact on the temporal behavior of a number of measured genes. The model thus sheds light on the mechanisms that underlie the variability of innate immune responses to different H1N1 viruses. link: http://identifiers.org/pubmed/24594370

Parameters:

Name Description
t_6 = 1.0 Reaction: IRF7m =>, Rate Law: compartment*IRF7m*ln(2)/t_6
K_20 = 6.0E-4; r_20 = 0.001; IC2 = 1.0; r_1 = 1.0E-4; IC1 = 1.0 Reaction: => TNFam; TFNenv, Rate Law: compartment*IC2*(r_1*IC1+r_20*TFNenv/(K_20+TFNenv))
k_26 = 0.018; IC2 = 1.0; r_4 = 1.0E-6; IC1 = 1.0 Reaction: => STATm; STATP2n, Rate Law: compartment*(r_4*IC1+k_26*STATP2n)*IC2
k_8 = 0.0036; IC2 = 1.0; r_3 = 1.0E-7; IC1 = 1.0 Reaction: => SOCSm; STATP2n, Rate Law: compartment*(r_3*IC1+k_8*STATP2n)*IC2
k_12 = 360.0; IC1 = 1.0 Reaction: => IRF7Pn; IRF7m, Rate Law: compartment*k_12*IRF7m*IC1
t_4 = 0.46 Reaction: SOCSm =>, Rate Law: compartment*SOCSm*ln(2)/t_4
t_8 = 2.0 Reaction: IFNam =>, Rate Law: compartment*IFNam*ln(2)/t_8
k_16 = 0.36; IC2 = 1.0 Reaction: => IFNam; IRF7Pn, Rate Law: compartment*k_16*IRF7Pn*IC2
t_3 = 0.56 Reaction: STATP2n =>, Rate Law: compartment*STATP2n*ln(2)/t_3
t_13 = 15.0 Reaction: STAT =>, Rate Law: compartment*STAT*ln(2)/t_13
C = 500000.0; v_max217 = 72360.0; K_217 = 0.002; gamma = 1.66030217499585E-15 Reaction: => IFNBenv, Rate Law: compartment*gamma*C*v_max217*IFNBenv/(K_217+IFNBenv)
t_9 = 2.0 Reaction: TNFam =>, Rate Law: compartment*TNFam*ln(2)/t_9
t_12 = 1.0 Reaction: STATm =>, Rate Law: compartment*STATm*ln(2)/t_12
k_5 = 3600.0; K_5 = 0.01; TJ = 3.83790087997253E-11 Reaction: => STATP2n; STAT, Rate Law: compartment*k_5*TJ*STAT/(2*(K_5+STAT))
r_0 = 0.001; IC2 = 1.0; k_15 = 3.6E-5; IC1 = 1.0 Reaction: => IFNBm; IRF7Pn, Rate Law: compartment*(r_0*IC1+k_15*IRF7Pn)*IC2
C = 500000.0; K_19 = 0.004; v_max19 = 165600.0; gamma = 1.66030217499585E-15 Reaction: => TFNenv; TNFam, Rate Law: compartment*gamma*C*v_max19*TNFam/(K_19+TNFam)
k_28 = 360.0 Reaction: => STAT; STATm, Rate Law: compartment*k_28*STATm
t_1 = 2.5 Reaction: IFNBm =>, Rate Law: compartment*IFNBm*ln(2)/t_1
IC2 = 1.0; k_11 = 3.6E-4; k_14 = 3.204E-7 Reaction: => IRF7m; STATP2n, IRF7Pn, Rate Law: compartment*(k_11*STATP2n+k_14*IRF7Pn)*IC2

States:

Name Description
IRF7m [C128883]
IRF7Pn [C128883]
TNFam [PR:000000134]
IFNBm [C20495]
TFNenv [PR:000000134]
IFNBenv [C20495]
STATm [C19618]
SOCSm [C97796]
IFNam [C20494]
IFNaenv [C20494]
STATP2n [C19618; SBO:0000607]
STAT [C19618]

Observables: none

BIOMD0000000059 @ v0.0.1

The model reproduces block A of Fig 5 and also Fig 3 (without the inclusion of Tg action). The model was successfully te…

We have developed a detailed mathematical model of ionic flux in beta-cells that includes the most essential channels and pumps in the plasma membrane. This model is coupled to equations describing Ca2+, inositol 1,4,5-trisphosphate (IP3), ATP, and Na+ homeostasis, including the uptake and release of Ca2+ by the endoplasmic reticulum (ER). In our model, metabolically derived ATP activates inward Ca2+ flux by regulation of ATP-sensitive K+ channels and depolarization of the plasma membrane. Results from the simulations support the hypothesis that intracellular Na+ and Ca2+ in the ER can be the main variables driving both fast (2-7 osc/min) and slow intracellular Ca2+ concentration oscillations (0.3-0.9 osc/min) and that the effect of IP3 on Ca2+ leak from the ER contributes to the pattern of slow calcium oscillations. Simulations also show that filling the ER Ca2+ stores leads to faster electrical bursting and Ca2+ oscillations. Specific Ca2+ oscillations in isolated beta-cell lines can also be simulated. link: http://identifiers.org/pubmed/12644446

Parameters:

Name Description
kadp = 3.7E-4 Time inverse Reaction: => ATP_cyt; ADP_cyt, Rate Law: Cytoplasm*kadp*ADP_cyt
F = 9.6485E16 Faraday constant; I_CRAN = 0.0 Current Reaction: => Na_cyt, Rate Law: (-I_CRAN)/F
katp = 5.0E-5 Time inverse Reaction: ATP_cyt =>, Rate Law: Cytoplasm*katp*ATP_cyt
kip = 3.0E-4 concentration per time; Kipca = 0.4 Concentration Reaction: => IP3_cyt; Ca_cyt, Rate Law: Cytoplasm*kip*Ca_cyt^2/(Ca_cyt^2+Kipca^2)
kdip = 4.0E-5 Time inverse Reaction: IP3_cyt =>, Rate Law: Cytoplasm*kdip*IP3_cyt
I_NaCa = 0.0 Current; F = 9.6485E16 Faraday constant Reaction: Na_cyt =>, Rate Law: 3*I_NaCa/F
katpca = 5.0E-5 per concentration per time Reaction: ATP_cyt => ; Ca_cyt, Rate Law: Cytoplasm*katpca*Ca_cyt*ATP_cyt
F = 9.6485E16 Faraday constant; I_CaPump = 0.0 Current Reaction: ATP_cyt =>, Rate Law: I_CaPump/F
Jout = 0.0 amount per time Reaction: Ca_er => Ca_cyt, Rate Law: Jout
fi = 0.01 dimensionless; F = 9.6485E16 Faraday constant; I_CaPump = 0.0 Current Reaction: Ca_cyt =>, Rate Law: fi*2*I_CaPump/(2*F)
I_Na = 0.0 Current; F = 9.6485E16 Faraday constant Reaction: => Na_cyt, Rate Law: (-I_Na)/F
ksg = 1.0E-4 Time inverse Reaction: Ca_cyt =>, Rate Law: Cytoplasm*ksg*Ca_cyt
F = 9.6485E16 Faraday constant; I_NaK = 0.0 Current Reaction: Na_cyt =>, Rate Law: 3*I_NaK/F
Jerp = 0.0 concentration per time Reaction: ATP_cyt =>, Rate Law: Cytoplasm*Jerp/2
I_NaCa = 0.0 Current; fi = 0.01 dimensionless; F = 9.6485E16 Faraday constant Reaction: => Ca_cyt, Rate Law: fi*2*I_NaCa/(2*F)
fi = 0.01 dimensionless; I_Vca = 0.0 Current; F = 9.6485E16 Faraday constant Reaction: => Ca_cyt, Rate Law: fi*(-I_Vca)/(2*F)

States:

Name Description
Na cyt [sodium(1+); Sodium cation]
ADP cyt [ADP; ADP]
ATP cyt [ATP; ATP]
Ca cyt [calcium(2+); Calcium cation]
IP3 cyt [1D-myo-inositol 1,4,5-trisphosphate; D-myo-Inositol 1,4,5-trisphosphate]
Ca er [calcium(2+); Calcium cation]

Observables: none

BIOMD0000000348 @ v0.0.1

This a model from the article: Glucose sensing in the pancreatic beta cell: a computational systems analysis. Fridl…

Pancreatic beta-cells respond to rising blood glucose by increasing oxidative metabolism, leading to an increased ATP/ADP ratio in the cytoplasm. This leads to a closure of KATP channels, depolarization of the plasma membrane, influx of calcium and the eventual secretion of insulin. Such mechanism suggests that beta-cell metabolism should have a functional regulation specific to secretion, as opposed to coupling to contraction. The goal of this work is to uncover contributions of the cytoplasmic and mitochondrial processes in this secretory coupling mechanism using mathematical modeling in a systems biology approach.We describe a mathematical model of beta-cell sensitivity to glucose. The cytoplasmic part of the model includes equations describing glucokinase, glycolysis, pyruvate reduction, NADH and ATP production and consumption. The mitochondrial part begins with production of NADH, which is regulated by pyruvate dehydrogenase. NADH is used in the electron transport chain to establish a proton motive force, driving the F1F0 ATPase. Redox shuttles and mitochondrial Ca2+ handling were also modeled.The model correctly predicts changes in the ATP/ADP ratio, Ca2+ and other metabolic parameters in response to changes in substrate delivery at steady-state and during cytoplasmic Ca2+ oscillations. Our analysis of the model simulations suggests that the mitochondrial membrane potential should be relatively lower in beta cells compared with other cell types to permit precise mitochondrial regulation of the cytoplasmic ATP/ADP ratio. This key difference may follow from a relative reduction in respiratory activity. The model demonstrates how activity of lactate dehydrogenase, uncoupling proteins and the redox shuttles can regulate beta-cell function in concert; that independent oscillations of cytoplasmic Ca2+ can lead to slow coupled metabolic oscillations; and that the relatively low production rate of reactive oxygen species in beta-cells under physiological conditions is a consequence of the relatively decreased mitochondrial membrane potential.This comprehensive model predicts a special role for mitochondrial control mechanisms in insulin secretion and ROS generation in the beta cell. The model can be used for testing and generating control hypotheses and will help to provide a more complete understanding of beta-cell glucose-sensing central to the physiology and pathology of pancreatic beta-cells. link: http://identifiers.org/pubmed/20497556

Parameters:

Name Description
Jgpd = NaN; kgpd = 1.0E-5; JGlu = NaN; Vi = 0.53 Reaction: G3P = (2*JGlu+(-Jgpd))*1/Vi+(-kgpd*G3P), Rate Law: (2*JGlu+(-Jgpd))*1/Vi+(-kgpd*G3P)
Jtnadh = NaN; Jgpd = NaN; JLDH = NaN; Vi = 0.53; knadhc = 1.0E-4 Reaction: NADHc = (Jgpd+(-Jtnadh)+(-JLDH))*1/Vi+(-knadhc*NADHc), Rate Law: (Jgpd+(-Jtnadh)+(-JLDH))*1/Vi+(-knadhc*NADHc)
fm = 3.0E-4; Vmmit = 0.0144; Juni = NaN; JNCa = NaN Reaction: Cam = fm*(Juni+(-JNCa))*1/Vmmit, Rate Law: fm*(Juni+(-JNCa))*1/Vmmit
Jtnadh = NaN; knadhm = 1.0E-4; Vmmit = 0.0144; JPYR = NaN; Jhres = NaN Reaction: NADHm = (4.6*JPYR+(-0.1*Jhres)+Jtnadh)*1/Vmmit+(-knadhm*NADHm), Rate Law: (4.6*JPYR+(-0.1*Jhres)+Jtnadh)*1/Vmmit+(-knadhm*NADHm)
Jph = NaN; Juni = NaN; Cmit = 5200.0; JNCa = NaN; Jhres = NaN; F = 96480.0; Jhl = NaN Reaction: Vm = (Jhres+(-Jph)+(-Jhl)+(-2*Juni)+(-JNCa))*F*1/Cmit, Rate Law: (Jhres+(-Jph)+(-Jhl)+(-2*Juni)+(-JNCa))*F*1/Cmit
Jgpd = NaN; Vmmit = 0.0144; JPYR = NaN; JLDH = NaN; Vi = 0.53 Reaction: PYR = (Jgpd+(-JPYR)+(-JLDH))*1/(Vi+Vmmit), Rate Law: (Jgpd+(-JPYR)+(-JLDH))*1/(Vi+Vmmit)
Jph = NaN; kATPCa = 9.0E-5; Cac = NaN; kATP = 4.0E-5; JGlu = NaN; Vi = 0.53 Reaction: ATP = (-(kATP+kATPCa*Cac)*ATP)+(2*JGlu+0.231*Jph)*1/Vi, Rate Law: (-(kATP+kATPCa*Cac)*ATP)+(2*JGlu+0.231*Jph)*1/Vi

States:

Name Description
G3P [glyceraldehyde 3-phosphate]
ATP [ATP]
PYR [pyruvate]
NADHm [NADH]
Vm [membrane potential]
NADHc [NADH]
Cam [calcium(2+)]

Observables: none

BIOMD0000000349 @ v0.0.1

This a model from the article: Glucose sensing in the pancreatic beta cell: a computational systems analysis. Fridl…

Pancreatic beta-cells respond to rising blood glucose by increasing oxidative metabolism, leading to an increased ATP/ADP ratio in the cytoplasm. This leads to a closure of KATP channels, depolarization of the plasma membrane, influx of calcium and the eventual secretion of insulin. Such mechanism suggests that beta-cell metabolism should have a functional regulation specific to secretion, as opposed to coupling to contraction. The goal of this work is to uncover contributions of the cytoplasmic and mitochondrial processes in this secretory coupling mechanism using mathematical modeling in a systems biology approach.We describe a mathematical model of beta-cell sensitivity to glucose. The cytoplasmic part of the model includes equations describing glucokinase, glycolysis, pyruvate reduction, NADH and ATP production and consumption. The mitochondrial part begins with production of NADH, which is regulated by pyruvate dehydrogenase. NADH is used in the electron transport chain to establish a proton motive force, driving the F1F0 ATPase. Redox shuttles and mitochondrial Ca2+ handling were also modeled.The model correctly predicts changes in the ATP/ADP ratio, Ca2+ and other metabolic parameters in response to changes in substrate delivery at steady-state and during cytoplasmic Ca2+ oscillations. Our analysis of the model simulations suggests that the mitochondrial membrane potential should be relatively lower in beta cells compared with other cell types to permit precise mitochondrial regulation of the cytoplasmic ATP/ADP ratio. This key difference may follow from a relative reduction in respiratory activity. The model demonstrates how activity of lactate dehydrogenase, uncoupling proteins and the redox shuttles can regulate beta-cell function in concert; that independent oscillations of cytoplasmic Ca2+ can lead to slow coupled metabolic oscillations; and that the relatively low production rate of reactive oxygen species in beta-cells under physiological conditions is a consequence of the relatively decreased mitochondrial membrane potential.This comprehensive model predicts a special role for mitochondrial control mechanisms in insulin secretion and ROS generation in the beta cell. The model can be used for testing and generating control hypotheses and will help to provide a more complete understanding of beta-cell glucose-sensing central to the physiology and pathology of pancreatic beta-cells. link: http://identifiers.org/pubmed/20497556

Parameters:

Name Description
Jgpd = NaN; kgpd = 1.0E-5; JGlu = NaN; Vi = 0.53 Reaction: G3P = (2*JGlu+(-Jgpd))*1/Vi+(-kgpd*G3P), Rate Law: (2*JGlu+(-Jgpd))*1/Vi+(-kgpd*G3P)
Jtnadh = NaN; Jgpd = NaN; JLDH = NaN; Vi = 0.53; knadhc = 1.0E-4 Reaction: NADHc = (Jgpd+(-Jtnadh)+(-JLDH))*1/Vi+(-knadhc*NADHc), Rate Law: (Jgpd+(-Jtnadh)+(-JLDH))*1/Vi+(-knadhc*NADHc)
fm = 3.0E-4; Vmmit = 0.0144; Juni = NaN; JNCa = NaN Reaction: Cam = fm*(Juni+(-JNCa))*1/Vmmit, Rate Law: fm*(Juni+(-JNCa))*1/Vmmit
Jtnadh = NaN; knadhm = 1.0E-4; Vmmit = 0.0144; JPYR = NaN; Jhres = NaN Reaction: NADHm = (4.6*JPYR+(-0.1*Jhres)+Jtnadh)*1/Vmmit+(-knadhm*NADHm), Rate Law: (4.6*JPYR+(-0.1*Jhres)+Jtnadh)*1/Vmmit+(-knadhm*NADHm)
Jph = NaN; Cmit = 1.82; Juni = NaN; JNCa = NaN; Jhres = NaN; Jhl = NaN Reaction: Vm = (Jhres+(-Jph)+(-Jhl)+(-2*Juni)+(-JNCa))*1/Cmit, Rate Law: (Jhres+(-Jph)+(-Jhl)+(-2*Juni)+(-JNCa))*1/Cmit
Jgpd = NaN; Vmmit = 0.0144; JPYR = NaN; JLDH = NaN; Vi = 0.53 Reaction: PYR = (Jgpd+(-JPYR)+(-JLDH))*1/(Vi+Vmmit), Rate Law: (Jgpd+(-JPYR)+(-JLDH))*1/(Vi+Vmmit)
Jph = NaN; kATPCa = 9.0E-5; Cac = NaN; kATP = 4.0E-5; JGlu = NaN; Vi = 0.53 Reaction: ATP = (-(kATP+kATPCa*Cac)*ATP)+(2*JGlu+0.231*Jph)*1/Vi, Rate Law: (-(kATP+kATPCa*Cac)*ATP)+(2*JGlu+0.231*Jph)*1/Vi

States:

Name Description
Cam [calcium(2+)]
ATP [ATP]
PYR [pyruvate]
NADHm [NADH]
Vm [membrane potential]
NADHc [NADH]
G3P [glyceraldehyde 3-phosphate]

Observables: none

BIOMD0000000301 @ v0.0.1

This is the model of the RTC3 counter described in the article: **Synthetic gene networks that count.** Friedland AE…

Synthetic gene networks can be constructed to emulate digital circuits and devices, giving one the ability to program and design cells with some of the principles of modern computing, such as counting. A cellular counter would enable complex synthetic programming and a variety of biotechnology applications. Here, we report two complementary synthetic genetic counters in Escherichia coli that can count up to three induction events: the first, a riboregulated transcriptional cascade, and the second, a recombinase-based cascade of memory units. These modular devices permit counting of varied user-defined inputs over a range of frequencies and can be expanded to count higher numbers. link: http://identifiers.org/pubmed/19478183

Parameters:

Name Description
sT = 0.8467; k_ara = 0.0571; s0_taRNA = 8.0E-4 Reaction: => taRNA; ara, Rate Law: cell*(sT*ara/(ara+k_ara)+s0_taRNA)
d_pT3 = 0.0069 Reaction: pT3 =>, Rate Law: cell*d_pT3*pT3
d_mGFP = 0.07 Reaction: mGFPcr =>, Rate Law: cell*d_mGFP*mGFPcr
k_pT7 = 3.8009; n7 = 2.602; km7 = 3.0455; s0_mT3cr = 3.0E-4 Reaction: => mT3cr; pT7, Rate Law: cell*(s0_mT3cr+k_pT7*pT7^n7/(km7^n7+pT7^n7))
s0_pT3 = 0.0; s_pT3k = 0.0115 Reaction: => pT3; taRNA, mT3cr, Rate Law: cell*(s0_pT3*mT3cr+s_pT3k*taRNA*mT3cr)
s_pT7k = 0.0766; s0_pT7 = 3.0E-4 Reaction: => pT7; taRNA, mT7cr, Rate Law: cell*(s0_pT7*mT7cr+s_pT7k*mT7cr*taRNA)
d_pGFP = 0.003 Reaction: pGFP =>, Rate Law: cell*d_pGFP*pGFP
pulse_flag = 0.0; cAra = 3.0E-4; dAra = 0.1201 Reaction: ara =>, Rate Law: cell*piecewise(cAra, (pulse_flag == 1) && (ara > 0), dAra*ara)
d_taRNA = 0.1177 Reaction: taRNA =>, Rate Law: cell*d_taRNA*taRNA
s0_pGFP = 0.1007; s_pGFPk = 0.9923 Reaction: => pGFP; taRNA, mGFPcr, Rate Law: cell*(s0_pGFP*mGFPcr+s_pGFPk*mGFPcr*taRNA)
km3 = 7.9075; k_pT3 = 3.006; s0_mGFPcr = 0.0123; n3 = 0.8892 Reaction: => mGFPcr; pT3, Rate Law: cell*(s0_mGFPcr+k_pT3*pT3^n3/(km3^n3+pT3^n3))
s0_mT7cr = 0.0252 Reaction: => mT7cr, Rate Law: cell*s0_mT7cr
d_mT3 = 0.0701 Reaction: mT3cr =>, Rate Law: cell*d_mT3*mT3cr
d_pT7 = 0.0056 Reaction: pT7 =>, Rate Law: cell*d_pT7*pT7
d_mT7 = 0.0706 Reaction: mT7cr =>, Rate Law: cell*d_mT7*mT7cr

States:

Name Description
pGFP [Green fluorescent protein; IPR000786]
mT7cr [T7 RNA polymerase; messenger RNA]
ara [L-Arabinose; L-arabinopyranose]
mGFPcr [IPR000786; messenger RNA]
pT3 [DNA-directed RNA polymerase; DNA-directed RNA polymerase complex]
pT7 [T7 RNA polymerase; DNA-directed RNA polymerase complex]
mT3cr [DNA-directed RNA polymerase; messenger RNA]
taRNA [positive regulation of translation, ncRNA-mediated; ribonucleic acid]

Observables: none

Fuentealb2016 - Genome-scale metabolic reconstruction (iPF215) of Piscirickettsia salmonis LF-89This model is described…

Piscirickettsia salmonis is a fish bacterium that causes the disease piscirickettsiosis in salmonids. This pathology is partially controlled by vaccines. The lack of knowledge has hindered its culture on laboratory and industrial scale. The study describes the metabolic phenotype of P. salmonis in culture. This study presents the first genome-scale model (iPF215) of the LF-89 strain of P. salmonis, describing the central metabolic pathway, biosynthesis and molecule degradation and transport mechanisms. The model was adjusted with experiment data, allowing the identification of the capacities that were not predicted by the automatic annotation of the genome sequences. The iPF215 model is comprised of 417 metabolites, 445 reactions and 215 genes, was used to reproduce the growth of P. salmonis (μmax 0.052±0.005h-1). The metabolic reconstruction of the P. salmonis LF-89 strain obtained in this research provides a baseline that describes the metabolic capacities of the bacterium and is the basis for developing improvements to its cultivation for vaccine formulation. link: http://identifiers.org/pubmed/27788423

Parameters: none

States: none

Observables: none

BIOMD0000000092 @ v0.0.1

. . . **[SBML](http://www.sbml.org/) level 2 code generated for the JWS Online project by Jacky Snoep using [PySCeS]…

A mathematical description was made of an autocatalytic zymogen activation mechanism involving both intra- and intermolecular routes. The reversible formation of an active intermediary enzyme-zymogen complex was included in the intermolecular activation route, thus allowing a Michaelis-Menten constant to be defined for the activation of the zymogen towards the active enzyme. Time-concentration equations describing the evolution of the species involved in the system were obtained. In addition, we have derived the corresponding kinetic equations for particular cases of the general model studied. Experimental design and kinetic data analysis procedures to evaluate the kinetic parameters, based on the derived kinetic equations, are suggested. The validity of the results obtained were checked by using simulated progress curves of the species involved. The model is generally good enough to be applied to the experimental kinetic study of the activation of different zymogens of physiological interest. The system is illustrated by following the transformation kinetics of pepsinogen into pepsin. link: http://identifiers.org/pubmed/15634334

Parameters:

Name Description
k1=0.004 sec_inv Reaction: z => w + e, Rate Law: compartment*k1*z
k3=5.4E-4 sec_inv Reaction: ez => w + e, Rate Law: compartment*k3*ez
k21=1000.0 M_inv_sec_inv; k22=2.1E-4 sec_inv Reaction: z + e => ez, Rate Law: compartment*(k21*e*z-k22*ez)

States:

Name Description
w Peptide
e Enzyme
z [zymogen granule]
ez [protein complex]

Observables: none

BIOMD0000000262 @ v0.0.1

EGF dependent Akt pathway model made by Kazuhiro A. Fujita. This is the EGF dependent Akt pathway model described in:…

In cellular signal transduction, the information in an external stimulus is encoded in temporal patterns in the activities of signaling molecules; for example, pulses of a stimulus may produce an increasing response or may produce pulsatile responses in the signaling molecules. Here, we show how the Akt pathway, which is involved in cell growth, specifically transmits temporal information contained in upstream signals to downstream effectors. We modeled the epidermal growth factor (EGF)-dependent Akt pathway in PC12 cells on the basis of experimental results. We obtained counterintuitive results indicating that the sizes of the peak amplitudes of receptor and downstream effector phosphorylation were decoupled; weak, sustained EGF receptor (EGFR) phosphorylation, rather than strong, transient phosphorylation, strongly induced phosphorylation of the ribosomal protein S6, a molecule downstream of Akt. Using frequency response analysis, we found that a three-component Akt pathway exhibited the property of a low-pass filter and that this property could explain decoupling of the peak amplitudes of receptor phosphorylation and that of downstream effectors. Furthermore, we found that lapatinib, an EGFR inhibitor used as an anticancer drug, converted strong, transient Akt phosphorylation into weak, sustained Akt phosphorylation, and, because of the low-pass filter characteristics of the Akt pathway, this led to stronger S6 phosphorylation than occurred in the absence of the inhibitor. Thus, an EGFR inhibitor can potentially act as a downstream activator of some effectors. link: http://identifiers.org/pubmed/20664065

Parameters:

Name Description
EGFR_turnover = 1.06386129269658E-4 per second Reaction: pro_EGFR => EGFR, Rate Law: Cell*EGFR_turnover*pro_EGFR
k1=0.00121498 per second Reaction: pAkt_S6 => pAkt + pS6, Rate Law: Cell*k1*pAkt_S6
k1=2.10189E-6 per conc per second; k2=5.1794E-15 per second Reaction: pAkt + S6 => pAkt_S6, Rate Law: Cell*(k1*pAkt*S6-k2*pAkt_S6)
k1=0.0305684 per second Reaction: pEGFR_Akt => pEGFR + pAkt, Rate Law: Cell*k1*pEGFR_Akt
EGF_conc_ramp = 30.0 ng_per_ml; EGF_conc_impulse = 0.0 ng_per_ml; EGF_conc_step = 0.0 ng_per_ml; ramp_time = 3600.0 seconds; pulse_time = 60.0 seconds Reaction: EGF = EGF_conc_step+piecewise(EGF_conc_impulse, time <= pulse_time, 0)+EGF_conc_ramp*time/ramp_time, Rate Law: missing
k1=0.0327962 per second Reaction: pAkt => Akt, Rate Law: Cell*k1*pAkt
k1=0.0997194 per second Reaction: pEGFR =>, Rate Law: Cell*k1*pEGFR
k1=0.00113102 per second Reaction: pS6 => S6, Rate Law: Cell*k1*pS6
k1=0.00673816; k2=0.040749 per second Reaction: EGF + EGFR => EGF_EGFR, Rate Law: Cell*(k1*EGF*EGFR-k2*EGF_EGFR)
k2=0.00517473 per second; k1=1.5543E-5 per conc per second Reaction: pEGFR + Akt => pEGFR_Akt, Rate Law: Cell*(k1*pEGFR*Akt-k2*pEGFR_Akt)
k1=0.0192391 per second Reaction: EGF_EGFR => pEGFR, Rate Law: Cell*k1*EGF_EGFR

States:

Name Description
EGFR [Egfr]
EGF EGFR [Egfr; Pro-epidermal growth factor]
Akt [RAC-gamma serine/threonine-protein kinase]
EGF [IPR006209]
pro EGFR [Egfr]
pS6 [40S ribosomal protein S6; Phosphoprotein]
pAkt [RAC-gamma serine/threonine-protein kinase; Phosphoprotein]
pEGFR [Egfr]
S6 [40S ribosomal protein S6]
pEGFR Akt [Egfr; RAC-gamma serine/threonine-protein kinase; Phosphoprotein]
pAkt S6 [40S ribosomal protein S6; RAC-gamma serine/threonine-protein kinase; Phosphoprotein]

Observables: none

BIOMD0000000264 @ v0.0.1

Akt pathway model with EGFR inhibitor made by Kazuhiro A. Fujita. This is the Akt pathway model with an EGFR inhibitor…

In cellular signal transduction, the information in an external stimulus is encoded in temporal patterns in the activities of signaling molecules; for example, pulses of a stimulus may produce an increasing response or may produce pulsatile responses in the signaling molecules. Here, we show how the Akt pathway, which is involved in cell growth, specifically transmits temporal information contained in upstream signals to downstream effectors. We modeled the epidermal growth factor (EGF)-dependent Akt pathway in PC12 cells on the basis of experimental results. We obtained counterintuitive results indicating that the sizes of the peak amplitudes of receptor and downstream effector phosphorylation were decoupled; weak, sustained EGF receptor (EGFR) phosphorylation, rather than strong, transient phosphorylation, strongly induced phosphorylation of the ribosomal protein S6, a molecule downstream of Akt. Using frequency response analysis, we found that a three-component Akt pathway exhibited the property of a low-pass filter and that this property could explain decoupling of the peak amplitudes of receptor phosphorylation and that of downstream effectors. Furthermore, we found that lapatinib, an EGFR inhibitor used as an anticancer drug, converted strong, transient Akt phosphorylation into weak, sustained Akt phosphorylation, and, because of the low-pass filter characteristics of the Akt pathway, this led to stronger S6 phosphorylation than occurred in the absence of the inhibitor. Thus, an EGFR inhibitor can potentially act as a downstream activator of some effectors. link: http://identifiers.org/pubmed/20664065

Parameters:

Name Description
k1=0.00121498 per second Reaction: pAkt_S6 => pAkt + pS6, Rate Law: Cell*k1*pAkt_S6
k1=2.10189E-6 per conc per second; k2=5.1794E-15 per second Reaction: pAkt + S6 => pAkt_S6, Rate Law: Cell*(k1*pAkt*S6-k2*pAkt_S6)
k1=0.0327962 per second Reaction: pAkt => Akt, Rate Law: Cell*k1*pAkt
EGF_conc_pulse = 0.0 ng_per_ml; EGF_conc_ramp = 0.0 ng_per_ml; EGF_conc_step = 30.0 ng_per_ml; ramp_time = 3600.0 seconds; pulse_time = 60.0 seconds Reaction: EGF = EGF_conc_step+piecewise(EGF_conc_pulse, time <= pulse_time, 0)+EGF_conc_ramp*time/ramp_time, Rate Law: missing
EGFR_turnover = 1.06386E-4 per second Reaction: pro_EGFR => EGFR, Rate Law: Cell*EGFR_turnover*pro_EGFR
k1=0.0997194 per second Reaction: pEGFR =>, Rate Law: Cell*k1*pEGFR
k1=0.0528141 per second Reaction: pEGFR_Akt => pEGFR + pAkt, Rate Law: Cell*k1*pEGFR_Akt
inhibitor_binding_kf = 2.43466029020655E-5 per conc per second; inhibitor_binding_kb = 5.25096686262403E-5 per second Reaction: Inhibitor + EGFR => EGFR_i, Rate Law: Cell*(inhibitor_binding_kf*Inhibitor*EGFR-inhibitor_binding_kb*EGFR_i)
k1=0.00113102 per second Reaction: pS6 => S6, Rate Law: Cell*k1*pS6
k2=0.00517473 per second; k1=1.5543E-5 per conc per second Reaction: pEGFR + Akt => pEGFR_Akt, Rate Law: Cell*(k1*pEGFR*Akt-k2*pEGFR_Akt)
k1=0.0192391 per second Reaction: EGF_EGFR => pEGFR, Rate Law: Cell*k1*EGF_EGFR
EGF_binding_kf = 0.00673816 ml_per_ng_per_sec; EGF_binding_kb = 0.040749 per second Reaction: EGF + EGFR_i => EGF_EGFR_i, Rate Law: Cell*(EGF_binding_kf*EGF*EGFR_i-EGF_binding_kb*EGF_EGFR_i)

States:

Name Description
Inhibitor [Lapatinib (INN); epidermal growth factor receptor binding]
EGFR [Egfr]
EGF EGFR [Egfr; Pro-epidermal growth factor]
Akt [RAC-gamma serine/threonine-protein kinase]
EGF EGFR i [lapatinib; Egfr; Pro-epidermal growth factor]
EGFR i [lapatinib; Egfr]
pro EGFR [Egfr]
EGF [Pro-epidermal growth factor; epidermal growth factor receptor binding]
pS6 [Phosphoprotein; 40S ribosomal protein S6]
pAkt [Phosphoprotein; RAC-gamma serine/threonine-protein kinase]
pEGFR [Egfr; Phosphoprotein]
S6 [40S ribosomal protein S6]
pEGFR Akt [RAC-gamma serine/threonine-protein kinase; Egfr; Phosphoprotein]
pAkt S6 [RAC-gamma serine/threonine-protein kinase; 40S ribosomal protein S6; Phosphoprotein]

Observables: none

BIOMD0000000263 @ v0.0.1

NGF dependent Akt pathway model made by Kazuhiro A. Fujita. This is the NGF dependent Akt pathway model described in:…

In cellular signal transduction, the information in an external stimulus is encoded in temporal patterns in the activities of signaling molecules; for example, pulses of a stimulus may produce an increasing response or may produce pulsatile responses in the signaling molecules. Here, we show how the Akt pathway, which is involved in cell growth, specifically transmits temporal information contained in upstream signals to downstream effectors. We modeled the epidermal growth factor (EGF)-dependent Akt pathway in PC12 cells on the basis of experimental results. We obtained counterintuitive results indicating that the sizes of the peak amplitudes of receptor and downstream effector phosphorylation were decoupled; weak, sustained EGF receptor (EGFR) phosphorylation, rather than strong, transient phosphorylation, strongly induced phosphorylation of the ribosomal protein S6, a molecule downstream of Akt. Using frequency response analysis, we found that a three-component Akt pathway exhibited the property of a low-pass filter and that this property could explain decoupling of the peak amplitudes of receptor phosphorylation and that of downstream effectors. Furthermore, we found that lapatinib, an EGFR inhibitor used as an anticancer drug, converted strong, transient Akt phosphorylation into weak, sustained Akt phosphorylation, and, because of the low-pass filter characteristics of the Akt pathway, this led to stronger S6 phosphorylation than occurred in the absence of the inhibitor. Thus, an EGFR inhibitor can potentially act as a downstream activator of some effectors. link: http://identifiers.org/pubmed/20664065

Parameters:

Name Description
NGF_conc_step = 0.0 ng_per_ml; NGF_conc_pulse = 0.0 ng_per_ml; NGF_conc_ramp = 30.0 ng_per_ml; ramp_time = 3600.0 seconds; pulse_time = 60.0 seconds Reaction: NGF = NGF_conc_step+piecewise(NGF_conc_pulse, time <= pulse_time, 0)+NGF_conc_ramp*time/ramp_time, Rate Law: missing
k2=1.47518E-10 per second; k1=0.0882701 per conc per second Reaction: pTrkA + Akt => pTrkA_Akt, Rate Law: Cell*(k1*pTrkA*Akt-k2*pTrkA_Akt)
k1=0.0202517 Reaction: pTrkA_Akt => pTrkA + pAkt, Rate Law: Cell*k1*pTrkA_Akt
k1=0.0056515 per second Reaction: pAkt_S6 => pAkt + pS6, Rate Law: Cell*k1*pAkt_S6
k2=5.23519 per second; k1=68.3666 per conc per second Reaction: pAkt + S6 => pAkt_S6, Rate Law: Cell*(k1*pAkt*S6-k2*pAkt_S6)
k1=2.93167E-4 per second Reaction: pS6 => S6, Rate Law: Cell*k1*pS6
TrkA_turnover = 0.0011032440769796 per second Reaction: pro_TrkA => TrkA, Rate Law: Cell*TrkA_turnover*pro_TrkA
k2=0.0133747; k1=0.00269408 Reaction: NGF + TrkA => NGF_TrkA, Rate Law: Cell*(k1*NGF*TrkA-k2*NGF_TrkA)
k1=0.00833178 per second Reaction: NGF_TrkA => pTrkA, Rate Law: Cell*k1*NGF_TrkA
k1=1.28135 per second Reaction: pAkt => Akt, Rate Law: Cell*k1*pAkt
k1=0.0684084 per second Reaction: pTrkA =>, Rate Law: Cell*k1*pTrkA

States:

Name Description
NGF TrkA [High affinity nerve growth factor receptor; Beta-nerve growth factor]
TrkA [High affinity nerve growth factor receptor]
NGF [Beta-nerve growth factor]
Akt [RAC-gamma serine/threonine-protein kinase]
pTrkA [High affinity nerve growth factor receptor]
pTrkA Akt [High affinity nerve growth factor receptor; RAC-gamma serine/threonine-protein kinase; Phosphoprotein]
pS6 [Phosphoprotein; 40S ribosomal protein S6]
pro TrkA [High affinity nerve growth factor receptor]
pAkt [Phosphoprotein; Active AKT [cytosol]]
S6 [40S ribosomal protein S6]
pAkt S6 [RAC-gamma serine/threonine-protein kinase; 40S ribosomal protein S6; Phosphoprotein]

Observables: none

BIOMD0000000067 @ v0.0.1

# A Synthetic Gene-Metabolic Oscillator **Reference:**[*Fung et al; Nature (2005) 435:118-122*](http://www.nature.com/na…

Autonomous oscillations found in gene expression and metabolic, cardiac and neuronal systems have attracted significant attention both because of their obvious biological roles and their intriguing dynamics. In addition, de novo designed oscillators have been demonstrated, using components that are not part of the natural oscillators. Such oscillators are useful in testing the design principles and in exploring potential applications not limited by natural cellular behaviour. To achieve transcriptional and metabolic integration characteristic of natural oscillators, here we designed and constructed a synthetic circuit in Escherichia coli K12, using glycolytic flux to generate oscillation through the signalling metabolite acetyl phosphate. If two metabolite pools are interconverted by two enzymes that are placed under the transcriptional control of acetyl phosphate, the system oscillates when the glycolytic rate exceeds a critical value. We used bifurcation analysis to identify the boundaries of oscillation, and verified these experimentally. This work demonstrates the possibility of using metabolic flux as a control factor in system-wide oscillation, as well as the predictability of a de novo gene-metabolic circuit designed using nonlinear dynamic analysis. link: http://identifiers.org/pubmed/15875027

Parameters:

Name Description
S0 = 0.5 Reaction: => AcCoA, Rate Law: compartment*S0
kTCA = 10.0 Reaction: AcCoA =>, Rate Law: compartment*kTCA*AcCoA
KM2 = 0.1; k2 = 0.8 Reaction: OAc => AcCoA; Acs, Rate Law: compartment*k2*Acs*OAc/(KM2+OAc)
kAck_f = 1.0; kAck_r = 1.0 Reaction: AcP => OAc, Rate Law: compartment*(kAck_f*AcP-kAck_r*OAc)
k3 = 0.01 Reaction: HOAc => HOAc_E, Rate Law: compartment*k3*(HOAc-HOAc_E)
KM1 = 0.06; k1 = 80.0 Reaction: AcCoA => AcP; Pta, Rate Law: compartment*k1*Pta*AcCoA/(KM1+AcCoA)
Kg3 = 0.001; alpha3 = 2.0; n = 2.0; alpha0 = 0.0 Reaction: => Pta; LacI, Rate Law: alpha3/(1+(LacI/Kg3)^n)+alpha0
kd = 0.06 Reaction: LacI =>, Rate Law: compartment*kd*LacI
Kg1 = 10.0; alpha1 = 0.1; n = 2.0; alpha0 = 0.0 Reaction: => LacI; AcP, Rate Law: compartment*(alpha1*(AcP/Kg1)^n/(1+(AcP/Kg1)^n)+alpha0)
alpha2 = 2.0; n = 2.0; alpha0 = 0.0; Kg2 = 10.0 Reaction: => Acs; AcP, Rate Law: compartment*(alpha2*(AcP/Kg2)^n/(1+(AcP/Kg2)^n)+alpha0)
H = 1.0E-7; Keq = 5.0E-4; C = 100.0 Reaction: OAc => HOAc, Rate Law: compartment*C*(OAc*H-Keq*HOAc)

States:

Name Description
LacI [transcriptional repressor complex]
HOAc E [acetate; Acetate]
OAc [acetate; Acetate]
AcCoA [acetyl-CoA; Acetyl-CoA]
Pta [Phosphate acetyltransferase]
HOAc [acetate; Acetate]
AcP [acetyl dihydrogen phosphate; Acetyl phosphate]
Acs [Acetyl-coenzyme A synthetase]

Observables: none

BIOMD0000000069 @ v0.0.1

The model was curated with XPP. The figure 3 was successfully reproduced.

MOTIVATION: The protein tyrosine kinase Src is involved in a multitude of biochemical pathways and cellular functions. A complex network of interactions with other kinases and phosphatases obscures its precise mode of operation. RESULTS: We have constructed a semi-quantitative computational dynamic systems model of the activation of Src at mitosis based on protein interactions described in the literature. Through numerical simulation and bifurcation analysis we show that Src regulation involves a bistable switch, a pattern increasingly recognised as essential to biochemical signalling. The switch is operated by the tyrosine kinase CSK, which itself is involved in a negative feedback loop with Src. Negative feedback generates an excitable system, which produces transient activation of Src. One of the system parameters, which is linked to the cyclin dependent kinase cdc2, controls excitability via a second bistable switch. This topology allows for differentiated responses to a multitude of signals. The model offers explanations for the existence of the positive and negative feedback loops involving protein tyrosine phosphatase alpha (PTPalpha) and translocation of CSK and predicts a specific relationship between Src phosphorylation and activity. link: http://identifiers.org/pubmed/16873466

Parameters:

Name Description
k1 = 1.0; k2 = 0.8; ptp_activity = NaN Reaction: srci => srco; Cbp_P_CSK, Rate Law: (k2*ptp_activity*srci-k1*Cbp_P_CSK*srco)*default
kCSKoff = 0.01; kCSKon = 0.1 Reaction: CSK_cytoplasm + Cbp_P => Cbp_P_CSK, Rate Law: (Cbp_P*kCSKon*CSK_cytoplasm-kCSKoff*Cbp_P_CSK)*default
src_activity = NaN; kCbp = 1.0 Reaction: Cbp => Cbp_P, Rate Law: kCbp*src_activity*Cbp*default
src_activity = NaN; p1 = 0.05; k3 = 1.0 Reaction: srco => srca, Rate Law: (k3*src_activity*srco-p1*srca)*default
p1 = 0.05; k4 = 10.0 Reaction: srcc => srci, Rate Law: default*k4*p1*srcc
p2 = 0.15; kPTP = 1.0; src_activity = NaN; p3 = 0.035 Reaction: PTP => PTP_pY789, Rate Law: default*((kPTP*src_activity+p3)*PTP-p2*PTP_pY789)

States:

Name Description
srcc [Proto-oncogene tyrosine-protein kinase Src]
PTP pY789 [Receptor-type tyrosine-protein phosphatase alpha]
Cbp P CSK [Tyrosine-protein kinase CSK; Phosphoprotein associated with glycosphingolipid-enriched microdomains 1]
Cbp P [Phosphoprotein associated with glycosphingolipid-enriched microdomains 1]
srco [Proto-oncogene tyrosine-protein kinase Src]
srci [Proto-oncogene tyrosine-protein kinase Src]
PTP [Receptor-type tyrosine-protein phosphatase alpha]
Cbp [Phosphoprotein associated with glycosphingolipid-enriched microdomains 1]
CSK cytoplasm [Tyrosine-protein kinase CSK]
srca [Proto-oncogene tyrosine-protein kinase Src]

Observables: none

Förster2008 - Genome-scale metabolic network of Saccharamyces cerevisiae (iFF708)This model is described in the article:…

The metabolic network in the yeast Saccharomyces cerevisiae was reconstructed using currently available genomic, biochemical, and physiological information. The metabolic reactions were compartmentalized between the cytosol and the mitochondria, and transport steps between the compartments and the environment were included. A total of 708 structural open reading frames (ORFs) were accounted for in the reconstructed network, corresponding to 1035 metabolic reactions. Further, 140 reactions were included on the basis of biochemical evidence resulting in a genome-scale reconstructed metabolic network containing 1175 metabolic reactions and 584 metabolites. The number of gene functions included in the reconstructed network corresponds to approximately 16% of all characterized ORFs in S. cerevisiae. Using the reconstructed network, the metabolic capabilities of S. cerevisiae were calculated and compared with Escherichia coli. The reconstructed metabolic network is the first comprehensive network for a eukaryotic organism, and it may be used as the basis for in silico analysis of phenotypic functions. link: http://identifiers.org/pubmed/12566402

Parameters: none

States: none

Observables: none

G


MODEL1112110003 @ v0.0.1

This a model from the article: Mathematical models of diabetes progression. De Gaetano A, Hardy T, Beck B, Abu-Radda…

Few attempts have been made to model mathematically the progression of type 2 diabetes. A realistic representation of the long-term physiological adaptation to developing insulin resistance is necessary for effectively designing clinical trials and evaluating diabetes prevention or disease modification therapies. Writing a good model for diabetes progression is difficult because the long time span of the disease makes experimental verification of modeling hypotheses extremely awkward. In this context, it is of primary importance that the assumptions underlying the model equations properly reflect established physiology and that the mathematical formulation of the model give rise only to physically plausible behavior of the solutions. In the present work, a model of the pancreatic islet compensation is formulated, its physiological assumptions are presented, some fundamental qualitative characteristics of its solutions are established, the numerical values assigned to its parameters are extensively discussed (also with reference to available cross-sectional epidemiologic data), and its performance over the span of a lifetime is simulated under various conditions, including worsening insulin resistance and primary replication defects. The differences with respect to two previously proposed models of diabetes progression are highlighted, and therefore, the model is proposed as a realistic, robust description of the evolution of the compensation of the glucose-insulin system in healthy and diabetic individuals. Model simulations can be run from the authors' web page. link: http://identifiers.org/pubmed/18780774

Parameters: none

States: none

Observables: none

This is a mathematical model that describes the interactions between cytotoxic T cells and tumor cells as influenced by…

The surface protein B7-H1, also called PD-L1 and CD274, is found on carcinomas of the lung, ovary, colon, and melanomas but not on most normal tissues. B7-H1 has been experimentally determined to be an antiapoptotic receptor on cancer cells, where B7-H1-positive cancer cells have been shown to be immune resistant, and in vitro experiments and mouse models have shown that B7-H1-negative tumor cells are significantly more susceptible to being repressed by the immune system. We derive a new mathematical model for studying the interaction between cytotoxic T cells and tumor cells as affected by B7-H1. By integrating experimental data into the model, we isolate the parameters that control the dynamics and obtain insights on the mechanisms that control apoptosis. link: http://identifiers.org/pubmed/21656310

Parameters:

Name Description
k_p = 0.097; k_m_2 = 80.0; k_m_1 = 2.2 Reaction: => P_Perforin; E_CTL, C_Cancer_Uncomplexed, Rate Law: compartment*k_p*E_CTL/((k_m_1+E_CTL)*k_m_2*C_Cancer_Uncomplexed)
ModelValue_11 = 1.0 Reaction: E_CTL = ModelValue_11-X_Complex, Rate Law: missing
k_2 = 1.0E-4 Reaction: X_Complex => C_Cancer_Uncomplexed, Rate Law: compartment*k_2*X_Complex
k_3 = 1.0E-4 Reaction: X_Complex =>, Rate Law: compartment*k_3*X_Complex
k = 0.035 Reaction: => C_Cancer_Uncomplexed, Rate Law: compartment*k*C_Cancer_Uncomplexed
k_1 = 1.0E-4 Reaction: C_Cancer_Uncomplexed => X_Complex; E_CTL, Rate Law: compartment*k_1*C_Cancer_Uncomplexed*E_CTL
k_5 = 0.003 Reaction: C_Cancer_Uncomplexed =>, Rate Law: compartment*k_5*C_Cancer_Uncomplexed^2
k_4 = 3.0 Reaction: P_Perforin + C_Cancer_Uncomplexed =>, Rate Law: compartment*k_4*P_Perforin*C_Cancer_Uncomplexed

States:

Name Description
P Perforin [Perforin]
X Complex [cytotoxic T cell; neoplastic cell; Complex]
T ast [neoplastic cell]
E CTL [cytotoxic T cell]
T Cancer Cell Total [neoplastic cell]
C Cancer Uncomplexed [neoplastic cell]

Observables: none

BIOMD0000000063 @ v0.0.1

This a model from the article: Fermentation pathway kinetics and metabolic flux control in suspended and immobilize…

Measurements of rates of glucose uptake and of glycerol and ethanol formation combined with knowledge of the metabolic pathways involved in S. cerevisiae were employed to obtain in vivo rates of reaction catalysed by pathway enzymes for suspended and alginate-entrapped cells at pH 4.5 and 5.5. Intracellular concentrations of substrates and effectors for most key pathway enzymes were estimated from in vivo phosphorus-31 nuclear magnetic resonance measurements. These data show the validity in vivo of kinetic models previously proposed for phosphofructokinase and pyruvate kinase based on in vitro studies. Kinetic representations of hexokinase, glycogen synthetase, and glyceraldehyde 3-phosphate dehydrogenase, which incorporate major regulatory properties of these enzymes, are all consistent with the in vivo data. This detailed model of pathway kinetics and these data on intracellular metabolite concentrations allow evaluation of flux-control coefficients for all key enzymes involved in glucose catabolism under the four different cell environments examined. This analysis indicates that alginate entrapment increases the glucose uptake rate and shifts the step most influencing ethanol production from glucose uptake to phosphofructokinase. The rate of ATP utilization in these nongrowing cells strongly limits ethanol production at pH 5.5 but is relatively insignificant at pH 4.5. link: http://identifiers.org/doi/10.1016/0141-0229(90)90033-M

Parameters:

Name Description
Ks2Glc=0.0062 milliMolar; Km2Glc=0.11 milliMolar; Vm2=68.5 mM per minute; Km2ATP=0.1 milliMolar Reaction: ATP + Glci => G6P, Rate Law: cytoplasm*Vm2/(1+Km2Glc/Glci+Km2ATP/ATP+Ks2Glc*Km2ATP/(Glci*ATP))
g6R=0.1 dimensionless; K6ADP=5.0 milliMolar; g6T=1.0 dimensionless; K6FDP=0.2 milliMolar; c6FDP=0.01 dimensionless; c6PEP=1.58793E-4 dimensionless; c6ADP=1.0 dimensionless; h6=1.14815E-7 dimensionless; Vm6=3440.0 mM per minute; K6PEP=0.00793966 milliMolar; q6=1.0 dimensionless; L60=164.084 dimensionless Reaction: PEP => ATP + EtOH; FDP, Rate Law: cytoplasm*Vm6*PEP/K6PEP*0.5*((-ATP)+(12*ATP-3*ATP^2)^0.5)/K6ADP*(g6R*(1+PEP/K6PEP+0.5*((-ATP)+(12*ATP-3*ATP^2)^0.5)/K6ADP+g6R*PEP/K6PEP*0.5*((-ATP)+(12*ATP-3*ATP^2)^0.5)/K6ADP)+q6*L60*((1+c6FDP*FDP/K6FDP)/(1+FDP/K6FDP))^2*g6T*c6PEP*PEP/K6PEP*c6ADP*0.5*((-ATP)+(12*ATP-3*ATP^2)^0.5)/K6ADP*(1+c6PEP*PEP/K6PEP+c6ADP*0.5*((-ATP)+(12*ATP-3*ATP^2)^0.5)/K6ADP+g6T*c6PEP*PEP/K6PEP*c6ADP*0.5*((-ATP)+(12*ATP-3*ATP^2)^0.5)/K6ADP))/((1+9.55*10^-9/h6)*((1+PEP/K6PEP+0.5*((-ATP)+(12*ATP-3*ATP^2)^0.5)/K6ADP+g6R*PEP/K6PEP*0.5*((-ATP)+(12*ATP-3*ATP^2)^0.5)/K6ADP)^2+L60*((1+c6FDP*FDP/K6FDP)/(1+FDP/K6FDP))^2*(1+c6PEP*PEP/K6PEP+c6ADP*0.5*((-ATP)+(12*ATP-3*ATP^2)^0.5)/K6ADP+g6T*c6PEP*PEP/K6PEP*c6ADP*0.5*((-ATP)+(12*ATP-3*ATP^2)^0.5)/K6ADP)^2))
Vm8=25.1 minute_inverse Reaction: ATP =>, Rate Law: cytoplasm*Vm8*ATP
g6R=0.1 dimensionless; K6ADP=5.0 milliMolar; g6T=1.0 dimensionless; K6FDP=0.2 milliMolar; c6FDP=0.01 dimensionless; c6PEP=1.58793E-4 dimensionless; c6ADP=1.0 dimensionless; h6=1.14815E-7 dimensionless; Vm7=203.0 mM per minute; K6PEP=0.00793966 milliMolar; q6=1.0 dimensionless; L60=164.084 dimensionless Reaction: FDP => Gly; PEP, ATP, Rate Law: Vm7*cytoplasm*PEP/K6PEP*0.5*((-ATP)+(12*ATP-3*ATP^2)^0.5)/K6ADP*(g6R*(1+PEP/K6PEP+0.5*((-ATP)+(12*ATP-3*ATP^2)^0.5)/K6ADP+g6R*PEP/K6PEP*0.5*((-ATP)+(12*ATP-3*ATP^2)^0.5)/K6ADP)+q6*L60*((1+c6FDP*FDP/K6FDP)/(1+FDP/K6FDP))^2*g6T*c6PEP*PEP/K6PEP*c6ADP*0.5*((-ATP)+(12*ATP-3*ATP^2)^0.5)/K6ADP*(1+c6PEP*PEP/K6PEP+c6ADP*0.5*((-ATP)+(12*ATP-3*ATP^2)^0.5)/K6ADP+g6T*c6PEP*PEP/K6PEP*c6ADP*0.5*((-ATP)+(12*ATP-3*ATP^2)^0.5)/K6ADP))/((1+9.55*10^-9/h6)*((1+PEP/K6PEP+0.5*((-ATP)+(12*ATP-3*ATP^2)^0.5)/K6ADP+g6R*PEP/K6PEP*0.5*((-ATP)+(12*ATP-3*ATP^2)^0.5)/K6ADP)^2+L60*((1+c6FDP*FDP/K6FDP)/(1+FDP/K6FDP))^2*(1+c6PEP*PEP/K6PEP+c6ADP*0.5*((-ATP)+(12*ATP-3*ATP^2)^0.5)/K6ADP+g6T*c6PEP*PEP/K6PEP*c6ADP*0.5*((-ATP)+(12*ATP-3*ATP^2)^0.5)/K6ADP)^2))
NADH=0.0806142 milliMolar; K5NADH=3.0E-4 milliMolar; K5AMP=1.1 milliMolar; K5ADP=1.5 milliMolar; Vm5=49.9 mM per minute; K5NAD=0.18 dimensionless; NAD=1.91939 milliMolar; K5ATP=2.5 milliMolar; K5G3P=0.0025 milliMolar Reaction: FDP => ATP + PEP, Rate Law: cytoplasm*Vm5/(1+K5G3P/(0.01*FDP)+(K5NAD/NAD+K5G3P*K5NAD/(NAD*0.01*FDP)+K5G3P*K5NAD*NADH/(NAD*0.01*FDP*K5NADH))*(1+0.5*((-ATP)+(12*ATP-3*ATP^2)^0.5)/K5ADP+((3-ATP)-0.5*((-ATP)+(12*ATP-3*ATP^2)^0.5))/K5AMP+ATP/K5ATP))
Vm1=19.7 mM per minute; Ki1G6P=3.7 minute_inverse Reaction: Glco => Glci; G6P, Rate Law: cytoplasm*(Vm1-Ki1G6P*G6P)
c4AMP=0.019 dimensionless; K4F6P=1.0 milliMolar; K4AMP=0.025 milliMolar; L40=3342.0 dimensionless; gT=1.0 dimensionless; c4F6P=5.0E-4 dimensionless; Vm4=31.7 mM per minute; K4ATP=0.06 milliMolar; c4ATP=1.0 dimensionless; g4R=10.0 dimensionless Reaction: ATP + G6P => FDP, Rate Law: cytoplasm*Vm4*g4R*0.3*G6P/K4F6P*ATP/K4ATP*(1+0.3*G6P/K4F6P+ATP/K4ATP+g4R*0.3*G6P/K4F6P*ATP/K4ATP)/((1+0.3*G6P/K4F6P+ATP/K4ATP+g4R*0.3*G6P/K4F6P*ATP/K4ATP)^2+L40*((1+c4AMP*((3-ATP)-0.5*((-ATP)+(12*ATP-3*ATP^2)^0.5))/K4AMP)/(1+((3-ATP)-0.5*((-ATP)+(12*ATP-3*ATP^2)^0.5))/K4AMP))^2*(1+c4F6P*0.3*G6P/K4F6P+c4ATP*ATP/K4ATP+gT*c4F6P*0.3*G6P/K4F6P*c4ATP*ATP/K4ATP)^2)
n3=8.25 dimensionless; K3Gly=2.0 milliMolar; Km30=1.0 milliMolar; Vm3=14.31 mM per minute; Km3G6P=1.1 milliMolar Reaction: ATP + G6P => Carbo, Rate Law: cytoplasm*1.1*Vm3*G6P^n3/(K3Gly^n3+G6P^n3)/(1+Km30/0.7*(1+Km3G6P/G6P))

States:

Name Description
ATP [ATP; ATP]
Gly [glycerol; Glycerol]
Glco [glucose; C00293]
EtOH [ethanol; Ethanol]
PEP [phosphoenolpyruvate; Phosphoenolpyruvate]
Carbo [glycogen; trehalose; Glycogen; alpha,alpha-Trehalose; glycogen]
Glci [glucose; C00293]
G6P [alpha-D-glucose 6-phosphate; alpha-D-Glucose 6-phosphate]
FDP [keto-D-fructose 1,6-bisphosphate; D-Fructose 1,6-bisphosphate]

Observables: none

MODEL1201070000 @ v0.0.1

This a model from the article: Effect of Na/Ca exchange on plateau fraction and [Ca]i in models for bursting in pancre…

In the presence of an insulinotropic glucose concentration, beta-cells, in intact pancreatic islets, exhibit periodic bursting electrical activity consisting of an alternation of active and silent phases. The fraction of time spent in the active phase over a period is called the plateau fraction and is correlated with the rate of insulin release. However, the mechanisms that regulate the plateau fraction remain unclear. In this paper we investigate the possible role of the plasma membrane Na+/Ca2+ exchange of the beta-cell in controlling the plateau fraction. We have extended different single-cell models to incorporate this Ca2+-activated electrogenic Ca2+ transporter. We find that the Na+/Ca2+ exchange can provide a physiological mechanism to increase the plateau fraction as the glucose concentration is raised. In addition, we show theoretically that the Na+/Ca2+ exchanger is a key regulator of the cytoplasmic calcium concentration in clusters of heterogeneous cells with gap-junctional electrical coupling. link: http://identifiers.org/pubmed/10388739

Parameters: none

States: none

Observables: none

MODEL1201070001 @ v0.0.1

This a model from the article: Effect of Na/Ca exchange on plateau fraction and [Ca]i in models for bursting in pancre…

In the presence of an insulinotropic glucose concentration, beta-cells, in intact pancreatic islets, exhibit periodic bursting electrical activity consisting of an alternation of active and silent phases. The fraction of time spent in the active phase over a period is called the plateau fraction and is correlated with the rate of insulin release. However, the mechanisms that regulate the plateau fraction remain unclear. In this paper we investigate the possible role of the plasma membrane Na+/Ca2+ exchange of the beta-cell in controlling the plateau fraction. We have extended different single-cell models to incorporate this Ca2+-activated electrogenic Ca2+ transporter. We find that the Na+/Ca2+ exchange can provide a physiological mechanism to increase the plateau fraction as the glucose concentration is raised. In addition, we show theoretically that the Na+/Ca2+ exchanger is a key regulator of the cytoplasmic calcium concentration in clusters of heterogeneous cells with gap-junctional electrical coupling. link: http://identifiers.org/pubmed/10388739

Parameters: none

States: none

Observables: none

MODEL1201140000 @ v0.0.1

This a model from the article: Effect of Na/Ca exchange on plateau fraction and [Ca]i in models for bursting in pancre…

In the presence of an insulinotropic glucose concentration, beta-cells, in intact pancreatic islets, exhibit periodic bursting electrical activity consisting of an alternation of active and silent phases. The fraction of time spent in the active phase over a period is called the plateau fraction and is correlated with the rate of insulin release. However, the mechanisms that regulate the plateau fraction remain unclear. In this paper we investigate the possible role of the plasma membrane Na+/Ca2+ exchange of the beta-cell in controlling the plateau fraction. We have extended different single-cell models to incorporate this Ca2+-activated electrogenic Ca2+ transporter. We find that the Na+/Ca2+ exchange can provide a physiological mechanism to increase the plateau fraction as the glucose concentration is raised. In addition, we show theoretically that the Na+/Ca2+ exchanger is a key regulator of the cytoplasmic calcium concentration in clusters of heterogeneous cells with gap-junctional electrical coupling. link: http://identifiers.org/pubmed/10388739

Parameters: none

States: none

Observables: none

The paper describes a model on the key components for tumor–immune dynamics in multiple myeloma. Created by COPASI 4.25…

In this work, we analyze a mathematical model we introduced previously for the dynamics of multiple myeloma and the immune system. We focus on four main aspects: (1) obtaining and justifying ranges and values for all parameters in the model; (2) determining a subset of parameters to which the model is most sensitive; (3) determining which parameters in this subset can be uniquely estimated given cer- tain types of data; and (4) exploring the model numerically. Using global sensitivity analysis techniques, we found that the model is most sensitive to certain growth, loss, and efficacy parameters. This anal- ysis provides the foundation for a future application of the model: prediction of optimal combination regimens in patients with multiple myeloma. link: http://identifiers.org/doi/10.1016/j.jtbi.2018.08.037

Parameters:

Name Description
kr = 80.0 1; rr = 0.0831 1/d Reaction: => Tr, Rate Law: compartment*rr*(1-Tr/kr)*Tr
dr = 0.0757 1/d Reaction: Tr =>, Rate Law: compartment*dr*Tr
dc = 0.02 1/d Reaction: Tc =>, Rate Law: compartment*dc*Tc
kc = 800.0 1; rc = 0.013 1/d Reaction: => Tc, Rate Law: compartment*rc*(1-Tc/kc)*Tc
sm = 0.001 1/d Reaction: => M, Rate Law: compartment*sm
rn = 0.04 1/d; kn = 450.0 1 Reaction: => N, Rate Law: compartment*rn*(1-N/kn)*N
bnm = 150.0 1; amm = 0.5 1; bmm = 3.0 1; brm = 25.0 1; anm = 5.0 1; acnm = 8.0 1; arm = 0.5 1; bcm = 375.0 1; dm = 0.002 1/d; acm = 5.0 1 Reaction: M => ; N, Tc, Tr, Rate Law: compartment*M*(anm*N/(bnm+N)+acm*Tc/(bcm+Tc)+acnm*N*Tc/((bnm+N)*(bcm+Tc)))*((1-amm*M/(bmm+M))-arm*Tr/(brm+Tr))*dm
bmc = 3.0 1; kc = 800.0 1; anc = 1.0 1; rc = 0.013 1/d; amc = 5.0 1; bnc = 150.0 1 Reaction: => Tc; N, M, Rate Law: compartment*rc*(1-Tc/kc)*(amc*M/(bmc+M)+anc*M/(bnc+M))*Tc
dm = 0.002 1/d Reaction: M =>, Rate Law: compartment*M*dm
rn = 0.04 1/d; kn = 450.0 1; bcn = 375.0 1; acn = 1.0 1 Reaction: => N; Tc, Rate Law: compartment*rn*(1-N/kn)*acn*Tc/(bcn+Tc)*N
amr = 2.0 1; kr = 80.0 1; bmr = 3.0 1; rr = 0.0831 1/d Reaction: => Tr; M, Rate Law: compartment*rr*(1-Tr/kr)*amr*M/(bmr+M)*Tr
km = 10.0 1; rm = 0.0175 1/d Reaction: => M, Rate Law: compartment*rm*(1-M/km)*M
dn = 0.025 1/d Reaction: N =>, Rate Law: compartment*dn*N
sn = 0.03 1/d Reaction: => N, Rate Law: compartment*sn

States:

Name Description
M [M Protein]
Tc [Activated Mature Cytotoxic T-Lymphocyte; CD8-positive, alpha-beta cytotoxic T cell]
N [Natural Killer Cell; mature natural killer cell]
Tr [regulatory T cell; CD4+ CD25+ Regulatory T Cells]

Observables: none

This model describes the concept of Cancer Stem Cells(CSC) differentiation and tumor-immune interaction into a generic m…

The tumor microenvironment comprising of the immune cells and cytokines acts as the 'soil' that nourishes a developing tumor. Lack of a comprehensive study of the interactions of this tumor microenvironment with the heterogeneous sub-population of tumor cells that arise from the differentiation of Cancer Stem Cells (CSC), i.e. the 'seed', has limited our understanding of the development of drug resistance and treatment failures in Cancer. Based on this seed and soil hypothesis, for the very first time, we have captured the concept of CSC differentiation and tumor-immune interaction into a generic model that has been validated with known experimental data. Using this model we report that as the CSC differentiation shifts from symmetric to asymmetric pattern, resistant cancer cells start accumulating in the tumor that makes it refractory to therapeutic interventions. Model analyses unveiled the presence of feedback loops that establish the dual role of M2 macrophages in regulating tumor proliferation. The study further revealed oscillations in the tumor sub-populations in the presence of TH1 derived IFN-γ that eliminates CSC; and the role of IL10 feedback in the regulation of TH1/TH2 ratio. These analyses expose important observations that are indicative of Cancer prognosis. Further, the model has been used for testing known treatment protocols to explore the reasons of failure of conventional treatment strategies and propose an improvised protocol that shows promising results in suppressing the proliferation of all the cellular sub-populations of the tumor and restoring a healthy TH1/TH2 ratio that assures better Cancer remission. link: http://identifiers.org/pubmed/30183728

Parameters:

Name Description
delta_S = 2.0E-7 1/d Reaction: Resistant_Stem_Cells_S_R =>, Rate Law: compartment*delta_S*Resistant_Stem_Cells_S_R
k9 = 0.001 1/ml; myu_Th1Ck3 = 0.1245 1/d Reaction: => Type_I_T_helper_Cell_T_H1; Cytokine_IL2, Rate Law: compartment*myu_Th1Ck3*Cytokine_IL2*Type_I_T_helper_Cell_T_H1/(Cytokine_IL2+k9)
myu_TcTreg = 1.5E-5 1/d; lambda_Tc3 = 5.0E10 1/ml Reaction: Cytotoxic_T_Cells_T_C => ; Regulatory_T_Cells_T_reg, Rate Law: compartment*myu_TcTreg*Cytotoxic_T_Cells_T_C*Regulatory_T_Cells_T_reg/(lambda_Tc3+Regulatory_T_Cells_T_reg)
delta_Th2 = 2.0 1/d Reaction: Type_II_T_helper_cells_T_H2 =>, Rate Law: compartment*delta_Th2*Type_II_T_helper_cells_T_H2
gamma_C = 0.1282 1/d; m_C = 0.01; K_tumor = 2.0E10; r_1 = 1.0E-4 Reaction: => Cancer_Cells_C, Rate Law: compartment*gamma_C*(1-m_C)*ln(0.5*K_tumor/(Cancer_Cells_C+r_1))
delta_Treg = 1.0 1/d Reaction: Regulatory_T_Cells_T_reg =>, Rate Law: compartment*delta_Treg*Regulatory_T_Cells_T_reg
lambda_Tc4 = 100000.0 1/ml; gamma_Tc = 1.0 1/d Reaction: => Cytotoxic_T_Cells_T_C; Type_I_T_helper_Cell_T_H1, Rate Law: compartment*gamma_Tc*Cytotoxic_T_Cells_T_C*Type_I_T_helper_Cell_T_H1/(Cytotoxic_T_Cells_T_C+lambda_Tc4)
p_1 = 0.2; p_2 = 0.05; gamma_S = 0.15 1/d Reaction: => Resistant_Stem_Cells_S_R, Rate Law: compartment*gamma_S*((1-p_1)-p_2)*Resistant_Stem_Cells_S_R
delta_CR = 5.37E-5 1/d Reaction: Resistant_Cancer_Cells_C_R =>, Rate Law: compartment*delta_CR*Resistant_Cancer_Cells_C_R
m_S = 4.0E-7; p_1 = 0.2; p_2 = 0.05; gamma_S = 0.15 1/d Reaction: Cancer_Stem_Cells_S => Resistant_Stem_Cells_S_R, Rate Law: compartment*gamma_S*m_S*((1-p_1/2)-p_2)*Cancer_Stem_Cells_S
myu_C2 = 0.9 1/d; k4 = 3.02 1/ml Reaction: Cancer_Cells_C => ; Interferon_gamma, Rate Law: compartment*myu_C2*Cancer_Cells_C*Interferon_gamma/(Interferon_gamma+k4)
tck = 0.1 1/d; ktc2 = 1.0E8 1/ml Reaction: Resistant_Stem_Cells_S_R => ; Cytotoxic_T_Cells_T_C, Rate Law: compartment*tck*Resistant_Stem_Cells_S_R*Cytotoxic_T_Cells_T_C/(ktc2+Cytotoxic_T_Cells_T_C)
myu_SR = 0.18 1/d; k2 = 10.0 1/ml Reaction: Resistant_Stem_Cells_S_R => ; Interferon_gamma, Rate Law: compartment*myu_SR*Resistant_Stem_Cells_S_R*Interferon_gamma/(Interferon_gamma+k2)
beta_Tc = 1.0E-8 1/d Reaction: => Interferon_gamma; Cytotoxic_T_Cells_T_C, Rate Law: compartment*beta_Tc*Cytotoxic_T_Cells_T_C
tck = 0.1 1/d; ktc3 = 1.0E9 1/ml Reaction: Cancer_Cells_C => ; Cytotoxic_T_Cells_T_C, Rate Law: compartment*tck*Cancer_Cells_C*Cytotoxic_T_Cells_T_C/(ktc3+Cytotoxic_T_Cells_T_C)
delta_Ck3 = 8.664339 1/d Reaction: Cytokine_IL2 =>, Rate Law: compartment*delta_Ck3*Cytokine_IL2
beta_M2 = 1.0E-15 1/d Reaction: => Cytokine_IL10; M2_Tumor_Associated_Macrophages, Rate Law: compartment*beta_M2*M2_Tumor_Associated_Macrophages
k6 = 6.9937 1/ml; myu_C2 = 0.9 1/d Reaction: Resistant_Cancer_Cells_C_R => ; Interferon_gamma, Rate Law: compartment*myu_C2*Resistant_Cancer_Cells_C_R*Interferon_gamma/(Interferon_gamma+k6)
beta_Th1CK3 = 1.0E-8 1/d Reaction: => Cytokine_IL2; Type_I_T_helper_Cell_T_H1, Rate Law: compartment*beta_Th1CK3*Type_I_T_helper_Cell_T_H1
myu_TcS = 1.0E-10 1/d; lambda_Tc2 = 500000.0 1/ml Reaction: Cytotoxic_T_Cells_T_C => ; Cancer_Stem_Cells_S, Resistant_Stem_Cells_S_R, Rate Law: compartment*myu_TcS*Cytotoxic_T_Cells_T_C*(Cancer_Stem_Cells_S+Resistant_Stem_Cells_S_R)/(Cytotoxic_T_Cells_T_C+lambda_Tc2)
delta_M1 = 1.02 1/d Reaction: M1_Tumor_Associated_Macrophages =>, Rate Law: compartment*delta_M1*M1_Tumor_Associated_Macrophages
beta_Th2 = 1.0E-9 1/d Reaction: => Cytokine_IL10; Type_II_T_helper_cells_T_H2, Rate Law: compartment*beta_Th2*Type_II_T_helper_cells_T_H2
tck = 0.1 1/d; ktc4 = 1.0E9 1/ml Reaction: Resistant_Cancer_Cells_C_R => ; Cytotoxic_T_Cells_T_C, Rate Law: compartment*tck*Resistant_Cancer_Cells_C_R*Cytotoxic_T_Cells_T_C/(ktc4+Cytotoxic_T_Cells_T_C)
delta_Ck2 = 6.1212 1/d Reaction: Interferon_gamma =>, Rate Law: compartment*delta_Ck2*Interferon_gamma
beta_Th1CK2 = 1.0E-7 1/d Reaction: => Interferon_gamma; Type_I_T_helper_Cell_T_H1, Rate Law: compartment*beta_Th1CK2*Type_I_T_helper_Cell_T_H1
p_1 = 0.2; gamma_S = 0.15 1/d Reaction: Resistant_Stem_Cells_S_R => Resistant_Stem_Cells_S_R + Resistant_Cancer_Cells_C_R, Rate Law: compartment*p_1*gamma_S*Resistant_Stem_Cells_S_R
p_2 = 0.05; gamma_S = 0.15 1/d Reaction: Cancer_Stem_Cells_S => Cancer_Cells_C, Rate Law: compartment*p_2*gamma_S*Cancer_Stem_Cells_S
ktc1 = 1.0E9 1/ml; tck = 0.1 1/d Reaction: Cancer_Stem_Cells_S => ; Cytotoxic_T_Cells_T_C, Rate Law: compartment*tck*Cancer_Stem_Cells_S*Cytotoxic_T_Cells_T_C/(ktc1+Cytotoxic_T_Cells_T_C)
m_C = 0.01; gamma_C = 0.1282 1/d Reaction: Cancer_Cells_C => Resistant_Cancer_Cells_C_R, Rate Law: compartment*m_C*gamma_C*Cancer_Cells_C
myu_C1 = 0.75 1/d; k3 = 2.0531 1/ml Reaction: => Cancer_Cells_C; Cytokine_IL10, Rate Law: compartment*myu_C1*Cancer_Cells_C*Cytokine_IL10/(Cytokine_IL10+k3)
k8 = 0.01 1/ml; myu_Th1Ck1 = 1.0E-9 1/d Reaction: Type_I_T_helper_Cell_T_H1 => ; Cytokine_IL10, Rate Law: compartment*myu_Th1Ck1*Cytokine_IL10*Type_I_T_helper_Cell_T_H1/(Cytokine_IL10+k8)
delta_Tc = 5.2939 1/d Reaction: Cytotoxic_T_Cells_T_C =>, Rate Law: compartment*delta_Tc*Cytotoxic_T_Cells_T_C
gamma_Th2 = 2.0 2/d; lambda_Th2 = 100000.0 1/ml Reaction: => Type_II_T_helper_cells_T_H2; M2_Tumor_Associated_Macrophages, Rate Law: compartment*gamma_Th2*Type_II_T_helper_cells_T_H2*M2_Tumor_Associated_Macrophages/(lambda_Th2+Type_II_T_helper_cells_T_H2)
myu_M2Ck1 = 0.01 1/d; k10 = 0.01 1/ml Reaction: => M2_Tumor_Associated_Macrophages; Cytokine_IL10, Rate Law: compartment*myu_M2Ck1*M2_Tumor_Associated_Macrophages*Cytokine_IL10/(Cytokine_IL10+k10)
lambda_M2 = 1000000.0 1/ml; gamma_M2 = 0.01 1/d Reaction: => M2_Tumor_Associated_Macrophages; Cancer_Cells_C, Resistant_Cancer_Cells_C_R, Rate Law: compartment*gamma_M2*M2_Tumor_Associated_Macrophages*(Cancer_Cells_C+Resistant_Cancer_Cells_C_R)/(M2_Tumor_Associated_Macrophages+lambda_M2)
delta_Ck1 = 19.757 1/d Reaction: Cytokine_IL10 =>, Rate Law: compartment*delta_Ck1*Cytokine_IL10
gamma_Tc = 1.0 1/d; lambda_Tc1 = 100000.0 1/ml Reaction: => Cytotoxic_T_Cells_T_C; Cancer_Cells_C, Resistant_Cancer_Cells_C_R, Rate Law: compartment*gamma_Tc*Cytotoxic_T_Cells_T_C*(Cancer_Cells_C+Resistant_Cancer_Cells_C_R)/(Cytotoxic_T_Cells_T_C+lambda_Tc1)
gamma_Treg = 0.3 1/d; lambda_Treg2 = 1.0E7 1/ml Reaction: => Regulatory_T_Cells_T_reg; M2_Tumor_Associated_Macrophages, Rate Law: compartment*gamma_Treg*Regulatory_T_Cells_T_reg*M2_Tumor_Associated_Macrophages/(Regulatory_T_Cells_T_reg+lambda_Treg2)
lambda_M1 = 1.0E8 1/ml; gamma_M1 = 0.7 1/d Reaction: => M1_Tumor_Associated_Macrophages; Cancer_Cells_C, Resistant_Cancer_Cells_C_R, Rate Law: compartment*gamma_M1*M1_Tumor_Associated_Macrophages*(Cancer_Cells_C+Resistant_Cancer_Cells_C_R)/(M1_Tumor_Associated_Macrophages+lambda_M1)
delta_Th1 = 2.0 1/d Reaction: Type_I_T_helper_Cell_T_H1 =>, Rate Law: compartment*delta_Th1*Type_I_T_helper_Cell_T_H1
lambda_Th1 = 100000.0 1/ml; gamma_Th1 = 2.0 1/d Reaction: => Type_I_T_helper_Cell_T_H1; M1_Tumor_Associated_Macrophages, Rate Law: compartment*gamma_Th1*Type_I_T_helper_Cell_T_H1*M1_Tumor_Associated_Macrophages/(lambda_Th1+Type_I_T_helper_Cell_T_H1)
gamma_C = 0.1282 1/d; K_tumor = 2.0E10; r_2 = 1.0E-5 Reaction: => Resistant_Cancer_Cells_C_R, Rate Law: compartment*gamma_C*Resistant_Cancer_Cells_C_R*ln(0.5*K_tumor/(Resistant_Cancer_Cells_C_R+r_2))
myu_M1Ck2 = 0.01 1/d; k7 = 0.2 1/ml Reaction: => M1_Tumor_Associated_Macrophages; Interferon_gamma, Rate Law: compartment*myu_M1Ck2*M1_Tumor_Associated_Macrophages*Interferon_gamma/(Interferon_gamma+k7)
k11 = 0.001 1/ml; myu_TregCk1 = 1.0E-7 1/d Reaction: => Regulatory_T_Cells_T_reg; Cytokine_IL10, Rate Law: compartment*myu_TregCk1*Cytokine_IL10*Regulatory_T_Cells_T_reg/(Regulatory_T_Cells_T_reg+k11)
myu_C1 = 0.75 1/d; k5 = 6.7979 1/ml Reaction: => Resistant_Cancer_Cells_C_R; Cytokine_IL10, Rate Law: compartment*myu_C1*Resistant_Cancer_Cells_C_R*Cytokine_IL10/(Cytokine_IL10+k5)
beta_Treg = 1.0E-10 1/d Reaction: => Cytokine_IL10; Regulatory_T_Cells_T_reg, Rate Law: compartment*beta_Treg*Regulatory_T_Cells_T_reg
myu_S = 0.17 1/d; k1 = 10.0 1/ml Reaction: Cancer_Stem_Cells_S => ; Interferon_gamma, Rate Law: compartment*myu_S*Cancer_Stem_Cells_S*Interferon_gamma/(Interferon_gamma+k1)
delta_M2 = 0.05 1/d Reaction: M2_Tumor_Associated_Macrophages =>, Rate Law: compartment*delta_M2*M2_Tumor_Associated_Macrophages
delta_C = 0.8055 1/d Reaction: Cancer_Cells_C =>, Rate Law: compartment*delta_C*Cancer_Cells_C

States:

Name Description
Interferon gamma [Interferon Gamma; Cytokine]
Cytokine IL10 [Cytokine; Interleukin-10]
Regulatory T Cells T reg [Cytotoxic and Regulatory T-Cell Molecule]
Cancer Cells C [Malignant Cell]
Cancer Stem Cells S [Cancer Stem Cell]
Type I T helper Cell T H1 [T-helper cell type 1; T-helper 1 cell differentiation]
Cytokine IL2 [Cytokine; Interleukin-2]
M1 Tumor Associated Macrophages [Tumor-Associated Macrophage; M1 Macrophage]
Resistant Stem Cells S R [Drug Resistance Status; Cancer Stem Cell]
Resistant Cancer Cells C R [Malignant Cell; Drug Resistance Status]
M2 Tumor Associated Macrophages [M2 Macrophage; Tumor-Associated Macrophage]
Cytotoxic T Cells T C [Cytotoxic and Regulatory T-Cell Molecule]
Type II T helper cells T H2 [T-helper 2 cell differentiation; T-helper cell type 2]
100000 SR 100000*SR

Observables: none

The paper describes a basic model of immune-tumor cell interactions. Created by COPASI 4.25 (Build 207) This model is…

Cancer immunotherapies rely on how interactions between cancer and immune system cells are constituted. The more essential to the emergence of the dynamical behavior of cancer growth these are, the more effectively they may be used as mechanisms for interventions. Mathematical modeling can help unearth such connections, and help explain how they shape the dynamics of cancer growth. Here, we explored whether there exist simple, consistent properties of cancer-immune system interaction (CISI) models that might be harnessed to devise effective immunotherapy approaches. We did this for a family of three related models of increasing complexity. To this end, we developed a base model of CISI, which captures some essential features of the more complex models built on it. We find that the base model and its derivates can reproduce biologically plausible behavior. This behavior is consistent with situations in which the suppressive effects exerted by cancer cells on immune cells dominate their proliferative effects. Under these circumstances, the model family may display a pattern of bistability, where two distinct, stable states (a cancer-free, and a full-grown cancer state) are possible, consistent with the notion of an immunological barrier. Increasing the effectiveness of immune-caused cancer cell killing may remove the basis for bistability, and abruptly tip the dynamics of the system into cancer-free state. In combination with the administration of immune effector cells, modifications in cancer cell killing may also be harnessed for immunotherapy without resolving the bistability. We use these ideas to test immunotherapeutic interventions in silico in a stochastic version of the base model. This bistability-reliant approach to cancer interventions might offer advantages over those that comprise gradual declines in cancer cell numbers. link: http://identifiers.org/doi/10.1101/498741

Parameters:

Name Description
a = 0.514 1/ks Reaction: => T, Rate Law: Tumor*a*T
k = 1.0E-4 1/ks Reaction: T => ; E, Rate Law: Tumor*k*T*E
m = -1.0E-6 1/ks Reaction: => E; T, Rate Law: Tumor*m*E*T
a = 0.514 1/ks; b = 1.02E-9 1 Reaction: T =>, Rate Law: Tumor*a*b*T*T
d = 0.02 1/ks Reaction: E =>, Rate Law: Tumor*d*E
s = 10.0 1/ks Reaction: => E, Rate Law: Tumor*s

States:

Name Description
T [neoplastic cell]
E [Effector Immune Cell; leukocyte]

Observables: none

Biofilms offer an excellent example of ecological interaction among bacteria. Temporal and spatial oscillations in biofi…

Biofilms offer an excellent example of ecological interaction among bacteria. Temporal and spatial oscillations in biofilms are an emerging topic. In this paper, we describe the metabolic oscillations in Bacillus subtilis biofilms by applying the smallest theoretical chemical reaction system showing Hopf bifurcation proposed by Wilhelm and Heinrich in 1995. The system involves three differential equations and a single bilinear term. We specifically select parameters that are suitable for the biological scenario of biofilm oscillations. We perform computer simulations and a detailed analysis of the system including bifurcation analysis and quasi-steady-state approximation. We also discuss the feedback structure of the system and the correspondence of the simulations to biological observations. Our theoretical work suggests potential scenarios about the oscillatory behaviour of biofilms and also serves as an application of a previously described chemical oscillator to a biological system. link: http://identifiers.org/pubmed/32257302

Parameters:

Name Description
k4 = 2.0 Reaction: Gp => Gi, Rate Law: compartment*k4*Gp
k5 = 2.3 Reaction: Gi => A, Rate Law: compartment*k5*Gi
b = 0.1 Reaction: => B; A, Gp, Rate Law: compartment*b*A*Gp*B
k3 = 4.0 Reaction: A =>, Rate Law: compartment*k3*A
GE = 30.0; k2 = 5.3; k1 = 0.3426 Reaction: => Gp; A, Rate Law: compartment*(k1*GE*Gp-k2*A*Gp)

States:

Name Description
B [biomass production]
A [ammonia]
Gi [CHEBI:32484; C25234]
Gp [CHEBI:32484; C25233]

Observables: none

BIOMD0000000008 @ v0.0.1

Gardner1998 - Cell Cycle GoldbeterMathematical modeling of cell division cycle (CDC) dynamics. The SBML file has been…

We demonstrate, by using mathematical modeling of cell division cycle (CDC) dynamics, a potential mechanism for precisely controlling the frequency of cell division and regulating the size of a dividing cell. Control of the cell cycle is achieved by artificially expressing a protein that reversibly binds and inactivates any one of the CDC proteins. In the simplest case, such as the checkpoint-free situation encountered in early amphibian embryos, the frequency of CDC oscillations can be increased or decreased by regulating the rate of synthesis, the binding rate, or the equilibrium constant of the binding protein. In a more complex model of cell division, where size-control checkpoints are included, we show that the same reversible binding reaction can alter the mean cell mass in a continuously dividing cell. Because this control scheme is general and requires only the expression of a single protein, it provides a practical means for tuning the characteristics of the cell cycle in vivo. link: http://identifiers.org/pubmed/9826676

Parameters:

Name Description
k1=0.5; K5=0.02 Reaction: C => ; X, Rate Law: C*k1*X*(C+K5)^-1
a2=0.05 Reaction: Z => C + Y, Rate Law: a2*Z
K4=0.1; V4=0.1 Reaction: X =>, Rate Law: V4*X*(K4+X)^-1
kd=0.02 Reaction: C =>, Rate Law: C*kd
kd=0.02; alpha=0.1 Reaction: Z => Y, Rate Law: alpha*kd*Z
a1=0.05 Reaction: C + Y => Z, Rate Law: a1*C*Y
alpha=0.1; d1=0.05 Reaction: Z => C, Rate Law: alpha*d1*Z
K3=0.2; V3 = NaN Reaction: => X, Rate Law: V3*(1+-1*X)*(K3+-1*X+1)^-1
K1=0.1; V1 = NaN Reaction: => M, Rate Law: (1+-1*M)*V1*(K1+-1*M+1)^-1
d1=0.05 Reaction: Y =>, Rate Law: d1*Y
vi=0.1 Reaction: => C, Rate Law: vi
K2=0.1; V2=0.25 Reaction: M =>, Rate Law: M*V2*(K2+M)^-1
vs=0.2 Reaction: => Y, Rate Law: vs

States:

Name Description
Y cyclin inhibitor
Z [IPR006670]
X [peptidase activity]
C [IPR006670]
M [Cyclin-dependent kinase 1-A; Cyclin-dependent kinase 1-B]

Observables: none

Gardner2000 - genetic toggle switch in E.coliThe behaviour of the genetic toggle switch and the conditions for bistabili…

It has been proposed' that gene-regulatory circuits with virtually any desired property can be constructed from networks of simple regulatory elements. These properties, which include multistability and oscillations, have been found in specialized gene circuits such as the bacteriophage lambda switch and the Cyanobacteria circadian oscillator. However, these behaviours have not been demonstrated in networks of non-specialized regulatory components. Here we present the construction of a genetic toggle switch-a synthetic, bistable gene-regulatory network-in Escherichia coli and provide a simple theory that predicts the conditions necessary for bistability. The toggle is constructed from any two repressible promoters arranged in a mutually inhibitory network. It is flipped between stable states using transient chemical or thermal induction and exhibits a nearly ideal switching threshold. As a practical device, the toggle switch forms a synthetic, addressable cellular memory unit and has implications for biotechnology, biocomputing and gene therapy. link: http://identifiers.org/pubmed/10659857

Parameters:

Name Description
parameter_7 = 0.0; parameter_2 = 15.6; parameter_4 = 1.0 Reaction: => species_2, Rate Law: compartment_1*parameter_2/(1+parameter_7^parameter_4)
k1=1.0 Reaction: species_1 => ; species_1, Rate Law: compartment_1*k1*species_1
parameter_1 = 156.25; parameter_3 = 2.5 Reaction: => species_1; species_2, species_2, Rate Law: compartment_1*parameter_1/(1+species_2^parameter_3)

States:

Name Description
species 2 [Tetracycline repressor protein class B from transposon Tn10]
species 1 [Lactose operon repressor]

Observables: none

This is a coupled multiscale mathematical model of malaria control and elimination containing four submodels: mosquito-t…

In this paper, we share with the biomathematics community a new coupled multiscale model which has the potential to inform policy and guide malaria control and elimination. The formulation of this multiscale model is based on integrating four submodels which are: (i) a sub-model for the mosquito-to-human transmission of malaria parasite, (ii) a sub-model for the human-to-mosquito transmission of malaria parasite, (iii) a within-mosquito malaria parasite population dynamics sub-model and (iv) a within-human malaria parasite population dynamics sub-model. The integration of the four submodels is achieved by assuming that the transmission parameters of the sub-model for the mosquito-to-human transmission of malaria at the epidemiological scale are functions of the dependent variables of the within-mosquito sporozoite population dynamics while the transmission parameters of the sub-model for the human-to-mosquito transmission of malaria are functions of the dependent variables of the within-human gametocyte population dynamics. This establishes a unidirectionally coupled multiscale model where the within-human and within-mosquito submodels are unidirectionally coupled to the human-to-mosquito and mosquito-to-human submodels. A fast and slow time scale analysis is performed on this system. The result is a simple multiscale model which describes the mechanics of malaria transmission in terms of the major components of the complete malaria parasite life-cycle. This multiscale modelling approach may be found useful in guiding malaria control and elimination. link: http://identifiers.org/pubmed/31128139

Parameters: none

States: none

Observables: none

Gebauer2016 - Genome-scale model of Caenorhabditis elegans metabolism (with bacteria)This model is one of the two versio…

We present a genome-scale model of Caenorhabditis elegans metabolism along with the public database ElegCyc (http://elegcyc.bioinf.uni-jena.de:1100), which represents a reference for metabolic pathways in the worm and allows for the visualization as well as analysis of omics datasets. Our model reflects the metabolic peculiarities of C. elegans that make it distinct from other higher eukaryotes and mammals, including mice and humans. We experimentally verify one of these peculiarities by showing that the lifespan-extending effect of L-tryptophan supplementation is dose dependent (hormetic). Finally, we show the utility of our model for analyzing omics datasets through predicting changes in amino acid concentrations after genetic perturbations and analyzing metabolic changes during normal aging as well as during two distinct, reactive oxygen species (ROS)-related lifespan-extending treatments. Our analyses reveal a notable similarity in metabolic adaptation between distinct lifespan-extending interventions and point to key pathways affecting lifespan in nematodes. link: http://identifiers.org/pubmed/27211858

Parameters: none

States: none

Observables: none

Gebauer2016 - Genome-scale model of Caenorhabditis elegans metabolism (without bacteria)This model is one of the two ver…

We present a genome-scale model of Caenorhabditis elegans metabolism along with the public database ElegCyc (http://elegcyc.bioinf.uni-jena.de:1100), which represents a reference for metabolic pathways in the worm and allows for the visualization as well as analysis of omics datasets. Our model reflects the metabolic peculiarities of C. elegans that make it distinct from other higher eukaryotes and mammals, including mice and humans. We experimentally verify one of these peculiarities by showing that the lifespan-extending effect of L-tryptophan supplementation is dose dependent (hormetic). Finally, we show the utility of our model for analyzing omics datasets through predicting changes in amino acid concentrations after genetic perturbations and analyzing metabolic changes during normal aging as well as during two distinct, reactive oxygen species (ROS)-related lifespan-extending treatments. Our analyses reveal a notable similarity in metabolic adaptation between distinct lifespan-extending interventions and point to key pathways affecting lifespan in nematodes. link: http://identifiers.org/pubmed/27211858

Parameters: none

States: none

Observables: none

MODEL1208280001 @ v0.0.1

Geier2011 - Integrin activationRule based model that integrates the available data to test the biololical hypotheses reg…

Integrin signaling regulates cell migration and plays a pivotal role in developmental processes and cancer metastasis. Integrin signaling has been studied extensively and much data is available on pathway components and interactions. Yet the data is fragmented and an integrated model is missing. We use a rule-based modeling approach to integrate available data and test biological hypotheses regarding the role of talin, Dok1 and PIPKI in integrin activation. The detailed biochemical characterization of integrin signaling provides us with measured values for most of the kinetics parameters. However, measurements are not fully accurate and the cellular concentrations of signaling proteins are largely unknown and expected to vary substantially across different cellular conditions. By sampling model behaviors over the physiologically realistic parameter range we find that the model exhibits only two different qualitative behaviors and these depend mainly on the relative protein concentrations, which offers a powerful point of control to the cell. Our study highlights the necessity to characterize model behavior not for a single parameter optimum, but to identify parameter sets that characterize different signaling modes. link: http://identifiers.org/pubmed/22110576

Parameters: none

States: none

Observables: none

This model simulates the colonization of the mouse gut with different strains of Yersinia enterocolitica. Thereby it tak…

The complex interplay of a pathogen with the host immune response and the endogenous microbiome determines the course and outcome of gastrointestinal infection (GI). Expansion of a pathogen within the gastrointestinal tract implies an increased risk to develop systemic infection. Through computational modeling, we aimed to calculate bacterial population dynamics in GI in order to predict infection course and outcome. For the implementation and parameterization of the model, oral mouse infection experiments with Yersinia enterocolitica were used. Our model takes into account pathogen specific characteristics, such as virulence, as well as host properties, such as microbial colonization resistance or immune responses. We were able to confirm the model calculations in these scenarios by experimental mouse infections and show that it is possible to computationally predict the infection course. Far future clinical application of computational modeling of infections may pave the way for personalized treatment and prevention strategies of GI. link: http://identifiers.org/doi/10.1101/2020.08.11.244202

Parameters: none

States: none

Observables: none

We propose an integrated computational model for the network of cyclin-dependent kinases (Cdks) that controls the dynami…

We propose an integrated computational model for the network of cyclin-dependent kinases (Cdks) that controls the dynamics of the mammalian cell cycle. The model contains four Cdk modules regulated by reversible phosphorylation, Cdk inhibitors, and protein synthesis or degradation. Growth factors (GFs) trigger the transition from a quiescent, stable steady state to self-sustained oscillations in the Cdk network. These oscillations correspond to the repetitive, transient activation of cyclin D/Cdk4-6 in G(1), cyclin E/Cdk2 at the G(1)/S transition, cyclin A/Cdk2 in S and at the S/G(2) transition, and cyclin B/Cdk1 at the G(2)/M transition. The model accounts for the following major properties of the mammalian cell cycle: (i) repetitive cell cycling in the presence of suprathreshold amounts of GF; (ii) control of cell-cycle progression by the balance between antagonistic effects of the tumor suppressor retinoblastoma protein (pRB) and the transcription factor E2F; and (iii) existence of a restriction point in G(1), beyond which completion of the cell cycle becomes independent of GF. The model also accounts for endoreplication. Incorporating the DNA replication checkpoint mediated by kinases ATR and Chk1 slows down the dynamics of the cell cycle without altering its oscillatory nature and leads to better separation of the S and M phases. The model for the mammalian cell cycle shows how the regulatory structure of the Cdk network results in its temporal self-organization, leading to the repetitive, sequential activation of the four Cdk modules that brings about the orderly progression along cell-cycle phases. link: http://identifiers.org/pubmed/20007375

Parameters:

Name Description
kpc3 = 0.025; eps = 17.0 Reaction: pRBp + E2F => pRBc2; pRBp, E2F, Rate Law: cell*kpc3*pRBp*E2F*eps
kdpb = 0.1; eps = 17.0 Reaction: Pb => ; Pb, Rate Law: cell*kdpb*Pb*eps
eps = 17.0; vs1p27 = 0.8 Reaction: => p27, Rate Law: cell*vs1p27*eps
V1 = 2.2; K1 = 0.1; eps = 17.0 Reaction: pRB => pRBp; pRB, Md, Mdp27, Rate Law: cell*V1*pRB/(K1+pRB)*(Md+Mdp27)*eps
Cdk4_tot = 1.5; eps = 17.0; kcom1 = 0.175 Reaction: Cd => Mdi; Mdi, Md, Mdp27, Rate Law: cell*kcom1*Cd*(Cdk4_tot-(Mdi+Md+Mdp27))*eps
eps = 17.0; K4b = 0.1; Vm4b = 0.7 Reaction: Cdc20a => Cdc20i; Cdc20a, Rate Law: cell*Vm4b*Cdc20a/(K4b+Cdc20a)*eps
K2b = 0.1; ib3 = 0.5; eps = 17.0; Vm2b = 2.1 Reaction: Mb => Mbi; Wee1, Mb, Rate Law: cell*Vm2b*(Wee1+ib3)*Mb/(K2b+Mb)*eps
V4 = 2.0; eps = 17.0; K4 = 0.1 Reaction: pRBpp => pRBp; pRBpp, Rate Law: cell*V4*pRBpp/(K4+pRBpp)*eps
kdecom3 = 0.1; eps = 17.0 Reaction: Mai => Ca; Mai, Rate Law: cell*kdecom3*Mai*eps
eps = 17.0; vsprb = 0.8 Reaction: => pRB, Rate Law: cell*vsprb*eps
eps = 17.0; kpc2 = 0.5 Reaction: pRBc1 => pRB + E2F; pRBc1, Rate Law: cell*kpc2*pRBc1*eps
kdpe = 0.075; eps = 17.0 Reaction: Pe => ; Pe, Rate Law: cell*kdpe*Pe*eps
Vm1a = 2.0; K1a = 0.1; eps = 17.0 Reaction: Mai => Ma; Mai, Pa, Rate Law: cell*Vm1a*Mai/(K1a+Mai)*Pa*eps
Ki13 = 0.1; eps = 17.0; Ki14 = 2.0; vs2p27 = 0.1 Reaction: => p27; E2F, pRB, pRBp, Rate Law: cell*vs2p27*E2F*Ki13/(Ki13+pRB)*Ki14/(Ki14+pRBp)*eps
GF = 1.0; vsap1 = 1.0; Kagf = 0.1; eps = 17.0 Reaction: => AP1, Rate Law: cell*vsap1*GF/(Kagf+GF)*eps
K2d = 0.1; Vm2d = 0.2; eps = 17.0 Reaction: Md => Mdi; Md, Rate Law: cell*Vm2d*Md/(K2d+Md)*eps
kc7 = 0.12; eps = 17.0 Reaction: Mb + p27 => Mbp27; Mb, p27, Rate Law: cell*kc7*Mb*p27*eps
kc6 = 0.125; eps = 17.0 Reaction: Map27 => Ma + p27; Map27, Rate Law: cell*kc6*Map27*eps
kdwee1 = 0.1; eps = 17.0 Reaction: Wee1 => ; Wee1, Rate Law: cell*kdwee1*Wee1*eps
kdap1 = 0.15; eps = 17.0 Reaction: AP1 => ; AP1, Rate Law: cell*kdap1*AP1*eps
K2 = 0.1; eps = 17.0; V2 = 2.0 Reaction: pRBp => pRB; pRBp, Rate Law: cell*V2*pRBp/(K2+pRBp)*eps
kdprbp = 0.06; eps = 17.0 Reaction: pRBp => ; pRBp, Rate Law: cell*kdprbp*pRBp*eps
eps = 17.0; Kdd = 0.1; Vdd = 5.0 Reaction: Cd => ; Cd, Rate Law: cell*Vdd*Cd/(Kdd+Cd)*eps
kc2 = 0.05; eps = 17.0 Reaction: Mdp27 => Md + p27; Mdp27, Rate Law: cell*kc2*Mdp27*eps
K8b = 0.1; Vm8b = 1.0; eps = 17.0 Reaction: Wee1p => Wee1; Wee1p, Rate Law: cell*Vm8b*Wee1p/(K8b+Wee1p)*eps
Kdp27p = 0.1; eps = 17.0; Kdp27skp2 = 0.1; Vdp27p = 5.0 Reaction: p27p => ; Skp2, p27p, Rate Law: cell*Vdp27p*Skp2/(Kdp27skp2+Skp2)*p27p/(Kdp27p+p27p)*eps
Cdk2_tot = 2.0; eps = 17.0; kcom2 = 0.2 Reaction: Ce => Mei; Mei, Me, Mep27, Mai, Ma, Map27, Rate Law: cell*kcom2*Ce*(Cdk2_tot-(Mei+Me+Mep27+Mai+Ma+Map27))*eps
Kde = 0.1; Vde = 3.0; Kdceskp2 = 2.0; eps = 17.0 Reaction: Ce => ; Skp2, Ce, Rate Law: cell*Vde*Skp2/(Kdceskp2+Skp2)*Ce/(Kde+Ce)*eps
kc1 = 0.15; eps = 17.0 Reaction: Md + p27 => Mdp27; Md, p27, Rate Law: cell*kc1*Md*p27*eps
kc5 = 0.15; eps = 17.0 Reaction: Ma + p27 => Map27; Ma, p27, Rate Law: cell*kc5*Ma*p27*eps
eps = 17.0; kc3 = 0.2 Reaction: Me + p27 => Mep27; Me, p27, Rate Law: cell*kc3*Me*p27*eps
kpc1 = 0.05; eps = 17.0 Reaction: pRB + E2F => pRBc1; pRB, E2F, Rate Law: cell*kpc1*pRB*E2F*eps
Ki8 = 2.0; eps = 17.0; Ki7 = 0.1; kcd2 = 0.005 Reaction: => Cd; E2F, pRB, pRBp, Rate Law: cell*kcd2*E2F*Ki7/(Ki7+pRB)*Ki8/(Ki8+pRBp)*eps
K1cdh1 = 0.01; eps = 17.0; V1cdh1 = 1.25 Reaction: Cdh1i => Cdh1a; Cdh1i, Rate Law: cell*V1cdh1*Cdh1i/(K1cdh1+Cdh1i)*eps
eps = 17.0; Ki9 = 0.1; Ki10 = 2.0; kce = 0.25 Reaction: => Ce; E2F, pRB, pRBp, Rate Law: cell*kce*E2F*Ki9/(Ki9+pRB)*Ki10/(Ki10+pRBp)*eps
eps = 17.0; K3b = 0.1; Vm3b = 8.0 Reaction: Cdc20i => Cdc20a; Cdc20i, Mb, Rate Law: cell*Vm3b*Cdc20i/(K3b+Cdc20i)*Mb*eps
kddp27p = 0.01; eps = 17.0 Reaction: p27p => ; p27p, Rate Law: cell*kddp27p*p27p*eps
kdecom4 = 0.1; eps = 17.0 Reaction: Mbi => Cb; Mbi, Rate Law: cell*kdecom4*Mbi*eps
eps = 17.0; kdecom2 = 0.1 Reaction: Mei => Ce; Mei, Rate Law: cell*kdecom2*Mei*eps
eps = 17.0; kcd1 = 0.4 Reaction: => Cd; AP1, Rate Law: cell*kcd1*AP1*eps
V2cdh1 = 8.0; K2cdh1 = 0.01; eps = 17.0 Reaction: Cdh1a => Cdh1i; Cdh1a, Ma, Mb, Rate Law: cell*V2cdh1*Cdh1a/(K2cdh1+Cdh1a)*(Ma+Mb)*eps
kdda = 0.005; eps = 17.0 Reaction: Ca => ; Ca, Rate Law: cell*kdda*Ca*eps
Vm1e = 2.0; eps = 17.0; K1e = 0.1 Reaction: Mei => Me; Mei, Pe, Rate Law: cell*Vm1e*Mei/(K1e+Mei)*Pe*eps
ATR_tot = 0.5; eps = 17.0; kaatr = 0.022 Reaction: Primer => ATR; ATR, Primer, Rate Law: cell*kaatr*(ATR_tot-ATR)*Primer*eps
kdde = 0.005; eps = 17.0 Reaction: Ce => ; Ce, Rate Law: cell*kdde*Ce*eps
K2p27 = 0.5; eps = 17.0; V2p27 = 0.1 Reaction: p27p => p27; p27p, Rate Law: cell*V2p27*p27p/(K2p27+p27p)*eps
eps = 17.0; Vda = 2.5; Kda = 1.1; Kacdc20 = 2.0 Reaction: Ca => ; Ca, Cdc20a, Rate Law: cell*Vda*Ca/(Kda+Ca)*Cdc20a/(Kacdc20+Cdc20a)*eps
K3 = 0.1; V3 = 1.0; eps = 17.0 Reaction: pRBp => pRBpp; pRBp, Me, Rate Law: cell*V3*pRBp/(K3+pRBp)*Me*eps
eps = 17.0; kdcdc20a = 0.05 Reaction: Cdc20a => ; Cdc20a, Rate Law: cell*kdcdc20a*Cdc20a*eps
eps = 17.0; kpc4 = 0.5 Reaction: pRBc2 => pRBp + E2F; pRBc2, Rate Law: cell*kpc4*pRBc2*eps
ib1 = 0.5; eps = 17.0; Vm2e = 1.4; K2e = 0.1 Reaction: Me => Mei; Wee1, Me, Rate Law: cell*Vm2e*(Wee1+ib1)*Me/(K2e+Me)*eps
Vm5e = 5.0; eps = 17.0; ae = 0.25; K5e = 0.1 Reaction: Pei => Pe; Me, Pei, Rate Law: cell*Vm5e*(Me+ae)*Pei/(K5e+Pei)*eps
kdecom1 = 0.1; eps = 17.0 Reaction: Mdi => Cd; Mdi, Rate Law: cell*kdecom1*Mdi*eps
kdpei = 0.15; eps = 17.0 Reaction: Pei => ; Pei, Rate Law: cell*kdpei*Pei*eps
V1cdc45 = 0.8; Cdc45_tot = 0.5; eps = 17.0; K1cdc45 = 0.02 Reaction: => Cdc45; Me, Rate Law: cell*V1cdc45*Me*(Cdc45_tot-Cdc45)/((K1cdc45+Cdc45_tot)-Cdc45)*eps
ksprim = 0.05; eps = 17.0 Reaction: => Primer; Pol, Rate Law: cell*ksprim*Pol*eps
kdprb = 0.01; eps = 17.0 Reaction: pRB => ; pRBp, Rate Law: cell*kdprb*pRBp*eps
kc4 = 0.1; eps = 17.0 Reaction: Mep27 => Me + p27; Mep27, Rate Law: cell*kc4*Mep27*eps
K7b = 0.1; eps = 17.0; ib = 0.75; Vm7b = 1.2 Reaction: Wee1 => Wee1p; Mb, Wee1, Rate Law: cell*Vm7b*(Mb+ib)*Wee1/(K7b+Wee1)*eps
V6e = 0.8; xe1 = 1.0; eps = 17.0; xe2 = 1.0; K6e = 0.1 Reaction: Pe => Pei; Chk1, Pe, Rate Law: cell*V6e*(xe1+xe2*Chk1)*Pe/(K6e+Pe)*eps
K2a = 0.1; Vm2a = 1.85; eps = 17.0; ib2 = 0.5 Reaction: Ma => Mai; Wee1, Ma, Rate Law: cell*Vm2a*(Wee1+ib2)*Ma/(K2a+Ma)*eps
kddd = 0.005; eps = 17.0 Reaction: Cd => ; Cd, Rate Law: cell*kddd*Cd*eps
kdcdc20i = 0.14; eps = 17.0 Reaction: Cdc20i => ; Cdc20i, Rate Law: cell*kdcdc20i*Cdc20i*eps
kdatr = 0.15; eps = 17.0 Reaction: ATR => Primer; ATR, Rate Law: cell*kdatr*ATR*eps
K1p27 = 0.5; eps = 17.0; V1p27 = 100.0 Reaction: p27 => p27p; p27, Me, Rate Law: cell*V1p27*p27/(K1p27+p27)*Me*eps
K1d = 0.1; Vm1d = 1.0; eps = 17.0 Reaction: Mdi => Md; Mdi, Rate Law: cell*Vm1d*Mdi/(K1d+Mdi)*eps
kc8 = 0.2; eps = 17.0 Reaction: Mbp27 => Mb + p27; Mbp27, Rate Law: cell*kc8*Mbp27*eps
kdprim = 0.15; eps = 17.0 Reaction: Primer => ; Primer, Rate Law: cell*kdprim*Primer*eps
eps = 17.0; kddp27 = 0.06 Reaction: p27 => ; p27, Rate Law: cell*kddp27*p27*eps
kca = 0.0375; Ki11 = 0.1; eps = 17.0; Ki12 = 2.0 Reaction: => Ca; E2F, pRB, pRBp, Rate Law: cell*kca*E2F*Ki11/(Ki11+pRB)*Ki12/(Ki12+pRBp)*eps
Cdk2_tot = 2.0; kcom3 = 0.2; eps = 17.0 Reaction: Ca => Mai; Mei, Me, Mep27, Mai, Ma, Map27, Rate Law: cell*kcom3*Ca*(Cdk2_tot-(Mei+Me+Mep27+Mai+Ma+Map27))*eps

States:

Name Description
Ce [G1/S-specific cyclin-E1; G1/S-specific cyclin-E2]
pRBc2 [Retinoblastoma-associated protein; Transcription factor E2F1]
Pe [M-phase inducer phosphatase 2; M-phase inducer phosphatase 3; M-phase inducer phosphatase 1; Phosphorylated Peptide]
Pei [M-phase inducer phosphatase 3; M-phase inducer phosphatase 2; M-phase inducer phosphatase 1]
Mbi [G2/mitotic-specific cyclin-B1; Cyclin-dependent kinase 1]
p27p [Cyclin-dependent kinase inhibitor 1B; Phosphorylated Peptide]
Cdc20a [Cell division cycle protein 20 homolog]
Mbp27 [G2/mitotic-specific cyclin-B1; Cyclin-dependent kinase 1; Cyclin-dependent kinase inhibitor 1B]
Map27 [Cyclin-A2; Cyclin-dependent kinase 2; Cyclin-dependent kinase inhibitor 1B]
Primer Primer
pRB [Retinoblastoma-associated protein]
AP1 [1,4-beta-D-Mannooligosaccharide]
Wee1 [Wee1-like protein kinase]
Mdi [G1/S-specific cyclin-D2; G1/S-specific cyclin-D3; Cyclin-dependent kinase 6; G1/S-specific cyclin-D1; Cyclin-dependent kinase 4]
Mdp27 [Cyclin-dependent kinase 4; Dehydrin Rab25; G1/S-specific cyclin-D1; G1/S-specific cyclin-D2; Cyclin-dependent kinase 6; Cyclin-dependent kinase inhibitor 1B]
ATR [Serine/threonine-protein kinase ATR]
Ma [Cyclin-A2; Cyclin-dependent kinase 2]
pRBc1 [Retinoblastoma-associated protein; Transcription factor E2F1]
Md [Cyclin-dependent kinase 6; G1/S-specific cyclin-D1; G1/S-specific cyclin-D2; Cyclin-dependent kinase 4; G1/S-specific cyclin-D3]
Cdc45 [Cell division control protein 45 homolog]
pRBpp [Retinoblastoma-associated protein; Phosphorylated Peptide]
Wee1p [Wee1-like protein kinase; Phosphorylated Peptide]
Mei [G1/S-specific cyclin-E1; G1/S-specific cyclin-E2; Cyclin-dependent kinase 2]
p27 [Cyclin-dependent kinase inhibitor 1B]
Cdh1i [Cadherin-1]
Mai [Cyclin-dependent kinase 2; Cyclin-A2]
Ca [Cyclin-A2]
pRBp [Retinoblastoma-associated protein; Phosphorylated Peptide]
Cd [G1/S-specific cyclin-D2; G1/S-specific cyclin-D3; G1/S-specific cyclin-D1]
Cdc20i [Cell division cycle protein 20 homolog]
Pb [M-phase inducer phosphatase 3; M-phase inducer phosphatase 1; M-phase inducer phosphatase 2; Phosphorylated Peptide]

Observables: none

We previously proposed a detailed, 39-variable model for the network of cyclin-dependent kinases (Cdks) that controls pr…

We previously proposed a detailed, 39-variable model for the network of cyclin-dependent kinases (Cdks) that controls progression along the successive phases of the mammalian cell cycle. Here, we propose a skeleton, 5-variable model for the Cdk network that can be seen as the backbone of the more detailed model for the mammalian cell cycle. In the presence of sufficient amounts of growth factor, the skeleton model also passes from a stable steady state to sustained oscillations of the various cyclin/Cdk complexes. This transition corresponds to the switch from quiescence to cell proliferation. Sequential activation of the cyclin/Cdk complexes allows the ordered progression along the G1, S, G2 and M phases of the cell cycle. The 5-variable model can also account for the existence of a restriction point in G1, and for endoreplication. Like the detailed model, it contains multiple oscillatory circuits and can display complex oscillatory behaviour such as quasi-periodic oscillations and chaos. We compare the dynamical properties of the skeleton model with those of the more detailed model for the mammalian cell cycle. link: http://identifiers.org/pubmed/22419972

Parameters:

Name Description
vsa = 0.175 Reaction: => cyclin_A_Cdk2; transcription_factor_E2F_active, Rate Law: nuclear*vsa*transcription_factor_E2F_active
Vdb = 0.28; Kdb = 0.005 Reaction: cyclin_B_Cdk1 => ; Cdc20_active, Rate Law: nuclear*Vdb*Cdc20_active*cyclin_B_Cdk1/(Kdb+cyclin_B_Cdk1)
Vda = 0.245; Kda = 0.1 Reaction: cyclin_A_Cdk2 => ; Cdc20_active, Rate Law: nuclear*Vda*Cdc20_active*cyclin_A_Cdk2/(Kda+cyclin_A_Cdk2)
K2cdc20 = 1.0; V2cdc20 = 0.35 Reaction: Cdc20_active =>, Rate Law: nuclear*V2cdc20*Cdc20_active/(K2cdc20+Cdc20_active)
vse = 0.21 Reaction: => cyclin_E_Cdk2; transcription_factor_E2F_active, Rate Law: nuclear*vse*transcription_factor_E2F_active
K1cdc20 = 1.0; V1cdc20 = 0.21 Reaction: => Cdc20_active; cyclin_B_Cdk1, Cdc20_total, Rate Law: nuclear*V1cdc20*cyclin_B_Cdk1*(Cdc20_total-Cdc20_active)/(K1cdc20+(Cdc20_total-Cdc20_active))
Kdd = 0.1; Vdd = 0.245 Reaction: cyclin_D_Cdk4_6 => ; cyclin_D_Cdk4_6, Rate Law: nuclear*Vdd*cyclin_D_Cdk4_6/(Kdd+cyclin_D_Cdk4_6)
V2e2f = 0.7; K2e2f = 0.01 Reaction: transcription_factor_E2F_active => ; cyclin_A_Cdk2, Rate Law: nuclear*V2e2f*transcription_factor_E2F_active/(K2e2f+transcription_factor_E2F_active)*cyclin_A_Cdk2
GF = 1.0; Kgf = 0.1; vsd = 0.175 Reaction: => cyclin_D_Cdk4_6, Rate Law: nuclear*vsd*GF/(Kgf+GF)
K1e2f = 0.01; V1e2f = 0.805 Reaction: => transcription_factor_E2F_active; E2F_total, cyclin_D_Cdk4_6, cyclin_E_Cdk2, Rate Law: nuclear*V1e2f*(E2F_total-transcription_factor_E2F_active)/((K1e2f+E2F_total)-transcription_factor_E2F_active)*(cyclin_D_Cdk4_6+cyclin_E_Cdk2)
Kde = 0.1; Vde = 0.35 Reaction: cyclin_E_Cdk2 => ; cyclin_A_Cdk2, Rate Law: nuclear*Vde*cyclin_A_Cdk2*cyclin_E_Cdk2/(Kde+cyclin_E_Cdk2)
vsb = 0.21 Reaction: => cyclin_B_Cdk1; cyclin_A_Cdk2, Rate Law: nuclear*vsb*cyclin_A_Cdk2

States:

Name Description
Cdc20 active [Cell division cycle protein 20 homolog; active; phosphorylated]
cyclin D Cdk4 6 [G1/S-specific cyclin-D1; Cyclin-dependent kinase 4; protein-containing complex]
transcription factor E2F active [Transcription factor E2F1; active]
cyclin B Cdk1 [Cyclin-dependent kinase 1; G2/mitotic-specific cyclin-B1; protein-containing complex]
cyclin E Cdk2 [G1/S-specific cyclin-E1; Cyclin-dependent kinase 2; protein-containing complex]
cyclin A Cdk2 [Cyclin-dependent kinase 2; Cyclin-A2; protein-containing complex]

Observables: none

The eukaryotic cell cycle is characterized by alternating oscillations in the activities of cyclin-dependent kinase (Cdk…

The eukaryotic cell cycle is characterized by alternating oscillations in the activities of cyclin-dependent kinase (Cdk) and the anaphase-promoting complex (APC). Successful completion of the cell cycle is dependent on the precise, temporally ordered appearance of these activities. A modest level of Cdk activity is sufficient to initiate DNA replication, but mitosis and APC activation require an elevated Cdk activity. In present-day eukaryotes, this temporal order is provided by a complex network of regulatory proteins that control both Cdk and APC activities via sharp thresholds, bistability, and time delays. Using simple computational models, we show here that these dynamical features of cell-cycle organization could emerge in a control system driven by a single Cdk/cyclin complex and APC wired in a negative-feedback loop. We show that ordered phosphorylation of cellular proteins could be explained by multisite phosphorylation/dephosphorylation and competition of substrates for interconverting kinase (Cdk) and phosphatase. In addition, the competition of APC substrates for ubiquitylation can create and maintain sustained oscillations in cyclin levels. We propose a sequence of models that gets closer and closer to a realistic model of cell-cycle control in yeast. Since these models lack the elaborate control mechanisms characteristic of modern eukaryotes, they suggest that bistability and time delay may have characterized eukaryotic cell divisions before the current cell-cycle control network evolved in all its complexity. link: http://identifiers.org/pubmed/23528096

Parameters:

Name Description
k_d1cdk = 0.01 Reaction: Cdk =>, Rate Law: nuclear*k_d1cdk*Cdk
K_dsec = 0.001; K_dcdk = 0.01; k_dsec = 0.4 Reaction: Securin => ; Anaphase_promoting_complex_Phosphorylated, Cdk, Rate Law: nuclear*k_dsec*Anaphase_promoting_complex_Phosphorylated*Securin/(K_dsec*(1+Cdk/K_dcdk)+Securin)
V_ssec = 0.1 Reaction: => Securin, Rate Law: nuclear*V_ssec
V_scdk = 0.06 Reaction: => Cdk, Rate Law: nuclear*V_scdk
K_dsec = 0.001; K_dcdk = 0.01; k_dcdk = 0.35 Reaction: Cdk => ; Anaphase_promoting_complex_Phosphorylated, Securin, Rate Law: nuclear*k_dcdk*Anaphase_promoting_complex_Phosphorylated*Cdk/(K_dcdk*(1+Securin/K_dsec)+Cdk)
K_1APC = 0.01; V_1APC = 0.15 Reaction: Anaphase_promoting_complex_Phosphorylated =>, Rate Law: nuclear*V_1APC*Anaphase_promoting_complex_Phosphorylated/(K_1APC+Anaphase_promoting_complex_Phosphorylated)
k_d1sec = 0.01 Reaction: Securin =>, Rate Law: nuclear*k_d1sec*Securin
k_2APC = 0.3; K_2APC = 0.01 Reaction: => Anaphase_promoting_complex_Phosphorylated; Cdk, Anaphase_promoting_complex, Rate Law: nuclear*k_2APC*Cdk*Anaphase_promoting_complex/(K_2APC+Anaphase_promoting_complex)

States:

Name Description
Anaphase promoting complex [anaphase-promoting complex]
Securin [Securin]
Anaphase promoting complex Phosphorylated [anaphase-promoting complex; phosphorylated]
Cdk [Cyclin-dependent kinase 1]

Observables: none

High proliferation rate and robustness are vital characteristics of bacterial pathogens to successfully colonize their h…

High proliferation rate and robustness are vital characteristics of bacterial pathogens that successfully colonize their hosts. The observation of drastically slow growth in some pathogens is thus paradoxical and remains unexplained. In this study, we sought to understand the slow (fastidious) growth of the plant pathogen Xylella fastidiosa. Using genome-scale metabolic network reconstruction, modeling, and experimental validation, we explored its metabolic capabilities. Despite genome reduction and slow growth, the pathogen’s metabolic network is complete but strikingly minimalist and lacking in robustness. Most alternative reactions were missing, especially those favoring fast growth, and were replaced by less efficient paths. We also found that the production of some virulence factors imposes a heavy burden on growth. Interestingly, some specific determinants of fastidious growth were also found in other slow-growing pathogens, enriching the view that these metabolic peculiarities are a pathogenicity strategy to remain at a low population level. link: http://identifiers.org/doi/10.1128/mSystems.00698-19

Parameters: none

States: none

Observables: none

The model is based on 'Developing a Minimally Structured Mathematical Model of Cancer Treatment with Oncolytic Viruses a…

Mathematical models of biological systems must strike a balance between being sufficiently complex to capture important biological features, while being simple enough that they remain tractable through analysis or simulation. In this work, we rigorously explore how to balance these competing interests when modeling murine melanoma treatment with oncolytic viruses and dendritic cell injections. Previously, we developed a system of six ordinary differential equations containing fourteen parameters that well describes experimental data on the efficacy of these treatments. Here, we explore whether this previously developed model is the minimal model needed to accurately describe the data. Using a variety of techniques, including sensitivity analyses and a parameter sloppiness analysis, we find that our model can be reduced by one variable and three parameters and still give excellent fits to the data. We also argue that our model is not too simple to capture the dynamics of the data, and that the original and minimal models make similar predictions about the efficacy and robustness of protocols not considered in experiments. Reducing the model to its minimal form allows us to increase the tractability of the system in the face of parametric uncertainty. link: http://identifiers.org/pubmed/30510594

Parameters:

Name Description
C_T = 1.428064 Reaction: => Tumor_targeting_T_cells_T; Infected_Cancer_Cell_I, Rate Law: compartment*C_T*Infected_Cancer_Cell_I
delta_I = 1.0 Reaction: Infected_Cancer_Cell_I =>, Rate Law: compartment*delta_I*Infected_Cancer_Cell_I
delta_V = 2.3 Reaction: Oncolytic_Adenovirus_V =>, Rate Law: compartment*delta_V*Oncolytic_Adenovirus_V
chi_D = 4.901894 Reaction: => Tumor_targeting_T_cells_T; Dendritic_Cells_D, Rate Law: compartment*chi_D*Dendritic_Cells_D
U_V = 0.0 Reaction: => Oncolytic_Adenovirus_V, Rate Law: compartment*U_V
r = 0.3198 Reaction: => Uninfected_Tumor_Cell_U, Rate Law: compartment*r*Uninfected_Tumor_Cell_U
c_kill = 0.623397; k0 = 2.0 Reaction: Uninfected_Tumor_Cell_U => ; Infected_Cancer_Cell_I, Tumor_targeting_T_cells_T, Total_cells_N, Rate Law: compartment*(k0+c_kill*Infected_Cancer_Cell_I)*Uninfected_Tumor_Cell_U*Tumor_targeting_T_cells_T/Total_cells_N
delta_T = 0.35 Reaction: Tumor_targeting_T_cells_T =>, Rate Law: compartment*delta_T*Tumor_targeting_T_cells_T
U_D = 0.0 Reaction: => Dendritic_Cells_D, Rate Law: compartment*U_D
beta = 1.008538 Reaction: Uninfected_Tumor_Cell_U => Infected_Cancer_Cell_I; Oncolytic_Adenovirus_V, Total_cells_N, Rate Law: compartment*beta*Uninfected_Tumor_Cell_U*Oncolytic_Adenovirus_V/Total_cells_N
alpha = 3.0; delta_I = 1.0 Reaction: => Oncolytic_Adenovirus_V; Infected_Cancer_Cell_I, Rate Law: compartment*alpha*delta_I*Infected_Cancer_Cell_I
delta_D = 0.35 Reaction: Dendritic_Cells_D =>, Rate Law: compartment*delta_D*Dendritic_Cells_D

States:

Name Description
total tumor cells [cancer; B16-F10 cell]
Infected Cancer Cell I [B16-F10 cell; cancer; Abnormal]
Uninfected Tumor Cell U [cancer; B16-F10 cell]
Dendritic Cells D [dendritic cell; Dendritic Cell]
Total cells N [B16-F10 cell; cancer; Natural Killer T-Cell]
Oncolytic Adenovirus V [Oncolytic; Adenoviridae]
Tumor targeting T cells T [Natural Killer T-Cell; Targeting]

Observables: none

The model is based on 'Developing a Minimally Structured Mathematical Model of Cancer Treatment with Oncolytic Viruses a…

Mathematical models of biological systems must strike a balance between being sufficiently complex to capture important biological features, while being simple enough that they remain tractable through analysis or simulation. In this work, we rigorously explore how to balance these competing interests when modeling murine melanoma treatment with oncolytic viruses and dendritic cell injections. Previously, we developed a system of six ordinary differential equations containing fourteen parameters that well describes experimental data on the efficacy of these treatments. Here, we explore whether this previously developed model is the minimal model needed to accurately describe the data. Using a variety of techniques, including sensitivity analyses and a parameter sloppiness analysis, we find that our model can be reduced by one variable and three parameters and still give excellent fits to the data. We also argue that our model is not too simple to capture the dynamics of the data, and that the original and minimal models make similar predictions about the efficacy and robustness of protocols not considered in experiments. Reducing the model to its minimal form allows us to increase the tractability of the system in the face of parametric uncertainty. link: http://identifiers.org/pubmed/30510594

Parameters:

Name Description
C_T = 1.698362 Reaction: => Tumor_targeting_T_cells_T; Infected_Cancer_Cell_I, Rate Law: compartment*C_T*Infected_Cancer_Cell_I
delta_I = 1.0 Reaction: Infected_Cancer_Cell_I =>, Rate Law: compartment*delta_I*Infected_Cancer_Cell_I
k0 = 2.0; c_kill = 0.595397 Reaction: Uninfected_Tumor_Cell_U => ; Infected_Cancer_Cell_I, Tumor_targeting_T_cells_T, Total_cells_N, Rate Law: compartment*(k0+c_kill*Infected_Cancer_Cell_I)*Uninfected_Tumor_Cell_U*Tumor_targeting_T_cells_T/Total_cells_N
chi_D = 4.675397 Reaction: => Tumor_targeting_T_cells_T; Dendritic_Cells_D, Rate Law: compartment*chi_D*Dendritic_Cells_D
delta_V = 2.3 Reaction: Oncolytic_Adenovirus_V =>, Rate Law: compartment*delta_V*Oncolytic_Adenovirus_V
U_V = 0.0 Reaction: => Oncolytic_Adenovirus_V, Rate Law: compartment*U_V
delta_A = 0.35 Reaction: Naive_T_cells_A =>, Rate Law: compartment*delta_A*Naive_T_cells_A
chi_A = 1.0 Reaction: => Tumor_targeting_T_cells_T; Naive_T_cells_A, Rate Law: compartment*chi_A*Naive_T_cells_A
r = 0.3198 Reaction: => Uninfected_Tumor_Cell_U, Rate Law: compartment*r*Uninfected_Tumor_Cell_U
delta_T = 0.35 Reaction: Tumor_targeting_T_cells_T =>, Rate Law: compartment*delta_T*Tumor_targeting_T_cells_T
C_A = 5.17E-4 Reaction: => Naive_T_cells_A; Infected_Cancer_Cell_I, Rate Law: compartment*C_A*Infected_Cancer_Cell_I
beta = 1.008538 Reaction: Uninfected_Tumor_Cell_U => Infected_Cancer_Cell_I; Oncolytic_Adenovirus_V, Total_cells_N, Rate Law: compartment*beta*Uninfected_Tumor_Cell_U*Oncolytic_Adenovirus_V/Total_cells_N
U_D = 0.0 Reaction: => Dendritic_Cells_D, Rate Law: compartment*U_D
alpha = 3.0; delta_I = 1.0 Reaction: => Oncolytic_Adenovirus_V; Infected_Cancer_Cell_I, Rate Law: compartment*alpha*delta_I*Infected_Cancer_Cell_I
delta_D = 0.35 Reaction: Dendritic_Cells_D =>, Rate Law: compartment*delta_D*Dendritic_Cells_D

States:

Name Description
total tumor cells [B16-F10 cell; cancer]
Infected Cancer Cell I [cancer; B16-F10 cell; Abnormal]
Naive T cells A [Natural Killer T-Cell]
Uninfected Tumor Cell U [cancer; B16-F10 cell]
Dendritic Cells D [Dendritic Cell; dendritic cell]
Total cells N [cancer; B16-F10 cell; Natural Killer T-Cell]
Oncolytic Adenovirus V [Adenoviridae; Oncolytic]
Tumor targeting T cells T [Natural Killer T-Cell; Targeting]

Observables: none

We present a mathematical model for analyzing, simulating, and quantitating the dynamic and steady-state characteristics…

We present a mathematical model for analyzing, simulating, and quantitating the dynamic and steady-state characteristics of receptor-mediated endocytosis. The basic processes considered by the model are ligand-receptor binding, diffusion of receptors and ligand-receptor complexes in the plane of the membrane toward and away from coated pits, binding of ligand-receptor complexes to coated pit proteins, endocytosis of coated pit contents, degradation of ligand, and recycling of undegraded receptors. The model accounts quantitatively for a wide variety of kinetic data and makes new predictions about steady-state characteristics. We show that for homogeneous receptors the slope of the Scatchard plot is not necessarily constant but can have a positive or negative derivative, depending on the concentration of coated pit proteins and their reactivity. This finding suggests that binding data, which show linear and concave curves, might be explainable be a simple coated pit-related mechanism. Similarly the relationship between the x-intercept and the number of receptors is also affected by kinetic parameters controlling endocytosis. We briefly discuss these results in terms of possible mechanisms for the action of tumor promoters, the large variations in receptor number and affinity in the literature, and methods for quantitative characterization of parameters. link: http://identifiers.org/pubmed/6149699

Parameters: none

States: none

Observables: none

Publication includes a mathematical model for how retinoic acid affects thrombomodulin gene and mRNA expression as well…

BACKGROUND:Clinical studies have shown that all-trans retinoic acid (RA), which is often used in treatment of cancer patients, improves hemostatic parameters and bleeding complications such as disseminated intravascular coagulation (DIC). However, the mechanisms underlying this improvement have yet to be elucidated. In vitro studies have reported that RA upregulates thrombomodulin (TM) expression on the endothelial cell surface. The objective of this study was to investigate how and to what extent the TM concentration changes after RA treatment in cancer patients, and how this variation influences the blood coagulation cascade. RESULTS:In this study, we introduced an ordinary differential equation (ODE) model of gene expression for the RA-induced upregulation of TM concentration. Coupling the gene expression model with a two-compartment pharmacokinetic model of RA, we obtained the time-dependent changes in TM and thrombomodulin-mRNA (TMR) concentrations following oral administration of RA. Our results indicated that the TM concentration reached its peak level almost 14 h after taking a single oral dose (110 [Formula: see text]) of RA. Continuous treatment with RA resulted in oscillatory expression of TM on the endothelial cell surface. We then coupled the gene expression model with a mechanistic model of the coagulation cascade, and showed that the elevated levels of TM over the course of RA therapy with a single daily oral dose (110 [Formula: see text]) of RA, reduced the peak thrombin levels and endogenous thrombin potential (ETP) up to 50 and 49%, respectively. We showed that progressive reductions in plasma levels of RA, observed in continuous RA therapy with a once-daily oral dose (110 [Formula: see text]) of RA, did not affect TM-mediated reduction of thrombin generation significantly. This finding prompts the hypothesis that continuous RA treatment has more consistent therapeutic effects on coagulation disorders than on cancer. CONCLUSIONS:Our results indicate that the oscillatory upregulation of TM expression on the endothelial cells over the course of RA therapy could potentially contribute to the treatment of coagulation abnormalities in cancer patients. Further studies on the impacts of RA therapy on the procoagulant activity of cancer cells are needed to better elucidate the mechanisms by which RA therapy improves hemostatic abnormalities in cancer. link: http://identifiers.org/pubmed/30764845

Parameters: none

States: none

Observables: none

One of the common misconceptions about COVID-19 disease is to assume that we will not see a recurrence after the first w…

One of the common misconceptions about COVID-19 disease is to assume that we will not see a recurrence after the first wave of the disease has subsided. This completely wrong perception causes people to disregard the necessary protocols and engage in some misbehavior, such as routine socializing or holiday travel. These conditions will put double pressure on the medical staff and endanger the lives of many people around the world. In this research, we are interested in analyzing the existing data to predict the number of infected people in the second wave of out-breaking COVID-19 in Iran. For this purpose, a model is proposed. The mathematical analysis corresponded to the model is also included in this paper. Based on proposed numerical simulations, several scenarios of progress of COVID-19 corresponding to the second wave of the disease in the coming months, will be discussed. We predict that the second wave of will be most severe than the first one. From the results, improving the recovery rate of people with weak immune systems via appropriate medical incentives is resulted as one of the most effective prescriptions to prevent the widespread unbridled outbreak of the second wave of COVID-19. link: http://identifiers.org/pubmed/32834656

Parameters: none

States: none

Observables: none

Computational modeling to predict MAP3K8 effects as mediator of resistance to vemurafenib in thyroid cancer stem cells

MOTIVATION: Val600Glu (V600E) mutation is the most common BRAF mutation detected in thyroid cancer. Hence, recent research efforts have been performed trying to explore several inhibitors of the V600E mutation-containing BRAF kinase as potential therapeutic options in thyroid cancer refractory to standard interventions. Among them, vemurafenib is a selective BRAF inhibitor approved by FDA for clinical practice. Unfortunately, vemurafenib often displays limited efficacy in poorly differentiated and anaplastic thyroid carcinomas probably because of intrinsic and/or acquired resistance mechanisms. In this view, cancer stem cells may represent a possible mechanism of resistance to vemurafenib, due to their self-renewal and chemo resistance properties.

RESULTS: We present a computational framework to suggest new potential targets to overcome drug resistance. It has been validated with an in vitro model based upon a spheroid-forming method able to isolate thyroid cancer stem cells that may mimic resistance to vemurafenib. Indeed, vemurafenib did not inhibit cell proliferation of BRAF V600E thyroid cancer stem cells, but rather stimulated cell proliferation along with a paradoxical overactivation of ERK and AKT pathways. The computational model identified a fundamental role of mitogen-activated protein kinase 8 (MAP3K8), a serine/threonine kinase expressed in thyroid cancer stem cells, in mediating this drug resistance. To confirm model prediction, we set a suitable in vitro experiment revealing that the treatment with MAP3K8 inhibitor restored the effect of vemurafenib in terms of both DNA fragmentation and PARP cleavage (apoptosis) in thyroid cancer stem cells. Moreover, MAP3K8 expression levels may be a useful marker to predict the response to vemurafenib. link: http://identifiers.org/pubmed/30481266

Parameters:

Name Description
km=0.1; Kcat=0.096 Reaction: species_9 => species_8; species_6, Rate Law: compartment_0*Kcat*species_6*species_9/(km+species_9)
Kcat=0.1; km=0.1 Reaction: IKKbeta_IKKalfa_IKKgamma_bRafINH_Active => species_10; bRafMutated, Rate Law: compartment_0*piecewise(Kcat*bRafMutated*IKKbeta_IKKalfa_IKKgamma_bRafINH_Active/(km+IKKbeta_IKKalfa_IKKgamma_bRafINH_Active), bRafMutated <= 1, 0)
k1=0.1 Reaction: PDK1Active => PDK1Inactive, Rate Law: compartment_0*k1*PDK1Active
Kcat=0.12; km=0.1 Reaction: species_7 => species_6; species_4, Rate Law: compartment_0*Kcat*species_4*species_7/(km+species_7)

States:

Name Description
species 9 [Dual specificity mitogen-activated protein kinase kinase 1; inactive]
FGF [Fibroblast growth factor 1]
TRAF1 TRAF2 TRAF3 Active [TNF receptor-associated factor 2; Q13114; Q13077; Active]
species 1 [Epidermal growth factor receptor]
mTORC2Active [Active; Rapamycin-insensitive companion of mTOR; Serine/threonine-protein kinase mTOR; Active]
species 16 [RAC-alpha serine/threonine-protein kinase; phosphorylated]
PDK1Inactive [3-phosphoinositide-dependent protein kinase 1; inactive]
species 0 [Epidermal growth factor receptor; phosphorylated]
species 25 [Pro-epidermal growth factor]
species 8 [Dual specificity mitogen-activated protein kinase kinase 1; Active]
species 17 [RAC-alpha serine/threonine-protein kinase]
species 15 [Phosphatidylinositol 3-kinase regulatory subunit alpha; inactive]
species 2 [Active; Son of sevenless homolog 1]
species 6 [RAF proto-oncogene serine/threonine-protein kinase; Active]
IKKbeta IKKalfa IKKgamma Inactive [Inhibitor of nuclear factor kappa-B kinase subunit alpha; Inhibitor of nuclear factor kappa-B kinase subunit beta; NF-kappa-B essential modulator; inactive]
Tpl2 NF kB bRafINH Inactive [P41279; CHEBI:75047; Nuclear factor NF-kappa-B p105 subunit; inactive]
species 10 [Mitogen-activated protein kinase 1; phosphorylated]
freeFGFR [Fibroblast growth factor receptor 1]
species 11 [Mitogen-activated protein kinase 1]
pTNFR2 [P20333; phosphorylated]
Tpl2 NF kB RasINH Active [Nuclear factor NF-kappa-B p105 subunit; C1902; P41279; Active]
PDK1Active [3-phosphoinositide-dependent protein kinase 1; Active]
bRafMutated [Serine/threonine-protein kinase B-raf; Mutation Abnormality]
species 3 [Son of sevenless homolog 1; inactive]
PIP3Inactive [1-phosphatidyl-1D-myo-inositol 4,5-bisphosphate]
IKKbeta IKKalfa IKKgamma Active [Inhibitor of nuclear factor kappa-B kinase subunit beta; NF-kappa-B essential modulator; Inhibitor of nuclear factor kappa-B kinase subunit alpha; Active]
TNF [Q5STB3]
freeTNFR1 [Tumor necrosis factor receptor superfamily member 1A]
species 4 [GTPase HRas; Active]
NIKActive [Mitogen-activated protein kinase kinase kinase 14; Active]
Grb2Inactive [Growth factor receptor-bound protein 2; inactive]
TRADD TRAF2 TRAF5 RIP1 Inactive [TNF receptor-associated factor 2; O00463; Receptor-interacting serine/threonine-protein kinase 1; Tumor necrosis factor receptor type 1-associated DEATH domain protein; inactive]
TRADD TRAF2 TRAF5 RIP1 Active [O00463; Receptor-interacting serine/threonine-protein kinase 1; TNF receptor-associated factor 2; Tumor necrosis factor receptor type 1-associated DEATH domain protein; Active]
TAB1 TAB2 TAB3 TAK1 Active [TGF-beta-activated kinase 1 and MAP3K7-binding protein 3; TGF-beta-activated kinase 1 and MAP3K7-binding protein 2; Mitogen-activated protein kinase kinase kinase 7; Q15750; Active]
pTNFR1 [Tumor necrosis factor receptor superfamily member 1A; phosphorylated]
mTORC1Inactive [inactive; Regulatory-associated protein of mTOR; Serine/threonine-protein kinase mTOR; inactive]
freeTNFR2 [P20333]
species 5 [GTPase HRas; inactive]
pFGFR [Fibroblast growth factor receptor 1; phosphorylated]
mTORC1Active [Active; Regulatory-associated protein of mTOR; Serine/threonine-protein kinase mTOR; Active]
TRAF1 TRAF2 TRAF3 bRafINH Inactive [CHEBI:75047; Q13077; Q13114; TNF receptor-associated factor 2; inactive]
TRAF1 TRAF2 TRAF3 Inactive [Q13114; Q13077; TNF receptor-associated factor 2; inactive]
species 14 [Phosphatidylinositol 3-kinase regulatory subunit alpha; Active]
species 7 [RAF proto-oncogene serine/threonine-protein kinase; inactive]

Observables: none

Giantsos-Adams2013 - Growth of glycocalyx under static conditionsThis model is described in the article: [Heparan Sulfa…

The local hemodynamic shear stress waveforms present in an artery dictate the endothelial cell phenotype. The observed decrease of the apical glycocalyx layer on the endothelium in atheroprone regions of the circulation suggests that the glycocalyx may have a central role in determining atherosclerotic plaque formation. However, the kinetics for the cells' ability to adapt its glycocalyx to the environment have not been quantitatively resolved. Here we report that the heparan sulfate component of the glycocalyx of HUVECs increases by 1.4-fold following the onset of high shear stress, compared to static cultured cells, with a time constant of 19 h. Cell morphology experiments show that 12 h are required for the cells to elongate, but only after 36 h have the cells reached maximal alignment to the flow vector. Our findings demonstrate that following enzymatic degradation, heparan sulfate is restored to the cell surface within 12 h under flow whereas the time required is 20 h under static conditions. We also propose a model describing the contribution of endocytosis and exocytosis to apical heparan sulfate expression. The change in HS regrowth kinetics from static to high-shear EC phenotype implies a differential in the rate of endocytic and exocytic membrane turnover. link: http://identifiers.org/pubmed/23805169

Parameters: none

States: none

Observables: none

Giantsos-Adams2013 - Growth of glycocalyx under static conditionsThis model is described in the article: [Heparan Sulfa…

The local hemodynamic shear stress waveforms present in an artery dictate the endothelial cell phenotype. The observed decrease of the apical glycocalyx layer on the endothelium in atheroprone regions of the circulation suggests that the glycocalyx may have a central role in determining atherosclerotic plaque formation. However, the kinetics for the cells' ability to adapt its glycocalyx to the environment have not been quantitatively resolved. Here we report that the heparan sulfate component of the glycocalyx of HUVECs increases by 1.4-fold following the onset of high shear stress, compared to static cultured cells, with a time constant of 19 h. Cell morphology experiments show that 12 h are required for the cells to elongate, but only after 36 h have the cells reached maximal alignment to the flow vector. Our findings demonstrate that following enzymatic degradation, heparan sulfate is restored to the cell surface within 12 h under flow whereas the time required is 20 h under static conditions. We also propose a model describing the contribution of endocytosis and exocytosis to apical heparan sulfate expression. The change in HS regrowth kinetics from static to high-shear EC phenotype implies a differential in the rate of endocytic and exocytic membrane turnover. link: http://identifiers.org/pubmed/23805169

Parameters:

Name Description
k3=0.96 Reaction: s6 => s1, Rate Law: default*Function_for_k3(default, k3, s6)
k2=0.05 Reaction: s2 => s1, Rate Law: default*Function_for_k2(default, k2, s2)
k1=0.05 Reaction: s1 => s2, Rate Law: default*Function_for_k1(default, k1, s1)
k8=0.005 Reaction: s4 => release, Rate Law: default*Function_for_k8(default, k8, s4)
k7=0.01 Reaction: s3 => s4, Rate Law: default*Function_for_k7(default, k7, s3)
k4=0.033 Reaction: s1 => shedding, Rate Law: default*Function_for_k4(default, k4, s1)
k6=0.01 Reaction: s2 => s3, Rate Law: default*Function_for_k6(default, k6, s2)

States:

Name Description
s1 [Heparan Sulfate]
release [Release]
shedding shedding
s6 [Golgi Apparatus]
s2 [early endosome]
s4 [lysosome]
s3 [late endosome]

Observables: none

A quantitative model of the initiation of DNA replication in Saccharomyces cerevisiae predicts the effects of system per…

Eukaryotic cell proliferation involves DNA replication, a tightly regulated process mediated by a multitude of protein factors. In budding yeast, the initiation of replication is facilitated by the heterohexameric origin recognition complex (ORC). ORC binds to specific origins of replication and then serves as a scaffold for the recruitment of other factors such as Cdt1, Cdc6, the Mcm2-7 complex, Cdc45 and the Dbf4-Cdc7 kinase complex. While many of the mechanisms controlling these associations are well documented, mathematical models are needed to explore the network's dynamic behaviour. We have developed an ordinary differential equation-based model of the protein-protein interaction network describing replication initiation.The model was validated against quantified levels of protein factors over a range of cell cycle timepoints. Using chromatin extracts from synchronized Saccharomyces cerevisiae cell cultures, we were able to monitor the in vivo fluctuations of several of the aforementioned proteins, with additional data obtained from the literature. The model behaviour conforms to perturbation trials previously reported in the literature, and accurately predicts the results of our own knockdown experiments. Furthermore, we successfully incorporated our replication initiation model into an established model of the entire yeast cell cycle, thus providing a comprehensive description of these processes.This study establishes a robust model of the processes driving DNA replication initiation. The model was validated against observed cell concentrations of the driving factors, and characterizes the interactions between factors implicated in eukaryotic DNA replication. Finally, this model can serve as a guide in efforts to generate a comprehensive model of the mammalian cell cycle in order to explore cancer-related phenotypes. link: http://identifiers.org/pubmed/22738223

Parameters: none

States: none

Observables: none

MODEL1173105855 @ v0.0.1

This a model from the article: A Case Study in Model-driven Synthetic Biology David Gilbert, Monika Heiner, Susan Ro…

We report on a case study in synthetic biology, demonstrating the model-driven design of a self-powering electrochemical biosensor. An essential result of the design process is a general template of a biosensor, which can be instantiated to be adapted to specific pollutants. This template represents a gene expression network extended by metabolic activity. We illustrate the model-based analysis of this template using qualitative, stochastic and continuous Petri nets and related analysis techniques, contributing to a reliable and robust design. link: http://identifiers.org/doi/10.1007/978-0-387-09655-1_15

Parameters: none

States: none

Observables: none

MODEL1009150000 @ v0.0.1

This is the genome-scale metabolic network of a hepatocyte described in the article: HepatoNet1: a comprehensive metab…

We present HepatoNet1, the first reconstruction of a comprehensive metabolic network of the human hepatocyte that is shown to accomplish a large canon of known metabolic liver functions. The network comprises 777 metabolites in six intracellular and two extracellular compartments and 2539 reactions, including 1466 transport reactions. It is based on the manual evaluation of >1500 original scientific research publications to warrant a high-quality evidence-based model. The final network is the result of an iterative process of data compilation and rigorous computational testing of network functionality by means of constraint-based modeling techniques. Taking the hepatic detoxification of ammonia as an example, we show how the availability of nutrients and oxygen may modulate the interplay of various metabolic pathways to allow an efficient response of the liver to perturbations of the homeostasis of blood compounds. link: http://identifiers.org/pubmed/20823849

Parameters: none

States: none

Observables: none

In Italy, 128,948 confirmed cases and 15,887 deaths of people who tested positive for SARS-CoV-2 were registered as of 5…

In Italy, 128,948 confirmed cases and 15,887 deaths of people who tested positive for SARS-CoV-2 were registered as of 5 April 2020. Ending the global SARS-CoV-2 pandemic requires implementation of multiple population-wide strategies, including social distancing, testing and contact tracing. We propose a new model that predicts the course of the epidemic to help plan an effective control strategy. The model considers eight stages of infection: susceptible (S), infected (I), diagnosed (D), ailing (A), recognized (R), threatened (T), healed (H) and extinct (E), collectively termed SIDARTHE. Our SIDARTHE model discriminates between infected individuals depending on whether they have been diagnosed and on the severity of their symptoms. The distinction between diagnosed and non-diagnosed individuals is important because the former are typically isolated and hence less likely to spread the infection. This delineation also helps to explain misperceptions of the case fatality rate and of the epidemic spread. We compare simulation results with real data on the COVID-19 epidemic in Italy, and we model possible scenarios of implementation of countermeasures. Our results demonstrate that restrictive social-distancing measures will need to be combined with widespread testing and contact tracing to end the ongoing COVID-19 pandemic. link: http://identifiers.org/pubmed/32322102

Parameters: none

States: none

Observables: none

This model was used to describe the behaviour of the synthetic open loop circuit in yeast, published in [1]. The accompa…

Feedback loops in biological networks, among others, enable differentiation and cell cycle progression, and increase robustness in signal transduction. In natural networks, feedback loops are often complex and intertwined, making it challenging to identify which loops are mainly responsible for an observed behavior. However, minimal synthetic replicas could allow for such identification. Here, we engineered a synthetic permease-inducer-repressor system in Saccharomyces cerevisiae to analyze if a transport-mediated positive feedback loop could be a core mechanism for the switch-like behavior in the regulation of metabolic gene networks such as the S. cerevisiae GAL system or the Escherichia coli lac operon. We characterized the synthetic circuit using deterministic and stochastic mathematical models. Similar to its natural counterparts, our synthetic system shows bistable and hysteretic behavior, and the inducer concentration range for bistability as well as the switching rates between the two stable states depend on the repressor concentration. Our results indicate that a generic permease-inducer-repressor circuit with a single feedback loop is sufficient to explain the experimentally observed bistable behavior of the natural systems. We anticipate that the approach of reimplementing natural systems with orthogonal parts to identify crucial network components is applicable to other natural systems such as signaling pathways. link: http://identifiers.org/pubmed/27148753

Parameters: none

States: none

Observables: none

MODEL1011090000 @ v0.0.1

This is the genome scale metabolic reconstruction of Lactobacillus plantarum described in the article: Understanding t…

Situations of extremely low substrate availability, resulting in slow growth, are common in natural environments. To mimic these conditions, Lactobacillus plantarum was grown in a carbon-limited retentostat with complete biomass retention. The physiology of extremely slow-growing L. plantarum–as studied by genome-scale modeling and transcriptomics–was fundamentally different from that of stationary-phase cells. Stress resistance mechanisms were not massively induced during transition to extremely slow growth. The energy-generating metabolism was remarkably stable and remained largely based on the conversion of glucose to lactate. The combination of metabolic and transcriptomic analyses revealed behaviors involved in interactions with the environment, more particularly with plants: production of plant hormones or precursors thereof, and preparedness for the utilization of plant-derived substrates. Accordingly, the production of compounds interfering with plant root development was demonstrated in slow-growing L. plantarum. Thus, conditions of slow growth and limited substrate availability seem to trigger a plant environment-like response, even in the absence of plant-derived material, suggesting that this might constitute an intrinsic behavior in L. plantarum. link: http://identifiers.org/pubmed/20865006

Parameters: none

States: none

Observables: none

BIOMD0000000098 @ v0.0.1

In a variety of cells, hormonal or neurotransmitter signals elicit a train of intracellular Ca2+ spikes. The analysis of…

The model reproduces the time profile of cytosolic and intracellular calcium as depicted in the upper panel of Fig 2 in the paper. The model was successfully tested on MathSBML and Jarnac.

This model originates from BioModels Database: A Database of Annotated Published Models. It is copyright (c) 2005-2009 The BioModels Team.

For more information see the terms of use.

To cite BioModels Database, please use Le Novère N., Bornstein B., Broicher A., Courtot M., Donizelli M., Dharuri H., Li L., Sauro H., Schilstra M., Shapiro B., Snoep J.L., Hucka M. (2006) BioModels Database: A Free, Centralized Database of Curated, Published, Quantitative Kinetic Models of Biochemical and Cellular Systems Nucleic Acids Res., 34: D689-D691.

Parameters:

Name Description
v0 = 1.0 uM_per_sec Reaction: => Z, Rate Law: cytosol*v0
beta = 0.301 dimensionless; v1 = 7.3 uM_per_sec Reaction: => Z, Rate Law: cytosol*v1*beta
k = 10.0 sec_inv Reaction: Z =>, Rate Law: cytosol*k*Z
kf = 1.0 sec_inv Reaction: Y => Z, Rate Law: store*kf*Y
Kr = 2.0 uM; m = 2.0 dimensionless; Ka = 0.9 uM; Vm3 = 500.0 uM_per_sec; p = 4.0 dimensionless Reaction: Y => Z, Rate Law: store*Vm3*Y^m*Z^p/((Kr^m+Y^m)*(Ka^p+Z^p))
K2 = 1.0 uM; n = 2.0 dimensionless; Vm2 = 65.0 uM_per_sec Reaction: Z => Y, Rate Law: cytosol*Vm2*Z^n/(K2^n+Z^n)

States:

Name Description
Y [calcium(2+); Calcium cation]
Z [calcium(2+); Calcium cation]

Observables: none

BIOMD0000000003 @ v0.0.1

Goldbeter1991 - Min Mit OscilMinimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase. This mo…

A minimal model for the mitotic oscillator is presented. The model, built on recent experimental advances, is based on the cascade of post-translational modification that modulates the activity of cdc2 kinase during the cell cycle. The model pertains to the situation encountered in early amphibian embryos, where the accumulation of cyclin suffices to trigger the onset of mitosis. In the first cycle of the bicyclic cascade model, cyclin promotes the activation of cdc2 kinase through reversible dephosphorylation, and in the second cycle, cdc2 kinase activates a cyclin protease by reversible phosphorylation. That cyclin activates cdc2 kinase while the kinase triggers the degradation of cyclin has suggested that oscillations may originate from such a negative feedback loop [Félix, M. A., Labbé, J. C., Dorée, M., Hunt, T. & Karsenti, E. (1990) Nature (London) 346, 379-382]. This conjecture is corroborated by the model, which indicates that sustained oscillations of the limit cycle type can arise in the cascade, provided that a threshold exists in the activation of cdc2 kinase by cyclin and in the activation of cyclin proteolysis by cdc2 kinase. The analysis shows how miototic oscillations may readily arise from time lags associated with these thresholds and from the delayed negative feedback provided by cdc2-induced cyclin degradation. A mechanism for the origin of the thresholds is proposed in terms of the phenomenon of zero-order ultrasensitivity previously described for biochemical systems regulated by covalent modification. link: http://identifiers.org/pubmed/1833774

Parameters:

Name Description
K2=0.005; V2=1.5 Reaction: M =>, Rate Law: cell*M*V2*(K2+M)^-1
K1=0.005; V1 = NaN Reaction: => M, Rate Law: cell*(1+-1*M)*V1*(K1+-1*M+1)^-1
kd=0.01 Reaction: C =>, Rate Law: C*cell*kd
vd=0.25; Kd=0.02 Reaction: C => ; X, Rate Law: C*cell*vd*X*(C+Kd)^-1
vi=0.025 Reaction: => C, Rate Law: cell*vi
K3=0.005; V3 = NaN Reaction: => X, Rate Law: cell*V3*(1+-1*X)*(K3+-1*X+1)^-1
V4=0.5; K4=0.005 Reaction: X =>, Rate Law: cell*V4*X*(K4+X)^-1

States:

Name Description
M [Cyclin-dependent kinase 1-B; Cyclin-dependent kinase 1-A]
C [Cyclin-C; IPR006670]
X [anaphase-promoting complex; CDC20:p-APC/C [cytosol]]

Observables: none

Goldbeter1991 - Min Mit Oscil, Expl InactThis model represents the inactive forms of CDC-2 Kinase and Cyclin Protease as…

A minimal model for the mitotic oscillator is presented. The model, built on recent experimental advances, is based on the cascade of post-translational modification that modulates the activity of cdc2 kinase during the cell cycle. The model pertains to the situation encountered in early amphibian embryos, where the accumulation of cyclin suffices to trigger the onset of mitosis. In the first cycle of the bicyclic cascade model, cyclin promotes the activation of cdc2 kinase through reversible dephosphorylation, and in the second cycle, cdc2 kinase activates a cyclin protease by reversible phosphorylation. That cyclin activates cdc2 kinase while the kinase triggers the degradation of cyclin has suggested that oscillations may originate from such a negative feedback loop [Félix, M. A., Labbé, J. C., Dorée, M., Hunt, T. & Karsenti, E. (1990) Nature (London) 346, 379-382]. This conjecture is corroborated by the model, which indicates that sustained oscillations of the limit cycle type can arise in the cascade, provided that a threshold exists in the activation of cdc2 kinase by cyclin and in the activation of cyclin proteolysis by cdc2 kinase. The analysis shows how miototic oscillations may readily arise from time lags associated with these thresholds and from the delayed negative feedback provided by cdc2-induced cyclin degradation. A mechanism for the origin of the thresholds is proposed in terms of the phenomenon of zero-order ultrasensitivity previously described for biochemical systems regulated by covalent modification. link: http://identifiers.org/pubmed/1833774

Parameters:

Name Description
K2=0.005; V2=1.5 Reaction: M => MI, Rate Law: cell*M*V2*(K2+M)^-1
K1=0.005; V1 = NaN Reaction: MI => M, Rate Law: cell*MI*V1*(K1+MI)^-1
kd=0.01 Reaction: C =>, Rate Law: C*cell*kd
vd=0.25; Kd=0.02 Reaction: C => ; X, Rate Law: C*cell*vd*X*(C+Kd)^-1
vi=0.025 Reaction: => C, Rate Law: cell*vi
K3=0.005; V3 = NaN Reaction: XI => X, Rate Law: cell*V3*XI*(K3+XI)^-1
V4=0.5; K4=0.005 Reaction: X => XI, Rate Law: cell*V4*X*(K4+X)^-1

States:

Name Description
MI [Cyclin-dependent kinase 1-B; Cyclin-dependent kinase 1-A]
M [Cyclin-dependent kinase 1-B; Cyclin-dependent kinase 1-A]
C [IPR006670]
XI Inactive Cyclin Protease
X Active Cyclin Protease

Observables: none

BIOMD0000000016 @ v0.0.1

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

The mechanism of circadian oscillations in the period protein (PER) in Drosophila is investigated by means of a theoretical model. Taking into account recent experimental observations, the model for the circadian clock is based on multiple phosphorylation of PER and on the negative feedback exerted by PER on the transcription of the period (per) gene. This minimal biochemical model provides a molecular basis for circadian oscillations of the limit cycle type. During oscillations, the peak in per mRNA precedes by several hours the peak in total PER protein. The results support the view that multiple PER phosphorylation introduces times delays which strengthen the capability of negative feedback to produce oscillations. The analysis shows that the rhythm only occurs in a range bounded by two critical values of the maximum rate of PER degradation. A similar result is obtained with respect to the rate of PER transport into the nucleus. The results suggest a tentative explanation for the altered period of per mutants, in terms of variations in the rate of PER degradation. link: http://identifiers.org/pubmed/8587874

Parameters:

Name Description
K3=2.0; V3=5.0 Reaction: P1 => P2, Rate Law: CYTOPLASM*V3*P1/(K3+P1)
V4=2.5; K4=2.0 Reaction: P2 => P1, Rate Law: CYTOPLASM*V4*P2/(K4+P2)
ks=0.38 Reaction: EmptySet => P0; M, Rate Law: ks*M*default
Vm=0.65; Km=0.5 Reaction: M => EmptySet, Rate Law: Vm*M*CYTOPLASM/(Km+M)
k2=1.3 Reaction: Pn => P2, Rate Law: k2*Pn*compartment_0000004
K2=2.0; V2=1.58 Reaction: P1 => P0, Rate Law: CYTOPLASM*V2*P1/(K2+P1)
KI=1.0; Vs=0.76; n=4.0 Reaction: EmptySet => M; Pn, Rate Law: default*Vs*KI^n/(KI^n+Pn^n)
k1=1.9 Reaction: P2 => Pn, Rate Law: k1*P2*CYTOPLASM
Vd=0.95; Kd=0.2 Reaction: P2 => EmptySet, Rate Law: CYTOPLASM*Vd*P2/(Kd+P2)
K1=2.0; V1=3.2 Reaction: P0 => P1, Rate Law: CYTOPLASM*V1*P0/(K1+P0)

States:

Name Description
M [messenger RNA; RNA]
Pn [Period circadian protein]
Pt [Period circadian protein]
P2 [Period circadian protein]
P1 [Period circadian protein]
P0 [Period circadian protein]

Observables: none

We consider a minimal cascade model previously proposed for the mitotic oscillator driving the embryonic cell division c…

We consider a minimal cascade model previously proposed for the mitotic oscillator driving the embryonic cell division cycle. The model is based on a bicyclic phosphorylation-dephosphorylation cascade involving cyclin and cdc2 kinase. By constructing stability diagrams showing domains of periodic behavior as a function of the maximum rates of the kinases and phosphatases involved in the two cycles of the cascade, we investigate the role of these converter enzymes in the oscillatory mechanism. Oscillations occur when the balance of kinase and phosphatase rates in each cycle is in a range bounded by two critical values. The results suggest ways to arrest the mitotic oscillator by altering the maximum rates of the converter enzymes. These results bear on the control of cell proliferation. link: http://identifiers.org/pubmed/8631387

Parameters:

Name Description
V3 = 0.0; K3 = 0.01 Reaction: => X, Rate Law: compartment*V3*(1-X)/((K3+1)-X)
K4 = 0.01; V4 = 0.5 Reaction: X =>, Rate Law: compartment*V4*X/(K4+X)
Kd = 0.02; vd = 0.25 Reaction: C => ; X, Rate Law: compartment*vd*X*C/(Kd+C)
V2 = 1.5; K2 = 0.01 Reaction: M =>, Rate Law: compartment*V2*M/(K2+M)
vi = 0.05 Reaction: => C, Rate Law: compartment*vi
K1 = 0.01; V1 = 0.0 Reaction: => M, Rate Law: compartment*V1*(1-M)/((K1+1)-M)
kd = 0.01 Reaction: C =>, Rate Law: compartment*kd*C

States:

Name Description
M [Kinase]
C [Rate Constant; Guanidine]
X [Phosphatase]

Observables: none

BIOMD0000000079 @ v0.0.1

This model is according to the paper of *A model for the dynamics of human weight cycling* by A. Goldbeter 2006.The fig…

The resolution to lose weight by cognitive restraint of nutritional intake often leads to repeated bouts of weight loss and regain, a phenomenon known as weight cycling or "yo-yo dieting". A simple mathematical model for weight cycling is presented. The model is based on a feedback of psychological nature by which a subject decides to reduce dietary intake once a threshold weight is exceeded. The analysis of the model indicates that sustained oscillations in body weight occur in a parameter range bounded by critical values. Only outside this range can body weight reach a stable steady state. The model provides a theoretical framework that captures key facets of weight cycling and suggests ways to control the phenomenon. The view that weight cycling represents self-sustained oscillations has indeed specific implications. In dynamical terms, to bring weight cycling to an end, parameter values should change in such a way as to induce the transition of body weight from sustained oscillations around an unstable steady state to a stable steady state. Maintaining weight under a critical value should prevent weight cycling and allow body weight to stabilize below the oscillatory range. link: http://identifiers.org/pubmed/16595882

Parameters:

Name Description
V=0.1; Km=0.2 Reaction: P =>, Rate Law: V*P/(Km+P)
k3=0.01; V3=6.0 Reaction: => R; P, Rate Law: P*V3*(1-R)/(k3+(1-R))
K1=0.01; V1=1.0 Reaction: => Q, Rate Law: V1*(1-Q)/(K1+(1-Q))
K2=0.01; V2=1.5 Reaction: Q => ; R, Rate Law: V2*R*Q/(K2+Q)
a=0.1 Reaction: => P; Q, Rate Law: body*a*Q
V=2.5; Km=0.01 Reaction: R =>, Rate Law: V*R/(Km+R)

States:

Name Description
Q Q
P P
R R

Observables: none

BIOMD0000000275 @ v0.0.1

This is the simple model without diffusion described in th epublication Sharp developmental thresholds defined through…

The establishment of thresholds along morphogen gradients in the embryo is poorly understood. Using mathematical modeling, we show that mutually inhibitory gradients can generate and position sharp morphogen thresholds in the embryonic space. Taking vertebrate segmentation as a paradigm, we demonstrate that the antagonistic gradients of retinoic acid (RA) and Fibroblast Growth Factor (FGF) along the presomitic mesoderm (PSM) may lead to the coexistence of two stable steady states. Here, we propose that this bistability is associated with abrupt switches in the levels of FGF and RA signaling, which permit the synchronized activation of segmentation genes, such as mesp2, in successive cohorts of PSM cells in response to the segmentation clock, thereby defining the future segments. Bistability resulting from mutual inhibition of RA and FGF provides a molecular mechanism for the all-or-none transitions assumed in the "clock and wavefront" somitogenesis model. Given that mutually antagonistic signaling gradients are common in development, such bistable switches could represent an important principle underlying embryonic patterning. link: http://identifiers.org/pubmed/17497689

Parameters:

Name Description
kd4 = 1.0 per min Reaction: F =>, Rate Law: PSM*kd4*F
m = 2.0 dimensionless; Ki = 0.2 nM; ks3 = 1.0 per min Reaction: => F; RA, M_F, Rate Law: PSM*ks3*M_F*Ki^m/(Ki^m+RA^m)
vs1 = NaN nM per min Reaction: => RA, Rate Law: PSM*vs1
ks2 = 1.0 per min Reaction: => C; M_C, Rate Law: PSM*ks2*M_C
kd5 = 0.0 per min Reaction: RA =>, Rate Law: PSM*kd5*RA
kd1 = 1.0 per nM per min Reaction: RA => ; C, Rate Law: PSM*kd1*RA*C
kd3 = 1.0 per min Reaction: M_C =>, Rate Law: PSM*kd3*M_C
kd2 = 0.28 per min Reaction: C =>, Rate Law: PSM*kd2*C
Ka = 0.2 nM; Vsc = 7.1 nM per min; n = 2.0 dimensionless; V0 = 0.365 nM per min Reaction: => M_C; F, Rate Law: PSM*(V0+Vsc*F^n/(Ka^n+F^n))
L = 50.0 arbit. length; M_0 = 5.0 nM; x = 15.0 arbit. length Reaction: M_F = M_0*x/L, Rate Law: missing

States:

Name Description
RA [retinoic acid]
C [retinoic acid 4-hydroxylase activity; CYP26C; CYP26B; CYP26A; Cytochrome P450 26B1; Cytochrome P450 26C1; Cytochrome P450 26A1; IPR001128]
M F [messenger RNA]
M C [IPR001128; m7G(5')pppR-mRNA; messenger RNA]
F [type 2 fibroblast growth factor receptor binding; type 1 fibroblast growth factor receptor binding; growth factor activity; Fibroblast growth factor 8; IPR002348]

Observables: none

This is a model of the coupled Natch, Wnt and FGF modules as described in: **A. Goldbeter and O. Pourquié** , Modelin…

The formation of somites in the course of vertebrate segmentation is governed by an oscillator known as the segmentation clock, which is characterized by a period ranging from 30 min to a few hours depending on the organism. This oscillator permits the synchronized activation of segmentation genes in successive cohorts of cells in the presomitic mesoderm in response to a periodic signal emitted by the segmentation clock, thereby defining the future segments. Recent microarray experiments [Dequeant, M.L., Glynn, E., Gaudenz, K., Wahl, M., Chen, J., Mushegian, A., Pourquie, O., 2006. A complex oscillating network of signaling genes underlies the mouse segmentation clock. Science 314, 1595-1598] indicate that the Notch, Wnt and Fibroblast Growth Factor (FGF) signaling pathways are involved in the mechanism of the segmentation clock. By means of computational modeling, we investigate the conditions in which sustained oscillations occur in these three signaling pathways. First we show that negative feedback mediated by the Lunatic Fringe protein on intracellular Notch activation can give rise to periodic behavior in the Notch pathway. We then show that negative feedback exerted by Axin2 on the degradation of beta-catenin through formation of the Axin2 destruction complex can produce oscillations in the Wnt pathway. Likewise, negative feedback on FGF signaling mediated by the phosphatase product of the gene MKP3/Dusp6 can produce oscillatory gene expression in the FGF pathway. Coupling the Wnt, Notch and FGF oscillators through common intermediates can lead to synchronized oscillations in the three signaling pathways or to complex periodic behavior, depending on the relative periods of oscillations in the three pathways. The phase relationships between cycling genes in the three pathways depend on the nature of the coupling between the pathways and on their relative autonomous periods. The model provides a framework for analyzing the dynamics of the segmentation clock in terms of a network of oscillating modules involving the Wnt, Notch and FGF signaling pathways. link: http://identifiers.org/pubmed/18308339

Parameters:

Name Description
theta = 1.5 dimensionless; vsB = 0.087 flux Reaction: => B, Rate Law: theta*cytosol*vsB
theta = 1.5 dimensionless; VMK = 5.08 flux; K1 = 0.28 nanomolar; KID = 0.5 nanomolar Reaction: B => Bp; AK, D, Kt, Rate Law: theta*cytosol*VMK*KID/(KID+D)*B/(K1+B)*AK/Kt
KaErk = 0.05 nanomolar; eta = 0.3 dimensionless; VMaErk = 3.3 flux Reaction: => ERKa; ERKi, Rasa, Rast, Rate Law: eta*cytosol*VMaErk*Rasa/Rast*ERKi/(KaErk+ERKi)
v0 = 0.06 flux; theta = 1.5 dimensionless Reaction: => MAx; BN, Rate Law: theta*cytosol*v0
theta = 1.5 dimensionless; vmd = 0.8 flux; Kmd = 0.48 nanomolar Reaction: MAx =>, Rate Law: theta*cytosol*vmd*MAx/(Kmd+MAx)
vdDusp = 2.0 flux; eta = 0.3 dimensionless; KdDusp = 0.5 nanomolar Reaction: Dusp =>, Rate Law: eta*cytosol*vdDusp*Dusp/(KdDusp+Dusp)
VMaX = 1.6 flux; eta = 0.3 dimensionless; KaX = 0.05 nanomolar Reaction: => Xa; ERKa, ERKt, Xi, Rate Law: eta*cytosol*VMaX*ERKa/ERKt*Xi/(KaX+Xi)
theta = 1.5 dimensionless; a1 = 1.8 second_order_rate_constant; d1 = 0.1 first_order_rate_constant Reaction: AK => A + K, Rate Law: theta*cytosol*(d1*AK-a1*A*K)
theta = 1.5 dimensionless; ksAx = 0.02 first_order_rate_constant Reaction: => A; MAx, Rate Law: theta*cytosol*ksAx*MAx
KdNa = 0.001 nanomolar; VdNa = 0.01 flux; epsilon = 0.3 dimensionless Reaction: Na =>, Rate Law: epsilon*cytosol*VdNa*Na/(KdNa+Na)
theta = 1.5 dimensionless; K2 = 0.03 nanomolar; VMP = 1.0 flux Reaction: Bp => B, Rate Law: theta*cytosol*VMP*Bp/(K2+Bp)
q = 2.0 dimensionless; KaMDusp = 0.5 nanomolar; eta = 0.3 dimensionless; VMsMDusp = 0.9 flux Reaction: => MDusp; Xa, Rate Law: eta*cytosol*VMsMDusp*Xa^q/(KaMDusp^q+Xa^q)
VdNan = 0.1 flux; KdNan = 0.001 nanomolar; epsilon = 0.3 dimensionless Reaction: Nan =>, Rate Law: epsilon*cytosol*VdNan*Nan/(KdNan+Nan)
VMaRas = 4.968 flux; KaFgf = 0.5 nanomolar; eta = 0.3 dimensionless; r = 2.0 dimensionless; KaRas = 0.103 nanomolar Reaction: => Rasa; Rasi, Fgf, Rate Law: eta*cytosol*VMaRas*Fgf^r/(KaFgf^r+Fgf^r)*Rasi/(KaRas+Rasi)
vdN = 2.82 flux; KdN = 1.4 nanomolar; epsilon = 0.3 dimensionless Reaction: N =>, Rate Law: epsilon*cytosol*vdN*N/(KdN+N)
KdErk = 0.05 nanomolar; eta = 0.3 dimensionless; kcDusp = 1.35 first_order_rate_constant Reaction: ERKa => ; Dusp, Rate Law: eta*cytosol*kcDusp*Dusp*ERKa/(KdErk+ERKa)
theta = 1.5 dimensionless; kd1 = 0.0 first_order_rate_constant Reaction: B =>, Rate Law: theta*cytosol*kd1*B
VMdMDusp = 0.5 flux; eta = 0.3 dimensionless; KdMDusp = 0.5 nanomolar Reaction: MDusp =>, Rate Law: eta*cytosol*VMdMDusp*MDusp/(KdMDusp+MDusp)
vdF = 0.39 flux; KdF = 0.37 nanomolar; epsilon = 0.3 dimensionless Reaction: F =>, Rate Law: epsilon*cytosol*vdF*F/(KdF+F)
ksF = 0.3 first_order_rate_constant; epsilon = 0.3 dimensionless Reaction: => F; MF, Rate Law: epsilon*cytosol*ksF*MF
vmF = 1.92 flux; KdMF = 0.768 nanomolar; epsilon = 0.3 dimensionless Reaction: MF =>, Rate Law: epsilon*cytosol*vmF*MF/(KdMF+MF)
theta = 1.5 dimensionless; m = 2.0 dimensionless; vMXa = 0.5 flux; KaXa = 0.05 nanomolar Reaction: => MAx; Xa, Rate Law: theta*cytosol*vMXa*Xa^m/(KaXa^m+Xa^m)
kt2 = 0.1 first_order_rate_constant; kt1 = 0.1 first_order_rate_constant; epsilon = 0.3 dimensionless Reaction: Na => Nan, Rate Law: epsilon*cytosol*(kt1*Na-kt2*Nan)
theta = 1.5 dimensionless; KaB = 0.7 nanomolar; vMB = 1.64 flux; n = 2.0 dimensionless Reaction: => MAx; BN, Rate Law: theta*cytosol*vMB*BN^n/(KaB^n+BN^n)
KdAx = 0.63 nanomolar; theta = 1.5 dimensionless; vdAx = 0.6 flux Reaction: A =>, Rate Law: theta*cytosol*vdAx*A/(KdAx+A)
VMdX = 0.5 flux; eta = 0.3 dimensionless; KdX = 0.05 nanomolar Reaction: Xa =>, Rate Law: eta*cytosol*VMdX*Xa/(KdX+Xa)
ksDusp = 0.5 first_order_rate_constant; eta = 0.3 dimensionless Reaction: => Dusp; MDusp, Rate Law: eta*cytosol*ksDusp*MDusp
theta = 1.5 dimensionless; kd2 = 7.062 first_order_rate_constant Reaction: Bp =>, Rate Law: theta*cytosol*kd2*Bp
vsFK = NaN flux; p = 2.0 dimensionless; KA = 0.05 nanomolar; epsilon = 0.3 dimensionless Reaction: => MF; Nan, Rate Law: epsilon*cytosol*vsFK*Nan^p/(KA^p+Nan^p)
j = 2.0 dimensionless; KIF = 0.5 nanomolar; epsilon = 0.3 dimensionless; kc = 3.45 first_order_rate_constant Reaction: N => Na; F, Rate Law: epsilon*cytosol*kc*N*KIF^j/(KIF^j+F^j)
theta = 1.5 dimensionless; kt3 = 0.7 first_order_rate_constant; kt4 = 1.5 first_order_rate_constant Reaction: BN => B, Rate Law: theta*cytosol*(kt4*BN-kt3*B)
vsN = 0.23 flux; epsilon = 0.3 dimensionless Reaction: => N, Rate Law: cytosol*epsilon*vsN
VMdRas = 0.41 flux; KdRas = 0.1 nanomolar; eta = 0.3 dimensionless Reaction: Rasa =>, Rate Law: eta*cytosol*VMdRas*Rasa/(KdRas+Rasa)

States:

Name Description
Na [IPR008297]
Xi [IPR006715]
Dusp [Dual specificity protein phosphatase 6]
A [Axin-2]
Rasi [GDP; IPR001806]
Nan [IPR008297]
ERKa [IPR008349]
Xa [IPR006715]
MF [messenger RNA; Beta-1,3-N-acetylglucosaminyltransferase lunatic fringe; IPR017374]
Bp [Catenin beta-1; IPR013284; Phosphoprotein]
B [IPR013284]
MAx [messenger RNA; AXIN2; Axin-2]
BN [Catenin beta-1; IPR013284]
MDusp [Dual specificity protein phosphatase 6; DUSP6]
N [Neurogenic locus notch homolog protein 1; IPR008297]
AK [Axin-2; Glycogen synthase kinase-3 beta]
K [Glycogen synthase kinase-3 beta]
ERKi [IPR008349]
F [IPR017374; Beta-1,3-N-acetylglucosaminyltransferase lunatic fringe]
Rasa [GTP; IPR001806]

Observables: none

A model for oscillations of Cdc2 kinase in embryonic cell cycles based on Michaelis–Menten phosphorylation–dephosphoryla…

Oscillations occur in a number of enzymatic systems as a result of feedback regulation. How Michaelis-Menten kinetics influences oscillatory behavior in enzyme systems is investigated in models for oscillations in the activity of phosphofructokinase (PFK) in glycolysis and of cyclin-dependent kinases in the cell cycle. The model for the PFK reaction is based on a product-activated allosteric enzyme reaction coupled to enzymatic degradation of the reaction product. The Michaelian nature of the product decay term markedly influences the period, amplitude and waveform of the oscillations. Likewise, a model for oscillations of Cdc2 kinase in embryonic cell cycles based on Michaelis-Menten phosphorylation-dephosphorylation kinetics shows that the occurrence and amplitude of the oscillations strongly depend on the ultrasensitivity of the enzymatic cascade that controls the activity of the cyclin-dependent kinase. link: http://identifiers.org/pubmed/23892075

Parameters:

Name Description
vs = 0.06 Reaction: => Cyclin, Rate Law: compartment*vs
V4 = 0.7; K4 = 0.01 Reaction: Active_APC =>, Rate Law: compartment*V4*Active_APC/(K4+Active_APC)
kd = 0.046; vd = 0.25; Kd = 0.001 Reaction: Cyclin => ; Active_APC, Rate Law: compartment*(vd*Active_APC*Cyclin/(Kd+Cyclin)+kd*Cyclin)
K1 = 0.002; V1 = 0.0784313725490196 Reaction: => Active_Cdc2_kinase, Rate Law: compartment*V1*(1-Active_Cdc2_kinase)/(K1+(1-Active_Cdc2_kinase))
K2 = 0.002; V2 = 2.0 Reaction: Active_Cdc2_kinase =>, Rate Law: compartment*V2*Active_Cdc2_kinase/(K2+Active_Cdc2_kinase)
V3 = 0.01; K3 = 0.01 Reaction: => Active_APC, Rate Law: compartment*V3*(1-Active_APC)/(K3+(1-Active_APC))

States:

Name Description
Cyclin [Guanidine]
Active Cdc2 kinase [0016746]
Active APC [anaphase-promoting complex]

Observables: none

BIOMD0000000118 @ v0.0.1

Model is according to the paper *Contribution of Persistent Na+ Current and M-Type K+ Current to Somatic Bursting in CA1…

The intrinsic firing modes of adult CA1 pyramidal cells vary along a continuum of "burstiness" from regular firing to rhythmic bursting, depending on the ionic composition of the extracellular milieu. Burstiness is low in neurons exposed to a normal extracellular Ca(2+) concentration (Ca(2+)), but is markedly enhanced by lowering Ca(2+), although not by blocking Ca(2+) and Ca(2+)-activated K(+) currents. We show, using intracellular recordings, that burstiness in low Ca(2+) persists even after truncating the apical dendrites, suggesting that bursts are generated by an interplay of membrane currents at or near the soma. To study the mechanisms of bursting, we have constructed a conductance-based, one-compartment model of CA1 pyramidal neurons. In this neuron model, reduced Ca(2+) is simulated by negatively shifting the activation curve of the persistent Na(+) current (I(NaP)) as indicated by recent experimental results. The neuron model accounts, with different parameter sets, for the diversity of firing patterns observed experimentally in both zero and normal Ca(2+). Increasing I(NaP) in the neuron model induces bursting and increases the number of spikes within a burst but is neither necessary nor sufficient for bursting. We show, using fast-slow analysis and bifurcation theory, that the M-type K(+) current (I(M)) allows bursting by shifting neuronal behavior between a silent and a tonically active state provided the kinetics of the spike generating currents are sufficiently, although not extremely, fast. We suggest that bursting in CA1 pyramidal cells can be explained by a single compartment "square bursting" mechanism with one slow variable, the activation of I(M). link: http://identifiers.org/pubmed/16807352

Parameters: none

States: none

Observables: none

BIOMD0000000119 @ v0.0.1

Model is according to the paper *Contribution of Persistent Na+ Current and M-Type K+ Current to Somatic Bursting in CA1…

The intrinsic firing modes of adult CA1 pyramidal cells vary along a continuum of "burstiness" from regular firing to rhythmic bursting, depending on the ionic composition of the extracellular milieu. Burstiness is low in neurons exposed to a normal extracellular Ca(2+) concentration (Ca(2+)), but is markedly enhanced by lowering Ca(2+), although not by blocking Ca(2+) and Ca(2+)-activated K(+) currents. We show, using intracellular recordings, that burstiness in low Ca(2+) persists even after truncating the apical dendrites, suggesting that bursts are generated by an interplay of membrane currents at or near the soma. To study the mechanisms of bursting, we have constructed a conductance-based, one-compartment model of CA1 pyramidal neurons. In this neuron model, reduced Ca(2+) is simulated by negatively shifting the activation curve of the persistent Na(+) current (I(NaP)) as indicated by recent experimental results. The neuron model accounts, with different parameter sets, for the diversity of firing patterns observed experimentally in both zero and normal Ca(2+). Increasing I(NaP) in the neuron model induces bursting and increases the number of spikes within a burst but is neither necessary nor sufficient for bursting. We show, using fast-slow analysis and bifurcation theory, that the M-type K(+) current (I(M)) allows bursting by shifting neuronal behavior between a silent and a tonically active state provided the kinetics of the spike generating currents are sufficiently, although not extremely, fast. We suggest that bursting in CA1 pyramidal cells can be explained by a single compartment "square bursting" mechanism with one slow variable, the activation of I(M). link: http://identifiers.org/pubmed/16807352

Parameters:

Name Description
ICa = NaN; tauCa = 13.0; uuCa = 0.13 Reaction: => Ca, Rate Law: compartment_0000001*((-uuCa)*ICa-Ca)/tauCa

States:

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

Observables: none

MODEL1002160000 @ v0.0.1

This model is from the article: Workflow for generating competing hypothesis from models with parameter uncertainty.…

Mathematical models are increasingly used in life sciences. However, contrary to other disciplines, biological models are typically over-parametrized and loosely constrained by scarce experimental data and prior knowledge. Recent efforts on analysis of complex models have focused on isolated aspects without considering an integrated approach-ranging from model building to derivation of predictive experiments and refutation or validation of robust model behaviours. Here, we develop such an integrative workflow, a sequence of actions expanding upon current efforts with the purpose of setting the stage for a methodology facilitating an extraction of core behaviours and competing mechanistic hypothesis residing within underdetermined models. To this end, we make use of optimization search algorithms, statistical (machine-learning) classification techniques and cluster-based analysis of the state variables' dynamics and their corresponding parameter sets. We apply the workflow to a mathematical model of fat accumulation in the arterial wall (atherogenesis), a complex phenomena with limited quantitative understanding, thus leading to a model plagued with inherent uncertainty. We find that the mathematical atherogenesis model can still be understood in terms of a few key behaviours despite the large number of parameters. This result enabled us to derive distinct mechanistic predictions from the model despite the lack of confidence in the model parameters. We conclude that building integrative workflows enable investigators to embrace modelling of complex biological processes despite uncertainty in parameters. link: http://identifiers.org/pubmed/22670212

Parameters: none

States: none

Observables: none

MODEL1011080001 @ v0.0.1

This is metabolic network reconstruction of Natronomonas pharaonis described in the article Characterization of growt…

Natronomonas pharaonis is an archaeon adapted to two extreme conditions: high salt concentration and alkaline pH. It has become one of the model organisms for the study of extremophilic life. Here, we present a genome-scale, manually curated metabolic reconstruction for the microorganism. The reconstruction itself represents a knowledge base of the haloalkaliphile's metabolism and, as such, would greatly assist further investigations on archaeal pathways. In addition, we experimentally determined several parameters relevant to growth, including a characterization of the biomass composition and a quantification of carbon and oxygen consumption. Using the metabolic reconstruction and the experimental data, we formulated a constraints-based model which we used to analyze the behavior of the archaeon when grown on a single carbon source. Results of the analysis include the finding that Natronomonas pharaonis, when grown aerobically on acetate, uses a carbon to oxygen consumption ratio that is theoretically near-optimal with respect to growth and energy production. This supports the hypothesis that, under simple conditions, the microorganism optimizes its metabolism with respect to the two objectives. We also found that the archaeon has a very low carbon efficiency of only about 35%. This inefficiency is probably due to a very low P/O ratio as well as to the other difficulties posed by its extreme environment. link: http://identifiers.org/pubmed/20543878

Parameters: none

States: none

Observables: none

This a model from the article: A computer simulation of the hypothalamic-pituitary-adrenal axis. Gonzalez-Heydrich J…

This paper describes the construction of a computer model that simulates the hypothalamic-pituitary-adrenal axis (HPA axis) regulation of cortisol production. It is presented to illustrate the process of physiological modeling using standard "off the shelf" technologies. The model simulates components of the HPA axis involved in the continuous secretion and elimination of cortisol, adrenocorticotropin (ACTH), and corticotropin releasing hormone (CRH). The physiological relations of these component pieces were modeled based on the current knowledge of their functioning. Rate constants, half lives, and receptor affinities were assigned values derived from the experimental literature. At its current level of development the model is able to accurately simulate the timing, magnitude and decay of the ACTH and cortisol concentration peaks resulting from the ovine-CRH stimulation test in normal and hypercortisolemic patients. The model will be used to predict the effects of lesions in different components of the HPA axis on the time course of cortisol and ACTH levels. We plan to use the model to explore the experimental conditions required to distinguish mechanisms underlying various disorders of the HPA axis, particularly depression. Efforts are currently underway to validate the model for a large variety of normal and pathological perturbations of the HPA axis. link: http://identifiers.org/pubmed/7949852

Parameters: none

States: none

Observables: none

This is a mathematical model for NF-κB oscillations, described by a set of ordinary nonlinear differential equations, wh…

We report the results of a numerical investigation of a mathematical model for NF-κB oscillations, described by a set of ordinary nonlinear differential equations, when perturbed by a circadian oscillation. The main result is that a circadian rhythm, even when it represents a weak perturbation, enhances the signaling capabilities of NF-κB oscillations. This is done by turning rest states into periodic oscillations, and periodic oscillations into quasiperiodic oscillations. Strong perturbations result in complex periodic oscillations and even in chaos. Circadian rhythms would then result in a NF-κB dynamics that is more complex than the simple oscillations and rest states, initially reported for this model. This renders it more amenable for information coding. link: http://identifiers.org/pubmed/23820037

Parameters:

Name Description
A = 0.007; epsilon = 2.0E-5 Reaction: => x; z, Rate Law: compartment*A*(1-x)/(epsilon+z)
k1=1.0 Reaction: y =>, Rate Law: compartment*k1*y
epsilon = 2.0E-5; C = 0.035 Reaction: z => ; x, Rate Law: compartment*C*z*(1-x)/(epsilon+z)
delta = 0.029; B = 954.5 Reaction: x => ; z, Rate Law: compartment*B*z*x/(delta+x)

States:

Name Description
x [NF-kB]
z [C104199]
y [C104199]

Observables: none

This model is from the article: Metabolic stasis in an ancient symbiosis: genome-scale metabolic networks from two Bla…

BACKGROUND: Cockroaches are terrestrial insects that strikingly eliminate waste nitrogen as ammonia instead of uric acid. Blattabacterium cuenoti (Mercier 1906) strains Bge and Pam are the obligate primary endosymbionts of the cockroaches Blattella germanica and Periplaneta americana, respectively. The genomes of both bacterial endosymbionts have recently been sequenced, making possible a genome-scale constraint-based reconstruction of their metabolic networks. The mathematical expression of a metabolic network and the subsequent quantitative studies of phenotypic features by Flux Balance Analysis (FBA) represent an efficient functional approach to these uncultivable bacteria. RESULTS: We report the metabolic models of Blattabacterium strains Bge (iCG238) and Pam (iCG230), comprising 296 and 289 biochemical reactions, associated with 238 and 230 genes, and 364 and 358 metabolites, respectively. Both models reflect both the striking similarities and the singularities of these microorganisms. FBA was used to analyze the properties, potential and limits of the models, assuming some environmental constraints such as aerobic conditions and the net production of ammonia from these bacterial systems, as has been experimentally observed. In addition, in silico simulations with the iCG238 model have enabled a set of carbon and nitrogen sources to be defined, which would also support a viable phenotype in terms of biomass production in the strain Pam, which lacks the first three steps of the tricarboxylic acid cycle. FBA reveals a metabolic condition that renders these enzymatic steps dispensable, thus offering a possible evolutionary explanation for their elimination. We also confirm, by computational simulations, the fragility of the metabolic networks and their host dependence. CONCLUSIONS: The minimized Blattabacterium metabolic networks are surprisingly similar in strains Bge and Pam, after 140 million years of evolution of these endosymbionts in separate cockroach lineages. FBA performed on the reconstructed networks from the two bacteria helps to refine the functional analysis of the genomes enabling us to postulate how slightly different host metabolic contexts drove their parallel evolution. link: http://identifiers.org/pubmed/22376077

Parameters: none

States: none

Observables: none

This model is from the article: Metabolic stasis in an ancient symbiosis: genome-scale metabolic networks from two Bla…

BACKGROUND: Cockroaches are terrestrial insects that strikingly eliminate waste nitrogen as ammonia instead of uric acid. Blattabacterium cuenoti (Mercier 1906) strains Bge and Pam are the obligate primary endosymbionts of the cockroaches Blattella germanica and Periplaneta americana, respectively. The genomes of both bacterial endosymbionts have recently been sequenced, making possible a genome-scale constraint-based reconstruction of their metabolic networks. The mathematical expression of a metabolic network and the subsequent quantitative studies of phenotypic features by Flux Balance Analysis (FBA) represent an efficient functional approach to these uncultivable bacteria. RESULTS: We report the metabolic models of Blattabacterium strains Bge (iCG238) and Pam (iCG230), comprising 296 and 289 biochemical reactions, associated with 238 and 230 genes, and 364 and 358 metabolites, respectively. Both models reflect both the striking similarities and the singularities of these microorganisms. FBA was used to analyze the properties, potential and limits of the models, assuming some environmental constraints such as aerobic conditions and the net production of ammonia from these bacterial systems, as has been experimentally observed. In addition, in silico simulations with the iCG238 model have enabled a set of carbon and nitrogen sources to be defined, which would also support a viable phenotype in terms of biomass production in the strain Pam, which lacks the first three steps of the tricarboxylic acid cycle. FBA reveals a metabolic condition that renders these enzymatic steps dispensable, thus offering a possible evolutionary explanation for their elimination. We also confirm, by computational simulations, the fragility of the metabolic networks and their host dependence. CONCLUSIONS: The minimized Blattabacterium metabolic networks are surprisingly similar in strains Bge and Pam, after 140 million years of evolution of these endosymbionts in separate cockroach lineages. FBA performed on the reconstructed networks from the two bacteria helps to refine the functional analysis of the genomes enabling us to postulate how slightly different host metabolic contexts drove their parallel evolution. link: http://identifiers.org/pubmed/22376077

Parameters: none

States: none

Observables: none

MODEL0911532520 @ v0.0.1

This a model from the article: Oscillatory behavior in enzymatic control processes. Goodwin BC. Adv Enzyme Regul 19…

link: http://identifiers.org/pubmed/5861813

Parameters: none

States: none

Observables: none

Gould2011 - Temperature Sensitive Circadian ClockThis model is a temperature sensitive version of Pokhilko *et al*.  20…

Circadian clocks exhibit 'temperature compensation', meaning that they show only small changes in period over a broad temperature range. Several clock genes have been implicated in the temperature-dependent control of period in Arabidopsis. We show that blue light is essential for this, suggesting that the effects of light and temperature interact or converge upon common targets in the circadian clock. Our data demonstrate that two cryptochrome photoreceptors differentially control circadian period and sustain rhythmicity across the physiological temperature range. In order to test the hypothesis that the targets of light regulation are sufficient to mediate temperature compensation, we constructed a temperature-compensated clock model by adding passive temperature effects into only the light-sensitive processes in the model. Remarkably, this model was not only capable of full temperature compensation and consistent with mRNA profiles across a temperature range, but also predicted the temperature-dependent change in the level of LATE ELONGATED HYPOCOTYL, a key clock protein. Our analysis provides a systems-level understanding of period control in the plant circadian oscillator. link: http://identifiers.org/pubmed/23511208

Parameters:

Name Description
p10 = 0.36 Reaction: => cNI; cNI_m, cNI_m, Rate Law: def*p10*cNI_m/def
m10 = 0.3 Reaction: cY => ; cY, Rate Law: def*m10*cY/def
g3 = 0.4; m3 = 0.2; p3 = 0.1; c = 3.0 Reaction: cL => ; cL, Rate Law: def*(m3*cL+p3*cL^c/(cL^c+g3^c))/def
m13 = 0.32; m22 = 2.0; D = 0.5; L = 0.5 Reaction: cP9 => ; cP9, Rate Law: def*(m13*L+m22*D)*cP9/def
m25 = 0.280006253789297; D = 0.5; m26 = 0.14; L = 0.5 Reaction: cTm => ; cTm, Rate Law: def*(m25*L+m26*D)*cTm/def
m7 = 0.5; D = 0.5; p5 = 1.0; m8 = 0.1; m6 = 0.250006065831407; L = 0.5 Reaction: cT => ; cZG, cZTL, cT, cZG, cZTL, Rate Law: def*((m6*L+m7*D)*cT*(p5*cZTL+cZG)+m8*cT)/def
n8 = 0.42; g11 = 0.7; j = 3.0; n9 = 0.26; k = 3.0; g10 = 0.7 Reaction: => cP7_m; cL, cLm, cP9, cL, cLm, cP9, Rate Law: def*(n8*(cLm+cL)^j/((cLm+cL)^j+g10^j)+n9*cP9^k/(cP9^k+g11^k))/def
m12 = 1.0 Reaction: cP9_m => ; cP9_m, Rate Law: def*m12*cP9_m/def
p14 = 0.45 Reaction: => cZTL, Rate Law: def*p14/def
g3 = 0.4; p3 = 0.1; c = 3.0 Reaction: => cLm; cL, cL, Rate Law: def*p3*cL^c/(cL^c+g3^c)/def
m14 = 0.28 Reaction: cP7_m => ; cP7_m, Rate Law: def*m14*cP7_m/def
n0 = 0.400002792587441; n1 = 1.8; g2 = 0.28; g1 = 0.1; q1 = 0.8; a = 2.0; b = 3.0; L = 0.5 Reaction: => cL_m; cNI, cP, cP7, cP9, cTm, cNI, cP, cP7, cP9, cTm, Rate Law: def*(n0*L+L*q1*cP+n1*cTm^b/(cTm^b+g2^b))*g1^a/((cP9+cP7+cNI)^a+g1^a)/def
g9 = 0.3; n7 = 0.2; i = 3.0; g8 = 0.14; q3 = 2.9; h = 2.0; n4 = 0.0; L = 0.5 Reaction: => cP9_m; cL, cP, cT, cL, cP, cT, Rate Law: def*(L*q3*cP+(n4*L+n7*cL^i/(cL^i+g9^i))*g8^h/(cT^h+g8^h))/def
m4 = 0.2 Reaction: cLm => ; cLm, Rate Law: def*m4*cLm/def
p4 = 0.268 Reaction: => cT; cT_m, cT_m, Rate Law: def*p4*cT_m/def
m18 = 1.0 Reaction: cG_m => ; cG_m, Rate Law: def*m18*cG_m/def
p6 = 0.44 Reaction: => cY; cY_m, cY_m, Rate Law: def*p6*cY_m/def
p8 = 0.7 Reaction: => cP9; cP9_m, cP9_m, Rate Law: def*p8*cP9_m/def
m20 = 1.2 Reaction: cZTL => ; cZTL, Rate Law: def*m20*cZTL/def
g16 = 0.2; n5 = 3.4; D = 0.5; q2 = 0.5; s = 3.0; g7 = 0.18; n6 = 1.25; L = 0.5; g = 2.0 Reaction: => cY_m; cL, cP, cT, cL, cP, cT, Rate Law: def*(L*q2*cP+(n5*L+n6*D)*g7^s/(cT^s+g7^s)*g16^g/(cL^g+g16^g))/def
m1 = 0.54001322056037; D = 0.5; m2 = 0.24; L = 0.5 Reaction: cL_m => ; cL_m, Rate Law: def*(m1*L+m2*D)*cL_m/def
g14 = 0.17; g15 = 0.4; n = 1.0; q4 = 0.6; o = 2.0; L = 0.5; n12 = 2.3499889284595 Reaction: => cG_m; cL, cP, cT, cL, cP, cT, Rate Law: def*(L*q4*cP+n12*L*g15^o/(cL^o+g15^o)*g14^n/(cT^n+g14^n))/def
m16 = 0.5 Reaction: cNI_m => ; cNI_m, Rate Law: def*m16*cNI_m/def
m11 = 1.0; L = 0.5 Reaction: cP => ; cP, Rate Law: def*m11*cP*L/def
m21 = 0.2 Reaction: cZG => ; cZG, Rate Law: def*m21*cZG/def
m24 = 0.405; D = 0.5; m17 = 0.3; L = 0.5 Reaction: cNI => ; cNI, Rate Law: def*(m17*L+m24*D)*cNI/def
D = 0.5; m15 = 0.310006139862489; L = 0.5; m23 = 1.0 Reaction: cP7 => ; cP7, Rate Law: def*(m15*L+m23*D)*cP7/def
g4 = 0.91; n2 = 0.7; g5 = 0.3; e = 2.0; n3 = 0.06; d = 2.5 Reaction: => cT_m; cL, cY, cL, cY, Rate Law: def*(n2*cY^d/(cY^d+g4^d)+n3)*g5^e/(cL^e+g5^e)/def
p9 = 0.4 Reaction: => cP7; cP7_m, cP7_m, Rate Law: def*p9*cP7_m/def
D = 0.5; p13 = 0.4; p12 = 30.0; L = 0.5 Reaction: cG + cZTL => cZG; cG, cZG, cZTL, Rate Law: def*(p12*L*cZTL*cG-p13*D*cZG)/def
m5 = 0.3 Reaction: cT_m => ; cT_m, Rate Law: def*m5*cT_m/def
m9 = 1.0 Reaction: cY_m => ; cY_m, Rate Law: def*m9*cY_m/def
D = 0.5; p7 = 0.3 Reaction: => cP; cP, Rate Law: def*p7*D*(1-cP)/def
p15 = 0.05; f = 3.0; g6 = 0.3 Reaction: => cTm; cT, cT, Rate Law: def*p15*cT^f/(cT^f+g6^f)/def
p11 = 0.23 Reaction: => cG; cG_m, cG_m, Rate Law: def*p11*cG_m/def
D = 0.5; p2 = 0.27; p1 = 0.400007560981732; L = 0.5 Reaction: => cL; cL_m, cL_m, Rate Law: def*cL_m*(p1*L+p2*D)/def
m19 = 0.2 Reaction: cG => ; cG, Rate Law: def*m19*cG/def
n10 = 0.18; g12 = 0.5; m = 2.0; n11 = 0.71; g13 = 0.6; l = 2.0 Reaction: => cNI_m; cLm, cP7, cLm, cP7, Rate Law: def*(n10*cLm^l/(cLm^l+g12^l)+n11*cP7^m/(cP7^m+g13^m))/def

States:

Name Description
cL m [messenger RNA]
cNI [inhibitor]
cG [Protein GIGANTEA]
cP9 [Two-component response regulator-like APRR9]
cP9 m [messenger RNA]
cZTL [Adagio protein 1]
cP7 m [messenger RNA]
cNI m [inhibitor; messenger RNA]
cG m [messenger RNA]
cY [protein]
cT m [messenger RNA]
cY m [messenger RNA; RNA]
cP cP
cLm [Protein CCA1; protein modification; Protein LHY]
cP7 [Two-component response regulator-like APRR7]
cT [Two-component response regulator-like APRR1]
cZG [Protein GIGANTEA; Adagio protein 1]
cTm [protein modification; Two-component response regulator-like APRR1]
cL [Protein CCA1; Protein LHY]

Observables: none

Constraint-based genome-scale Metabolic Model of Methanococcus maripaludis S2

Methane is a major energy source for heating and electricity. Its production by methanogenic bacteria is widely known in nature. M. maripaludis S2 is a fully sequenced hydrogenotrophic methanogen and an excellent laboratory strain with robust genetic tools. However, a quantitative systems biology model to complement these tools is absent in the literature. To understand and enhance its methanogenesis from CO2, this work presents the first constraint-based genome-scale metabolic model (iMM518). It comprises 570 reactions, 556 distinct metabolites, and 518 genes along with gene-protein-reaction (GPR) associations, and covers 30% of open reading frames (ORFs). The model was validated using biomass growth data and experimental phenotypic studies from the literature. Its comparison with the in silico models of Methanosarcina barkeri, Methanosarcina acetivorans, and Sulfolobus solfataricus P2 shows M. maripaludis S2 to be a better organism for producing methane. Using the model, genes essential for growth were identified, and the efficacies of alternative carbon, hydrogen and nitrogen sources were studied. The model can predict the effects of reengineering M. maripaludis S2 to guide or expedite experimental efforts. link: http://identifiers.org/pubmed/24553424

Parameters: none

States: none

Observables: none

MODEL1006230092 @ v0.0.1

This a model from the article: A novel computational model of the human ventricular action potential and Ca transient.…

We have developed a detailed mathematical model for Ca handling and ionic currents in the human ventricular myocyte. Our aims were to: (1) simulate basic excitation-contraction coupling phenomena; (2) use realistic repolarizing K current densities; (3) reach steady-state. The model relies on the framework of the rabbit myocyte model previously developed by our group, with subsarcolemmal and junctional compartments where ion channels sense higher [Ca] vs. bulk cytosol. Ion channels and transporters have been modeled on the basis of the most recent experimental data from human ventricular myocytes. Rapidly and slowly inactivating components of I(to) have been formulated to differentiate between endocardial and epicardial myocytes. Transmural gradients of Ca handling proteins and Na pump were also simulated. The model has been validated against a wide set of experimental data including action potential duration (APD) adaptation and restitution, frequency-dependent increase in Ca transient peak and Na. Interestingly, Na accumulation at fast heart rate is a major determinant of APD shortening, via outward shifts in Na pump and Na-Ca exchange currents. We investigated the effects of blocking K currents on APD and repolarization reserve: I(Ks) block does not affect the former and slightly reduces the latter; I(K1) blockade modestly increases APD and more strongly reduces repolarization reserve; I(Kr) blockers significantly prolong APD, an effect exacerbated as pacing frequency is decreased, in good agreement with experimental results in human myocytes. We conclude that this model provides a useful framework to explore excitation-contraction coupling mechanisms and repolarization abnormalities at the single myocyte level. link: http://identifiers.org/pubmed/19835882

Parameters: none

States: none

Observables: none

BIOMD0000000321 @ v0.0.1

Grange2001 - L-dopa PK modelA pharmacokinetics of L-dopa in rats after administration of L-dopa alone (this model: BIOMD…

PURPOSE: To study the PK interaction of L-dopa/benserazide in rats. METHODS: Male rats received a single oral dose of 80 mg/kg L-dopa or 20 mg/kg benserazide or 80/20 mg/kg L-dopa/benserazide. Based on plasma concentrations the kinetics of L-dopa, 3-O-methyldopa (3-OMD), benserazide, and its metabolite Ro 04-5127 were characterized by noncompartmental analysis and a compartmental model where total L-dopa clearance was the sum of the clearances mediated by amino-acid-decarboxylase (AADC), catechol-O-methyltransferase and other enzymes. In the model Ro 04-5127 inhibited competitively the L-dopa clearance by AADC. RESULTS: The coadministration of L-dopa/benserazide resulted in a major increase in systemic exposure to L-dopa and 3-OMD and a decrease in L-dopa clearance. The compartmental model allowed an adequate description of the observed L-dopa and 3-OMD concentrations in the absence and presence of benserazide. It had an advantage over noncompartmental analysis because it could describe the temporal change of inhibition and recovery of AADC. CONCLUSIONS: Our study is the first investigation where the kinetics of benserazide and Ro 04-5127 have been described by a compartmental model. The L-dopa/benserazide model allowed a mechanism-based view of the L-dopa/benserazide interaction and supports the hypothesis that Ro 04-5127 is the primary active metabolite of benserazide. link: http://identifiers.org/pubmed/11587490

Parameters:

Name Description
CL_rest = NaN l_per_h Reaction: C_dopa =>, Rate Law: CL_rest*C_dopa
F_b = NaN dimensionless; ka_b = 2.11 per_h Reaction: A_dopa => C_dopa, Rate Law: ka_b*A_dopa*F_b
CL_COMT = NaN l_per_h Reaction: C_dopa => C_OMD, Rate Law: CL_COMT*C_dopa
CL_AADC = NaN l_per_h Reaction: C_dopa =>, Rate Law: CL_AADC*C_dopa
CL_OMD = 0.012 Reaction: C_OMD =>, Rate Law: CL_OMD*C_OMD

States:

Name Description
C OMD [metabolite; 9307]
C dopa [L-dopa; 3,4-Dihydroxy-L-phenylalanine; 6047]
A dopa [L-dopa; 6047; 3,4-Dihydroxy-L-phenylalanine]

Observables: none

Grange2001 - PK interaction of L-dopa and benserazideA pharmacokinetics of L-dopa in rats after administration of L-dopa…

PURPOSE: To study the PK interaction of L-dopa/benserazide in rats. METHODS: Male rats received a single oral dose of 80 mg/kg L-dopa or 20 mg/kg benserazide or 80/20 mg/kg L-dopa/benserazide. Based on plasma concentrations the kinetics of L-dopa, 3-O-methyldopa (3-OMD), benserazide, and its metabolite Ro 04-5127 were characterized by noncompartmental analysis and a compartmental model where total L-dopa clearance was the sum of the clearances mediated by amino-acid-decarboxylase (AADC), catechol-O-methyltransferase and other enzymes. In the model Ro 04-5127 inhibited competitively the L-dopa clearance by AADC. RESULTS: The coadministration of L-dopa/benserazide resulted in a major increase in systemic exposure to L-dopa and 3-OMD and a decrease in L-dopa clearance. The compartmental model allowed an adequate description of the observed L-dopa and 3-OMD concentrations in the absence and presence of benserazide. It had an advantage over noncompartmental analysis because it could describe the temporal change of inhibition and recovery of AADC. CONCLUSIONS: Our study is the first investigation where the kinetics of benserazide and Ro 04-5127 have been described by a compartmental model. The L-dopa/benserazide model allowed a mechanism-based view of the L-dopa/benserazide interaction and supports the hypothesis that Ro 04-5127 is the primary active metabolite of benserazide. link: http://identifiers.org/pubmed/11587490

Parameters:

Name Description
CL_M = 4.29 l_per_h Reaction: C1_M =>, Rate Law: CL_M*C1_M
CL_rest = NaN l_per_h Reaction: C_dopa =>, Rate Law: CL_rest*C_dopa
CL_dM = 1.06 l_per_h Reaction: C1_M => C2_M, Rate Law: CL_dM*(C1_M-C2_M)
fm = 0.15 dimensionless; CL_B = 1.67 l_per_h Reaction: C1_B => C1_M, Rate Law: fm/(1-fm)*CL_B*C1_B
CL_COMT = NaN l_per_h Reaction: C_dopa => C_OMD, Rate Law: CL_COMT*C_dopa
ka_c = 1.29; F_c = NaN dimensionless Reaction: A_dopa => C_dopa, Rate Law: ka_c*A_dopa*F_c
ka_M = 2.47 Reaction: A_M => C1_M, Rate Law: ka_M*A_M
CL_OMD = 0.00895 l_per_h Reaction: C_OMD =>, Rate Law: CL_OMD*C_OMD
ka_B = 0.94; F_B = 0.022 dimensionless Reaction: A_B =>, Rate Law: ka_B*A_B*(1-F_B)
CL_B = 1.67 l_per_h Reaction: C1_B =>, Rate Law: CL_B*C1_B
CL_AADC = NaN l_per_h Reaction: C_dopa =>, Rate Law: CL_AADC*C_dopa
CL_dB = 0.072 l_per_h Reaction: C1_B => C2_B, Rate Law: CL_dB*(C1_B-C2_B)

States:

Name Description
C1 M [metabolite; 188973]
C OMD [9307; metabolite]
C2 B [Benserazide (USAN/INN); 2327]
A B [Benserazide (USAN/INN); 2327]
C1 B [Benserazide (USAN/INN); 2327]
C dopa [L-dopa; 3,4-Dihydroxy-L-phenylalanine; 6047]
A dopa [L-dopa; 3,4-Dihydroxy-L-phenylalanine; 6047]
A M [metabolite; 188973]
C2 M [metabolite; 188973]

Observables: none

BIOMD0000000854 @ v0.0.1

This is a simple, linear, four-compartment ordinary differential equation (ODE) model Akt activation that tracks both th…

Akt/PKB is a biochemical regulator that functions as an important cross-talk node between several signalling pathways in the mammalian cell. In particular, Akt is a key mediator of glucose transport in response to insulin. The phosphorylation (activation) of only a small percentage of the Akt pool of insulin-sensitive cells results in maximal translocation of glucose transporter 4 (GLUT4) to the plasma membrane (PM). This enables the diffusion of glucose into the cell. The dysregulation of Akt signalling is associated with the development of diabetes, cancer and cardiovascular disease. Akt is synthesised in the cytoplasm in the inactive state. Under the influence of insulin, it moves to the PM, where it is phosphorylated to form pAkt. Although phosphorylation occurs only at the PM, pAkt is found in many cellular locations, including the PM, the cytoplasm, and the nucleus. Indeed, the spatial distribution of pAkt within the cell appears to be an important determinant of downstream regulation. Here we present a simple, linear, four-compartment ordinary differential equation (ODE) model of Akt activation that tracks both the biochemical state and the physical location of Akt. This model embodies the main features of the activation of this important cross-talk node and is consistent with the experimental data. In particular, it allows different downstream signalling motifs without invoking separate feedback pathways. Moreover, the model is computationally tractable, readily analysed, and elucidates some of the apparent anomalies in insulin signalling via Akt. link: http://identifiers.org/pubmed/26992575

Parameters:

Name Description
beta1 = 2.2; koff = 0.35 Reaction: Ap => Pp, Rate Law: compartment*beta1*koff*Ap
kin = 0.55 Reaction: Pp => Pc, Rate Law: compartment*kin*Pp
koff = 0.35 Reaction: Pc => Ac, Rate Law: compartment*koff*Pc
alpha1 = 0.014; kin = 0.55 Reaction: Pc => Pp, Rate Law: compartment*alpha1*kin*Pc

States:

Name Description
Ap [AKT kinase; plasma membrane]
Pp [AKT kinase; phosphoprotein; plasma membrane]
Ac [AKT kinase; cytosol]
Pc [AKT kinase; phosphoprotein; cytosol]

Observables: none

This model is built by COPASI 4.24(Build 197), based on paper: Mathematical Approach to Differentiate Spontaneous and I…

PURPOSE:Drug resistance is a major impediment to the success of cancer treatment. Resistance is typically thought to arise from random genetic mutations, after which mutated cells expand via Darwinian selection. However, recent experimental evidence suggests that progression to drug resistance need not occur randomly, but instead may be induced by the treatment itself via either genetic changes or epigenetic alterations. This relatively novel notion of resistance complicates the already challenging task of designing effective treatment protocols. MATERIALS AND METHODS:To better understand resistance, we have developed a mathematical modeling framework that incorporates both spontaneous and drug-induced resistance. RESULTS:Our model demonstrates that the ability of a drug to induce resistance can result in qualitatively different responses to the same drug dose and delivery schedule. We have also proven that the induction parameter in our model is theoretically identifiable and propose an in vitro protocol that could be used to determine a treatment's propensity to induce resistance. link: http://identifiers.org/pubmed/30969799

Parameters:

Name Description
alpha = 0.01; epsilon = 1.0E-6; u = 0.0 Reaction: Sensitive_tumor_S => Resistant_tumor_R, Rate Law: compartment*(epsilon+alpha*u)*Sensitive_tumor_S
p_r = 0.2 Reaction: => Resistant_tumor_R; Sensitive_tumor_S, Rate Law: compartment*p_r*(1-(Sensitive_tumor_S+Resistant_tumor_R))*Resistant_tumor_R
d = 1.0; u = 0.0 Reaction: Sensitive_tumor_S =>, Rate Law: compartment*d*u*Sensitive_tumor_S

States:

Name Description
Resistant tumor R [resistant to; cancer]
Tumor Volume V [cancer; tumor size; Tumor Size]
Sensitive tumor S [cancer; 0000516]

Observables: none

Guisoni2016 - Cis-regulatory system (CRS) can drive sustained oscillationsThis model is described in the article: [Prom…

It is well known that single-gene circuits with negative feedback loop can lead to oscillatory gene expression when they operate with time delay. In order to generate these oscillations many processes can contribute to properly timing such delay. Here we show that the time delay coming from the transitions between internal states of the cis-regulatory system (CRS) can drive sustained oscillations in an auto-repressive single-gene circuit operating in a small volume like a cell. We found that the cooperative binding of repressor molecules is not mandatory for a oscillatory behavior if there are enough binding sites in the CRS. These oscillations depend on an adequate balance between the CRS kinetic, and the synthesis/degradation rates of repressor molecules. This finding suggest that the multi-site CRS architecture can play a key role for oscillatory behavior of gene expression. Finally, our results can also help to synthetic biologists on the design of the promoters architecture for new genetic oscillatory circuits. link: http://identifiers.org/pubmed/26958852

Parameters: none

States: none

Observables: none

Bridging systems biology and pharmacokinetics–pharmacodynamics has resulted in models that are highly complex and compli…

Bridging systems biology and pharmacokinetics-pharmacodynamics has resulted in models that are highly complex and complicated. They usually contain large numbers of states and parameters and describe multiple input-output relationships. Based on any given data set relating to a specific input-output process, it is possible that some states of the system are either less important or have no influence at all. In this study, we explore a simplification of a systems pharmacology model of the coagulation network for use in describing the time course of fibrinogen recovery after a brown snake bite. The technique of proper lumping is used to simplify the 62-state systems model to a 5-state model that describes the brown snake venom-fibrinogen relationship while maintaining an appropriate mechanistic relationship. The simplified 5-state model explains the observed decline and recovery in fibrinogen concentrations well. The techniques used in this study can be applied to other multiscale models. link: http://identifiers.org/pubmed/24402117

Parameters: none

States: none

Observables: none

This is a mathematical model describing describing the population dynamics of microbes infected by lytic viruses.

Viral infections of microbial cells often culminate in lysis and the release of new virus particles. However, viruses of microbes can also initiate chronic infections, in which new viruses particles are released via budding and without cell lysis. In chronic infections, viral genomes may also be passed on from mother to daughter cells during division. The consequences of chronic infections for the population dynamics of viruses and microbes remains under-explored. In this paper we present a model of chronic infections as well as a model of interactions between lytic and chronic viruses competing for the same microbial population. In the chronic only model, we identify conditions underlying complex bifurcations such as saddle-node, backward and Hopfbifurcations, leading to parameter regions with multiple attractors and/or oscillatory behavior. We then utilize invasion analysis to examine the coupled nonlinear system of microbes, lytic viruses, and chronic viruses. In so doing we find unexpected results, including a regime in which the chronic virus requires the lytic virus for survival, invasion, and persistence. In this regime, lytic viruses decrease total cell densities, so that a subpopulation of chronically infected cells experience decreased niche competition. As such, even when chronically infected cells have a growth disadvantage, lytic viruses can, paradoxically, enable the proliferation of both chronically infected cells and chronic viruses. We discuss the implications of our results for understanding the ecology and long-term evolution of heterogeneous viral strategies. link: http://identifiers.org/pubmed/30389532

Parameters:

Name Description
eta = 1.5 Reaction: I =>, Rate Law: compartment*eta*I
phi = 1.73925271309261E-10 Reaction: S + V_L => I, Rate Law: compartment*phi*S*V_L
mu = 0.0866 Reaction: V_L =>, Rate Law: compartment*mu*V_L
r = 0.339; N = 8.3E8; K = 8.947E8 Reaction: => S, Rate Law: compartment*r*S*(1-N/K)
d = 0.0416666666666667 Reaction: I =>, Rate Law: compartment*d*I
beta = 20.0; eta = 1.5 Reaction: => V_L; I, Rate Law: compartment*beta*eta*I

States:

Name Description
I [infected cell]
S [C14187]
V L [C14368]

Observables: none

This is a mathematical model describing describing the population dynamics of microbes infected by chronically infecting…

Viral infections of microbial cells often culminate in lysis and the release of new virus particles. However, viruses of microbes can also initiate chronic infections, in which new viruses particles are released via budding and without cell lysis. In chronic infections, viral genomes may also be passed on from mother to daughter cells during division. The consequences of chronic infections for the population dynamics of viruses and microbes remains under-explored. In this paper we present a model of chronic infections as well as a model of interactions between lytic and chronic viruses competing for the same microbial population. In the chronic only model, we identify conditions underlying complex bifurcations such as saddle-node, backward and Hopfbifurcations, leading to parameter regions with multiple attractors and/or oscillatory behavior. We then utilize invasion analysis to examine the coupled nonlinear system of microbes, lytic viruses, and chronic viruses. In so doing we find unexpected results, including a regime in which the chronic virus requires the lytic virus for survival, invasion, and persistence. In this regime, lytic viruses decrease total cell densities, so that a subpopulation of chronically infected cells experience decreased niche competition. As such, even when chronically infected cells have a growth disadvantage, lytic viruses can, paradoxically, enable the proliferation of both chronically infected cells and chronic viruses. We discuss the implications of our results for understanding the ecology and long-term evolution of heterogeneous viral strategies. link: http://identifiers.org/pubmed/30389532

Parameters:

Name Description
r_tilde = 0.2; N = 8.3E8; K = 8.947E8 Reaction: => C, Rate Law: compartment*r_tilde*C*(1-N/K)
alpha = 0.1 Reaction: => V_C; C, Rate Law: compartment*alpha*C
mu = 0.0866 Reaction: V_C =>, Rate Law: compartment*mu*V_C
r = 0.339; N = 8.3E8; K = 8.947E8 Reaction: => S, Rate Law: compartment*r*S*(1-N/K)
d = 0.0416666666666667 Reaction: S =>, Rate Law: compartment*d*S
d_tilde = 0.05 Reaction: C =>, Rate Law: compartment*d_tilde*C
phi_tilde = 5.0E-12 Reaction: S + V_C => C, Rate Law: compartment*phi_tilde*S*V_C

States:

Name Description
V C [C14368]
S [C14187]
C [C14283; C14141]

Observables: none

This a model from the article: Inclusion of the glucocorticoid receptor in a hypothalamic pituitary adrenal axis model…

The body's primary stress management system is the hypothalamic pituitary adrenal (HPA) axis. The HPA axis responds to physical and mental challenge to maintain homeostasis in part by controlling the body's cortisol level. Dysregulation of the HPA axis is implicated in numerous stress-related diseases.We developed a structured model of the HPA axis that includes the glucocorticoid receptor (GR). This model incorporates nonlinear kinetics of pituitary GR synthesis. The nonlinear effect arises from the fact that GR homodimerizes after cortisol activation and induces its own synthesis in the pituitary. This homodimerization makes possible two stable steady states (low and high) and one unstable state of cortisol production resulting in bistability of the HPA axis. In this model, low GR concentration represents the normal steady state, and high GR concentration represents a dysregulated steady state. A short stress in the normal steady state produces a small perturbation in the GR concentration that quickly returns to normal levels. Long, repeated stress produces persistent and high GR concentration that does not return to baseline forcing the HPA axis to an alternate steady state. One consequence of increased steady state GR is reduced steady state cortisol, which has been observed in some stress related disorders such as Chronic Fatigue Syndrome (CFS).Inclusion of pituitary GR expression resulted in a biologically plausible model of HPA axis bistability and hypocortisolism. High GR concentration enhanced cortisol negative feedback on the hypothalamus and forced the HPA axis into an alternative, low cortisol state. This model can be used to explore mechanisms underlying disorders of the HPA axis. link: http://identifiers.org/pubmed/17300722

Parameters: none

States: none

Observables: none

This a model from the article: Inclusion of the glucocorticoid receptor in a hypothalamic pituitary adrenal axis model…

The body's primary stress management system is the hypothalamic pituitary adrenal (HPA) axis. The HPA axis responds to physical and mental challenge to maintain homeostasis in part by controlling the body's cortisol level. Dysregulation of the HPA axis is implicated in numerous stress-related diseases.We developed a structured model of the HPA axis that includes the glucocorticoid receptor (GR). This model incorporates nonlinear kinetics of pituitary GR synthesis. The nonlinear effect arises from the fact that GR homodimerizes after cortisol activation and induces its own synthesis in the pituitary. This homodimerization makes possible two stable steady states (low and high) and one unstable state of cortisol production resulting in bistability of the HPA axis. In this model, low GR concentration represents the normal steady state, and high GR concentration represents a dysregulated steady state. A short stress in the normal steady state produces a small perturbation in the GR concentration that quickly returns to normal levels. Long, repeated stress produces persistent and high GR concentration that does not return to baseline forcing the HPA axis to an alternate steady state. One consequence of increased steady state GR is reduced steady state cortisol, which has been observed in some stress related disorders such as Chronic Fatigue Syndrome (CFS).Inclusion of pituitary GR expression resulted in a biologically plausible model of HPA axis bistability and hypocortisolism. High GR concentration enhanced cortisol negative feedback on the hypothalamus and forced the HPA axis into an alternative, low cortisol state. This model can be used to explore mechanisms underlying disorders of the HPA axis. link: http://identifiers.org/pubmed/17300722

Parameters: none

States: none

Observables: none

BIOMD0000000436 @ v0.0.1

Gupta2009 - Eicosanoid MetabolismIntegrated model of eicosanoid metabolism and signaling based on lipidomics flux analys…

There is increasing evidence for a major and critical involvement of lipids in signal transduction and cellular trafficking, and this has motivated large-scale studies on lipid pathways. The Lipid Metabolites and Pathways Strategy consortium is actively investigating lipid metabolism in mammalian cells and has made available time-course data on various lipids in response to treatment with KDO(2)-lipid A (a lipopolysaccharide analog) of macrophage RAW 264.7 cells. The lipids known as eicosanoids play an important role in inflammation. We have reconstructed an integrated network of eicosanoid metabolism and signaling based on the KEGG pathway database and the literature and have developed a kinetic model. A matrix-based approach was used to estimate the rate constants from experimental data and these were further refined using generalized constrained nonlinear optimization. The resulting model fits the experimental data well for all species, and simulated enzyme activities were similar to their literature values. The quantitative model for eicosanoid metabolism that we have developed can be used to design experimental studies utilizing genetic and pharmacological perturbations to probe fluxes in lipid pathways. link: http://identifiers.org/pubmed/19486676

Parameters:

Name Description
k9 = 0.187 (0.0002778*s)^(-1) Reaction: HETE =>, Rate Law: k9*HETE
k21 = 0.034 (0.0002778*s)^(-1) Reaction: PGJ2 => dPGJ2, Rate Law: k21*PGJ2
DGactivity = 1.0 dimensionless; DNA = 1.0 μg; k10 = 0.024 μg*(3600*s)^(-1) Reaction: AA => PGH2; DG, Rate Law: k10*DGactivity*AA/DNA
k16 = 1.0E-15 (0.0002778*s)^(-1) Reaction: PGF2a =>, Rate Law: k16*PGF2a
k8 = 0.007 (0.0002778*s)^(-1) Reaction: AA => HETE, Rate Law: k8*AA
k20 = 0.014 (0.0002778*s)^(-1) Reaction: dPGD2 =>, Rate Law: k20*dPGD2
DGactivity = 1.0 dimensionless; GPChoratio = 1.0 dimensionless; DNA = 1.0 μg; k5 = 1.0E-15 μg*(3600*s)^(-1) Reaction: GPCho => AA; DG, Rate Law: k5*DGactivity*GPChoratio*GPCho/DNA
k17 = 3.116 (0.0002778*s)^(-1) Reaction: PGH2 => PGD2, Rate Law: k17*PGH2
LPSactivity = 0.0 dimensionless; GPChoratio = 1.0 dimensionless; k6 = 0.33 (0.0002778*s)^(-1) Reaction: GPCho => AA; LPS, Rate Law: k6*GPCho*GPChoratio*LPSactivity
k22 = 0.116 (0.0002778*s)^(-1) Reaction: dPGJ2 =>, Rate Law: k22*dPGJ2
k2 = 1.0E-15 (0.0002778*s)^(-1) Reaction: FA => AA, Rate Law: k2*FA
k14 = 1.0E-15 (0.0002778*s)^(-1) Reaction: PGE2 =>, Rate Law: k14*PGE2
k19 = 0.029 (0.0002778*s)^(-1) Reaction: PGD2 => dPGD2, Rate Law: k19*PGD2
k11 = 0.111 (0.0002778*s)^(-1) Reaction: AA => PGH2; LPS, Rate Law: k11*AA
k18 = 0.054 (0.0002778*s)^(-1) Reaction: PGD2 => PGJ2, Rate Law: k18*PGD2
LPSactivity = 0.0 dimensionless; k1 = 355.637 (0.0002778*s)^(-1); onepmol = 1.0 pmol Reaction: FA => AA; LPS, Rate Law: k1*onepmol*LPSactivity
LPSactivity = 0.0 dimensionless; k12 = 0.098 (0.0002778*s)^(-1) Reaction: AA => PGH2, Rate Law: k12*AA*LPSactivity
k3 = 1.0E-15 (0.0002778*s)^(-1); DGactivity = 1.0 dimensionless; DNA = 1.0 μg; DGperDNA = 1.0 pmol*μg^(-1) Reaction: DG => AA, Rate Law: k3*DGactivity*DGperDNA*DNA
k4 = 1.0E-15 (0.0002778*s)^(-1) Reaction: AA =>, Rate Law: k4*AA
k15 = 0.061 (0.0002778*s)^(-1) Reaction: PGH2 => PGF2a, Rate Law: k15*PGH2
k13 = 0.204 (0.0002778*s)^(-1) Reaction: PGH2 => PGE2, Rate Law: k13*PGH2
k7 = 1.0E-15 (0.0002778*s)^(-1); GPChoratio = 1.0 dimensionless Reaction: GPCho => AA, Rate Law: k7*GPChoratio*GPCho

States:

Name Description
PGJ2 [Prostaglandin J2; LMFA03010019; prostaglandin J2]
FA [fatty acid]
HETE [LMFA03060085]
dPGJ2 [15-Deoxy-Delta12,14-PGJ2; LMFA03010021; 15-deoxy-Delta(12,14)-prostaglandin J2]
PGD2 [Prostaglandin D2; LMFA03010004; prostaglandin D2]
dPGD2 [LMFA03010051]
GPCho [phosphatidylcholine(1+)]
PGF2a [Prostaglandin F2alpha; LMFA03010002; prostaglandin F2alpha]
PGH2 [prostaglandin H2]
AA [Arachidonate; LMFA01030001; arachidonic acid]
DG [1,2-diglyceride]
PGE2 [LMFA03010003]

Observables: none

This is a four dimensionsal ordinary differential equation mathematical model that explores the contribution of PI3P dur…

Mycobacterium tuberculosis (Mtb) is a highly successful intracellular pathogen because of its ability to modulate host's anti-microbial pathways. Phagocytosis acts as the first line of defence against microbial infection. However, Mtb inhibits Phosphatidylinositol 3-phosphate (PI3P) oscillations which is required for phagolysosomal fusion. Here we attempted to understand the mechanisms by which Mtb eliminates phagosome-lysosome fusion. To address this, we built a four dimensional ordinary differential equation model and explored the contribution of PI3P during Mtb phagocytosis. Using this model, we identified some sensitive parameters that influence the dynamics of host-pathogen interactions. We observed that PI3P dynamics can be controlled by regulating the intracellular calcium oscillations. Some plausible methods to restore PI3P oscillations are ER flux rate, recruitment rate of proteins, like Rab GTPase, and cooperativity coefficient of calcium dependent consumption of calmodulin. Further, we investigated whether modulation of these pathways is a potential therapeutic intervention strategy. Here we showed that RyR2 agonist caffeine stimulated calcium influx and inhibited growth of intracellular Mtb in macrophages. Taken together, we demonstrate that modulation of host calcium level is a plausible strategy for killing of intracellular Mtb. link: http://identifiers.org/pubmed/31002776

Parameters: none

States: none

Observables: none

MODEL0911376350 @ v0.0.1

This a model from the article: Circulation: overall regulation. Guyton AC, Coleman TG, Granger HJ. Annu Rev Physiol…

link: http://identifiers.org/pubmed/4334846

Parameters: none

States: none

Observables: none

MODEL0911342562 @ v0.0.1

This a model from the article: Circulation: overall regulation. Guyton AC, Coleman TG, Granger HJ. Annu Rev Physiol…

link: http://identifiers.org/pubmed/4334846

Parameters: none

States: none

Observables: none

MODEL0911309080 @ v0.0.1

This a model from the article: Circulation: overall regulation. Guyton AC, Coleman TG, Granger HJ. Annu Rev Physiol…

link: http://identifiers.org/pubmed/4334846

Parameters: none

States: none

Observables: none

MODEL0911272039 @ v0.0.1

This a model from the article: Circulation: overall regulation. Guyton AC, Coleman TG, Granger HJ. Annu Rev Physiol…

link: http://identifiers.org/pubmed/4334846

Parameters: none

States: none

Observables: none

MODEL0911270005 @ v0.0.1

This a model from the article: Circulation: overall regulation. Guyton AC, Coleman TG, Granger HJ. Annu Rev Physiol…

link: http://identifiers.org/pubmed/4334846

Parameters: none

States: none

Observables: none

MODEL0912160000 @ v0.0.1

This a model from the article: Circulation: overall regulation. Guyton AC, Coleman TG, Granger HJ. Annu Rev Physiol…

link: http://identifiers.org/pubmed/4334846

Parameters: none

States: none

Observables: none

MODEL0912160001 @ v0.0.1

This a model from the article: Circulation: overall regulation. Guyton AC, Coleman TG, Granger HJ. Annu Rev Physiol…

link: http://identifiers.org/pubmed/4334846

Parameters: none

States: none

Observables: none

MODEL0911231713 @ v0.0.1

This a model from the article: Circulation: overall regulation. Guyton AC, Coleman TG, Granger HJ. Annu Rev Physiol…

link: http://identifiers.org/pubmed/4334846

Parameters: none

States: none

Observables: none

MODEL0911270006 @ v0.0.1

This a model from the article: Circulation: overall regulation. Guyton AC, Coleman TG, Granger HJ. Annu Rev Physiol…

link: http://identifiers.org/pubmed/4334846

Parameters: none

States: none

Observables: none

MODEL0911202318 @ v0.0.1

This a model from the article: Circulation: overall regulation. Guyton AC, Coleman TG, Granger HJ. Annu Rev Physiol…

link: http://identifiers.org/pubmed/4334846

Parameters: none

States: none

Observables: none

MODEL0911169699 @ v0.0.1

This a model from the article: Circulation: overall regulation. Guyton AC, Coleman TG, Granger HJ. Annu Rev Physiol…

link: http://identifiers.org/pubmed/4334846

Parameters: none

States: none

Observables: none

MODEL0911091440 @ v0.0.1

This a model from the article: Circulation: overall regulation. Guyton AC, Coleman TG, Granger HJ. Annu Rev Physiol…

link: http://identifiers.org/pubmed/4334846

Parameters: none

States: none

Observables: none

MODEL0911047946 @ v0.0.1

This a model from the article: Circulation: overall regulation. Guyton AC, Coleman TG, Granger HJ. Annu Rev Physiol…

link: http://identifiers.org/pubmed/4334846

Parameters: none

States: none

Observables: none

MODEL0910928451 @ v0.0.1

This a model from the article: Circulation: overall regulation. Guyton AC, Coleman TG, Granger HJ. Annu Rev Physiol…

link: http://identifiers.org/pubmed/4334846

Parameters: none

States: none

Observables: none

MODEL0910896131 @ v0.0.1

This a model from the article: Circulation: overall regulation. Guyton AC, Coleman TG, Granger HJ. Annu Rev Physiol…

link: http://identifiers.org/pubmed/4334846

Parameters: none

States: none

Observables: none

MODEL0910846879 @ v0.0.1

This a model from the article: Circulation: overall regulation. Guyton AC, Coleman TG, Granger HJ. Annu Rev Physiol…

link: http://identifiers.org/pubmed/4334846

Parameters: none

States: none

Observables: none

MODEL0909931851 @ v0.0.1

This a model from the article: Circulation: overall regulation. Guyton AC, Coleman TG, Granger HJ. Annu Rev Physiol…

link: http://identifiers.org/pubmed/4334846

Parameters: none

States: none

Observables: none

Model for the Let-7-mediated coupling between the CDK network driving the cell cycle and the malignant cell transformati…

The microRNA Let-7 controls the expression of proteins that belong to two distinct gene regulatory networks, namely, a cyclin-dependent kinase (Cdk) network driving the cell cycle and a cell transformation network that can undergo an epigenetic switch between a non-transformed and a malignant transformed cell state. Using mathematical modeling and transcriptomic data analysis, we here investigate how Let-7 controls the Cdk-dependent cell cycle network, and how it couples the latter with the transformation network. We also assess the consequence of this coupling on cancer progression. Our analysis shows that the switch from a quiescent to a proliferative state depends on the relative levels of Let-7 and several cell cycle activators. Numerical simulations further indicate that the Let-7-coupled cell cycle and transformation networks mutually control each other, and our model identifies key players for this mutual control. Transcriptomic data analysis from The Cancer Genome Atlas (TCGA) suggests that the two networks are activated in cancer, in particular in gastrointestinal cancers, and that the activation levels vary significantly among patients affected by a same cancer type. Our mathematical model, when applied to a heterogeneous cell population, suggests that heterogeneity among tumors may in part result from stochastic switches between a non-transformed cell state with low proliferative capability and a transformed cell state with high proliferative property. The model further predicts that Let-7 may reduce tumor heterogeneity by decreasing the occurrence of stochastic switches towards a transformed, proliferative cell state. In conclusion, we identified the key components responsible for the qualitative dynamics of two networks interconnected by Let-7. The two networks are heterogeneously activated in several cancers, thereby stressing the need to consider patient’s specific characteristics to optimize therapeutic strategies. link: http://identifiers.org/doi/10.3389/fphys.2019.00848

Parameters: none

States: none

Observables: none

BIOMD0000000192 @ v0.0.1

This model represents a concentration gradient of RanGTP across the nuclear envelope. This gradient is generated by dist…

Here, we analyse the RanGTPase system and its coupling to receptor-mediated nuclear transport. Our simulations predict nuclear RanGTP levels in HeLa cells to be very sensitive towards the cellular energy charge and to exceed the cytoplasmic concentration approximately 1000-fold. The steepness of the RanGTP gradient appears limited by both the cytoplasmic RanGAP concentration and the imperfect retention of nuclear RanGTP by nuclear pore complexes (NPCs), but not by the nucleotide exchange activity of RCC1. Neither RanBP1 nor the NPC localization of RanGAP has a significant direct impact on the RanGTP gradient. NTF2-mediated import of Ran appears to be the bottleneck for maximal capacity of Ran-driven nuclear transport. We show that unidirectional nuclear transport can be faithfully simulated without the assumption of a vectorial NPC passage; transport receptors only need to reversibly cross NPCs and switch their affinity for cargo in response to the RanGTP gradient. A significant RanGTP gradient after nuclear envelope (NE) breakdown can apparently exist only in large cytoplasm. This indicates that RanGTP gradients can provide positional information for mitotic spindle and NE assembly in early embryonic cells, but hardly any in small somatic cells. link: http://identifiers.org/pubmed/12606574

Parameters:

Name Description
kpermRanGDP=0.12 psec Reaction: RanGDP_nuc => RanGDP_cy, Rate Law: kpermRanGDP*nucleus*(RanGDP_nuc-RanGDP_cy)
kon=0.3 pmicroMpsec; koff=4.0E-4 psec Reaction: RanGTP_cy + RanBP1 => RanGTP_RanBP1, Rate Law: (kon*RanGTP_cy*RanBP1-koff*RanGTP_RanBP1)*cytoplasm
r7=11.0 pmicroMpsec; r2=21.0 psec Reaction: RCC1_RanGDP => RCC1_Ran + GDP, Rate Law: nucleus*(r2*RCC1_RanGDP-r7*RCC1_Ran*GDP)
r5=100.0 pmicroMpsec; r4=55.0 psec Reaction: RCC1_RanGTP => RanGTP_nuc + RCC1, Rate Law: nucleus*(r4*RCC1_RanGTP-r5*RanGTP_nuc*RCC1)
r3=0.6 pmicroMpsec; r6=19.0 psec Reaction: RCC1_Ran + GTP => RCC1_RanGTP, Rate Law: nucleus*(r3*RCC1_Ran*GTP-r6*RCC1_RanGTP)
kpermRanGTP=0.03 psec Reaction: RanGTP_nuc => RanGTP_cy, Rate Law: kpermRanGTP*nucleus*(RanGTP_nuc-RanGTP_cy)
Km_GAP=0.7 microM; kcat_GAP=10.6 psec Reaction: RanGTP_cy => RanGDP_cy; RanGAP, Rate Law: cytoplasm*kcat_GAP*RanGTP_cy*RanGAP/(Km_GAP+RanGTP_cy)
kcat=10.8 psec; Km=0.1 microM Reaction: RanGTP_RanBP1 => RanGDP_cy + RanBP1; RanGAP, Rate Law: cytoplasm*kcat*RanGTP_RanBP1*RanGAP/(RanGTP_RanBP1+Km)
r8=55.0 psec; r1=74.0 pmicroMpsec Reaction: RanGDP_nuc + RCC1 => RCC1_RanGDP, Rate Law: nucleus*(r1*RanGDP_nuc*RCC1-r8*RCC1_RanGDP)

States:

Name Description
RCC1 RanGTP [GTP; GTP-binding nuclear protein Ran; Regulator of chromosome condensation; GTP]
RanGDP nuc [GTP-binding nuclear protein Ran; GDP]
GDP [GDP; GDP]
RCC1 [RCC1; Regulator of chromosome condensation]
RanGDP cy [GTP-binding nuclear protein Ran; GDP]
RanGTP nuc [GTP-binding nuclear protein Ran; GTP]
GTP [GTP; GTP]
RCC1 RanGDP [GDP; Regulator of chromosome condensation; GTP-binding nuclear protein Ran; GDP]
RanGTP cy [GTP-binding nuclear protein Ran; GTP]
RanBP1 [IPR000156; Ran-specific GTPase-activating protein]
RanGTP RanBP1 [GTP-binding nuclear protein Ran; Ran-specific GTPase-activating protein; GTP]
RCC1 Ran [Regulator of chromosome condensation; GTP-binding nuclear protein Ran]

Observables: none

H


BIOMD0000000109 @ v0.0.1

This model is according to the paper *A systems biology dynamical model of mammalian G1 cell cycle progression.* Supple…

The current dogma of G(1) cell-cycle progression relies on growth factor-induced increase of cyclin D:Cdk4/6 complex activity to partially inactivate pRb by phosphorylation and to sequester p27(Kip1)-triggering activation of cyclin E:Cdk2 complexes that further inactivate pRb. pRb oscillates between an active, hypophosphorylated form associated with E2F transcription factors in early G(1) phase and an inactive, hyperphosphorylated form in late G(1), S and G(2)/M phases. However, under constant growth factor stimulation, cells show constitutively active cyclin D:Cdk4/6 throughout the cell cycle and thereby exclude cyclin D:Cdk4/6 inactivation of pRb. To address this paradox, we developed a mathematical model of G(1) progression using physiological expression and activity profiles from synchronized cells exposed to constant growth factors and included a metabolically responsive, activating modifier of cyclin E:Cdk2. Our mathematical model accurately simulates G(1) progression, recapitulates observations from targeted gene deletion studies and serves as a foundation for development of therapeutics targeting G(1) cell-cycle progression. link: http://identifiers.org/pubmed/17299420

Parameters:

Name Description
kbYCyclinEYYCdk2 = 5.01E-5 Reaction: Cdk2Y010 + CyclinE => Cdk2Y011, Rate Law: kbYCyclinEYYCdk2*Cdk2Y010*CyclinE*X
kuYD4YYpRb = 0.1 Reaction: Cdk4Y01YpRbY00YpRbY10YInt => pRbY00 + Cdk4Y01, Rate Law: X*kuYD4YYpRb*Cdk4Y01YpRbY00YpRbY10YInt
kbYAPCCYYCyclinA = 1.61E-5 Reaction: CyclinA + APCC => APCCYCyclinAYInt, Rate Law: X*kbYAPCCYYCyclinA*CyclinA*APCC
kuYp27YYCdk4 = 0.1 Reaction: Cdk4Y11 => Cdk4Y01 + p27, Rate Law: kuYp27YYCdk4*Cdk4Y11*X
kdYE2F = 0.006465 Reaction: pRbY01 => pRbY00, Rate Law: kdYE2F*pRbY01*X
kbYCyclinAYYCdk2 = 9.52E-5 Reaction: Cdk2Y010 + CyclinA => Cdk2Y012, Rate Law: X*kbYCyclinAYYCdk2*Cdk2Y010*CyclinA
ktYpRbYYDephos = 0.023194 Reaction: pRbY20 => pRbY00, Rate Law: X*ktYpRbYYDephos*pRbY20
kuYE2FYYpRb = 0.1 Reaction: pRbY01 => pRbY00 + E2F, Rate Law: X*kuYE2FYYpRb*pRbY01
kupYE2YYpRb = 4.78271 Reaction: Cdk2Y011YpRbY10YpRbY20YInt => pRbY20 + Cdk2Y011, Rate Law: X*kupYE2YYpRb*Cdk2Y011YpRbY10YpRbY20YInt
kdYCyclinE = 0.05 Reaction: Cdk2Y011 => Cdk2Y010, Rate Law: kdYCyclinE*Cdk2Y011*X
kbYA2YYpRb = 6.25E-5 Reaction: pRbY11 + Cdk2Y012 => Cdk2Y012YpRbY11YpRbY21YInt, Rate Law: X*kbYA2YYpRb*pRbY11*Cdk2Y012
kuYp27YYCdk2 = 0.1 Reaction: Cdk2Y101 => Cdk2Y001 + p27, Rate Law: kuYp27YYCdk2*Cdk2Y101*X
kupYA2YYpRb = 0.200091 Reaction: Cdk2Y012YpRbY11YpRbY21YInt => pRbY21 + Cdk2Y012, Rate Law: X*kupYA2YYpRb*Cdk2Y012YpRbY11YpRbY21YInt
kdYCyclinA = 0.05 Reaction: Cdk2Y012 => Cdk2Y010, Rate Law: kdYCyclinA*Cdk2Y012*X
kYact = 0.0 Reaction: Cdk2Y000 => Cdk2Y010, Rate Law: kYact*Cdk2Y000*X
kdYEmi1 = 0.018158 Reaction: APCCYEmi1 => APCC, Rate Law: kdYEmi1*APCCYEmi1*X
kdYp27 = 0.001575 Reaction: Cdk2Y102 => Cdk2Y002, Rate Law: kdYp27*Cdk2Y102*X
kuYCyclinAYYCdk2 = 0.1 Reaction: Cdk2Y012 => Cdk2Y010 + CyclinA, Rate Law: X*kuYCyclinAYYCdk2*Cdk2Y012
kbYp27YYCdk2 = 1.23E-5 Reaction: Cdk2Y000 + p27 => Cdk2Y100, Rate Law: kbYp27YYCdk2*Cdk2Y000*p27*X
kbYE2YYpRb = 5.74E-5 Reaction: pRbY10 + Cdk2Y011 => Cdk2Y011YpRbY10YpRbY20YInt, Rate Law: X*kbYE2YYpRb*pRbY10*Cdk2Y011
kuYCyclinEYYCdk2 = 0.1 Reaction: Cdk2Y001 => Cdk2Y000 + CyclinE, Rate Law: kuYCyclinEYYCdk2*Cdk2Y001*X
kudYAPCCYYCyclinA = 4.999555 Reaction: APCCYCdk2Y000YCdk2Y002YInt => Cdk2Y000 + APCC, Rate Law: X*kudYAPCCYYCyclinA*APCCYCdk2Y000YCdk2Y002YInt
kuYAPCCYYCyclinA = 0.1 Reaction: APCCYCyclinAYInt => CyclinA + APCC, Rate Law: X*kuYAPCCYYCyclinA*APCCYCyclinAYInt
kbYD4YYpRb = 3.15E-5 Reaction: pRbY01 + Cdk4Y01 => Cdk4Y01YpRbY01YpRbY11YInt, Rate Law: X*kbYD4YYpRb*pRbY01*Cdk4Y01
kuYA2YYpRb = 0.1 Reaction: Cdk2Y012YpRbY10YpRbY20YInt => pRbY10 + Cdk2Y012, Rate Law: X*kuYA2YYpRb*Cdk2Y012YpRbY10YpRbY20YInt
kupYA1YYpRb = 0.202132 Reaction: Cdk1Y11YpRbY11YpRbY21YInt => pRbY21 + Cdk1Y11, Rate Law: X*kupYA1YYpRb*Cdk1Y11YpRbY11YpRbY21YInt
kuYE2YYpRb = 0.1 Reaction: Cdk2Y011YpRbY10YpRbY20YInt => pRbY10 + Cdk2Y011, Rate Law: X*kuYE2YYpRb*Cdk2Y011YpRbY10YpRbY20YInt
kbYE2FYYpRb = 9.66E-6 Reaction: pRbY00 + E2F => pRbY01, Rate Law: X*kbYE2FYYpRb*pRbY00*E2F
kd1Yp27 = 0.071149 Reaction: Cdk2Y111 => Cdk2Y011, Rate Law: kd1Yp27*Cdk2Y111*X

States:

Name Description
APCCYCdk1Y10YCdk1Y11YInt [Cyclin-dependent kinase 1; Anaphase-promoting complex subunit 2; IPR015453]
hyperphosphorylatedYpRb hyperphosphorylatedYpRb
Cdk2Y011YpRbY11YpRbY21YInt [G1/S-specific cyclin-E1; Cyclin-dependent kinase 2; Retinoblastoma-associated protein; IPR015633]
APCC [anaphase-promoting complex; Anaphase-promoting complex subunit 2]
Cdk2Y100 [Cyclin-dependent kinase 2; IPR015456]
Cdk2Y010 [Cyclin-dependent kinase 2]
pRbY01 [Rb-E2F complex]
Cdk2Y011 [Cyclin-dependent kinase 2; G1/S-specific cyclin-E1]
pRbY00 [Retinoblastoma-associated protein]
Cdk2Y012 [Cyclin-dependent kinase 2; IPR015453]
Cdk2Y012YpRbY10YpRbY20YInt [Cyclin-dependent kinase 2; Retinoblastoma-associated protein; IPR015453]
hypophosphorylatedYpRb hypophosphorylatedYpRb
pRbY11 [Retinoblastoma-associated protein; Rb-E2F complex]
p27 [IPR015456]
pRbY10 [Retinoblastoma-associated protein]
Cdk2Y001 [Cyclin-dependent kinase 2; G1/S-specific cyclin-E1]
pRbY21 [Retinoblastoma-associated protein; Rb-E2F complex]
Cdk2Y011YpRbY10YpRbY20YInt [G1/S-specific cyclin-E1; Cyclin-dependent kinase 2; Retinoblastoma-associated protein]
Cdk2Y012YpRbY11YpRbY21YInt [Cyclin-dependent kinase 2; Retinoblastoma-associated protein; IPR015453; IPR015633]
APCCYCdk1Y00YCdk1Y01YInt [Anaphase-promoting complex subunit 2; Cyclin-dependent kinase 1; IPR015453]
Cdk2Y002 [Cyclin-dependent kinase 2]

Observables: none

Haffez2017 - RAR interaction with synthetic analogues This model is described in the article: [The molecular basis of…

All-trans-retinoic acid (ATRA) and its synthetic analogues EC23 and EC19 direct cellular differentiation by interacting as ligands for the retinoic acid receptor (RARα, β and γ) family of nuclear receptor proteins. To date, a number of crystal structures of natural and synthetic ligands complexed to their target proteins have been solved, providing molecular level snap-shots of ligand binding. However, a deeper understanding of receptor and ligand flexibility and conformational freedom is required to develop stable and effective ATRA analogues for clinical use. Therefore, we have used molecular modelling techniques to define RAR interactions with ATRA and two synthetic analogues, EC19 and EC23, and compared their predicted biochemical activities to experimental measurements of relative ligand affinity and recruitment of coactivator proteins. A comprehensive molecular docking approach that explored the conformational space of the ligands indicated that ATRA is able to bind the three RAR proteins in a number of conformations with one extended structure being favoured. In contrast the biologically-distinct isomer, 9-cis-retinoic acid (9CRA), showed significantly less conformational flexibility in the RAR binding pockets. These findings were used to inform docking studies of the synthetic retinoids EC23 and EC19, and their respective methyl esters. EC23 was found to be an excellent mimic for ATRA, and occupied similar binding modes to ATRA in all three target RAR proteins. In comparison, EC19 exhibited an alternative binding mode which reduces the strength of key polar interactions in RARα/γ but is well-suited to the larger RARβ binding pocket. In contrast, docking of the corresponding esters revealed the loss of key polar interactions which may explain the much reduced biological activity. Our computational results were complemented using an in vitro binding assay based on FRET measurements, which showed that EC23 was a strongly binding, pan-agonist of the RARs, while EC19 exhibited specificity for RARβ, as predicted by the docking studies. These findings can account for the distinct behaviour of EC23 and EC19 in cellular differentiation assays, and additionally, the methods described herein can be further applied to the understanding of the molecular basis for the selectivity of different retinoids to RARα, β and γ. link: http://identifiers.org/doi/10.1039/C6MD00680A

Parameters:

Name Description
k2=0.2; k1=0.014 Reaction: LR + CA => LRCA, Rate Law: RAR_retinoids*(k1*LR*CA-k2*LRCA)
k1=0.6; k2=0.1 Reaction: L + R => LR, Rate Law: RAR_retinoids*(k1*L*R-k2*LR)

States:

Name Description
LR [all-trans-retinoic acid; Retinoic acid receptor alpha]
LRCA [all-trans-retinoic acid; Retinoic acid receptor alpha]
CA [fluorescin; peptide]
L [all-trans-retinoic acid]
R [Retinoic acid receptor alpha]

Observables: none

MODEL1006230014 @ v0.0.1

This a model from the article: The follicular automaton model: effect of stochasticity and of synchronization of hair…

Human scalp hair consists of a set of about 10(5)follicles which progress independently through developmental cycles. Each hair follicle successively goes through the anagen (A), catagen (C), telogen (T) and latency (L) phases that correspond, respectively, to growth, arrest and hair shedding before a new anagen phase is initiated. Long-term experimental observations in a group of ten male, alopecic and non-alopecic volunteers allowed determination of the characteristics of hair follicle cycles. On the basis of these observations, we previously proposed a follicular automaton model to simulate the dynamics of human hair cycles and the development of different patterns of alopecia [Halloy et al. (2000) Proc. Natl Acad. Sci. U.S.A.97, 8328-8333]. The automaton model is defined by a set of rules that govern the stochastic transitions of each follicle between the successive states A, T, L and the subsequent return to A. These transitions occur independently for each follicle, after time intervals given stochastically by a distribution characterized by a mean and a standard deviation. The follicular automaton model was shown to account both for the dynamical transitions observed in a single follicle, and for the behaviour of an ensemble of independently cycling follicles. Here, we extend these results and investigate additional properties of the model. We present a deterministic version of the follicular automaton. We show that numerical simulations of the stochastic version of the automaton yield steady-state level of follicles in the different phases which approach the levels predicted by the deterministic equations as the number of follicles progressively increases. Only the stochastic version can successfully reproduce the fluctuations of the fractions of follicles in each of the three phases, observed in small follicle populations. When the standard deviation is reduced or when the follicles become otherwise synchronized, e.g. by a periodic external signal inducing the transition of anagen follicles into telogen phase, large-amplitude oscillations occur in the fractions of follicles in the three phases. These oscillations are not observed in humans but are reminiscent of the phenomenon of moulting observed in a number of mammalian species. link: http://identifiers.org/pubmed/11846603

Parameters: none

States: none

Observables: none

Hamey2017 - Blood stem cell regulatory networkThis model is described in the article: [Reconstructing blood stem cell r…

Adult blood contains a mixture of mature cell types, each with specialized functions. Single hematopoietic stem cells (HSCs) have been functionally shown to generate all mature cell types for the lifetime of the organism. Differentiation of HSCs toward alternative lineages must be balanced at the population level by the fate decisions made by individual cells. Transcription factors play a key role in regulating these decisions and operate within organized regulatory programs that can be modeled as transcriptional regulatory networks. As dysregulation of single HSC fate decisions is linked to fatal malignancies such as leukemia, it is important to understand how these decisions are controlled on a cell-by-cell basis. Here we developed and applied a network inference method, exploiting the ability to infer dynamic information from single-cell snapshot expression data based on expression profiles of 48 genes in 2,167 blood stem and progenitor cells. This approach allowed us to infer transcriptional regulatory network models that recapitulated differentiation of HSCs into progenitor cell types, focusing on trajectories toward megakaryocyte–erythrocyte progenitors and lymphoid-primed multipotent progenitors. By comparing these two models, we identified and subsequently experimentally validated a difference in the regulation of nuclear factor, erythroid 2 (Nfe2) and core-binding factor, runt domain, alpha subunit 2, translocated to, 3 homolog (Cbfa2t3h) by the transcription factor Gata2. Our approach confirms known aspects of hematopoiesis, provides hypotheses about regulation of HSC differentiation, and is widely applicable to other hierarchical biological systems to uncover regulatory relationships. link: http://identifiers.org/doi/10.1073/pnas.1610609114

Parameters: none

States: none

Observables: none

Hamey2017 - Blood stem cell regulatory network (LMPP network)This model is described in the article: [Reconstructing bl…

Adult blood contains a mixture of mature cell types, each with specialized functions. Single hematopoietic stem cells (HSCs) have been functionally shown to generate all mature cell types for the lifetime of the organism. Differentiation of HSCs toward alternative lineages must be balanced at the population level by the fate decisions made by individual cells. Transcription factors play a key role in regulating these decisions and operate within organized regulatory programs that can be modeled as transcriptional regulatory networks. As dysregulation of single HSC fate decisions is linked to fatal malignancies such as leukemia, it is important to understand how these decisions are controlled on a cell-by-cell basis. Here we developed and applied a network inference method, exploiting the ability to infer dynamic information from single-cell snapshot expression data based on expression profiles of 48 genes in 2,167 blood stem and progenitor cells. This approach allowed us to infer transcriptional regulatory network models that recapitulated differentiation of HSCs into progenitor cell types, focusing on trajectories toward megakaryocyte–erythrocyte progenitors and lymphoid-primed multipotent progenitors. By comparing these two models, we identified and subsequently experimentally validated a difference in the regulation of nuclear factor, erythroid 2 (Nfe2) and core-binding factor, runt domain, alpha subunit 2, translocated to, 3 homolog (Cbfa2t3h) by the transcription factor Gata2. Our approach confirms known aspects of hematopoiesis, provides hypotheses about regulation of HSC differentiation, and is widely applicable to other hierarchical biological systems to uncover regulatory relationships. link: http://identifiers.org/doi/10.1073/pnas.1610609114

Parameters: none

States: none

Observables: none

its a nine species reduced model of Hockin 2002. Model uses different level of reduction (5,7,9,11) and testing the best…

Mathematical modeling of thrombosis typically involves modeling the coagulation cascade. Models of coagulation generally involve the reaction kinetics for dozens of proteins. The resulting system of equations is difficult to parameterize and its numerical solution is challenging when coupled to blood flow or other physics important to clotting. Prior research suggests that essential aspects of coagulation may be reproduced by simpler models. This evidence motivates a systematic approach to model reduction. We herein introduce an automated framework to generate reduced-order models of blood coagulation. The framework consists of nested optimizations, where an outer optimization selects the optimal species for the reduced-order model and an inner optimization selects the optimal reaction rates for the new coagulation network. The framework was tested on an established 34-species coagulation model to rigorously consider what level of model fidelity is necessary to capture essential coagulation dynamics. The results indicate that a nine-species reduced-order model is sufficient to reproduce the thrombin dynamics of the benchmark 34-species model for a range of tissue factor concentrations, including those not included in the optimization process. Further model reduction begins to compromise the ability to capture the thrombin generation process. The framework proposed herein enables automated development of reduced-order models of coagulation that maintain essential dynamics used to model thrombosis. link: http://identifiers.org/pubmed/31161687

Parameters:

Name Description
k1=121.267 Reaction: TF + X => Xa_Va, Rate Law: compartment*k1*TF*X
k1=0.0201671 Reaction: IIa => IIa_ATIII, Rate Law: compartment*k1*IIa
k1=77540.2 Reaction: Xa_Va_II => Xa_Va + mIIa, Rate Law: compartment*k1*Xa_Va_II
k1=2.56984E12 Reaction: Xa_Va + II => Xa_Va_II, Rate Law: compartment*k1*Xa_Va*II
k1=4.74645E-16 Reaction: TF + X + II => TF + X + IIa, Rate Law: compartment*k1*TF*X*II
k1=6.96794E10 Reaction: Xa_Va + mIIa => Xa_Va + IIa, Rate Law: compartment*k1*Xa_Va*mIIa
k1=0.00472749 Reaction: mIIa => mIIa_ATIII, Rate Law: compartment*k1*mIIa

States:

Name Description
mIIa [Prothrombin]
mIIa ATIII [Prothrombin; Antithrombin-III]
IIa [Prothrombin]
IIa ATIII [Antithrombin-III; Prothrombin]
X [Coagulation factor X]
Xa Va [Coagulation factor X; Coagulation factor V]
Xa Va II [Coagulation factor V; Coagulation factor X; Prothrombin]
TF [Tissue factor]
II [Prothrombin]

Observables: none

its a seven species reduced model of Hockin 2002. Model uses different level of reduction (5,7,9,11) and testing the bes…

Mathematical modeling of thrombosis typically involves modeling the coagulation cascade. Models of coagulation generally involve the reaction kinetics for dozens of proteins. The resulting system of equations is difficult to parameterize and its numerical solution is challenging when coupled to blood flow or other physics important to clotting. Prior research suggests that essential aspects of coagulation may be reproduced by simpler models. This evidence motivates a systematic approach to model reduction. We herein introduce an automated framework to generate reduced-order models of blood coagulation. The framework consists of nested optimizations, where an outer optimization selects the optimal species for the reduced-order model and an inner optimization selects the optimal reaction rates for the new coagulation network. The framework was tested on an established 34-species coagulation model to rigorously consider what level of model fidelity is necessary to capture essential coagulation dynamics. The results indicate that a nine-species reduced-order model is sufficient to reproduce the thrombin dynamics of the benchmark 34-species model for a range of tissue factor concentrations, including those not included in the optimization process. Further model reduction begins to compromise the ability to capture the thrombin generation process. The framework proposed herein enables automated development of reduced-order models of coagulation that maintain essential dynamics used to model thrombosis. link: http://identifiers.org/pubmed/31161687

Parameters: none

States: none

Observables: none

This model provides an in silico mathematical platform to explore the interactions between chimeric antigen receptor-mod…

Advances in genetic engineering have made it possible to reprogram individual immune cells to express receptors that recognise markers on tumour cell surfaces. The process of re-engineering T cell lymphocytes to express Chimeric Antigen Receptors (CARs), and then re-infusing the CAR-modified T cells into patients to treat various cancers is referred to as CAR T cell therapy. This therapy is being explored in clinical trials - most prominently for B Cell Acute Lymphoblastic Leukaemia (B-ALL), a common B cell malignancy, for which CAR T cell therapy has led to remission in up to 90% of patients. Despite this extraordinary response rate, however, potentially fatal inflammatory side effects occur in up to 10% of patients who have positive responses. Further, approximately 50% of patients who initially respond to the therapy relapse. Significant improvement is thus necessary before the therapy can be made widely available for use in the clinic.

To inform future development, we develop a mathematical model to explore interactions between CAR T cells, inflammatory toxicity, and individual patients’ tumour burdens in silico. This paper outlines the underlying system of coupled ordinary differential equations designed based on well-known immunological principles and widely accepted views on the mechanism of toxicity development in CAR T cell therapy for B-ALL - and reports in silico outcomes in relationship to standard and recently conjectured predictors of toxicity in a heterogeneous, randomly generated patient population. Our initial results and analyses are consistent with and connect immunological mechanisms to the clinically observed, counterintuitive hypothesis that initial tumour burden is a stronger predictor of toxicity than is the dose of CAR T cells administered to patients.

We outline how the mechanism of action in CAR T cell therapy can give rise to such non-standard trends in toxicity development, and demonstrate the utility of mathematical modelling in understanding the relationship between predictors of toxicity, mechanism of action, and patient outcomes. link: http://identifiers.org/doi/10.1101/049908

Parameters:

Name Description
p_1 = 0.002 Reaction: => Inflam; B, C_e, H_e, Rate Law: compartment*p_1*B*(C_e+H_e)
r_4 = 0.1; Lymphocyte_Term = 0.0 Reaction: => L; L, Rate Law: compartment*r_4*L*Lymphocyte_Term
p_0 = 200.0 Reaction: => Inflam, Rate Law: compartment*p_0
d_3 = 0.004 Reaction: C_e =>, Rate Law: compartment*d_3*C_e
d_4 = 0.004 Reaction: H_e =>, Rate Law: compartment*d_4*H_e
d_1 = 2.0E-4 Reaction: B => ; C_e, Rate Law: compartment*d_1*B*C_e
Lymphocyte_Term = 0.0; r_3 = 0.1 Reaction: => H_m; H_m, Rate Law: compartment*r_3*H_m*Lymphocyte_Term
k = 4800.0; r_1 = 0.003 Reaction: => B; B, Rate Law: compartment*r_1*B*(1-B/k)
b = 800.0; a_3 = 8.0E-5 Reaction: H_m => ; B, Inflam, Rate Law: compartment*a_3*B*H_m*Inflam^2/(Inflam^2+b^2)
n = 6.0; b = 800.0; a_1 = 4.0E-7; a_2 = 2.0 Reaction: => C_e; B, C_m, Inflam, H_e, Rate Law: compartment*2^n*a_1*B*C_m*Inflam^2/(Inflam^2+b^2)*(1+a_2*H_e)
b = 800.0; a_1 = 4.0E-7; a_2 = 2.0 Reaction: C_m => ; B, H_e, Inflam, Rate Law: compartment*a_1*B*C_m*(1+a_2*H_e)*Inflam^2/(Inflam^2+b^2)
p_2 = 0.4 Reaction: => L, Rate Law: compartment*p_2
d_2 = 1.5 Reaction: Inflam =>, Rate Law: compartment*d_2*Inflam
n = 6.0; b = 800.0; a_3 = 8.0E-5 Reaction: => H_e; B, H_m, Inflam, Rate Law: compartment*2^n*a_3*B*H_m*Inflam^2/(Inflam^2+b^2)
d_5 = 2.0E-4 Reaction: L =>, Rate Law: compartment*d_5*L
r_2 = 0.1; Lymphocyte_Term = 0.0 Reaction: => C_m; C_m, Inflam, Rate Law: compartment*r_2*C_m*Lymphocyte_Term

States:

Name Description
H m [helper T cell]
B [BTO:0000731]
C m [cytotoxic T cell]
Inflam [inflammatory response]
H e [helper T cell]
C e [cytotoxic T cell]
L [lymphocyte]

Observables: none

Mathematical model of blood coagulation. Reused Wajima2009 model with modifications to reactions 27 (formation of Va:Xa…

Warfarin is the anticoagulant of choice for venous thromboembolism (VTE) treatment, although its suppression of the endogenous clot-dissolution complex APC:PS may ultimately lead to longer time-to-clot dissolution profiles, resulting in increased risk of re-thrombosis. This detrimental effect might not occur during VTE treatment using other anticoagulants, such as rivaroxaban or enoxaparin, given their different mechanisms of action within the coagulation network. A quantitative systems pharmacology model was developed describing the coagulation network to monitor clotting factor levels under warfarin, enoxaparin, and rivaroxaban treatment. The model allowed for estimation of all factor rate constants and production rates. Predictions of individual coagulation factor time courses under steady-state warfarin, enoxaparin, and rivaroxaban treatment reflected the suppression of protein C and protein S under warfarin compared to rivaroxaban and enoxaparin. The model may be used as a tool during clinical practice to predict effects of anticoagulants on individual clotting factor time courses and optimize antithrombotic therapy. link: http://identifiers.org/pubmed/27647667

Parameters: none

States: none

Observables: none

The p53 transcription factor is a regulator of key cellular processes including DNA repair, cell cycle arrest, and apopt…

The p53 transcription factor is a regulator of key cellular processes including DNA repair, cell cycle arrest, and apoptosis. In this theoretical study, we investigate how the complex circuitry of the p53 network allows for stochastic yet unambiguous cell fate decision-making. The proposed Markov chain model consists of the regulatory core and two subordinated bistable modules responsible for cell cycle arrest and apoptosis. The regulatory core is controlled by two negative feedback loops (regulated by Mdm2 and Wip1) responsible for oscillations, and two antagonistic positive feedback loops (regulated by phosphatases Wip1 and PTEN) responsible for bistability. By means of bifurcation analysis of the deterministic approximation we capture the recurrent solutions (i.e., steady states and limit cycles) that delineate temporal responses of the stochastic system. Direct switching from the limit-cycle oscillations to the "apoptotic" steady state is enabled by the existence of a subcritical Neimark-Sacker bifurcation in which the limit cycle loses its stability by merging with an unstable invariant torus. Our analysis provides an explanation why cancer cell lines known to have vastly diverse expression levels of Wip1 and PTEN exhibit a broad spectrum of responses to DNA damage: from a fast transition to a high level of p53 killer (a p53 phosphoform which promotes commitment to apoptosis) in cells characterized by high PTEN and low Wip1 levels to long-lasting p53 level oscillations in cells having PTEN promoter methylated (as in, e.g., MCF-7 cell line). link: http://identifiers.org/pubmed/26928575

Parameters:

Name Description
u6 = 1.0E-4 Reaction: Cyclin_E_p21_complex => p21__free + Cyclin_E__free, Rate Law: nuclear*u6*Cyclin_E_p21_complex
g16 = 1.0E-4 Reaction: Mdm2_nuc_S166S186p_S395p =>, Rate Law: nuclear*g16*Mdm2_nuc_S166S186p_S395p
b2 = 0.003 Reaction: BclXL__free + Bad_0__free =>, Rate Law: cytoplasm*b2*BclXL__free*Bad_0__free
s1 = 0.1; q0_wip1 = 1.0E-5; q1_wip1 = 3.0E-13; h = 2.0; q2 = 0.003 Reaction: => Wip1_mRNA; p53_arrester, Rate Law: nuclear*s1*(q0_wip1+q1_wip1*p53_arrester^h)/(q2+q0_wip1+q1_wip1*p53_arrester^h)
b3 = 0.003 Reaction: Bad_phosphorylated__free => ; Fourteen33_free, Rate Law: b3*Fourteen33_free*Bad_phosphorylated__free
p3 = 3.0E-8 Reaction: p53_0phosphorylated => p53_arrester; ATM_phosphorylated, Rate Law: nuclear*p3*ATM_phosphorylated*p53_0phosphorylated
g17 = 3.0E-4 Reaction: proCaspase =>, Rate Law: nuclear*g17*proCaspase
g6 = 3.0E-5 Reaction: PTEN =>, Rate Law: nuclear*g6*PTEN
g14 = 1.0E-4 Reaction: Mdm2_cyt_0phosphorylated =>, Rate Law: cytoplasm*g14*Mdm2_cyt_0phosphorylated
t5 = 0.1 Reaction: => p21__free; p21_mRNA, Rate Law: nuclear*t5*p21_mRNA
d9 = 3.0E-5 Reaction: Bad_phosphorylated__free => Bad_0__free, Rate Law: cytoplasm*d9*Bad_phosphorylated__free
d4 = 1.0E-10 Reaction: p53_killer => p53_arrester; Wip1, Rate Law: nuclear*d4*Wip1*p53_killer
s8 = 30.0 Reaction: => HIPK2, Rate Law: nuclear*s8
d8 = 1.0E-4 Reaction: AKT_phosphorylated =>, Rate Law: cytoplasm*d8*AKT_phosphorylated
h = 2.0; p1 = 3.0E-4; M1 = 5.0 Reaction: => ATM_phosphorylated; ATM_0, DNA_double_strand_break, Rate Law: nuclear*p1*ATM_0*DNA_double_strand_break^h/(DNA_double_strand_break^h+M1^h)
s9 = 30.0; M3 = 200000.0 Reaction: => Cyclin_E__free; E2F1, Rate Law: nuclear*s9*E2F1^2/(M3^2+E2F1^2)
g7 = 1.0E-13 Reaction: HIPK2 => ; SIAH1_0, Mdm2_nuc_S166S186phosphorylated, Rate Law: nuclear*g7*HIPK2*(SIAH1_0+Mdm2_nuc_S166S186phosphorylated)^2
s10 = 3.0 Reaction: => Cyclin_E__free, Rate Law: nuclear*s10
g20 = 1.0E-4 Reaction: Cyclin_E__free =>, Rate Law: nuclear*g20*Cyclin_E__free
q1_p21 = 3.0E-13; q0_p21 = 1.0E-5; s5 = 0.1; h = 2.0; q2 = 0.003 Reaction: => p21_mRNA; p53_arrester, Rate Law: nuclear*s5*(q0_p21+q1_p21*p53_arrester^h)/(q2+q0_p21+q1_p21*p53_arrester^h)
p8 = 3.0E-9 Reaction: => PIP3; PIP2, PI3K_tot, Rate Law: nuclear*p8*PIP2*PI3K_tot
p7 = 3.0E-9 Reaction: Bad_0__free => Bad_phosphorylated__free; AKT_phosphorylated, Rate Law: cytoplasm*p7*AKT_phosphorylated*Bad_0__free
t1 = 0.1 Reaction: => Wip1; Wip1_mRNA, Rate Law: nuclear*t1*Wip1_mRNA
u3 = 0.001 Reaction: => Bad_phosphorylated__free; Bad_phosphorylated_Fourteen33_complex, Rate Law: cytoplasm*u3*Bad_phosphorylated_Fourteen33_complex
s7 = 30.0 Reaction: => proCaspase, Rate Law: nuclear*s7
p11 = 1.0E-10 Reaction: p53_0phosphorylated => p53_S46phosphorylated; HIPK2, Rate Law: nuclear*p11*HIPK2*p53_0phosphorylated
d7 = 3.0E-7 Reaction: PIP3 => ; PTEN, Rate Law: nuclear*d7*PTEN*PIP3
d10 = 1.0E-4 Reaction: p53_killer => p53_S46phosphorylated, Rate Law: nuclear*d10*p53_killer
t3 = 0.1 Reaction: => Mdm2_cyt_0phosphorylated; Mdm2_mRNA, Rate Law: t3*Mdm2_mRNA
u2 = 0.001 Reaction: => Bad_0__free; BclXL_Bad_complex, Rate Law: cytoplasm*u2*BclXL_Bad_complex
s6 = 300.0 Reaction: => p53_0phosphorylated, Rate Law: nuclear*s6
DNA_DSB_due_to_IR = 0.0333333333333333; h1 = 1.0E-6; is_IR_switched_on = 0.0; h2 = 1.0E-13; DNA_DSB_max = 1000000.0 Reaction: => DNA_double_strand_break; Caspase, DNA_double_strand_break, Rate Law: nuclear*(h1*DNA_DSB_due_to_IR*is_IR_switched_on+h2*Caspase)*(DNA_DSB_max-DNA_double_strand_break)
g18 = 3.0E-4 Reaction: Caspase =>, Rate Law: nuclear*g18*Caspase
p5 = 1.0E-8 Reaction: Mdm2_cyt_0phosphorylated => Mdm2_cyt_S166S186phosphorylated; AKT_phosphorylated, Rate Law: cytoplasm*p5*AKT_phosphorylated*Mdm2_cyt_0phosphorylated
d5 = 1.0E-4 Reaction: Mdm2_cyt_S166S186phosphorylated => Mdm2_cyt_0phosphorylated, Rate Law: cytoplasm*d5*Mdm2_cyt_S166S186phosphorylated
d11 = 1.0E-10 Reaction: p53_S46phosphorylated => p53_0phosphorylated; Wip1, Rate Law: nuclear*d11*Wip1*p53_S46phosphorylated
t2 = 0.1 Reaction: => PTEN; PTEN_mRNA, Rate Law: nuclear*t2*PTEN_mRNA
a1 = 3.0E-10 Reaction: proCaspase => Caspase; Bax__free, Rate Law: nuclear*a1*Bax__free*proCaspase
rep = 0.001; DNA_DSB_RepairCplx_total = 20.0 Reaction: DNA_double_strand_break =>, Rate Law: nuclear*DNA_double_strand_break*rep/(DNA_double_strand_break+DNA_DSB_RepairCplx_total)
g101 = 1.0E-5; h = 2.0; g11 = 1.0E-11 Reaction: p53_0phosphorylated => ; Mdm2_nuc_S166S186phosphorylated, Rate Law: nuclear*(g101+g11*Mdm2_nuc_S166S186phosphorylated^h)*p53_0phosphorylated
g3 = 3.0E-4 Reaction: Mdm2_mRNA =>, Rate Law: nuclear*g3*Mdm2_mRNA
p12 = 1.0E-9 Reaction: => AKT_phosphorylated; AKT_0, PIP3, Rate Law: p12*AKT_0*PIP3
g5 = 3.0E-4 Reaction: p21_mRNA =>, Rate Law: nuclear*g5*p21_mRNA
p2 = 1.0E-8 Reaction: SIAH1_0 => ; ATM_phosphorylated, Rate Law: nuclear*p2*ATM_phosphorylated*SIAH1_0
d6 = 1.0E-10 Reaction: Mdm2_nuc_S166S186p_S395p => Mdm2_nuc_S166S186phosphorylated; Wip1, Rate Law: nuclear*d6*Wip1*Mdm2_nuc_S166S186p_S395p
q1_pten = 3.0E-13; s2 = 0.03; h = 2.0; q0_pten = 1.0E-5; q2 = 0.003 Reaction: => PTEN_mRNA; p53_killer, Rate Law: nuclear*s2*(q0_pten+q1_pten*p53_killer^h)/(q2+q0_pten+q1_pten*p53_killer^h)
d3 = 1.0E-4 Reaction: p53_arrester => p53_0phosphorylated, Rate Law: nuclear*d3*p53_arrester
a2 = 1.0E-12 Reaction: proCaspase => Caspase, Rate Law: nuclear*a2*Caspase^2*proCaspase
g8 = 3.0E-4 Reaction: Wip1 =>, Rate Law: nuclear*g8*Wip1
g15 = 3.0E-5 Reaction: Mdm2_nuc_S166S186phosphorylated =>, Rate Law: nuclear*g15*Mdm2_nuc_S166S186phosphorylated
d1 = 1.0E-8 Reaction: ATM_phosphorylated => ; Wip1, Rate Law: nuclear*d1*Wip1*ATM_phosphorylated
g101 = 1.0E-5; h = 2.0; g12 = 1.0E-13 Reaction: p53_arrester => ; Mdm2_nuc_S166S186phosphorylated, Rate Law: nuclear*(g101+g12*Mdm2_nuc_S166S186phosphorylated^h)*p53_arrester
g19 = 3.0E-4 Reaction: p21__free =>, Rate Law: nuclear*g19*p21__free
i1 = 0.001 Reaction: Mdm2_cyt_S166S186phosphorylated => Mdm2_nuc_S166S186phosphorylated, Rate Law: i1*Mdm2_cyt_S166S186phosphorylated
h = 2.0; g10 = 1.0E-5; g13 = 1.0E-13 Reaction: p53_S46phosphorylated => ; Mdm2_nuc_S166S186phosphorylated, Rate Law: nuclear*(g10+g13*Mdm2_nuc_S166S186phosphorylated^h)*p53_S46phosphorylated
g2 = 3.0E-4 Reaction: PTEN_mRNA =>, Rate Law: nuclear*g2*PTEN_mRNA
b5 = 1.0E-5 Reaction: p21__free + Cyclin_E__free => Cyclin_E_p21_complex, Rate Law: nuclear*b5*p21__free*Cyclin_E__free
q0_mdm2 = 1.0E-4; q1_mdm2 = 3.0E-13; h = 2.0; s3 = 0.1; q2 = 0.003 Reaction: => Mdm2_mRNA; p53_arrester, Rate Law: nuclear*s3*(q0_mdm2+q1_mdm2*p53_arrester^h)/(q2+q0_mdm2+q1_mdm2*p53_arrester^h)
p4 = 1.0E-10 Reaction: p53_arrester => p53_killer; HIPK2, Rate Law: nuclear*p4*HIPK2*p53_arrester
d2 = 3.0E-5 Reaction: => SIAH1_0; SIAH1_phosphorylated, Rate Law: nuclear*d2*SIAH1_phosphorylated
g1 = 3.0E-4 Reaction: Wip1_mRNA =>, Rate Law: nuclear*g1*Wip1_mRNA
p6 = 1.0E-8 Reaction: Mdm2_nuc_S166S186phosphorylated => Mdm2_nuc_S166S186p_S395p; ATM_phosphorylated, Rate Law: nuclear*p6*ATM_phosphorylated*Mdm2_nuc_S166S186phosphorylated

States:

Name Description
Mdm2 nuc S166S186p S395p [E3 ubiquitin-protein ligase Mdm2; phosphorylated]
Caspase [Caspase-2]
Wip1 [Protein phosphatase 1D]
BclXL free [Bcl-2-like protein 1]
Bad phosphorylated free [Bcl2-associated agonist of cell death; phosphorylated]
PTEN [Phosphatidylinositol 3,4,5-trisphosphate 3-phosphatase and dual-specificity protein phosphatase PTEN]
proCaspase [Precursor]
p53 S46phosphorylated [Cellular tumor antigen p53; phosphorylated]
p53 0phosphorylated [Cellular tumor antigen p53; phosphorylated]
p53 arrester [Cellular tumor antigen p53]
Wip1 mRNA [Protein phosphatase 1D; ribonucleic acid]
PTEN mRNA [Phosphatidylinositol 3,4,5-trisphosphate 3-phosphatase and dual-specificity protein phosphatase PTEN; ribonucleic acid]
PIP2 PIP2
Bad phosphorylated Fourteen33 complex [14-3-3 protein sigma; Bcl2-associated agonist of cell death; phosphorylated]
p53 killer [Cellular tumor antigen p53]
Mdm2 cyt S166S186phosphorylated [E3 ubiquitin-protein ligase Mdm2; phosphorylated]
PIP3 PIP3
p21 free [p21 RAS Protein]
Bad 0 free [Bcl2-associated agonist of cell death]
ATM 0 [Serine-protein kinase ATM]
Rb phosphorylated [Retinoblastoma-associated protein; phosphorylated]
Cyclin E p21 complex [p21 RAS Protein; G1/S-specific cyclin-E2]
SIAH1 phosphorylated [E3 ubiquitin-protein ligase SIAH1; phosphorylated]
AKT phosphorylated [RAC-alpha serine/threonine-protein kinase; phosphorylated]
E2F1 [Transcription factor E2F1]
AKT 0 [RAC-alpha serine/threonine-protein kinase]
Fourteen33 free [14-3-3 protein sigma]
Mdm2 nuc S166S186phosphorylated [E3 ubiquitin-protein ligase Mdm2; phosphorylated]
Cyclin E free [G1/S-specific cyclin-E2]
Mdm2 cyt 0phosphorylated [E3 ubiquitin-protein ligase Mdm2; phosphorylated]
BclXL Bad complex [Bcl2-associated agonist of cell death; Bcl-2-like protein 1]
SIAH1 0 [E3 ubiquitin-protein ligase SIAH1]
HIPK2 [Homeodomain-interacting protein kinase 2]
DNA double strand break [site of double-strand break]
ATM phosphorylated [Serine-protein kinase ATM; phosphorylated]
Mdm2 mRNA [E3 ubiquitin-protein ligase Mdm2; ribonucleic acid]
p21 mRNA [p21 RAS Protein; ribonucleic acid]

Observables: none

BIOMD0000000146 @ v0.0.1

Figure4 and Figure5 can be simulated by Copasi. Figure4 can be simulated in MathSBML as well. There are some typos in th…

ErbB tyrosine kinase receptors mediate mitogenic signal cascade by binding a variety of ligands and recruiting the different cassettes of adaptor proteins. In the present study, we examined heregulin (HRG)-induced signal transduction of ErbB4 receptor and found that the phosphatidylinositol 3'-kinase (PI3K)-Akt pathway negatively regulated the extracellular signal-regulated kinase (ERK) cascade by phosphorylating Raf-1 on Ser(259). As the time-course kinetics of Akt and ERK activities seemed to be transient and complex, we constructed a mathematical simulation model for HRG-induced ErbB4 receptor signalling to explain the dynamics of the regulation mechanism in this signal transduction cascade. The model reflected well the experimental results observed in HRG-induced ErbB4 cells and in other modes of growth hormone-induced cell signalling that involve Raf-Akt cross-talk. The model suggested that HRG signalling is regulated by protein phosphatase 2A as well as Raf-Akt cross-talk, and protein phosphatase 2A modulates the kinase activity in both the PI3K-Akt and MAPK (mitogen-activated protein kinase) pathways. link: http://identifiers.org/pubmed/12691603

Parameters:

Name Description
k_7 = 546.0; k7 = 60.0 Reaction: RShP + GS => RShGS, Rate Law: compartment_0000001*(k7*RShP*GS-k_7*RShGS)
k1 = 0.0012; k_1 = 7.6E-4 Reaction: R + HRG => RHRG, Rate Law: compartment_0000001*(k1*R*HRG-k_1*RHRG)
k_6 = 5.0; k6 = 20.0 Reaction: RShc => RShP, Rate Law: compartment_0000001*(k6*RShc-k_6*RShP)
K22 = 60.0; K20 = 160.0; k20 = 0.3 Reaction: ERKP => ERK; ERKPP, MKP3, Rate Law: compartment_0000001*k20*MKP3*ERKP/(K20*(1+ERKPP/K22)+ERKP)
V28 = 17000.0; K28 = 9.02 Reaction: PIP3 => P_I, Rate Law: compartment_0000001*V28*PIP3/(K28+PIP3)
k17 = 2.9; K15 = 317.0; K17 = 317.0 Reaction: MEKP => MEKPP; MEK, Rafstar, Rate Law: compartment_0000001*k17*Rafstar*MEKP/(K17*(1+MEK/K15)+MEKP)
k18 = 0.058; K16 = 2200.0; K33 = 12.0; K18 = 60.0; K31 = 4.35 Reaction: MEKPP => MEKP; AktPIP, AktPIPP, PP2A, Rate Law: compartment_0000001*k18*PP2A*MEKPP/(K18*(1+MEKP/K16+AktPIPP/K31+AktPIPP/K33)+MEKPP)
K16 = 2200.0; K33 = 12.0; K18 = 60.0; k16 = 0.058; K31 = 4.35 Reaction: MEKP => MEK; MEKPP, AktPIP, AktPIPP, PP2A, Rate Law: compartment_0000001*k16*PP2A*MEKP/(K16*(1+MEKPP/K18+AktPIP/K31+AktPIPP/K33)+MEKP)
k2 = 0.01; k_2 = 0.1 Reaction: RHRG => RHRG2, Rate Law: compartment_0000001*(k2*RHRG^2-k_2*RHRG2)
K4 = 50.0; V4 = 62.5 Reaction: RP => RHRG2, Rate Law: compartment_0000001*V4*RP/(K4+RP)
k29 = 507.0; k_29 = 234.0 Reaction: PIP3 + Akt => AktPIP3, Rate Law: compartment_0000001*(k29*PIP3*Akt-k_29*AktPIP3)
K19 = 146000.0; K21 = 146000.0; k19 = 9.5 Reaction: ERK => ERKP; MEKPP, Rate Law: compartment_0000001*k19*MEKPP*ERK/(K19*(1+ERKP/K21)+ERK)
K16 = 2200.0; K33 = 12.0; K18 = 60.0; k31 = 0.107; K31 = 4.35 Reaction: AktPIP => AktPIP3; MEKP, MEKPP, AktPIPP, PP2A, Rate Law: compartment_0000001*k31*PP2A*AktPIP/(K31*(1+MEKP/K16+MEKPP/K18+AktPIPP/K33)+AktPIP)
k_9 = 0.0; k9 = 40.8 Reaction: ShGS => GS + ShP, Rate Law: compartment_0000001*(k9*ShGS-k_9*GS*ShP)
K12 = 0.0571; V12 = 0.289 Reaction: RasGTP => RasGDP, Rate Law: compartment_0000001*V12*RasGTP/(K12+RasGTP)
k8 = 2040.0; k_8 = 15700.0 Reaction: RShGS => ShGS + RP, Rate Law: compartment_0000001*(k8*RShGS-k_8*ShGS*RP)
K26 = 3680.0; V26 = 2620.0 Reaction: PI3Kstar => PI3K, Rate Law: compartment_0000001*V26*PI3Kstar/(K26+PI3Kstar)
K22 = 60.0; K20 = 160.0; k22 = 0.27 Reaction: ERKPP => ERKP; MKP3, Rate Law: compartment_0000001*k22*MKP3*ERKPP/(K22*(1+ERKP/K20)+ERKPP)
V30 = 20000.0; K30 = 80000.0; K32 = 80000.0 Reaction: AktPIP3 => AktPIP, Rate Law: compartment_0000001*V30*AktPIP3/(K30*(1+AktPIP/K32)+AktPIP3)
K33 = 12.0; K16 = 2200.0; K18 = 60.0; K31 = 4.35; k33 = 0.211 Reaction: AktPIPP => AktPIP; MEKP, MEKPP, PP2A, Rate Law: compartment_0000001*k33*PP2A*AktPIPP/(K33*(1+MEKP/K16+MEKPP/K18+AktPIP/K31)+AktPIPP)
k_3 = 0.01; k3 = 1.0 Reaction: RHRG2 => RP, Rate Law: compartment_0000001*(k3*RHRG2-k_3*RP)
k5 = 0.1; k_5 = 1.0 Reaction: RP + Shc => RShc, Rate Law: compartment_0000001*(k5*RP*Shc-k_5*RShc)
K19 = 146000.0; k21 = 16.0; K21 = 146000.0 Reaction: ERKP => ERKPP; MEKPP, ERK, Rate Law: compartment_0000001*k21*MEKPP*ERKP/(K21*(1+ERK/K19)+ERKP)
V10 = 0.0154; K10 = 340.0 Reaction: ShP => Shc, Rate Law: compartment_0000001*V10*ShP/(K10+ShP)
k24 = 9.85; k_24 = 0.0985 Reaction: RPI3K => RPI3Kstar, Rate Law: compartment_0000001*(k24*RPI3K-k_24*RPI3Kstar)
k11 = 0.222; K11 = 0.181 Reaction: RasGDP => RasGTP; ShGS, Rate Law: compartment_0000001*k11*ShGS*RasGDP/(K11+RasGDP)
k13 = 1.53; K13 = 11.7 Reaction: Raf => Rafstar; RasGTP, Rate Law: compartment_0000001*k13*RasGTP*Raf/(K13+Raf)
K30 = 80000.0; K32 = 80000.0; V32 = 20000.0 Reaction: AktPIP => AktPIPP; AktPIP3, Rate Law: compartment_0000001*V32*AktPIP/(K32*(1+AktPIP3/K30)+AktPIP)
k15 = 3.5; K15 = 317.0; K17 = 317.0 Reaction: MEK => MEKP; Rafstar, Rate Law: compartment_0000001*k15*Rafstar*MEK/(K15*(1+MEKP/K17)+MEK)
k_23 = 2.0; k23 = 0.1 Reaction: RP + PI3K => RPI3K, Rate Law: compartment_0000001*(k23*RP*PI3K-k_23*RPI3K)
k34 = 0.001; k_34 = 0.0 Reaction: RP => internalization, Rate Law: compartment_0000001*(k34*RP-k_34*internalization)
k_25 = 0.047; k25 = 45.8 Reaction: RPI3Kstar => RP + PI3Kstar, Rate Law: compartment_0000001*(k25*RPI3Kstar-k_25*RP*PI3Kstar)
K27 = 39.1; k27 = 16.9 Reaction: P_I => PIP3; PI3Kstar, Rate Law: compartment_0000001*k27*PI3Kstar*P_I/(K27+P_I)
k14 = 0.00673; K14 = 8.07 Reaction: Rafstar => Raf; AktPIPP, E, Rate Law: compartment_0000001*k14*(AktPIPP+E)*Rafstar/(K14+Rafstar)

States:

Name Description
Rafstar [Serine/threonine-protein kinase B-raf]
RHRG2 [IPR002154; receptor complex]
Shc [IPR001452; IPR000980]
Akt [IPR015744]
MEKP [phosphate(3-); IPR003527]
ShGS ShGS
RasGDP [GDP; IPR015592; IPR013753]
RP [receptor complex]
RShP RShP
AktPIPP [1-phosphatidyl-1D-myo-inositol 3,4-bisphosphate; IPR015744]
PIP3 [1-phosphatidyl-1D-myo-inositol 3,4,5-trisphosphate]
RPI3K [receptor complex; phosphatidylinositol 3-kinase complex]
PI3Kstar [phosphatidylinositol 3-kinase complex]
RShGS RShGS
internalization internalization
AktPIP [phosphatidylinositol 3-phosphate; IPR015744]
MEK [IPR003527]
PI3K [phosphatidylinositol 3-kinase complex]
ERKPP [diphosphate(4-); IPR008349; diphosphate(4-); IPR008350]
P I [phosphatidylinositol 3-phosphate]
ERKP [phosphate(3-); IPR008349; phosphate(3-); IPR008350]
GS GS
RPI3Kstar [phosphatidylinositol 3-kinase complex; receptor complex]
AktPIP3 [1-phosphatidyl-1D-myo-inositol 3,4,5-trisphosphate; IPR015744]
ShP ShP
HRG [IPR002154]
RHRG [IPR002154; receptor complex]
MEKPP [diphosphate ion; IPR003527]
Raf [Serine/threonine-protein kinase B-raf]
RasGTP [GTP; IPR015592; IPR013753]
ERK [IPR003527; IPR008349; IPR008350]
RShc RShc
R [receptor complex; Receptor tyrosine-protein kinase erbB-4]

Observables: none

A mathematical model of regulation of the G1-S transition of the mammalian cell cycle has been formulated to organize av…

A mathematical model of regulation of the G1-S transition of the mammalian cell cycle has been formulated to organize available experimental molecular-level information in a systematic quantitative framework and to evaluate the ability of this manifestation of current knowledge to calculate correctly experimentally observed phenotypes. This model includes nine components and includes cyclin-cdk complexes, a pocket protein (pRb), a transcription factor (E2F-1), and a cyclin-cdk complex inhibitor. Simulation of the model equations yields stable oscillatory solutions corresponding to cell proliferation and asymptotically stable solutions corresponding to cell cycle arrest (quiescence). Bifurcation analysis of the system suggests changes in the intracellular concentrations of either E2F or cyclin E can activate cell proliferation and that co-overexpression of these molecules can prevent cell proliferation. Further analysis suggests that the amount of inhibitor necessary to prevent cell proliferation is independent of the concentrations of cyclin E and E2F and depends only on the equilibrium ratio between the bound and unbound forms of the inhibitor to the complex. link: http://identifiers.org/pubmed/10550769

Parameters: none

States: none

Observables: none

MODEL0848676877 @ v0.0.1

This a model from the article: Mathematical model of human growth hormone (hGH)-stimulated cell proliferation explains…

Human growth hormone (hGH) is a therapeutically important endocrine factor that signals various cell types. Structurally and functionally, the interactions of hGH with its receptor have been resolved in fine detail, such that hGH and hGH receptor variants can be practically engineered by either random or rational approaches to achieve significant changes in the free energies of binding. A somewhat unique feature of hGH action is its homodimerization of two hGH receptors, which is required for intracellular signaling and stimulation of cell proliferation, yet the potencies of hGH mutants in cell-based assays rarely correlate with their overall receptor-binding avidities. Here, a mathematical model of hGH-stimulated cell signaling is posed, accounting not only for binding interactions at the cell surface but induction of receptor endocytosis and downregulation as well. Receptor internalization affects ligand potency by imposing a limit on the lifetime of an active receptor complex, irrespective of ligand-receptor binding properties. The model thus explains, in quantitative terms, the numerous published observations regarding hGH receptor agonism and antagonism and challenges the interpretations of previous studies that have not considered receptor trafficking as a central regulatory mechanism in hGH signaling. link: http://identifiers.org/pubmed/15458315

Parameters: none

States: none

Observables: none

MODEL1004070000 @ v0.0.1

This is the Unlabelled model as described in: Simulation of the Pentose Cycle in Lactating Rat Mammary Gland Haut M…

A computer model representing the pentose cycle, the tricarboxylic acid cycle and glycolysis in slices of lactating rat mammary glands has been constructed. This model is based primarily on the studies, with radioactive chemicals, of Abraham & Chaikoff (1959) [although some of the discrepant data of Katz & Wals (1972) could be accommodated by changing one enzyme activity]. Data obtained by using [1-(14)C]-, [6-(14)C]- and [3,4-(14)C]-glucose were simulated, as well as data obtained by using unlabelled glucose (for which some new experimental data are presented). Much past work on the pentose cycle has been mainly concerned with the division of glucose flow between the pentose cycle and glycolysis, and has relied on the assumption that the system is in steady state (both labelled and unlabelled). This assumption may not apply to lactating rat mammary glands, since the model shows that the percentage flow through the shunt progressively decreased for the first 2h of a 3h experiment, and we were unable to construct a completely steady-state model. The model allows examination of many quantitative features of the system, especially the amount of material passing through key enzymes, some of which appear to be regulated by NADP(+) concentrations as proposed by McLean (1960). Supplementary information for this paper has been deposited as Supplementary Publication SUP 50023 at the British Museum (Lending Division) (formerly the National Lending Library for Science and Technology), Boston Spa, Yorks. LS23 7BQ, U.K., from whom copies can be obtained on the terms indicated in Biochem. J. (1973) 131, 5. link: http://identifiers.org/pubmed/4154746

Parameters: none

States: none

Observables: none

MODEL4780784080 @ v0.0.1

This model features the phosphorylation of rat brain neuronal NOS expressed in E. coli or Sf9 cells, which leads to a de…

Phosphorylation of neuronal nitric-oxide synthase (nNOS) by Ca2+/calmodulin (CaM)-dependent protein kinases (CaM kinases) including CaM kinase Ialpha (CaM-K Ialpha), CaM kinase IIalpha (CaM-K IIalpha), and CaM kinase IV (CaM-K IV), was studied. It was found that purified recombinant nNOS was phosphorylated by CaM-K Ialpha, CaM-K IIalpha, and CaM-K IV at Ser847 in vitro. Replacement of Ser847 with Ala (S847A) prevented phosphorylation by CaM kinases. Phosphorylated recombinant wild-type nNOS at Ser847 (approximately 0.5 mol of phosphate incorporation into nNOS) exhibited a 30% decrease of Vmax with little change of both the Km for L-arginine and Kact for CaM relative to unphosphorylated enzyme. The activity of mutant S847D was decreased to a level 50-60% as much as the wild-type enzyme. The decreased NOS enzyme activity of phosphorylated nNOS at Ser847 and mutant S847D was partially due to suppression of CaM binding, but not to impairment of dimer formation which is thought to be essential for enzyme activation. Inactive nNOS lacking CaM-binding ability was generated by mutation of Lys732-Lys-Leu to Asp732-Asp-Glu (Watanabe, Y., Hu, Y., and Hidaka, H. (1997) FEBS Lett. 403, 75-78). It was phosphorylated by CaM kinases, as was the wild-type enzyme, indicating that CaM-nNOS binding was not required for the phosphorylation reaction. We developed antibody NP847, which specifically recognize nNOS in its phosphorylated state at Ser847. Using the antibody NP847, we obtained evidence that nNOS is phosphorylated at Ser847 in rat brain. Thus, our results suggest that CaM kinase-induced phosphorylation of nNOS at Ser847 alters the activity control of this enzyme. link: http://identifiers.org/pubmed/10400690

Parameters: none

States: none

Observables: none

MODEL9087255381 @ v0.0.1

This is a model of tight coupling between the AMPAR trafficking bistability, and the CaMKII autophosphorylation bistabil…

Changes in the synaptic connection strengths between neurons are believed to play a role in memory formation. An important mechanism for changing synaptic strength is through movement of neurotransmitter receptors and regulatory proteins to and from the synapse. Several activity-triggered biochemical events control these movements. Here we use computer models to explore how these putative memory-related changes can be stabilised long after the initial trigger, and beyond the lifetime of synaptic molecules. We base our models on published biochemical data and experiments on the activity-dependent movement of a glutamate receptor, AMPAR, and a calcium-dependent kinase, CaMKII. We find that both of these molecules participate in distinct bistable switches. These simulated switches are effective for long periods despite molecular turnover and biochemical fluctuations arising from the small numbers of molecules in the synapse. The AMPAR switch arises from a novel self-recruitment process where the presence of sufficient receptors biases the receptor movement cycle to insert still more receptors into the synapse. The CaMKII switch arises from autophosphorylation of the kinase. The switches may function in a tightly coupled manner, or relatively independently. The latter case leads to multiple stable states of the synapse. We propose that similar self-recruitment cycles may be important for maintaining levels of many molecules that undergo regulated movement, and that these may lead to combinatorial possible stable states of systems like the synapse. link: http://identifiers.org/pubmed/16110334

Parameters: none

States: none

Observables: none

MODEL9087474843 @ v0.0.1

This is a model of weak coupling between the AMPAR traffikcing bistability, and the CaMKII autophosphorylation bistabili…

Changes in the synaptic connection strengths between neurons are believed to play a role in memory formation. An important mechanism for changing synaptic strength is through movement of neurotransmitter receptors and regulatory proteins to and from the synapse. Several activity-triggered biochemical events control these movements. Here we use computer models to explore how these putative memory-related changes can be stabilised long after the initial trigger, and beyond the lifetime of synaptic molecules. We base our models on published biochemical data and experiments on the activity-dependent movement of a glutamate receptor, AMPAR, and a calcium-dependent kinase, CaMKII. We find that both of these molecules participate in distinct bistable switches. These simulated switches are effective for long periods despite molecular turnover and biochemical fluctuations arising from the small numbers of molecules in the synapse. The AMPAR switch arises from a novel self-recruitment process where the presence of sufficient receptors biases the receptor movement cycle to insert still more receptors into the synapse. The CaMKII switch arises from autophosphorylation of the kinase. The switches may function in a tightly coupled manner, or relatively independently. The latter case leads to multiple stable states of the synapse. We propose that similar self-recruitment cycles may be important for maintaining levels of many molecules that undergo regulated movement, and that these may lead to combinatorial possible stable states of systems like the synapse. link: http://identifiers.org/pubmed/16110334

Parameters: none

States: none

Observables: none

MODEL9086207764 @ v0.0.1

This is model 0 from Hayer and Bhalla, PLoS Comput Biol 2005. It has a bistable model of AMPAR traffic, plus a non-bista…

Changes in the synaptic connection strengths between neurons are believed to play a role in memory formation. An important mechanism for changing synaptic strength is through movement of neurotransmitter receptors and regulatory proteins to and from the synapse. Several activity-triggered biochemical events control these movements. Here we use computer models to explore how these putative memory-related changes can be stabilised long after the initial trigger, and beyond the lifetime of synaptic molecules. We base our models on published biochemical data and experiments on the activity-dependent movement of a glutamate receptor, AMPAR, and a calcium-dependent kinase, CaMKII. We find that both of these molecules participate in distinct bistable switches. These simulated switches are effective for long periods despite molecular turnover and biochemical fluctuations arising from the small numbers of molecules in the synapse. The AMPAR switch arises from a novel self-recruitment process where the presence of sufficient receptors biases the receptor movement cycle to insert still more receptors into the synapse. The CaMKII switch arises from autophosphorylation of the kinase. The switches may function in a tightly coupled manner, or relatively independently. The latter case leads to multiple stable states of the synapse. We propose that similar self-recruitment cycles may be important for maintaining levels of many molecules that undergo regulated movement, and that these may lead to combinatorial possible stable states of systems like the synapse. link: http://identifiers.org/pubmed/16110334

Parameters: none

States: none

Observables: none

MODEL9086518048 @ v0.0.1

This is the basic model of AMPAR trafficking bistability. It is based on Hayer and Bhalla, PLoS Comput. Biol. 2005. It i…

Changes in the synaptic connection strengths between neurons are believed to play a role in memory formation. An important mechanism for changing synaptic strength is through movement of neurotransmitter receptors and regulatory proteins to and from the synapse. Several activity-triggered biochemical events control these movements. Here we use computer models to explore how these putative memory-related changes can be stabilised long after the initial trigger, and beyond the lifetime of synaptic molecules. We base our models on published biochemical data and experiments on the activity-dependent movement of a glutamate receptor, AMPAR, and a calcium-dependent kinase, CaMKII. We find that both of these molecules participate in distinct bistable switches. These simulated switches are effective for long periods despite molecular turnover and biochemical fluctuations arising from the small numbers of molecules in the synapse. The AMPAR switch arises from a novel self-recruitment process where the presence of sufficient receptors biases the receptor movement cycle to insert still more receptors into the synapse. The CaMKII switch arises from autophosphorylation of the kinase. The switches may function in a tightly coupled manner, or relatively independently. The latter case leads to multiple stable states of the synapse. We propose that similar self-recruitment cycles may be important for maintaining levels of many molecules that undergo regulated movement, and that these may lead to combinatorial possible stable states of systems like the synapse. link: http://identifiers.org/pubmed/16110334

Parameters: none

States: none

Observables: none

MODEL9086953089 @ v0.0.1

This is the complete model of CaMKII bistability, model 3. It exhibits bistability in CaMKII activation due to autophosp…

Changes in the synaptic connection strengths between neurons are believed to play a role in memory formation. An important mechanism for changing synaptic strength is through movement of neurotransmitter receptors and regulatory proteins to and from the synapse. Several activity-triggered biochemical events control these movements. Here we use computer models to explore how these putative memory-related changes can be stabilised long after the initial trigger, and beyond the lifetime of synaptic molecules. We base our models on published biochemical data and experiments on the activity-dependent movement of a glutamate receptor, AMPAR, and a calcium-dependent kinase, CaMKII. We find that both of these molecules participate in distinct bistable switches. These simulated switches are effective for long periods despite molecular turnover and biochemical fluctuations arising from the small numbers of molecules in the synapse. The AMPAR switch arises from a novel self-recruitment process where the presence of sufficient receptors biases the receptor movement cycle to insert still more receptors into the synapse. The CaMKII switch arises from autophosphorylation of the kinase. The switches may function in a tightly coupled manner, or relatively independently. The latter case leads to multiple stable states of the synapse. We propose that similar self-recruitment cycles may be important for maintaining levels of many molecules that undergo regulated movement, and that these may lead to combinatorial possible stable states of systems like the synapse. link: http://identifiers.org/pubmed/16110334

Parameters: none

States: none

Observables: none

MODEL9086926384 @ v0.0.1

This is the model of CaMKII bistability, model 3. It exhibits bistability in CaMKII activation due to autophosphorylatio…

Changes in the synaptic connection strengths between neurons are believed to play a role in memory formation. An important mechanism for changing synaptic strength is through movement of neurotransmitter receptors and regulatory proteins to and from the synapse. Several activity-triggered biochemical events control these movements. Here we use computer models to explore how these putative memory-related changes can be stabilised long after the initial trigger, and beyond the lifetime of synaptic molecules. We base our models on published biochemical data and experiments on the activity-dependent movement of a glutamate receptor, AMPAR, and a calcium-dependent kinase, CaMKII. We find that both of these molecules participate in distinct bistable switches. These simulated switches are effective for long periods despite molecular turnover and biochemical fluctuations arising from the small numbers of molecules in the synapse. The AMPAR switch arises from a novel self-recruitment process where the presence of sufficient receptors biases the receptor movement cycle to insert still more receptors into the synapse. The CaMKII switch arises from autophosphorylation of the kinase. The switches may function in a tightly coupled manner, or relatively independently. The latter case leads to multiple stable states of the synapse. We propose that similar self-recruitment cycles may be important for maintaining levels of many molecules that undergo regulated movement, and that these may lead to combinatorial possible stable states of systems like the synapse. link: http://identifiers.org/pubmed/16110334

Parameters: none

States: none

Observables: none

MODEL9086628127 @ v0.0.1

This is a highly simplified model of the AMPAR trafficking cycle that exhibits bistability. It is model 2 from Hayer and…

Changes in the synaptic connection strengths between neurons are believed to play a role in memory formation. An important mechanism for changing synaptic strength is through movement of neurotransmitter receptors and regulatory proteins to and from the synapse. Several activity-triggered biochemical events control these movements. Here we use computer models to explore how these putative memory-related changes can be stabilised long after the initial trigger, and beyond the lifetime of synaptic molecules. We base our models on published biochemical data and experiments on the activity-dependent movement of a glutamate receptor, AMPAR, and a calcium-dependent kinase, CaMKII. We find that both of these molecules participate in distinct bistable switches. These simulated switches are effective for long periods despite molecular turnover and biochemical fluctuations arising from the small numbers of molecules in the synapse. The AMPAR switch arises from a novel self-recruitment process where the presence of sufficient receptors biases the receptor movement cycle to insert still more receptors into the synapse. The CaMKII switch arises from autophosphorylation of the kinase. The switches may function in a tightly coupled manner, or relatively independently. The latter case leads to multiple stable states of the synapse. We propose that similar self-recruitment cycles may be important for maintaining levels of many molecules that undergo regulated movement, and that these may lead to combinatorial possible stable states of systems like the synapse. link: http://identifiers.org/pubmed/16110334

Parameters: none

States: none

Observables: none

This is a mathematical model of pancreatic cancer which includes descriptions of regulatory T cell activity and inhibiti…

In this paper, we investigate a mathematical model of pancreatic cancer, which extends the existing pancreatic cancer models with regulatory T cells (Tregs) and Treg inhibitory therapy. The model consists of tumor-immune interaction and immune suppression from Tregs. In the absence of treatments, we first characterize the system dynamics by locating equilibrium points and determining stability properties. Next, cytokine induced killer (CIK) immunotherapy is incorporated. Numerical simulations of prognostic results illustrate that the median overall survival associated with treatment can be prolonged approximately from 7 to 13 months, which is consistent with the clinical data. Furthermore, we consider cyclophosphamide (CTX) therapy as well as the combined therapy with CIK and CTX. Intensive simulation results suggest that both CTX therapy and the combined CIK/CTX therapy can reduce the number of Tregs and increase the overall survival (OS), but Tregs and tumor cells will gradually rise to equilibrium state as long as therapies are ceased. link: http://identifiers.org/doi/10.1142/S021833901750005X

Parameters:

Name Description
r_e = 5.0E-12 Reaction: => E_CD8; N_Killer, C_PCC, Rate Law: compartment*r_e*N_Killer*C_PCC
b_e = 0.02 Reaction: E_CD8 =>, Rate Law: compartment*b_e*E_CD8
b_c = 1.5E-11 Reaction: C_PCC => ; N_Killer, Rate Law: compartment*b_c*N_Killer*C_PCC
g_h = 0.3; tau_1_alpha_1 = 2.2483E11; p_h = 0.125 Reaction: => H_T_Helper, Rate Law: compartment*p_h*H_T_Helper*H_T_Helper/(g_h*tau_1_alpha_1+H_T_Helper)
b_h = 0.0012 Reaction: H_T_Helper =>, Rate Law: compartment*b_h*H_T_Helper
delta_e = 1.0E-10 Reaction: E_CD8 => ; R_T_Regulatory, Rate Law: compartment*delta_e*R_T_Regulatory*E_CD8
gamma_2_tau_3 = 4.4691E-13; r_2 = 0.286; d_c = 7.87E-5; r_1 = 0.345 Reaction: C_PCC => ; E_CD8, R_T_Regulatory, Rate Law: compartment*d_c*E_CD8*C_PCC/((1+r_1*R_T_Regulatory)*(1+r_2*gamma_2_tau_3*C_PCC))
a_n = 130000.0 Reaction: => N_Killer, Rate Law: compartment*a_n
c_n = 1.0E-13 Reaction: N_Killer => ; C_PCC, Rate Law: compartment*c_n*N_Killer*C_PCC
c_e = 3.42E-12 Reaction: E_CD8 => ; C_PCC, Rate Law: compartment*c_e*E_CD8*C_PCC
beta_3_tau_2 = 4.4691E-13; f_n = 0.125; h_n = 0.3; beta_1_tau_2 = 4.4691E-13; beta_2_tau_2 = 4.4691E-13 Reaction: => N_Killer; E_CD8, H_T_Helper, Rate Law: compartment*f_n*N_Killer*(beta_1_tau_2*E_CD8+beta_2_tau_2*N_Killer+beta_3_tau_2*H_T_Helper)/(h_n+beta_1_tau_2*E_CD8+beta_2_tau_2*N_Killer+beta_3_tau_2*H_T_Helper)
tau_1_alpha_1 = 2.2483E11; p_e = 0.125; g_e = 0.3 Reaction: => E_CD8; H_T_Helper, Rate Law: compartment*p_e*H_T_Helper*E_CD8/(g_e*tau_1_alpha_1+H_T_Helper)
a_r = 2.0E-4 Reaction: => R_T_Regulatory; E_CD8, Rate Law: compartment*a_r*E_CD8
lambda_p = 0.015 Reaction: P_PSC =>, Rate Law: compartment*lambda_p*P_PSC
a_c = 1.02E-11; k_c = 0.0195; mu_c = 1.821414E-21 Reaction: => C_PCC; P_PSC, Rate Law: compartment*(k_c+mu_c*P_PSC)*C_PCC*(1-a_c*C_PCC)
a = 560000.0 Reaction: => R_T_Regulatory, Rate Law: compartment*a
tau_1_alpha_1 = 2.2483E11; g_r = 0.3; p_r = 0.125 Reaction: => R_T_Regulatory; H_T_Helper, Rate Law: compartment*p_r*H_T_Helper*R_T_Regulatory/(g_r*tau_1_alpha_1+H_T_Helper)
a_h = 360000.0 Reaction: => H_T_Helper, Rate Law: compartment*a_h
beta_3_tau_2 = 4.4691E-13; f_h = 0.125; h_h = 0.3; beta_1_tau_2 = 4.4691E-13; beta_2_tau_2 = 4.4691E-13 Reaction: => H_T_Helper; E_CD8, N_Killer, Rate Law: compartment*f_h*H_T_Helper*(beta_1_tau_2*E_CD8+beta_2_tau_2*N_Killer+beta_3_tau_2*H_T_Helper)/(h_h+beta_1_tau_2*E_CD8+beta_2_tau_2*N_Killer+beta_3_tau_2*H_T_Helper)
delta_r = 0.023 Reaction: R_T_Regulatory =>, Rate Law: compartment*delta_r*R_T_Regulatory
beta_3_tau_2 = 4.4691E-13; h_e = 0.3; f_e = 0.125; beta_1_tau_2 = 4.4691E-13; beta_2_tau_2 = 4.4691E-13 Reaction: => E_CD8; N_Killer, H_T_Helper, Rate Law: compartment*f_e*E_CD8*(beta_1_tau_2*E_CD8+beta_2_tau_2*N_Killer+beta_3_tau_2*H_T_Helper)/(h_e+beta_1_tau_2*E_CD8+beta_2_tau_2*N_Killer+beta_3_tau_2*H_T_Helper)
r = 1.0E-11 Reaction: R_T_Regulatory => ; N_Killer, Rate Law: compartment*r*N_Killer*R_T_Regulatory
k_p = 0.00195; f_p = 0.125; mu_p = 5.6E7; a_p = 1.7857E-9 Reaction: => P_PSC; C_PCC, Rate Law: compartment*(k_p+f_p*C_PCC/(mu_p+C_PCC))*P_PSC*(1-a_p*P_PSC)
b_r = 4.0E-4 Reaction: => R_T_Regulatory; H_T_Helper, Rate Law: compartment*b_r*H_T_Helper
g_n = 0.3; tau_1_alpha_1 = 2.2483E11; p_n = 0.125 Reaction: => N_Killer; H_T_Helper, Rate Law: compartment*p_n*H_T_Helper*N_Killer/(g_n*tau_1_alpha_1+H_T_Helper)
a_e = 13000.0 Reaction: => E_CD8, Rate Law: compartment*a_e
delta_h = 1.0E-10 Reaction: H_T_Helper => ; R_T_Regulatory, Rate Law: compartment*delta_h*R_T_Regulatory*H_T_Helper
b_n = 0.015 Reaction: N_Killer =>, Rate Law: compartment*b_n*N_Killer
delta_n = 1.0E-10 Reaction: N_Killer =>, Rate Law: compartment*delta_n*N_Killer

States:

Name Description
N Killer [natural killer cell]
P PSC [pancreatic stellate cell]
E CD8 [CD8-Positive T-Lymphocyte]
H T Helper [helper T-lymphocyte]
R T Regulatory [regulatory T-lymphocyte]
C PCC [pancreatic cancer cell]

Observables: none

Heavner2012 - Metabolic Network of S.cerevisiaeThis SBML representation of the yeast metabolic network is made available…

Efforts to improve the computational reconstruction of the Saccharomyces cerevisiae biochemical reaction network and to refine the stoichiometrically constrained metabolic models that can be derived from such a reconstruction have continued since the first stoichiometrically constrained yeast genome scale metabolic model was published in 2003. Continuing this ongoing process, we have constructed an update to the Yeast Consensus Reconstruction, Yeast 5. The Yeast Consensus Reconstruction is a product of efforts to forge a community-based reconstruction emphasizing standards compliance and biochemical accuracy via evidence-based selection of reactions. It draws upon models published by a variety of independent research groups as well as information obtained from biochemical databases and primary literature.Yeast 5 refines the biochemical reactions included in the reconstruction, particularly reactions involved in sphingolipid metabolism; updates gene-reaction annotations; and emphasizes the distinction between reconstruction and stoichiometrically constrained model. Although it was not a primary goal, this update also improves the accuracy of model prediction of viability and auxotrophy phenotypes and increases the number of epistatic interactions. This update maintains an emphasis on standards compliance, unambiguous metabolite naming, and computer-readable annotations available through a structured document format. Additionally, we have developed MATLAB scripts to evaluate the model's predictive accuracy and to demonstrate basic model applications such as simulating aerobic and anaerobic growth. These scripts, which provide an independent tool for evaluating the performance of various stoichiometrically constrained yeast metabolic models using flux balance analysis, are included as Additional files 1, 2 and 3.Yeast 5 expands and refines the computational reconstruction of yeast metabolism and improves the predictive accuracy of a stoichiometrically constrained yeast metabolic model. It differs from previous reconstructions and models by emphasizing the distinction between the yeast metabolic reconstruction and the stoichiometrically constrained model, and makes both available as Additional file 4 and Additional file 5 and at http://yeast.sf.net/ as separate systems biology markup language (SBML) files. Through this separation, we intend to make the modeling process more accessible, explicit, transparent, and reproducible. link: http://identifiers.org/pubmed/22663945

Parameters: none

States: none

Observables: none

Model V simulating stress induction with stress inputs on PI3K, Akt-pS473 and mTORC1. The model scheme is depicted in Fi…

All cells and organisms exhibit stress-coping mechanisms to ensure survival. Cytoplasmic protein-RNA assemblies termed stress granules are increasingly recognized to promote cellular survival under stress. Thus, they might represent tumor vulnerabilities that are currently poorly explored. The translationinhibitory eIF2α kinases are established as main drivers of stress granule assembly. Using a systems approach, we identify the translation enhancers PI3K and MAPK/p38 as pro-stressgranule- kinases. They act through the metabolic master regulator mammalian target of rapamycin complex 1 (mTORC1) to promote stress granule assembly.When highly active, PI3K is the main driver of stress granules; however, the impact of p38 becomes apparent as PI3K activity declines. PI3K and p38 thus act in a hierarchical manner to drive mTORC1 activity and stress granule assembly. Of note, this signaling hierarchy is also present in human breast cancer tissue. Importantly, only the recognition of the PI3K-p38 hierarchy under stress enabled the discovery of p38’s role in stress granule formation. In summary, we assign a new prosurvival function to the key oncogenic kinases PI3K link: http://identifiers.org/doi/10.26508/lsa.201800257

Parameters: none

States: none

Observables: none

All cells and organisms exhibit stress-coping mechanisms to ensure survival. Cytoplasmic protein-RNA assemblies termed s…

All cells and organisms exhibit stress-coping mechanisms to ensure survival. Cytoplasmic protein-RNA assemblies termed stress granules are increasingly recognized to promote cellular survival under stress. Thus, they might represent tumor vulnerabilities that are currently poorly explored. The translation-inhibitory eIF2α kinases are established as main drivers of stress granule assembly. Using a systems approach, we identify the translation enhancers PI3K and MAPK/p38 as pro-stress-granule-kinases. They act through the metabolic master regulator mammalian target of rapamycin complex 1 (mTORC1) to promote stress granule assembly. When highly active, PI3K is the main driver of stress granules; however, the impact of p38 becomes apparent as PI3K activity declines. PI3K and p38 thus act in a hierarchical manner to drive mTORC1 activity and stress granule assembly. Of note, this signaling hierarchy is also present in human breast cancer tissue. Importantly, only the recognition of the PI3K-p38 hierarchy under stress enabled the discovery of p38's role in stress granule formation. In summary, we assign a new pro-survival function to the key oncogenic kinases PI3K and p38, as they hierarchically promote stress granule formation. link: http://identifiers.org/pubmed/30923191

Parameters: none

States: none

Observables: none

All cells and organisms exhibit stress-coping mechanisms toensure survival. Cytoplasmic protein-RNA assemblies termedstr…

All cells and organisms exhibit stress-coping mechanisms to ensure survival. Cytoplasmic protein-RNA assemblies termed stress granules are increasingly recognized to promote cellular survival under stress. Thus, they might represent tumor vulnerabilities that are currently poorly explored. The translation-inhibitory eIF2α kinases are established as main drivers of stress granule assembly. Using a systems approach, we identify the translation enhancers PI3K and MAPK/p38 as pro-stress-granule-kinases. They act through the metabolic master regulator mammalian target of rapamycin complex 1 (mTORC1) to promote stress granule assembly. When highly active, PI3K is the main driver of stress granules; however, the impact of p38 becomes apparent as PI3K activity declines. PI3K and p38 thus act in a hierarchical manner to drive mTORC1 activity and stress granule assembly. Of note, this signaling hierarchy is also present in human breast cancer tissue. Importantly, only the recognition of the PI3K-p38 hierarchy under stress enabled the discovery of p38's role in stress granule formation. In summary, we assign a new pro-survival function to the key oncogenic kinases PI3K and p38, as they hierarchically promote stress granule formation. link: http://identifiers.org/pubmed/30923191

Parameters:

Name Description
a1_X11_0 = 0.106711200647841; a2_X11_0 = 1.00000017501247E-5; a_X6_Y2 = 1.00000114154884E-5; b_X11_1 = 0.182804161260864; b_X11_2 = 0.224858434757367; Y2 = 1.0 Reaction: => X11_3; X10_0, X10_1, X10_2, X10_3, X11_1, X11_2, X11_3, X5_0, X9_0, X9_2, Rate Law: default*(((X11_2*(Y2*a_X6_Y2+2*a2_X11_0*(X10_0/(X10_0+X10_1+X10_2+X10_3)-1)*(X9_0/(X9_0+X9_2)-1))-X11_3*b_X11_2)-X11_3*b_X11_1)+2*X11_1*X5_0*a1_X11_0)/default
ModelValue_114 = 0.996685919963556 Reaction: fourEBP1_pT37_46_obs = ModelValue_114*X12_1, Rate Law: missing
a1_X11_0 = 0.106711200647841; a_X6_Y2 = 1.00000114154884E-5; b_X11_1 = 0.182804161260864; b_X11_2 = 0.224858434757367; Y2 = 1.0 Reaction: => X11_1; X10_0, X10_1, X10_2, X10_3, X11_0, X11_1, X11_3, X5_0, X9_0, X9_2, Rate Law: default*(((X11_3*b_X11_2-X11_1*b_X11_1)+X11_0*(Y2*a_X6_Y2+a1_X11_0*(X10_0/(X10_0+X10_1+X10_2+X10_3)-1)*(X9_0/(X9_0+X9_2)-1)))-2*X11_1*X5_0*a1_X11_0)/default
b_X2_2 = 0.106214679132925; a1_X2_0 = 0.0014976539751451 Reaction: => X2_0; X11_1, X11_3, X1_1, X2_0, X2_2, Rate Law: default*((X2_2*b_X2_2-X1_1*X2_0)-X2_0*a1_X2_0*(X11_1+X11_3))/default
Y5 = 0.0; a2_X8_0 = 0.210752496177883; k_stress_2 = 0.00999999977724154; Y3 = 1.0; b_X8_1 = 0.0462909157235242; b_X8_2 = 0.0100376101872374 Reaction: => X8_2; X4_1, X5_1, X8_0, X8_2, X8_3, Rate Law: default*(((X8_3*b_X8_1-X8_2*b_X8_2)-X8_0*(0.83*Y5-1)*(X4_1*a2_X8_0+Y3*k_stress_2))+2*X5_1*X8_2*a2_X8_0*(0.83*Y5-1))/default
a_X6_Y2 = 1.00000114154884E-5; b_X12_1 = 0.0102134541960737; a_X12_0 = 0.198339568602839; Y2 = 1.0 Reaction: => X12_0; X10_0, X10_1, X10_2, X10_3, X12_0, X12_1, X9_0, X9_2, Rate Law: default*(X12_1*b_X12_1-X12_0*(Y2*a_X6_Y2+a_X12_0*(X10_0/(X10_0+X10_1+X10_2+X10_3)-1)*(X9_0/(X9_0+X9_2)-1)))/default
Y5 = 0.0; a1_X8_0 = 0.584037889511307; a2_X8_0 = 0.210752496177883; k_stress_2 = 0.00999999977724154; Y3 = 1.0; b_X8_1 = 0.0462909157235242; b_X8_2 = 0.0100376101872374 Reaction: => X8_0; X4_1, X5_1, X8_0, X8_1, X8_2, Rate Law: default*(X8_1*b_X8_1+X8_2*b_X8_2+X8_0*(0.83*Y5-1)*(X4_1*a2_X8_0+Y3*k_stress_2)+X5_1*X8_0*a1_X8_0*(0.83*Y5-1))/default
b_X5_1 = 0.077833118821602; a_X5_0 = 9.99999969718096 Reaction: => X5_0; X4_1, X5_0, X5_1, Rate Law: default*(X5_1*b_X5_1-X4_1*X5_0*a_X5_0)/default
b_X10_2 = 0.011959597261903; b_X10_1 = 0.00263737900398121; a_X6_Y2 = 1.00000114154884E-5; a1_X10_0 = 1.04880466121365E-5; a2_X10_0 = 0.196797907822297; Y2 = 1.0 Reaction: => X10_0; X10_0, X10_1, X10_2, X10_3, X8_1, X8_3, X9_0, X9_2, Rate Law: default*(((X10_1*b_X10_1+X10_2*b_X10_2)-X10_0*(Y2*a_X6_Y2+a1_X10_0*(X10_0/(X10_0+X10_1+X10_2+X10_3)-1)*(X9_0/(X9_0+X9_2)-1)))-X10_0*a2_X10_0*(X8_1+X8_3))/default
ModelValue_113 = 3.98428884870299 Reaction: PRAS40_pS183_obs = ModelValue_113*X10_1+ModelValue_113*X10_3, Rate Law: missing
k_stress_1 = 9.99999999995476; Y3 = 1.0; Y4 = 1.0; b_X4_1 = 1.08358100911056E-5; a_X4_0 = 1.11095303548777E-4 Reaction: => X4_0; X2_1, X4_0, X4_1, Rate Law: default*(X4_1*b_X4_1+X4_0*(X2_1*a_X4_0+Y3*k_stress_1)*(Y4-1))/default
ModelValue_116 = 74.7402331598434 Reaction: p70_S6K_pT229_obs = ModelValue_116*X11_2+ModelValue_116*X11_3, Rate Law: missing
b_X10_2 = 0.011959597261903; b_X10_1 = 0.00263737900398121; a_X6_Y2 = 1.00000114154884E-5; a2_X10_0 = 0.196797907822297; a_X10_2 = 9.99999999991509; Y2 = 1.0 Reaction: => X10_2; X10_0, X10_1, X10_2, X10_3, X8_1, X8_3, X9_0, X9_2, Rate Law: default*(((X10_3*b_X10_1-X10_2*b_X10_2)-X10_2*(Y2*a_X6_Y2+a_X10_2*(X10_0/(X10_0+X10_1+X10_2+X10_3)-1)*(X9_0/(X9_0+X9_2)-1)))+X10_0*a2_X10_0*(X8_1+X8_3))/default
ModelValue_117 = 997.421063173575 Reaction: IRS1_pS636_639_obs = ModelValue_117*X2_2, Rate Law: missing
ModelValue_109 = 1.54625898449999 Reaction: Akt_pT308_obs = ModelValue_109*X8_1+ModelValue_109*X8_3, Rate Law: missing
a2_X11_0 = 1.00000017501247E-5; a_X6_Y2 = 1.00000114154884E-5; b_X11_1 = 0.182804161260864; b_X11_2 = 0.224858434757367; Y2 = 1.0 Reaction: => X11_2; X10_0, X10_1, X10_2, X10_3, X11_0, X11_2, X11_3, X5_0, X9_0, X9_2, Rate Law: default*(((X11_3*b_X11_1-X11_2*b_X11_2)-X11_2*(Y2*a_X6_Y2+2*a2_X11_0*(X10_0/(X10_0+X10_1+X10_2+X10_3)-1)*(X9_0/(X9_0+X9_2)-1)))+X11_0*X5_0*a2_X11_0)/default
ModelValue_112 = 10.1154012696402 Reaction: PRAS40_pT246_obs = ModelValue_112*X10_2+ModelValue_112*X10_3, Rate Law: missing
a_X10_1 = 1.00000000000206E-5; b_X10_2 = 0.011959597261903; b_X10_1 = 0.00263737900398121; a_X6_Y2 = 1.00000114154884E-5; a1_X10_0 = 1.04880466121365E-5; Y2 = 1.0 Reaction: => X10_1; X10_0, X10_1, X10_2, X10_3, X8_1, X8_3, X9_0, X9_2, Rate Law: default*(((X10_3*b_X10_2-X10_1*b_X10_1)+X10_0*(Y2*a_X6_Y2+a1_X10_0*(X10_0/(X10_0+X10_1+X10_2+X10_3)-1)*(X9_0/(X9_0+X9_2)-1)))-X10_1*a_X10_1*(X8_1+X8_3))/default
a1_X8_0 = 0.584037889511307; Y5 = 0.0; a2_X8_0 = 0.210752496177883; b_X8_1 = 0.0462909157235242; b_X8_2 = 0.0100376101872374 Reaction: => X8_3; X4_1, X5_1, X8_1, X8_2, X8_3, Rate Law: default*((((-X8_3)*b_X8_1-X8_3*b_X8_2)-2*X4_1*X8_1*a1_X8_0*(0.83*Y5-1))-2*X5_1*X8_2*a2_X8_0*(0.83*Y5-1))/default
a1_X8_0 = 0.584037889511307; Y5 = 0.0; b_X8_1 = 0.0462909157235242; b_X8_2 = 0.0100376101872374 Reaction: => X8_1; X4_1, X5_1, X8_0, X8_1, X8_3, Rate Law: default*(((X8_3*b_X8_2-X8_1*b_X8_1)+2*X4_1*X8_1*a1_X8_0*(0.83*Y5-1))-X5_1*X8_0*a1_X8_0*(0.83*Y5-1))/default
a2_X9_0 = 0.0216220006084923; b_X9_2 = 0.0369559223359753 Reaction: => X9_0; X8_1, X8_3, X9_0, X9_2, Rate Law: default*(X9_2*b_X9_2-X9_0*a2_X9_0*(X8_1+X8_3))/default
ModelValue_115 = 86.0602161862265 Reaction: p70_S6K_pT389_obs = ModelValue_115*X11_1+ModelValue_115*X11_3, Rate Law: missing
a_X10_1 = 1.00000000000206E-5; b_X10_2 = 0.011959597261903; a_X6_Y2 = 1.00000114154884E-5; b_X10_1 = 0.00263737900398121; a_X10_2 = 9.99999999991509; Y2 = 1.0 Reaction: => X10_3; X10_0, X10_1, X10_2, X10_3, X8_1, X8_3, X9_0, X9_2, Rate Law: default*(((X10_2*(Y2*a_X6_Y2+a_X10_2*(X10_0/(X10_0+X10_1+X10_2+X10_3)-1)*(X9_0/(X9_0+X9_2)-1))-X10_3*b_X10_2)-X10_3*b_X10_1)+X10_1*a_X10_1*(X8_1+X8_3))/default
Y1 = 0.0 Reaction: => X1_1; X1_0, X1_1, Rate Law: default*(X1_0*Y1-X1_1)/default
ModelValue_111 = 2.71349287061239 Reaction: TSC1_TSC2_pT1462_obs = ModelValue_111*X9_2, Rate Law: missing
ModelValue_110 = 11.9261080736157 Reaction: Akt_pS473_obs = ModelValue_110*X8_2+ModelValue_110*X8_3, Rate Law: missing

States:

Name Description
X2 2 X2_2
X8 2 X8_2
X9 2 X9_2
X1 1 X1_1
X9 0 X9_0
X1 0 X1_0
X12 1 X12_1
IRS1 pS636 639 obs IRS1_pS636-639_obs
TSC1 TSC2 pT1462 obs TSC1_TSC2_pT1462_obs
PRAS40 pT246 obs PRAS40_pT246_obs
X8 1 X8_1
X10 0 X10_0
X2 1 X2_1
X8 3 X8_3
X4 0 X4_0
X10 2 X10_2
X10 3 X10_3
p70 S6K pT229 obs p70_S6K_pT229_obs
X5 0 X5_0
Akt pS473 obs Akt_pS473_obs
X8 0 X8_0
PRAS40 pS183 obs PRAS40_pS183_obs
X11 1 X11_1
X4 1 X4_1
X12 0 X12_0
fourEBP1 pT37 46 obs fourEBP1_pT37_46_obs
X5 1 X5_1
p70 S6K pT389 obs p70_S6K_pT389_obs
X10 1 X10_1
X11 3 X11_3
X2 0 X2_0
X11 2 X11_2
Akt pT308 obs Akt_pT308_obs
X11 0 X11_0

Observables: none

BIOMD0000000411 @ v0.0.1

This model is from the article: Modeling temperature entrainment of circadian clocks using the Arrhenius equation and…

Endogenous circadian rhythms allow living organisms to anticipate daily variations in their natural environment. Temperature regulation and entrainment mechanisms of circadian clocks are still poorly understood. To better understand the molecular basis of these processes, we built a mathematical model based on experimental data examining temperature regulation of the circadian RNA-binding protein CHLAMY1 from the unicellular green alga Chlamydomonas reinhardtii, simulating the effect of temperature on the rates by applying the Arrhenius equation. Using numerical simulations, we demonstrate that our model is temperature-compensated and can be entrained to temperature cycles of various length and amplitude. The range of periods that allow entrainment of the model depends on the shape of the temperature cycles and is larger for sinusoidal compared to rectangular temperature curves. We show that the response to temperature of protein (de)phosphorylation rates play a key role in facilitating temperature entrainment of the oscillator in Chlamydomonas reinhardtii. We systematically investigated the response of our model to single temperature pulses to explain experimentally observed phase response curves. link: http://identifiers.org/pubmed/23729908

Parameters:

Name Description
T = 291.0; T2 = 296.0; k=0.4; parameter_3 = 8.31447; v=2.6; h=2.0; parameter_7 = 84000.0 Reaction: s2 => s9; s11, Rate Law: default*v*exp(parameter_7/parameter_3*(T2-T)/(T*T2))/(k+s11^h)
T = 291.0; T2 = 296.0; parameter_3 = 8.31447; v=3.0; parameter_6 = 50000.0; Km=2.0 Reaction: s9 => species_12, Rate Law: default*v*exp(parameter_6/parameter_3*(T2-T)/(T*T2))*s9/(Km+s9)
T = 291.0; T2 = 296.0; parameter_3 = 8.31447; E=67000.0; v=30.0; Km=2.0 Reaction: species_1 => species_12, Rate Law: default*v*exp(E/parameter_3*(T2-T)/(T*T2))*species_1/(Km+species_1)
T = 291.0; T2 = 296.0; parameter_1 = 1.0; parameter_3 = 8.31447; parameter_9 = 60000.0 Reaction: species_1 => species_3, Rate Law: default*parameter_1*exp(parameter_9/parameter_3*(T2-T)/(T*T2))*species_1
T = 291.0; T2 = 296.0; parameter_3 = 8.31447; E=67000.0; v=20.0; Km=4.0 Reaction: species_4 => species_12, Rate Law: default*v*exp(E/parameter_3*(T2-T)/(T*T2))*species_4/(Km+species_4)
T = 291.0; T2 = 296.0; v=2.2; parameter_3 = 8.31447; parameter_6 = 50000.0; Km=0.2 Reaction: s10 => species_12, Rate Law: default*v*exp(parameter_6/parameter_3*(T2-T)/(T*T2))*s10/(Km+s10)
T = 291.0; T2 = 296.0; parameter_10 = 67000.0; parameter_3 = 8.31447; parameter_2 = 0.5 Reaction: species_3 => species_1, Rate Law: default*parameter_2*exp(parameter_10/parameter_3*(T2-T)/(T*T2))*species_3
T = 291.0; T2 = 296.0; parameter_3 = 8.31447; v=10.0; parameter_7 = 84000.0; a=2.0 Reaction: species_3 + s11 => species_4, Rate Law: default*v*exp(parameter_7/parameter_3*(T2-T)/(T*T2))*species_3*s11^a
T = 291.0; T2 = 296.0; parameter_3 = 8.31447; E=67000.0; parameter_8 = 1.0; Km=1.0 Reaction: species_3 => species_12, Rate Law: default*parameter_8*exp(E/parameter_3*(T2-T)/(T*T2))*species_3/(Km+species_3)
T = 291.0; T2 = 296.0; parameter_3 = 8.31447; v=0.1; parameter_6 = 50000.0 Reaction: s10 => s11, Rate Law: default*v*exp(parameter_6/parameter_3*(T2-T)/(T*T2))*s10
T = 291.0; T2 = 296.0; parameter_3 = 8.31447; E=67000.0; v=19.0 Reaction: species_2 => species_1, Rate Law: default*v*exp(E/parameter_3*(T2-T)/(T*T2))*species_2
T = 291.0; T2 = 296.0; parameter_3 = 8.31447; parameter_6 = 50000.0; v=1.5; Km=1.4 Reaction: s11 => species_12, Rate Law: default*v*exp(parameter_6/parameter_3*(T2-T)/(T*T2))*s11/(Km+s11)
T = 291.0; T2 = 296.0; parameter_3 = 8.31447; parameter_7 = 84000.0; v=5.0 Reaction: s13 => s10; s9, Rate Law: default*v*exp(parameter_7/parameter_3*(T2-T)/(T*T2))*s9

States:

Name Description
species 2 [RNA binding protein]
s11 [RNA binding protein; Phosphoprotein]
s13 [RNA binding protein]
species 1 [RNA binding protein]
species 3 [RNA binding protein; Phosphoprotein]
s2 [RNA binding protein]
species 4 [RNA binding protein; RNA binding protein]
s9 [RNA binding protein]
species 12 junk
s10 [RNA binding protein]

Observables: none

This is a detailed model of NAD biosynthesis and consumption representing pathway variances across kingdoms.

Nicotinamide adenine dinucleotide (NAD) provides an important link between metabolism and signal transduction and has emerged as central hub between bioenergetics and all major cellular events. NAD-dependent signaling (e.g., by sirtuins and poly–adenosine diphosphate [ADP] ribose polymerases [PARPs]) consumes considerable amounts of NAD. To maintain physiological functions, NAD consumption and biosynthesis need to be carefully balanced. Using extensive phylogenetic analyses, mathematical modeling of NAD metabolism, and experimental verification, we show that the diversification of NAD-dependent signaling in vertebrates depended on 3 critical evolutionary events: 1) the transition of NAD biosynthesis to exclusive usage of nicotinamide phosphoribosyltransferase (NamPT); 2) the occurrence of nicotinamide N-methyltransferase (NNMT), which diverts nicotinamide (Nam) from recycling into NAD, preventing Nam accumulation and inhibition of NAD-dependent signaling reactions; and 3) structural adaptation of NamPT, providing an unusually high affinity toward Nam, necessary to maintain NAD levels. Our results reveal an unexpected coevolution and kinetic interplay between NNMT and NamPT that enables extensive NAD signaling. This has implications for therapeutic strategies of NAD supplementation and the use of NNMT or NamPT inhibitors in disease treatment. link: http://identifiers.org/doi/10.1073/pnas.1902346116

Parameters: none

States: none

Observables: none

The model is based on MODEL1905220001 but has two compartments that have different composition of the biosynthetic enzym…

Nicotinamide adenine dinucleotide (NAD) provides an important link between metabolism and signal transduction and has emerged as central hub between bioenergetics and all major cellular events. NAD-dependent signaling (e.g., by sirtuins and poly–adenosine diphosphate [ADP] ribose polymerases [PARPs]) consumes considerable amounts of NAD. To maintain physiological functions, NAD consumption and biosynthesis need to be carefully balanced. Using extensive phylogenetic analyses, mathematical modeling of NAD metabolism, and experimental verification, we show that the diversification of NAD-dependent signaling in vertebrates depended on 3 critical evolutionary events: 1) the transition of NAD biosynthesis to exclusive usage of nicotinamide phosphoribosyltransferase (NamPT); 2) the occurrence of nicotinamide N-methyltransferase (NNMT), which diverts nicotinamide (Nam) from recycling into NAD, preventing Nam accumulation and inhibition of NAD-dependent signaling reactions; and 3) structural adaptation of NamPT, providing an unusually high affinity toward Nam, necessary to maintain NAD levels. Our results reveal an unexpected coevolution and kinetic interplay between NNMT and NamPT that enables extensive NAD signaling. This has implications for therapeutic strategies of NAD supplementation and the use of NNMT or NamPT inhibitors in disease treatment. link: http://identifiers.org/doi/10.1073/pnas.1902346116

Parameters: none

States: none

Observables: none

Heinemann2005 - Genome-scale reconstruction of Staphylococcus aureus (iMH551)This model is described in the article: [I…

A genome-scale metabolic model of the Gram-positive, facultative anaerobic opportunistic pathogen Staphylococcus aureus N315 was constructed based on current genomic data, literature, and physiological information. The model comprises 774 metabolic processes representing approximately 23% of all protein-coding regions. The model was extensively validated against experimental observations and it correctly predicted main physiological properties of the wild-type strain, such as aerobic and anaerobic respiration and fermentation. Due to the frequent involvement of S. aureus in hospital-acquired bacterial infections combined with its increasing antibiotic resistance, we also investigated the clinically relevant phenotype of small colony variants and found that the model predictions agreed with recent findings of proteome analyses. This indicates that the model is useful in assisting future experiments to elucidate the interrelationship of bacterial metabolism and resistance. To help directing future studies for novel chemotherapeutic targets, we conducted a large-scale in silico gene deletion study that identified 158 essential intracellular reactions. A more detailed analysis showed that the biosynthesis of glycans and lipids is rather rigid with respect to circumventing gene deletions, which should make these areas particularly interesting for antibiotic development. The combination of this stoichiometric model with transcriptomic and proteomic data should allow a new quality in the analysis of clinically relevant organisms and a more rationalized system-level search for novel drug targets. link: http://identifiers.org/pubmed/16155945

Parameters: none

States: none

Observables: none

MODEL0848507209 @ v0.0.1

This a model from the article: A mathematical model of luteinizing hormone release from ovine pituitary cells in perif…

We model the effect of gonadotropin-releasing hormone (GnRH) on the production of luteinizing hormone (LH) by the ovine pituitary. GnRH, released by the hypothalamus, stimulates the secretion of LH from the pituitary. If stimulus pulses are regular, LH response will follow a similar pattern. However, during application of GnRH at high frequencies or concentrations or with continuous application, the pituitary delivers a decreased release of LH (termed desensitization). The proposed mathematical model consists of a system of nonlinear differential equations and incorporates two possible mechanisms to account for this observed behavior: desensitized receptor and limited, available LH. Desensitization was provoked experimentally in vitro by using ovine pituitary cells in a perifusion system. The model was fit to resulting experimental data by using maximum-likelihood estimation. Consideration of smaller models revealed that the desensitized receptor is significant. Limited, available LH was significant in three of four chambers. Throughout, the proposed model was in excellent agreement with experimental data. link: http://identifiers.org/pubmed/9843750

Parameters: none

States: none

Observables: none

BIOMD0000000842 @ v0.0.1

This model is from the article: Competing G protein-coupled receptor kinases balance G protein and β-arrestin signalin…

Seven-transmembrane receptors (7TMRs) are involved in nearly all aspects of chemical communications and represent major drug targets. 7TMRs transmit their signals not only via heterotrimeric G proteins but also through β-arrestins, whose recruitment to the activated receptor is regulated by G protein-coupled receptor kinases (GRKs). In this paper, we combined experimental approaches with computational modeling to decipher the molecular mechanisms as well as the hidden dynamics governing extracellular signal-regulated kinase (ERK) activation by the angiotensin II type 1A receptor (AT(1A)R) in human embryonic kidney (HEK)293 cells. We built an abstracted ordinary differential equations (ODE)-based model that captured the available knowledge and experimental data. We inferred the unknown parameters by simultaneously fitting experimental data generated in both control and perturbed conditions. We demonstrate that, in addition to its well-established function in the desensitization of G-protein activation, GRK2 exerts a strong negative effect on β-arrestin-dependent signaling through its competition with GRK5 and 6 for receptor phosphorylation. Importantly, we experimentally confirmed the validity of this novel GRK2-dependent mechanism in both primary vascular smooth muscle cells naturally expressing the AT(1A)R, and HEK293 cells expressing other 7TMRs. link: http://identifiers.org/pubmed/22735336

Parameters:

Name Description
k14 = 0.0311 Reaction: Hbarr2RP1 => barr2 + HRP1; Hbarr2RP1, Rate Law: compartmentOne*k14*Hbarr2RP1/compartmentOne
k8 = 1.77 Reaction: PKC_a => PKC; PKC_a, Rate Law: compartmentOne*k8*PKC_a/compartmentOne
k24 = 0.347 Reaction: Hbarr2RP2 => barr2 + HRP2; Hbarr2RP2, Rate Law: compartmentOne*k24*Hbarr2RP2/compartmentOne
k18 = 0.59; GRK56 = 1.5180818 Reaction: HR => HRP2; GRK5_6, Rate Law: compartmentOne*k18*GRK56*HR/compartmentOne
k5 = 2.65 Reaction: ERK + PKC_a => GpERK + PKC_a; ERK, PKC_a, Rate Law: compartmentOne*k5*ERK*PKC_a/compartmentOne
k23 = 1.05 Reaction: HRbarr2 => barr2 + HR; HRbarr2, Rate Law: compartmentOne*k23*HRbarr2/compartmentOne
k12 = 2.59 Reaction: barr2 + HRP1 => Hbarr2RP1; barr2, HRP1, Rate Law: compartmentOne*k12*barr2*HRP1/compartmentOne
k21 = 4.2E-4 Reaction: ERK + HRbarr2 => bpERK + HRbarr2; ERK, HRbarr2, Rate Law: compartmentOne*k21*ERK*HRbarr2/compartmentOne
k25 = 0.762 Reaction: bpERK => ERK; bpERK, Rate Law: compartmentOne*k25*bpERK/compartmentOne
k22 = 14.44 Reaction: ERK + Hbarr2RP2 => bpERK + Hbarr2RP2; ERK, Hbarr2RP2, Rate Law: compartmentOne*k22*ERK*Hbarr2RP2/compartmentOne
k3 = 4.63 Reaction: G_a + PIP2 => DAG + G_a; G_a, PIP2, Rate Law: compartmentOne*k3*G_a*PIP2/compartmentOne
k17 = 0.0665 Reaction: HRP2 => HR; HRP2, Rate Law: compartmentOne*k17*HRP2/compartmentOne
k0 = 3.11E-4 Reaction: G => G_a; G, Rate Law: compartmentOne*k0*G/compartmentOne
k2 = 7.6 Reaction: G + HR => G_a + HR; G, HR, Rate Law: compartmentOne*k2*G*HR/compartmentOne
k1 = 0.0178 Reaction: G + HRP1 => G_a + HRP1; G, HRP1, Rate Law: compartmentOne*k1*G*HRP1/compartmentOne
k16 = 0.0723 Reaction: Hbarr2RP1 => barr2 + HR; Hbarr2RP1, Rate Law: compartmentOne*k16*Hbarr2RP1/compartmentOne
k9 = 3.04 Reaction: GpERK => ERK; GpERK, Rate Law: compartmentOne*k9*GpERK/compartmentOne
k20 = 1.04 Reaction: barr2 + HRP2 => Hbarr2RP2; barr2, HRP2, Rate Law: compartmentOne*k20*barr2*HRP2/compartmentOne
k11 = 2.61 Reaction: barr1 + HRP1 => Hbarr1RP1; barr1, HRP1, Rate Law: compartmentOne*k11*barr1*HRP1/compartmentOne
GRK23 = 0.899447579; k10 = 2.27 Reaction: HR => HRP1; GRK2_3, Rate Law: compartmentOne*k10*GRK23*HR/compartmentOne
k6 = 5.0985 Reaction: G_a => G; G_a, Rate Law: compartmentOne*k6*G_a/compartmentOne
k7 = 0.461 Reaction: DAG => PIP2; DAG, Rate Law: compartmentOne*k7*DAG/compartmentOne
k4 = 0.0787 Reaction: DAG + PKC => DAG + PKC_a; DAG, PKC, Rate Law: compartmentOne*k4*DAG*PKC/compartmentOne
k19 = 0.205 Reaction: barr2 + HR => HRbarr2; barr2, HR, Rate Law: compartmentOne*k19*barr2*HR/compartmentOne
k15 = 6.54E-5 Reaction: Hbarr1RP1 => barr1 + HR; Hbarr1RP1, Rate Law: compartmentOne*k15*Hbarr1RP1/compartmentOne
k13 = 0.00619 Reaction: Hbarr1RP1 => barr1 + HRP1; Hbarr1RP1, Rate Law: compartmentOne*k13*Hbarr1RP1/compartmentOne

States:

Name Description
DAG [CDP-diacylglycerol]
GpERK [Mitogen-activated protein kinase 3; phosphorylated]
HR [P01019; P30556]
PIP2 [CHEBI:83417]
barr2 [Beta-arrestin-2]
G [Guanine nucleotide-binding protein G(s) subunit alpha isoforms short]
barr1 [P49407]
Hbarr2RP2 [P30556; P01019; Beta-arrestin-2; phosphorylated]
Hbarr2RP1 [P01019; P30556; Beta-arrestin-2; phosphorylated]
HRbarr2 [P01019; P30556; Beta-arrestin-2]
G a [Guanine nucleotide-binding protein G(s) subunit alpha isoforms short; active]
pERK [Mitogen-activated protein kinase 3; phosphorylated]
bpERK [Mitogen-activated protein kinase 3; phosphorylated]
ERK [Mitogen-activated protein kinase 3]
HRP1 [P30556; P01019; phosphorylated]
Hbarr1RP1 [P30556; P49407; P01019; phosphorylated]
PKC a [Protein kinase C alpha type; active]
HRP2 [P01019; P30556; phosphorylated]
PKC [Protein kinase C alpha type]

Observables: none

MODEL1006230084 @ v0.0.1

This a model from the article: Computational modeling of cardiovascular response to orthostatic stress. Heldt T, Shi…

The objective of this study is to develop a model of the cardiovascular system capable of simulating the short-term (< or = 5 min) transient and steady-state hemodynamic responses to head-up tilt and lower body negative pressure. The model consists of a closed-loop lumped-parameter representation of the circulation connected to set-point models of the arterial and cardiopulmonary baroreflexes. Model parameters are largely based on literature values. Model verification was performed by comparing the simulation output under baseline conditions and at different levels of orthostatic stress to sets of population-averaged hemodynamic data reported in the literature. On the basis of experimental evidence, we adjusted some model parameters to simulate experimental data. Orthostatic stress simulations are not statistically different from experimental data (two-sided test of significance with Bonferroni adjustment for multiple comparisons). Transient response characteristics of heart rate to tilt also compare well with reported data. A case study is presented on how the model is intended to be used in the future to investigate the effects of post-spaceflight orthostatic intolerance. link: http://identifiers.org/pubmed/11842064

Parameters: none

States: none

Observables: none

MODEL1006230103 @ v0.0.1

This a model from the article: Computational modeling of cardiovascular response to orthostatic stress. Heldt T, Shi…

The objective of this study is to develop a model of the cardiovascular system capable of simulating the short-term (< or = 5 min) transient and steady-state hemodynamic responses to head-up tilt and lower body negative pressure. The model consists of a closed-loop lumped-parameter representation of the circulation connected to set-point models of the arterial and cardiopulmonary baroreflexes. Model parameters are largely based on literature values. Model verification was performed by comparing the simulation output under baseline conditions and at different levels of orthostatic stress to sets of population-averaged hemodynamic data reported in the literature. On the basis of experimental evidence, we adjusted some model parameters to simulate experimental data. Orthostatic stress simulations are not statistically different from experimental data (two-sided test of significance with Bonferroni adjustment for multiple comparisons). Transient response characteristics of heart rate to tilt also compare well with reported data. A case study is presented on how the model is intended to be used in the future to investigate the effects of post-spaceflight orthostatic intolerance. link: http://identifiers.org/pubmed/11842064

Parameters: none

States: none

Observables: none

MODEL1006230113 @ v0.0.1

This a model from the article: Computational modeling of cardiovascular response to orthostatic stress. Heldt T, Shi…

The objective of this study is to develop a model of the cardiovascular system capable of simulating the short-term (< or = 5 min) transient and steady-state hemodynamic responses to head-up tilt and lower body negative pressure. The model consists of a closed-loop lumped-parameter representation of the circulation connected to set-point models of the arterial and cardiopulmonary baroreflexes. Model parameters are largely based on literature values. Model verification was performed by comparing the simulation output under baseline conditions and at different levels of orthostatic stress to sets of population-averaged hemodynamic data reported in the literature. On the basis of experimental evidence, we adjusted some model parameters to simulate experimental data. Orthostatic stress simulations are not statistically different from experimental data (two-sided test of significance with Bonferroni adjustment for multiple comparisons). Transient response characteristics of heart rate to tilt also compare well with reported data. A case study is presented on how the model is intended to be used in the future to investigate the effects of post-spaceflight orthostatic intolerance. link: http://identifiers.org/pubmed/11842064

Parameters: none

States: none

Observables: none

BIOMD0000000463 @ v0.0.1

Heldt2012 - Influenza Virus ReplicationThe model describes the life cycle of influenza A virus in a mammalian cell inclu…

Influenza viruses transcribe and replicate their negative-sense RNA genome inside the nucleus of host cells via three viral RNA species. In the course of an infection, these RNAs show distinct dynamics, suggesting that differential regulation takes place. To investigate this regulation in a systematic way, we developed a mathematical model of influenza virus infection at the level of a single mammalian cell. It accounts for key steps of the viral life cycle, from virus entry to progeny virion release, while focusing in particular on the molecular mechanisms that control viral transcription and replication. We therefore explicitly consider the nuclear export of viral genome copies (vRNPs) and a recent hypothesis proposing that replicative intermediates (cRNA) are stabilized by the viral polymerase complex and the nucleoprotein (NP). Together, both mechanisms allow the model to capture a variety of published data sets at an unprecedented level of detail. Our findings provide theoretical support for an early regulation of replication by cRNA stabilization. However, they also suggest that the matrix protein 1 (M1) controls viral RNA levels in the late phase of infection as part of its role during the nuclear export of viral genome copies. Moreover, simulations show an accumulation of viral proteins and RNA toward the end of infection, indicating that transport processes or budding limits virion release. Thus, our mathematical model provides an ideal platform for a systematic and quantitative evaluation of influenza virus replication and its complex regulation. link: http://identifiers.org/pubmed/22593159

Parameters:

Name Description
parameter_17 = 1.0 Reaction: species_28 + species_29 + species_30 => species_11; species_28, species_29, species_30, Rate Law: compartment_1*parameter_17*species_28*species_29*species_30
parameter_13 = 3.01E-4 Reaction: species_19 + species_13 => species_9; species_19, species_13, Rate Law: compartment_1*parameter_13*species_19*species_13
parameter_43 = 20.2922077922078 Reaction: species_9 => species_9 + species_24; species_9, Rate Law: compartment_1*parameter_43*species_9
parameter_20 = 0.09 Reaction: species_9 => ; species_9, Rate Law: compartment_1*parameter_20*species_9
parameter_40 = 13.4698275862069 Reaction: species_9 => species_9 + species_21; species_9, Rate Law: compartment_1*parameter_40*species_9
parameter_8 = 6.0 Reaction: species_8 => species_9; species_8, Rate Law: compartment_1*parameter_8*species_8
parameter_10 = 13.86 Reaction: species_17 => species_17 + species_18; species_17, Rate Law: compartment_1*parameter_10*species_17
parameter_28 = 8.1 Reaction: species_26 => species_26 + species_34; species_26, Rate Law: compartment_1*parameter_28*species_26
parameter_14 = 1.39E-6 Reaction: species_9 + species_14 => species_15; species_9, species_14, Rate Law: compartment_1*parameter_14*species_9*species_14
parameter_21 = 0.33 Reaction: species_22 => ; species_22, Rate Law: compartment_1*parameter_21*species_22
parameter_15 = 1.0E-6 Reaction: species_15 + species_31 => species_16; species_15, species_31, Rate Law: compartment_1*parameter_15*species_15*species_31
parameter_16 = 405.0 Reaction: species_22 => species_22 + species_30; species_22, Rate Law: compartment_1*parameter_16*species_22
parameter_11 = 1.38 Reaction: species_9 => species_9 + species_10; species_9, Rate Law: compartment_1*parameter_11*species_9
parameter_29 = 50.625 Reaction: species_27 => species_27 + species_31; species_27, Rate Law: compartment_1*parameter_29*species_27
parameter_27 = 396.9 Reaction: species_26 => species_26 + species_14; species_26, Rate Law: compartment_1*parameter_27*species_26
parameter_39 = 13.4698275862069 Reaction: species_9 => species_9 + species_20; species_9, Rate Law: compartment_1*parameter_39*species_9
parameter_19 = 36.36 Reaction: species_10 => ; species_10, Rate Law: compartment_1*parameter_19*species_10
parameter_2 = 4.55E-4; parameter_4 = 5.46218487394958 Reaction: species_3 + species_4 => species_5; species_3, species_4, species_5, Rate Law: compartment_1*(parameter_2*species_3*species_4-parameter_4*species_5)
parameter_22 = 4.25 Reaction: species_19 => ; species_19, Rate Law: compartment_1*parameter_22*species_19
parameter_7 = 3.08411764705882 Reaction: species_6 => ; species_6, Rate Law: compartment_1*parameter_7*species_6
parameter_45 = 31.0945273631841 Reaction: species_9 => species_9 + species_26; species_9, Rate Law: compartment_1*parameter_45*species_9
parameter_6 = 3.21 Reaction: species_6 => species_7 + species_8; species_6, Rate Law: compartment_1*parameter_6*species_6
parameter_44 = 22.4497126436782 Reaction: species_9 => species_9 + species_25; species_9, Rate Law: compartment_1*parameter_44*species_9
parameter_1 = 0.0809; parameter_3 = 7.15929203539823 Reaction: species_3 + species_1 => species_2; species_3, species_1, species_2, Rate Law: compartment_1*(parameter_1*species_3*species_1-parameter_3*species_2)
parameter_42 = 17.7859988616961 Reaction: species_9 => species_9 + species_23; species_9, Rate Law: compartment_1*parameter_42*species_9
parameter_46 = 36.0023041474654 Reaction: species_9 => species_9 + species_27; species_9, Rate Law: compartment_1*parameter_46*species_9
parameter_12 = 1.0 Reaction: species_18 + species_11 => species_19; species_18, species_11, Rate Law: compartment_1*parameter_12*species_18*species_11
parameter_41 = 14.1338760741746 Reaction: species_9 => species_9 + species_22; species_9, Rate Law: compartment_1*parameter_41*species_9
KmB=450.0; KmE=1000.0; KmC=5000.0; KmD=10000.0; KmF=30000.0; parameter_18 = 0.0037; KmH=1650.0; KmG=400.0 Reaction: species_16 + species_11 + species_13 + species_14 + species_31 + species_32 + species_33 + species_34 => species_35; species_16, species_11, species_32, species_13, species_33, species_14, species_34, species_31, Rate Law: compartment_1*parameter_18*species_16*species_11*species_32*species_13*species_33*species_14*species_34*species_31/((species_11+KmB)*(species_32+KmC)*(species_13+KmD)*(species_33+KmE)*(species_14+KmF)*(species_34+KmG)*(species_31+KmH))
parameter_5 = 4.8 Reaction: species_5 => species_6 + species_4; species_5, Rate Law: compartment_1*parameter_5*species_5

States:

Name Description
species 9 [nucleus; intracellular ribonucleoprotein complex]
species 27 Rm8
species 31 [Nuclear export protein]
species 1 [sialic acid]
species 20 Rm1
species 4 Blo
species 16 [cytoplasm; Matrix protein 1; intracellular ribonucleoprotein complex]
species 18 [Influenza A virus (strain A/Puerto Rico/8/1934 H1N1)]
species 28 [RNA-directed RNA polymerase catalytic subunit]
species 39 total vRNA of a segment
species 34 [Matrix protein 2Matrix protein 2]
species 21 Rm2
species 8 [cytoplasm; intracellular ribonucleoprotein complex]
species 17 [intracellular ribonucleoprotein complex]
species 12 [RNA viral genome; viral RNA-directed RNA polymerase complex]
species 25 Rm6
species 5 [virion attachment to host cell; virion]
species 15 [nucleus; Matrix protein 1; intracellular ribonucleoprotein complex]
species 29 [Polymerase basic protein 2]
species 2 [virion attachment to host cell; virion]
species 30 [Polymerase acidic protein]
species 6 [endosome; virion]
species 38 total vRNA
species 19 [RNA viral genome; viral RNA-directed RNA polymerase complex]
species 10 [RNA viral genome; transcription, RNA-templated]
species 33 [Neuraminidase]
species 11 [viral RNA-directed RNA polymerase complex]
species 24 Rm5
species 14 [Matrix protein 1]
species 22 Rm3
species 3 [extracellular region; virion]
species 23 Rm4
species 7 [fusion of virus membrane with host endosome membrane; viral membrane; endosome membrane]
species 26 Rm7
species 13 [Nucleoprotein]

Observables: none

This model is decribed in the article: Dilution and titration of cell-cycle regulators may control cell size in budding…

The size of a cell sets the scale for all biochemical processes within it, thereby affecting cellular fitness and survival. Hence, cell size needs to be kept within certain limits and relatively constant over multiple generations. However, how cells measure their size and use this information to regulate growth and division remains controversial. Here, we present two mechanistic mathematical models of the budding yeast (S. cerevisiae) cell cycle to investigate competing hypotheses on size control: inhibitor dilution and titration of nuclear sites. Our results suggest that an inhibitor-dilution mechanism, in which cell growth dilutes the transcriptional inhibitor Whi5 against the constant activator Cln3, can facilitate size homeostasis. This is achieved by utilising a positive feedback loop to establish a fixed size threshold for the START transition, which efficiently couples cell growth to cell cycle progression. Yet, we show that inhibitor dilution cannot reproduce the size of mutants that alter the cell’s overall ploidy and WHI5 gene copy number. By contrast, size control through titration of Cln3 against a constant number of genomic binding sites for the transcription factor SBF recapitulates both size homeostasis and the size of these mutant strains. Moreover, this model produces an imperfect ‘sizer’ behaviour in G1 and a ‘timer’ in S/G2/M, which combine to yield an ‘adder’ over the whole cell cycle; an observation recently made in experiments. Hence, our model connects these phenomenological data with the molecular details of the cell cycle, providing a systems-level perspective of budding yeast size control. link: http://identifiers.org/doi/10.1371/journal.pcbi.1006548

Parameters: none

States: none

Observables: none

Heldt2018 - Proliferation-quiescence decision in response to DNA damageThis model is described in the article: [A compr…

Human cells that suffer mild DNA damage can enter a reversible state of growth arrest known as quiescence. This decision to temporarily exit the cell cycle is essential to prevent the propagation of mutations, and most cancer cells harbor defects in the underlying control system. Here we present a mechanistic mathematical model to study the proliferation-quiescence decision in nontransformed human cells. We show that two bistable switches, the restriction point (RP) and the G1/S transition, mediate this decision by integrating DNA damage and mitogen signals. In particular, our data suggest that the cyclin-dependent kinase inhibitor p21 (Cip1/Waf1), which is expressed in response to DNA damage, promotes quiescence by blocking positive feedback loops that facilitate G1 progression downstream of serum stimulation. Intriguingly, cells exploit bistability in the RP to convert graded p21 and mitogen signals into an all-or-nothing cell-cycle response. The same mechanism creates a window of opportunity where G1 cells that have passed the RP can revert to quiescence if exposed to DNA damage. We present experimental evidence that cells gradually lose this ability to revert to quiescence as they progress through G1 and that the onset of rapid p21 degradation at the G1/S transition prevents this response altogether, insulating S phase from mild, endogenous DNA damage. Thus, two bistable switches conspire in the early cell cycle to provide both sensitivity and robustness to external stimuli. link: http://identifiers.org/pubmed/29463760

Parameters:

Name Description
kReDamP53 = 0.005; kReDam = 0.001; jDam = 0.5 Reaction: Dam => ; P53, Rate Law: Cell*(kReDam+kReDamP53*P53/(jDam+Dam))*Dam
kSyDna = 0.0093 Reaction: aRc => aRc + Dna, Rate Law: Cell*kSyDna*aRc
kDeE2f = 0.05 Reaction: RbE2f => Rb, Rate Law: Cell*kDeE2f*RbE2f
kDsRcPc = 0.001; kAsRcPc = 0.01 Reaction: iPcna + pRc => iRc, Rate Law: Cell*(kAsRcPc*iPcna*pRc-kDsRcPc*iRc)
kDpRb = 0.05 Reaction: pRb => Rb, Rate Law: Cell*kDpRb*pRb
kDeE1C1 = 0.005 Reaction: E1C1 => C1, Rate Law: Cell*kDeE1C1*E1C1
kDsRbE2f = 0.005; kAsRbE2f = 5.0 Reaction: Rb + E2f => RbE2f, Rate Law: Cell*(kAsRbE2f*Rb*E2f-kDsRbE2f*RbE2f)
kPhC1Ca = 1.0; kPhC1 = 0.0; kPhC1Ce = 0.01 Reaction: C1 => pC1; Ce, Ca, Rate Law: Cell*(kPhC1+kPhC1Ce*Ce+kPhC1Ca*Ca)*C1
kDeE1 = 5.0E-4 Reaction: E1 =>, Rate Law: Cell*kDeE1*E1
kExPc = 0.006 Reaction: aPcna =>, Rate Law: Cell*kExPc*aPcna
kImPc = 0.003 Reaction: => aPcna, Rate Law: Cell*kImPc
n = 6.0; kPhRc = 0.1; jCy = 1.8 Reaction: Rc => pRc; Ce, Ca, Rate Law: Cell*kPhRc*(Ce+Ca)^n/(jCy^n+(Ce+Ca)^n)*Rc
kDsE1C1 = 0.01; kAsE1C1 = 10.0 Reaction: E1 + C1 => E1C1, Rate Law: Cell*(kAsE1C1*E1*C1-kDsE1C1*E1C1)
kDeCaC1 = 2.0; kDeCa = 0.01 Reaction: CaP21 => P21; C1, Rate Law: Cell*(kDeCa+kDeCaC1*C1)*CaP21
kGeDam = 0.001 Reaction: => Dam, Rate Law: Cell*kGeDam
kPhRbCe = 0.3; Cd = 0.65; kPhRbCd = 0.2; kPhRbCa = 0.3 Reaction: RbE2f => pRb + E2f; Ce, Ca, Rate Law: Cell*(kPhRbCd*Cd+kPhRbCe*Ce+kPhRbCa*Ca)*RbE2f
Skp2 = 1.0; kDeP21 = 0.0025; kDeP21aRc = 1.0; Cdt2 = 1.0; kDeP21Cy = 0.007 Reaction: iRc => aRc; Ce, Ca, aRc, Rate Law: Cell*(kDeP21+kDeP21Cy*Skp2*(Ce+Ca)+kDeP21aRc*Cdt2*aRc)*iRc
kSyCe = 0.01 Reaction: E2f => E2f + Ce, Rate Law: Cell*kSyCe*E2f
kDsCyP21 = 0.05; kAsCyP21 = 1.0 Reaction: Ce + P21 => CeP21, Rate Law: Cell*(kAsCyP21*Ce*P21-kDsCyP21*CeP21)
kDsPcP21 = 0.01; kAsPcP21 = 100.0 Reaction: aRc + P21 => iRc, Rate Law: Cell*(kAsPcP21*aRc*P21-kDsPcP21*iRc)
kDeCeCa = 0.015; kDeCe = 0.004 Reaction: CeP21 => P21; Ca, Rate Law: Cell*(kDeCe+kDeCeCa*Ca)*CeP21
kDePr = 1.0E-4; kDeCaC1 = 2.0 Reaction: Pr => ; C1, Rate Law: Cell*(kDePr+kDeCaC1*C1)*Pr
kSyE2f = 0.03; jSyE2f = 0.2; kSyE2fE2f = 0.04 Reaction: => E2f; E2f, Rate Law: Cell*(kSyE2f+kSyE2fE2f*E2f/(jSyE2f+E2f))
kSyP53 = 0.05 Reaction: => P53, Rate Law: Cell*kSyP53
kDpC1 = 0.05 Reaction: pC1 => C1, Rate Law: Cell*kDpC1*pC1
kSyCa = 0.02 Reaction: E2f => E2f + Ca, Rate Law: Cell*kSyCa*E2f
kSyPr = 0.01 Reaction: => Pr, Rate Law: Cell*kSyPr
kSyE1 = 0.005 Reaction: E2f => E2f + E1, Rate Law: Cell*kSyE1*E2f
kSyP21 = 0.002; kSyP21P53 = 0.008 Reaction: => P21; P53, Rate Law: Cell*(kSyP21+kSyP21P53*P53)
kGeDamArc = 0.012 Reaction: aRc => aRc + Dam, Rate Law: Cell*kGeDamArc*aRc
kDpRc = 0.05 Reaction: pRc => Rc, Rate Law: Cell*kDpRc*pRc
kDeP53 = 0.05; jP53 = 0.01 Reaction: P53 => ; Dam, Rate Law: Cell*kDeP53/(jP53+Dam)*P53

States:

Name Description
tE1 [F-box only protein 5]
tC1 [anaphase-promoting complex]
E2f [Transcription factor E2F1; active]
Ce [Cyclin-dependent kinase 2; protein-containing complex; G1/S-specific cyclin-E1; active]
aRc [Pre-Replication Complex; active]
Rc [Pre-Replication Complex]
C1 [anaphase-promoting complex; active]
tP21 [Cyclin-dependent kinase inhibitor 1]
Pr Activity_probe_of_APC_C_Cdh1
P53 [Cellular tumor antigen p53]
P21 [Cyclin-dependent kinase inhibitor 1]
aPcna [Proliferating cell nuclear antigen; active]
E1 [F-box only protein 5]
CeP21 [Cyclin-dependent kinase 2; inactive; G1/S-specific cyclin-E1; protein-containing complex]
pC1 [anaphase-promoting complex; phosphorylated; inactive]
RbE2f [Retinoblastoma-like protein 2; protein-containing complex; Transcription factor E2F1; inactive]
tRb [Retinoblastoma-like protein 2]
iRc [Pre-Replication Complex; inactive]
Rb [Retinoblastoma-like protein 2]
E1C1 [F-box only protein 5; protein-containing complex; anaphase-promoting complex; inactive]
CaP21 [Cyclin-A2; inactive; Cyclin-dependent kinase inhibitor 1; protein-containing complex; Cyclin-dependent kinase 2]
iPcna [Proliferating cell nuclear antigen; inactive]
Dam [DNA; damaged]
tCe [Cyclin-dependent kinase 2; protein-containing complex; G1/S-specific cyclin-E1]
Dna [DNA]
tE2f [Transcription factor E2F1]
pRb [Retinoblastoma-like protein 2; increased phosphorylation]
tCa [Cyclin-A2; protein-containing complex; Cyclin-dependent kinase 2]
Ca [Cyclin-dependent kinase 2; Cyclin-A2; protein-containing complex]
pRc [Pre-Replication Complex; phosphorylated; urn:miriam:sbo:SBO%3A0000643]

Observables: none

This model is described in the article: A single light-responsive sizer can control multiple-fission cycles in Chlamydom…

Most eukaryotic cells execute binary division after each mass doubling in order to maintain size homeostasis by coordinating cell growth and division. By contrast, the photosynthetic green alga Chlamydomonas can grow more than 8-fold during daytime and then, at night, undergo rapid cycles of DNA replication, mitosis, and cell division, producing up to 16 daughter cells. Here, we propose a mechanistic model for multiple-fission cycles and cell-size control in Chlamydomonas. The model comprises a light-sensitive and size-dependent biochemical toggle switch that acts as a sizer, guarding transitions into and exit from a phase of cell-division cycle oscillations. This simple “sizer-oscillator” arrangement reproduces the experimentally observed features of multiple-fission cycles and the response of Chlamydomonas cells to different light-dark regimes. Our model also makes specific predictions about the size dependence of the time of onset of cell division after cells are transferred from light to dark conditions, and we confirm these predictions by single-cell experiments. Collectively, our results provide a new perspective on the concept of a “commitment point” during the growth of Chlamydomonas cells and hint at intriguing similarities of cell-size control in different eukaryotic lineages. link: http://identifiers.org/doi/10.1016/j.cub.2019.12.026

Parameters: none

States: none

Observables: none

Henry2009 - Genome-scale metabolic network of Bacillus subtilis (iBsu1103)This model is described in the article: [iBsu…

BACKGROUND: Bacillus subtilis is an organism of interest because of its extensive industrial applications, its similarity to pathogenic organisms, and its role as the model organism for Gram-positive, sporulating bacteria. In this work, we introduce a new genome-scale metabolic model of B. subtilis 168 called iBsu1103. This new model is based on the annotated B. subtilis 168 genome generated by the SEED, one of the most up-to-date and accurate annotations of B. subtilis 168 available. RESULTS: The iBsu1103 model includes 1,437 reactions associated with 1,103 genes, making it the most complete model of B. subtilis available. The model also includes Gibbs free energy change (DeltarG' degrees ) values for 1,403 (97%) of the model reactions estimated by using the group contribution method. These data were used with an improved reaction reversibility prediction method to identify 653 (45%) irreversible reactions in the model. The model was validated against an experimental dataset consisting of 1,500 distinct conditions and was optimized by using an improved model optimization method to increase model accuracy from 89.7% to 93.1%. CONCLUSIONS: Basing the iBsu1103 model on the annotations generated by the SEED significantly improved the model completeness and accuracy compared with the most recent previously published model. The enhanced accuracy of the iBsu1103 model also demonstrates the efficacy of the improved reaction directionality prediction method in accurately identifying irreversible reactions in the B. subtilis metabolism. The proposed improved model optimization methodology was also demonstrated to be effective in minimally adjusting model content to improve model accuracy. link: http://identifiers.org/pubmed/19555510

Parameters: none

States: none

Observables: none

MODEL1812210002 @ v0.0.1

The spindle assembly checkpoint (SAC) is an evolutionarily conserved mechanism, exclusively sensitive to the states of k…

The spindle assembly checkpoint (SAC) is an evolutionarily conserved mechanism, exclusively sensitive to the states of kinetochores attached to microtubules. During metaphase, the anaphase-promoting complex/cyclosome (APC/C) is inhibited by the SAC but it rapidly switches to its active form following proper attachment of the final spindle. It had been thought that APC/C activity is an all-or-nothing response, but recent findings have demonstrated that it switches steadily. In this study, we develop a detailed mathematical model that considers all 92 human kinetochores and all major proteins involved in SAC activation and silencing. We perform deterministic and spatially-stochastic simulations and find that certain spatial properties do not play significant roles. Furthermore, we show that our model is consistent with in-vitro mutation experiments of crucial proteins as well as the recently-suggested rheostat switch behavior, measured by Securin or CyclinB concentration. Considering an autocatalytic feedback loop leads to an all-or-nothing toggle switch in the underlying core components, while the output signal of the SAC still behaves like a rheostat switch. The results of this study support the hypothesis that the SAC signal varies with increasing number of attached kinetochores, even though it might still contain toggle switches in some of its components. link: http://identifiers.org/pubmed/28634351

Parameters: none

States: none

Observables: none

Hermansen2015 - denovo biosynthesis of pyrimidines in yeastThis model is described in the article: [Characterizing sele…

Selection on proteins is typically measured with the assumption that each protein acts independently. However, selection more likely acts at higher levels of biological organization, requiring an integrative view of protein function. Here, we built a kinetic model for de novo pyrimidine biosynthesis in the yeast Saccharomyces cerevisiae to relate pathway function to selective pressures on individual protein-encoding genes.Gene families across yeast were constructed for each member of the pathway and the ratio of nonsynonymous to synonymous nucleotide substitution rates (dN/dS) was estimated for each enzyme from S. cerevisiae and closely related species. We found a positive relationship between the influence that each enzyme has on pathway function and its selective constraint.We expect this trend to be locally present for enzymes that have pathway control, but over longer evolutionary timescales we expect that mutation-selection balance may change the enzymes that have pathway control. link: http://identifiers.org/pubmed/26511837

Parameters:

Name Description
K_Mp = 5.48714446027226; g_pyr = 0.198306450999093 Reaction: utp => ; utp, Rate Law: compartment*g_pyr*utp/(K_Mp+utp)/compartment
prpp = 0.181644900226225; vmax5 = 5227.49670547203; K_m5 = 0.0195216150005324 Reaction: oro => omp; oro, Rate Law: compartment*vmax5*oro*prpp/(K_m5+oro*prpp)/compartment
d = 0.1 Reaction: cp => ; cp, Rate Law: compartment*d*cp/compartment
K_m7 = 0.166382738667754; vmax7 = 5.83104141997666 Reaction: udp => utp; udp, Rate Law: compartment*vmax7*udp/(K_m7+udp)/compartment
vmax3 = 28.6613123782585; K_m3 = 1.27179181717468 Reaction: ca => dho; ca, Rate Law: compartment*vmax3*ca/(K_m3+ca)/compartment
K_m6 = 20.3406449182435; vmax6 = 34.9720846528477 Reaction: omp => ump; omp, Rate Law: compartment*vmax6*omp/(K_m6+omp)/compartment
K_m4 = 0.0160033122150611; vmax4 = 91.7802875108298 Reaction: dho => oro; dho, Rate Law: compartment*vmax4*dho/(K_m4+dho)/compartment
K_asp = 0.168308889432487; vmax2 = 2.44590712912244; K_m2 = 2.00489353757245; asp = 0.0972544685826559; K_utp = 1.413855257896 Reaction: cp => ca; utp, cp, utp, Rate Law: compartment*vmax2*cp*asp/((1+utp/K_utp)*(K_m2+cp)*(K_asp+asp))/compartment
K_q = 0.05784981576165; K_bc = 2.3716657188714; atp = 0.150650172583633; bc = 1.52264278250403; glu = 0.54620785996429; vmax1 = 3.61602627459517; K_utp = 1.413855257896; K_atp = 1.28940553329954 Reaction: => cp; utp, utp, Rate Law: compartment*vmax1*bc*glu*atp/((1+utp/K_utp)*(K_atp+atp)*(K_bc+bc)*(K_q+glu))/compartment
K_m8 = 0.00435621076587497; vmax8 = 0.162943604164789 Reaction: utp => ctp; utp, Rate Law: compartment*vmax8*utp/(K_m8+utp)/compartment
vmax10 = 6.55543523218919; K_m10 = 0.0267841313759584 Reaction: ump => udp; ump, Rate Law: compartment*vmax10*ump/(K_m10+ump)/compartment

States:

Name Description
udp [UDP; UDP]
utp [UTP; UTP]
dho [(S)-Dihydroorotate; (S)-dihydroorotic acid]
omp [Orotidine 5'-phosphate; orotidine 5'-phosphate]
ctp [CTP; CTP]
ump [UMP; UMP]
ca [N-Carbamoyl-L-aspartate; N-carbamoyl-L-aspartic acid]
oro [Orotate; orotic acid]
cp [Carbamoyl phosphate; carbamoyl phosphate]

Observables: none

BIOMD0000000162 @ v0.0.1

The model reproduces the time profiles of Calcium in the spine and dendrites as depicted in Fig 8 and Fig 9 of the paper…

Modeling and simulation of the calcium signaling events that precede long-term depression of synaptic activity in cerebellar Purkinje cells are performed using the Virtual Cell biological modeling framework. It is found that the unusually high density and low sensitivity of inositol-1,4,5-trisphosphate receptors (IP3R) are critical to the ability of the cell to generate and localize a calcium spike in a single dendritic spine. The results also demonstrate the model's capability to simulate the supralinear calcium spike observed experimentally during coincident activation of the parallel and climbing fibers. The sensitivity of the calcium spikes to certain biological and geometrical effects is investigated as well as the mechanisms that underlie the cell's ability to generate the supralinear spike. The sensitivity of calcium release rates from the IP3R to calcium concentrations, as well as IP3 concentrations, allows the calcium spike to form. The diffusion barrier caused by the small radius of the spine neck is shown to be important, as a threshold radius is observed above which a spike cannot be formed. Additionally, the calcium buffer capacity and diffusion rates from the spine are found to be important parameters in shaping the calcium spike. link: http://identifiers.org/pubmed/16169982

Parameters:

Name Description
I=0.0 dimensionless*A*m^(-2); KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol; Jmax2=21000.0 1E-57*dimensionless*item^(-4)*m^6*mol*s^(-1); dI=20.0 0.001*dimensionless*m^(-3)*mol; Kact=0.3 0.001*dimensionless*m^(-3)*mol Reaction: Ca_Cytosol => Ca_ER; IP3_Cytosol, h_ERM, ERDensity_ERM, Rate Law: (-ERDensity_ERM*Jmax2*(1+(-0.00166112956810631*Ca_Cytosol*1/(0.00166112956810631*Ca_ER)))*(h_ERM*0.00166112956810631*IP3_Cytosol*0.00166112956810631*Ca_Cytosol*1/(0.00166112956810631*IP3_Cytosol+dI)*1/(0.00166112956810631*Ca_Cytosol+Kact))^3)*ERM*1*1/KMOLE
D=28.0 1E-12*dimensionless*m^2*s^(-1); D28kB_F=4.16951 0.001*dimensionless*m^(-3)*mol; r_n=0.1 μm; r_D=1.0 μm; KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol; l_n=0.66 μm; l_star=27.9812 μm; lc=5.6265 μm Reaction: D28kB_D_Cytosol => ; D28kB_Cytosol, Rate Law: (D*r_n^2*(0.00166112956810631*D28kB_D_Cytosol+(-0.00166112956810631*D28kB_Cytosol))*1/l_n*1/r_D^2*1/l_star+D*(0.00166112956810631*D28kB_D_Cytosol+(-D28kB_F))*1/l_star*1/lc)*Cytosol*1*1/KMOLE
r_d=1.0 μm; r_n=0.1 μm; PABMg_F=60.47222 0.001*dimensionless*m^(-3)*mol; KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol; l_n=0.66 μm; l_star=27.9812 μm; D=43.0 1E-12*dimensionless*m^2*s^(-1); lc=5.6265 μm Reaction: PABMg_D_Cytosol => ; PABMg_Cytosol, Rate Law: (D*r_n^2*(0.00166112956810631*PABMg_D_Cytosol+(-0.00166112956810631*PABMg_Cytosol))*1/l_n*1/r_d^2*1/l_star+D*(0.00166112956810631*PABMg_D_Cytosol+(-PABMg_F))*1/l_star*1/lc)*Cytosol*1*1/KMOLE
r_n=0.1 μm; r_D=1.0 μm; KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol; l_n=0.66 μm; l_star=27.9812 μm; Ca_F=0.045 0.001*dimensionless*m^(-3)*mol; D=223.0 1E-12*dimensionless*m^2*s^(-1); lc=5.6265 μm Reaction: Ca_D_Cytosol => ; Ca_Cytosol, Rate Law: (D*r_n^2*(0.00166112956810631*Ca_D_Cytosol+(-0.00166112956810631*Ca_Cytosol))*1/l_n*1/r_D^2*1/l_star+D*(0.00166112956810631*Ca_D_Cytosol+(-Ca_F))*1/l_star*1/lc)*Cytosol*1*1/KMOLE
Kf=430.0 1000*dimensionless*m^3*mol^(-1)*s^(-1); KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol; Kr=140.0 s^(-1) Reaction: Ca_D_Cytosol + CG_D_Cytosol => CGB_D_Cytosol, Rate Law: (Kf*0.00166112956810631*Ca_D_Cytosol*0.00166112956810631*CG_D_Cytosol+(-Kr*0.00166112956810631*CGB_D_Cytosol))*Cytosol*1*1/KMOLE
l=0.66 μm; r_neck=0.1 μm; KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol; r_spine=0.288 μm; D=223.0 1E-12*dimensionless*m^2*s^(-1) Reaction: Ca_Cytosol => ; Ca_D_Cytosol, Rate Law: 0.75*D*(0.00166112956810631*Ca_Cytosol+(-0.00166112956810631*Ca_D_Cytosol))*r_neck^2*1/l*1/r_spine^3*Cytosol*1*1/KMOLE
r_d=1.0 μm; r_n=0.1 μm; KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol; l_n=0.66 μm; l_star=27.9812 μm; CG_F=140.47567 0.001*dimensionless*m^(-3)*mol; D=15.0 1E-12*dimensionless*m^2*s^(-1); lc=5.6265 μm Reaction: CG_D_Cytosol => ; CG_Cytosol, Rate Law: (D*r_n^2*(0.00166112956810631*CG_D_Cytosol+(-0.00166112956810631*CG_Cytosol))*1/l_n*1/r_d^2*1/l_star+D*(0.00166112956810631*CG_D_Cytosol+(-CG_F))*1/l_star*1/lc)*Cytosol*1*1/KMOLE
r_d=1.0 μm; r_n=0.1 μm; KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol; l_n=0.66 μm; l_star=27.9812 μm; PABCa_F=16.32481 0.001*dimensionless*m^(-3)*mol; D=43.0 1E-12*dimensionless*m^2*s^(-1); lc=5.6265 μm Reaction: PABCa_D_Cytosol => ; PABCa_Cytosol, Rate Law: (D*r_n^2*(0.00166112956810631*PABCa_D_Cytosol+(-0.00166112956810631*PABCa_Cytosol))*1/l_n*1/r_d^2*1/l_star+D*(0.00166112956810631*PABCa_D_Cytosol+(-PABCa_F))*1/l_star*1/lc)*Cytosol*1*1/KMOLE
SVR=3.0 μm^(-1); Js=0.0 1E-9*dimensionless*m^(-2)*mol*s^(-1); Rs=0.288 dimensionless; KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol; pulses_ar = 0.0 Reaction: => IP3_Cytosol, Rate Law: SVR*Js*pulses_ar*1/Rs*Cytosol*1*1/KMOLE
KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol; Kf=43.5 1000*dimensionless*m^3*mol^(-1)*s^(-1); Kr=35.8 s^(-1) Reaction: D28k_D_Cytosol + Ca_D_Cytosol => D28kB_D_Cytosol, Rate Law: (Kf*0.00166112956810631*D28k_D_Cytosol*0.00166112956810631*Ca_D_Cytosol+(-Kr*0.00166112956810631*D28kB_D_Cytosol))*Cytosol*1*1/KMOLE
l=0.66 μm; r_neck=0.1 μm; KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol; r_spine=0.288 μm; D=43.0 1E-12*dimensionless*m^2*s^(-1) Reaction: PA_Cytosol => ; PA_D_Cytosol, Rate Law: 0.75*D*(0.00166112956810631*PA_Cytosol+(-0.00166112956810631*PA_D_Cytosol))*r_neck^2*1/l*1/r_spine^3*Cytosol*1*1/KMOLE
D=28.0 1E-12*dimensionless*m^2*s^(-1); r_n=0.1 μm; r_D=1.0 μm; D28k_F=75.83049 0.001*dimensionless*m^(-3)*mol; KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol; l_n=0.66 μm; l_star=27.9812 μm; lc=5.6265 μm Reaction: D28k_D_Cytosol => ; D28k_Cytosol, Rate Law: (D*r_n^2*(0.00166112956810631*D28k_D_Cytosol+(-0.00166112956810631*D28k_Cytosol))*1/l_n*1/r_D^2*1/l_star+D*(0.00166112956810631*D28k_D_Cytosol+(-D28k_F))*1/l_star*1/lc)*Cytosol*1*1/KMOLE
D=283.0 1E-12*dimensionless*m^2*s^(-1); r_d=1.0 μm; r_n=0.1 μm; KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol; l_n=0.66 μm; l_star=27.9812 μm; IP3_F=0.16 0.001*dimensionless*m^(-3)*mol; lc=5.6265 μm Reaction: IP3_D_Cytosol => ; IP3_Cytosol, Rate Law: (D*r_n^2*(0.00166112956810631*IP3_D_Cytosol+(-0.00166112956810631*IP3_Cytosol))*1/l_n*1/r_d^2*1/l_star+D*(0.00166112956810631*IP3_D_Cytosol+(-IP3_F))*1/l_star*1/lc)*Cytosol*1*1/KMOLE
Kf=107.0 1000*dimensionless*m^3*mol^(-1)*s^(-1); Kr=0.95 s^(-1); KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol Reaction: PA_Cytosol + Ca_Cytosol => PABCa_Cytosol, Rate Law: (Kf*0.00166112956810631*PA_Cytosol*0.00166112956810631*Ca_Cytosol+(-Kr*0.00166112956810631*PABCa_Cytosol))*Cytosol*1*1/KMOLE
vP=3.75 1E-21*dimensionless*item^(-1)*mol*s^(-1); I=0.0 dimensionless*A*m^(-2); KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol; kP=0.27 Reaction: Ca_D_Cytosol => Ca_D_ER; ERDensity_D_ERM, Rate Law: ERDensity_D_ERM*vP*0.00166112956810631*Ca_D_Cytosol*0.00166112956810631*Ca_D_Cytosol*1/(kP*kP+0.00166112956810631*Ca_D_Cytosol*0.00166112956810631*Ca_D_Cytosol)*ERM*1*1/KMOLE
Kf=0.8 1000*dimensionless*m^3*mol^(-1)*s^(-1); Kr=25.0 s^(-1); KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol Reaction: PA_Cytosol + Mg_Cytosol => PABMg_Cytosol, Rate Law: (Kf*0.00166112956810631*PA_Cytosol*0.00166112956810631*Mg_Cytosol+(-Kr*0.00166112956810631*PABMg_Cytosol))*Cytosol*1*1/KMOLE
D=28.0 1E-12*dimensionless*m^2*s^(-1); l=0.66 μm; r_neck=0.1 μm; KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol; r_spine=0.288 μm Reaction: D28k_Cytosol => ; D28k_D_Cytosol, Rate Law: 0.75*D*(0.00166112956810631*D28k_Cytosol+(-0.00166112956810631*D28k_D_Cytosol))*r_neck^2*1/l*1/r_spine^3*Cytosol*1*1/KMOLE
vL=0.12396 1E-21*dimensionless*item^(-1)*mol*s^(-1); I=0.0 dimensionless*A*m^(-2); KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol Reaction: Ca_Cytosol => Ca_ER; ERDensity_ERM, Rate Law: (-ERDensity_ERM*vL*(1+(-0.00166112956810631*Ca_Cytosol*1/(0.00166112956810631*Ca_ER))))*ERM*1*1/KMOLE
D=28.0 1E-12*dimensionless*m^2*s^(-1); r_n=0.1 μm; r_D=1.0 μm; KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol; l_n=0.66 μm; l_star=27.9812 μm; D28kB_high_F=6.98896 0.001*dimensionless*m^(-3)*mol; lc=5.6265 μm Reaction: D28kB_high_D_Cytosol => ; D28kB_high_Cytosol, Rate Law: (D*r_n^2*(0.00166112956810631*D28kB_high_D_Cytosol+(-0.00166112956810631*D28kB_high_Cytosol))*1/l_n*1/r_D^2*1/l_star+D*(0.00166112956810631*D28kB_high_D_Cytosol+(-D28kB_high_F))*1/l_star*1/lc)*Cytosol*1*1/KMOLE
Kr=2.6 s^(-1); Kf=5.5 1000*dimensionless*m^3*mol^(-1)*s^(-1); KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol Reaction: Ca_Cytosol + D28k_high_Cytosol => D28kB_high_Cytosol, Rate Law: (Kf*0.00166112956810631*Ca_Cytosol*0.00166112956810631*D28k_high_Cytosol+(-Kr*0.00166112956810631*D28kB_high_Cytosol))*Cytosol*1*1/KMOLE
I=0.0 dimensionless*A*m^(-2); KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol; flux1_ar = 0.0 Reaction: Ca_D_Extracellular => Ca_D_Cytosol, Rate Law: flux1_ar*PM*1*1/KMOLE
I=0.0 dimensionless*A*m^(-2); Kon=2.7 1E15*dimensionless*item*m*mol^(-1)*s^(-1); Kinh=0.2 0.001*dimensionless*m^(-3)*mol Reaction: h_ERM => ; Ca_Cytosol, Rate Law: (-(Kinh+(-(0.00166112956810631*Ca_Cytosol+Kinh)*h_ERM))*Kon)*ERM
r_d=1.0 μm; r_n=0.1 μm; KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol; l_n=0.66 μm; l_star=27.9812 μm; CGB_F=19.5243 0.001*dimensionless*m^(-3)*mol; D=15.0 1E-12*dimensionless*m^2*s^(-1); lc=5.6265 μm Reaction: CGB_D_Cytosol => ; CGB_Cytosol, Rate Law: (D*r_n^2*(0.00166112956810631*CGB_D_Cytosol+(-0.00166112956810631*CGB_Cytosol))*1/l_n*1/r_d^2*1/l_star+D*(0.00166112956810631*CGB_D_Cytosol+(-CGB_F))*1/l_star*1/lc)*Cytosol*1*1/KMOLE
I=0.0 dimensionless*A*m^(-2); KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol; flux0_ar = 0.0 Reaction: Ca_Extracellular => Ca_Cytosol, Rate Law: flux0_ar*PM*1*1/KMOLE
D=28.0 1E-12*dimensionless*m^2*s^(-1); r_n=0.1 μm; r_D=1.0 μm; KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol; l_n=0.66 μm; l_star=27.9812 μm; D28k_high_F=73.01104 0.001*dimensionless*m^(-3)*mol; lc=5.6265 μm Reaction: D28k_high_D_Cytosol => ; D28k_high_Cytosol, Rate Law: (D*r_n^2*(0.00166112956810631*D28k_high_D_Cytosol+(-0.00166112956810631*D28k_high_Cytosol))*1/l_n*1/r_D^2*1/l_star+D*(0.00166112956810631*D28k_high_D_Cytosol+(-D28k_high_F))*1/l_star*1/lc)*Cytosol*1*1/KMOLE
l=0.66 μm; D=283.0 1E-12*dimensionless*m^2*s^(-1); r_neck=0.1 μm; KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol; r_spine=0.288 μm Reaction: IP3_Cytosol => ; IP3_D_Cytosol, Rate Law: 0.75*D*(0.00166112956810631*IP3_Cytosol+(-0.00166112956810631*IP3_D_Cytosol))*r_neck^2*1/l*1/r_spine^3*Cytosol*1*1/KMOLE
PA_F=3.20298 0.001*dimensionless*m^(-3)*mol; r_d=1.0 μm; r_n=0.1 μm; KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol; l_n=0.66 μm; l_star=27.9812 μm; D=43.0 1E-12*dimensionless*m^2*s^(-1); lc=5.6265 μm Reaction: PA_D_Cytosol => ; PA_Cytosol, Rate Law: (D*r_n^2*(0.00166112956810631*PA_D_Cytosol+(-0.00166112956810631*PA_Cytosol))*1/l_n*1/r_d^2*1/l_star+D*(0.00166112956810631*PA_D_Cytosol+(-PA_F))*1/l_star*1/lc)*Cytosol*1*1/KMOLE
l=0.66 μm; r_neck=0.1 μm; KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol; r_spine=0.288 μm; D=15.0 1E-12*dimensionless*m^2*s^(-1) Reaction: CGB_Cytosol => ; CGB_D_Cytosol, Rate Law: 0.75*D*(0.00166112956810631*CGB_Cytosol+(-0.00166112956810631*CGB_D_Cytosol))*r_neck^2*1/l*1/r_spine^3*Cytosol*1*1/KMOLE
Kdegr=0.14 s^(-1); KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol; IP3_CytosolD=0.16 0.001*dimensionless*m^(-3)*mol Reaction: IP3_D_Cytosol =>, Rate Law: Kdegr*(0.00166112956810631*IP3_D_Cytosol+(-IP3_CytosolD))*Cytosol*1*1/KMOLE
IP3_CytosolS=0.16 0.001*dimensionless*m^(-3)*mol; Kdegr=0.14 s^(-1); KMOLE = 0.00166112956810631 1E-21*dimensionless*item^(-1)*mol Reaction: IP3_Cytosol =>, Rate Law: Kdegr*(0.00166112956810631*IP3_Cytosol+(-IP3_CytosolS))*Cytosol*1*1/KMOLE

States:

Name Description
Ca D Extracellular [calcium(2+); Calcium cation]
CGB Cytosol CGB_Cytosol
PABCa D Cytosol [Parvalbumin alpha; Calcium cation; calcium(2+); Parvalbumin alpha]
D28kB high D Cytosol [Calbindin]
D28k D Cytosol [Calbindin]
Ca D ER [calcium(2+); Calcium cation]
CG D Cytosol CG_D_Cytosol
PA Cytosol [Parvalbumin alpha]
h D ERM h_D_ERM
D28k Cytosol [Calbindin]
D28kB high Cytosol [Calbindin]
D28kB Cytosol [Calbindin]
Ca ER [calcium(2+); Calcium cation]
D28k high D Cytosol [Calbindin]
D28k high Cytosol [Calbindin]
IP3 D Cytosol [1D-myo-inositol 1,4,5-trisphosphate; D-myo-Inositol 1,4,5-trisphosphate]
Ca D Cytosol [calcium(2+); Calcium cation]
D28kB D Cytosol [Calbindin]
CG Cytosol CG_Cytosol
PABMg Cytosol [Parvalbumin alpha; Magnesium cation; magnesium atom; Parvalbumin alpha]
h ERM h_ERM
PA D Cytosol [Parvalbumin alpha]
Mg Cytosol [magnesium(2+); Magnesium cation]
CGB D Cytosol CGB_D_Cytosol
PABMg D Cytosol [Parvalbumin alpha; Magnesium cation; magnesium atom; Parvalbumin alpha]
Ca Cytosol [calcium(2+); Calcium cation]
IP3 Cytosol [1D-myo-inositol 1,4,5-trisphosphate; D-myo-Inositol 1,4,5-trisphosphate]
Ca Extracellular [calcium(2+); Calcium cation]
Mg D Cytosol [magnesium(2+); Magnesium cation]
PABCa Cytosol [Parvalbumin alpha; Calcium cation; calcium(2+); Parvalbumin alpha]

Observables: none

MODEL0072364382 @ v0.0.1

This is a reconstruction of the biochemical network of the yeast *Saccharomyces cerevisiae* carried out at a jamboree o…

Genomic data allow the large-scale manual or semi-automated assembly of metabolic network reconstructions, which provide highly curated organism-specific knowledge bases. Although several genome-scale network reconstructions describe Saccharomyces cerevisiae metabolism, they differ in scope and content, and use different terminologies to describe the same chemical entities. This makes comparisons between them difficult and underscores the desirability of a consolidated metabolic network that collects and formalizes the 'community knowledge' of yeast metabolism. We describe how we have produced a consensus metabolic network reconstruction for S. cerevisiae. In drafting it, we placed special emphasis on referencing molecules to persistent databases or using database-independent forms, such as SMILES or InChI strings, as this permits their chemical structure to be represented unambiguously and in a manner that permits automated reasoning. The reconstruction is readily available via a publicly accessible database and in the Systems Biology Markup Language (http://www.comp-sys-bio.org/yeastnet). It can be maintained as a resource that serves as a common denominator for studying the systems biology of yeast. Similar strategies should benefit communities studying genome-scale metabolic networks of other organisms. link: http://identifiers.org/pubmed/18846089

Parameters: none

States: none

Observables: none

BIOMD0000000408 @ v0.0.1

This model is from the article: Analyzing the functional properties of the creatine kinase system with multiscale '…

In this study the function of the two isoforms of creatine kinase (CK; EC 2.7.3.2) in myocardium is investigated. The 'phosphocreatine shuttle' hypothesis states that mitochondrial and cytosolic CK plays a pivotal role in the transport of high-energy phosphate (HEP) groups from mitochondria to myofibrils in contracting muscle. Temporal buffering of changes in ATP and ADP is another potential role of CK. With a mathematical model, we analyzed energy transport and damping of high peaks of ATP hydrolysis during the cardiac cycle. The analysis was based on multiscale data measured at the level of isolated enzymes, isolated mitochondria and on dynamic response times of oxidative phosphorylation measured at the whole heart level. Using 'sloppy modeling' ensemble simulations, we derived confidence intervals for predictions of the contributions by phosphocreatine (PCr) and ATP to the transfer of HEP from mitochondria to sites of ATP hydrolysis. Our calculations indicate that only 15±8% (mean±SD) of transcytosolic energy transport is carried by PCr, contradicting the PCr shuttle hypothesis. We also predicted temporal buffering capabilities of the CK isoforms protecting against high peaks of ATP hydrolysis (3750 µMs(-1)) in myofibrils. CK inhibition by 98% in silico leads to an increase in amplitude of mitochondrial ATP synthesis pulsation from 215±23 to 566±31 µMs(-1), while amplitudes of oscillations in cytosolic ADP concentration double from 77±11 to 146±1 µM. Our findings indicate that CK acts as a large bandwidth high-capacity temporal energy buffer maintaining cellular ATP homeostasis and reducing oscillations in mitochondrial metabolism. However, the contribution of CK to the transport of high-energy phosphate groups appears limited. Mitochondrial CK activity lowers cytosolic inorganic phosphate levels while cytosolic CK has the opposite effect. link: http://identifiers.org/pubmed/21912519

Parameters:

Name Description
j_ck_mm = 0.0 μmol*l^(-1)*s^(-1) Reaction: Cr + ATP => PCr + ADP, Rate Law: j_ck_mm
Kadp = 25.0 μmol*l^(-1); Vmaxsyn = 1503.74 μmol*l^(-1)*s^(-1); Kpi = 800.0 μmol*l^(-1) Reaction: P_ii + ADPi => ATPi, Rate Law: Vmaxsyn*ADPi*P_ii/(Kadp*Kpi*(1+ADPi/Kadp+P_ii/Kpi+ADPi*P_ii/(Kadp*Kpi)))
j_ck_mi = 0.0 μmol*l^(-1)*s^(-1) Reaction: ATPi + Cri => PCri + ADPi, Rate Law: j_ck_mi
j_diff_adp = 0.0 μmol*l^(-1)*s^(-1) Reaction: ADPi => ADP, Rate Law: j_diff_adp
j_diff_pcr = 1.0 μmol*l^(-1)*s^(-1) Reaction: PCri => PCr, Rate Law: j_diff_pcr
j_diff_atp = 1.0 μmol*l^(-1)*s^(-1) Reaction: ATPi => ATP, Rate Law: j_diff_atp
j_diff_cr = 0.0 μmol*l^(-1)*s^(-1) Reaction: Cri => Cr, Rate Law: j_diff_cr
Jhyd = 486.5 μmol*l^(-1)*s^(-1) Reaction: ATP => ADP + P_i, Rate Law: Jhyd
j_diff_pi = 0.0 μmol*l^(-1)*s^(-1) Reaction: P_ii => P_i, Rate Law: j_diff_pi

States:

Name Description
P ii [inorganic phosphate]
PCr [N-phosphocreatine; Phosphocreatine; B00422; 5359]
PCri [N-phosphocreatine; Phosphocreatine; 5359; B00422]
ATP [ATP; ATP; 3304; B01125]
Cr [creatine; Creatine; 3594; B00084]
ATPi [ATP; ATP; 3304; B01125]
ADPi [ADP; ADP; 3310; B01130]
Cri [creatine; Creatine; 3594; B00084]
ADP [ADP; ADP; 3310; B01130]
P i [inorganic phosphate]

Observables: none

MODEL0848444339 @ v0.0.1

This a model from the article: Excitation-contraction coupling and extracellular calcium transients in rabbit atrium:…

Interactions of electrogenic sodium-calcium exchange, calcium channel and sarcoplasmic reticulum in the mammalian heart have been explored by simulation of extracellular calcium transients measured with tetramethylmurexide in rabbit atrium. The approach has been to use the simplest possible formulations of these mechanisms, which together with a minimum number of additional mechanisms allow reconstruction of action potentials, intracellular calcium transients and extracellular calcium transients. A 3:1 sodium-calcium exchange stoichiometry is assumed. Calcium-channel inactivation is assumed to take place by a voltage-dependent mechanism, which is accelerated by a rise in intracellular calcium; intracellular calcium release becomes a major physiological regulator of calcium influx via calcium channels. A calcium release mechanism is assumed, which is both calcium- and voltage-sensitive, and which undergoes prolonged inactivation. 200 microM cytosolic calcium buffer is assumed. For most simulations only instantaneous potassium conductances are simulated so as to study the other mechanisms independently of time- and calcium-dependent outward current. Thus, the model reconstructs extracellular calcium transients and typical action-potential configuration changes during steady-state and non-steady-state stimulation from the mechanisms directly involved in trans-sarcolemmal calcium movements. The model predicts relatively small trans-sarcolemmal calcium movements during regular stimulation (ca. 2 mumol kg-1 fresh mass per excitation); calcium current is fully activated within 2 ms of excitation, inactivation is substantially complete within 30 ms, and sodium-calcium exchange significantly resists repolarization from approximately -30 mV. Net calcium movements many times larger are possible during non-steady-state stimulation. Long action potentials at premature excitations or after inhibition of calcium release can be supported almost exclusively by calcium current (net calcium influx 5-30 mumol kg-1 fresh mass); action potentials during potentiated post-stimulatory contractions can be supported almost exclusively by sodium-calcium exchange (net calcium efflux 4-20 mumol kg-1 fresh mass). Large calcium movements between the extracellular space and the sarcoplasmic reticulum can take place through the cytosol with virtually no contractile activation. The simulations provide integrated explanations of electrical activity, contractile function and trans-sarcolemmal calcium movements, which were outside the explanatory range of previous models. link: http://identifiers.org/pubmed/2884668

Parameters: none

States: none

Observables: none

MODEL0848342500 @ v0.0.1

This a model from the article: A simplified local control model of calcium-induced calcium release in cardiac ventricu…

Calcium (Ca2+)-induced Ca2+ release (CICR) in cardiac myocytes exhibits high gain and is graded. These properties result from local control of Ca2+ release. Existing local control models of Ca2+ release in which interactions between L-Type Ca2+ channels (LCCs) and ryanodine-sensitive Ca2+ release channels (RyRs) are simulated stochastically are able to reconstruct these properties, but only at high computational cost. Here we present a general analytical approach for deriving simplified models of local control of CICR, consisting of low-dimensional systems of coupled ordinary differential equations, from these more complex local control models in which LCC-RyR interactions are simulated stochastically. The resulting model, referred to as the coupled LCC-RyR gating model, successfully reproduces a range of experimental data, including L-Type Ca2+ current in response to voltage-clamp stimuli, inactivation of LCC current with and without Ca2+ release from the sarcoplasmic reticulum, voltage-dependence of excitation-contraction coupling gain, graded release, and the force-frequency relationship. The model does so with low computational cost. link: http://identifiers.org/pubmed/15465866

Parameters: none

States: none

Observables: none

Hingant2014 - Micellar On-Pathway Intermediate in Prion Amyloid FormationHingant2014 - Micellar On-Pathway Intermediate…

In a previous work by Alvarez-Martinez et al. (2011), the authors pointed out some fallacies in the mainstream interpretation of the prion amyloid formation. It appeared necessary to propose an original hypothesis able to reconcile the in vitro data with the predictions of a mathematical model describing the problem. Here, a model is developed accordingly with the hypothesis that an intermediate on-pathway leads to the conformation of the prion protein into an amyloid competent isoform thanks to a structure, called micelles, formed from hydrodynamic interaction. The authors also compare data to the prediction of their model and propose a new hypothesis for the formation of infectious prion amyloids. link: http://identifiers.org/pubmed/25101755

Parameters: none

States: none

Observables: none

This is the simple version of the two mathematical models presented by Ho et al. It is a model comprised of simple ordin…

Two mathematical models described by simple ordinary differential equations are developed to investigate the Hong Kong influenza epidemic during 2017-2018 winter, based on overall epidemic dynamics and different influenza subtypes. The first model, describing the overall epidemic dynamics, provides the starting data for the second model which different influenza subtypes, and whose dynamics is further investigated. Weekly data from December 2017 to May 2018 are obtained from the data base of the Centre of Health Protection in Hong Kong, and used to parametrise the models. With the help of these models, we investigate the impact of different vaccination strategies and determine the corresponding critical vaccination coverage for different vaccine efficacies. The results suggest that at least 72% of Hong Kong population should have been vaccinated during 2017-2018 winter to prevent the seasonal epidemic by herd immunity (while data showed that only a maximum of 11.6% of the population were vaccinated). Our results also show that the critical vaccination coverage decreases with increasing vaccine efficacy, and the increase in one influenza subtype vaccine efficacy may lead to an increase in infections caused by a different subtype. link: http://identifiers.org/pubmed/31128142

Parameters:

Name Description
r = 0.0155; A = 0.1155 Reaction: S => V + V_e, Rate Law: compartment*r*(1-V_e/A)
beta = 2.7516 Reaction: S => I, Rate Law: compartment*beta*I*S
k = 1.51338 Reaction: V => I, Rate Law: compartment*k*I*V
gamma = 2.1272 Reaction: I => R, Rate Law: compartment*gamma*I

States:

Name Description
I [C17005; influenza infection]
S [C17005; Susceptibility]
V e [C17005; C49287; C28385]
V [C17005; C28385]
R [C17005; 0009785]

Observables: none

BIOMD0000000335 @ v0.0.1

This model is from the article: A model for the stoichiometric regulation of blood coagulation. Hockin MF, Jones…

We have developed a model of the extrinsic blood coagulation system that includes the stoichiometric anticoagulants. The model accounts for the formation, expression, and propagation of the vitamin K-dependent procoagulant complexes and extends our previous model by including: (a) the tissue factor pathway inhibitor (TFPI)-mediated inactivation of tissue factor (TF).VIIa and its product complexes; (b) the antithrombin-III (AT-III)-mediated inactivation of IIa, mIIa, factor VIIa, factor IXa, and factor Xa; (c) the initial activation of factor V and factor VIII by thrombin generated by factor Xa-membrane; (d) factor VIIIa dissociation/activity loss; (e) the binding competition and kinetic activation steps that exist between TF and factors VII and VIIa; and (f) the activation of factor VII by IIa, factor Xa, and factor IXa. These additions to our earlier model generate a model consisting of 34 differential equations with 42 rate constants that together describe the 27 independent equilibrium expressions, which describe the fates of 34 species. Simulations are initiated by "exposing" picomolar concentrations of TF to an electronic milieu consisting of factors II, IX, X, VII, VIIa, V, and VIIII, and the anticoagulants TFPI and AT-III at concentrations found in normal plasma or associated with coagulation pathology. The reaction followed in terms of thrombin generation, proceeds through phases that can be operationally defined as initiation, propagation, and termination. The generation of thrombin displays a nonlinear dependence upon TF, AT-III, and TFPI and the combination of these latter inhibitors displays kinetic thresholds. At subthreshold TF, thrombin production/expression is suppressed by the combination of TFPI and AT-III; for concentrations above the TF threshold, the bolus of thrombin produced is quantitatively equivalent. A comparison of the model with empirical laboratory data illustrates that most experimentally observable parameters are captured, and the pathology that results in enhanced or deficient thrombin generation is accurately described. link: http://identifiers.org/pubmed/11893748

Parameters:

Name Description
k15 = 1.8 Reaction: TF_VIIa_IX => TF_VIIa + IXa, Rate Law: compartment_1*k15*TF_VIIa_IX
k6 = 1.3E7 Reaction: Xa + VII => Xa + VIIa, Rate Law: compartment_1*k6*Xa*VII
k27 = 0.2; k28 = 4.0E8 Reaction: Xa + Va => Xa_Va, Rate Law: compartment_1*(k28*Xa*Va-k27*Xa_Va)
k21 = 1.0E8; k20 = 0.001 Reaction: IXa_VIIIa + X => IXa_VIIIa_X, Rate Law: compartment_1*(k21*IXa_VIIIa*X-k20*IXa_VIIIa_X)
k29 = 103.0; k30 = 1.0E8 Reaction: Xa_Va + II => Xa_Va_II, Rate Law: compartment_1*(k30*Xa_Va*II-k29*Xa_Va_II)
k40 = 490.0 Reaction: IXa + ATIII => IXa_ATIII, Rate Law: compartment_1*k40*IXa*ATIII
k37 = 5.0E7 Reaction: TF_VIIa + Xa_TFPI => TF_VIIa_Xa_TFPI, Rate Law: compartment_1*k37*TF_VIIa*Xa_TFPI
k41 = 7100.0 Reaction: IIa + ATIII => IIa_ATIII, Rate Law: compartment_1*k41*IIa*ATIII
k9 = 2.5E7; k8 = 1.05 Reaction: TF_VIIa + X => TF_VIIa_X, Rate Law: compartment_1*(k9*TF_VIIa*X-k8*TF_VIIa_X)
k17 = 2.0E7 Reaction: IIa + VIII => IIa + VIIIa, Rate Law: compartment_1*k17*IIa*VIII
k23 = 22000.0; k24 = 0.006 Reaction: VIIIa => VIIIa1_L + VIIIa2, Rate Law: compartment_1*(k24*VIIIa-k23*VIIIa1_L*VIIIa2)
k25 = 0.001 Reaction: IXa_VIIIa_X => VIIIa1_L + VIIIa2 + X + IXa, Rate Law: compartment_1*k25*IXa_VIIIa_X
k35 = 1.1E-4; k36 = 3.2E8 Reaction: TF_VIIa_Xa + TFPI => TF_VIIa_Xa_TFPI, Rate Law: compartment_1*(k36*TF_VIIa_Xa*TFPI-k35*TF_VIIa_Xa_TFPI)
k32 = 1.5E7 Reaction: mIIa + Xa_Va => IIa + Xa_Va, Rate Law: compartment_1*k32*mIIa*Xa_Va
k16 = 7500.0 Reaction: Xa + II => Xa + IIa, Rate Law: compartment_1*k16*Xa*II
k5 = 440000.0 Reaction: TF_VIIa + VII => TF_VIIa + VIIa, Rate Law: compartment_1*k5*TF_VIIa*VII
k10 = 6.0 Reaction: TF_VIIa_X => TF_VIIa_Xa, Rate Law: compartment_1*k10*TF_VIIa_X
k4 = 2.3E7; k3 = 0.0031 Reaction: TF + VIIa => TF_VIIa, Rate Law: compartment_1*(k4*TF*VIIa-k3*TF_VIIa)
k38 = 1500.0 Reaction: Xa + ATIII => Xa_ATIII, Rate Law: compartment_1*k38*Xa*ATIII
k7 = 23000.0 Reaction: IIa + VII => IIa + VIIa, Rate Law: compartment_1*k7*IIa*VII
k26 = 2.0E7 Reaction: IIa + V => IIa + Va, Rate Law: compartment_1*k26*IIa*V
k39 = 7100.0 Reaction: mIIa + ATIII => mIIa_ATIII, Rate Law: compartment_1*k39*mIIa*ATIII
k31 = 63.5 Reaction: Xa_Va_II => Xa_Va + mIIa, Rate Law: compartment_1*k31*Xa_Va_II
k34 = 900000.0; k33 = 3.6E-4 Reaction: Xa + TFPI => Xa_TFPI, Rate Law: compartment_1*(k34*Xa*TFPI-k33*Xa_TFPI)
k2 = 3200000.0; k1 = 0.0031 Reaction: TF + VII => TF_VII, Rate Law: compartment_1*(k2*TF*VII-k1*TF_VII)
k22 = 8.2 Reaction: IXa_VIIIa_X => IXa_VIIIa + Xa, Rate Law: compartment_1*k22*IXa_VIIIa_X
k12 = 2.2E7; k11 = 19.0 Reaction: TF_VIIa + Xa => TF_VIIa_Xa, Rate Law: compartment_1*(k12*TF_VIIa*Xa-k11*TF_VIIa_Xa)
k42 = 230.0 Reaction: TF_VIIa + ATIII => TF_VIIa_ATIII, Rate Law: compartment_1*k42*TF_VIIa*ATIII
k19 = 1.0E7; k18 = 0.005 Reaction: IXa + VIIIa => IXa_VIIIa, Rate Law: compartment_1*(k19*IXa*VIIIa-k18*IXa_VIIIa)
k14 = 1.0E7; k13 = 2.4 Reaction: TF_VIIa + IX => TF_VIIa_IX, Rate Law: compartment_1*(k14*TF_VIIa*IX-k13*TF_VIIa_IX)

States:

Name Description
IIa ATIII [Antithrombin-III; Prothrombin]
VIII [Coagulation factor VIII]
TFPI [Tissue factor pathway inhibitor]
Xa ATIII [Coagulation factor X; Antithrombin-III]
V [Coagulation factor V]
Xa Va II [Prothrombin; Coagulation factor V; Coagulation factor X]
ATIII [Antithrombin-III]
Xa [Coagulation factor X]
VIIIa1 L [Coagulation factor VIII]
TF VIIa ATIII [Tissue factor; Antithrombin-III; Coagulation factor VII]
IXa ATIII [Coagulation factor IX; Antithrombin-III]
TF VIIa X [Tissue factor; Coagulation factor X; Coagulation factor VII]
TF VIIa Xa [Tissue factor; Coagulation factor X; Coagulation factor VII]
TF [Tissue factor]
TF VIIa Xa TFPI [Tissue factor; Coagulation factor X; Coagulation factor VII; Tissue factor pathway inhibitor]
mIIa ATIII [Antithrombin-III; Prothrombin]
TF VII [Tissue factor; Coagulation factor VII]
X [Coagulation factor X]
Xa Va [Coagulation factor V; Coagulation factor X]
VIIIa2 [Coagulation factor VIII]
TF VIIa [Tissue factor; Coagulation factor VII]
VIIIa [Coagulation factor VIII]
Va [Coagulation factor V]
IIa [Prothrombin]
mIIa [Prothrombin]
VIIa [Coagulation factor VII]
IXa VIIIa X [Coagulation factor X; Coagulation factor IX; Coagulation factor VIII]
Xa TFPI [Coagulation factor X; Tissue factor pathway inhibitor]
TF VIIa IX [Tissue factor; Coagulation factor IX; Coagulation factor VII]
IXa [Coagulation factor IX]
VII [Coagulation factor VII]
II [Prothrombin]
IX [Coagulation factor IX]
IXa VIIIa [Coagulation factor IX; Coagulation factor VIII]

Observables: none

BIOMD0000000020 @ v0.0.1

This is an implementation of the Hodgkin-Huxley model of the electrical behavior of the squid axon membrane from: **A…

link: http://identifiers.org/pubmed/12991237

Parameters: none

States: none

Observables: none

BIOMD0000000017 @ v0.0.1

This a model from the article: Metabolic engineering of lactic acid bacteria, the combined approach: kinetic modelli…

Everyone who has ever tried to radically change metabolic fluxes knows that it is often harder to determine which enzymes have to be modified than it is to actually implement these changes. In the more traditional genetic engineering approaches 'bottle-necks' are pinpointed using qualitative, intuitive approaches, but the alleviation of suspected 'rate-limiting' steps has not often been successful. Here the authors demonstrate that a model of pyruvate distribution in Lactococcus lactis based on enzyme kinetics in combination with metabolic control analysis clearly indicates the key control points in the flux to acetoin and diacetyl, important flavour compounds. The model presented here (available at http://jjj.biochem.sun.ac.za/wcfs.html) showed that the enzymes with the greatest effect on this flux resided outside the acetolactate synthase branch itself. Experiments confirmed the predictions of the model, i.e. knocking out lactate dehydrogenase and overexpressing NADH oxidase increased the flux through the acetolactate synthase branch from 0 to 75% of measured product formation rates. link: http://identifiers.org/pubmed/11932446

Parameters:

Name Description
Kaclac_9=10.0; V_9=106.0; Kacet_9=100.0 Reaction: AcLac => AcetoinIn, Rate Law: V_9*AcLac/Kaclac_9/(1+AcLac/Kaclac_9+AcetoinIn/Kacet_9)
k_14=3.0E-4 Reaction: AcLac => AcetoinIn, Rate Law: k_14*AcLac
Kaccoa_3=0.008; Knad_3=0.4; Kcoa_3=0.014; Kpyr_3=1.0; V_3=259.0; Knadh_3=0.1; Ki_3=46.4159 Reaction: NAD + pyruvate + CoA => NADH + AcCoA, Rate Law: V_3*pyruvate/Kpyr_3*NAD/Knad_3*CoA/Kcoa_3*NAD/(NAD+Ki_3*NADH)/((1+pyruvate/Kpyr_3)*(1+NAD/Knad_3+NADH/Knadh_3)*(1+CoA/Kcoa_3+AcCoA/Kaccoa_3))
V_10=200.0; Kacet_10=5.0 Reaction: AcetoinIn => AcetoinOut, Rate Law: V_10*AcetoinIn/Kacet_10/(1+AcetoinIn/Kacet_10)
n_12=2.58; Katp_12=6.196; V_12=900.0 Reaction: ATP => ADP, Rate Law: V_12*(ATP/(ADP*Katp_12))^n_12/(1+(ATP/(ADP*Katp_12))^n_12)
Keq_11=1400.0; Knad_11=0.16; V_11=105.0; Knadh_11=0.02; Kacet_11=0.06; Kbut_11=2.6 Reaction: NADH + AcetoinIn => NAD + Butanediol, Rate Law: V_11*(AcetoinIn*NADH-Butanediol*NAD/Keq_11)/(Kacet_11*Knadh_11)/((1+AcetoinIn/Kacet_11+Butanediol/Kbut_11)*(1+NADH/Knadh_11+NAD/Knad_11))
V_13=118.0; Knadh_13=0.041; Ko_13=0.2; Knad_13=1.0 Reaction: NADH + O2 => NAD, Rate Law: V_13*NADH*O2/(Knadh_13*Ko_13)/((1+NADH/Knadh_13+NAD/Knad_13)*(1+O2/Ko_13))
Kadp_1=0.04699; V_1=2397.0; Kglc_1=0.1; Knad_1=0.1412; Katp_1=0.01867; Kpyr_1=2.5; Knadh_1=0.08999 Reaction: ADP + NAD + halfglucose => ATP + NADH + pyruvate, Rate Law: 2*V_1*halfglucose/(2*Kglc_1)*NAD/Knad_1*ADP/Kadp_1/((1+halfglucose/(2*Kglc_1)+pyruvate/Kpyr_1)*(1+NAD/Knad_1+NADH/Knadh_1)*(1+ADP/Kadp_1+ATP/Katp_1))
Knadh_7=0.05; V_7=162.0; Ketoh_7=1.0; Knad_7=0.08; Keq_7=12354.9; Kaco_7=0.03 Reaction: NADH + AcO => NAD + EtOH, Rate Law: V_7*(AcO*NADH-EtOH*NAD/Keq_7)/(Kaco_7*Knadh_7)/((1+NAD/Knad_7+NADH/Knadh_7)*(1+AcO/Kaco_7+EtOH/Ketoh_7))
Kaccoa_6=0.007; Kaco_6=10.0; V_6=97.0; Keq_6=1.0; Kcoa_6=0.008; Knad_6=0.08; Knadh_6=0.025 Reaction: NADH + AcCoA => NAD + CoA + AcO, Rate Law: V_6*(AcCoA*NADH-CoA*NAD*AcO/Keq_6)/(Kaccoa_6*Knadh_6)/((1+NAD/Knad_6+NADH/Knadh_6)*(1+AcCoA/Kaccoa_6+CoA/Kcoa_6)*(1+AcO/Kaco_6))
V_5=2700.0; Kac_5=7.0; Keq_5=174.217; Kacp_5=0.16; Kadp_5=0.5; Katp_5=0.07 Reaction: ADP + AcP => ATP + Ac, Rate Law: V_5*(AcP*ADP-Ac*ATP/Keq_5)/(Kadp_5*Kacp_5)/((1+AcP/Kacp_5+Ac/Kac_5)*(1+ADP/Kadp_5+ATP/Katp_5))
Kaclac_8=100.0; Kpyr_8=50.0; n_8=2.4; V_8=600.0; Keq_8=9.0E12 Reaction: pyruvate => AcLac, Rate Law: V_8*pyruvate/Kpyr_8*(1-AcLac/(pyruvate*Keq_8))*(pyruvate/Kpyr_8+AcLac/Kaclac_8)^(n_8-1)/(1+(pyruvate/Kpyr_8+AcLac/Kaclac_8)^n_8)
Knadh_2=0.08; Knad_2=2.4; Klac_2=100.0; V_2=5118.0; Kpyr_2=1.5; Keq_2=21120.69 Reaction: NADH + pyruvate => NAD + lactate, Rate Law: V_2*(pyruvate*NADH-lactate*NAD/Keq_2)/(Kpyr_2*Knadh_2)/((1+pyruvate/Kpyr_2+lactate/Klac_2)*(1+NADH/Knadh_2+NAD/Knad_2))
Kpi_4=2.6; Kacp_4=0.7; Kipi_4=2.6; Kicoa_4=0.029; V_4=42.0; Keq_4=0.0065; Kiaccoa_4=0.2; Kiacp_4=0.2 Reaction: AcCoA + PO4 => CoA + AcP, Rate Law: V_4*(AcCoA*PO4-AcP*CoA/Keq_4)/(Kiaccoa_4*Kpi_4)/(1+AcCoA/Kiaccoa_4+PO4/Kipi_4+AcP/Kiacp_4+CoA/Kicoa_4+AcCoA*PO4/(Kiaccoa_4*Kpi_4)+AcP*CoA/(Kacp_4*Kicoa_4))

States:

Name Description
CoA [coenzyme A; CoA]
halfglucose halfglucose
ATP [ATP; ATP]
NADH [NADH; NADH]
lactate [lactate; (S)-Lactate]
AcetoinOut [acetoin; Acetoin]
EtOH [ethanol; Ethanol]
AcO [acetaldehyde; Acetaldehyde]
PO4 [phosphate(3-); Orthophosphate]
AcCoA [acetyl-CoA; Acetyl-CoA]
AcLac [2-acetyllactic acid; 2-Acetolactate]
pyruvate [pyruvate; Pyruvate]
AcP [acetyl dihydrogen phosphate; Acetyl phosphate]
ADP [ADP; ADP]
NAD [NAD(+); NAD+]
Ac [acetate; Acetate]
AcetoinIn [acetoin; Acetoin]
Butanediol [(S,S)-butane-2,3-diol; (R,R)-butane-2,3-diol; (S,S)-Butane-2,3-diol; (R,R)-Butane-2,3-diol]
O2 [dioxygen; Oxygen]

Observables: none

BIOMD0000000802 @ v0.0.1

The paper describes a model of ADCC. Created by COPASI 4.26 (Build 213) This model is described in the article:…

Immunotherapies exploit the immune system to target and kill cancer cells, while sparing healthy tissue. Antibody therapies, an important class of immunotherapies, involve the binding to specific antigens on the surface of the tumour cells of antibodies that activate natural killer (NK) cells to kill the tumour cells. Preclinical assessment of molecules that may cause antibody-dependent cellular cytotoxicity (ADCC) involves co-culturing cancer cells, NK cells and antibody in vitro for several hours and measuring subsequent levels of tumour cell lysis. Here we develop a mathematical model of such an in vitro ADCC assay, formulated as a system of time-dependent ordinary differential equations and in which NK cells kill cancer cells at a rate which depends on the amount of antibody bound to each cancer cell. Numerical simulations generated using experimentally-based parameter estimates reveal that the system evolves on two timescales: a fast timescale on which antibodies bind to receptors on the surface of the tumour cells, and NK cells form complexes with the cancer cells, and a longer time-scale on which the NK cells kill the cancer cells. We construct approximate model solutions on each timescale, and show that they are in good agreement with numerical simulations of the full system. Our results show how the processes involved in ADCC change as the initial concentration of antibody and NK-cancer cell ratio are varied. We use these results to explain what information about the tumour cell kill rate can be extracted from the cytotoxicity assays. link: http://identifiers.org/pubmed/28970093

Parameters:

Name Description
y = 1.0 1; a2 = 1.44 1 Reaction: => A; R, S, Rate Law: tme*a2*y*R*S
a1 = 0.001 1 Reaction: A => ; R, S, Rate Law: tme*a1*(1-R)*A*S
v1 = 120.0 1; u = 20.0 1 Reaction: => C; S, Rate Law: tme*v1*(u-C)*(S-C)
f = 0.0 1 Reaction: S => ; C, Rate Law: tme*f*C
v2 = 14.4 1 Reaction: C =>, Rate Law: tme*v2*C
y = 1.0 1; a1 = 0.001 1 Reaction: => R; A, Rate Law: tme*a1/y*(1-R)*A
a2 = 1.44 1 Reaction: R =>, Rate Law: tme*a2*R

States:

Name Description
S [malignant cell]
A [Antibody]
C [Complex]
R [Complex]

Observables: none

BIOMD0000000139 @ v0.0.1

The model corresponds to the knock out model of beta-/-, epsilon -/- and reproduces the upper panel in Fig 2C. In order…

Nuclear localization of the transcriptional activator NF-kappaB (nuclear factor kappaB) is controlled in mammalian cells by three isoforms of NF-kappaB inhibitor protein: IkappaBalpha, -beta, and - epsilon. Based on simplifying reductions of the IkappaB-NF-kappaB signaling module in knockout cell lines, we present a computational model that describes the temporal control of NF-kappaB activation by the coordinated degradation and synthesis of IkappaB proteins. The model demonstrates that IkappaBalpha is responsible for strong negative feedback that allows for a fast turn-off of the NF-kappaB response, whereas IkappaBbeta and - epsilon function to reduce the system's oscillatory potential and stabilize NF-kappaB responses during longer stimulations. Bimodal signal-processing characteristics with respect to stimulus duration are revealed by the model and are shown to generate specificity in gene expression. link: http://identifiers.org/pubmed/12424381

Parameters:

Name Description
r6 = 0.66 Reaction: IKK_IkBeps_NFkB => NFkB + IKK, Rate Law: cytoplasm*r6*IKK_IkBeps_NFkB
a1 = 1.35; d1 = 0.075 Reaction: IKK + IkBalpha => IKK_IkBalpha, Rate Law: cytoplasm*(a1*IkBalpha*IKK-d1*IKK_IkBalpha)
r2 = 0.09 Reaction: IKK_IkBbeta => IKK, Rate Law: cytoplasm*r2*IKK_IkBbeta
r5 = 0.45 Reaction: IKK_IkBbeta_NFkB => NFkB + IKK, Rate Law: cytoplasm*r5*IKK_IkBbeta_NFkB
tr1 = 0.2448 Reaction: => IkBeps; IkBeps_transcript, Rate Law: nucleus*tr1*IkBeps_transcript
deg4 = 0.00135 Reaction: IkBeps_NFkB => NFkB, Rate Law: cytoplasm*deg4*IkBeps_NFkB
tr2a = 9.25E-5 Reaction: => IkBalpha_transcript, Rate Law: nucleus*tr2a
tr3 = 0.0168 Reaction: IkBalpha_transcript =>, Rate Law: nucleus*tr3*IkBalpha_transcript
tp2 = 0.012; tp1 = 0.018 Reaction: IkBalpha => IkBalpha_nuc, Rate Law: cytoplasm*tp1*IkBalpha-nucleus*tp2*IkBalpha_nuc
k1 = 5.4; k01 = 0.0048 Reaction: NFkB => NFkB_nuc, Rate Law: cytoplasm*k1*NFkB-nucleus*k01*NFkB_nuc
tr2 = 0.99 Reaction: => IkBalpha_transcript; NFkB_nuc, Rate Law: nucleus*tr2*NFkB_nuc^2
tr2b = 0.0 Reaction: => IkBbeta_transcript, Rate Law: nucleus*tr2b
flag_for_after_trigger = 0.5; k2_IkBbeta_nuc_NFkB_nuc=0.0069; fr_after_trigger = 0.5 Reaction: IkBbeta_nuc_NFkB_nuc => IkBbeta_NFkB, Rate Law: nucleus*k2_IkBbeta_nuc_NFkB_nuc*(fr_after_trigger+flag_for_after_trigger)*IkBbeta_nuc_NFkB_nuc
d6 = 0.03; a6 = 30.0 Reaction: NFkB + IKK_IkBeps => IKK_IkBeps_NFkB, Rate Law: cytoplasm*(a6*IKK_IkBeps*NFkB-d6*IKK_IkBeps_NFkB)
tr2e = 0.0 Reaction: => IkBeps_transcript, Rate Law: nucleus*tr2e
a8 = 2.88; d2 = 0.105 Reaction: IKK + IkBbeta_NFkB => IKK_IkBbeta_NFkB, Rate Law: cytoplasm*(a8*IKK*IkBbeta_NFkB-d2*IKK_IkBbeta_NFkB)
a2 = 0.36; d2 = 0.105 Reaction: IKK + IkBbeta => IKK_IkBbeta, Rate Law: cytoplasm*(a2*IkBbeta*IKK-d2*IKK_IkBbeta)
r4 = 1.224 Reaction: IKK_IkBalpha_NFkB => NFkB + IKK, Rate Law: cytoplasm*r4*IKK_IkBalpha_NFkB
r3 = 0.132 Reaction: IKK_IkBeps => IKK, Rate Law: cytoplasm*r3*IKK_IkBeps
k2 = 0.828 Reaction: IkBalpha_nuc_NFkB_nuc => IkBalpha_NFkB, Rate Law: nucleus*k2*IkBalpha_nuc_NFkB_nuc
r1 = 0.2442 Reaction: IKK_IkBalpha => IKK, Rate Law: cytoplasm*r1*IKK_IkBalpha
d5 = 0.03; a5 = 30.0 Reaction: NFkB_nuc + IkBbeta_nuc => IkBbeta_nuc_NFkB_nuc, Rate Law: nucleus*(a5*IkBbeta_nuc*NFkB_nuc-d5*IkBbeta_nuc_NFkB_nuc)
a9 = 4.2; d3 = 0.105 Reaction: IKK + IkBeps_NFkB => IKK_IkBeps_NFkB, Rate Law: cytoplasm*(a9*IKK*IkBeps_NFkB-d3*IKK_IkBeps_NFkB)
deg1 = 0.00678 Reaction: IkBeps =>, Rate Law: cytoplasm*deg1*IkBeps
d4 = 0.03; a4 = 30.0 Reaction: NFkB_nuc + IkBalpha_nuc => IkBalpha_nuc_NFkB_nuc, Rate Law: nucleus*(a4*IkBalpha_nuc*NFkB_nuc-d4*IkBalpha_nuc_NFkB_nuc)
k02 = 0.0072 Reaction: IKK =>, Rate Law: cytoplasm*k02*IKK
a7 = 11.1; d1 = 0.075 Reaction: IKK + IkBalpha_NFkB => IKK_IkBalpha_NFkB, Rate Law: cytoplasm*(a7*IKK*IkBalpha_NFkB-d1*IKK_IkBalpha_NFkB)
a3 = 0.54; d3 = 0.105 Reaction: IKK + IkBeps => IKK_IkBeps, Rate Law: cytoplasm*(a3*IkBeps*IKK-d3*IKK_IkBeps)
k2_eps = 0.624 Reaction: IkBeps_nuc_NFkB_nuc => IkBeps_NFkB, Rate Law: nucleus*0.5*k2_eps*IkBeps_nuc_NFkB_nuc

States:

Name Description
IkBalpha nuc [NF-kappa-B inhibitor alpha]
IkBeps nuc [NF-kappa-B inhibitor epsilon]
IkBbeta nuc NFkB nuc [Nuclear factor NF-kappa-B p105 subunit; NF-kappa-B inhibitor beta]
IKK [Inhibitor of nuclear factor kappa-B kinase subunit alpha; NF-kappa-B essential modulator; Inhibitor of nuclear factor kappa-B kinase subunit beta]
IkBeps nuc NFkB nuc [Nuclear factor NF-kappa-B p105 subunit; NF-kappa-B inhibitor epsilon]
IKK IkBbeta NFkB [Nuclear factor NF-kappa-B p105 subunit; NF-kappa-B inhibitor beta; NF-kappa-B essential modulator; Inhibitor of nuclear factor kappa-B kinase subunit beta; Inhibitor of nuclear factor kappa-B kinase subunit alpha]
IkBbeta transcript IkBbeta_transcript
IkBbeta NFkB [Nuclear factor NF-kappa-B p105 subunit; NF-kappa-B inhibitor beta]
IkBalpha NFkB [NF-kappa-B inhibitor alpha; Nuclear factor NF-kappa-B p105 subunit]
IKK IkBbeta [NF-kappa-B inhibitor beta; Inhibitor of nuclear factor kappa-B kinase subunit alpha; NF-kappa-B essential modulator; Inhibitor of nuclear factor kappa-B kinase subunit beta]
IkBbeta nuc [NF-kappa-B inhibitor beta]
IkBeps transcript IkBeps_transcript
IKK IkBalpha NFkB [Nuclear factor NF-kappa-B p105 subunit; NF-kappa-B inhibitor alpha; Inhibitor of nuclear factor kappa-B kinase subunit alpha; NF-kappa-B essential modulator; Inhibitor of nuclear factor kappa-B kinase subunit beta]
IkBalpha [NF-kappa-B inhibitor alpha]
IkBalpha nuc NFkB nuc [Nuclear factor NF-kappa-B p105 subunit; NF-kappa-B inhibitor alpha]
IKK IkBeps [NF-kappa-B inhibitor epsilon; Inhibitor of nuclear factor kappa-B kinase subunit alpha; NF-kappa-B essential modulator; Inhibitor of nuclear factor kappa-B kinase subunit beta]
IKK IkBeps NFkB [Nuclear factor NF-kappa-B p105 subunit; Inhibitor of nuclear factor kappa-B kinase subunit alpha; NF-kappa-B essential modulator; Inhibitor of nuclear factor kappa-B kinase subunit beta; NF-kappa-B inhibitor epsilon]
IkBeps NFkB [Nuclear factor NF-kappa-B p105 subunit; NF-kappa-B inhibitor epsilon]
IkBeps [NF-kappa-B inhibitor epsilon]
IkBbeta [NF-kappa-B inhibitor beta]
IKK IkBalpha [NF-kappa-B inhibitor alpha; Inhibitor of nuclear factor kappa-B kinase subunit alpha; NF-kappa-B essential modulator; Inhibitor of nuclear factor kappa-B kinase subunit beta]
NFkB nuc [Nuclear factor NF-kappa-B p105 subunit]
NFkB [Nuclear factor NF-kappa-B p105 subunit]
IkBalpha transcript IkBalpha_transcript

Observables: none

BIOMD0000000140 @ v0.0.1

This model corresponds to the IkB-NFkB signaling in wild type cells and reproduces the dynamics of the species as depict…

Nuclear localization of the transcriptional activator NF-kappaB (nuclear factor kappaB) is controlled in mammalian cells by three isoforms of NF-kappaB inhibitor protein: IkappaBalpha, -beta, and - epsilon. Based on simplifying reductions of the IkappaB-NF-kappaB signaling module in knockout cell lines, we present a computational model that describes the temporal control of NF-kappaB activation by the coordinated degradation and synthesis of IkappaB proteins. The model demonstrates that IkappaBalpha is responsible for strong negative feedback that allows for a fast turn-off of the NF-kappaB response, whereas IkappaBbeta and - epsilon function to reduce the system's oscillatory potential and stabilize NF-kappaB responses during longer stimulations. Bimodal signal-processing characteristics with respect to stimulus duration are revealed by the model and are shown to generate specificity in gene expression. link: http://identifiers.org/pubmed/12424381

Parameters:

Name Description
r6 = 0.66 Reaction: IKK_IkBeps_NFkB => NFkB + IKK, Rate Law: cytoplasm*r6*IKK_IkBeps_NFkB
r2 = 0.09 Reaction: IKK_IkBbeta => IKK, Rate Law: cytoplasm*r2*IKK_IkBbeta
a1 = 1.35; d1 = 0.075 Reaction: IKK + IkBalpha => IKK_IkBalpha, Rate Law: cytoplasm*(a1*IkBalpha*IKK-d1*IKK_IkBalpha)
r5 = 0.45 Reaction: IKK_IkBbeta_NFkB => NFkB + IKK, Rate Law: cytoplasm*r5*IKK_IkBbeta_NFkB
tr1 = 0.2448 Reaction: => IkBalpha; IkBalpha_transcript, Rate Law: nucleus*tr1*IkBalpha_transcript
tr2b = 1.068E-5 Reaction: => IkBbeta_transcript, Rate Law: nucleus*tr2b
a7 = 11.1; d1 = 0.075 Reaction: IKK + IkBalpha_NFkB => IKK_IkBalpha_NFkB, Rate Law: cytoplasm*(a7*IKK*IkBalpha_NFkB-d1*IKK_IkBalpha_NFkB)
tr2a = 9.25E-5 Reaction: => IkBalpha_transcript, Rate Law: nucleus*tr2a
tr2e = 7.62E-6 Reaction: => IkBeps_transcript, Rate Law: nucleus*tr2e
tr3 = 0.0168 Reaction: IkBbeta_transcript =>, Rate Law: nucleus*tr3*IkBbeta_transcript
tp2 = 0.012; tp1 = 0.018 Reaction: IkBalpha => IkBalpha_nuc, Rate Law: cytoplasm*tp1*IkBalpha-nucleus*tp2*IkBalpha_nuc
k1 = 5.4; k01 = 0.0048 Reaction: NFkB => NFkB_nuc, Rate Law: cytoplasm*k1*NFkB-nucleus*k01*NFkB_nuc
tr2 = 0.99 Reaction: => IkBalpha_transcript; NFkB_nuc, Rate Law: nucleus*tr2*NFkB_nuc^2
flag_for_after_trigger = 0.5; k2_IkBbeta_nuc_NFkB_nuc=0.0069; fr_after_trigger = 0.5 Reaction: IkBbeta_nuc_NFkB_nuc => IkBbeta_NFkB, Rate Law: nucleus*k2_IkBbeta_nuc_NFkB_nuc*(fr_after_trigger+flag_for_after_trigger)*IkBbeta_nuc_NFkB_nuc
d6 = 0.03; a6 = 30.0 Reaction: NFkB + IKK_IkBeps => IKK_IkBeps_NFkB, Rate Law: cytoplasm*(a6*IKK_IkBeps*NFkB-d6*IKK_IkBeps_NFkB)
a8 = 2.88; d2 = 0.105 Reaction: IKK + IkBbeta_NFkB => IKK_IkBbeta_NFkB, Rate Law: cytoplasm*(a8*IKK*IkBbeta_NFkB-d2*IKK_IkBbeta_NFkB)
a2 = 0.36; d2 = 0.105 Reaction: IKK + IkBbeta => IKK_IkBbeta, Rate Law: cytoplasm*(a2*IkBbeta*IKK-d2*IKK_IkBbeta)
r4 = 1.224 Reaction: IKK_IkBalpha_NFkB => NFkB + IKK, Rate Law: cytoplasm*r4*IKK_IkBalpha_NFkB
r3 = 0.132 Reaction: IKK_IkBeps => IKK, Rate Law: cytoplasm*r3*IKK_IkBeps
k2 = 0.828 Reaction: IkBalpha_nuc_NFkB_nuc => IkBalpha_NFkB, Rate Law: nucleus*k2*IkBalpha_nuc_NFkB_nuc
r1 = 0.2442 Reaction: IKK_IkBalpha => IKK, Rate Law: cytoplasm*r1*IKK_IkBalpha
d5 = 0.03; a5 = 30.0 Reaction: NFkB_nuc + IkBbeta_nuc => IkBbeta_nuc_NFkB_nuc, Rate Law: nucleus*(a5*IkBbeta_nuc*NFkB_nuc-d5*IkBbeta_nuc_NFkB_nuc)
a9 = 4.2; d3 = 0.105 Reaction: IKK + IkBeps_NFkB => IKK_IkBeps_NFkB, Rate Law: cytoplasm*(a9*IKK*IkBeps_NFkB-d3*IKK_IkBeps_NFkB)
deg1 = 0.00678 Reaction: IkBalpha =>, Rate Law: cytoplasm*deg1*IkBalpha
deg4 = 0.00135 Reaction: IkBeps_NFkB => NFkB, Rate Law: cytoplasm*deg4*IkBeps_NFkB
a3 = 0.54; d3 = 0.105 Reaction: IKK + IkBeps => IKK_IkBeps, Rate Law: cytoplasm*(a3*IkBeps*IKK-d3*IKK_IkBeps)
d4 = 0.03; a4 = 30.0 Reaction: NFkB_nuc + IkBalpha_nuc => IkBalpha_nuc_NFkB_nuc, Rate Law: nucleus*(a4*IkBalpha_nuc*NFkB_nuc-d4*IkBalpha_nuc_NFkB_nuc)
k02 = 0.0072 Reaction: IKK =>, Rate Law: cytoplasm*k02*IKK
k2_eps = 0.624 Reaction: IkBeps_nuc_NFkB_nuc => IkBeps_NFkB, Rate Law: nucleus*0.5*k2_eps*IkBeps_nuc_NFkB_nuc

States:

Name Description
IkBalpha nuc [NF-kappa-B inhibitor alpha]
IkBeps nuc [NF-kappa-B inhibitor epsilon]
IkBbeta nuc NFkB nuc [NF-kappa-B inhibitor beta; Nuclear factor NF-kappa-B p105 subunit]
IKK [Inhibitor of nuclear factor kappa-B kinase subunit beta; NF-kappa-B essential modulator; Inhibitor of nuclear factor kappa-B kinase subunit alpha]
IkBeps nuc NFkB nuc [NF-kappa-B inhibitor epsilon; Nuclear factor NF-kappa-B p105 subunit]
IKK IkBbeta NFkB [Inhibitor of nuclear factor kappa-B kinase subunit alpha; Inhibitor of nuclear factor kappa-B kinase subunit beta; NF-kappa-B essential modulator; NF-kappa-B inhibitor beta; Nuclear factor NF-kappa-B p105 subunit]
IkBbeta transcript IkBbeta_transcript
IkBbeta NFkB [NF-kappa-B inhibitor beta; Nuclear factor NF-kappa-B p105 subunit]
IkBalpha NFkB [Nuclear factor NF-kappa-B p105 subunit; NF-kappa-B inhibitor alpha]
IKK IkBbeta [Inhibitor of nuclear factor kappa-B kinase subunit beta; NF-kappa-B essential modulator; Inhibitor of nuclear factor kappa-B kinase subunit alpha; NF-kappa-B inhibitor beta]
IkBbeta nuc [NF-kappa-B inhibitor beta]
IkBeps transcript IkBeps_transcript
IKK IkBalpha NFkB [Inhibitor of nuclear factor kappa-B kinase subunit beta; NF-kappa-B essential modulator; Inhibitor of nuclear factor kappa-B kinase subunit alpha; NF-kappa-B inhibitor alpha; Nuclear factor NF-kappa-B p105 subunit]
IkBalpha [NF-kappa-B inhibitor alpha]
IKK IkBeps [Inhibitor of nuclear factor kappa-B kinase subunit beta; NF-kappa-B essential modulator; Inhibitor of nuclear factor kappa-B kinase subunit alpha; NF-kappa-B inhibitor epsilon]
IkBalpha nuc NFkB nuc [NF-kappa-B inhibitor alpha; Nuclear factor NF-kappa-B p105 subunit]
IKK IkBeps NFkB [NF-kappa-B inhibitor epsilon; Inhibitor of nuclear factor kappa-B kinase subunit beta; NF-kappa-B essential modulator; Inhibitor of nuclear factor kappa-B kinase subunit alpha; Nuclear factor NF-kappa-B p105 subunit]
IkBeps NFkB [NF-kappa-B inhibitor epsilon; Nuclear factor NF-kappa-B p105 subunit]
IkBeps [NF-kappa-B inhibitor epsilon]
IkBbeta [NF-kappa-B inhibitor beta]
IKK IkBalpha [Inhibitor of nuclear factor kappa-B kinase subunit beta; NF-kappa-B essential modulator; Inhibitor of nuclear factor kappa-B kinase subunit alpha; NF-kappa-B inhibitor alpha]
NFkB nuc [Nuclear factor NF-kappa-B p105 subunit]
NFkB [Nuclear factor NF-kappa-B p105 subunit]
IkBalpha transcript IkBalpha_transcript

Observables: none

BIOMD0000000284 @ v0.0.1

This model is the reaction sequence SEQFB, a model pathway of a branched system with sequential feedback interactions fo…

METAMOD, a BBC microcomputer-based software package for steady-state modelling and control analysis of model metabolic pathways, is described, The package consists of two programs. METADEF allows the user to define the pathway in terms of reactions, rate equations and initial concentrations of metabolites. METACAL uses one of two algorithms to calculate the steady-state concentrations and fluxes. One algorithm uses the current ratio of production and consumption rates of variable metabolites to adjust iteratively their concentrations in such a way that they converge towards the steady state. The other algorithm solves the roots of the system equations by means of a quasi-Newtonian procedure. Control analysis allows the calculation of elasticity, control and response coefficients, by means of finite difference approximation. METAMOD is interactive and easy to use, and suitable for teaching and research purposes. link: http://identifiers.org/pubmed/3450367

Parameters: none

States:

Name Description
Y Y
B B
Z Z
A A
X X
C C
D D
E E
F F

Observables: none

MODEL1304300000 @ v0.0.1

Hofmeyr1996 - metabolic control analysisUnderstanding of genetic mechanisms would not be possible by studying the proper…

The formulation of the standard summation and connectivity relationships as a statement that the matrix of all the elasticities in a system is the inverse of the matrix of all the control coefficients is completely general, provided that only control coefficients for independent fluxes and concentrations are considered, and that the elasticity matrix is written to take account of the stoichiometry of the pathway and the implied dependences between concentrations. This generally implies that co-response analysis is also general, i.e. that all of the elasticities and all of the control coefficients in any system, regardless of branching, feedback effects, moiety conservation or other complications, can be determined by comparing the effects of perturbations of the enzyme activities on the steady-state fluxes and concentrations of the pathway. The approach requires no quantitative information about the magnitudes of the effects on the individual enzyme activities, and consequently no enzymes need to be studied in isolation from the pathway. link: http://identifiers.org/pubmed/8944170

Parameters: none

States: none

Observables: none

Holmes2006 - Hill's model of muscle contractionThis model is described in the article: [Teaching from classic papers: H…

A. V. Hill's 1938 paper "The heat of shortening and the dynamic constants of muscle" is an enduring classic, presenting detailed methods, meticulous experiments, and the model of muscle contraction that now bears Hill's name. Pairing a simulation based on Hill's model with a reading of his paper allows students to follow his thought process to discover key principles of muscle physiology and gain insight into how to develop quantitative models of physiological processes. In this article, the experience of the author using this approach in a graduate biomedical engineering course is outlined, along with suggestions for adapting this approach to other audiences. link: http://identifiers.org/pubmed/16709736

Parameters: none

States: none

Observables: none

BIOMD0000000070 @ v0.0.1

. . . **[SBML](http://www.sbml.org/) level 2 code generated for the JWS Online project by Jacky Snoep using [PySCeS](…

Cellular functions are ultimately linked to metabolic fluxes brought about by thousands of chemical reactions and transport processes. The synthesis of the underlying enzymes and membrane transporters causes the cell a certain 'effort' of energy and external resources. Considering that those cells should have had a selection advantage during natural evolution that enabled them to fulfil vital functions (such as growth, defence against toxic compounds, repair of DNA alterations, etc.) with minimal effort, one may postulate the principle of flux minimization, as follows: given the available external substrates and given a set of functionally important 'target' fluxes required to accomplish a specific pattern of cellular functions, the stationary metabolic fluxes have to become a minimum. To convert this principle into a mathematical method enabling the prediction of stationary metabolic fluxes, the total flux in the network is measured by a weighted linear combination of all individual fluxes whereby the thermodynamic equilibrium constants are used as weighting factors, i.e. the more the thermodynamic equilibrium lies on the right-hand side of the reaction, the larger the weighting factor for the backward reaction. A linear programming technique is applied to minimize the total flux at fixed values of the target fluxes and under the constraint of flux balance (= steady-state conditions) with respect to all metabolites. The theoretical concept is applied to two metabolic schemes: the energy and redox metabolism of erythrocytes, and the central metabolism of Methylobacterium extorquens AM1. The flux rates predicted by the flux-minimization method exhibit significant correlations with flux rates obtained by either kinetic modelling or direct experimental determination. Larger deviations occur for segments of the network composed of redundant branches where the flux-minimization method always attributes the total flux to the thermodynamically most favourable branch. Nevertheless, compared with existing methods of structural modelling, the principle of flux minimization appears to be a promising theoretical approach to assess stationary flux rates in metabolic systems in cases where a detailed kinetic model is not yet available. link: http://identifiers.org/pubmed/15233787

Parameters:

Name Description
kATPasev15=1.68 hour_inverse Reaction: MgATP => Phi + MgADP, Rate Law: compartment*kATPasev15*MgATP
KR5Pv22=2.2 mM; Vmaxv22=730.0 mM_per_hour; KRu5Pv22=0.78 mM; Keqv22=3.0 dimensionless Reaction: Rul5P => Rib5P, Rate Law: compartment*Vmaxv22*(Rul5P-Rib5P/Keqv22)/(Rul5P+KRu5Pv22*(1+Rib5P/KR5Pv22))
K2PGv10=1.0 mM; Keqv10=0.145 dimensionless; K3PGv10=5.0 mM; Vmaxv10=2000.0 mM_per_hour Reaction: Gri3P => Gri2P, Rate Law: compartment*Vmaxv10*(Gri3P-Gri2P/Keqv10)/(Gri3P+K3PGv10*(1+Gri2P/K2PGv10))
Kv20=0.03 hour_inverse Reaction: GSH => GSSG, Rate Law: compartment*Kv20*GSH
Keqv7=1455.0 dimensionless; Vmaxv7=5000.0 mM_per_hour; KMgADPv7=0.35 mM; K3PGv7=1.2 mM; K13P2Gv7=0.002 mM; KMgATPv7=0.48 mM Reaction: MgADP + Gri13P2 => MgATP + Gri3P, Rate Law: compartment*Vmaxv7/(KMgADPv7*K13P2Gv7)*(MgADP*Gri13P2-MgATP*Gri3P/Keqv7)/(((1+MgADP/KMgADPv7)*(1+Gri13P2/K13P2Gv7)+(1+MgATP/KMgATPv7)*(1+Gri3P/K3PGv7))-1)
Vmaxv13=2800000.0 per_mM_hour; Keqv13=9090.0 dimensionless Reaction: NADH + Pyr => Lac + NAD, Rate Law: compartment*Vmaxv13*(Pyr*NADH-Lac*NAD/Keqv13)
KAMPv3=0.033 mM; KFru6Pv3=0.1 mM; Keqv3=100000.0 dimensionless; KATPv3=0.01 mM; Vmaxv3=239.0 mM_per_hour; KMgATPv3=0.068 mM; L0v3=0.001072 dimensionless; KMgv3=0.44 mM Reaction: MgATP + Fru6P => Fru16P2 + MgADP; ATPf, Mgf, AMPf, MgAMP, Rate Law: compartment*Vmaxv3*(Fru6P*MgATP-Fru16P2*MgADP/Keqv3)/((Fru6P+KFru6Pv3)*(MgATP+KMgATPv3)*(1+L0v3*((1+ATPf/KATPv3)*(1+Mgf/KMgv3)/((1+(AMPf+MgAMP)/KAMPv3)*(1+Fru6P/KFru6Pv3)))^4))
KGSHv19=20.0 mM; Vmaxv19=90.0 mM_per_hour; KGSSGv19=0.0652 mM; KNADPHv19=0.00852 mM; KNADPv19=0.07 mM; Keqv19=1.04 dimensionless Reaction: GSSG + NADPHf => GSH + NADPf, Rate Law: compartment*Vmaxv19*(GSSG*NADPHf/(KGSSGv19*KNADPHv19)-GSH^2/KGSHv19^2*NADPf/(KNADPv19*Keqv19))/(1+NADPHf*(1+GSSG/KGSSGv19)/KNADPHv19+NADPf/KNADPv19*(1+GSH*(1+GSH/KGSHv19)/KGSHv19))
KNADPv17=0.00367 mM; KG6Pv17=0.0667 mM; Keqv17=2000.0 dimensionless; KATPv17=0.749 mM; Vmaxv17=162.0 mM_per_hour; KPGA23v17=2.289 mM; KNADPHv17=0.00312 mM Reaction: Glc6P + NADPf => GlcA6P + NADPHf; ATPf, MgATP, Gri23P2f, MgGri23P2, Rate Law: compartment*Vmaxv17/KG6Pv17/KNADPv17*(Glc6P*NADPf-GlcA6P*NADPHf/Keqv17)/(1+NADPf*(1+Glc6P/KG6Pv17)/KNADPv17+(ATPf+MgATP)/KATPv17+NADPHf/KNADPHv17+(Gri23P2f+MgGri23P2)/KPGA23v17)
KNADPHv18=0.0045 mM; Keqv18=141.7 dimensionless; KATPv18=0.154 mM; K6PG1v18=0.01 mM; KNADPv18=0.018 mM; K6PG2v18=0.058 mM; KPGA23v18=0.12 mM; Vmaxv18=1575.0 mM_per_hour Reaction: GlcA6P + NADPf => Rul5P + NADPHf; Gri23P2f, MgGri23P2, ATPf, MgATP, Rate Law: compartment*Vmaxv18/K6PG1v18/KNADPv18*(GlcA6P*NADPf-Rul5P*NADPHf/Keqv18)/((1+NADPf/KNADPv18)*(1+GlcA6P/K6PG1v18+(Gri23P2f+MgGri23P2)/KPGA23v18)+(ATPf+MgATP)/KATPv18+NADPHf*(1+GlcA6P/K6PG2v18)/KNADPHv18)
KdATP=0.072 mM; EqMult=1.0E7 hour_inverse Reaction: MgATP => Mgf + ATPf, Rate Law: compartment*EqMult*(MgATP-Mgf*ATPf/KdATP)
EqMult=1.0E7 hour_inverse; Kd2=1.0E-5 mM Reaction: P2NADP => P2f + NADPf, Rate Law: compartment*EqMult*(P2NADP-P2f*NADPf/Kd2)
Keqv8=100000.0 dimensionless; K23P2Gv8=0.04 mM; kDPGMv8=76000.0 hour_inverse Reaction: Gri13P2 => Gri23P2f; MgGri23P2, Rate Law: compartment*kDPGMv8*(Gri13P2-(Gri23P2f+MgGri23P2)/Keqv8)/(1+(Gri23P2f+MgGri23P2)/K23P2Gv8)
Kd23P2G=1.667 mM; EqMult=1.0E7 hour_inverse Reaction: MgGri23P2 => Mgf + Gri23P2f, Rate Law: compartment*EqMult*(MgGri23P2-Mgf*Gri23P2f/Kd23P2G)
KR5Pv25=0.57 mM; Keqv25=100000.0 dimensionless; Vmaxv25=1.1 mM_per_hour; KATPv25=0.03 mM Reaction: MgATP + Rib5P => MgAMP + PRPP, Rate Law: compartment*Vmaxv25*(Rib5P*MgATP-PRPP*MgAMP/Keqv25)/((KATPv25+MgATP)*(KR5Pv25+Rib5P))
K6v23=0.00774 dimensionless; K7v23=48.8 dimensionless; K4v23=0.00496 mM; K1v23=0.4177 mM; K5v23=0.41139 dimensionless; Vmaxv23=23.5 mM_per_hour; Keqv23=1.05 dimensionless; K2v23=0.3055 mM; K3v23=12.432 mM Reaction: Xul5P + Rib5P => GraP + Sed7P, Rate Law: compartment*Vmaxv23*(Rib5P*Xul5P-GraP*Sed7P/Keqv23)/((K1v23+Rib5P)*Xul5P+(K2v23+K6v23*Sed7P)*Rib5P+(K3v23+K5v23*Sed7P)*GraP+K4v23*Sed7P+K7v23*Xul5P*GraP)
EqMult=1.0E7 hour_inverse; Kd4=2.0E-4 mM Reaction: P2NADPH => P2f + NADPHf, Rate Law: compartment*EqMult*(P2NADPH-P2f*NADPHf/Kd4)
KMGlcv1=0.1 mM; Keqv1=3900.0 mM; Vmax1v1=15.8 mM_per_hour; Vmax2v1=33.2 mM_per_hour; Inhibv1=1.0 dimensionless; KMgATPv1=1.44 mM; KGlc6Pv1=0.0045 mM; K23P2Gv1=2.7 mM; KMgATPMgv1=1.14 mM; KMgv1=1.03 mM; KMg23P2Gv1=3.44 mM Reaction: Glcin + MgATP => Glc6P + MgADP; Mgf, Gri23P2f, MgGri23P2, Rate Law: compartment*Inhibv1*Glcin/(Glcin+KMGlcv1)*Vmax1v1/KMgATPv1*((MgATP+Vmax2v1/Vmax1v1*MgATP*Mgf/KMgATPMgv1)-Glc6P*MgADP/Keqv1)/(1+MgATP/KMgATPv1*(1+Mgf/KMgATPMgv1)+Mgf/KMgv1+(1.55+Glc6P/KGlc6Pv1)*(1+Mgf/KMgv1)+(Gri23P2f+MgGri23P2)/K23P2Gv1+Mgf*(Gri23P2f+MgGri23P2)/(KMgv1*KMg23P2Gv1))
Vmaxv28=10000.0 hour_inverse; Keqv28=1.0 dimensionless Reaction: Lacex => Lac, Rate Law: compartment*Vmaxv28*(Lacex-Lac/Keqv28)
Keqv2=0.3925 dimensionless; KGlc6Pv2=0.182 mM; Vmaxv2=935.0 mM_per_hour; KFru6Pv2=0.071 mM Reaction: Glc6P => Fru6P, Rate Law: compartment*Vmaxv2*(Glc6P-Fru6P/Keqv2)/(Glc6P+KGlc6Pv2*(1+Fru6P/KFru6Pv2))
Vmaxv26=23.5 mM_per_hour; K6v26=0.122 dimensionless; K5v26=0.0287 dimensionless; Keqv26=1.2 dimensionless; K4v26=3.0E-4 mM; K3v26=0.0548 mM; K2v26=0.3055 mM; K7v26=0.215 dimensionless; K1v26=0.00184 mM Reaction: Xul5P + E4P => GraP + Fru6P, Rate Law: compartment*Vmaxv26*(E4P*Xul5P-GraP*Fru6P/Keqv26)/((K1v26+E4P)*Xul5P+(K2v26+K6v26*Fru6P)*E4P+(K3v26+K5v26*Fru6P)*GraP+K4v26*Fru6P+K7v26*Xul5P*GraP)
Vmaxv29=10000.0 hour_inverse; Keqv29=1.0 dimensionless Reaction: Pyrex => Pyr, Rate Law: compartment*Vmaxv29*(Pyrex-Pyr/Keqv29)
Vmaxv21=4634.0 mM_per_hour; KX5Pv21=0.5 mM; KRu5Pv21=0.19 mM; Keqv21=2.7 dimensionless Reaction: Rul5P => Xul5P, Rate Law: compartment*Vmaxv21*(Rul5P-Xul5P/Keqv21)/(Rul5P+KRu5Pv21*(1+Xul5P/KX5Pv21))
Keqv27=1.0 dimensionless; Vmaxv27=100.0 hour_inverse Reaction: Phiex => Phi, Rate Law: compartment*Vmaxv27*(Phiex-Phi/Keqv27)
L0v12=19.0 dimensionless; Vmaxv12=570.0 mM_per_hour; KMgADPv12=0.474 mM; KPEPv12=0.225 mM; Keqv12=13790.0 dimensionless; KATPv12=3.39 mM; KFru16P2v12=0.005 mM Reaction: PEP + MgADP => MgATP + Pyr; ATPf, Fru16P2, Rate Law: compartment*Vmaxv12*(PEP*MgADP-Pyr*MgATP/Keqv12)/((PEP+KPEPv12)*(MgADP+KMgADPv12)*(1+L0v12*(1+(ATPf+MgATP)/KATPv12)^4/((1+PEP/KPEPv12)^4*(1+Fru16P2/KFru16P2v12)^4)))
EqMult=1.0E7 hour_inverse; Kd1=2.0E-4 mM Reaction: P1NADP => P1f + NADPf, Rate Law: compartment*EqMult*(P1NADP-P1f*NADPf/Kd1)
KdAMP=16.64 mM; EqMult=1.0E7 hour_inverse Reaction: MgAMP => Mgf + AMPf, Rate Law: compartment*EqMult*(MgAMP-Mgf*AMPf/KdAMP)
K13P2Gv6=0.0035 mM; Keqv6=1.92E-4 dimensionless; KNADHv6=0.0083 mM; KGraPv6=0.005 mM; Vmaxv6=4300.0 mM_per_hour; KNADv6=0.05 mM; KPv6=3.9 mM Reaction: GraP + Phi + NAD => NADH + Gri13P2, Rate Law: compartment*Vmaxv6/(KNADv6*KGraPv6*KPv6)*(NAD*GraP*Phi-Gri13P2*NADH/Keqv6)/(((1+NAD/KNADv6)*(1+GraP/KGraPv6)*(1+Phi/KPv6)+(1+NADH/KNADHv6)*(1+Gri13P2/K13P2Gv6))-1)
Vmaxv4=98.91000366 mM_per_hour; KiGraPv4=0.0572 mM; KiiGraPv4=0.176 mM; KGraPv4=0.1906 mM; KFru16P2v4=0.0071 mM; Keqv4=0.114 mM; KDHAPv4=0.0364 mM Reaction: Fru16P2 => GraP + DHAP, Rate Law: compartment*Vmaxv4/KFru16P2v4*(Fru16P2-GraP*DHAP/Keqv4)/(1+Fru16P2/KFru16P2v4+GraP/KiGraPv4+DHAP*(GraP+KGraPv4)/(KDHAPv4*KiGraPv4)+Fru16P2*GraP/(KFru16P2v4*KiiGraPv4))
KAMPv16=0.08 mM; KADPv16=0.11 mM; KATPv16=0.09 mM; Keqv16=0.25 dimensionless; Vmaxv16=1380.0 mM_per_hour Reaction: MgATP + AMPf => ADPf + MgADP, Rate Law: compartment*Vmaxv16/(KATPv16*KAMPv16)*(MgATP*AMPf-MgADP*ADPf/Keqv16)/((1+MgATP/KATPv16)*(1+AMPf/KAMPv16)+(MgADP+ADPf)/KADPv16+MgADP*ADPf/KADPv16^2)
Keqv5=0.0407 dimensionless; KGraPv5=0.428 mM; KDHAPv5=0.838 mM; Vmaxv5=5456.600098 mM_per_hour Reaction: DHAP => GraP, Rate Law: compartment*Vmaxv5*(DHAP-GraP/Keqv5)/(DHAP+KDHAPv5*(1+GraP/KGraPv5))
KdADP=0.76 mM; EqMult=1.0E7 hour_inverse Reaction: MgADP => Mgf + ADPf, Rate Law: compartment*EqMult*(MgADP-Mgf*ADPf/KdADP)
Keqv14=14181.8 dimensionless; kLDHv14=243.4 per_mM_hour Reaction: Pyr + NADPHf => Lac + NADPf, Rate Law: compartment*kLDHv14*(Pyr*NADPHf-Lac*NADPf/Keqv14)
Keqv0=1.0 dimensionless; KMoutv0=1.7 mM; alfav0=0.54 dimensionless; Vmaxv0=33.6 mM_per_hour; KMinv0=6.9 mM Reaction: Glcout => Glcin, Rate Law: compartment*Vmaxv0/KMoutv0*(Glcout-Glcin/Keqv0)/(1+Glcout/KMoutv0+Glcin/KMinv0+alfav0*Glcout*Glcin/KMoutv0/KMinv0)
Keqv11=1.7 dimensionless; K2PGv11=1.0 mM; Vmaxv11=1500.0 mM_per_hour; KPEPv11=1.0 mM Reaction: Gri2P => PEP, Rate Law: compartment*Vmaxv11*(Gri2P-PEP/Keqv11)/(Gri2P+K2PGv11*(1+PEP/KPEPv11))
K6v24=0.4653 dimensionless; Keqv24=1.05 dimensionless; K5v24=0.8683 dimensionless; Vmaxv24=27.2 mM_per_hour; K1v24=0.00823 mM; K2v24=0.04765 mM; K7v24=2.524 dimensionless; K3v24=0.1733 mM; K4v24=0.006095 mM Reaction: GraP + Sed7P => E4P + Fru6P, Rate Law: compartment*Vmaxv24*(Sed7P*GraP-E4P*Fru6P/Keqv24)/((K1v24+GraP)*Sed7P+(K2v24+K6v24*Fru6P)*GraP+(K3v24+K5v24*Fru6P)*E4P+K4v24*Fru6P+K7v24*Sed7P*E4P)
Keqv9=100000.0 dimensionless; Vmaxv9=0.53 mM_per_hour; K23P2Gv9=0.2 mM Reaction: Gri23P2f => Gri3P + Phi; MgGri23P2, Rate Law: compartment*Vmaxv9*((Gri23P2f+MgGri23P2)-Gri3P/Keqv9)/(Gri23P2f+MgGri23P2+K23P2Gv9)
Kd3=1.0E-5 mM; EqMult=1.0E7 hour_inverse Reaction: P1NADPH => P1f + NADPHf, Rate Law: compartment*EqMult*(P1NADPH-P1f*NADPHf/Kd3)

States:

Name Description
ADPf [ADP; ADP]
Rib5P [aldehydo-D-ribose 5-phosphate; D-Ribose 5-phosphate]
NADPf [NADP(+); NADP+]
Glc6P [alpha-D-glucose 6-phosphate; alpha-D-Glucose 6-phosphate]
Fru16P2 [beta-D-fructofuranose 1,6-bisphosphate; beta-D-Fructose 1,6-bisphosphate]
Rul5P [D-ribulose 5-phosphate; D-Ribulose 5-phosphate]
GraP [D-glyceraldehyde 3-phosphate; D-Glyceraldehyde 3-phosphate]
DHAP [dihydroxyacetone phosphate; Glycerone phosphate]
GSSG [glutathione disulfide; Glutathione disulfide]
MgATP [magnesium atom; ATP; Magnesium cation; ATP; magnesium(2+)]
AMPf [AMP; AMP]
Phi [phosphate ion]
NADPHf [NADPH; NADPH]
Gri3P [3-phospho-D-glyceric acid; 3-Phospho-D-glycerate]
Gri13P2 [3-phospho-D-glyceroyl dihydrogen phosphate; 3-Phospho-D-glyceroyl phosphate]
Sed7P [Sedoheptulose 7-phosphate; sedoheptulose 7-phosphate]
GSH [glutathione; Glutathione]
Gri23P2f [2,3-bisphospho-D-glyceric acid; 2,3-Bisphospho-D-glycerate]
GlcA6P [6-O-phosphono-D-glucono-1,5-lactone; D-Glucono-1,5-lactone 6-phosphate]
NADH [NADH; NADH]
Xul5P [D-xylulose 5-phosphate; D-Xylulose 5-phosphate]
MgADP [magnesium atom; ADP; Magnesium cation; ADP; magnesium(2+)]
Mgf [magnesium atom; Magnesium cation]
Pyr [pyruvate; Pyruvate; pyruvic acid]
E4P [D-erythrose 4-phosphate(2-); D-Erythrose 4-phosphate]
Lac [(R)-Lactate; (R)-lactic acid]
MgAMP [magnesium atom; AMP; Magnesium cation; AMP; magnesium(2+)]
Gri2P [2-phospho-D-glyceric acid; 2-Phospho-D-glycerate]
PEP [Phosphoenolpyruvate; phosphoenolpyruvate; phosphoenolpyruvate]
Glcin [glucose; C00293]
NAD [NAD(+); NAD+]
Fru6P [beta-D-fructofuranose 6-phosphate; beta-D-Fructose 6-phosphate]

Observables: none

Hong2004 - Genome-scale metabolic network of Mannheimia succiniciproducens (iSH335)This model is described in the articl…

The rumen represents the first section of a ruminant animal's stomach, where feed is collected and mixed with microorganisms for initial digestion. The major gas produced in the rumen is CO(2) (65.5 mol%), yet the metabolic characteristics of capnophilic (CO(2)-loving) microorganisms are not well understood. Here we report the 2,314,078 base pair genome sequence of Mannheimia succiniciproducens MBEL55E, a recently isolated capnophilic Gram-negative bacterium from bovine rumen, and analyze its genome contents and metabolic characteristics. The metabolism of M. succiniciproducens was found to be well adapted to the oxygen-free rumen by using fumarate as a major electron acceptor. Genome-scale metabolic flux analysis indicated that CO(2) is important for the carboxylation of phosphoenolpyruvate to oxaloacetate, which is converted to succinic acid by the reductive tricarboxylic acid cycle and menaquinone systems. This characteristic metabolism allows highly efficient production of succinic acid, an important four-carbon industrial chemical. link: http://identifiers.org/pubmed/15378067

Parameters: none

States: none

Observables: none

BIOMD0000000216 @ v0.0.1

This a model from the article: Minimum criteria for DNA damage-induced phase advances in circadian rhythms. Hong CI…

Robust oscillatory behaviors are common features of circadian and cell cycle rhythms. These cyclic processes, however, behave distinctively in terms of their periods and phases in response to external influences such as light, temperature, nutrients, etc. Nevertheless, several links have been found between these two oscillators. Cell division cycles gated by the circadian clock have been observed since the late 1950s. On the other hand, ionizing radiation (IR) treatments cause cells to undergo a DNA damage response, which leads to phase shifts (mostly advances) in circadian rhythms. Circadian gating of the cell cycle can be attributed to the cell cycle inhibitor kinase Wee1 (which is regulated by the heterodimeric circadian clock transcription factor, BMAL1/CLK), and possibly in conjunction with other cell cycle components that are known to be regulated by the circadian clock (i.e., c-Myc and cyclin D1). It has also been shown that DNA damage-induced activation of the cell cycle regulator, Chk2, leads to phosphorylation and destruction of a circadian clock component (i.e., PER1 in Mus or FRQ in Neurospora crassa). However, the molecular mechanism underlying how DNA damage causes predominantly phase advances in the circadian clock remains unknown. In order to address this question, we employ mathematical modeling to simulate different phase response curves (PRCs) from either dexamethasone (Dex) or IR treatment experiments. Dex is known to synchronize circadian rhythms in cell culture and may generate both phase advances and delays. We observe unique phase responses with minimum delays of the circadian clock upon DNA damage when two criteria are met: (1) existence of an autocatalytic positive feedback mechanism in addition to the time-delayed negative feedback loop in the clock system and (2) Chk2-dependent phosphorylation and degradation of PERs that are not bound to BMAL1/CLK. link: http://identifiers.org/pubmed/19424508

Parameters:

Name Description
ka = 100.0 Reaction: CP => CP2, Rate Law: system*ka*CP^2
kica = 20.0 Reaction: CP2 + TF => IC, Rate Law: system*kica*CP2*TF
chk2 = 0.0 Reaction: CP =>, Rate Law: system*chk2*CP
kicd = 0.01 Reaction: IC => CP2 + TF, Rate Law: system*kicd*IC
Dex = 0.0 Reaction: => M, Rate Law: system*Dex/system
kms = 1.0; n = 2.0; J = 0.3 Reaction: => M; TF, Rate Law: system*kms*TF^n/(J^n+TF^n)/system
Jp = 0.05; kp1 = 10.0 Reaction: CP => ; CP2, IC, Rate Law: system*kp1*CP/(Jp+CP+2*CP2+2*IC)/system
kmd = 0.1 Reaction: M =>, Rate Law: system*kmd*M
kcpd = 0.525 Reaction: CP =>, Rate Law: system*kcpd*CP
kd = 0.01 Reaction: CP2 => CP, Rate Law: system*kd*CP2
chk2c = 0.0 Reaction: IC => TF, Rate Law: system*chk2c*IC
kcp2d = 0.0525 Reaction: IC => TF, Rate Law: system*kcp2d*IC
kcps = 0.5 Reaction: => CP; M, Rate Law: system*kcps*M
Jp = 0.05; kp2 = 0.1 Reaction: IC => TF; CP2, CP, Rate Law: system*kp2*IC/(Jp+CP+2*CP2+2*IC)/system

States:

Name Description
CP [Circadian locomoter output cycles protein kaput]
IC [Dual specificity protein kinase CLK1; Aryl hydrocarbon receptor nuclear translocator-like protein 1; Circadian locomoter output cycles protein kaput]
M [messenger RNA; RNA]
TF [Dual specificity protein kinase CLK1; Aryl hydrocarbon receptor nuclear translocator-like protein 1]
CPtot CPtot
CP2 [Circadian locomoter output cycles protein kaput]

Observables: none

Hoppe2012 - Predicting changes in metabolic function using transcript profilesMeasuring metabolite concentrations, react…

Genome-wide transcript profiles are often the only available quantitative data for a particular perturbation of a cellular system and their interpretation with respect to the metabolism is a major challenge in systems biology, especially beyond on/off distinction of genes. We present a method that predicts activity changes of metabolic functions by scoring reference flux distributions based on relative transcript profiles, providing a ranked list of most regulated functions. Then, for each metabolic function, the involved genes are ranked upon how much they represent a specific regulation pattern. Compared with the naïve pathway-based approach, the reference modes can be chosen freely, and they represent full metabolic functions, thus, directly provide testable hypotheses for the metabolic study. In conclusion, the novel method provides promising functions for subsequent experimental elucidation together with outstanding associated genes, solely based on transcript profiles. link: http://identifiers.org/doi/10.4230/OASIcs.GCB.2012.1

Parameters: none

States: none

Observables: none

BIOMD0000000667 @ v0.0.1

Hornberg2005 - MAPKsignallingLarge model of the ERK signalling network. Results from this model were used to generate a…

Oncogenesis results from changes in kinetics or in abundance of proteins in signal transduction networks. Recently, it was shown that control of signalling cannot reside in a single gene product, and might well be dispersed over many components. Which of the reactions in these complex networks are most important, and how can the existing molecular information be used to understand why particular genes are oncogenes whereas others are not? We implement a new method to help address such questions. We apply control analysis to a detailed kinetic model of the epidermal growth factor-induced mitogen-activated protein kinase network. We determine the control of each reaction with respect to three biologically relevant characteristics of the output of this network: the amplitude, duration and integrated output of the transient phosphorylation of extracellular signal-regulated kinase (ERK). We confirm that control is distributed, but far from randomly: a small proportion of reactions substantially control signalling. In particular, the activity of Raf is in control of all characteristics of the transient profile of ERK phosphorylation, which may clarify why Raf is an oncogene. Most reactions that really matter for one signalling characteristic are also important for the other characteristics. Our analysis also predicts the effects of mutations and changes in gene expression. link: http://identifiers.org/pubmed/16007170

Parameters:

Name Description
kd55 = 5.7 Reaction: ERK_P_MEKPP => ERK_PP + MEK_PP, Rate Law: Compartment*kd55*ERK_P_MEKPP
k18 = 2.5E-5; kd18 = 1.3 Reaction: Ras_GDP + _EGF_EGFR__2_GAP_SHC__Grb2_Sos => _EGF_EGFR__2_GAP_SHC__Grb2_Sos_Ras_GDP, Rate Law: Compartment*(k18*Ras_GDP*_EGF_EGFR__2_GAP_SHC__Grb2_Sos-kd18*_EGF_EGFR__2_GAP_SHC__Grb2_Sos_Ras_GDP)
kd19 = 0.5; k19 = 1.66E-7 Reaction: Ras_GTP + _EGF_EGFR__2_GAP_Grb2_Sos => _EGF_EGFR__2_GAP_Grb2_Sos_Ras_GDP, Rate Law: Compartment*(k19*Ras_GTP*_EGF_EGFR__2_GAP_Grb2_Sos-kd19*_EGF_EGFR__2_GAP_Grb2_Sos_Ras_GDP)
k37 = 1.5E-6; kd37 = 0.3 Reaction: _EGF_EGFRi__2_GAP + Shc_0 => _EGF_EGFRi__2_GAP_SHC_0, Rate Law: Compartment*(k37*_EGF_EGFRi__2_GAP*Shc_0-kd37*_EGF_EGFRi__2_GAP_SHC_0)
kd20 = 0.4; k20 = 3.5E-6 Reaction: _EGF_EGFR__2_GAP_SHC__Grb2_Sos + Ras_GTP_ => _EGF_EGFR__2_GAP_SHC__Grb2_Sos_Ras_GTP, Rate Law: Compartment*(k20*_EGF_EGFR__2_GAP_SHC__Grb2_Sos*Ras_GTP_-kd20*_EGF_EGFR__2_GAP_SHC__Grb2_Sos_Ras_GTP)
kd57 = 0.246 Reaction: ERKi_P_phosphatase3 => ERK + phosphatase3, Rate Law: Compartment*kd57*ERKi_P_phosphatase3
k40 = 5.0E-5; kd40 = 0.064 Reaction: Sos + Shc__Grb2 => Shc__Grb2_Sos, Rate Law: Compartment*(k40*Sos*Shc__Grb2-kd40*Shc__Grb2_Sos)
k21 = 3.66E-7; kd21 = 0.023 Reaction: _EGF_EGFR__2_GAP_SHC__Grb2_Sos + Ras_GDP => _EGF_EGFR__2_GAP_SHC__Grb2_Sos_Ras_GTP, Rate Law: Compartment*(k21*_EGF_EGFR__2_GAP_SHC__Grb2_Sos*Ras_GDP-kd21*_EGF_EGFR__2_GAP_SHC__Grb2_Sos_Ras_GTP)
kd50 = 0.5; k50 = 4.5E-7 Reaction: phosphatse2 + MEKi_P => MEKi_P_phosphatase2, Rate Law: Compartment*(k50*phosphatse2*MEKi_P-kd50*MEKi_P_phosphatase2)
k6 = 5.0E-4 Reaction: _EGF_EGFR__2_GAP_Grb2 => _EGF_EGFRi__2_GAP_Grb2, Rate Law: Compartment*k6*_EGF_EGFR__2_GAP_Grb2
k44 = 1.95E-5; kd52 = 0.033 Reaction: MEK_P + Raf_0 => MEK_P_Raf, Rate Law: Compartment*(k44*MEK_P*Raf_0-kd52*MEK_P_Raf)
kd127 = 1.0E-4; k127 = 0.0 Reaction: ERK_PP + _EGF_EGFR__2_GAP_Grb2_Sos_deg => _EGF_EGFR__2_GAP_Grb2_Sos_ERK_PP, Rate Law: Compartment*(k127*ERK_PP*_EGF_EGFR__2_GAP_Grb2_Sos_deg-kd127*_EGF_EGFR__2_GAP_Grb2_Sos_ERK_PP)
kd25 = 0.0214; k25 = 1.66E-5 Reaction: Sos + _EGF_EGFR__2_GAP_SHC__Grb2 => _EGF_EGFR__2_GAP_SHC__Grb2_Sos, Rate Law: Compartment*(k25*Sos*_EGF_EGFR__2_GAP_SHC__Grb2-kd25*_EGF_EGFR__2_GAP_SHC__Grb2_Sos)
k32 = 4.0E-7; kd32 = 0.1 Reaction: _EGF_EGFRi__2_GAP + Shc__Grb2_Sos => _EGF_EGFRi__2_GAP_SHC__Grb2_Sos, Rate Law: Compartment*(k32*_EGF_EGFRi__2_GAP*Shc__Grb2_Sos-kd32*_EGF_EGFRi__2_GAP_SHC__Grb2_Sos)
kd17 = 0.06; k17 = 1.66E-5 Reaction: Sos + _EGF_EGFR__2_GAP_Grb2 => _EGF_EGFR__2_GAP_Grb2_Sos, Rate Law: Compartment*(k17*Sos*_EGF_EGFR__2_GAP_Grb2-kd17*_EGF_EGFR__2_GAP_Grb2_Sos)
k60 = 0.0055 Reaction: _EGF_EGFRi__2_GAP_SHC => _EGF_EGFRi___2deg, Rate Law: Compartment*k60*_EGF_EGFRi__2_GAP_SHC
k34 = 7.5E-6; kd34 = 0.03 Reaction: _EGF_EGFRi__2_GAP + Grb2_Sos => _EGF_EGFRi__2_GAP_Grb2_Sos, Rate Law: Compartment*(k34*_EGF_EGFRi__2_GAP*Grb2_Sos-kd34*_EGF_EGFRi__2_GAP_Grb2_Sos)
k126 = 1.66E-7; kd126 = 2.0 Reaction: ERKi_PP + Sos => Sos_ERKi_PP, Rate Law: Compartment*(k126*ERKi_PP*Sos-kd126*Sos_ERKi_PP)
kd23 = 0.06; k23 = 6.0 Reaction: _EGF_EGFRi__2_GAP_SHC => _EGF_EGFRi__2_GAP_SHC_0, Rate Law: Compartment*(k23*_EGF_EGFRi__2_GAP_SHC-kd23*_EGF_EGFRi__2_GAP_SHC_0)
kd63 = 0.275; k16 = 1.66E-5 Reaction: _EGF_EGFRi__2_GAP + Grb2 => _EGF_EGFRi__2_GAP_Grb2, Rate Law: Compartment*(k16*_EGF_EGFRi__2_GAP*Grb2-kd63*_EGF_EGFRi__2_GAP_Grb2)
kd10 = 0.011; k10b = 0.0543 Reaction: EGFRi + EGFi => EGF_EGFRi, Rate Law: Compartment*(k10b*EGFRi*EGFi-kd10*EGF_EGFRi)
kd45 = 3.5 Reaction: MEK_Raf => MEK_P + Raf_0, Rate Law: Compartment*kd45*MEK_Raf
k56 = 2.35E-5; kd56 = 0.6 Reaction: ERK_PP + phosphatase3 => ERK_PP_phosphatase3, Rate Law: Compartment*(k56*ERK_PP*phosphatase3-kd56*ERK_PP_phosphatase3)
k58 = 8.33E-6; kd58 = 0.5 Reaction: phosphatase3 + ERK_P => ERK_P_phosphatase3, Rate Law: Compartment*(k58*phosphatase3*ERK_P-kd58*ERK_P_phosphatase3)
k13 = 2.17 Reaction: => EGFR, Rate Law: Compartment*k13
k61 = 6.7E-4 Reaction: EGFi => EGFideg, Rate Law: Compartment*k61*EGFi
kd35 = 0.0015; k35 = 7.5E-6 Reaction: Sos + Grb2 => Grb2_Sos, Rate Law: Compartment*(k35*Sos*Grb2-kd35*Grb2_Sos)
kd49 = 0.0568 Reaction: MEK_P_phosphatase2 => MEK + phosphatse2, Rate Law: Compartment*kd49*MEK_P_phosphatase2
k22 = 3.5E-5; kd22 = 0.1 Reaction: Shc + _EGF_EGFRi__2_GAP => _EGF_EGFRi__2_GAP_SHC, Rate Law: Compartment*(k22*Shc*_EGF_EGFRi__2_GAP-kd22*_EGF_EGFRi__2_GAP_SHC)
kd53 = 16.0 Reaction: ERK_MEK_PP => MEK_PP + ERK_P, Rate Law: Compartment*kd53*ERK_MEK_PP
kd41 = 0.0429; k41 = 5.0E-5 Reaction: Grb2_Sos + _EGF_EGFR__2_GAP_SHC_0 => _EGF_EGFR__2_GAP_SHC__Grb2_Sos, Rate Law: Compartment*(k41*Grb2_Sos*_EGF_EGFR__2_GAP_SHC_0-kd41*_EGF_EGFR__2_GAP_SHC__Grb2_Sos)
k16 = 1.66E-5; kd24 = 0.55 Reaction: Grb2 + _EGF_EGFRi__2_GAP_SHC_0 => _EGF_EGFRi__2_GAP_SHC__Grb2, Rate Law: Compartment*(k16*Grb2*_EGF_EGFRi__2_GAP_SHC_0-kd24*_EGF_EGFRi__2_GAP_SHC__Grb2)
kd4 = 0.00166; k4 = 1.73E-7 Reaction: _EGF_EGFR__2_GAP_Grb2 + Prot => _EGF_EGFR__2_GAP_Grb2_Prot, Rate Law: Compartment*(k4*_EGF_EGFR__2_GAP_Grb2*Prot-kd4*_EGF_EGFR__2_GAP_Grb2_Prot)
k52 = 8.91E-5; kd44 = 0.0183 Reaction: ERK + MEKi_PP => ERKi_MEKi_PP_0, Rate Law: Compartment*(k52*ERK*MEKi_PP-kd44*ERKi_MEKi_PP_0)
kd8 = 0.2; k8 = 1.66E-6 Reaction: _EGF_EGFRi__2 + GAP => _EGF_EGFRi__2_GAP, Rate Law: Compartment*(k8*_EGF_EGFRi__2*GAP-kd8*_EGF_EGFRi__2_GAP)
kd36 = 0.0; k36 = 0.005 Reaction: Shc_0 => Shc, Rate Law: Compartment*(k36*Shc_0-kd36*Shc)

States:

Name Description
MEK Raf [RAF proto-oncogene serine/threonine-protein kinase; Dual specificity mitogen-activated protein kinase kinase 1]
EGF EGFRi 2 GAP SHC [Shc-EGFR complex]
EGF EGFR 2 GAP SHC Grb2 Sos Ras GTP [EGFR-Shc-Grb2-Sos complex; Cell division control protein 42 homolog; GTPase KRas]
EGFR [Epidermal growth factor receptor]
Shc [SHC-transforming protein 1]
phosphatse2 [Dual specificity protein phosphatase 3]
EGF EGFR 2 GAP SHC Grb2 [Shc-EGFR complex; Growth factor receptor-bound protein 2]
EGF EGFR 2 GAP Grb2 [Grb2-EGFR complex]
EGF EGFR 2 GAP SHC 0 [Shc-EGFR complex]
EGF EGFR 2 GAP SHC Grb2 Sos Ras GDP [EGFR-Shc-Grb2-Sos complex; GTPase KRas; Cell division control protein 42 homolog]
Prot [Interleukin-4 receptor subunit alpha]
ERK P [Phosphoprotein; Mitogen-activated protein kinase 1]
EGF EGFRi 2 GAP SHC Grb2 Sos [EGFR-Shc-Grb2-Sos complex]
phosphatase3 [Dual specificity protein phosphatase 3]
ERK P phosphatase3 [Phosphoprotein; Dual specificity protein phosphatase 3; Mitogen-activated protein kinase 1]
EGF EGFRi 2 GAP SHC 0 [Shc-EGFR complex]
Grb2 Sos [Growth factor receptor-bound protein 2; Son of sevenless homolog 1]
EGF EGFR 2 GAP SHC [Shc-EGFR complex]
Sos [Son of sevenless homolog 1]
EGF EGFRi 2 GAP [Pro-epidermal growth factor; Epidermal growth factor receptor; Ras GTPase-activating protein 1]
ERK PP phosphatase3 [Phosphoprotein; Mitogen-activated protein kinase 1; Dual specificity protein phosphatase 3]
ERK MEK PP [Mitogen-activated protein kinase 1; Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]
Grb2 [Growth factor receptor-bound protein 2]
MEK P phosphatase2 [Phosphoprotein; Dual specificity mitogen-activated protein kinase kinase 1; Dual specificity protein phosphatase 3]
EGFi [Pro-epidermal growth factor]
ERK P MEKPP [Dual specificity mitogen-activated protein kinase kinase 1; Mitogen-activated protein kinase 1; Phosphoprotein]
EGF EGFR 2 GAP SHC Grb2 Sos [EGFR-Shc-Grb2-Sos complex]
MEK P Raf [RAF proto-oncogene serine/threonine-protein kinase; Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]
ERK [Mitogen-activated protein kinase 1]
EGF EGFR 2 GAP Grb2 Sos [EGFR-Grb2-Sos complex]
MEK P [Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]
ERK PP [Phosphoprotein; Mitogen-activated protein kinase 1]

Observables: none

BIOMD0000000084 @ v0.0.1

**[SBML](http://www.sbml.org/) level 2 code generated for the JWS Online project by Jacky Snoep using [PySCeS](http://p…

General and simple principles are identified that govern signal transduction. The effects of kinase and phosphatase inhibition on a MAP kinase pathway are first examined in silico. Quantitative measures for the control of signal amplitude, duration and integral strength are introduced. We then identify and prove new principles, such that total control on signal amplitude and on final signal strength must amount to zero, and total control on signal duration and on integral signal intensity must equal -1. Collectively, kinases control amplitudes more than duration, whereas phosphatases tend to control both. We illustrate and validate these principles experimentally: (a) a kinase inhibitor affects the amplitude of EGF-induced ERK phosphorylation much more than its duration and (b) a phosphatase inhibitor influences both signal duration and signal amplitude, in particular long after EGF administration. Implications for the cellular decision between growth and differentiation are discussed. link: http://identifiers.org/pubmed/15634347

Parameters:

Name Description
Vm4=0.3; Km4=1.0 Reaction: x1p => x1, Rate Law: Vm4*x1p/(Km4+x1p)
Km5=0.1; k5=1.0 Reaction: x2 => x2p; x1p, Rate Law: k5*x1p*x2/(Km5+x2)
Vm2=0.01; Km2=0.1 Reaction: Rin => R, Rate Law: Vm2*Rin/(Km2+Rin)
k7=1.0; Km7=0.1 Reaction: x3 => x3p; x2p, Rate Law: k7*x2p*x3/(Km7+x3)
Vm1=1.0; Km1=0.1 Reaction: R => Rin, Rate Law: Vm1*R/(Km1+R)
Km3=0.1; k3=1.0 Reaction: x1 => x1p; R, Rate Law: k3*R*x1/(Km3+x1)
Km6=1.0; Vm6=0.3 Reaction: x2p => x2, Rate Law: Vm6*x2p/(Km6+x2p)
Vm8=0.3; Ki8=1.0; Km8=1.0; Inh=0.0 Reaction: x3p => x3, Rate Law: Vm8*x3p/Km8/(1+x3p/Km8+Inh/Ki8)

States:

Name Description
x1p [RAF proto-oncogene serine/threonine-protein kinase]
x1 [RAF proto-oncogene serine/threonine-protein kinase]
x2 [Dual specificity mitogen-activated protein kinase kinase 1]
Rin [Receptor protein-tyrosine kinase]
x3p [Mitogen-activated protein kinase 1]
R [Receptor protein-tyrosine kinase]
x3