SBMLBioModels: I - M

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I


This a model from the article: Which model to use for cortical spiking neurons? Izhikevich EM. IEEE Trans Neural N…

We discuss the biological plausibility and computational efficiency of some of the most useful models of spiking and bursting neurons. We compare their applicability to large-scale simulations of cortical neural networks. link: http://identifiers.org/pubmed/15484883

Parameters: none

States: none

Observables: none

This a model from the article: Which model to use for cortical spiking neurons? Izhikevich EM. IEEE Trans Neural N…

We discuss the biological plausibility and computational efficiency of some of the most useful models of spiking and bursting neurons. We compare their applicability to large-scale simulations of cortical neural networks. link: http://identifiers.org/pubmed/15484883

Parameters: none

States: none

Observables: none

J


Hepatocyte growth factor (HGF) signaling through its receptor Met has been implicated in hepatocellular carcinoma tumori…

Hepatocyte growth factor (HGF) signaling through its receptor Met has been implicated in hepatocellular carcinoma tumorigenesis and progression. Met interaction with integrins is shown to modulate the downstream signaling to Akt and ERK (extracellular-regulated kinase). In this study, we developed a mechanistically detailed systems biology model of HGF/Met signaling pathway that incorporated specific interactions with integrins to investigate the efficacy of integrin-binding peptide, AXT050, as monotherapy and in combination with other therapeutics targeting this pathway. Here we report that the modeled dynamics of the response to AXT050 revealed that receptor trafficking is sufficient to explain the effect of Met-integrin interactions on HGF signaling. Furthermore, the model predicted patient-specific synergy and antagonism of efficacy and potency for combination of AXT050 with sorafenib, cabozantinib, and rilotumumab. Overall, the model provides a valuable framework for studying the efficacy of drugs targeting receptor tyrosine kinase interaction with integrins, and identification of synergistic drug combinations for the patients. link: http://identifiers.org/pubmed/31452933

Parameters: none

States: none

Observables: none

MODEL0847869198 @ v0.0.1

This a model from the article: Cardiac Ca2+ dynamics: the roles of ryanodine receptor adaptation and sarcoplasmic reti…

We construct a detailed mathematical model for Ca2+ regulation in the ventricular myocyte that includes novel descriptions of subcellular mechanisms based on recent experimental findings: 1) the Keizer-Levine model for the ryanodine receptor (RyR), which displays adaptation at elevated Ca2+; 2) a model for the L-type Ca2+ channel that inactivates by mode switching; and 3) a restricted subspace into which the RyRs and L-type Ca2+ channels empty and interact via Ca2+. We add membrane currents from the Luo-Rudy Phase II ventricular cell model to our description of Ca2+ handling to formulate a new model for ventricular action potentials and Ca2+ regulation. The model can simulate Ca2+ transients during an action potential similar to those seen experimentally. The subspace [Ca2+] rises more rapidly and reaches a higher level (10-30 microM) than the bulk myoplasmic Ca2+ (peak [Ca2+]i approximately 1 microM). Termination of sarcoplasmic reticulum (SR) Ca2+ release is predominately due to emptying of the SR, but is influenced by RyR adaptation. Because force generation is roughly proportional to peak myoplasmic Ca2+, we use [Ca2+]i in the model to explore the effects of pacing rate on force generation. The model reproduces transitions seen in force generation due to changes in pacing that cannot be simulated by previous models. Simulation of such complex phenomena requires an interplay of both RyR adaptation and the degree of SR Ca2+ loading. This model, therefore, shows improved behavior over existing models that lack detailed descriptions of subcellular Ca2+ regulatory mechanisms. link: http://identifiers.org/pubmed/9512016

Parameters: none

States: none

Observables: none

BIOMD0000000641 @ v0.0.1

Jaiswal2017 - Cell cycle arrestThis model is described in the article: [ATM/Wip1 activities at chromatin control Plk1 r…

After DNA damage, the cell cycle is arrested to avoid propagation of mutations. Arrest in G2 phase is initiated by ATM-/ATR-dependent signaling that inhibits mitosis-promoting kinases such as Plk1. At the same time, Plk1 can counteract ATR-dependent signaling and is required for eventual resumption of the cell cycle. However, what determines when Plk1 activity can resume remains unclear. Here, we use FRET-based reporters to show that a global spread of ATM activity on chromatin and phosphorylation of ATM targets including KAP1 control Plk1 re-activation. These phosphorylations are rapidly counteracted by the chromatin-bound phosphatase Wip1, allowing cell cycle restart despite persistent ATM activity present at DNA lesions. Combining experimental data and mathematical modeling, we propose a model for how the minimal duration of cell cycle arrest is controlled. Our model shows how cell cycle restart can occur before completion of DNA repair and suggests a mechanism for checkpoint adaptation in human cells. link: http://identifiers.org/pubmed/28607002

Parameters:

Name Description
Kcc2a = 1.0; Kch2cc = 1.0; Km10 = 10.0; Kt2cc = 10.0 Reaction: CellCact = ((Kcc2a+CellCact)*CellCina/(Km10+CellCina)-Kt2cc*Timeract*CellCact/(Km10+CellCact))-Kch2cc*CellCact*Effectoract/(Km10+CellCact), Rate Law: ((Kcc2a+CellCact)*CellCina/(Km10+CellCina)-Kt2cc*Timeract*CellCact/(Km10+CellCact))-Kch2cc*CellCact*Effectoract/(Km10+CellCact)
Kti2t = 10.0; Km1 = 1.0; Kd2t = 2.0 Reaction: Timeract = Kd2t*Damage*Timerinact/(Km1+Timerinact)-Kti2t*Timeract/(Km1+Timeract), Rate Law: Kd2t*Damage*Timerinact/(Km1+Timerinact)-Kti2t*Timeract/(Km1+Timeract)
Km10 = 10.0; Kd2ch = 1.0; Kcc2ch = 1.0 Reaction: Effectoract = Kd2ch*Damage*Effectorina/(Km10+Effectorina)-Kcc2ch*CellCact*Effectoract/(Km10+Effectoract), Rate Law: Kd2ch*Damage*Effectorina/(Km10+Effectorina)-Kcc2ch*CellCact*Effectoract/(Km10+Effectoract)

States:

Name Description
NHEJ [double-strand break repair via nonhomologous end joining]
HR [double-strand break repair via homologous recombination]
CellCact [Serine/threonine-protein kinase PLK1]
Effectoract [Serine/threonine-protein kinase ATR]
Effectorina [Serine/threonine-protein kinase ATR]
Timeract [Serine-protein kinase ATM]
CellCina [Serine/threonine-protein kinase PLK1]
Damage [DNA damage response, detection of DNA damage]
Timerinact [Serine-protein kinase ATM]

Observables: none

MODEL1103210001 @ v0.0.1

**Dynamic simulation of the human red blood cell metabolic network** Neema Jamshidi, Jeremy S. Edwards, Tom Fahland, G…

We have developed a Mathematica application package to perform dynamic simulations of the red blood cell (RBC) metabolic network. The package relies on, and integrates, many years of mathematical modeling and biochemical work on red blood cell metabolism. The extensive data regarding the red blood cell metabolic network and the previous kinetic analysis of all the individual components makes the human RBC an ideal 'model' system for mathematical metabolic models. The Mathematica package can be used to understand the dynamics and regulatory characteristics of the red blood cell. link: http://identifiers.org/pubmed/11294796

Parameters: none

States: none

Observables: none

Jamshidi2007 - Genome-scale metabolic network of Mycobacterium tuberculosis (iNJ661)This model is described in the artic…

BACKGROUND: Mycobacterium tuberculosis continues to be a major pathogen in the third world, killing almost 2 million people a year by the most recent estimates. Even in industrialized countries, the emergence of multi-drug resistant (MDR) strains of tuberculosis hails the need to develop additional medications for treatment. Many of the drugs used for treatment of tuberculosis target metabolic enzymes. Genome-scale models can be used for analysis, discovery, and as hypothesis generating tools, which will hopefully assist the rational drug development process. These models need to be able to assimilate data from large datasets and analyze them. RESULTS: We completed a bottom up reconstruction of the metabolic network of Mycobacterium tuberculosis H37Rv. This functional in silico bacterium, iNJ661, contains 661 genes and 939 reactions and can produce many of the complex compounds characteristic to tuberculosis, such as mycolic acids and mycocerosates. We grew this bacterium in silico on various media, analyzed the model in the context of multiple high-throughput data sets, and finally we analyzed the network in an 'unbiased' manner by calculating the Hard Coupled Reaction (HCR) sets, groups of reactions that are forced to operate in unison due to mass conservation and connectivity constraints. CONCLUSION: Although we observed growth rates comparable to experimental observations (doubling times ranging from about 12 to 24 hours) in different media, comparisons of gene essentiality with experimental data were less encouraging (generally about 55%). The reasons for the often conflicting results were multi-fold, including gene expression variability under different conditions and lack of complete biological knowledge. Some of the inconsistencies between in vitro and in silico or in vivo and in silico results highlight specific loci that are worth further experimental investigations. Finally, by considering the HCR sets in the context of known drug targets for tuberculosis treatment we proposed new alternative, but equivalent drug targets. link: http://identifiers.org/pubmed/17555602

Parameters: none

States: none

Observables: none

Duchenne muscular dystrophy (DMD) is a genetic disease that results in the death of affected boys by early adulthood.The…

Duchenne muscular dystrophy (DMD) is a genetic disease that results in the death of affected boys by early adulthood. The genetic defect responsible for DMD has been known for over 25 years, yet at present there is neither cure nor effective treatment for DMD. During early disease onset, the mdx mouse has been validated as an animal model for DMD and use of this model has led to valuable but incomplete insights into the disease process. For example, immune cells are thought to be responsible for a significant portion of muscle cell death in the mdx mouse; however, the role and time course of the immune response in the dystrophic process have not been well described. In this paper we constructed a simple mathematical model to investigate the role of the immune response in muscle degeneration and subsequent regeneration in the mdx mouse model of Duchenne muscular dystrophy. Our model suggests that the immune response contributes substantially to the muscle degeneration and regeneration processes. Furthermore, the analysis of the model predicts that the immune system response oscillates throughout the life of the mice, and the damaged fibers are never completely cleared. link: http://identifiers.org/pubmed/25013809

Parameters: none

States: none

Observables: none

Mathematical model of pro- and anti-inflammatory response, inflammation/damage and infection dynamics in BALB/c mouse wi…

The immune system is a complex system of chemical and cellular interactions that responds quickly to queues that signal infection and then reverts to a basal level once the challenge is eliminated. Here, we present a general, four-component model of the immune system's response to a Staphylococcal aureus (S. aureus) infection, using ordinary differential equations. To incorporate both the infection and the immune system, we adopt the style of compartmenting the system to include bacterial dynamics, damage and inflammation to the host, and the host response. We incorporate interactions not previously represented including cross-talk between inflammation/damage and the infection and the suppression of the anti-inflammatory pathway in response to inflammation/damage. As a result, the most relevant equilibrium of the system, representing the health state, is an all-positive basal level. The model is able to capture eight different experimental outcomes for mice challenged with intratibial osteomyelitis due to S. aureus, primarily involving immunomodulation and vaccine therapies. For further validation and parameter exploration, we perform a parameter sensitivity analysis which suggests that the model is very stable with respect to variations in parameters, indicates potential immunomodulation strategies and provides a possible explanation for the difference in immune potential for different mouse strains. link: http://identifiers.org/pubmed/24814512

Parameters:

Name Description
mu_1 = 0.12; K_B = 1.0; alpha_1 = 0.27; beta_1 = 0.01; rho_1 = 0.2 Reaction: => pro_inflammatory__P; inflammation__I, bacterial_infection__B, anti_inflammatory__A, Rate Law: BALB_c_Mouse*((alpha_1*inflammation__I+rho_1*bacterial_infection__B)*(1-pro_inflammatory__P)-(beta_1*anti_inflammatory__A+mu_1*(1-bacterial_infection__B/K_B))*pro_inflammatory__P)
K_B = 1.0; beta_4 = 5.0; g = 0.9; alpha_4 = 1.5; gamma = 0.01 Reaction: => bacterial_infection__B; inflammation__I, pro_inflammatory__P, Rate Law: BALB_c_Mouse*(((g*(1-bacterial_infection__B/K_B)+alpha_4*inflammation__I)-beta_4*pro_inflammatory__P)*bacterial_infection__B+exp((-1)*gamma*time))
mu_2 = 0.25; beta_2 = 0.135; K_B = 1.0; alpha_2 = 0.11 Reaction: => anti_inflammatory__A; pro_inflammatory__P, inflammation__I, bacterial_infection__B, Rate Law: BALB_c_Mouse*(alpha_2*pro_inflammatory__P-(beta_2*inflammation__I+mu_2*(1-bacterial_infection__B/K_B))*anti_inflammatory__A)
beta_3 = 2.0; rho_2 = 0.45; alpha_3 = 1.05; mu_3 = 0.0174 Reaction: => inflammation__I; pro_inflammatory__P, bacterial_infection__B, anti_inflammatory__A, Rate Law: BALB_c_Mouse*((alpha_3*pro_inflammatory__P+rho_2*bacterial_infection__B)-(beta_3*anti_inflammatory__A+mu_3)*inflammation__I)

States:

Name Description
inflammation I [Inflammation]
bacterial infection B [Staphylococcus aureus infection]
pro inflammatory P [inflammatory response; Th17 cell; Th1 cell]
anti inflammatory A [regulatory T-lymphocyte]

Observables: none

The paper describes a model on the trastuzumab-induced immune response in murine(mouse) HER2+ breast cancer. Created by…

The goal of this study is to develop an integrated, mathematical–experimental approach for understanding the interactions between the immune system and the effects of trastuzumab on breast cancer that overexpresses the human epidermal growth factor receptor 2 (HER2+). A system of coupled, ordinary differential equations was constructed to describe the temporal changes in tumour growth, along with intratumoural changes in the immune response, vascularity, necrosis and hypoxia. The mathematical model is calibrated with serially acquired experimental data of tumour volume, vascularity, necrosis and hypoxia obtained from either imaging or histology from a murine model of HER2+ breast cancer. Sensitivity analysis shows that model components are sensitive for 12 of 13 parameters, but accounting for uncertainty in the parameter values, model simulations still agree with the experimental data. Given theinitial conditions, the mathematical model predicts an increase in the immune infiltrates over time in the treated animals. Immunofluorescent staining results are presented that validate this prediction by showing an increased co-staining of CD11c and F4/80 (proteins expressed by dendritic cells and/or macrophages) in the total tissue for the treated tumours compared to the controls. We posit that the proposed mathematical–experimental approach can be used to elucidate driving interactions between the trastuzumab-induced responses in the tumour and the immune system that drive the stabilization of vasculature while simultaneously decreasing tumour growth—conclusions revealed by the mathematical model that were not deducible from the experimental data alone. link: http://identifiers.org/doi/10.1093/imammb/dqy014

Parameters:

Name Description
ut = 0.187 1/ms Reaction: T => ; I, Rate Law: tumor*ut*T*I
beta = 0.027 1/ms Reaction: => N; V, Rate Law: tumor*(beta+beta*V*N)
beta = 0.027 1/ms; un = 0.911 1/ms Reaction: N => ; V, I, Rate Law: tumor*(beta*V+beta*N+un*N*I)
an = 0.2 1/ms; av = 0.199 1/ms Reaction: => I; V, N, Rate Law: tumor*(av*V+an*N)
ai = 0.045 1/ms; at = 0.101 1/ms Reaction: => V; T, I, Rate Law: tumor*(at*T+ai*I)
rho = 1.523 1; g = 0.044 1/ms Reaction: => T; H, Rate Law: tumor*g*T*(rho*H+1)
gamma = 0.743 1/ms; delta = 0.284 1 Reaction: H => ; V, Rate Law: tumor*(gamma*delta*H*H+gamma*V*H)
ai = 0.045 1/ms; uv = 1.723 1/ms; at = 0.101 1/ms Reaction: V => ; T, I, Rate Law: tumor*(at*T*V+ai*I*V+uv*V*T)
an = 0.2 1/ms; av = 0.199 1/ms; ui = 0.722 1/ms Reaction: I => ; V, N, T, Rate Law: tumor*(av*V*I+an*N*I+ui*I*T)

States:

Name Description
I [immune response to tumor cell]
T [Tumor Volume]
N [necrotic cell death]
V V
H [Hypoxia]

Observables: none

MODEL1006230013 @ v0.0.1

This a model from the article: Mathematical modeling of the hypothalamic-pituitary-adrenal system activity. Jelic S,…

Mathematical modeling has proven to be valuable in understanding of the complex biological systems dynamics. In the present report we have developed an initial model of the hypothalamic-pituitary-adrenal system self-regulatory activity. A four-dimensional non-linear differential equation model of the hormone secretion was formulated and used to analyze plasma cortisol levels in humans. The aim of this work was to explore in greater detail the role of this system in normal, homeostatic, conditions, since it is the first and unavoidable step in further understanding of the role of this complex neuroendocrine system in pathophysiological conditions. Neither the underlying mechanisms nor the physiological significance of this system are fully understood yet. link: http://identifiers.org/pubmed/16112688

Parameters: none

States: none

Observables: none

BIOMD0000000399 @ v0.0.1

This is a model described in the article: Thermodynamically Consistent Model Calibration in Chemical Kinetics. Garrett…

BACKGROUND: The dynamics of biochemical reaction systems are constrained by the fundamental laws of thermodynamics, which impose well-defined relationships among the reaction rate constants characterizing these systems. Constructing biochemical reaction systems from experimental observations often leads to parameter values that do not satisfy the necessary thermodynamic constraints. This can result in models that are not physically realizable and may lead to inaccurate, or even erroneous, descriptions of cellular function. RESULTS: We introduce a thermodynamically consistent model calibration (TCMC) method that can be effectively used to provide thermodynamically feasible values for the parameters of an open biochemical reaction system. The proposed method formulates the model calibration problem as a constrained optimization problem that takes thermodynamic constraints (and, if desired, additional non-thermodynamic constraints) into account. By calculating thermodynamically feasible values for the kinetic parameters of a well-known model of the EGF/ERK signaling cascade, we demonstrate the qualitative and quantitative significance of imposing thermodynamic constraints on these parameters and the effectiveness of our method for accomplishing this important task. MATLAB software, using the Systems Biology Toolbox 2.1, can be accessed from http://www.cis.jhu.edu/~goutsias/CSS lab/software.html. An SBML file containing the thermodynamically feasible EGF/ERK signaling cascade model can be found in the BioModels database. CONCLUSIONS: TCMC is a simple and flexible method for obtaining physically plausible values for the kinetic parameters of open biochemical reaction systems. It can be effectively used to recalculate a thermodynamically consistent set of parameter values for existing thermodynamically infeasible biochemical reaction models of cellular function as well as to estimate thermodynamically feasible values for the parameters of new models. Furthermore, TCMC can provide dimensionality reduction, better estimation performance, and lower computational complexity, and can help to alleviate the problem of data overfitting. link: http://identifiers.org/pubmed/21548948

Parameters:

Name Description
k20 = 5.17656E-5 peritempermin; kr20 = 12.816 permin Reaction: x35 + x43 => x37, Rate Law: k20*x35*x43-kr20*x37
kr41 = 44.60169 permin; k41 = 0.001522817 peritempermin Reaction: x30 + x33 => x35, Rate Law: k41*x30*x33-kr41*x35
kr56 = 1.229629 permin; k56 = 0.004700229 peritempermin Reaction: x83 + x60 => x84, Rate Law: k56*x83*x60-kr56*x84
kr42 = 1.870396 permin; k42 = 0.009688174 peritempermin Reaction: x44 + x45 => x46, Rate Law: k42*x44*x45-kr42*x46
k25 = 6.871213E-4 peritempermin; kr25 = 1.218132 permin Reaction: x24 + x34 => x35, Rate Law: k25*x24*x34-kr25*x35
k52 = 0.003826571 peritempermin; kr52 = 19.85279 permin Reaction: x51 + x57 => x58, Rate Law: k52*x51*x57-kr52*x58
k6 = 4.123214E-4 permin; kr6 = 0.294324 permin Reaction: x34 => x65, Rate Law: k6*x34-kr6*x65
kr50 = 9.954943 permin; k50 = 5.464454E-4 peritempermin Reaction: x53 + x49 => x54, Rate Law: k50*x53*x49-kr50*x54
kr14 = 196.6479 permin; k14 = 6.370566E-7 peritempermin Reaction: x8 + x14 => x17, Rate Law: k14*x8*x14-kr14*x17
k49 = 10.73099 permin Reaction: x79 => x47 + x53, Rate Law: k49*x79
k8 = 5.174108E-4 peritempermin; kr8 = 0.9058936 permin Reaction: x5 + x14 => x15, Rate Law: k8*x5*x14-kr8*x15
k60 = 0.08693199 permin Reaction: x8 => x87, Rate Law: k60*x8
k5 = NaN permin Reaction: x93 => x9 + x67, Rate Law: k5*x93
k58 = 1.714511E-4 peritempermin; kr58 = 0.1138168 permin Reaction: x60 + x57 => x62, Rate Law: k58*x60*x57-kr58*x62
k3 = 31.71871 permin; kr3 = 2.220991 permin Reaction: x4 => x5, Rate Law: k3*x4-kr3*x5
k33 = 10.96212 permin; kr33 = 1.788597E-5 peritempermin Reaction: x38 => x40 + x30, Rate Law: k33*x38-kr33*x40*x30
k4 = 3.047285E-5 peritempermin; kr4 = 0.1230832 permin Reaction: x34 + x12 => x91, Rate Law: k4*x34*x12-kr4*x91
kr37 = 5.477036E-6 peritempermin; k37 = 29.34687 permin Reaction: x34 => x15 + x39, Rate Law: k37*x34-kr37*x15*x39
k45 = 6340.081 permin Reaction: x48 => x49 + x45, Rate Law: k45*x48
k59 = 6.409354 permin Reaction: x62 => x55 + x60, Rate Law: k59*x62
k22 = 1.445554E-4 peritempermin; kr22 = 0.6220457 permin Reaction: x31 + x15 => x32, Rate Law: k22*x31*x15-kr22*x32
k47 = 1632.425 permin Reaction: x50 => x51 + x45, Rate Law: k47*x50
k34 = 0.2467995 permin; kr34 = 1.283286E-4 peritempermin Reaction: x25 => x15 + x30, Rate Law: k34*x25-kr34*x15*x30
k7 = 0.003011324 permin Reaction: x5 => x8, Rate Law: k7*x5
Km36 = 7.719778E14 items; Vm36 = 615.0325 itemspermin Reaction: x40 => x31, Rate Law: Vm36*x40/(Km36+x40)
k19 = 349.772 permin; kr19 = 5.84737E-6 peritempermin Reaction: x36 => x35 + x28, Rate Law: k19*x36-kr19*x35*x28
k21 = 0.4722901 permin; kr21 = 1.714441E-5 peritempermin Reaction: x37 => x35 + x26, Rate Law: k21*x37-kr21*x35*x26
kr24 = 563.2135 permin; k24 = 0.007178843 peritempermin Reaction: x22 + x33 => x34, Rate Law: k24*x22*x33-kr24*x34
k18 = 0.004463938 peritempermin; kr18 = 11.1361 permin Reaction: x26 + x66 => x67, Rate Law: k18*x26*x66-kr18*x67
k48 = 6.874119E-4 peritempermin; kr48 = 1489.015 permin Reaction: x51 + x53 => x52, Rate Law: k48*x51*x53-kr48*x52
k32 = 14.19908 permin; kr32 = 5.54527E-5 peritempermin Reaction: x35 => x15 + x38, Rate Law: k32*x35-kr32*x15*x38
kr23 = 17.39321 permin; k23 = 420.3359 permin Reaction: x32 => x33, Rate Law: k23*x32-kr23*x33
kr44 = 0.5985189 permin; k44 = 0.001406622 peritempermin Reaction: x47 + x45 => x48, Rate Law: k44*x47*x45-kr44*x48
k55 = 1120.398 permin Reaction: x82 => x83 + x77, Rate Law: k55*x82
k57 = 19.75184 permin Reaction: x84 => x81 + x60, Rate Law: k57*x84
kr35 = 3.866434E-4 peritempermin; k35 = 1.836058 permin Reaction: x30 => x24 + x22, Rate Law: k35*x30-kr35*x24*x22

States:

Name Description
x85 [Phosphoprotein; Mitogen-activated protein kinase 1; MI:0501]
x89 [GDP; Pro-epidermal growth factor; Epidermal growth factor receptor; Ras GTPase-activating protein 1; Growth factor receptor-bound protein 2; Son of sevenless homolog 1; GTPase HRas; AP-type membrane coat adaptor complex]
x93 [GDP; Pro-epidermal growth factor; Epidermal growth factor receptor; Ras GTPase-activating protein 1; SHC-transforming protein 2; Growth factor receptor-bound protein 2; Son of sevenless homolog 1; GTPase HRas; AP-type membrane coat adaptor complex]
x62 [Phosphoprotein; Mitogen-activated protein kinase 1; MI:0501]
x26 [GDP; GTPase HRas]
x45 [RAF proto-oncogene serine/threonine-protein kinase]
x66 [Son of sevenless homolog 1; Growth factor receptor-bound protein 2; SHC-transforming protein 2; Ras GTPase-activating protein 1; Epidermal growth factor receptor; Pro-epidermal growth factor]
x91 [Pro-epidermal growth factor; Epidermal growth factor receptor; Ras GTPase-activating protein 1; SHC-transforming protein 2; Growth factor receptor-bound protein 2; AP-type membrane coat adaptor complex]
x59 [Mitogen-activated protein kinase 1; Phosphoprotein]
x44 [MI:0501]
x61 [Phosphoprotein; Mitogen-activated protein kinase 1; MI:0501]
x50 [Phosphoprotein; RAF proto-oncogene serine/threonine-protein kinase; Dual specificity mitogen-activated protein kinase kinase 1]
x31 [SHC-transforming protein 2; 605217]
x33 [SHC-transforming protein 2; Ras GTPase-activating protein 1; Epidermal growth factor receptor; Pro-epidermal growth factor]
x47 [Dual specificity mitogen-activated protein kinase kinase 1; Mitogen-activated protein kinase kinase 1Mitogen-activated protein kinase kinase 1, isoform CRA_acDNA FLJ76051, highly similar to Homo sapiens mitogen-activated protein kinase kinase 1 (MAP2K1), mRNA; 176872]
x92 [Pro-epidermal growth factor; Epidermal growth factor receptor; Ras GTPase-activating protein 1; SHC-transforming protein 2; Growth factor receptor-bound protein 2; Son of sevenless homolog 1; AP-type membrane coat adaptor complex]
x8 [Epidermal growth factor receptor; Pro-epidermal growth factor]
x28 [GTP; GTPase HRas]
x35 [Son of sevenless homolog 1; Growth factor receptor-bound protein 2; SHC-transforming protein 2; Ras GTPase-activating protein 1; Epidermal growth factor receptor; Pro-epidermal growth factor]
x43 [GTP; GTPase HRas]
x64 [SHC-transforming protein 2; Ras GTPase-activating protein 1; Epidermal growth factor receptor; Pro-epidermal growth factor]
x36 [GDP; GTPase HRas; Son of sevenless homolog 1; Growth factor receptor-bound protein 2; SHC-transforming protein 2; Ras GTPase-activating protein 1; Epidermal growth factor receptor; Pro-epidermal growth factor]
x4 [EGF:EGFR dimer [plasma membrane]; Pro-epidermal growth factor; Epidermal growth factor receptor]
x32 [SHC-transforming protein 2; Ras GTPase-activating protein 1; Epidermal growth factor receptor; Pro-epidermal growth factor]
x27 [GDP; GTPase HRas; Son of sevenless homolog 1; Growth factor receptor-bound protein 2; Ras GTPase-activating protein 1; Epidermal growth factor receptor; Pro-epidermal growth factor]
x60 [MI:0501]
x30 [Son of sevenless homolog 1; Growth factor receptor-bound protein 2]
x58 [Phosphoprotein; Mitogen-activated protein kinase 1; Dual specificity mitogen-activated protein kinase kinase 1]
x84 [Phosphoprotein; Mitogen-activated protein kinase 1; MI:0501]
x88 [Pro-epidermal growth factor; Epidermal growth factor receptor; Growth factor receptor-bound protein 2; Ras GTPase-activating protein 1; Son of sevenless homolog 1; AP-type membrane coat adaptor complex]
x34 [Growth factor receptor-bound protein 2; SHC-transforming protein 2; Ras GTPase-activating protein 1; Epidermal growth factor receptor; Pro-epidermal growth factor]
x51 [Dual specificity mitogen-activated protein kinase kinase 1; Phosphoprotein]
x94 [GTP; Pro-epidermal growth factor; Epidermal growth factor receptor; Ras GTPase-activating protein 1; SHC-transforming protein 2; Growth factor receptor-bound protein 2; Son of sevenless homolog 1; GTPase HRas; AP-type membrane coat adaptor complex]
x29 [GTP; GTPase HRas; Son of sevenless homolog 1; Growth factor receptor-bound protein 2; Ras GTPase-activating protein 1; Epidermal growth factor receptor; Pro-epidermal growth factor]
x53 [MI:0501]
x37 [GTP; GTPase HRas; Son of sevenless homolog 1; Growth factor receptor-bound protein 2; SHC-transforming protein 2; Ras GTPase-activating protein 1; Epidermal growth factor receptor; Pro-epidermal growth factor]
x5 [Phosphoprotein; Pro-epidermal growth factor; Epidermal growth factor receptor]
x63 [SHC-transforming protein 2; Ras GTPase-activating protein 1; Pro-epidermal growth factor; Epidermal growth factor receptor]
x48 [RAF proto-oncogene serine/threonine-protein kinase; Dual specificity mitogen-activated protein kinase kinase 1]
x52 [Phosphoprotein; Protein phosphatase 1 regulatory subunit 12C; Dual specificity mitogen-activated protein kinase kinase 1]
x83 [Mitogen-activated protein kinase 1; Phosphoprotein]
x49 [Dual specificity mitogen-activated protein kinase kinase 1; Mitogen-activated protein kinase kinase 1Mitogen-activated protein kinase kinase 1, isoform CRA_acDNA FLJ76051, highly similar to Homo sapiens mitogen-activated protein kinase kinase 1 (MAP2K1), mRNA; Phosphoprotein; 176872]
x65 [Growth factor receptor-bound protein 2; SHC-transforming protein 2; Ras GTPase-activating protein 1; Pro-epidermal growth factor; Epidermal growth factor receptor]

Observables: none

The paper describes a model of oncolytic virotherapy. Created by COPASI 4.26 (Build 213) This model is described in t…

Oncolytic virotherapy is an experimental cancer treatment that uses genetically engineered viruses to target and kill cancer cells. One major limitation of this treatment is that virus particles are rapidly cleared by the immune system, preventing them from arriving at the tumour site. To improve virus survival and infectivity Kim et al. (Biomaterials 32(9):2314-2326, 2011) modified virus particles with the polymer polyethylene glycol (PEG) and the monoclonal antibody herceptin. Whilst PEG modification appeared to improve plasma retention and initial infectivity, it also increased the virus particle arrival time. We derive a mathematical model that describes the interaction between tumour cells and an oncolytic virus. We tune our model to represent the experimental data by Kim et al. (2011) and obtain optimised parameters. Our model provides a platform from which predictions may be made about the response of cancer growth to other treatment protocols beyond those in the experiments. Through model simulations, we find that the treatment protocol affects the outcome dramatically. We quantify the effects of dosage strategy as a function of tumour cell replication and tumour carrying capacity on the outcome of oncolytic virotherapy as a treatment. The relative significance of the modification of the virus and the crucial role it plays in optimising treatment efficacy are explored. link: http://identifiers.org/pubmed/29644518

Parameters:

Name Description
a = 0.0 1; di = 0.0 1/d Reaction: => V; I, Rate Law: tme*burst(a, di, I)
di = 0.0 1/d Reaction: I =>, Rate Law: tme*di*I
r = 0.037 1/d; L = 3.49E9 1 Reaction: => S, Rate Law: tme*tg(r, L, S)
b = 0.0 1/d Reaction: S => I; V, T, Rate Law: tme*inf(b, S, V, T)
dv = 0.0 1/d Reaction: V =>, Rate Law: tme*dv*V

States:

Name Description
S [neoplastic cell]
I [neoplastic cell]
T [neoplastic cell]
V [Oncolytic Virus]

Observables: none

This is a mathematical model using a Gompertz growth law to describe the in vivo dynamics of a cancer under treatment wi…

Oncolytic viruses are genetically engineered to treat growing tumours and represent a very promising therapeutic strategy. Using a Gompertz growth law, we discuss a model that captures the in vivo dynamics of a cancer under treatment with an oncolytic virus. With the aid of local stability analysis and bifurcation plots, the typical interactions between virus and tumour are investigated. The system shows a singular equilibrium and a number of nonlinear behaviours that have interesting biological consequences, such as long-period oscillations and bistable states where two different outcomes can occur depending on the initial conditions. Complete tumour eradication appears to be possible only for parameter combinations where viral characteristics match well with the tumour growth rate. Interestingly, the model shows that therapies with a high initial injection or involving a highly effective virus do not universally result in successful strategies for eradication. Further, the use of additional, "boosting" injection schedules does not always lead to complete eradication. Our framework, instead, suggests that low viral loads can be in some cases more effective than high loads, and that a less resilient virus can help avoid high amplitude oscillations between tumours and virus. Finally, the model points to a number of interesting findings regarding the role of oscillations and bistable states between a tumour and an oncolytic virus. Strategies for the elimination of such fluctuations depend strongly on the initial viral load and the combination of parameters describing the features of the tumour and virus. link: http://identifiers.org/pubmed/31400344

Parameters:

Name Description
m = 0.1; K = 100.0 Reaction: => U, Rate Law: compartment*m*ln(K/U)*U
xi = 0.01 Reaction: I => V, Rate Law: compartment*xi*I
gamma = 0.1 Reaction: V =>, Rate Law: compartment*gamma*V

States:

Name Description
I [neoplastic cell; infected cell]
U [neoplastic cell; uninfected]
V [Oncolytic Virus]

Observables: none

MODEL1009150002 @ v0.0.1

This is the genome-scale metabolic network described in the article: Computational reconstruction of tissue-specific m…

The computational study of human metabolism has been advanced with the advent of the first generic (non-tissue specific) stoichiometric model of human metabolism. In this study, we present a new algorithm for rapid reconstruction of tissue-specific genome-scale models of human metabolism. The algorithm generates a tissue-specific model from the generic human model by integrating a variety of tissue-specific molecular data sources, including literature-based knowledge, transcriptomic, proteomic, metabolomic and phenotypic data. Applying the algorithm, we constructed the first genome-scale stoichiometric model of hepatic metabolism. The model is verified using standard cross-validation procedures, and through its ability to carry out hepatic metabolic functions. The model's flux predictions correlate with flux measurements across a variety of hormonal and dietary conditions, and improve upon the predictive performance obtained using the original, generic human model (prediction accuracy of 0.67 versus 0.46). Finally, the model better predicts biomarker changes in genetic metabolic disorders than the generic human model (accuracy of 0.67 versus 0.59). The approach presented can be used to construct other human tissue-specific models, and be applied to other organisms. link: http://identifiers.org/pubmed/20823844

Parameters: none

States: none

Observables: none

MODEL1108260010 @ v0.0.1

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

A model of a proteolytic positive-feedback loop, similar in general terms to feedback loops that occur in blood coagulation and other systems, has been examined by both explicit and numerical analysis. In this loop, modeled as a closed system, each enzyme (E1, E2) catalyzes the formation of the other from its respective zymogen (Z1, Z2), and both enzymes are subject to irreversible inhibition. The system shows three major characteristics. (1) No significant Z1 or Z2 activation occurs unless the combination of initial conditions and kinetic parameters is above a threshold level. This threshold occurs when the product of the enzyme generation rates equals the product of their inhibition rates. When the formation-rate product is less than the inhibition-rate product, there is no response: E1 and E2 generation is minimal and the lag time is effectively infinite. Conversely, when the generation-rate product exceeds the inhibition-rate product, explosive formation of both E1 and E2 is seen. For responses exceeding the threshold, the following obtain. (2) The lag time in E1 and E2 generation is a highly nonlinear function of the zymogen concentrations and the enzyme generation and inhibition rates. In contrast, there is a simple logarithmic relationship between the lag time and the initial trace concentration of the enzyme that is responsible for initiating the system; in this model, E1. (3) The extent of Z1 and Z2 activation is similarly a nonlinear function of the conditions and parameters but is independent of the initiating trace level of E1.(ABSTRACT TRUNCATED AT 250 WORDS) link: http://identifiers.org/pubmed/8512937

Parameters: none

States: none

Observables: none

Jiang2007 - GSIS system, Pancreatic Beta CellsDescription of a core kinetic model of the glucose-stimulated insulin secr…

The construction and characterization of a core kinetic model of the glucose-stimulated insulin secretion system (GSIS) in pancreatic beta cells is described. The model consists of 44 enzymatic reactions, 59 metabolic state variables, and 272 parameters. It integrates five subsystems: glycolysis, the TCA cycle, the respiratory chain, NADH shuttles, and the pyruvate cycle. It also takes into account compartmentalization of the reactions in the cytoplasm and mitochondrial matrix. The model shows expected behavior in its outputs, including the response of ATP production to starting glucose concentration and the induction of oscillations of metabolite concentrations in the glycolytic pathway and in ATP and ADP concentrations. Identification of choke points and parameter sensitivity analysis indicate that the glycolytic pathway, and to a lesser extent the TCA cycle, are critical to the proper behavior of the system, while parameters in other components such as the respiratory chain are less critical. Notably, however, sensitivity analysis identifies the first reactions of nonglycolytic pathways as being important for the behavior of the system. The model is robust to deletion of malic enzyme activity, which is absent in mouse pancreatic beta cells. The model represents a step toward the construction of a model with species-specific parameters that can be used to understand mouse models of diabetes and the relationship of these mouse models to the human disease state. link: http://identifiers.org/pubmed/17514510

Parameters:

Name Description
K1ATP=6.3E-5; V1=5.0E-4; K1GLC=1.0E-4 Reaction: GLC + ATP_cyt => F6P + ADP_cyt, Rate Law: CYTOPLASM*V1*ATP_cyt*GLC/((K1GLC+GLC)*(K1ATP+ATP_cyt))
kminus2=1400.0; k4=214.0; v31_MDH=3.8617E-7; k3=4650.0; k2=3.5E7; kminus1=26.0; kminus4=260000.0; kminus3=570000.0; k1=3.4E7 Reaction: NADH_cyt + OXA_cyt => Mal_cyt + NAD, Rate Law: CYTOPLASM*v31_MDH*(k1*k2*k3*k4*NADH_cyt*OXA_cyt-kminus1*kminus2*kminus3*kminus4*Mal_cyt*NAD)/(kminus1*(kminus2+k3)*k4+k1*(kminus2+k3)*k4*NADH_cyt+kminus1*(kminus2+k3)*kminus4*NAD+k2*k3*k4*OXA_cyt+kminus1*kminus2*kminus3*Mal_cyt+k1*k2*(k3+k4)*NADH_cyt*OXA_cyt+(kminus1+kminus2)*kminus3*kminus4*Mal_cyt*NAD+k1+kminus2+kminus3*NADH_cyt*Mal_cyt+k1*k2*kminus3*NADH_cyt*OXA_cyt*Mal_cyt+k2*k3*kminus4*OXA_cyt*NAD+k2*kminus3*kminus4*OXA_cyt*Mal_cyt*NAD)
KcR=31.44; Ks=5.0E-4; v11_ACO=3.8617E-7; KcF=20.47; Kp=1.1E-4 Reaction: Cit => IsoCit, Rate Law: MATRIX*(KcF*Kp*Cit-KcR*Ks*IsoCit)*v11_ACO/(Ks*IsoCit+Kp*Cit+Ks*Kp)
KmQ=7.5E-6; KmC=4.5E-4; Kib=2.0E-5; KmP=6.0E-4; Kip=0.07; Kiq=5.0E-6; Kir=6.7E-6; v15_SCS=3.8617E-7; KmB=3.5E-5; Kc2=100.0; KmA=5.0E-6; KmP2=6.0E-4; Kia=4.0E-4; Keq=8.375; Kic=3.0E-5; Kc1=100.0; KmC2=4.5E-4 Reaction: GDP + SCoA + Pi => Suc + GTP + CoA, Rate Law: MATRIX*(GDP*SCoA*pi-Suc*GTP*CoA/Keq)*(Kc1*v15_SCS+Kc2*v15_SCS*(KmC*Suc/KmC2*Kip+pi/KmC2))/(Kia*KmB*pi+KmB*GDP*pi+KmA*SCoA*pi+KmC*GDP*SCoA+GDP*SCoA*pi+GDP*SCoA*pi*pi/KmC2+Kia*KmB*KmC*Suc/Kip+Kia*KmB*KmC*Suc*GTP/Kip/Kiq+Kia*KmB*KmC*Suc*CoA/Kip/Kir+Kia*KmB*Kic*GTP*CoA/KmQ/Kir+Kia*KmB*KmC*Suc*GTP*CoA/Kip/KmQ/Kir+Kia*KmB*KmC*Suc*Suc*GTP*CoA/Kip/KmP2/KmQ/Kir+Kia*KmB*pi*GTP/Kiq+Kia*KmB*pi*CoA/Kir+Kia*KmB*pi*GTP*CoA/KmQ/Kir+Kia*KmB*pi*Suc*GTP*CoA/KmP2/KmQ/Kir+KmB*KmC*GDP*Suc/Kip+KmA*KmC*SCoA*Suc/Kip+KmC*GDP*SCoA*Suc/Kip+KmC*GDP*SCoA*pi*Suc/KmC2/Kip+KmA*SCoA*pi*GTP/Kiq+KmB*GDP*pi*CoA/Kir+KmA*KmC*SCoA*Suc*GTP/Kip/Kiq+KmB*KmC*GDP*Suc*CoA/Kip/Kir)
KmS1=9.0E-4; v32_AspTA=3.8617E-7; KmP2=0.004; Keq=6.2; KiP2=0.0083; KcF=300.0; KmP1=4.0E-5; KiS1=0.002; KcR=1000.0; KmS2=1.0E-4 Reaction: Asp_cyt + OG_cyt => OXA_cyt + Glu_cyt, Rate Law: CYTOPLASM*KcF*KcR*v32_AspTA*(Asp_cyt*OG_cyt-OXA_cyt*Glu_cyt/Keq)/(KcR*KmS2*Asp_cyt+KcR*KmS1*OG_cyt+KcF*KmP2*OXA_cyt/Keq+KcF*KmP1*Glu_cyt/Keq+KcR*Asp_cyt*OG_cyt+KcF*KmP2*Asp_cyt*OXA_cyt/(Keq*KiS1)+KcF*OXA_cyt*Glu_cyt/Keq+KcR*KmS1*OG_cyt*Glu_cyt/KiP2)
KiP2=0.0028; v22_AGC=3.3211E-4; KiS2=0.0032; KcR=10.0; KcF=10.0; alpha=1.0; delta=1.0; KiS1=8.0E-5; KiP1=1.8E-4; beta=1.0; gamma=1.0 Reaction: Glu_cyt + Asp => Asp_cyt + Glu, Rate Law: MATRIX*(Asp*Glu_cyt/alpha/KiS1/KiS2*KcF-Glu*Asp_cyt/beta/KiP1/KiP2*KcR)*v22_AGC/(1+Asp/KiS1+Glu_cyt/KiS2+Glu/KiP1+Asp_cyt/KiP2+Asp*Glu_cyt/alpha/KiS1/KiS2+Glu*Asp_cyt/beta/KiP1/KiP2+Glu_cyt*Asp_cyt/gamma/KiS2/KiP2+Asp*Glu/delta/KiS1/KiP1)
e=6.4E-4; v12_IDHa=3.8617E-7; b=29.6; f=3.6E-4; d=7.8E-5; KcF=105.0; c=2.3E-4 Reaction: IsoCit + NAD_p => OG + NADH; ADP, Rate Law: MATRIX*KcF*v12_IDHa*(IsoCit*IsoCit+b*ADP*IsoCit)/(IsoCit*IsoCit+c*IsoCit+d*ADP+e*ADP*IsoCit+f)
Kiq=3.5E-5; KmP=5.9E-7; v9_PDC=3.8617E-7; Kic=1.8E-4; KmC=5.0E-5; KmA=2.5E-5; KcF=856.0; KmR=6.9E-7; KmB=1.3E-5; Kip=6.0E-5; Kib=3.0E-4; Kir=3.6E-5; Kia=5.5E-4 Reaction: Pyr + CoA + NAD_p => CO2 + Acetyl_CoA + NADH, Rate Law: MATRIX*KcF*v9_PDC*Pyr*CoA*NAD_p/(KmC*Pyr*CoA+KmB*Pyr*NAD_p+KmA*CoA*NAD_p+Pyr*CoA*NAD_p+KmA*KmP*Kib*Kic/KmR/Kip/Kiq*Acetyl_CoA*NADH+KmC/Kir*Pyr*CoA*NADH+KmB/Kiq*Pyr*NAD_p*Acetyl_CoA+KmA*KmP*Kib*Kic/KmR/Kip/Kia/Kiq*Pyr*Acetyl_CoA*NADH)
V=3.99E-8; K=3.4E-5; v37_GUT2P=0.001 Reaction: G3P + FAD => FADH2 + DHAP, Rate Law: CYTOPLASM*V*v37_GUT2P*G3P/(K+G3P)
KiP1=0.0014; KiS1=3.0E-4; KiS2=7.0E-4; KiP2=1.7E-4; alpha=1.0; delta=1.0; beta=1.0; gamma=1.0; v30_OGC=3.3211E-4; KcR=4.83; KcF=3.675 Reaction: Mal_cyt + OG => OG_cyt + Mal, Rate Law: MATRIX*(OG*Mal_cyt/alpha/KiS1/KiS2*KcF-Mal*OG_cyt/beta/KiP1/KiP2*KcR)*v30_OGC/(1+OG/KiS1+Mal_cyt/KiS2+Mal/KiP1+OG_cyt/KiP2+OG*Mal_cyt/alpha/KiS1/KiS2+Mal*OG_cyt/beta/KiP1/KiP2+Mal_cyt*OG_cyt/gamma/KiS2/KiP2+OG*Mal/delta/KiS1/KiP1)
KmP1=1.08E-6; KiP2=1.19E-5; Keq=8.99; KiS1=7.6E-5; KiS2=2.4E-7; KcR=0.3; KmP2=2.42E-5; KcF=2.18; KmS1=3.9E-5; v35_ACD=3.3211E-5; KmS2=1.2E-7; KiP1=7.53E-5 Reaction: FADH2 + ETFox => ETFred + FAD, Rate Law: MATRIX*KcF*KcR*v35_ACD*(FADH2*ETFox-ETFred*FAD/Keq)/(KcR*KiS1*KmS2+KcR*KmS2*FADH2+KcR*KmS1*ETFox+KcF*KmP2*ETFred/Keq+KcF*KmP1*FAD/Keq+KcR*FADH2*ETFox+KcF*KmP2*FADH2*ETFred/(Keq*KiS1)+KcF*ETFred*FAD/Keq+KcR*KmS1*ETFox*FAD/KiP2+KcR*FADH2*ETFox*ETFred/KiP1+KcF*ETFox*ETFred*FAD/(KiS2*Keq))
KiS2=4.4E-4; v42_CIC=3.3211E-4; KiS1=1.3E-4; KcF=5.6; KcR=3.5; alpha=1.0; delta=1.0; beta=1.0; gamma=1.0; KiP1=3.3E-4; KiP2=4.18E-5 Reaction: IsoCitcyt + Mal => Mal_cyt + IsoCit, Rate Law: MATRIX*(IsoCitcyt*Mal/alpha/KiS1/KiS2*KcF-Mal_cyt*IsoCit/beta/KiP1/KiP2*KcR)*v42_CIC/(1+IsoCitcyt/KiS1+Mal/KiS2+Mal_cyt/KiP1+IsoCit/KiP2+IsoCitcyt*Mal/alpha/KiS1/KiS2+Mal_cyt*IsoCit/beta/KiP1/KiP2+Mal*IsoCit/gamma/KiS2/KiP2+IsoCitcyt*Mal_cyt/delta/KiS1/KiP1)
Kb=4.5E-6; v10_CS=3.8617E-7; Kia=5.0E-6; Kc=3.9E-5; Ka=5.0E-6; Keq=1.8E7; Kid=0.0043; V=0.004833; Kib=4.5E-6 Reaction: Cit_cyt + CoA_cyt => OXA_cyt + Acetyl_CoA_cyt, Rate Law: CYTOPLASM*Kid*Kc*V*Acetyl_CoA_cyt*OXA_cyt*v10_CS/(Acetyl_CoA_cyt*OXA_cyt+Ka*OXA_cyt+Kb*Acetyl_CoA_cyt+Kia*Kib)/(Keq*Kia*Kb)
K4NAD=0.001; K4GAP=0.001; V4=0.01 Reaction: GAP + NAD => DPG + NADH_cyt, Rate Law: CYTOPLASM*V4*NAD*GAP/((K4GAP+GAP)*(K4NAD+NAD))
KmP=3.0E-4; Kib=7.4E-4; KmR=6.0E-4; KmC=5.0E-5; Kic=1.0E-4; KmB=2.5E-5; Kia=7.2E-4; KmA=2.2E-4; Kir=2.5E-5; Kip=1.1E-6; Kiq=8.1E-5; v14_OGDC=3.8617E-7; KcF=177.0 Reaction: OG + CoA + NAD_p => CO2 + SCoA + NADH, Rate Law: MATRIX*KcF*v14_OGDC*OG*CoA*NAD_p/(KmC*OG*CoA+KmB*OG*NAD_p+KmA*CoA*NAD_p+OG*CoA*NAD_p+KmA*KmP*Kib*Kic/KmR/Kip/Kiq*SCoA*NADH+KmC/Kir*OG*CoA*NADH+KmB/Kiq*OG*NAD_p*SCoA+KmA*KmP*Kib*Kic/KmR/Kip/Kia/Kiq*OG*SCoA*NADH)
v34_ETF_QO=3.3211E-5; KcR=101.0; KiS1=3.1E-7; KmS1=3.1E-7; KmP1=3.2E-7; Keq=0.66; KiP2=3.0E-7; KmP2=4.2E-9; KmS2=3.9E-7; KcF=78.0 Reaction: ETFred + Q => ETFox + QH2, Rate Law: MATRIX*KcF*KcR*v34_ETF_QO*(ETFred*Q-ETFox*QH2/Keq)/(KcR*KmS2*ETFred+KcR*KmS1*Q+KcF*KmP2*ETFox/Keq+KcF*KmP1*QH2/Keq+KcR*ETFred*Q+KcF*KmP2*ETFred*ETFox/(Keq*KiS1)+KcF*ETFox*QH2/Keq+KcR*KmS1*Q*QH2/KiP2)
KmS1=9.0E-4; KmP2=0.004; Keq=6.2; KiP2=0.0083; KcF=300.0; KmP1=4.0E-5; KiS1=0.002; KcR=1000.0; KmS2=1.0E-4; v21_AspTA=3.8617E-7 Reaction: OXA + Glu => Asp + OG, Rate Law: MATRIX*KcF*KcR*v21_AspTA*(OXA*Glu-Asp*OG/Keq)/(KcR*KmS2*OXA+KcR*KmS1*Glu+KcF*KmP2*Asp/Keq+KcF*KmP1*OG/Keq+KcR*OXA*Glu+KcF*KmP2*OXA*Asp/(Keq*KiS1)+KcF*Asp*OG/Keq+KcR*KmS1*Glu*OG/KiP2)
KmP1=3.0E-7; KmP2=1.5E-6; KmS1=3.0E-5; KiP2=5.6E-6; Keq=0.037; KiS1=4.1E-6; v16_SDH=9.9211E-5; KmS2=6.9E-5; KcR=1.73; KcF=69.3 Reaction: Suc + Q => Fum + QH2, Rate Law: MATRIX*KcF*KcR*v16_SDH*(Suc*Q-Fum*QH2/Keq)/(KcR*KmS2*Suc+KcR*KmS1*Q+KcF*KmP2*Fum/Keq+KcF*KmP1*QH2/Keq+KcR*Suc*Q+KcF*KmP2*Suc*Fum/(Keq*KiS1)+KcF*Fum*QH2/Keq+KcR*KmS1*Q*QH2/KiP2)
KmS1=9.2E-6; KmP1=9.9E-6; KcF=498.0; v24_Complex_I=3.3211E-4; KmP2=5.9E-5; KcR=229.0; KiP2=9.8E-8; KiS1=2.1E-8; KmS2=2.6E-4; Keq=407.9 Reaction: NADH + Q => NAD_p + QH2, Rate Law: MATRIX*KcF*KcR*v24_Complex_I*(NADH*Q-NAD_p*QH2/Keq)/(KcR*KmS2*NADH+KcR*KmS1*Q+KcF*KmP2*NAD_p/Keq+KcF*KmP1*QH2/Keq+KcR*NADH*Q+KcF*KmP2*NADH*NAD_p/(Keq*KiS1)+KcF*NAD_p*QH2/Keq+KcR*KmS1*Q*QH2/KiP2)
Knadp=0.011; Kcat=0.333; Kmal=1.25E-4; v39_MDH=3.8617E-7 Reaction: Mal_cyt + NADP_cyt => NADPH_cyt + PYR_cyt, Rate Law: CYTOPLASM*v39_MDH*Kcat*Mal_cyt*NADP_cyt/((Kmal+Mal_cyt)*(Knadp+NADP_cyt))
KiS1=0.0087; Keq=0.69; KmS2=4.0E-4; KmP2=4.0E-4; KcR=0.15; KcF=337.0; KiP2=0.012; v20_AlaTA=3.8617E-7; KmS1=0.002; KmP1=0.032 Reaction: Ala + OG => Glu + Pyr, Rate Law: MATRIX*KcF*KcR*v20_AlaTA*(Ala*OG-Glu*Pyr/Keq)/(KcR*KmS2*Ala+KcR*KmS1*OG+KcF*KmP2*Glu/Keq+KcF*KmP1*Pyr/Keq+KcR*Ala*OG+KcF*KmP2*Ala*Glu/(Keq*KiS1)+KcF*Glu*Pyr/Keq+KcR*KmS1*OG*Pyr/KiP2)
k3b=0.05; k3f=1.0 Reaction: FBP => GAP, Rate Law: CYTOPLASM*(k3f*FBP-k3b*GAP^2)
Kib=4.0E-6; v10_CS=3.8617E-7; V=0.005267; Kia=1.0E-5; Ka=1.18E-5; Kb=4.8E-6 Reaction: OXA + Acetyl_CoA => Cit + CoA, Rate Law: MATRIX*V*Acetyl_CoA*OXA*v10_CS/(Acetyl_CoA*OXA+Ka*OXA+Kb*Acetyl_CoA+Kia*Kib)
KiS2=4.4E-4; KiS1=1.3E-4; KcF=5.6; KcR=3.5; alpha=1.0; delta=1.0; v33_CIC=3.3211E-4; beta=1.0; gamma=1.0; KiP1=3.3E-4; KiP2=4.18E-5 Reaction: Cit_cyt + Mal => Mal_cyt + Cit, Rate Law: MATRIX*(Cit_cyt*Mal/alpha/KiS1/KiS2*KcF-Mal_cyt*Cit/beta/KiP1/KiP2*KcR)*v33_CIC/(1+Cit_cyt/KiS1+Mal/KiS2+Mal_cyt/KiP1+Cit/KiP2+Cit_cyt*Mal/alpha/KiS1/KiS2+Mal_cyt*Cit/beta/KiP1/KiP2+Mal*Cit/gamma/KiS2/KiP2+Cit_cyt*Mal_cyt/delta/KiS1/KiP1)
k9b=10000.0; k9f=10000.0 Reaction: AMP + ATP_cyt => ADP_cyt, Rate Law: CYTOPLASM*(k9f*AMP*ATP_cyt-k9b*ADP_cyt^2)
V=0.0399; K=34.0; v38_GUT2P=0.001 Reaction: NADH_cyt + DHAP => G3P + NAD, Rate Law: CYTOPLASM*V*v38_GUT2P*NADH_cyt/(K+NADH_cyt)
k8f=1000.0; k8b=0.143 Reaction: PYR_cyt + NADH_cyt => LAC + NAD, Rate Law: CYTOPLASM*(k8f*NADH_cyt*PYR_cyt-k8b*NAD*LAC)
k2=0.017; K2ATP=1.0E-5; V2=0.0015; K2=1.6E-9 Reaction: F6P + ATP_cyt => FBP + ADP_cyt; AMP, Rate Law: CYTOPLASM*V2*ATP_cyt*F6P^2/((K2*(1+k2*(ATP_cyt/AMP)^2)+F6P^2)*(K2ATP+ATP_cyt))
KcR=20.0; KmB=0.00163; KcF=200.0; Kic=1.3E-4; Kia=1.5E-4; v36_PC=3.8617E-7; Kiq=1.9E-4; Kib=0.0016; Keq=9.0; KmR=5.1E-5; KmC=3.7E-4; KmQ=2.4E-4; Kip=0.0079; Kir=2.4E-4; KmP=0.016; KmA=1.1E-4 Reaction: ATP + CO2 + Pyr => Pi + ADP + OXA, Rate Law: MATRIX*KcF*KcR*v36_PC*(ATP*CO2*Pyr-pi*ADP*OXA/Keq)/(Kia*KmB*KcR*Pyr+KmC*KcR*ATP*CO2+KmA*KcR*CO2*Pyr+KmB*KcR*ATP*Pyr+KcR*ATP*CO2*Pyr+Kip*KmQ*KcF*OXA/Keq+KmQ*KcF*pi*OXA/Keq+KmP*KcF*ADP*OXA/Keq+KmR*KcF*pi*ADP/Keq+KcF*pi*ADP*OXA/Keq+Kia*KmB*KcR*Pyr*pi/Kip+Kia*KmB*KcR*Pyr*ADP/Kia+Kiq*KmP*KcF*CO2*OXA/Kib/Keq+Kia*KmP*KcF*ATP*OXA/Kia/Keq+KmA*KcR*ATP*CO2*OXA/Kir+KmR*KcF*Pyr*pi*ADP/Kic/Keq+KmA*KcR*CO2*Pyr*ADP/Kiq+KmA*KcR*CO2*Pyr*pi/Kip+KmP*KcF*CO2*ADP*OXA/Kib/Keq+KmQ*KcF*CO2*pi*OXA/Kib/Keq)
Kp=2.5E-5; Ks=5.0E-6; KcF=800.0; v17_FM=3.8617E-7; KcR=900.0 Reaction: Fum => Mal, Rate Law: MATRIX*(KcF*Kp*Fum-KcR*Ks*Mal)*v17_FM/(Ks*Mal+Kp*Fum+Ks*Kp)
Km=0.01295; Kcat=130.5; v44_MDH=3.8617E-7 Reaction: Mal + NADP_p => NADPH + Pyr, Rate Law: MATRIX*v44_MDH*Kcat*Mal/(Km+Mal)
KcR=31.44; v29_ACO=3.8617E-7; Ks=5.0E-4; KcF=20.47; Kp=1.1E-4 Reaction: Cit_cyt => IsoCitcyt, Rate Law: CYTOPLASM*(KcF*Kp*Cit_cyt-KcR*Ks*IsoCitcyt)*v29_ACO/(Ks*IsoCitcyt+Kp*Cit_cyt+Ks*Kp)
v40_AAC=3.3211E-4; V=0.1667; K=0.012 Reaction: ADP_cyt => ADP, Rate Law: MATRIX*V*v40_AAC*ADP_cyt/(K+ADP_cyt)
KiP2=0.0019; KmP2=1.7E-4; KcF=0.39; KcR=0.04; v18_MDH=3.8617E-7; KmP1=0.0016; KiS1=1.1E-5; KiP1=0.0071; KmS1=7.2E-5; KiS2=1.0E-4; KmS2=1.1E-4 Reaction: Mal + NAD_p => NADH + OXA, Rate Law: MATRIX*(KcF*Mal*NAD_p/KiS1/KmS2-KcR*OXA*NADH/KmP1/KiP2)*v18_MDH/(1+Mal/KiS1+KmS1*NAD_p/KiS1/KmS2+KmP2*OXA/KmP1/KiP2+NADH/KiP2+Mal*NAD_p/KiS1/KmS2+KmP2*Mal*OXA/KiS1/KmP1/KiP2+KmS1*NAD_p*NADH/KiS1/KmS2/KiP2+OXA*NADH/KmP1*KiP2+Mal*NAD_p*OXA/KiS1/KmS2/KiP1+NAD_p*OXA*NADH/KiS2/KmP1/KiP2)
k5b=500.0; k5f=1000.0 Reaction: DPG + ADP_cyt => PEP + ATP_cyt, Rate Law: CYTOPLASM*(k5f*DPG*ADP_cyt-k5b*PEP*ATP_cyt)
flow = 0.011 Reaction: LAC =>, Rate Law: CYTOPLASM*LAC*flow
v41_IDHc=3.8617E-7; phir13=1.3E-10; phir123=4.6E-14; phi12=9.0E-8; phi0=0.051; phir23=9.4E-8; phi2=9.6E-7; phir1=3.7E-7; phir12=6.0E-12; phir2=2.9E-5; phir3=2.5E-4; phir0=0.066; phi1=9.5E-8 Reaction: IsoCitcyt + NADP_cyt => OG_cyt + NADPH_cyt; CO2, Rate Law: CYTOPLASM*v41_IDHc*(IsoCitcyt*NADP_cyt/(phi0*IsoCitcyt*NADP_cyt+phi1*NADP_cyt+phi2*IsoCitcyt+phi12)-OG_cyt*NADPH_cyt*CO2/(phir0*OG_cyt*NADPH_cyt*CO2+phir1*NADPH_cyt*CO2+phir2*OG_cyt*CO2+phir3*OG_cyt*NADPH_cyt+phir12*CO2+phir13*NADPH_cyt+phir23*OG_cyt+phir123))
V=0.075; v28_Complex_V=0.0033211; Km=0.0045; Ki=0.047 Reaction: ADP + Pi => ATP + H2O, Rate Law: MATRIX*v28_Complex_V*V*ADP/(Km+ADP+ADP*ADP/Ki)
KmB=3.0E-6; Kb2=5.7E-6; KcF=426.8; Kq2=1.9E-6; v25_Complex_III=9.963E-9; Kq1=2.8E-6; Kb1=5.4E-6; KmA=2.8E-5; k8=622.1 Reaction: QH2 + Cytc3p => Q + Cytc2p, Rate Law: MT_IMS*KcF*v25_Complex_III*QH2*Cytc3p/((KmA*Kq2*Kb2+KmA*Kq2*Cytc3p+KcF/k8*Kq1*QH2*Kb1+KcF/k8*Kq1*QH2*Cytc3p)*Cytc2p+KmA*Cytc3p+KmB*QH2+QH2*Cytc3p)

States:

Name Description
G3P [sn-Glycerol 3-phosphate; sn-glycerol 3-phosphate]
Cit [Citrate; citric acid]
Ala [L-Alanine; L-alanine]
SCoA [Succinyl-CoA; succinyl-CoA]
Glu cyt [L-Glutamate; L-glutamic acid]
GDP [GDP; GDP]
OXA [Oxaloacetate; oxaloacetic acid]
FADH2 [FADH2; FADH2]
IsoCitcyt [Isocitrate; isocitric acid]
Asp [L-Aspartate; L-aspartic acid]
OG cyt [2-Oxoglutarate; 2-oxoglutaric acid]
QH2 [ubiquinol; Ubiquinol]
GAP [D-Glyceraldehyde 3-phosphate; D-glyceraldehyde 3-phosphate]
Acetyl CoA cyt [Acetyl-CoA; acetyl-CoA]
ATP cyt [C0002]
ETFox [Electron-transferring flavoprotein]
PEP [Phosphoenolpyruvate; phosphoenolpyruvate]
NAD [NAD(+); NAD+]
H2O [H2O; water]
ADP [C0008]
OG [2-Oxoglutarate; 2-oxoglutaric acid]
Q [ubiquinones; Ubiquinone]
DPG [3-Phospho-D-glyceroyl phosphate; 3-phospho-D-glyceroyl dihydrogen phosphate]
ATP [C0002]
AMP [AMP; AMP]
DHAP [Glycerone phosphate; dihydroxyacetone phosphate]
GTP [GTP; GTP]
Mal [(S)-Malate; (S)-malic acid]
NAD p [NAD+; NAD(+)]
NADH cyt [NADH; NADH]
Mal cyt [(S)-Malate; (S)-malic acid]
Glu [L-Glutamate; L-glutamic acid]
Fum [Fumarate; fumaric acid]
IsoCit [Isocitrate; isocitric acid]
Suc [Succinate; succinic acid]
OXA cyt [Oxaloacetate; oxaloacetic acid]
CoA [CoA; coenzyme A]
NADH [NADH; NADH]
CoA cyt [CoA; coenzyme A]
LAC [(S)-Lactate; (S)-lactic acid]
Pi [Orthophosphate; phosphate(3-)]
Cit cyt [Citrate; citric acid]
FAD [FAD; FAD]
Asp cyt [L-Aspartate; L-aspartic acid]
ETFred [Reduced electron-transferring flavoprotein]
PYR cyt [Pyruvate; pyruvic acid]
Acetyl CoA [Acetyl-CoA; acetyl-CoA]

Observables: none

This is a mathematical model describing the hematopoietic lineages with leukemia lineages, as controlled by end-product…

BACKGROUND:The haematopoietic lineages with leukaemia lineages are considered in this paper. In particular, we mainly consider that haematopoietic lineages are tightly controlled by negative feedback inhibition of end-product. Actually, leukemia has been found 100 years ago. Up to now, the exact mechanism is still unknown, and many factors are thought to be associated with the pathogenesis of leukemia. Nevertheless, it is very necessary to continue the profound study of the pathogenesis of leukemia. Here, we propose a new mathematical model which include some negative feedback inhibition from the terminally differentiated cells of haematopoietic lineages to the haematopoietic stem cells and haematopoietic progenitor cells in order to describe the regulatory mechanisms mentioned above by a set of ordinary differential equations. Afterwards, we carried out detailed dynamical bifurcation analysis of the model, and obtained some meaningful results. RESULTS:In this work, we mainly perform the analysis of the mathematic model by bifurcation theory and numerical simulations. We have not only incorporated some new negative feedback mechanisms to the existing model, but also constructed our own model by using the modeling method of stem cell theory with probability method. Through a series of qualitative analysis and numerical simulations, we obtain that the weak negative feedback for differentiation probability is conducive to the cure of leukemia. However, with the strengthening of negative feedback, leukemia will be more difficult to be cured, and even induce death. In contrast, strong negative feedback for differentiation rate of progenitor cells can promote healthy haematopoiesis and suppress leukaemia. CONCLUSIONS:These results demonstrate that healthy progenitor cells are bestowed a competitive advantage over leukaemia stem cells. Weak g1, g2, and h1 enable the system stays in the healthy state. However, strong h2 can promote healthy haematopoiesis and suppress leukaemia. link: http://identifiers.org/pubmed/29745850

Parameters:

Name Description
v_1_D = 0.5; Z_1 = 10.0; p_1_D = 0.45; K_1 = 1.0 Reaction: => S_HSC, Rate Law: compartment*p_1_D*(K_1-Z_1)*v_1_D*S_HSC
v_1_D = 0.5; p_1_D = 0.45 Reaction: S_HSC => A_PC, Rate Law: compartment*(1-p_1_D)*v_1_D*S_HSC
p_2_D = 0.68; K_2 = 1.0; v_2_D = 0.72; Z_2 = 10.0 Reaction: => A_PC, Rate Law: compartment*p_2_D*(K_2-Z_2)*v_2_D*A_PC
p_30 = 0.8; v_30 = 0.7 Reaction: L_LSC => T_TDLC, Rate Law: compartment*(1-p_30)*v_30*L_LSC
p_2_D = 0.68; v_2_D = 0.72 Reaction: A_PC => D_TDSC, Rate Law: compartment*(1-p_2_D)*v_2_D*A_PC
d_2 = 0.3 Reaction: T_TDLC =>, Rate Law: compartment*d_2*T_TDLC
p_30 = 0.8; v_30 = 0.7; K_2 = 1.0; Z_2 = 10.0 Reaction: => L_LSC, Rate Law: compartment*p_30*(K_2-Z_2)*v_30*L_LSC
d_1 = 0.275 Reaction: D_TDSC =>, Rate Law: compartment*d_1*D_TDSC

States:

Name Description
S HSC [C12551]
A PC [C12662]
T TDLC [EFO:0002954; C41069]
L LSC [C41069]
D TDSC [C12551; EFO:0002954]

Observables: none

MODEL1201230000 @ v0.0.1

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

One of the most obvious phenotypes of a cell is its metabolic activity, which is defined by the fluxes in the metabolic network. Although experimental methods to determine intracellular fluxes are well established, only a limited number of fluxes can be resolved. Especially in eukaryotes such as yeast, compartmentalization and the existence of many parallel routes render exact flux analysis impossible using current methods. To gain more insight into the metabolic operation of S. cerevisiae we developed a new computational approach where we characterize the flux solution space by determining elementary flux modes (EFMs) that are subsequently classified as thermodynamically feasible or infeasible on the basis of experimental metabolome data. This allows us to provably rule out the contribution of certain EFMs to the in vivo flux distribution. From the 71 million EFMs in a medium size metabolic network of S. cerevisiae, we classified 54% as thermodynamically feasible. By comparing the thermodynamically feasible and infeasible EFMs, we could identify reaction combinations that span the cytosol and mitochondrion and, as a system, cannot operate under the investigated glucose batch conditions. Besides conclusions on single reactions, we found that thermodynamic constraints prevent the import of redox cofactor equivalents into the mitochondrion due to limits on compartmental cofactor concentrations. Our novel approach of incorporating quantitative metabolite concentrations into the analysis of the space of all stoichiometrically feasible flux distributions allows generating new insights into the system-level operation of the intracellular fluxes without making assumptions on metabolic objectives of the cell. link: http://identifiers.org/pubmed/22416224

Parameters: none

States: none

Observables: none

BIOMD0000000336 @ v0.0.1

Jones1994_BloodCoagulationThis model is built based on the experimental findings described in Lawson et al., 1994 (PMID:…

A mathematical simulation of the tissue factor pathway to the generation of thrombin has been developed using a combination of empirical, estimated, and deduced rate constants for reactions involving the activation of factor IX, X, V, and VIII, in the formation of thrombin, as well as rate constants for the assembly of the coagulation enzyme complexes which involve factor VIIIa-factor IXa (intrinsic tenase) and factor Va-Xa (prothrombinase) assembled on phospholipid membrane. Differential equations describing the fate of each species in the reaction were developed and solved using an interactive procedure based upon the Runge-Kutta technique. In addition to the theoretical considerations involving the reactions of the tissue factor pathway, a physical constraint associated with the stability of the factor VIIIa-factor IXa complex has been incorporated into the model based upon the empirical observations associated with the stability of this complex. The model system provides a realistic accounting of the fates of each of the proteins in the coagulation reaction through a range of initiator (factor VIIa-tissue factor) concentrations ranging from 5 pM to 5 nM. The model is responsive to alterations in the concentrations of factor VIII, factor V, and their respective activated species, factor VIIIa and factor Va, and overall provides a reasonable approximation of empirical data. The computer model permits the assessment of the reaction over a broad range of conditions and provides a useful tool for the development and management of reaction studies. link: http://identifiers.org/pubmed/8083242

Parameters:

Name Description
k3 = 1.0E7 Reaction: VIII + Xa => Xa + VIIIa, Rate Law: compartment_1*k3*VIII*Xa
k15 = 100000.0 Reaction: IX + Xa => Xa + IXa, Rate Law: compartment_1*k15*IX*Xa
k11 = 0.3 Reaction: IX_TF_VIIa => TF_VIIa + IXa, Rate Law: compartment_1*k11*IX_TF_VIIa
k2 = 2.0E7 Reaction: V + IIa => IIa + Va, Rate Law: compartment_1*k2*V*IIa
k5 = 1.0E7 Reaction: mIIa + Va_Xa => Va_Xa + IIa, Rate Law: compartment_1*k5*mIIa*Va_Xa
k19 = 70.0; k6 = 1.0E8 Reaction: II + Va_Xa => II_Va_Xa, Rate Law: compartment_1*(k6*II*Va_Xa-k19*II_Va_Xa)
k18 = 0.001; k6 = 1.0E8 Reaction: X + VIIIa_IXa => X_VIIIa_IXa, Rate Law: compartment_1*(k6*X*VIIIa_IXa-k18*X_VIIIa_IXa)
k17 = 44.0; k6 = 1.0E8 Reaction: X + TF_VIIa => X_TF_VIIa, Rate Law: compartment_1*(k6*X*TF_VIIa-k17*X_TF_VIIa)
k1 = 2.0E7 Reaction: V + Xa => Xa + Va, Rate Law: compartment_1*k1*V*Xa
k6 = 1.0E8; k10 = 0.4 Reaction: Va + Xa => Va_Xa, Rate Law: compartment_1*(k6*Va*Xa-k10*Va_Xa)
k14 = 32.0 Reaction: II_Va_Xa => Va_Xa + mIIa, Rate Law: compartment_1*k14*II_Va_Xa
k12 = 1.15 Reaction: X_TF_VIIa => TF_VIIa + Xa, Rate Law: compartment_1*k12*X_TF_VIIa
k16 = 24.0; k6 = 1.0E8 Reaction: IX + TF_VIIa => IX_TF_VIIa, Rate Law: compartment_1*(k6*IX*TF_VIIa-k16*IX_TF_VIIa)
k13 = 8.2 Reaction: X_VIIIa_IXa => VIIIa_IXa + Xa, Rate Law: compartment_1*k13*X_VIIIa_IXa
k7 = 1.0E7; k9 = 0.005 Reaction: VIIIa + IXa => VIIIa_IXa, Rate Law: compartment_1*(k7*VIIIa*IXa-k9*VIIIa_IXa)
I = 0.0 Reaction: VIIIa_IXa => ; VIIIa_IXa, Rate Law: compartment_1*(compartment_1*abs(I-VIIIa_IXa)+(I-VIIIa_IXa))/compartment_1
k4 = 2.0E7 Reaction: VIII + IIa => IIa + VIIIa, Rate Law: compartment_1*k4*VIII*IIa

States:

Name Description
IX TF VIIa [Tissue factor; Coagulation factor IX]
VIII [Coagulation factor VIII]
X [Coagulation factor X]
II Va Xa [Prothrombin; Coagulation factor V; Coagulation factor X]
V [Coagulation factor V]
Xa [Coagulation factor X]
TF VIIa [Tissue factor]
VIIIa [Coagulation factor VIII]
X TF VIIa [Tissue factor; Coagulation factor X]
Va [Coagulation factor V]
IIa [Prothrombin]
mIIa [Prothrombin]
Va Xa [Coagulation factor V; Coagulation factor X]
IXa [Coagulation factor IX]
VIIIa IXa [Coagulation factor IX; Coagulation factor VIII]
II [Prothrombin]
IX [Coagulation factor IX]
X VIIIa IXa [Coagulation factor X; Coagulation factor IX; Coagulation factor VIII]

Observables: none

This model is based on paper, based on its cell cycle dynamics model: Strategies in regulating glioblastoma signaling p…

Glioblastoma multiforme is one of the most invasive type of glial tumors, which rapidly grows and commonly spreads into nearby brain tissue. It is a devastating brain cancer that often results in death within approximately 12 to 15 months after diagnosis. In this work, optimal control theory was applied to regulate intracellular signaling pathways of miR-451-AMPK-mTOR-cell cycle dynamics via glucose and drug intravenous administration infusions. Glucose level is controlled to activate miR-451 in the up-stream pathway of the model. A potential drug blocking the inhibitory pathway of mTOR by AMPK complex is incorporated to explore regulation of the down-stream pathway to the cell cycle. Both miR-451 and mTOR levels are up-regulated inducing cell proliferation and reducing invasion in the neighboring tissues. Concomitant and alternating glucose and drug infusions are explored under various circumstances to predict best clinical outcomes with least administration costs. link: http://identifiers.org/pubmed/31009513

Parameters:

Name Description
k_9 = 0.3 Reaction: => Plk1; mass_s, CycB, Rate Law: compartment*k_9*mass_s*CycB*(1-Plk1)
S_2 = 1.2; epsilon_2 = 0.02 Reaction: => mTOR_R, Rate Law: compartment*S_2/epsilon_2
S_1 = 0.2; epsilon_1 = 0.02 Reaction: => AMPK_A, Rate Law: compartment*S_1/epsilon_1
k_7 = 3.0; J_7 = 0.001 Reaction: => p55cdc_A; Plk1, p55cdc_T, Rate Law: compartment*k_7*Plk1*(p55cdc_T-p55cdc_A)/((J_7+p55cdc_T)-p55cdc_A)
k_2 = 0.12 Reaction: CycB =>, Rate Law: compartment*k_2*CycB
u_1 = 0.0 Reaction: => Glucose_G, Rate Law: compartment*u_1
n_1 = 10.0; K_m = 0.5; zeta_1 = 2.5 Reaction: mass_s = mass+zeta_1*(1/mTOR_R)^n_1/(K_m^n_1+(1/mTOR_R)^n_1), Rate Law: missing
epsilon_2 = 0.02 Reaction: mTOR_R => ; mTOR_R, Rate Law: compartment*mTOR_R/epsilon_2
k_8 = 1.5; J_8 = 0.001; Mad = 1.0 Reaction: p55cdc_A =>, Rate Law: compartment*k_8*Mad*p55cdc_A/(J_8+p55cdc_A)
k_10 = 0.06 Reaction: Plk1 =>, Rate Law: compartment*k_10*Plk1
k_4 = 105.0; J_4 = 0.04 Reaction: Cdh1 => ; mass_s, CycB, Rate Law: compartment*k_4*mass_s*CycB*Cdh1/(J_4+Cdh1)
u_2 = 0.0 Reaction: => Drug_D, Rate Law: compartment*u_2
k_6 = 0.3 Reaction: p55cdc_T =>, Rate Law: compartment*k_6*p55cdc_T
myu_G = 0.5 Reaction: Glucose_G =>, Rate Law: compartment*myu_G*Glucose_G
myu_0 = 0.033; m = 10.0 Reaction: => mass, Rate Law: compartment*myu_0*mass*(1-mass/m)
k_5 = 0.015 Reaction: => p55cdc_T, Rate Law: compartment*k_5
myu_D = 1.316 Reaction: Drug_D =>, Rate Law: compartment*myu_D*Drug_D
l_6 = 1.0; epsilon_2 = 0.02; gamma = 1.0; l_5 = 4.0 Reaction: => mTOR_R; deltaD, AMPK_A, Rate Law: compartment*l_5*l_6^2/(epsilon_2*(l_6^2+deltaD*gamma*AMPK_A^2))
HIF = 0.9999999999; p27_p21 = 1.05 Reaction: CycB =>, Rate Law: compartment*p27_p21*HIF*CycB
n = 4.0; J_5 = 0.3; k_5_ = 0.6 Reaction: => p55cdc_T; CycB, mass_s, Rate Law: compartment*k_5_*(CycB*mass_s)^n/(J_5^n+(CycB*mass_s)^n)
k_1 = 0.12 Reaction: => CycB, Rate Law: compartment*k_1
J_3 = 0.04; k_3 = 3.0 Reaction: => Cdh1, Rate Law: compartment*k_3*(1-Cdh1)/((J_3+1)-Cdh1)
l_3 = 4.0; beta = 1.0; l_4 = 1.0; epsilon_1 = 0.02 Reaction: => AMPK_A; miR_451_M, Rate Law: compartment*l_3*l_4^2/(epsilon_1*(l_4^2+beta*miR_451_M^2))
k_3_ = 30.0; J_3 = 0.04 Reaction: => Cdh1; p55cdc_A, Rate Law: compartment*k_3_*p55cdc_A*(1-Cdh1)/((J_3+1)-Cdh1)
l_2 = 1.0; l_1 = 4.0; alpha = 1.6 Reaction: => miR_451_M; Glucose_G, AMPK_A, Rate Law: compartment*(Glucose_G+l_1*l_2^2/(l_2^2+alpha*AMPK_A^2))
epsilon_1 = 0.02 Reaction: AMPK_A =>, Rate Law: compartment*AMPK_A/epsilon_1
k_2_ = 4.5 Reaction: CycB => ; Cdh1, Rate Law: compartment*k_2_*Cdh1*CycB

States:

Name Description
AMPK A [5'-AMP-activated protein kinase catalytic subunit alpha-2; 5'-AMP-Activated Protein Kinase]
Glucose G [glucose]
p55cdc A [Cell division cycle protein 20 homolog]
deltaD deltaD
Drug D [drug]
Plk1 [Serine/threonine-protein kinase PLK1]
mTOR R [CCO:2475; Serine/threonine-protein kinase mTOR; MTOR Gene]
CycB [G2/mitotic-specific cyclin-B3]
mass [Mass]
Cdh1 [Fizzy-related protein homolog]
miR 451 M [cAMP-regulated phosphoprotein 19; MIR451A Pre-miRNA]
p55cdc T [Cell division cycle protein 20 homolog]
mass s [Mass]

Observables: none

This model is based on paper: Strategies in regulating glioblastoma signaling pathways and anti-invasion therapy Abs…

Glioblastoma multiforme is one of the most invasive type of glial tumors, which rapidly grows and commonly spreads into nearby brain tissue. It is a devastating brain cancer that often results in death within approximately 12 to 15 months after diagnosis. In this work, optimal control theory was applied to regulate intracellular signaling pathways of miR-451-AMPK-mTOR-cell cycle dynamics via glucose and drug intravenous administration infusions. Glucose level is controlled to activate miR-451 in the up-stream pathway of the model. A potential drug blocking the inhibitory pathway of mTOR by AMPK complex is incorporated to explore regulation of the down-stream pathway to the cell cycle. Both miR-451 and mTOR levels are up-regulated inducing cell proliferation and reducing invasion in the neighboring tissues. Concomitant and alternating glucose and drug infusions are explored under various circumstances to predict best clinical outcomes with least administration costs. link: http://identifiers.org/pubmed/31009513

Parameters:

Name Description
myu_D = 1.316 Reaction: Drug_D =>, Rate Law: compartment*myu_D*Drug_D
l_6 = 1.0; epsilon_2 = 0.02; gamma = 1.0; l_5 = 4.0 Reaction: => mTOR_R; deltaD, AMPK_A, Rate Law: compartment*l_5*l_6^2/(epsilon_2*(l_6^2+deltaD*gamma*AMPK_A^2))
S_2 = 1.2; epsilon_2 = 0.02 Reaction: => mTOR_R, Rate Law: compartment*S_2/epsilon_2
S_1 = 0.2; epsilon_1 = 0.02 Reaction: => AMPK_A, Rate Law: compartment*S_1/epsilon_1
l_3 = 4.0; beta = 1.0; l_4 = 1.0; epsilon_1 = 0.02 Reaction: => AMPK_A; miR_451_M, Rate Law: compartment*l_3*l_4^2/(epsilon_1*(l_4^2+beta*miR_451_M^2))
epsilon_2 = 0.02 Reaction: mTOR_R => ; mTOR_R, Rate Law: compartment*mTOR_R/epsilon_2
u_1 = 0.0 Reaction: => Glucose_G, Rate Law: compartment*u_1
l_2 = 1.0; l_1 = 4.0; alpha = 1.6 Reaction: => miR_451_M; Glucose_G, AMPK_A, Rate Law: compartment*(Glucose_G+l_1*l_2^2/(l_2^2+alpha*AMPK_A^2))
u_2 = 0.0 Reaction: => Drug_D, Rate Law: compartment*u_2
epsilon_1 = 0.02 Reaction: AMPK_A =>, Rate Law: compartment*AMPK_A/epsilon_1
myu_G = 0.5 Reaction: Glucose_G =>, Rate Law: compartment*myu_G*Glucose_G

States:

Name Description
Drug D [drug]
AMPK A [5'-AMP-activated protein kinase catalytic subunit alpha-2; 5'-AMP-Activated Protein Kinase]
mTOR R [CCO:2475; MTOR Gene; Serine/threonine-protein kinase mTOR]
Glucose G [glucose]
miR 451 M [MIR451A Pre-miRNA; cAMP-regulated phosphoprotein 19]
deltaD deltaD

Observables: none

This is a Systems Biology Markup Language (SBML) file, generated by MathSBML 2.5.13 (4 May 2006) 13-May-2006 20:05:11.20…

The above-ground tissues of higher plants are generated from a small region of cells situated at the plant apex called the shoot apical meristem. An important genetic control circuit modulating the size of the Arabidopsis thaliana meristem is a feed-back network between the CLAVATA3 and WUSCHEL genes. Although the expression patterns for these genes do not overlap, WUSCHEL activity is both necessary and sufficient (when expressed ectopically) for the induction of CLAVATA3 expression. However, upregulation of CLAVATA3 in conjunction with the receptor kinase CLAVATA1 results in the downregulation of WUSCHEL. Despite much work, experimental data for this network are incomplete and additional hypotheses are needed to explain the spatial locations and dynamics of these expression domains. Predictive mathematical models describing the system should provide a useful tool for investigating and discriminating among possible hypotheses, by determining which hypotheses best explain observed gene expression dynamics.We are developing a method using in vivo live confocal microscopy to capture quantitative gene expression data and create templates for computational models. We present two models accounting for the organization of the WUSCHEL expression domain. Our preferred model uses a reaction-diffusion mechanism in which an activator induces WUSCHEL expression. This model is able to organize the WUSCHEL expression domain. In addition, the model predicts the dynamical reorganization seen in experiments where cells, including the WUSCHEL domain, are ablated, and it also predicts the spatial expansion of the WUSCHEL domain resulting from removal of the CLAVATA3 signal.An extended description of the model framework and image processing algorithms can be found at http://www.computableplant.org, together with additional results and simulation movies.http://www.computableplant.org/ and alternatively for a direct link to the page, http://computableplant.ics.uci.edu/bti1036 can be accessed. link: http://identifiers.org/pubmed/15961462

Parameters: none

States: none

Observables: none

K


Kaiser2014 - Salmonella persistence after ciprofloxacin treatment The model describes the bacterial tolerance to antibi…

In vivo, antibiotics are often much less efficient than ex vivo and relapses can occur. The reasons for poor in vivo activity are still not completely understood. We have studied the fluoroquinolone antibiotic ciprofloxacin in an animal model for complicated Salmonellosis. High-dose ciprofloxacin treatment efficiently reduced pathogen loads in feces and most organs. However, the cecum draining lymph node (cLN), the gut tissue, and the spleen retained surviving bacteria. In cLN, approximately 10%-20% of the bacteria remained viable. These phenotypically tolerant bacteria lodged mostly within CD103⁺CX₃CR1⁻CD11c⁺ dendritic cells, remained genetically susceptible to ciprofloxacin, were sufficient to reinitiate infection after the end of the therapy, and displayed an extremely slow growth rate, as shown by mathematical analysis of infections with mixed inocula and segregative plasmid experiments. The slow growth was sufficient to explain recalcitrance to antibiotics treatment. Therefore, slow-growing antibiotic-tolerant bacteria lodged within dendritic cells can explain poor in vivo antibiotic activity and relapse. Administration of LPS or CpG, known elicitors of innate immune defense, reduced the loads of tolerant bacteria. Thus, manipulating innate immunity may augment the in vivo activity of antibiotics. link: http://identifiers.org/pubmed/24558351

Parameters:

Name Description
mu1 = 297.78957 per_day; r3 = 4.5867007 per_day; t1 = 1.0 day; c10 = 2.43E-7 per_day; r1 = 2.8195198 per_day; t5 = 5.0 day; t3 = 3.0 day; r10 = 0.3757764 per_day; mu5 = 0.0 per_day; r5 = 1.8812956 per_day; c5 = 2.497735 per_day; t10 = 10.0 day; c1 = 0.0 per_day; c3 = 5.042901 per_day; mu10 = 0.0 per_day; mu3 = 0.0 per_day Reaction: L = piecewise(mu1+(r1-c1)*L, (time >= 0) && (time <= t1), mu3+(r3-c3)*L, (time > t1) && (time <= t3), mu5+(r5-c5)*L, (time > t3) && (time <= t5), mu10+(r10-c10)*L, (time > t5) && (time <= t10)), Rate Law: piecewise(mu1+(r1-c1)*L, (time >= 0) && (time <= t1), mu3+(r3-c3)*L, (time > t1) && (time <= t3), mu5+(r5-c5)*L, (time > t3) && (time <= t5), mu10+(r10-c10)*L, (time > t5) && (time <= t10))

States:

Name Description
L [Salmonella enterica subsp. enterica serovar Typhimurium str. DT104]

Observables: none

MODEL1011020000 @ v0.0.1

This is the map described in and accompanying the article: **A comprehensive molecular interaction map of the budding…

With the accumulation of data on complex molecular machineries coordinating cell-cycle dynamics, coupled with its central function in disease patho-physiologies, it is becoming increasingly important to collate the disparate knowledge sources into a comprehensive molecular network amenable to systems-level analyses. In this work, we present a comprehensive map of the budding yeast cell-cycle, curating reactions from ∼600 original papers. Toward leveraging the map as a framework to explore the underlying network architecture, we abstract the molecular components into three planes–signaling, cell-cycle core and structural planes. The planar view together with topological analyses facilitates network-centric identification of functions and control mechanisms. Further, we perform a comparative motif analysis to identify around 194 motifs including feed-forward, mutual inhibitory and feedback mechanisms contributing to cell-cycle robustness. We envisage the open access, comprehensive cell-cycle map to open roads toward community-based deeper understanding of cell-cycle dynamics. link: http://identifiers.org/pubmed/20865008

Parameters: none

States: none

Observables: none

Kallenberger2014 - CD95L induced apoptosis initiated by caspase-8, CD95 HeLa cells (cis/trans variant)The paper describe…

Apoptosis in response to the ligand CD95L (also known as Fas ligand) is initiated by caspase-8, which is activated by dimerization and self-cleavage at death-inducing signaling complexes (DISCs). Previous work indicated that the degree of substrate cleavage by caspase-8 determines whether a cell dies or survives in response to a death stimulus. To determine how a death ligand stimulus is effectively translated into caspase-8 activity, we assessed this activity over time in single cells with compartmentalized probes that are cleaved by caspase-8 and used multiscale modeling to simultaneously describe single-cell and population data with an ensemble of single-cell models. We derived and experimentally validated a minimal model in which cleavage of caspase-8 in the enzymatic domain occurs in an interdimeric manner through interaction between DISCs, whereas prodomain cleavage sites are cleaved in an intradimeric manner within DISCs. Modeling indicated that sustained membrane-bound caspase-8 activity is followed by transient cytosolic activity, which can be interpreted as a molecular timer mechanism reflected by a limited lifetime of active caspase-8. The activation of caspase-8 by combined intra- and interdimeric cleavage ensures weak signaling at low concentrations of CD95L and strongly accelerated activation at higher ligand concentrations, thereby contributing to precise control of apoptosis. link: http://identifiers.org/pubmed/24619646

Parameters:

Name Description
kD374probe = 0.00152252549827479 Reaction: PrNES_mCherry => PrNES + mCherry; p43, p18, PrNES_mCherry, p43, p18, Rate Law: kD374probe*PrNES_mCherry*(p43+p18)*cell
kdiss_p18 = 0.0949914492651531 Reaction: p18 => p18inactive; p18, Rate Law: kdiss_p18*p18*cell
kD216 = 0.0114186392006403 Reaction: p43 => p18 + DISC; p43, Rate Law: kD216*p43*cell
kon_FADD = 8.11711012144556E-4; CD95act = 0.0 Reaction: FADD => DISC; FADD, Rate Law: kon_FADD*CD95act*FADD*cell
kDISC = 4.91828591049766E-4 Reaction: p55free + DISC => DISCp55; p55free, DISC, Rate Law: kDISC*p55free*DISC*cell
kD374trans_p55 = 4.46994772958953E-4 Reaction: p30 => p18 + DISC; DISCp55, p30, p30, DISCp55, Rate Law: kD374trans_p55*p30*(DISCp55+p30)*cell
kD374trans_p43 = 0.00343995957326369 Reaction: p30 => p18 + DISC; p43, p30, p43, Rate Law: kD374trans_p43*p30*p43*cell
koff_FADD = 0.00566528253772301 Reaction: DISC => FADD; DISC, Rate Law: koff_FADD*DISC*cell
kBid = 5.2867403363568E-4 Reaction: Bid => tBid; p43, p18, Bid, p43, p18, Rate Law: kBid*Bid*(p43+p18)*cell

States:

Name Description
Bid [BH3-interacting domain death agonist]
PrNES mCherry [SBO:0000178; probe; Red fluorescent protein drFP583; nuclear_export_signal]
p30 [CASP8]
FADD [FAS-associated death domain protein]
p18 [Caspase-8]
p43 [CASP8 and FADD-like apoptosis regulator]
DISC [death-inducing signaling complex]
p55free [CASP8]
PrER [probe; Calnexin]
mCherry [Red fluorescent protein drFP583]
DISCp55 [CASP8; death-inducing signaling complex]
PrER mGFP [SBO:0000178; probe; Calnexin; Green fluorescent protein]
mGFP [Green fluorescent protein]
PrNES [probe; nuclear_export_signal]
p18inactive [inactive; Caspase-8]
tBid [BH3-interacting domain death agonist; mitochondrial outer membrane permeabilization]

Observables: none

Kallenberger2014 - CD95L induced apoptosis initiated by caspase-8, CD95 HeLa cells (cis/trans-cis/trans variant)The pape…

Apoptosis in response to the ligand CD95L (also known as Fas ligand) is initiated by caspase-8, which is activated by dimerization and self-cleavage at death-inducing signaling complexes (DISCs). Previous work indicated that the degree of substrate cleavage by caspase-8 determines whether a cell dies or survives in response to a death stimulus. To determine how a death ligand stimulus is effectively translated into caspase-8 activity, we assessed this activity over time in single cells with compartmentalized probes that are cleaved by caspase-8 and used multiscale modeling to simultaneously describe single-cell and population data with an ensemble of single-cell models. We derived and experimentally validated a minimal model in which cleavage of caspase-8 in the enzymatic domain occurs in an interdimeric manner through interaction between DISCs, whereas prodomain cleavage sites are cleaved in an intradimeric manner within DISCs. Modeling indicated that sustained membrane-bound caspase-8 activity is followed by transient cytosolic activity, which can be interpreted as a molecular timer mechanism reflected by a limited lifetime of active caspase-8. The activation of caspase-8 by combined intra- and interdimeric cleavage ensures weak signaling at low concentrations of CD95L and strongly accelerated activation at higher ligand concentrations, thereby contributing to precise control of apoptosis. link: http://identifiers.org/pubmed/24619646

Parameters:

Name Description
kD374trans_p55 = 5.43518631342483E-4 Reaction: DISCp55 => p43; DISCp55, p30, DISCp55, p30, Rate Law: kD374trans_p55*DISCp55*(DISCp55+p30)*cell
kD374 = 6.44612643975149E-4 Reaction: DISCp55 => p43; DISCp55, Rate Law: kD374*DISCp55*cell
kDISC = 3.64965874405544E-4 Reaction: p55free + DISC => DISCp55; p55free, DISC, Rate Law: kDISC*p55free*DISC*cell
kdiss_p18 = 0.064713651554491 Reaction: p18 => p18inactive; p18, Rate Law: kdiss_p18*p18*cell
kD374trans_p43 = 0.00413530054938906 Reaction: p30 => p18 + DISC; p43, p30, p43, Rate Law: kD374trans_p43*p30*p43*cell
kD374probe = 0.00153710001025539 Reaction: PrNES_mCherry => PrNES + mCherry; p43, p18, PrNES_mCherry, p43, p18, Rate Law: kD374probe*PrNES_mCherry*(p43+p18)*cell
kD216trans_p43 = 5.29906975294056E-5 Reaction: p43 => p18 + DISC; p43, p43, Rate Law: kD216trans_p43*p43*p43*cell
kBid = 5.2134055139547E-4 Reaction: Bid => tBid; p43, p18, Bid, p43, p18, Rate Law: kBid*Bid*(p43+p18)*cell
kD216trans_p55 = 2.23246421372882E-4 Reaction: p43 => p18 + DISC; DISCp55, p30, p43, DISCp55, p30, Rate Law: kD216trans_p55*p43*(DISCp55+p30)*cell
koff_FADD = 0.00130854998177646 Reaction: DISC => FADD; DISC, Rate Law: koff_FADD*DISC*cell
kD216 = 0.00639775937416746 Reaction: DISCp55 => p30; DISCp55, Rate Law: kD216*DISCp55*cell
CD95act = 0.0; kon_FADD = 0.00108871858684363 Reaction: FADD => DISC; FADD, Rate Law: kon_FADD*CD95act*FADD*cell

States:

Name Description
Bid [BH3-interacting domain death agonist]
PrNES mCherry [SBO:0000178; probe; Red fluorescent protein drFP583; nuclear_export_signal]
p30 [CASP8]
FADD [FAS-associated death domain protein]
p18 [Caspase-8]
p43 [CASP8 and FADD-like apoptosis regulator]
DISC [death-inducing signaling complex]
p55free [CASP8]
PrER [probe; Calnexin]
mCherry [Red fluorescent protein drFP583]
PrER mGFP [SBO:0000178; probe; Calnexin; Green fluorescent protein]
DISCp55 [CASP8; death-inducing signaling complex]
mGFP [Green fluorescent protein]
PrNES [probe; nuclear_export_signal]
p18inactive [inactive; Caspase-8]
tBid [BH3-interacting domain death agonist; mitochondrial outer membrane permeabilization]

Observables: none

Kallenberger2014 - CD95L induced apoptosis initiated by caspase-8, wild-type HeLa cells (cis/trans variant)The paper des…

Apoptosis in response to the ligand CD95L (also known as Fas ligand) is initiated by caspase-8, which is activated by dimerization and self-cleavage at death-inducing signaling complexes (DISCs). Previous work indicated that the degree of substrate cleavage by caspase-8 determines whether a cell dies or survives in response to a death stimulus. To determine how a death ligand stimulus is effectively translated into caspase-8 activity, we assessed this activity over time in single cells with compartmentalized probes that are cleaved by caspase-8 and used multiscale modeling to simultaneously describe single-cell and population data with an ensemble of single-cell models. We derived and experimentally validated a minimal model in which cleavage of caspase-8 in the enzymatic domain occurs in an interdimeric manner through interaction between DISCs, whereas prodomain cleavage sites are cleaved in an intradimeric manner within DISCs. Modeling indicated that sustained membrane-bound caspase-8 activity is followed by transient cytosolic activity, which can be interpreted as a molecular timer mechanism reflected by a limited lifetime of active caspase-8. The activation of caspase-8 by combined intra- and interdimeric cleavage ensures weak signaling at low concentrations of CD95L and strongly accelerated activation at higher ligand concentrations, thereby contributing to precise control of apoptosis. link: http://identifiers.org/pubmed/24619646

Parameters:

Name Description
kD374probe = 0.00152252549827479 Reaction: PrNES_mCherry => PrNES + mCherry; p43, p18, PrNES_mCherry, p43, p18, Rate Law: kD374probe*PrNES_mCherry*(p43+p18)*cell
kdiss_p18 = 0.0949914492651531 Reaction: p18 => p18inactive; p18, Rate Law: kdiss_p18*p18*cell
kon_FADD = 8.11711012144556E-4; CD95act = 0.0 Reaction: FADD => DISC; FADD, Rate Law: kon_FADD*CD95act*FADD*cell
kD216 = 0.0114186392006403 Reaction: p43 => p18 + DISC; p43, Rate Law: kD216*p43*cell
kDISC = 4.91828591049766E-4 Reaction: p55free + DISC => DISCp55; p55free, DISC, Rate Law: kDISC*p55free*DISC*cell
kBid = 5.2867403363568E-4 Reaction: Bid => tBid; p43, p18, Bid, p43, p18, Rate Law: kBid*Bid*(p43+p18)*cell
kD374trans_p55 = 4.46994772958953E-4 Reaction: p30 => p18 + DISC; DISCp55, p30, p30, DISCp55, Rate Law: kD374trans_p55*p30*(DISCp55+p30)*cell
koff_FADD = 0.00566528253772301 Reaction: DISC => FADD; DISC, Rate Law: koff_FADD*DISC*cell
kD374trans_p43 = 0.00343995957326369 Reaction: p30 => p18 + DISC; p43, p30, p43, Rate Law: kD374trans_p43*p30*p43*cell

States:

Name Description
Bid [BH3-interacting domain death agonist]
PrNES mCherry [SBO:0000178; probe; Red fluorescent protein drFP583; nuclear_export_signal]
p30 [CASP8]
FADD [FAS-associated death domain protein]
p18 [Caspase-8]
p43 [CASP8 and FADD-like apoptosis regulator]
DISC [death-inducing signaling complex]
p55free [CASP8]
PrER [probe; Calnexin]
mCherry [Red fluorescent protein drFP583]
PrER mGFP [SBO:0000178; probe; Calnexin; Green fluorescent protein]
DISCp55 [CASP8; death-inducing signaling complex]
mGFP [Green fluorescent protein]
PrNES [probe; nuclear_export_signal]
p18inactive [inactive; Caspase-8]
tBid [BH3-interacting domain death agonist; mitochondrial outer membrane permeabilization]

Observables: none

Kallenberger2014 - CD95L induced apoptosis initiated by caspase-8, wild-type HeLa cells (cis/trans-cis/trans variant)The…

Apoptosis in response to the ligand CD95L (also known as Fas ligand) is initiated by caspase-8, which is activated by dimerization and self-cleavage at death-inducing signaling complexes (DISCs). Previous work indicated that the degree of substrate cleavage by caspase-8 determines whether a cell dies or survives in response to a death stimulus. To determine how a death ligand stimulus is effectively translated into caspase-8 activity, we assessed this activity over time in single cells with compartmentalized probes that are cleaved by caspase-8 and used multiscale modeling to simultaneously describe single-cell and population data with an ensemble of single-cell models. We derived and experimentally validated a minimal model in which cleavage of caspase-8 in the enzymatic domain occurs in an interdimeric manner through interaction between DISCs, whereas prodomain cleavage sites are cleaved in an intradimeric manner within DISCs. Modeling indicated that sustained membrane-bound caspase-8 activity is followed by transient cytosolic activity, which can be interpreted as a molecular timer mechanism reflected by a limited lifetime of active caspase-8. The activation of caspase-8 by combined intra- and interdimeric cleavage ensures weak signaling at low concentrations of CD95L and strongly accelerated activation at higher ligand concentrations, thereby contributing to precise control of apoptosis. link: http://identifiers.org/pubmed/24619646

Parameters:

Name Description
kD374trans_p55 = 5.43518631342483E-4 Reaction: DISCp55 => p43; DISCp55, p30, DISCp55, p30, Rate Law: kD374trans_p55*DISCp55*(DISCp55+p30)*cell
kD374 = 6.44612643975149E-4 Reaction: DISCp55 => p43; DISCp55, Rate Law: kD374*DISCp55*cell
kdiss_p18 = 0.064713651554491 Reaction: p18 => p18inactive; p18, Rate Law: kdiss_p18*p18*cell
kDISC = 3.64965874405544E-4 Reaction: p55free + DISC => DISCp55; p55free, DISC, Rate Law: kDISC*p55free*DISC*cell
kD374trans_p43 = 0.00413530054938906 Reaction: DISCp55 => p43; p43, DISCp55, p43, Rate Law: kD374trans_p43*DISCp55*p43*cell
kD374probe = 0.00153710001025539 Reaction: PrNES_mCherry => PrNES + mCherry; p43, p18, PrNES_mCherry, p43, p18, Rate Law: kD374probe*PrNES_mCherry*(p43+p18)*cell
kD216trans_p43 = 5.29906975294056E-5 Reaction: DISCp55 => p30; p43, DISCp55, p43, Rate Law: kD216trans_p43*DISCp55*p43*cell
kBid = 5.2134055139547E-4 Reaction: Bid => tBid; p43, p18, Bid, p43, p18, Rate Law: kBid*Bid*(p43+p18)*cell
kD216trans_p55 = 2.23246421372882E-4 Reaction: DISCp55 => p30; DISCp55, p30, DISCp55, p30, Rate Law: kD216trans_p55*DISCp55*(DISCp55+p30)*cell
koff_FADD = 0.00130854998177646 Reaction: DISC => FADD; DISC, Rate Law: koff_FADD*DISC*cell
kD216 = 0.00639775937416746 Reaction: DISCp55 => p30; DISCp55, Rate Law: kD216*DISCp55*cell
CD95act = 0.0; kon_FADD = 0.00108871858684363 Reaction: FADD => DISC; FADD, Rate Law: kon_FADD*CD95act*FADD*cell

States:

Name Description
Bid [BH3-interacting domain death agonist]
PrNES mCherry [SBO:0000178; probe; Red fluorescent protein drFP583; nuclear_export_signal]
p30 [CASP8]
FADD [FAS-associated death domain protein]
p18 [Caspase-8]
p43 [CASP8 and FADD-like apoptosis regulator]
DISC [death-inducing signaling complex]
p55free [CASP8]
PrER [probe; Calnexin]
mCherry [Red fluorescent protein drFP583]
DISCp55 [CASP8; death-inducing signaling complex]
mGFP [Green fluorescent protein]
PrER mGFP [SBO:0000178; probe; Calnexin; Green fluorescent protein]
PrNES [probe; nuclear_export_signal]
p18inactive [inactive; Caspase-8]
tBid [BH3-interacting domain death agonist; mitochondrial outer membrane permeabilization]

Observables: none

Kamihira2000 - calcitonin fibrillation kineticsThis model studies the kinetics of human calcitonin fibrillation describe…

Conformational transitions of human calcitonin (hCT) during fibril formation in the acidic and neutral conditions were investigated by high-resolution solid-state 13C NMR spectroscopy. In aqueous acetic acid solution (pH 3.3), a local alpha-helical form is present around Gly10 whereas a random coil form is dominant as viewed from Phe22, Ala26, and Ala31 in the monomer form on the basis of the 13C chemical shifts. On the other hand, a local beta-sheet form as viewed from Gly10 and Phe22, and both beta-sheet and random coil as viewed from Ala26 and Ala31 were detected in the fibril at pH 3.3. The results indicate that conformational transitions from alpha-helix to beta-sheet, and from random coil to beta-sheet forms occurred in the central and C-terminus regions, respectively, during the fibril formation. The increased 13C resonance intensities of fibrils after a certain delay time suggests that the fibrillation can be explained by a two-step reaction mechanism in which the first step is a homogeneous association to form a nucleus, and the second step is an autocatalytic heterogeneous fibrillation. In contrast to the fibril at pH 3.3, the fibril at pH 7.5 formed a local beta-sheet conformation at the central region and exhibited a random coil at the C-terminus region. Not only a hydrophobic interaction among the amphiphilic alpha-helices, but also an electrostatic interaction between charged side chains can play an important role for the fibril formation at pH 7.5 and 3.3 acting as electrostatically favorable and unfavorable interactions, respectively. These results suggest that hCT fibrils are formed by stacking antiparallel beta-sheets at pH 7.5 and a mixture of antiparallel and parallel beta-sheets at pH 3.3. link: http://identifiers.org/pubmed/10850796

Parameters:

Name Description
k2 = 2.29; a = 5.85E-5 Reaction: => f, Rate Law: compartment_*k2*a*f
k1 = 2.79E-6 Reaction: => f, Rate Law: compartment_*k1

States:

Name Description
f [Calcitonin]

Observables: none

Kamminga2017 - Metabolic model of Mycoplasma hyopneumoniae growthThis model is described in the article: [Metabolic mod…

Mycoplasma hyopneumoniae is cultured on large-scale to produce antigen for inactivated whole-cell vaccines against respiratory disease in pigs. However, the fastidious nutrient requirements of this minimal bacterium and the low growth rate make it challenging to reach sufficient biomass yield for antigen production. In this study, we sequenced the genome of M. hyopneumoniae strain 11 and constructed a high quality constraint-based genome-scale metabolic model of 284 chemical reactions and 298 metabolites. We validated the model with time-series data of duplicate fermentation cultures to aim for an integrated model describing the dynamic profiles measured in fermentations. The model predicted that 84% of cellular energy in a standard M. hyopneumoniae cultivation was used for non-growth associated maintenance and only 16% of cellular energy was used for growth and growth associated maintenance. Following a cycle of model-driven experimentation in dedicated fermentation experiments, we were able to increase the fraction of cellular energy used for growth through pyruvate addition to the medium. This increase in turn led to an increase in growth rate and a 2.3 times increase in the total biomass concentration reached after 3-4 days of fermentation, enhancing the productivity of the overall process. The model presented provides a solid basis to understand and further improve M. hyopneumoniae fermentation processes. Biotechnol. Bioeng. 2017;9999: 1-9. © 2017 Wiley Periodicals, Inc. link: http://identifiers.org/pubmed/28600895

Parameters: none

States: none

Observables: none

MODEL0911270007 @ v0.0.1

This a model from the article: A theoretical model of type I collagen proteolysis by matrix metalloproteinase (MMP) 2…

One well documented family of enzymes responsible for the proteolytic processes that occur in the extracellular matrix is the soluble and membrane-associated matrix metalloproteinases. Here we present the first theoretical model of the biochemical network describing the proteolysis of collagen I by matrix metalloproteinases 2 (MMP2) and membrane type 1 matrix metalloproteinases (MT1-MMP) in the presence of the tissue inhibitor of metalloproteinases 2 (TIMP2) in a bulk, cell-free, well stirred environment. The model can serve as a tool for describing quantitatively the activation of the MMP2 proenzyme (pro-MMP2), the ectodomain shedding of MT1-MMP, and the collagenolysis arising from both of the enzymes. We show that pro-MMP2 activation, a process that involves a trimer formation of the proenzyme with TIMP2 and MT1-MMP, is suppressed at high inhibitor levels and paradoxically attains maximum only at intermediate TIMP2 concentrations. We also calculate the conditions for which pro-MMP2 activation is maximal. Furthermore we demonstrate that the ectodomain shedding of MT1-MMP can serve as a mechanism controlling the MT1-MMP availability and therefore the pro-MMP2 activation. Finally the proteolytic synergism of MMP2 and MT1-MMP is introduced and described quantitatively. The model provides us a tool to determine the conditions under which the synergism is optimized. Our approach is the first step toward a more complete description of the proteolytic processes that occur in the extracellular matrix and include a wider spectrum of enzymes and substrates as well as naturally occurring or artificial inhibitors. link: http://identifiers.org/pubmed/15252025

Parameters: none

States: none

Observables: none

Karapetyan2016 - Genetic oscillatory network - Activator Titration Circuit (ATC)This model is described in the article:…

Genetic oscillators, such as circadian clocks, are constantly perturbed by molecular noise arising from the small number of molecules involved in gene regulation. One of the strongest sources of stochasticity is the binary noise that arises from the binding of a regulatory protein to a promoter in the chromosomal DNA. In this study, we focus on two minimal oscillators based on activator titration and repressor titration to understand the key parameters that are important for oscillations and for overcoming binary noise. We show that the rate of unbinding from the DNA, despite traditionally being considered a fast parameter, needs to be slow to broaden the space of oscillatory solutions. The addition of multiple, independent DNA binding sites further expands the oscillatory parameter space for the repressor-titration oscillator and lengthens the period of both oscillators. This effect is a combination of increased effective delay of the unbinding kinetics due to multiple binding sites and increased promoter ultrasensitivity that is specific for repression. We then use stochastic simulation to show that multiple binding sites increase the coherence of oscillations by mitigating the binary noise. Slow values of DNA unbinding rate are also effective in alleviating molecular noise due to the increased distance from the bifurcation point. Our work demonstrates how the number of DNA binding sites and slow unbinding kinetics, which are often omitted in biophysical models of gene circuits, can have a significant impact on the temporal and stochastic dynamics of genetic oscillators. link: http://identifiers.org/pubmed/26764732

Parameters:

Name Description
t_32 = 0.0 Reaction: G3 => G2 + A2; G3, Rate Law: yeast*t_32*G3
a_01 = 2.49202551834131E-4 Reaction: G0 + A2 => G1; G0, A2, Rate Law: yeast*a_01*G0*A2
delta_m = 0.0186 Reaction: rA => ; rA, Rate Law: yeast*delta_m*rA
a_23 = 0.0 Reaction: G2 + A2 => G3; G2, A2, Rate Law: yeast*a_23*G2*A2
delta_p = 0.0077 Reaction: I => ; I, Rate Law: yeast*delta_p*I
t_21 = 0.0 Reaction: G2 => G1 + A2; G2, Rate Law: yeast*t_21*G2
epsilon_1 = 6.0 Reaction: A2 => A; A2, Rate Law: yeast*epsilon_1*A2
a_12 = 0.0 Reaction: G1 + A2 => G2; G1, A2, Rate Law: yeast*a_12*G1*A2
rho_f = 0.1781 Reaction: G0 => G0 + rI; G0, Rate Law: yeast*rho_f*G0
epsilon = 0.024 Reaction: AI => A + I; AI, Rate Law: yeast*epsilon*AI
beta = 14.109 Reaction: rA => rA + A; rA, Rate Law: yeast*beta*rA
rho_b = 5.343 Reaction: G1 => G1 + rI; G1, Rate Law: yeast*rho_b*G1
t_10 = 0.02 Reaction: G1 => G0 + A2; G1, Rate Law: yeast*t_10*G1
gamma = 0.025 Reaction: A + I => AI; A, I, Rate Law: yeast*gamma*A*I
rho_0 = 0.975493874916701 Reaction: => rA, Rate Law: yeast*rho_0

States:

Name Description
G3 G3
I I
rI rI
A A
G1 G1
A2 [IPR004827]
rA rA
G2 G2
G0 G0
AI AI

Observables: none

Karapetyan2016 - Genetic oscillatory network - Repressor Titration Circuit (RTC)This model is described in the article:…

Genetic oscillators, such as circadian clocks, are constantly perturbed by molecular noise arising from the small number of molecules involved in gene regulation. One of the strongest sources of stochasticity is the binary noise that arises from the binding of a regulatory protein to a promoter in the chromosomal DNA. In this study, we focus on two minimal oscillators based on activator titration and repressor titration to understand the key parameters that are important for oscillations and for overcoming binary noise. We show that the rate of unbinding from the DNA, despite traditionally being considered a fast parameter, needs to be slow to broaden the space of oscillatory solutions. The addition of multiple, independent DNA binding sites further expands the oscillatory parameter space for the repressor-titration oscillator and lengthens the period of both oscillators. This effect is a combination of increased effective delay of the unbinding kinetics due to multiple binding sites and increased promoter ultrasensitivity that is specific for repression. We then use stochastic simulation to show that multiple binding sites increase the coherence of oscillations by mitigating the binary noise. Slow values of DNA unbinding rate are also effective in alleviating molecular noise due to the increased distance from the bifurcation point. Our work demonstrates how the number of DNA binding sites and slow unbinding kinetics, which are often omitted in biophysical models of gene circuits, can have a significant impact on the temporal and stochastic dynamics of genetic oscillators. link: http://identifiers.org/pubmed/26764732

Parameters:

Name Description
t_32 = 0.0 Reaction: G3 => G2 + R2; G3, Rate Law: yeast*t_32*G3
a_01 = 2.49202551834131E-4 Reaction: G0 + R2 => G1; G0, R2, Rate Law: yeast*a_01*G0*R2
a_23 = 0.0 Reaction: G2 + R2 => G3; G2, R2, Rate Law: yeast*a_23*G2*R2
rho_0 = 0.468598473029544 Reaction: => rI, Rate Law: yeast*rho_0
delta_p = 0.0077 Reaction: I => ; I, Rate Law: yeast*delta_p*I
t_21 = 0.0 Reaction: G2 => G1 + R2; G2, Rate Law: yeast*t_21*G2
rho_b = 0.245950413223141 Reaction: G3 => G3 + rR; G3, Rate Law: yeast*rho_b*G3
rho_f = 0.8928 Reaction: G0 => G0 + rR; G0, Rate Law: yeast*rho_f*G0
epsilon_1 = 6.0 Reaction: R2 => R; R2, Rate Law: yeast*epsilon_1*R2
a_12 = 0.0 Reaction: G1 + R2 => G2; G1, R2, Rate Law: yeast*a_12*G1*R2
epsilon = 0.024 Reaction: RI => R + I; RI, Rate Law: yeast*epsilon*RI
beta = 14.109 Reaction: rI => rI + I; rI, Rate Law: yeast*beta*rI
delta_m = 0.0159 Reaction: rR => ; rR, Rate Law: yeast*delta_m*rR
t_10 = 0.02 Reaction: G1 => G0 + R2; G1, Rate Law: yeast*t_10*G1
gamma = 0.025 Reaction: R + I => RI; R, I, Rate Law: yeast*gamma*R*I

States:

Name Description
G3 G3
I I
rI rI
G1 G1
RI RI
G2 G2
G0 G0
R2 R2
rR rR
R R

Observables: none

Karlstaedt2012 - CardioNet, A Human Metabolic NetworkCardioNet is a functionally validated metabolic network of the huma…

BACKGROUND: Availability of oxygen and nutrients in the coronary circulation is a crucial determinant of cardiac performance. Nutrient composition of coronary blood may significantly vary in specific physiological and pathological conditions, for example, administration of special diets, long-term starvation, physical exercise or diabetes. Quantitative analysis of cardiac metabolism from a systems biology perspective may help to a better understanding of the relationship between nutrient supply and efficiency of metabolic processes required for an adequate cardiac output. RESULTS: Here we present CardioNet, the first large-scale reconstruction of the metabolic network of the human cardiomyocyte comprising 1793 metabolic reactions, including 560 transport processes in six compartments. We use flux-balance analysis to demonstrate the capability of the network to accomplish a set of 368 metabolic functions required for maintaining the structural and functional integrity of the cell. Taking the maintenance of ATP, biosynthesis of ceramide, cardiolipin and further important phospholipids as examples, we analyse how a changed supply of glucose, lactate, fatty acids and ketone bodies may influence the efficiency of these essential processes. CONCLUSIONS: CardioNet is a functionally validated metabolic network of the human cardiomyocyte that enables theorectical studies of cellular metabolic processes crucial for the accomplishment of an adequate cardiac output. link: http://identifiers.org/pubmed/22929619

Parameters: none

States: none

Observables: none

This model is described in the article: **Glucose 6-phosphate accumulates via phosphoglucose isomerase inhibition in he…

Rationale: Metabolic and structural remodeling is a hallmark of heart failure. This remodeling involves activation of the mammalian target of rapamycin (mTOR) signaling pathway, but little is known on how intermediary metabolites are integrated as metabolic signals. Objective: We investigated the metabolic control of cardiac glycolysis and explored the potential of glucose 6-phosphate to regulate glycolytic flux and mTOR activation. Methods and Results: We developed a kinetic model of cardiomyocyte carbohydrate metabolism, CardioGlyco, to study the metabolic control of myocardial glycolysis and glucose 6-phosphate levels. Metabolic control analysis revealed that glucose 6-phosphate concentration is dependent on phosphoglucose isomerase activity. Next, we integrated ex vivo tracer studies with mathematical simulations to test how changes in glucose supply and glycolytic flux affect mTOR activation. Nutrient deprivation promoted a tight coupling between glucose uptake and oxidation, glucose 6-phosphate reduction, and increased protein-protein interaction between hexokinase II and mTOR. We validated the in silico modeling in cultured adult mouse ventricular cardiomyocytes by modulating phosphoglucose isomerase activity using erythrose 4-phosphate. Inhibition of glycolytic flux at the level of phosphoglucose isomerase caused glucose 6-phosphate accumulation, which correlated with increased mTOR activation. Using click chemistry, we labeled newly synthesized proteins and confirmed that inhibition of phosphoglucose isomerase increases protein synthesis. Conclusions: The reduction of phosphoglucose isomerase activity directly affects myocyte growth by regulating mTOR activation. link: http://identifiers.org/pubmed/31698999

Parameters: none

States: none

Observables: none

Kavšček2015 - Genome-scale metabolic model of Yarrowia lipolytica (iMK735)This model is described in the article: [Opti…

Yarrowia lipolytica is a non-conventional yeast that is extensively investigated for its ability to excrete citrate or to accumulate large amounts of storage lipids, which is of great significance for single cell oil production. Both traits are thus of interest for basic research as well as for biotechnological applications but they typically occur simultaneously thus lowering the respective yields. Therefore, engineering of strains with high lipid content relies on novel concepts such as computational simulation to better understand the two competing processes and to eliminate citrate excretion.Using a genome-scale model (GSM) of baker's yeast as a scaffold, we reconstructed the metabolic network of Y. lipolytica and optimized it for use in flux balance analysis (FBA), with the aim to simulate growth and lipid production phases of this yeast. We validated our model and found the predictions of the growth behavior of Y. lipolytica in excellent agreement with experimental data. Based on these data, we successfully designed a fed-batch strategy to avoid citrate excretion during the lipid production phase. Further analysis of the network suggested that the oxygen demand of Y. lipolytica is reduced upon induction of lipid synthesis. According to this finding we hypothesized that a reduced aeration rate might induce lipid accumulation. This prediction was indeed confirmed experimentally. In a fermentation combining these two strategies lipid content of the biomass was increased by 80%, and lipid yield was improved more than four-fold, compared to standard conditions.Genome scale network reconstructions provide a powerful tool to predict the effects of genetic modifications and the metabolic response to environmental conditions. The high accuracy and the predictive value of a newly reconstructed GSM of Y. lipolytica to optimize growth conditions for lipid accumulation are demonstrated. Based on these findings, further strategies for engineering Y. lipolytica towards higher efficiency in single cell oil production are discussed. link: http://identifiers.org/pubmed/26503450

Parameters: none

States: none

Observables: none

This is a mathematical model of the Wnt signaling pathway in medulloblastoma comprised of two compartments. Composed of…

Deregulation of signaling pathways and subsequent abnormal interactions of downstream genes very often results in carcinogenesis. In this paper, we propose a two-compartment model describing intricate dynamics of the target genes of the Wnt signaling pathway in medulloblastoma. The system of nine nonlinear ordinary differential equations accounts for the formation and dissociation of complexes as well as for the transcription, translation and transport between the cytoplasm and the nucleus. We focus on the interplay between MYC and SGK1 (serum and glucocorticoid-inducible kinase 1), which are the products of Wnt/β-catenin signaling pathway, and GSK3β (glycogen synthase kinase). Numerical simulations of the model solutions yield a better understanding of the process and indicate the importance of the SGK1 gene in the development of medulloblastoma, which has been confirmed in our recent experiments. The model is calibrated based on the gene expression microarray data for two types of medulloblastoma, characterized by monosomy and trisomy of chromosome 6q to highlight the difference between diagnoses. link: http://identifiers.org/pubmed/24685888

Parameters: none

States: none

Observables: none

This a model from the article: Diffusion induced oscillatory insulin secretion. Keener JP. Bull Math Biol. 2001 Jul…

Oscillatory secretion of insulin has been observed in many different experimental preparations. Here we examine a mathematical model for in vitro insulin secretion from pancreatic beta cells in a flow-through reactor. The analysis shows that oscillations result because of an important interplay between flow rate of the reactor and insulin diffusion. In particular, if the ratio of flow rate to volume of the reaction bed is too large, oscillations are eliminated, in contradiction to the conclusions of Maki and Keizer (L. W. Maki and Keizer J. Mathematical analysis of a proposed mechanism for oscillatory insulin secretion in perifused HIT-15 cells. Bull. Math. Biol., 57(1995), 569-591). Furthermore, with reasonable numbers for the experimental parameters and the diffusion of insulin, the model equations do not exhibit oscillations. link: http://identifiers.org/pubmed/11497161

Parameters: none

States: none

Observables: none

Kees2018 - Genome-scale constraint-based model of the mucin-degrader <I>Akkermansia muciniphila</I>This model is descr…

The abundance of the human intestinal symbiont Akkermansia muciniphila has found to be inversely correlated with several diseases, including metabolic syndrome and obesity. A. muciniphila is known to use mucin as sole carbon and nitrogen source. To study the physiology and the potential for therapeutic applications of this bacterium, we designed a defined minimal medium. The composition of the medium was based on the genome-scale metabolic model of A. muciniphila and the composition of mucin. Our results indicate that A. muciniphila does not code for GlmS, the enzyme that mediates the conversion of fructose-6-phosphate (Fru6P) to glucosamine-6-phosphate (GlcN6P), which is essential in peptidoglycan formation. The only annotated enzyme that could mediate this conversion is Amuc-NagB on locus Amuc_1822. We found that Amuc-NagB was unable to form GlcN6P from Fru6P at physiological conditions, while it efficiently catalyzed the reverse reaction. To overcome this inability, N-acetylglucosamine needs to be present in the medium for A. muciniphila growth. With these findings, the genome-scale metabolic model was updated and used to accurately predict growth of A. muciniphila on synthetic media. The finding that A. muciniphila has a necessity for GlcNAc, which is present in mucin further prompts the adaptation to its mucosal niche. link: http://identifiers.org/pubmed/29377524

Parameters: none

States: none

Observables: none

BIOMD0000000060 @ v0.0.1

The model reproduces the time profile of Open probability of the ryanodine receptor as shown in Fig 2A and 2B of the pap…

A simplified mechanism that mimics "adaptation" of the ryanodine receptor (RyR) has been developed and its significance for Ca2+(-)induced Ca2+ release and Ca2+ oscillations investigated. For parameters that reproduce experimental data for the RyR from cardiac cells, adaptation of the RyR in combination with sarco/endoplasmic reticulum Ca2+ ATPase Ca2+ pumps in the internal stores can give rise to either low [Cai2+] steady states or Ca2+ oscillations coexisting with unphysiologically high [Cai2+] steady states. In this closed-cell-type model rapid, adaptation-dependent Ca2+ oscillations occur only in limited ranges of parameters. In the presence of Ca2+ influx and efflux from outside the cell (open-cell model) Ca2+ oscillations occur for a wide range of physiological parameter values and have a period that is determined by the rate of Ca2+ refilling of the stores. Although the rate of adaptation of the RyR has a role in determining the shape and the period of the Ca2+ spike, it is not essential for their existence. This is in marked contrast with what is observed for the inositol 1,4,5-trisphosphate receptor for which the biphasic activation and inhibition of its activity by Ca2+ are sufficient to produce oscillations. Results for this model are compared with those based on Ca2+(-)induced Ca2+ release alone in the bullfrog sympathetic neuron. This kinetic model should be suitable for analyzing phenomena associated with "Ca2+ sparks," including their merger into Ca2+ waves in cardiac myocytes. link: http://identifiers.org/pubmed/8968617

Parameters:

Name Description
kc_minus=0.1 per_second; kc_plus=1.75 per_second Reaction: Po1 => Pc2; Po1, Rate Law: kc_plus*Po1-kc_minus*Pc2
ka_plus=1500.0 microM-4sec-1; ka_minus=28.8 per_second; Ca=0.9 microM; n=4.0 dimensionless Reaction: Po1 => Pc1; Po1, Rate Law: ka_minus*Po1-ka_plus*Ca^n*Pc1
m=3.0 dimensionless; kb_plus=1500.0 microM-3sec-1; kb_minus=385.9 per_second; Ca=0.9 microM Reaction: Po1 => Po2; Po1, Rate Law: kb_plus*Ca^m*Po1-kb_minus*Po2

States:

Name Description
Po2 [Ryanodine receptor 1]
Pc2 [Ryanodine receptor 1]
Pc1 [Ryanodine receptor 1]
Po1 [Ryanodine receptor 1]

Observables: none

Kerkhoven2013 - Glycolysis and Pentose Phosphate Pathway in T.brucei - MODEL BThere are six models (Model A, B, C, C-fru…

Dynamic models of metabolism can be useful in identifying potential drug targets, especially in unicellular organisms. A model of glycolysis in the causative agent of human African trypanosomiasis, Trypanosoma brucei, has already shown the utility of this approach. Here we add the pentose phosphate pathway (PPP) of T. brucei to the glycolytic model. The PPP is localized to both the cytosol and the glycosome and adding it to the glycolytic model without further adjustments leads to a draining of the essential bound-phosphate moiety within the glycosome. This phosphate "leak" must be resolved for the model to be a reasonable representation of parasite physiology. Two main types of theoretical solution to the problem could be identified: (i) including additional enzymatic reactions in the glycosome, or (ii) adding a mechanism to transfer bound phosphates between cytosol and glycosome. One example of the first type of solution would be the presence of a glycosomal ribokinase to regenerate ATP from ribose 5-phosphate and ADP. Experimental characterization of ribokinase in T. brucei showed that very low enzyme levels are sufficient for parasite survival, indicating that other mechanisms are required in controlling the phosphate leak. Examples of the second type would involve the presence of an ATP:ADP exchanger or recently described permeability pores in the glycosomal membrane, although the current absence of identified genes encoding such molecules impedes experimental testing by genetic manipulation. Confronted with this uncertainty, we present a modeling strategy that identifies robust predictions in the context of incomplete system characterization. We illustrate this strategy by exploring the mechanism underlying the essential function of one of the PPP enzymes, and validate it by confirming the model predictions experimentally. link: http://identifiers.org/pubmed/24339766

Parameters:

Name Description
PPI_c_Keq=5.6; PPI_c_Vmax=72.0; PPI_c_KmRul5P=1.4; PPI_c_KmRib5P=4.0 Reaction: Rul5P_c => Rib5P_c; Rul5P_c, Rib5P_c, Rate Law: PPI_c_Vmax*Rul5P_c*(1-Rib5P_c/(PPI_c_Keq*Rul5P_c))/(PPI_c_KmRul5P*(1+Rul5P_c/PPI_c_KmRul5P+Rib5P_c/PPI_c_KmRib5P))
GDA_g_k=600.0 Reaction: Gly3P_g + DHAP_c => Gly3P_c + DHAP_g; Gly3P_g, DHAP_c, Gly3P_c, DHAP_g, Rate Law: Gly3P_g*GDA_g_k*DHAP_c-Gly3P_c*GDA_g_k*DHAP_g
_3PGAT_g_k=250.0 Reaction: _3PGA_g => _3PGA_c; _3PGA_g, _3PGA_c, Rate Law: _3PGAT_g_k*_3PGA_g-_3PGAT_g_k*_3PGA_c
GPO_c_Vmax=368.0; GPO_c_KmGly3P=1.7 Reaction: Gly3P_c => DHAP_c; Gly3P_c, Rate Law: GPO_c_Vmax*Gly3P_c/(GPO_c_KmGly3P*(1+Gly3P_c/GPO_c_KmGly3P))
HXK_g_Vmax=1774.68; HXK_g_KmADP=0.126; HXK_g_Keq=759.0; HXK_g_KmATP=0.116; HXK_g_KmGlc6P=2.7; HXK_g_KmGlc=0.1 Reaction: ATP_g + Glc_g => Glc6P_g + ADP_g; Glc_g, ATP_g, Glc6P_g, ADP_g, Rate Law: HXK_g_Vmax*Glc_g*ATP_g*(1-Glc6P_g*ADP_g/(HXK_g_Keq*Glc_g*ATP_g))/(HXK_g_KmGlc*HXK_g_KmATP*(1+Glc_g/HXK_g_KmGlc+Glc6P_g/HXK_g_KmGlc6P)*(1+ATP_g/HXK_g_KmATP+ADP_g/HXK_g_KmADP))
PGI_g_Vmax=1305.0; PGI_g_Ki6PG=0.14; PGI_g_KmGlc6P=0.4; PGI_g_Keq=0.457; PGI_g_KmFru6P=0.12 Reaction: Glc6P_g => Fru6P_g; _6PG_g, Glc6P_g, Fru6P_g, _6PG_g, Rate Law: PGI_g_Vmax*Glc6P_g*(1-Fru6P_g/(PGI_g_Keq*Glc6P_g))/(PGI_g_KmGlc6P*(1+Glc6P_g/PGI_g_KmGlc6P+Fru6P_g/PGI_g_KmFru6P+_6PG_g/PGI_g_Ki6PG))
NADPHu_c_k=2.0 Reaction: NADPH_c => NADP_c; NADPH_c, Rate Law: NADPHu_c_k*NADPH_c
ALD_g_KmDHAP=0.015; ALD_g_KiGA3P=0.098; ALD_g_KmGA3P=0.067; ALD_g_Vmax=560.0; ALD_g_KmFru16BP=0.009; ALD_g_KiADP=1.51; ALD_g_KiAMP=3.65; ALD_g_Keq=0.084; ALD_g_KiATP=0.68 Reaction: Fru16BP_g => GA3P_g + DHAP_g; ATP_g, ADP_g, AMP_g, Fru16BP_g, GA3P_g, DHAP_g, ATP_g, ADP_g, AMP_g, Rate Law: ALD_g_Vmax*Fru16BP_g*(1-GA3P_g*DHAP_g/(Fru16BP_g*ALD_g_Keq))/(ALD_g_KmFru16BP*(1+ATP_g/ALD_g_KiATP+ADP_g/ALD_g_KiADP+AMP_g/ALD_g_KiAMP)*(1+GA3P_g/ALD_g_KmGA3P+DHAP_g/ALD_g_KmDHAP+Fru16BP_g/(ALD_g_KmFru16BP*(1+ATP_g/ALD_g_KiATP+ADP_g/ALD_g_KiADP+AMP_g/ALD_g_KiAMP))+GA3P_g*DHAP_g/(ALD_g_KmGA3P*ALD_g_KmDHAP)+Fru16BP_g*GA3P_g/(ALD_g_KmFru16BP*ALD_g_KiGA3P*(1+ATP_g/ALD_g_KiATP+ADP_g/ALD_g_KiADP+AMP_g/ALD_g_KiAMP))))
G6PP_c_KmGlc6P=5.6; G6PP_c_Vmax=28.0; G6PP_c_Keq=263.0; G6PP_c_KmGlc=5.6 Reaction: Glc6P_c => Glc_c; Glc6P_c, Glc_c, Rate Law: G6PP_c_Vmax*Glc6P_c*(1-Glc_c/(G6PP_c_Keq*Glc6P_c))/(G6PP_c_KmGlc6P*(1+Glc6P_c/G6PP_c_KmGlc6P+Glc_c/G6PP_c_KmGlc))
PYK_c_KmPyr=50.0; PYK_c_KiADP=0.64; PYK_c_Vmax=1020.0; PYK_c_KmADP=0.114; PYK_c_Keq=10800.0; PYK_c_KiATP=0.57; PYK_c_KmATP=15.0; PYK_c_KmPEP=0.34; PYK_c_n=2.5 Reaction: PEP_c + ADP_c => Pyr_c + ATP_c; ADP_c, Pyr_c, ATP_c, PEP_c, Rate Law: PYK_c_Vmax*ADP_c*(1-Pyr_c*ATP_c/(PYK_c_Keq*PEP_c*ADP_c))*(PEP_c/(PYK_c_KmPEP*(1+ADP_c/PYK_c_KiADP+ATP_c/PYK_c_KiATP)))^PYK_c_n/(PYK_c_KmADP*(1+(PEP_c/(PYK_c_KmPEP*(1+ADP_c/PYK_c_KiADP+ATP_c/PYK_c_KiATP)))^PYK_c_n+Pyr_c/PYK_c_KmPyr)*(1+ADP_c/PYK_c_KmADP+ATP_c/PYK_c_KmATP))
ATPu_c_k=50.0 Reaction: ATP_c => ADP_c; ATP_c, ADP_c, Rate Law: ATPu_c_k*ATP_c/ADP_c
G6PDH_g_KmNADPH=1.0E-4; G6PDH_g_Keq=5.02; G6PDH_g_KmNADP=0.0094; G6PDH_g_KmGlc6P=0.058; G6PDH_g_Vmax=8.4; G6PDH_g_Km6PGL=0.04 Reaction: Glc6P_g + NADP_g => _6PGL_g + NADPH_g; Glc6P_g, NADP_g, _6PGL_g, NADPH_g, Rate Law: G6PDH_g_Vmax*Glc6P_g*NADP_g*(1-_6PGL_g*NADPH_g/(G6PDH_g_Keq*Glc6P_g*NADP_g))/(G6PDH_g_KmGlc6P*G6PDH_g_KmNADP*(1+Glc6P_g/G6PDH_g_KmGlc6P+_6PGL_g/G6PDH_g_Km6PGL)*(1+NADP_g/G6PDH_g_KmNADP+NADPH_g/G6PDH_g_KmNADPH))
TR_c_KmTS2=0.0069; TR_c_KmTSH2=0.0018; TR_c_KmNADPH=7.7E-4; TR_c_Vmax=252.0; TR_c_Keq=434.0; TR_c_KmNADP=0.081 Reaction: TS2_c + NADPH_c => NADP_c + TSH2_c; TS2_c, NADPH_c, TSH2_c, NADP_c, Rate Law: TR_c_Vmax*TS2_c*NADPH_c*(1-TSH2_c*NADP_c/(TR_c_Keq*TS2_c*NADPH_c))/(TR_c_KmTS2*TR_c_KmNADPH*(1+TS2_c/TR_c_KmTS2+TSH2_c/TR_c_KmTSH2)*(1+NADPH_c/TR_c_KmNADPH+NADP_c/TR_c_KmNADP))
AK_g_k2=1000.0; AK_g_k1=480.0 Reaction: ADP_g => AMP_g + ATP_g; ADP_g, AMP_g, ATP_g, Rate Law: AK_g_k1*ADP_g^2-AMP_g*ATP_g*AK_g_k2
PyrT_c_Vmax=230.0; PyrT_c_KmPyr=1.96 Reaction: Pyr_c => Pyr_e; Pyr_c, Rate Law: PyrT_c_Vmax*Pyr_c/(PyrT_c_KmPyr*(1+Pyr_c/PyrT_c_KmPyr))
G6PDH_c_Vmax=8.4; G6PDH_c_Keq=5.02; G6PDH_c_KmNADP=0.0094; G6PDH_c_KmNADPH=1.0E-4; G6PDH_c_Km6PGL=0.04; G6PDH_c_KmGlc6P=0.058 Reaction: Glc6P_c + NADP_c => NADPH_c + _6PGL_c; Glc6P_c, NADP_c, _6PGL_c, NADPH_c, Rate Law: G6PDH_c_Vmax*Glc6P_c*NADP_c*(1-_6PGL_c*NADPH_c/(G6PDH_c_Keq*Glc6P_c*NADP_c))/(G6PDH_c_KmGlc6P*G6PDH_c_KmNADP*(1+Glc6P_c/G6PDH_c_KmGlc6P+_6PGL_c/G6PDH_c_Km6PGL)*(1+NADP_c/G6PDH_c_KmNADP+NADPH_c/G6PDH_c_KmNADPH))
HXK_c_KmATP=0.116; HXK_c_KmGlc=0.1; HXK_c_Vmax=154.32; HXK_c_KmADP=0.126; HXK_c_Keq=759.0; HXK_c_KmGlc6P=2.7 Reaction: Glc_c + ATP_c => Glc6P_c + ADP_c; Glc_c, ATP_c, Glc6P_c, ADP_c, Rate Law: HXK_c_Vmax*Glc_c*ATP_c*(1-Glc6P_c*ADP_c/(HXK_c_Keq*Glc_c*ATP_c))/(HXK_c_KmGlc*HXK_c_KmATP*(1+Glc_c/HXK_c_KmGlc+Glc6P_c/HXK_c_KmGlc6P)*(1+ATP_c/HXK_c_KmATP+ADP_c/HXK_c_KmADP))
GAPDH_g_Vmax=720.9; GAPDH_g_Km13BPGA=0.1; GAPDH_g_KmNAD=0.45; GAPDH_g_KmNADH=0.02; GAPDH_g_KmGA3P=0.15; GAPDH_g_Keq=0.066 Reaction: GA3P_g + NAD_g + Pi_g => NADH_g + _13BPGA_g; GA3P_g, NAD_g, _13BPGA_g, NADH_g, Rate Law: GAPDH_g_Vmax*GA3P_g*NAD_g*(1-_13BPGA_g*NADH_g/(GAPDH_g_Keq*GA3P_g*NAD_g))/(GAPDH_g_KmGA3P*GAPDH_g_KmNAD*(1+GA3P_g/GAPDH_g_KmGA3P+_13BPGA_g/GAPDH_g_Km13BPGA)*(1+NAD_g/GAPDH_g_KmNAD+NADH_g/GAPDH_g_KmNADH))
PGL_g_Km6PGL=0.05; PGL_g_Km6PG=0.05; PGL_g_Vmax=5.0; PGL_g_Keq=20000.0; PGL_g_k=0.055 Reaction: _6PGL_g => _6PG_g; _6PGL_g, _6PG_g, Rate Law: glycosome*PGL_g_k*(_6PGL_g-_6PG_g/PGL_g_Keq)+PGL_g_Vmax*_6PGL_g*(1-_6PG_g/(PGL_g_Keq*_6PGL_g))/(PGL_g_Km6PGL*(1+_6PGL_g/PGL_g_Km6PGL+_6PG_g/PGL_g_Km6PG))
TOX_c_k=2.0 Reaction: TSH2_c => TS2_c; TSH2_c, Rate Law: TOX_c_k*TSH2_c
ENO_c_Vmax=598.0; ENO_c_Km2PGA=0.054; ENO_c_Keq=4.17; ENO_c_KmPEP=0.24 Reaction: _2PGA_c => PEP_c; _2PGA_c, PEP_c, Rate Law: ENO_c_Vmax*_2PGA_c*(1-PEP_c/(ENO_c_Keq*_2PGA_c))/(ENO_c_Km2PGA*(1+_2PGA_c/ENO_c_Km2PGA+PEP_c/ENO_c_KmPEP))
PFK_g_Vmax=1708.0; PFK_g_KsATP=0.0393; PFK_g_KmFru6P=0.999; PFK_g_KmADP=1.0; PFK_g_KmATP=0.0648; PFK_g_Ki2=10.7; PFK_g_Ki1=15.8; PFK_g_Keq=1035.0 Reaction: ATP_g + Fru6P_g => Fru16BP_g + ADP_g; Fru6P_g, ATP_g, Fru16BP_g, ADP_g, Rate Law: PFK_g_Vmax*PFK_g_Ki1*Fru6P_g*ATP_g*(1-Fru16BP_g*ADP_g/(PFK_g_Keq*Fru6P_g*ATP_g))/(PFK_g_KmFru6P*PFK_g_KmATP*(Fru16BP_g+PFK_g_Ki1)*(PFK_g_KsATP/PFK_g_KmATP+Fru6P_g/PFK_g_KmFru6P+ATP_g/PFK_g_KmATP+ADP_g/PFK_g_KmADP+Fru16BP_g*ADP_g/(PFK_g_KmADP*PFK_g_Ki2)+Fru6P_g*ATP_g/(PFK_g_KmFru6P*PFK_g_KmATP)))
_6PGDH_g_KmNADP=0.001; _6PGDH_g_KmNADPH=6.0E-4; _6PGDH_g_Keq=47.0; _6PGDH_g_Km6PG=0.0035; _6PGDH_g_KmRul5P=0.03; _6PGDH_g_Vmax=10.6 Reaction: _6PG_g + NADP_g => Rul5P_g + CO2_g + NADPH_g; _6PG_g, NADP_g, Rul5P_g, NADPH_g, Rate Law: _6PGDH_g_Vmax*_6PG_g*NADP_g*(1-Rul5P_g*NADPH_g/(_6PGDH_g_Keq*_6PG_g*NADP_g))/(_6PGDH_g_Km6PG*_6PGDH_g_KmNADP*(1+_6PG_g/_6PGDH_g_Km6PG+Rul5P_g/_6PGDH_g_KmRul5P)*(1+NADP_g/_6PGDH_g_KmNADP+NADPH_g/_6PGDH_g_KmNADPH))
GlcT_c_Vmax=111.7; GlcT_c_KmGlc=1.0; GlcT_c_alpha=0.75 Reaction: Glc_e => Glc_c; Glc_e, Glc_c, Rate Law: GlcT_c_Vmax*(Glc_e-Glc_c)/(GlcT_c_KmGlc+Glc_e+Glc_c+GlcT_c_alpha*Glc_e*Glc_c/GlcT_c_KmGlc)
TPI_g_Keq=0.046; TPI_g_KmDHAP=1.2; TPI_g_KmGA3P=0.25; TPI_g_Vmax=999.3 Reaction: DHAP_g => GA3P_g; DHAP_g, GA3P_g, Rate Law: TPI_g_Vmax*DHAP_g*(1-GA3P_g/(TPI_g_Keq*DHAP_g))/(TPI_g_KmDHAP*(1+DHAP_g/TPI_g_KmDHAP+GA3P_g/TPI_g_KmGA3P))
NADPHu_g_k=2.0 Reaction: NADPH_g => NADP_g; NADPH_g, Rate Law: NADPHu_g_k*NADPH_g
PGAM_c_Km3PGA=0.15; PGAM_c_Vmax=225.0; PGAM_c_Km2PGA=0.16; PGAM_c_Keq=0.17 Reaction: _3PGA_c => _2PGA_c; _3PGA_c, _2PGA_c, Rate Law: PGAM_c_Vmax*_3PGA_c*(1-_2PGA_c/(PGAM_c_Keq*_3PGA_c))/(PGAM_c_Km3PGA*(1+_3PGA_c/PGAM_c_Km3PGA+_2PGA_c/PGAM_c_Km2PGA))
G3PDH_g_KmDHAP=0.1; G3PDH_g_KmNAD=0.4; G3PDH_g_Vmax=465.0; G3PDH_g_Keq=17085.0; G3PDH_g_KmNADH=0.01; G3PDH_g_KmGly3P=2.0 Reaction: NADH_g + DHAP_g => Gly3P_g + NAD_g; DHAP_g, NADH_g, Gly3P_g, NAD_g, Rate Law: G3PDH_g_Vmax*DHAP_g*NADH_g*(1-Gly3P_g*NAD_g/(G3PDH_g_Keq*DHAP_g*NADH_g))/(G3PDH_g_KmDHAP*G3PDH_g_KmNADH*(1+DHAP_g/G3PDH_g_KmDHAP+Gly3P_g/G3PDH_g_KmGly3P)*(1+NADH_g/G3PDH_g_KmNADH+NAD_g/G3PDH_g_KmNAD))
GK_g_Keq=8.37E-4; GK_g_KmATP=0.24; GK_g_KmGly=0.44; GK_g_KmADP=0.56; GK_g_KmGly3P=3.83; GK_g_Vmax=200.0 Reaction: Gly3P_g + ADP_g => Gly_e + ATP_g; Gly3P_g, ADP_g, Gly_e, ATP_g, Rate Law: GK_g_Vmax*Gly3P_g*ADP_g*(1-Gly_e*ATP_g/(GK_g_Keq*Gly3P_g*ADP_g))/(GK_g_KmGly3P*GK_g_KmADP*(1+Gly3P_g/GK_g_KmGly3P+Gly_e/GK_g_KmGly)*(1+ADP_g/GK_g_KmADP+ATP_g/GK_g_KmATP))
GlcT_g_k2=250000.0; GlcT_g_k1=250000.0 Reaction: Glc_c => Glc_g; Glc_c, Glc_g, Rate Law: GlcT_g_k1*Glc_c-GlcT_g_k2*Glc_g
PGL_c_Km6PG=0.05; PGL_c_k=0.055; PGL_c_Vmax=28.0; PGL_c_Km6PGL=0.05; PGL_c_Keq=20000.0 Reaction: _6PGL_c => _6PG_c; _6PGL_c, _6PG_c, Rate Law: PGL_c_k*cytosol*(_6PGL_c-_6PG_c/PGL_c_Keq)+PGL_c_Vmax*_6PGL_c*(1-_6PG_c/(PGL_c_Keq*_6PGL_c))/(PGL_c_Km6PGL*(1+_6PGL_c/PGL_c_Km6PGL+_6PG_c/PGL_c_Km6PG))
_6PGDH_c_KmNADP=0.001; _6PGDH_c_Keq=47.0; _6PGDH_c_Vmax=10.6; _6PGDH_c_KmNADPH=6.0E-4; _6PGDH_c_Km6PG=0.0035; _6PGDH_c_KmRul5P=0.03 Reaction: NADP_c + _6PG_c => CO2_c + NADPH_c + Rul5P_c; _6PG_c, NADP_c, Rul5P_c, NADPH_c, Rate Law: _6PGDH_c_Vmax*_6PG_c*NADP_c*(1-Rul5P_c*NADPH_c/(_6PGDH_c_Keq*_6PG_c*NADP_c))/(_6PGDH_c_Km6PG*_6PGDH_c_KmNADP*(1+_6PG_c/_6PGDH_c_Km6PG+Rul5P_c/_6PGDH_c_KmRul5P)*(1+NADP_c/_6PGDH_c_KmNADP+NADPH_c/_6PGDH_c_KmNADPH))
PPI_g_KmRul5P=1.4; PPI_g_Vmax=72.0; PPI_g_Keq=5.6; PPI_g_KmRib5P=4.0 Reaction: Rul5P_g => Rib5P_g; Rul5P_g, Rib5P_g, Rate Law: PPI_g_Vmax*Rul5P_g*(1-Rib5P_g/(PPI_g_Keq*Rul5P_g))/(PPI_g_KmRul5P*(1+Rul5P_g/PPI_g_KmRul5P+Rib5P_g/PPI_g_KmRib5P))
AK_c_k1=480.0; AK_c_k2=1000.0 Reaction: ADP_c => AMP_c + ATP_c; ADP_c, AMP_c, ATP_c, Rate Law: AK_c_k1*ADP_c^2-AMP_c*ATP_c*AK_c_k2
PGK_g_Km13BPGA=0.003; PGK_g_Vmax=2862.0; PGK_g_KmADP=0.1; PGK_g_Km3PGA=1.62; PGK_g_KmATP=0.29; PGK_g_Keq=3377.0 Reaction: _13BPGA_g + ADP_g => _3PGA_g + ATP_g; _13BPGA_g, ADP_g, _3PGA_g, ATP_g, Rate Law: PGK_g_Vmax*_13BPGA_g*ADP_g*(1-_3PGA_g*ATP_g/(PGK_g_Keq*_13BPGA_g*ADP_g))/(PGK_g_Km13BPGA*PGK_g_KmADP*(1+_13BPGA_g/PGK_g_Km13BPGA+_3PGA_g/PGK_g_Km3PGA)*(1+ADP_g/PGK_g_KmADP+ATP_g/PGK_g_KmATP))

States:

Name Description
6PG g [6-phospho-D-gluconic acid]
6PG c [6-phospho-D-gluconic acid]
TS2 c [trypanothione]
Rul5P g [D-ribulose 5-phosphate(2-)]
Glc6P c [D-glucopyranose 6-phosphate]
PEP c [phosphoenolpyruvate]
ATP g [ATP]
CO2 g [carbon dioxide]
Glc c [glucose]
GA3P g [glyceraldehyde 3-phosphate]
Fru16BP g [alpha-D-fructofuranose 1,6-bisphosphate]
Glc g [glucose]
Glc e [glucose]
TSH2 c [trypanothione disulfide]
Pyr e [pyruvate]
ADP g [ADP]
13BPGA g [683]
NADP c [NADP(+)]
DHAP g [glycerone phosphate(2-)]
NAD g [NAD]
NADH g [NADH]
Pyr c [pyruvate]
CO2 c [carbon dioxide]
6PGL g [6-phosphogluconolactonase3.1.1.17]
Fru6P g [444848]
2PGA c [59]
Gly3P c [glycerol 1-phosphate]
Rib5P c [aldehydo-D-ribose 5-phosphate(2-)]
3PGA c [3-phospho-D-glyceric acid]
NADP g [NADP(+)]
Rib5P g [aldehydo-D-ribose 5-phosphate(2-)]
Pi g [phosphatidylinositol]
Glc6P g [D-glucopyranose 6-phosphate]
ATP c [ATP]
DHAP c [glycerone phosphate(2-)]
NADPH c [NADPH]
Gly e [glycerol]
6PGL c [6-phosphogluconolactonase3.1.1.17]
Gly3P g [glycerol 1-phosphate]
ADP c [ADP]
AMP g [AMP]
Rul5P c [D-ribulose 5-phosphate(2-)]
3PGA g [3-phospho-D-glyceric acid]
AMP c [AMP]
NADPH g [NADPH]

Observables: none

Kerkhoven2013 - Glycolysis and Pentose Phosphate Pathway in T.brucei -MODEL C (with glucosomal ribokinase)There are six…

Dynamic models of metabolism can be useful in identifying potential drug targets, especially in unicellular organisms. A model of glycolysis in the causative agent of human African trypanosomiasis, Trypanosoma brucei, has already shown the utility of this approach. Here we add the pentose phosphate pathway (PPP) of T. brucei to the glycolytic model. The PPP is localized to both the cytosol and the glycosome and adding it to the glycolytic model without further adjustments leads to a draining of the essential bound-phosphate moiety within the glycosome. This phosphate "leak" must be resolved for the model to be a reasonable representation of parasite physiology. Two main types of theoretical solution to the problem could be identified: (i) including additional enzymatic reactions in the glycosome, or (ii) adding a mechanism to transfer bound phosphates between cytosol and glycosome. One example of the first type of solution would be the presence of a glycosomal ribokinase to regenerate ATP from ribose 5-phosphate and ADP. Experimental characterization of ribokinase in T. brucei showed that very low enzyme levels are sufficient for parasite survival, indicating that other mechanisms are required in controlling the phosphate leak. Examples of the second type would involve the presence of an ATP:ADP exchanger or recently described permeability pores in the glycosomal membrane, although the current absence of identified genes encoding such molecules impedes experimental testing by genetic manipulation. Confronted with this uncertainty, we present a modeling strategy that identifies robust predictions in the context of incomplete system characterization. We illustrate this strategy by exploring the mechanism underlying the essential function of one of the PPP enzymes, and validate it by confirming the model predictions experimentally. link: http://identifiers.org/pubmed/24339766

Parameters:

Name Description
RK_g_Keq=0.0036; RK_g_KmRib=0.51; RK_g_Vmax=10.0; RK_g_KmRib5P=0.39; RK_g_KmADP=0.25; RK_g_KmATP=0.24 Reaction: ADP_g + Rib5P_g => ATP_g + Rib_g; Rib5P_g, ADP_g, Rib_g, ATP_g, Rate Law: RK_g_Vmax*Rib5P_g*ADP_g*(1-Rib_g*ATP_g/(RK_g_Keq*Rib5P_g*ADP_g))/(RK_g_KmRib5P*RK_g_KmADP*(1+Rib5P_g/RK_g_KmRib5P+Rib_g/RK_g_KmRib)*(1+ADP_g/RK_g_KmADP+ATP_g/RK_g_KmATP))
PPI_c_Keq=5.6; PPI_c_Vmax=72.0; PPI_c_KmRul5P=1.4; PPI_c_KmRib5P=4.0 Reaction: Rul5P_c => Rib5P_c; Rul5P_c, Rib5P_c, Rate Law: PPI_c_Vmax*Rul5P_c*(1-Rib5P_c/(PPI_c_Keq*Rul5P_c))/(PPI_c_KmRul5P*(1+Rul5P_c/PPI_c_KmRul5P+Rib5P_c/PPI_c_KmRib5P))
GDA_g_k=600.0 Reaction: Gly3P_g + DHAP_c => Gly3P_c + DHAP_g; Gly3P_g, DHAP_c, Gly3P_c, DHAP_g, Rate Law: Gly3P_g*GDA_g_k*DHAP_c-Gly3P_c*GDA_g_k*DHAP_g
GPO_c_Vmax=368.0; GPO_c_KmGly3P=1.7 Reaction: Gly3P_c => DHAP_c; Gly3P_c, Rate Law: GPO_c_Vmax*Gly3P_c/(GPO_c_KmGly3P*(1+Gly3P_c/GPO_c_KmGly3P))
_3PGAT_g_k=250.0 Reaction: _3PGA_g => _3PGA_c; _3PGA_g, _3PGA_c, Rate Law: _3PGAT_g_k*_3PGA_g-_3PGAT_g_k*_3PGA_c
PGI_g_Vmax=1305.0; PGI_g_Ki6PG=0.14; PGI_g_KmGlc6P=0.4; PGI_g_Keq=0.457; PGI_g_KmFru6P=0.12 Reaction: Glc6P_g => Fru6P_g; _6PG_g, Glc6P_g, Fru6P_g, _6PG_g, Rate Law: PGI_g_Vmax*Glc6P_g*(1-Fru6P_g/(PGI_g_Keq*Glc6P_g))/(PGI_g_KmGlc6P*(1+Glc6P_g/PGI_g_KmGlc6P+Fru6P_g/PGI_g_KmFru6P+_6PG_g/PGI_g_Ki6PG))
HXK_g_Vmax=1774.68; HXK_g_KmADP=0.126; HXK_g_Keq=759.0; HXK_g_KmATP=0.116; HXK_g_KmGlc6P=2.7; HXK_g_KmGlc=0.1 Reaction: ATP_g + Glc_g => Glc6P_g + ADP_g; Glc_g, ATP_g, Glc6P_g, ADP_g, Rate Law: HXK_g_Vmax*Glc_g*ATP_g*(1-Glc6P_g*ADP_g/(HXK_g_Keq*Glc_g*ATP_g))/(HXK_g_KmGlc*HXK_g_KmATP*(1+Glc_g/HXK_g_KmGlc+Glc6P_g/HXK_g_KmGlc6P)*(1+ATP_g/HXK_g_KmATP+ADP_g/HXK_g_KmADP))
ALD_g_KmDHAP=0.015; ALD_g_KiGA3P=0.098; ALD_g_KmGA3P=0.067; ALD_g_Vmax=560.0; ALD_g_KmFru16BP=0.009; ALD_g_KiADP=1.51; ALD_g_KiAMP=3.65; ALD_g_Keq=0.084; ALD_g_KiATP=0.68 Reaction: Fru16BP_g => GA3P_g + DHAP_g; ATP_g, ADP_g, AMP_g, Fru16BP_g, GA3P_g, DHAP_g, ATP_g, ADP_g, AMP_g, Rate Law: ALD_g_Vmax*Fru16BP_g*(1-GA3P_g*DHAP_g/(Fru16BP_g*ALD_g_Keq))/(ALD_g_KmFru16BP*(1+ATP_g/ALD_g_KiATP+ADP_g/ALD_g_KiADP+AMP_g/ALD_g_KiAMP)*(1+GA3P_g/ALD_g_KmGA3P+DHAP_g/ALD_g_KmDHAP+Fru16BP_g/(ALD_g_KmFru16BP*(1+ATP_g/ALD_g_KiATP+ADP_g/ALD_g_KiADP+AMP_g/ALD_g_KiAMP))+GA3P_g*DHAP_g/(ALD_g_KmGA3P*ALD_g_KmDHAP)+Fru16BP_g*GA3P_g/(ALD_g_KmFru16BP*ALD_g_KiGA3P*(1+ATP_g/ALD_g_KiATP+ADP_g/ALD_g_KiADP+AMP_g/ALD_g_KiAMP))))
NADPHu_c_k=2.0 Reaction: NADPH_c => NADP_c; NADPH_c, Rate Law: NADPHu_c_k*NADPH_c
ATPu_c_k=50.0 Reaction: ATP_c => ADP_c; ATP_c, ADP_c, Rate Law: ATPu_c_k*ATP_c/ADP_c
PYK_c_KmPyr=50.0; PYK_c_KiADP=0.64; PYK_c_Vmax=1020.0; PYK_c_KmADP=0.114; PYK_c_Keq=10800.0; PYK_c_KiATP=0.57; PYK_c_KmATP=15.0; PYK_c_KmPEP=0.34; PYK_c_n=2.5 Reaction: PEP_c + ADP_c => Pyr_c + ATP_c; ADP_c, Pyr_c, ATP_c, PEP_c, Rate Law: PYK_c_Vmax*ADP_c*(1-Pyr_c*ATP_c/(PYK_c_Keq*PEP_c*ADP_c))*(PEP_c/(PYK_c_KmPEP*(1+ADP_c/PYK_c_KiADP+ATP_c/PYK_c_KiATP)))^PYK_c_n/(PYK_c_KmADP*(1+(PEP_c/(PYK_c_KmPEP*(1+ADP_c/PYK_c_KiADP+ATP_c/PYK_c_KiATP)))^PYK_c_n+Pyr_c/PYK_c_KmPyr)*(1+ADP_c/PYK_c_KmADP+ATP_c/PYK_c_KmATP))
G6PP_c_KmGlc6P=5.6; G6PP_c_Vmax=28.0; G6PP_c_Keq=263.0; G6PP_c_KmGlc=5.6 Reaction: Glc6P_c => Glc_c; Glc6P_c, Glc_c, Rate Law: G6PP_c_Vmax*Glc6P_c*(1-Glc_c/(G6PP_c_Keq*Glc6P_c))/(G6PP_c_KmGlc6P*(1+Glc6P_c/G6PP_c_KmGlc6P+Glc_c/G6PP_c_KmGlc))
G6PDH_g_KmNADPH=1.0E-4; G6PDH_g_Keq=5.02; G6PDH_g_KmNADP=0.0094; G6PDH_g_KmGlc6P=0.058; G6PDH_g_Vmax=8.4; G6PDH_g_Km6PGL=0.04 Reaction: Glc6P_g + NADP_g => _6PGL_g + NADPH_g; Glc6P_g, NADP_g, _6PGL_g, NADPH_g, Rate Law: G6PDH_g_Vmax*Glc6P_g*NADP_g*(1-_6PGL_g*NADPH_g/(G6PDH_g_Keq*Glc6P_g*NADP_g))/(G6PDH_g_KmGlc6P*G6PDH_g_KmNADP*(1+Glc6P_g/G6PDH_g_KmGlc6P+_6PGL_g/G6PDH_g_Km6PGL)*(1+NADP_g/G6PDH_g_KmNADP+NADPH_g/G6PDH_g_KmNADPH))
TR_c_KmTS2=0.0069; TR_c_KmTSH2=0.0018; TR_c_KmNADPH=7.7E-4; TR_c_Vmax=252.0; TR_c_Keq=434.0; TR_c_KmNADP=0.081 Reaction: TS2_c + NADPH_c => NADP_c + TSH2_c; TS2_c, NADPH_c, TSH2_c, NADP_c, Rate Law: TR_c_Vmax*TS2_c*NADPH_c*(1-TSH2_c*NADP_c/(TR_c_Keq*TS2_c*NADPH_c))/(TR_c_KmTS2*TR_c_KmNADPH*(1+TS2_c/TR_c_KmTS2+TSH2_c/TR_c_KmTSH2)*(1+NADPH_c/TR_c_KmNADPH+NADP_c/TR_c_KmNADP))
AK_g_k2=1000.0; AK_g_k1=480.0 Reaction: ADP_g => AMP_g + ATP_g; ADP_g, AMP_g, ATP_g, Rate Law: AK_g_k1*ADP_g^2-AMP_g*ATP_g*AK_g_k2
PyrT_c_Vmax=230.0; PyrT_c_KmPyr=1.96 Reaction: Pyr_c => Pyr_e; Pyr_c, Rate Law: PyrT_c_Vmax*Pyr_c/(PyrT_c_KmPyr*(1+Pyr_c/PyrT_c_KmPyr))
G6PDH_c_Vmax=8.4; G6PDH_c_Keq=5.02; G6PDH_c_KmNADP=0.0094; G6PDH_c_KmNADPH=1.0E-4; G6PDH_c_Km6PGL=0.04; G6PDH_c_KmGlc6P=0.058 Reaction: Glc6P_c + NADP_c => NADPH_c + _6PGL_c; Glc6P_c, NADP_c, _6PGL_c, NADPH_c, Rate Law: G6PDH_c_Vmax*Glc6P_c*NADP_c*(1-_6PGL_c*NADPH_c/(G6PDH_c_Keq*Glc6P_c*NADP_c))/(G6PDH_c_KmGlc6P*G6PDH_c_KmNADP*(1+Glc6P_c/G6PDH_c_KmGlc6P+_6PGL_c/G6PDH_c_Km6PGL)*(1+NADP_c/G6PDH_c_KmNADP+NADPH_c/G6PDH_c_KmNADPH))
HXK_c_KmATP=0.116; HXK_c_KmGlc=0.1; HXK_c_Vmax=154.32; HXK_c_KmADP=0.126; HXK_c_Keq=759.0; HXK_c_KmGlc6P=2.7 Reaction: Glc_c + ATP_c => Glc6P_c + ADP_c; Glc_c, ATP_c, Glc6P_c, ADP_c, Rate Law: HXK_c_Vmax*Glc_c*ATP_c*(1-Glc6P_c*ADP_c/(HXK_c_Keq*Glc_c*ATP_c))/(HXK_c_KmGlc*HXK_c_KmATP*(1+Glc_c/HXK_c_KmGlc+Glc6P_c/HXK_c_KmGlc6P)*(1+ATP_c/HXK_c_KmATP+ADP_c/HXK_c_KmADP))
GAPDH_g_Vmax=720.9; GAPDH_g_Km13BPGA=0.1; GAPDH_g_KmNAD=0.45; GAPDH_g_KmNADH=0.02; GAPDH_g_KmGA3P=0.15; GAPDH_g_Keq=0.066 Reaction: GA3P_g + NAD_g + Pi_g => NADH_g + _13BPGA_g; GA3P_g, NAD_g, _13BPGA_g, NADH_g, Rate Law: GAPDH_g_Vmax*GA3P_g*NAD_g*(1-_13BPGA_g*NADH_g/(GAPDH_g_Keq*GA3P_g*NAD_g))/(GAPDH_g_KmGA3P*GAPDH_g_KmNAD*(1+GA3P_g/GAPDH_g_KmGA3P+_13BPGA_g/GAPDH_g_Km13BPGA)*(1+NAD_g/GAPDH_g_KmNAD+NADH_g/GAPDH_g_KmNADH))
TOX_c_k=2.0 Reaction: TSH2_c => TS2_c; TSH2_c, Rate Law: TOX_c_k*TSH2_c
PGL_g_Km6PGL=0.05; PGL_g_Km6PG=0.05; PGL_g_Vmax=5.0; PGL_g_Keq=20000.0; PGL_g_k=0.055 Reaction: _6PGL_g => _6PG_g; _6PGL_g, _6PG_g, Rate Law: glycosome*PGL_g_k*(_6PGL_g-_6PG_g/PGL_g_Keq)+PGL_g_Vmax*_6PGL_g*(1-_6PG_g/(PGL_g_Keq*_6PGL_g))/(PGL_g_Km6PGL*(1+_6PGL_g/PGL_g_Km6PGL+_6PG_g/PGL_g_Km6PG))
ENO_c_Vmax=598.0; ENO_c_Km2PGA=0.054; ENO_c_Keq=4.17; ENO_c_KmPEP=0.24 Reaction: _2PGA_c => PEP_c; _2PGA_c, PEP_c, Rate Law: ENO_c_Vmax*_2PGA_c*(1-PEP_c/(ENO_c_Keq*_2PGA_c))/(ENO_c_Km2PGA*(1+_2PGA_c/ENO_c_Km2PGA+PEP_c/ENO_c_KmPEP))
PFK_g_Vmax=1708.0; PFK_g_KsATP=0.0393; PFK_g_KmFru6P=0.999; PFK_g_KmADP=1.0; PFK_g_KmATP=0.0648; PFK_g_Ki2=10.7; PFK_g_Ki1=15.8; PFK_g_Keq=1035.0 Reaction: ATP_g + Fru6P_g => Fru16BP_g + ADP_g; Fru6P_g, ATP_g, Fru16BP_g, ADP_g, Rate Law: PFK_g_Vmax*PFK_g_Ki1*Fru6P_g*ATP_g*(1-Fru16BP_g*ADP_g/(PFK_g_Keq*Fru6P_g*ATP_g))/(PFK_g_KmFru6P*PFK_g_KmATP*(Fru16BP_g+PFK_g_Ki1)*(PFK_g_KsATP/PFK_g_KmATP+Fru6P_g/PFK_g_KmFru6P+ATP_g/PFK_g_KmATP+ADP_g/PFK_g_KmADP+Fru16BP_g*ADP_g/(PFK_g_KmADP*PFK_g_Ki2)+Fru6P_g*ATP_g/(PFK_g_KmFru6P*PFK_g_KmATP)))
_6PGDH_g_KmNADP=0.001; _6PGDH_g_KmNADPH=6.0E-4; _6PGDH_g_Keq=47.0; _6PGDH_g_Km6PG=0.0035; _6PGDH_g_KmRul5P=0.03; _6PGDH_g_Vmax=10.6 Reaction: _6PG_g + NADP_g => Rul5P_g + CO2_g + NADPH_g; _6PG_g, NADP_g, Rul5P_g, NADPH_g, Rate Law: _6PGDH_g_Vmax*_6PG_g*NADP_g*(1-Rul5P_g*NADPH_g/(_6PGDH_g_Keq*_6PG_g*NADP_g))/(_6PGDH_g_Km6PG*_6PGDH_g_KmNADP*(1+_6PG_g/_6PGDH_g_Km6PG+Rul5P_g/_6PGDH_g_KmRul5P)*(1+NADP_g/_6PGDH_g_KmNADP+NADPH_g/_6PGDH_g_KmNADPH))
GlcT_c_Vmax=111.7; GlcT_c_KmGlc=1.0; GlcT_c_alpha=0.75 Reaction: Glc_e => Glc_c; Glc_e, Glc_c, Rate Law: GlcT_c_Vmax*(Glc_e-Glc_c)/(GlcT_c_KmGlc+Glc_e+Glc_c+GlcT_c_alpha*Glc_e*Glc_c/GlcT_c_KmGlc)
TPI_g_Keq=0.046; TPI_g_KmDHAP=1.2; TPI_g_KmGA3P=0.25; TPI_g_Vmax=999.3 Reaction: DHAP_g => GA3P_g; DHAP_g, GA3P_g, Rate Law: TPI_g_Vmax*DHAP_g*(1-GA3P_g/(TPI_g_Keq*DHAP_g))/(TPI_g_KmDHAP*(1+DHAP_g/TPI_g_KmDHAP+GA3P_g/TPI_g_KmGA3P))
NADPHu_g_k=2.0 Reaction: NADPH_g => NADP_g; NADPH_g, Rate Law: NADPHu_g_k*NADPH_g
PGAM_c_Km3PGA=0.15; PGAM_c_Vmax=225.0; PGAM_c_Km2PGA=0.16; PGAM_c_Keq=0.17 Reaction: _3PGA_c => _2PGA_c; _3PGA_c, _2PGA_c, Rate Law: PGAM_c_Vmax*_3PGA_c*(1-_2PGA_c/(PGAM_c_Keq*_3PGA_c))/(PGAM_c_Km3PGA*(1+_3PGA_c/PGAM_c_Km3PGA+_2PGA_c/PGAM_c_Km2PGA))
G3PDH_g_KmDHAP=0.1; G3PDH_g_KmNAD=0.4; G3PDH_g_Vmax=465.0; G3PDH_g_Keq=17085.0; G3PDH_g_KmNADH=0.01; G3PDH_g_KmGly3P=2.0 Reaction: NADH_g + DHAP_g => Gly3P_g + NAD_g; DHAP_g, NADH_g, Gly3P_g, NAD_g, Rate Law: G3PDH_g_Vmax*DHAP_g*NADH_g*(1-Gly3P_g*NAD_g/(G3PDH_g_Keq*DHAP_g*NADH_g))/(G3PDH_g_KmDHAP*G3PDH_g_KmNADH*(1+DHAP_g/G3PDH_g_KmDHAP+Gly3P_g/G3PDH_g_KmGly3P)*(1+NADH_g/G3PDH_g_KmNADH+NAD_g/G3PDH_g_KmNAD))
GK_g_Keq=8.37E-4; GK_g_KmATP=0.24; GK_g_KmGly=0.44; GK_g_KmADP=0.56; GK_g_KmGly3P=3.83; GK_g_Vmax=200.0 Reaction: Gly3P_g + ADP_g => Gly_e + ATP_g; Gly3P_g, ADP_g, Gly_e, ATP_g, Rate Law: GK_g_Vmax*Gly3P_g*ADP_g*(1-Gly_e*ATP_g/(GK_g_Keq*Gly3P_g*ADP_g))/(GK_g_KmGly3P*GK_g_KmADP*(1+Gly3P_g/GK_g_KmGly3P+Gly_e/GK_g_KmGly)*(1+ADP_g/GK_g_KmADP+ATP_g/GK_g_KmATP))
GlcT_g_k2=250000.0; GlcT_g_k1=250000.0 Reaction: Glc_c => Glc_g; Glc_c, Glc_g, Rate Law: GlcT_g_k1*Glc_c-GlcT_g_k2*Glc_g
PGL_c_Km6PG=0.05; PGL_c_k=0.055; PGL_c_Vmax=28.0; PGL_c_Km6PGL=0.05; PGL_c_Keq=20000.0 Reaction: _6PGL_c => _6PG_c; _6PGL_c, _6PG_c, Rate Law: PGL_c_k*cytosol*(_6PGL_c-_6PG_c/PGL_c_Keq)+PGL_c_Vmax*_6PGL_c*(1-_6PG_c/(PGL_c_Keq*_6PGL_c))/(PGL_c_Km6PGL*(1+_6PGL_c/PGL_c_Km6PGL+_6PG_c/PGL_c_Km6PG))
AK_c_k1=480.0; AK_c_k2=1000.0 Reaction: ADP_c => AMP_c + ATP_c; ADP_c, AMP_c, ATP_c, Rate Law: AK_c_k1*ADP_c^2-AMP_c*ATP_c*AK_c_k2
_6PGDH_c_KmNADP=0.001; _6PGDH_c_Keq=47.0; _6PGDH_c_Vmax=10.6; _6PGDH_c_KmNADPH=6.0E-4; _6PGDH_c_Km6PG=0.0035; _6PGDH_c_KmRul5P=0.03 Reaction: NADP_c + _6PG_c => CO2_c + NADPH_c + Rul5P_c; _6PG_c, NADP_c, Rul5P_c, NADPH_c, Rate Law: _6PGDH_c_Vmax*_6PG_c*NADP_c*(1-Rul5P_c*NADPH_c/(_6PGDH_c_Keq*_6PG_c*NADP_c))/(_6PGDH_c_Km6PG*_6PGDH_c_KmNADP*(1+_6PG_c/_6PGDH_c_Km6PG+Rul5P_c/_6PGDH_c_KmRul5P)*(1+NADP_c/_6PGDH_c_KmNADP+NADPH_c/_6PGDH_c_KmNADPH))
PPI_g_KmRul5P=1.4; PPI_g_Vmax=72.0; PPI_g_Keq=5.6; PPI_g_KmRib5P=4.0 Reaction: Rul5P_g => Rib5P_g; Rul5P_g, Rib5P_g, Rate Law: PPI_g_Vmax*Rul5P_g*(1-Rib5P_g/(PPI_g_Keq*Rul5P_g))/(PPI_g_KmRul5P*(1+Rul5P_g/PPI_g_KmRul5P+Rib5P_g/PPI_g_KmRib5P))
PGK_g_Km13BPGA=0.003; PGK_g_Vmax=2862.0; PGK_g_KmADP=0.1; PGK_g_Km3PGA=1.62; PGK_g_KmATP=0.29; PGK_g_Keq=3377.0 Reaction: _13BPGA_g + ADP_g => _3PGA_g + ATP_g; _13BPGA_g, ADP_g, _3PGA_g, ATP_g, Rate Law: PGK_g_Vmax*_13BPGA_g*ADP_g*(1-_3PGA_g*ATP_g/(PGK_g_Keq*_13BPGA_g*ADP_g))/(PGK_g_Km13BPGA*PGK_g_KmADP*(1+_13BPGA_g/PGK_g_Km13BPGA+_3PGA_g/PGK_g_Km3PGA)*(1+ADP_g/PGK_g_KmADP+ATP_g/PGK_g_KmATP))

States:

Name Description
6PG g [6-phospho-D-gluconic acid]
6PG c [6-phospho-D-gluconic acid]
Rul5P g [D-ribulose 5-phosphate(2-)]
TS2 c [trypanothione]
Glc6P c [D-glucopyranose 6-phosphate]
PEP c [phosphoenolpyruvate]
CO2 g [carbon dioxide]
ATP g [ATP]
GA3P g [glyceraldehyde 3-phosphate]
Glc c [glucose]
Fru16BP g [alpha-D-fructofuranose 1,6-bisphosphate]
Glc g [glucose]
Glc e [glucose]
TSH2 c [trypanothione disulfide]
Pyr e [pyruvate]
ADP g [ADP]
13BPGA g [683]
NADP c [NADP(+)]
DHAP g [glycerone phosphate(2-)]
NAD g [NAD]
NADH g [NADH]
Pyr c [pyruvate]
CO2 c [carbon dioxide]
6PGL g [6-phosphogluconolactonase3.1.1.17]
Fru6P g [444848]
2PGA c [59]
Gly3P c [glycerol 1-phosphate]
Rib5P c [aldehydo-D-ribose 5-phosphate(2-)]
3PGA c [3-phospho-D-glyceric acid]
NADP g [NADP(+)]
Rib g [ribose]
Rib5P g [aldehydo-D-ribose 5-phosphate(2-)]
Pi g [phosphatidylinositol]
Glc6P g [D-glucopyranose 6-phosphate]
ATP c [ATP]
DHAP c [glycerone phosphate(2-)]
NADPH c [NADPH]
Gly e [glycerol]
6PGL c [6-phosphogluconolactonase3.1.1.17]
Gly3P g [glycerol 1-phosphate]
ADP c [ADP]
AMP g [AMP]
Rul5P c [D-ribulose 5-phosphate(2-)]
3PGA g [3-phospho-D-glyceric acid]
AMP c [AMP]
NADPH g [NADPH]

Observables: none

Kerkhoven2013 - Glycolysis and Pentose Phosphate Pathway in T.brucei - MODEL C in fructose medium (with glucosomal ribok…

Dynamic models of metabolism can be useful in identifying potential drug targets, especially in unicellular organisms. A model of glycolysis in the causative agent of human African trypanosomiasis, Trypanosoma brucei, has already shown the utility of this approach. Here we add the pentose phosphate pathway (PPP) of T. brucei to the glycolytic model. The PPP is localized to both the cytosol and the glycosome and adding it to the glycolytic model without further adjustments leads to a draining of the essential bound-phosphate moiety within the glycosome. This phosphate "leak" must be resolved for the model to be a reasonable representation of parasite physiology. Two main types of theoretical solution to the problem could be identified: (i) including additional enzymatic reactions in the glycosome, or (ii) adding a mechanism to transfer bound phosphates between cytosol and glycosome. One example of the first type of solution would be the presence of a glycosomal ribokinase to regenerate ATP from ribose 5-phosphate and ADP. Experimental characterization of ribokinase in T. brucei showed that very low enzyme levels are sufficient for parasite survival, indicating that other mechanisms are required in controlling the phosphate leak. Examples of the second type would involve the presence of an ATP:ADP exchanger or recently described permeability pores in the glycosomal membrane, although the current absence of identified genes encoding such molecules impedes experimental testing by genetic manipulation. Confronted with this uncertainty, we present a modeling strategy that identifies robust predictions in the context of incomplete system characterization. We illustrate this strategy by exploring the mechanism underlying the essential function of one of the PPP enzymes, and validate it by confirming the model predictions experimentally. link: http://identifiers.org/pubmed/24339766

Parameters:

Name Description
RK_g_Keq=0.0036; RK_g_KmRib=0.51; RK_g_Vmax=10.0; RK_g_KmRib5P=0.39; RK_g_KmADP=0.25; RK_g_KmATP=0.24 Reaction: ADP_g + Rib5P_g => ATP_g + Rib_g; Rib5P_g, ADP_g, Rib_g, ATP_g, Rate Law: RK_g_Vmax*Rib5P_g*ADP_g*(1-Rib_g*ATP_g/(RK_g_Keq*Rib5P_g*ADP_g))/(RK_g_KmRib5P*RK_g_KmADP*(1+Rib5P_g/RK_g_KmRib5P+Rib_g/RK_g_KmRib)*(1+ADP_g/RK_g_KmADP+ATP_g/RK_g_KmATP))
_3PGAT_g_k=250.0 Reaction: _3PGA_g => _3PGA_c; _3PGA_g, _3PGA_c, Rate Law: _3PGAT_g_k*_3PGA_g-_3PGAT_g_k*_3PGA_c
GDA_g_k=600.0 Reaction: Gly3P_g + DHAP_c => Gly3P_c + DHAP_g; Gly3P_g, DHAP_c, Gly3P_c, DHAP_g, Rate Law: Gly3P_g*GDA_g_k*DHAP_c-Gly3P_c*GDA_g_k*DHAP_g
GPO_c_Vmax=368.0; GPO_c_KmGly3P=1.7 Reaction: Gly3P_c => DHAP_c; Gly3P_c, Rate Law: GPO_c_Vmax*Gly3P_c/(GPO_c_KmGly3P*(1+Gly3P_c/GPO_c_KmGly3P))
PPI_c_Keq=5.6; PPI_c_Vmax=72.0; PPI_c_KmRul5P=1.4; PPI_c_KmRib5P=4.0 Reaction: Rul5P_c => Rib5P_c; Rul5P_c, Rib5P_c, Rate Law: PPI_c_Vmax*Rul5P_c*(1-Rib5P_c/(PPI_c_Keq*Rul5P_c))/(PPI_c_KmRul5P*(1+Rul5P_c/PPI_c_KmRul5P+Rib5P_c/PPI_c_KmRib5P))
PGI_g_Vmax=1305.0; PGI_g_Ki6PG=0.14; PGI_g_KmGlc6P=0.4; PGI_g_Keq=0.457; PGI_g_KmFru6P=0.12 Reaction: Glc6P_g => Fru6P_g; _6PG_g, Glc6P_g, Fru6P_g, _6PG_g, Rate Law: PGI_g_Vmax*Glc6P_g*(1-Fru6P_g/(PGI_g_Keq*Glc6P_g))/(PGI_g_KmGlc6P*(1+Glc6P_g/PGI_g_KmGlc6P+Fru6P_g/PGI_g_KmFru6P+_6PG_g/PGI_g_Ki6PG))
ALD_g_KmDHAP=0.015; ALD_g_KiGA3P=0.098; ALD_g_KmGA3P=0.067; ALD_g_Vmax=560.0; ALD_g_KmFru16BP=0.009; ALD_g_KiADP=1.51; ALD_g_KiAMP=3.65; ALD_g_Keq=0.084; ALD_g_KiATP=0.68 Reaction: Fru16BP_g => GA3P_g + DHAP_g; ATP_g, ADP_g, AMP_g, Fru16BP_g, GA3P_g, DHAP_g, ATP_g, ADP_g, AMP_g, Rate Law: ALD_g_Vmax*Fru16BP_g*(1-GA3P_g*DHAP_g/(Fru16BP_g*ALD_g_Keq))/(ALD_g_KmFru16BP*(1+ATP_g/ALD_g_KiATP+ADP_g/ALD_g_KiADP+AMP_g/ALD_g_KiAMP)*(1+GA3P_g/ALD_g_KmGA3P+DHAP_g/ALD_g_KmDHAP+Fru16BP_g/(ALD_g_KmFru16BP*(1+ATP_g/ALD_g_KiATP+ADP_g/ALD_g_KiADP+AMP_g/ALD_g_KiAMP))+GA3P_g*DHAP_g/(ALD_g_KmGA3P*ALD_g_KmDHAP)+Fru16BP_g*GA3P_g/(ALD_g_KmFru16BP*ALD_g_KiGA3P*(1+ATP_g/ALD_g_KiATP+ADP_g/ALD_g_KiADP+AMP_g/ALD_g_KiAMP))))
ATPu_c_k=50.0 Reaction: ATP_c => ADP_c; ATP_c, ADP_c, Rate Law: ATPu_c_k*ATP_c/ADP_c
NADPHu_c_k=2.0 Reaction: NADPH_c => NADP_c; NADPH_c, Rate Law: NADPHu_c_k*NADPH_c
PYK_c_KmPyr=50.0; PYK_c_KiADP=0.64; PYK_c_Vmax=1020.0; PYK_c_KmADP=0.114; PYK_c_Keq=10800.0; PYK_c_KiATP=0.57; PYK_c_KmATP=15.0; PYK_c_KmPEP=0.34; PYK_c_n=2.5 Reaction: PEP_c + ADP_c => Pyr_c + ATP_c; ADP_c, Pyr_c, ATP_c, PEP_c, Rate Law: PYK_c_Vmax*ADP_c*(1-Pyr_c*ATP_c/(PYK_c_Keq*PEP_c*ADP_c))*(PEP_c/(PYK_c_KmPEP*(1+ADP_c/PYK_c_KiADP+ATP_c/PYK_c_KiATP)))^PYK_c_n/(PYK_c_KmADP*(1+(PEP_c/(PYK_c_KmPEP*(1+ADP_c/PYK_c_KiADP+ATP_c/PYK_c_KiATP)))^PYK_c_n+Pyr_c/PYK_c_KmPyr)*(1+ADP_c/PYK_c_KmADP+ATP_c/PYK_c_KmATP))
G6PP_c_KmGlc6P=5.6; G6PP_c_Vmax=28.0; G6PP_c_Keq=263.0; G6PP_c_KmGlc=5.6 Reaction: Glc6P_c => Glc_c; Glc6P_c, Glc_c, Rate Law: G6PP_c_Vmax*Glc6P_c*(1-Glc_c/(G6PP_c_Keq*Glc6P_c))/(G6PP_c_KmGlc6P*(1+Glc6P_c/G6PP_c_KmGlc6P+Glc_c/G6PP_c_KmGlc))
G6PDH_g_KmNADPH=1.0E-4; G6PDH_g_Keq=5.02; G6PDH_g_KmNADP=0.0094; G6PDH_g_KmGlc6P=0.058; G6PDH_g_Vmax=8.4; G6PDH_g_Km6PGL=0.04 Reaction: Glc6P_g + NADP_g => _6PGL_g + NADPH_g; Glc6P_g, NADP_g, _6PGL_g, NADPH_g, Rate Law: G6PDH_g_Vmax*Glc6P_g*NADP_g*(1-_6PGL_g*NADPH_g/(G6PDH_g_Keq*Glc6P_g*NADP_g))/(G6PDH_g_KmGlc6P*G6PDH_g_KmNADP*(1+Glc6P_g/G6PDH_g_KmGlc6P+_6PGL_g/G6PDH_g_Km6PGL)*(1+NADP_g/G6PDH_g_KmNADP+NADPH_g/G6PDH_g_KmNADPH))
TR_c_KmTS2=0.0069; TR_c_KmTSH2=0.0018; TR_c_KmNADPH=7.7E-4; TR_c_Vmax=252.0; TR_c_Keq=434.0; TR_c_KmNADP=0.081 Reaction: TS2_c + NADPH_c => NADP_c + TSH2_c; TS2_c, NADPH_c, TSH2_c, NADP_c, Rate Law: TR_c_Vmax*TS2_c*NADPH_c*(1-TSH2_c*NADP_c/(TR_c_Keq*TS2_c*NADPH_c))/(TR_c_KmTS2*TR_c_KmNADPH*(1+TS2_c/TR_c_KmTS2+TSH2_c/TR_c_KmTSH2)*(1+NADPH_c/TR_c_KmNADPH+NADP_c/TR_c_KmNADP))
AK_g_k2=1000.0; AK_g_k1=480.0 Reaction: ADP_g => AMP_g + ATP_g; ADP_g, AMP_g, ATP_g, Rate Law: AK_g_k1*ADP_g^2-AMP_g*ATP_g*AK_g_k2
HXK_g_Vmax=1774.68; HXK_g_KiFru6P=2.7; HXK_g_KiFru=0.35; HXK_g_KmADP=0.126; HXK_g_Keq=759.0; HXK_g_KmATP=0.116; HXK_g_KmGlc6P=2.7; HXK_g_KmGlc=0.1 Reaction: ATP_g + Glc_g => Glc6P_g + ADP_g; Fru_g, Fru6P_g, Glc_g, ATP_g, Glc6P_g, ADP_g, Fru_g, Fru6P_g, Rate Law: HXK_g_Vmax*Glc_g*ATP_g*(1-Glc6P_g*ADP_g/(HXK_g_Keq*Glc_g*ATP_g))/(HXK_g_KmGlc*HXK_g_KmATP*(1+Glc_g/HXK_g_KmGlc+Glc6P_g/HXK_g_KmGlc6P)*(1+ATP_g/HXK_g_KmATP+ADP_g/HXK_g_KmADP+Fru_g/HXK_g_KiFru+Fru6P_g/HXK_g_KiFru6P))
G6PDH_c_Vmax=8.4; G6PDH_c_Keq=5.02; G6PDH_c_KmNADP=0.0094; G6PDH_c_KmNADPH=1.0E-4; G6PDH_c_Km6PGL=0.04; G6PDH_c_KmGlc6P=0.058 Reaction: Glc6P_c + NADP_c => NADPH_c + _6PGL_c; Glc6P_c, NADP_c, _6PGL_c, NADPH_c, Rate Law: G6PDH_c_Vmax*Glc6P_c*NADP_c*(1-_6PGL_c*NADPH_c/(G6PDH_c_Keq*Glc6P_c*NADP_c))/(G6PDH_c_KmGlc6P*G6PDH_c_KmNADP*(1+Glc6P_c/G6PDH_c_KmGlc6P+_6PGL_c/G6PDH_c_Km6PGL)*(1+NADP_c/G6PDH_c_KmNADP+NADPH_c/G6PDH_c_KmNADPH))
FruT_c_Vmax=69.1; FruT_c_alpha=0.75; FruT_c_KmFru=3.91 Reaction: Fru_e => Fru_c; Fru_e, Fru_c, Rate Law: FruT_c_Vmax*(Fru_e-Fru_c)/(FruT_c_KmFru+Fru_e+Fru_c+FruT_c_alpha*Fru_e*Fru_c/FruT_c_KmFru)
GAPDH_g_Vmax=720.9; GAPDH_g_Km13BPGA=0.1; GAPDH_g_KmNAD=0.45; GAPDH_g_KmNADH=0.02; GAPDH_g_KmGA3P=0.15; GAPDH_g_Keq=0.066 Reaction: GA3P_g + NAD_g + Pi_g => NADH_g + _13BPGA_g; GA3P_g, NAD_g, _13BPGA_g, NADH_g, Rate Law: GAPDH_g_Vmax*GA3P_g*NAD_g*(1-_13BPGA_g*NADH_g/(GAPDH_g_Keq*GA3P_g*NAD_g))/(GAPDH_g_KmGA3P*GAPDH_g_KmNAD*(1+GA3P_g/GAPDH_g_KmGA3P+_13BPGA_g/GAPDH_g_Km13BPGA)*(1+NAD_g/GAPDH_g_KmNAD+NADH_g/GAPDH_g_KmNADH))
TOX_c_k=2.0 Reaction: TSH2_c => TS2_c; TSH2_c, Rate Law: TOX_c_k*TSH2_c
PGL_g_Km6PGL=0.05; PGL_g_Km6PG=0.05; PGL_g_Vmax=5.0; PGL_g_Keq=20000.0; PGL_g_k=0.055 Reaction: _6PGL_g => _6PG_g; _6PGL_g, _6PG_g, Rate Law: glycosome*PGL_g_k*(_6PGL_g-_6PG_g/PGL_g_Keq)+PGL_g_Vmax*_6PGL_g*(1-_6PG_g/(PGL_g_Keq*_6PGL_g))/(PGL_g_Km6PGL*(1+_6PGL_g/PGL_g_Km6PGL+_6PG_g/PGL_g_Km6PG))
ENO_c_Vmax=598.0; ENO_c_Km2PGA=0.054; ENO_c_Keq=4.17; ENO_c_KmPEP=0.24 Reaction: _2PGA_c => PEP_c; _2PGA_c, PEP_c, Rate Law: ENO_c_Vmax*_2PGA_c*(1-PEP_c/(ENO_c_Keq*_2PGA_c))/(ENO_c_Km2PGA*(1+_2PGA_c/ENO_c_Km2PGA+PEP_c/ENO_c_KmPEP))
PFK_g_Vmax=1708.0; PFK_g_KsATP=0.0393; PFK_g_KmFru6P=0.999; PFK_g_KmADP=1.0; PFK_g_KmATP=0.0648; PFK_g_Ki2=10.7; PFK_g_Ki1=15.8; PFK_g_Keq=1035.0 Reaction: ATP_g + Fru6P_g => Fru16BP_g + ADP_g; Fru6P_g, ATP_g, Fru16BP_g, ADP_g, Rate Law: PFK_g_Vmax*PFK_g_Ki1*Fru6P_g*ATP_g*(1-Fru16BP_g*ADP_g/(PFK_g_Keq*Fru6P_g*ATP_g))/(PFK_g_KmFru6P*PFK_g_KmATP*(Fru16BP_g+PFK_g_Ki1)*(PFK_g_KsATP/PFK_g_KmATP+Fru6P_g/PFK_g_KmFru6P+ATP_g/PFK_g_KmATP+ADP_g/PFK_g_KmADP+Fru16BP_g*ADP_g/(PFK_g_KmADP*PFK_g_Ki2)+Fru6P_g*ATP_g/(PFK_g_KmFru6P*PFK_g_KmATP)))
_6PGDH_g_KmNADP=0.001; _6PGDH_g_KmNADPH=6.0E-4; _6PGDH_g_Keq=47.0; _6PGDH_g_Km6PG=0.0035; _6PGDH_g_KmRul5P=0.03; _6PGDH_g_Vmax=10.6 Reaction: _6PG_g + NADP_g => Rul5P_g + CO2_g + NADPH_g; _6PG_g, NADP_g, Rul5P_g, NADPH_g, Rate Law: _6PGDH_g_Vmax*_6PG_g*NADP_g*(1-Rul5P_g*NADPH_g/(_6PGDH_g_Keq*_6PG_g*NADP_g))/(_6PGDH_g_Km6PG*_6PGDH_g_KmNADP*(1+_6PG_g/_6PGDH_g_Km6PG+Rul5P_g/_6PGDH_g_KmRul5P)*(1+NADP_g/_6PGDH_g_KmNADP+NADPH_g/_6PGDH_g_KmNADPH))
TPI_g_Keq=0.046; TPI_g_KmDHAP=1.2; TPI_g_KmGA3P=0.25; TPI_g_Vmax=999.3 Reaction: DHAP_g => GA3P_g; DHAP_g, GA3P_g, Rate Law: TPI_g_Vmax*DHAP_g*(1-GA3P_g/(TPI_g_Keq*DHAP_g))/(TPI_g_KmDHAP*(1+DHAP_g/TPI_g_KmDHAP+GA3P_g/TPI_g_KmGA3P))
FruT_g_k1=250000.0; FruT_g_k2=250000.0 Reaction: Fru_c => Fru_g; Fru_c, Fru_g, Rate Law: FruT_g_k1*Fru_c-FruT_g_k2*Fru_g
GlcT_c_Vmax=111.7; GlcT_c_KmGlc=1.0; GlcT_c_alpha=0.75 Reaction: Glc_e => Glc_c; Glc_e, Glc_c, Rate Law: GlcT_c_Vmax*(Glc_e-Glc_c)/(GlcT_c_KmGlc+Glc_e+Glc_c+GlcT_c_alpha*Glc_e*Glc_c/GlcT_c_KmGlc)
NADPHu_g_k=2.0 Reaction: NADPH_g => NADP_g; NADPH_g, Rate Law: NADPHu_g_k*NADPH_g
PGAM_c_Km3PGA=0.15; PGAM_c_Vmax=225.0; PGAM_c_Km2PGA=0.16; PGAM_c_Keq=0.17 Reaction: _3PGA_c => _2PGA_c; _3PGA_c, _2PGA_c, Rate Law: PGAM_c_Vmax*_3PGA_c*(1-_2PGA_c/(PGAM_c_Keq*_3PGA_c))/(PGAM_c_Km3PGA*(1+_3PGA_c/PGAM_c_Km3PGA+_2PGA_c/PGAM_c_Km2PGA))
G3PDH_g_KmDHAP=0.1; G3PDH_g_KmNAD=0.4; G3PDH_g_Vmax=465.0; G3PDH_g_Keq=17085.0; G3PDH_g_KmNADH=0.01; G3PDH_g_KmGly3P=2.0 Reaction: NADH_g + DHAP_g => Gly3P_g + NAD_g; DHAP_g, NADH_g, Gly3P_g, NAD_g, Rate Law: G3PDH_g_Vmax*DHAP_g*NADH_g*(1-Gly3P_g*NAD_g/(G3PDH_g_Keq*DHAP_g*NADH_g))/(G3PDH_g_KmDHAP*G3PDH_g_KmNADH*(1+DHAP_g/G3PDH_g_KmDHAP+Gly3P_g/G3PDH_g_KmGly3P)*(1+NADH_g/G3PDH_g_KmNADH+NAD_g/G3PDH_g_KmNAD))
GK_g_Keq=8.37E-4; GK_g_KmATP=0.24; GK_g_KmGly=0.44; GK_g_KmADP=0.56; GK_g_KmGly3P=3.83; GK_g_Vmax=200.0 Reaction: Gly3P_g + ADP_g => Gly_e + ATP_g; Gly3P_g, ADP_g, Gly_e, ATP_g, Rate Law: GK_g_Vmax*Gly3P_g*ADP_g*(1-Gly_e*ATP_g/(GK_g_Keq*Gly3P_g*ADP_g))/(GK_g_KmGly3P*GK_g_KmADP*(1+Gly3P_g/GK_g_KmGly3P+Gly_e/GK_g_KmGly)*(1+ADP_g/GK_g_KmADP+ATP_g/GK_g_KmATP))
GlcT_g_k2=250000.0; GlcT_g_k1=250000.0 Reaction: Glc_c => Glc_g; Glc_c, Glc_g, Rate Law: GlcT_g_k1*Glc_c-GlcT_g_k2*Glc_g
PGL_c_Km6PG=0.05; PGL_c_k=0.055; PGL_c_Vmax=28.0; PGL_c_Km6PGL=0.05; PGL_c_Keq=20000.0 Reaction: _6PGL_c => _6PG_c; _6PGL_c, _6PG_c, Rate Law: PGL_c_k*cytosol*(_6PGL_c-_6PG_c/PGL_c_Keq)+PGL_c_Vmax*_6PGL_c*(1-_6PG_c/(PGL_c_Keq*_6PGL_c))/(PGL_c_Km6PGL*(1+_6PGL_c/PGL_c_Km6PGL+_6PG_c/PGL_c_Km6PG))
HXK_c_KmATP=0.116; HXK_c_KmGlc=0.1; HXK_c_KiFru6P=2.7; HXK_c_Vmax=154.32; HXK_c_KmADP=0.126; HXK_c_KiFru=0.35; HXK_c_Keq=759.0; HXK_c_KmGlc6P=2.7 Reaction: Glc_c + ATP_c => Glc6P_c + ADP_c; Fru_c, Fru6P_c, Glc_c, ATP_c, Glc6P_c, ADP_c, Fru_c, Fru6P_c, Rate Law: HXK_c_Vmax*Glc_c*ATP_c*(1-Glc6P_c*ADP_c/(HXK_c_Keq*Glc_c*ATP_c))/(HXK_c_KmGlc*HXK_c_KmATP*(1+Glc_c/HXK_c_KmGlc+Glc6P_c/HXK_c_KmGlc6P)*(1+ATP_c/HXK_c_KmATP+ADP_c/HXK_c_KmADP+Fru_c/HXK_c_KiFru+Fru6P_c/HXK_c_KiFru6P))
_6PGDH_c_KmNADP=0.001; _6PGDH_c_Keq=47.0; _6PGDH_c_Vmax=10.6; _6PGDH_c_KmNADPH=6.0E-4; _6PGDH_c_Km6PG=0.0035; _6PGDH_c_KmRul5P=0.03 Reaction: NADP_c + _6PG_c => CO2_c + NADPH_c + Rul5P_c; _6PG_c, NADP_c, Rul5P_c, NADPH_c, Rate Law: _6PGDH_c_Vmax*_6PG_c*NADP_c*(1-Rul5P_c*NADPH_c/(_6PGDH_c_Keq*_6PG_c*NADP_c))/(_6PGDH_c_Km6PG*_6PGDH_c_KmNADP*(1+_6PG_c/_6PGDH_c_Km6PG+Rul5P_c/_6PGDH_c_KmRul5P)*(1+NADP_c/_6PGDH_c_KmNADP+NADPH_c/_6PGDH_c_KmNADPH))
AK_c_k1=480.0; AK_c_k2=1000.0 Reaction: ADP_c => AMP_c + ATP_c; ADP_c, AMP_c, ATP_c, Rate Law: AK_c_k1*ADP_c^2-AMP_c*ATP_c*AK_c_k2
PPI_g_KmRul5P=1.4; PPI_g_Vmax=72.0; PPI_g_Keq=5.6; PPI_g_KmRib5P=4.0 Reaction: Rul5P_g => Rib5P_g; Rul5P_g, Rib5P_g, Rate Law: PPI_g_Vmax*Rul5P_g*(1-Rib5P_g/(PPI_g_Keq*Rul5P_g))/(PPI_g_KmRul5P*(1+Rul5P_g/PPI_g_KmRul5P+Rib5P_g/PPI_g_KmRib5P))
HXKfru_c_KmFru=0.35; HXKfru_c_KiGlc6P=2.7; HXKfru_c_KmADP=0.126; HXKfru_c_Keq=631.0; HXKfru_c_KmATP=0.116; HXKfru_c_KmFru6P=2.7; HXKfru_c_Vmax=154.32; HXKfru_c_KiGlc=0.1 Reaction: Fru_c + ATP_c => ADP_c + Fru6P_c; Glc_c, Glc6P_c, Fru_c, ATP_c, Fru6P_c, ADP_c, Glc_c, Glc6P_c, Rate Law: HXKfru_c_Vmax*Fru_c*ATP_c*(1-Fru6P_c*ADP_c/(HXKfru_c_Keq*Fru_c*ATP_c))/(HXKfru_c_KmFru*HXKfru_c_KmATP*(1+Fru_c/HXKfru_c_KmFru+Fru6P_c/HXKfru_c_KmFru6P)*(1+ATP_c/HXKfru_c_KmATP+ADP_c/HXKfru_c_KmADP+Glc_c/HXKfru_c_KiGlc+Glc6P_c/HXKfru_c_KiGlc6P))
PGK_g_Km13BPGA=0.003; PGK_g_Vmax=2862.0; PGK_g_KmADP=0.1; PGK_g_Km3PGA=1.62; PGK_g_KmATP=0.29; PGK_g_Keq=3377.0 Reaction: _13BPGA_g + ADP_g => _3PGA_g + ATP_g; _13BPGA_g, ADP_g, _3PGA_g, ATP_g, Rate Law: PGK_g_Vmax*_13BPGA_g*ADP_g*(1-_3PGA_g*ATP_g/(PGK_g_Keq*_13BPGA_g*ADP_g))/(PGK_g_Km13BPGA*PGK_g_KmADP*(1+_13BPGA_g/PGK_g_Km13BPGA+_3PGA_g/PGK_g_Km3PGA)*(1+ADP_g/PGK_g_KmADP+ATP_g/PGK_g_KmATP))
HXKfru_g_Keq=631.0; HXKfru_g_KmATP=0.116; HXKfru_g_KmFru6P=2.7; HXKfru_g_KiGlc6P=2.7; HXKfru_g_KmADP=0.126; HXKfru_g_KiGlc=0.1; HXKfru_g_Vmax=1774.68; HXKfru_g_KmFru=0.35 Reaction: Fru_g + ATP_g => ADP_g + Fru6P_g; Glc_g, Glc6P_g, Fru_g, ATP_g, Fru6P_g, ADP_g, Glc_g, Glc6P_g, Rate Law: HXKfru_g_Vmax*Fru_g*ATP_g*(1-Fru6P_g*ADP_g/(HXKfru_g_Keq*Fru_g*ATP_g))/(HXKfru_g_KmFru*HXKfru_g_KmATP*(1+Fru_g/HXKfru_g_KmFru+Fru6P_g/HXKfru_g_KmFru6P)*(1+ATP_g/HXKfru_g_KmATP+ADP_g/HXKfru_g_KmADP+Glc_g/HXKfru_g_KiGlc+Glc6P_g/HXKfru_g_KiGlc6P))

States:

Name Description
6PG g [6-phospho-D-gluconic acid]
6PG c [6-phospho-D-gluconic acid]
TS2 c [trypanothione]
PEP c [phosphoenolpyruvate]
Glc6P c [D-glucopyranose 6-phosphate]
Rul5P g [D-ribulose 5-phosphate(2-)]
ATP g [ATP]
CO2 g [carbon dioxide]
Glc c [glucose]
Fru6P c [444848]
Fru g [fructose]
Glc g [glucose]
Glc e [glucose]
TSH2 c [trypanothione disulfide]
ADP g [ADP]
13BPGA g [683]
NADP c [NADP(+)]
Fru c [fructose]
DHAP g [glycerone phosphate(2-)]
NADH g [NADH]
Fru e [fructose]
CO2 c [carbon dioxide]
6PGL g [6-phosphogluconolactonase3.1.1.17]
Fru6P g [444848]
2PGA c [59]
Gly3P c [glycerol 1-phosphate]
Rib5P c [aldehydo-D-ribose 5-phosphate(2-)]
3PGA c [3-phospho-D-glyceric acid]
NADP g [NADP(+)]
Rib g [aromatic annulene]
Rib5P g [ribose]
Pi g [phosphatidylinositol]
Glc6P g [D-glucopyranose 6-phosphate]
ATP c [ATP]
DHAP c [glycerone phosphate(2-)]
NADPH c [NADPH]
Gly3P g [glycerol 1-phosphate]
ADP c [ADP]
AMP g [AMP]
Rul5P c [D-ribulose 5-phosphate(2-)]
3PGA g [3-phospho-D-glyceric acid]
AMP c [AMP]
NADPH g [NADPH]

Observables: none

Kerkhoven2013 - Glycolysis and Pentose Phosphate Pathway in T.brucei - MODEL D (with ATP:ADP antiporter)There are six mo…

Dynamic models of metabolism can be useful in identifying potential drug targets, especially in unicellular organisms. A model of glycolysis in the causative agent of human African trypanosomiasis, Trypanosoma brucei, has already shown the utility of this approach. Here we add the pentose phosphate pathway (PPP) of T. brucei to the glycolytic model. The PPP is localized to both the cytosol and the glycosome and adding it to the glycolytic model without further adjustments leads to a draining of the essential bound-phosphate moiety within the glycosome. This phosphate "leak" must be resolved for the model to be a reasonable representation of parasite physiology. Two main types of theoretical solution to the problem could be identified: (i) including additional enzymatic reactions in the glycosome, or (ii) adding a mechanism to transfer bound phosphates between cytosol and glycosome. One example of the first type of solution would be the presence of a glycosomal ribokinase to regenerate ATP from ribose 5-phosphate and ADP. Experimental characterization of ribokinase in T. brucei showed that very low enzyme levels are sufficient for parasite survival, indicating that other mechanisms are required in controlling the phosphate leak. Examples of the second type would involve the presence of an ATP:ADP exchanger or recently described permeability pores in the glycosomal membrane, although the current absence of identified genes encoding such molecules impedes experimental testing by genetic manipulation. Confronted with this uncertainty, we present a modeling strategy that identifies robust predictions in the context of incomplete system characterization. We illustrate this strategy by exploring the mechanism underlying the essential function of one of the PPP enzymes, and validate it by confirming the model predictions experimentally. link: http://identifiers.org/pubmed/24339766

Parameters:

Name Description
ATPT_g_KmATP=0.02; ATPT_g_Keq=1.0; ATPT_g_Vmax=1.5; ATPT_g_KmADP=0.02 Reaction: ADP_g + ATP_c => ATP_g + ADP_c; ADP_g, ATP_c, ADP_c, ATP_g, Rate Law: ATPT_g_Vmax*ADP_g*ATP_c*(1-ADP_c*ATP_g/(ATPT_g_Keq*ADP_g*ATP_c))/(ATPT_g_KmADP*ATPT_g_KmATP*(1+ADP_g/ATPT_g_KmADP+ADP_c/ATPT_g_KmADP)*(1+ATP_c/ATPT_g_KmATP+ATP_g/ATPT_g_KmATP))
PPI_c_Keq=5.6; PPI_c_Vmax=72.0; PPI_c_KmRul5P=1.4; PPI_c_KmRib5P=4.0 Reaction: Rul5P_c => Rib5P_c; Rul5P_c, Rib5P_c, Rate Law: PPI_c_Vmax*Rul5P_c*(1-Rib5P_c/(PPI_c_Keq*Rul5P_c))/(PPI_c_KmRul5P*(1+Rul5P_c/PPI_c_KmRul5P+Rib5P_c/PPI_c_KmRib5P))
GDA_g_k=600.0 Reaction: Gly3P_g + DHAP_c => Gly3P_c + DHAP_g; Gly3P_g, DHAP_c, Gly3P_c, DHAP_g, Rate Law: Gly3P_g*GDA_g_k*DHAP_c-Gly3P_c*GDA_g_k*DHAP_g
GPO_c_Vmax=368.0; GPO_c_KmGly3P=1.7 Reaction: Gly3P_c => DHAP_c; Gly3P_c, Rate Law: GPO_c_Vmax*Gly3P_c/(GPO_c_KmGly3P*(1+Gly3P_c/GPO_c_KmGly3P))
_3PGAT_g_k=250.0 Reaction: _3PGA_g => _3PGA_c; _3PGA_g, _3PGA_c, Rate Law: _3PGAT_g_k*_3PGA_g-_3PGAT_g_k*_3PGA_c
PGI_g_Vmax=1305.0; PGI_g_Ki6PG=0.14; PGI_g_KmGlc6P=0.4; PGI_g_Keq=0.457; PGI_g_KmFru6P=0.12 Reaction: Glc6P_g => Fru6P_g; _6PG_g, Glc6P_g, Fru6P_g, _6PG_g, Rate Law: PGI_g_Vmax*Glc6P_g*(1-Fru6P_g/(PGI_g_Keq*Glc6P_g))/(PGI_g_KmGlc6P*(1+Glc6P_g/PGI_g_KmGlc6P+Fru6P_g/PGI_g_KmFru6P+_6PG_g/PGI_g_Ki6PG))
HXK_g_Vmax=1774.68; HXK_g_KmADP=0.126; HXK_g_Keq=759.0; HXK_g_KmATP=0.116; HXK_g_KmGlc6P=2.7; HXK_g_KmGlc=0.1 Reaction: ATP_g + Glc_g => Glc6P_g + ADP_g; Glc_g, ATP_g, Glc6P_g, ADP_g, Rate Law: HXK_g_Vmax*Glc_g*ATP_g*(1-Glc6P_g*ADP_g/(HXK_g_Keq*Glc_g*ATP_g))/(HXK_g_KmGlc*HXK_g_KmATP*(1+Glc_g/HXK_g_KmGlc+Glc6P_g/HXK_g_KmGlc6P)*(1+ATP_g/HXK_g_KmATP+ADP_g/HXK_g_KmADP))
NADPHu_c_k=2.0 Reaction: NADPH_c => NADP_c; NADPH_c, Rate Law: NADPHu_c_k*NADPH_c
ATPu_c_k=50.0 Reaction: ATP_c => ADP_c; ATP_c, ADP_c, Rate Law: ATPu_c_k*ATP_c/ADP_c
G6PP_c_KmGlc6P=5.6; G6PP_c_Vmax=28.0; G6PP_c_Keq=263.0; G6PP_c_KmGlc=5.6 Reaction: Glc6P_c => Glc_c; Glc6P_c, Glc_c, Rate Law: G6PP_c_Vmax*Glc6P_c*(1-Glc_c/(G6PP_c_Keq*Glc6P_c))/(G6PP_c_KmGlc6P*(1+Glc6P_c/G6PP_c_KmGlc6P+Glc_c/G6PP_c_KmGlc))
PYK_c_KmPyr=50.0; PYK_c_KiADP=0.64; PYK_c_Vmax=1020.0; PYK_c_KmADP=0.114; PYK_c_Keq=10800.0; PYK_c_KiATP=0.57; PYK_c_KmATP=15.0; PYK_c_KmPEP=0.34; PYK_c_n=2.5 Reaction: PEP_c + ADP_c => Pyr_c + ATP_c; ADP_c, Pyr_c, ATP_c, PEP_c, Rate Law: PYK_c_Vmax*ADP_c*(1-Pyr_c*ATP_c/(PYK_c_Keq*PEP_c*ADP_c))*(PEP_c/(PYK_c_KmPEP*(1+ADP_c/PYK_c_KiADP+ATP_c/PYK_c_KiATP)))^PYK_c_n/(PYK_c_KmADP*(1+(PEP_c/(PYK_c_KmPEP*(1+ADP_c/PYK_c_KiADP+ATP_c/PYK_c_KiATP)))^PYK_c_n+Pyr_c/PYK_c_KmPyr)*(1+ADP_c/PYK_c_KmADP+ATP_c/PYK_c_KmATP))
ALD_g_KmDHAP=0.015; ALD_g_KiGA3P=0.098; ALD_g_KmGA3P=0.067; ALD_g_Vmax=560.0; ALD_g_KmFru16BP=0.009; ALD_g_KiADP=1.51; ALD_g_KiAMP=3.65; ALD_g_Keq=0.084; ALD_g_KiATP=0.68 Reaction: Fru16BP_g => GA3P_g + DHAP_g; ATP_g, ADP_g, AMP_g, Fru16BP_g, GA3P_g, DHAP_g, ATP_g, ADP_g, AMP_g, Rate Law: ALD_g_Vmax*Fru16BP_g*(1-GA3P_g*DHAP_g/(Fru16BP_g*ALD_g_Keq))/(ALD_g_KmFru16BP*(1+ATP_g/ALD_g_KiATP+ADP_g/ALD_g_KiADP+AMP_g/ALD_g_KiAMP)*(1+GA3P_g/ALD_g_KmGA3P+DHAP_g/ALD_g_KmDHAP+Fru16BP_g/(ALD_g_KmFru16BP*(1+ATP_g/ALD_g_KiATP+ADP_g/ALD_g_KiADP+AMP_g/ALD_g_KiAMP))+GA3P_g*DHAP_g/(ALD_g_KmGA3P*ALD_g_KmDHAP)+Fru16BP_g*GA3P_g/(ALD_g_KmFru16BP*ALD_g_KiGA3P*(1+ATP_g/ALD_g_KiATP+ADP_g/ALD_g_KiADP+AMP_g/ALD_g_KiAMP))))
G6PDH_g_KmNADPH=1.0E-4; G6PDH_g_Keq=5.02; G6PDH_g_KmNADP=0.0094; G6PDH_g_KmGlc6P=0.058; G6PDH_g_Vmax=8.4; G6PDH_g_Km6PGL=0.04 Reaction: Glc6P_g + NADP_g => _6PGL_g + NADPH_g; Glc6P_g, NADP_g, _6PGL_g, NADPH_g, Rate Law: G6PDH_g_Vmax*Glc6P_g*NADP_g*(1-_6PGL_g*NADPH_g/(G6PDH_g_Keq*Glc6P_g*NADP_g))/(G6PDH_g_KmGlc6P*G6PDH_g_KmNADP*(1+Glc6P_g/G6PDH_g_KmGlc6P+_6PGL_g/G6PDH_g_Km6PGL)*(1+NADP_g/G6PDH_g_KmNADP+NADPH_g/G6PDH_g_KmNADPH))
TR_c_KmTS2=0.0069; TR_c_KmTSH2=0.0018; TR_c_KmNADPH=7.7E-4; TR_c_Vmax=252.0; TR_c_Keq=434.0; TR_c_KmNADP=0.081 Reaction: TS2_c + NADPH_c => NADP_c + TSH2_c; TS2_c, NADPH_c, TSH2_c, NADP_c, Rate Law: TR_c_Vmax*TS2_c*NADPH_c*(1-TSH2_c*NADP_c/(TR_c_Keq*TS2_c*NADPH_c))/(TR_c_KmTS2*TR_c_KmNADPH*(1+TS2_c/TR_c_KmTS2+TSH2_c/TR_c_KmTSH2)*(1+NADPH_c/TR_c_KmNADPH+NADP_c/TR_c_KmNADP))
AK_g_k2=1000.0; AK_g_k1=480.0 Reaction: ADP_g => AMP_g + ATP_g; ADP_g, AMP_g, ATP_g, Rate Law: AK_g_k1*ADP_g^2-AMP_g*ATP_g*AK_g_k2
PyrT_c_Vmax=230.0; PyrT_c_KmPyr=1.96 Reaction: Pyr_c => Pyr_e; Pyr_c, Rate Law: PyrT_c_Vmax*Pyr_c/(PyrT_c_KmPyr*(1+Pyr_c/PyrT_c_KmPyr))
G6PDH_c_Vmax=8.4; G6PDH_c_Keq=5.02; G6PDH_c_KmNADP=0.0094; G6PDH_c_KmNADPH=1.0E-4; G6PDH_c_Km6PGL=0.04; G6PDH_c_KmGlc6P=0.058 Reaction: Glc6P_c + NADP_c => NADPH_c + _6PGL_c; Glc6P_c, NADP_c, _6PGL_c, NADPH_c, Rate Law: G6PDH_c_Vmax*Glc6P_c*NADP_c*(1-_6PGL_c*NADPH_c/(G6PDH_c_Keq*Glc6P_c*NADP_c))/(G6PDH_c_KmGlc6P*G6PDH_c_KmNADP*(1+Glc6P_c/G6PDH_c_KmGlc6P+_6PGL_c/G6PDH_c_Km6PGL)*(1+NADP_c/G6PDH_c_KmNADP+NADPH_c/G6PDH_c_KmNADPH))
HXK_c_KmATP=0.116; HXK_c_KmGlc=0.1; HXK_c_Vmax=154.32; HXK_c_KmADP=0.126; HXK_c_Keq=759.0; HXK_c_KmGlc6P=2.7 Reaction: Glc_c + ATP_c => Glc6P_c + ADP_c; Glc_c, ATP_c, Glc6P_c, ADP_c, Rate Law: HXK_c_Vmax*Glc_c*ATP_c*(1-Glc6P_c*ADP_c/(HXK_c_Keq*Glc_c*ATP_c))/(HXK_c_KmGlc*HXK_c_KmATP*(1+Glc_c/HXK_c_KmGlc+Glc6P_c/HXK_c_KmGlc6P)*(1+ATP_c/HXK_c_KmATP+ADP_c/HXK_c_KmADP))
GAPDH_g_Vmax=720.9; GAPDH_g_Km13BPGA=0.1; GAPDH_g_KmNAD=0.45; GAPDH_g_KmNADH=0.02; GAPDH_g_KmGA3P=0.15; GAPDH_g_Keq=0.066 Reaction: GA3P_g + NAD_g + Pi_g => NADH_g + _13BPGA_g; GA3P_g, NAD_g, _13BPGA_g, NADH_g, Rate Law: GAPDH_g_Vmax*GA3P_g*NAD_g*(1-_13BPGA_g*NADH_g/(GAPDH_g_Keq*GA3P_g*NAD_g))/(GAPDH_g_KmGA3P*GAPDH_g_KmNAD*(1+GA3P_g/GAPDH_g_KmGA3P+_13BPGA_g/GAPDH_g_Km13BPGA)*(1+NAD_g/GAPDH_g_KmNAD+NADH_g/GAPDH_g_KmNADH))
PGL_g_Km6PGL=0.05; PGL_g_Km6PG=0.05; PGL_g_Vmax=5.0; PGL_g_Keq=20000.0; PGL_g_k=0.055 Reaction: _6PGL_g => _6PG_g; _6PGL_g, _6PG_g, Rate Law: glycosome*PGL_g_k*(_6PGL_g-_6PG_g/PGL_g_Keq)+PGL_g_Vmax*_6PGL_g*(1-_6PG_g/(PGL_g_Keq*_6PGL_g))/(PGL_g_Km6PGL*(1+_6PGL_g/PGL_g_Km6PGL+_6PG_g/PGL_g_Km6PG))
TOX_c_k=2.0 Reaction: TSH2_c => TS2_c; TSH2_c, Rate Law: TOX_c_k*TSH2_c
ENO_c_Vmax=598.0; ENO_c_Km2PGA=0.054; ENO_c_Keq=4.17; ENO_c_KmPEP=0.24 Reaction: _2PGA_c => PEP_c; _2PGA_c, PEP_c, Rate Law: ENO_c_Vmax*_2PGA_c*(1-PEP_c/(ENO_c_Keq*_2PGA_c))/(ENO_c_Km2PGA*(1+_2PGA_c/ENO_c_Km2PGA+PEP_c/ENO_c_KmPEP))
PFK_g_Vmax=1708.0; PFK_g_KsATP=0.0393; PFK_g_KmFru6P=0.999; PFK_g_KmADP=1.0; PFK_g_KmATP=0.0648; PFK_g_Ki2=10.7; PFK_g_Ki1=15.8; PFK_g_Keq=1035.0 Reaction: ATP_g + Fru6P_g => Fru16BP_g + ADP_g; Fru6P_g, ATP_g, Fru16BP_g, ADP_g, Rate Law: PFK_g_Vmax*PFK_g_Ki1*Fru6P_g*ATP_g*(1-Fru16BP_g*ADP_g/(PFK_g_Keq*Fru6P_g*ATP_g))/(PFK_g_KmFru6P*PFK_g_KmATP*(Fru16BP_g+PFK_g_Ki1)*(PFK_g_KsATP/PFK_g_KmATP+Fru6P_g/PFK_g_KmFru6P+ATP_g/PFK_g_KmATP+ADP_g/PFK_g_KmADP+Fru16BP_g*ADP_g/(PFK_g_KmADP*PFK_g_Ki2)+Fru6P_g*ATP_g/(PFK_g_KmFru6P*PFK_g_KmATP)))
GlcT_c_Vmax=111.7; GlcT_c_KmGlc=1.0; GlcT_c_alpha=0.75 Reaction: Glc_e => Glc_c; Glc_e, Glc_c, Rate Law: GlcT_c_Vmax*(Glc_e-Glc_c)/(GlcT_c_KmGlc+Glc_e+Glc_c+GlcT_c_alpha*Glc_e*Glc_c/GlcT_c_KmGlc)
TPI_g_Keq=0.046; TPI_g_KmDHAP=1.2; TPI_g_KmGA3P=0.25; TPI_g_Vmax=999.3 Reaction: DHAP_g => GA3P_g; DHAP_g, GA3P_g, Rate Law: TPI_g_Vmax*DHAP_g*(1-GA3P_g/(TPI_g_Keq*DHAP_g))/(TPI_g_KmDHAP*(1+DHAP_g/TPI_g_KmDHAP+GA3P_g/TPI_g_KmGA3P))
_6PGDH_g_KmNADP=0.001; _6PGDH_g_KmNADPH=6.0E-4; _6PGDH_g_Keq=47.0; _6PGDH_g_Km6PG=0.0035; _6PGDH_g_KmRul5P=0.03; _6PGDH_g_Vmax=10.6 Reaction: _6PG_g + NADP_g => Rul5P_g + CO2_g + NADPH_g; _6PG_g, NADP_g, Rul5P_g, NADPH_g, Rate Law: _6PGDH_g_Vmax*_6PG_g*NADP_g*(1-Rul5P_g*NADPH_g/(_6PGDH_g_Keq*_6PG_g*NADP_g))/(_6PGDH_g_Km6PG*_6PGDH_g_KmNADP*(1+_6PG_g/_6PGDH_g_Km6PG+Rul5P_g/_6PGDH_g_KmRul5P)*(1+NADP_g/_6PGDH_g_KmNADP+NADPH_g/_6PGDH_g_KmNADPH))
NADPHu_g_k=2.0 Reaction: NADPH_g => NADP_g; NADPH_g, Rate Law: NADPHu_g_k*NADPH_g
PGAM_c_Km3PGA=0.15; PGAM_c_Vmax=225.0; PGAM_c_Km2PGA=0.16; PGAM_c_Keq=0.17 Reaction: _3PGA_c => _2PGA_c; _3PGA_c, _2PGA_c, Rate Law: PGAM_c_Vmax*_3PGA_c*(1-_2PGA_c/(PGAM_c_Keq*_3PGA_c))/(PGAM_c_Km3PGA*(1+_3PGA_c/PGAM_c_Km3PGA+_2PGA_c/PGAM_c_Km2PGA))
G3PDH_g_KmDHAP=0.1; G3PDH_g_KmNAD=0.4; G3PDH_g_Vmax=465.0; G3PDH_g_Keq=17085.0; G3PDH_g_KmNADH=0.01; G3PDH_g_KmGly3P=2.0 Reaction: NADH_g + DHAP_g => Gly3P_g + NAD_g; DHAP_g, NADH_g, Gly3P_g, NAD_g, Rate Law: G3PDH_g_Vmax*DHAP_g*NADH_g*(1-Gly3P_g*NAD_g/(G3PDH_g_Keq*DHAP_g*NADH_g))/(G3PDH_g_KmDHAP*G3PDH_g_KmNADH*(1+DHAP_g/G3PDH_g_KmDHAP+Gly3P_g/G3PDH_g_KmGly3P)*(1+NADH_g/G3PDH_g_KmNADH+NAD_g/G3PDH_g_KmNAD))
GK_g_Keq=8.37E-4; GK_g_KmATP=0.24; GK_g_KmGly=0.44; GK_g_KmADP=0.56; GK_g_KmGly3P=3.83; GK_g_Vmax=200.0 Reaction: Gly3P_g + ADP_g => Gly_e + ATP_g; Gly3P_g, ADP_g, Gly_e, ATP_g, Rate Law: GK_g_Vmax*Gly3P_g*ADP_g*(1-Gly_e*ATP_g/(GK_g_Keq*Gly3P_g*ADP_g))/(GK_g_KmGly3P*GK_g_KmADP*(1+Gly3P_g/GK_g_KmGly3P+Gly_e/GK_g_KmGly)*(1+ADP_g/GK_g_KmADP+ATP_g/GK_g_KmATP))
GlcT_g_k2=250000.0; GlcT_g_k1=250000.0 Reaction: Glc_c => Glc_g; Glc_c, Glc_g, Rate Law: GlcT_g_k1*Glc_c-GlcT_g_k2*Glc_g
PGL_c_Km6PG=0.05; PGL_c_k=0.055; PGL_c_Vmax=28.0; PGL_c_Km6PGL=0.05; PGL_c_Keq=20000.0 Reaction: _6PGL_c => _6PG_c; _6PGL_c, _6PG_c, Rate Law: PGL_c_k*cytosol*(_6PGL_c-_6PG_c/PGL_c_Keq)+PGL_c_Vmax*_6PGL_c*(1-_6PG_c/(PGL_c_Keq*_6PGL_c))/(PGL_c_Km6PGL*(1+_6PGL_c/PGL_c_Km6PGL+_6PG_c/PGL_c_Km6PG))
AK_c_k1=480.0; AK_c_k2=1000.0 Reaction: ADP_c => AMP_c + ATP_c; ADP_c, AMP_c, ATP_c, Rate Law: AK_c_k1*ADP_c^2-AMP_c*ATP_c*AK_c_k2
_6PGDH_c_KmNADP=0.001; _6PGDH_c_Keq=47.0; _6PGDH_c_Vmax=10.6; _6PGDH_c_KmNADPH=6.0E-4; _6PGDH_c_Km6PG=0.0035; _6PGDH_c_KmRul5P=0.03 Reaction: NADP_c + _6PG_c => CO2_c + NADPH_c + Rul5P_c; _6PG_c, NADP_c, Rul5P_c, NADPH_c, Rate Law: _6PGDH_c_Vmax*_6PG_c*NADP_c*(1-Rul5P_c*NADPH_c/(_6PGDH_c_Keq*_6PG_c*NADP_c))/(_6PGDH_c_Km6PG*_6PGDH_c_KmNADP*(1+_6PG_c/_6PGDH_c_Km6PG+Rul5P_c/_6PGDH_c_KmRul5P)*(1+NADP_c/_6PGDH_c_KmNADP+NADPH_c/_6PGDH_c_KmNADPH))
PPI_g_KmRul5P=1.4; PPI_g_Vmax=72.0; PPI_g_Keq=5.6; PPI_g_KmRib5P=4.0 Reaction: Rul5P_g => Rib5P_g; Rul5P_g, Rib5P_g, Rate Law: PPI_g_Vmax*Rul5P_g*(1-Rib5P_g/(PPI_g_Keq*Rul5P_g))/(PPI_g_KmRul5P*(1+Rul5P_g/PPI_g_KmRul5P+Rib5P_g/PPI_g_KmRib5P))
PGK_g_Km13BPGA=0.003; PGK_g_Vmax=2862.0; PGK_g_KmADP=0.1; PGK_g_Km3PGA=1.62; PGK_g_KmATP=0.29; PGK_g_Keq=3377.0 Reaction: _13BPGA_g + ADP_g => _3PGA_g + ATP_g; _13BPGA_g, ADP_g, _3PGA_g, ATP_g, Rate Law: PGK_g_Vmax*_13BPGA_g*ADP_g*(1-_3PGA_g*ATP_g/(PGK_g_Keq*_13BPGA_g*ADP_g))/(PGK_g_Km13BPGA*PGK_g_KmADP*(1+_13BPGA_g/PGK_g_Km13BPGA+_3PGA_g/PGK_g_Km3PGA)*(1+ADP_g/PGK_g_KmADP+ATP_g/PGK_g_KmATP))

States:

Name Description
6PG g [6-phospho-D-gluconic acid]
6PG c [6-phospho-D-gluconic acid]
Rul5P g [D-ribulose 5-phosphate(2-)]
TS2 c [trypanothione]
Glc6P c [D-glucopyranose 6-phosphate]
PEP c [phosphoenolpyruvate]
CO2 g [carbon dioxide]
ATP g [ATP]
Glc c [glucose]
GA3P g [glyceraldehyde 3-phosphate]
Fru16BP g [alpha-D-fructofuranose 1,6-bisphosphate]
Glc g [glucose]
Glc e [glucose]
TSH2 c [trypanothione disulfide]
Pyr e [pyruvate]
ADP g [ADP]
13BPGA g [683]
NADP c [NADP(+)]
DHAP g [CHEBI_57622]
NAD g [NAD]
NADH g [NADH]
Pyr c [pyruvate]
CO2 c [carbon dioxide]
6PGL g [6-phosphogluconolactonase3.1.1.17]
Fru6P g [444848]
2PGA c [59]
Gly3P c [glycerol 1-phosphate]
Rib5P c [aldehydo-D-ribose 5-phosphate(2-)]
NADP g [NADP(+)]
Rib5P g [aldehydo-D-ribose 5-phosphate(2-)]
Pi g [phosphatidylinositol]
Glc6P g [D-glucopyranose 6-phosphate]
ATP c [ATP]
DHAP c [glycerone phosphate(2-)]
NADPH c [NADPH]
Gly e [glycerol]
6PGL c [6-phosphogluconolactonase3.1.1.17]
Gly3P g [glycerol 1-phosphate]
ADP c [ADP]
AMP g [AMP]
Rul5P c [D-ribulose 5-phosphate(2-)]
3PGA g [3-phospho-D-glyceric acid]
AMP c [AMP]
NADPH g [NADPH]

Observables: none

Kerkhoven2013 - Glycolysis and Pentose Phosphate Pathway in T.brucei - MODEL D in fructose medium (with ATP:ADP antiport…

Dynamic models of metabolism can be useful in identifying potential drug targets, especially in unicellular organisms. A model of glycolysis in the causative agent of human African trypanosomiasis, Trypanosoma brucei, has already shown the utility of this approach. Here we add the pentose phosphate pathway (PPP) of T. brucei to the glycolytic model. The PPP is localized to both the cytosol and the glycosome and adding it to the glycolytic model without further adjustments leads to a draining of the essential bound-phosphate moiety within the glycosome. This phosphate "leak" must be resolved for the model to be a reasonable representation of parasite physiology. Two main types of theoretical solution to the problem could be identified: (i) including additional enzymatic reactions in the glycosome, or (ii) adding a mechanism to transfer bound phosphates between cytosol and glycosome. One example of the first type of solution would be the presence of a glycosomal ribokinase to regenerate ATP from ribose 5-phosphate and ADP. Experimental characterization of ribokinase in T. brucei showed that very low enzyme levels are sufficient for parasite survival, indicating that other mechanisms are required in controlling the phosphate leak. Examples of the second type would involve the presence of an ATP:ADP exchanger or recently described permeability pores in the glycosomal membrane, although the current absence of identified genes encoding such molecules impedes experimental testing by genetic manipulation. Confronted with this uncertainty, we present a modeling strategy that identifies robust predictions in the context of incomplete system characterization. We illustrate this strategy by exploring the mechanism underlying the essential function of one of the PPP enzymes, and validate it by confirming the model predictions experimentally. link: http://identifiers.org/pubmed/24339766

Parameters:

Name Description
ATPT_g_KmATP=0.02; ATPT_g_Keq=1.0; ATPT_g_Vmax=1.5; ATPT_g_KmADP=0.02 Reaction: ADP_g + ATP_c => ATP_g + ADP_c; ADP_g, ATP_c, ADP_c, ATP_g, Rate Law: ATPT_g_Vmax*ADP_g*ATP_c*(1-ADP_c*ATP_g/(ATPT_g_Keq*ADP_g*ATP_c))/(ATPT_g_KmADP*ATPT_g_KmATP*(1+ADP_g/ATPT_g_KmADP+ADP_c/ATPT_g_KmADP)*(1+ATP_c/ATPT_g_KmATP+ATP_g/ATPT_g_KmATP))
_3PGAT_g_k=250.0 Reaction: _3PGA_g => _3PGA_c; _3PGA_g, _3PGA_c, Rate Law: _3PGAT_g_k*_3PGA_g-_3PGAT_g_k*_3PGA_c
PPI_c_Keq=5.6; PPI_c_Vmax=72.0; PPI_c_KmRul5P=1.4; PPI_c_KmRib5P=4.0 Reaction: Rul5P_c => Rib5P_c; Rul5P_c, Rib5P_c, Rate Law: PPI_c_Vmax*Rul5P_c*(1-Rib5P_c/(PPI_c_Keq*Rul5P_c))/(PPI_c_KmRul5P*(1+Rul5P_c/PPI_c_KmRul5P+Rib5P_c/PPI_c_KmRib5P))
GDA_g_k=600.0 Reaction: Gly3P_g + DHAP_c => Gly3P_c + DHAP_g; Gly3P_g, DHAP_c, Gly3P_c, DHAP_g, Rate Law: Gly3P_g*GDA_g_k*DHAP_c-Gly3P_c*GDA_g_k*DHAP_g
GPO_c_Vmax=368.0; GPO_c_KmGly3P=1.7 Reaction: Gly3P_c => DHAP_c; Gly3P_c, Rate Law: GPO_c_Vmax*Gly3P_c/(GPO_c_KmGly3P*(1+Gly3P_c/GPO_c_KmGly3P))
NADPHu_c_k=2.0 Reaction: NADPH_c => NADP_c; NADPH_c, Rate Law: NADPHu_c_k*NADPH_c
ATPu_c_k=50.0 Reaction: ATP_c => ADP_c; ATP_c, ADP_c, Rate Law: ATPu_c_k*ATP_c/ADP_c
ALD_g_KmDHAP=0.015; ALD_g_KiGA3P=0.098; ALD_g_KmGA3P=0.067; ALD_g_Vmax=560.0; ALD_g_KmFru16BP=0.009; ALD_g_KiADP=1.51; ALD_g_KiAMP=3.65; ALD_g_Keq=0.084; ALD_g_KiATP=0.68 Reaction: Fru16BP_g => GA3P_g + DHAP_g; ATP_g, ADP_g, AMP_g, Fru16BP_g, GA3P_g, DHAP_g, ATP_g, ADP_g, AMP_g, Rate Law: ALD_g_Vmax*Fru16BP_g*(1-GA3P_g*DHAP_g/(Fru16BP_g*ALD_g_Keq))/(ALD_g_KmFru16BP*(1+ATP_g/ALD_g_KiATP+ADP_g/ALD_g_KiADP+AMP_g/ALD_g_KiAMP)*(1+GA3P_g/ALD_g_KmGA3P+DHAP_g/ALD_g_KmDHAP+Fru16BP_g/(ALD_g_KmFru16BP*(1+ATP_g/ALD_g_KiATP+ADP_g/ALD_g_KiADP+AMP_g/ALD_g_KiAMP))+GA3P_g*DHAP_g/(ALD_g_KmGA3P*ALD_g_KmDHAP)+Fru16BP_g*GA3P_g/(ALD_g_KmFru16BP*ALD_g_KiGA3P*(1+ATP_g/ALD_g_KiATP+ADP_g/ALD_g_KiADP+AMP_g/ALD_g_KiAMP))))
PYK_c_KmPyr=50.0; PYK_c_KiADP=0.64; PYK_c_Vmax=1020.0; PYK_c_KmADP=0.114; PYK_c_Keq=10800.0; PYK_c_KiATP=0.57; PYK_c_KmATP=15.0; PYK_c_KmPEP=0.34; PYK_c_n=2.5 Reaction: PEP_c + ADP_c => Pyr_c + ATP_c; ADP_c, Pyr_c, ATP_c, PEP_c, Rate Law: PYK_c_Vmax*ADP_c*(1-Pyr_c*ATP_c/(PYK_c_Keq*PEP_c*ADP_c))*(PEP_c/(PYK_c_KmPEP*(1+ADP_c/PYK_c_KiADP+ATP_c/PYK_c_KiATP)))^PYK_c_n/(PYK_c_KmADP*(1+(PEP_c/(PYK_c_KmPEP*(1+ADP_c/PYK_c_KiADP+ATP_c/PYK_c_KiATP)))^PYK_c_n+Pyr_c/PYK_c_KmPyr)*(1+ADP_c/PYK_c_KmADP+ATP_c/PYK_c_KmATP))
G6PP_c_KmGlc6P=5.6; G6PP_c_Vmax=28.0; G6PP_c_Keq=263.0; G6PP_c_KmGlc=5.6 Reaction: Glc6P_c => Glc_c; Glc6P_c, Glc_c, Rate Law: G6PP_c_Vmax*Glc6P_c*(1-Glc_c/(G6PP_c_Keq*Glc6P_c))/(G6PP_c_KmGlc6P*(1+Glc6P_c/G6PP_c_KmGlc6P+Glc_c/G6PP_c_KmGlc))
G6PDH_g_KmNADPH=1.0E-4; G6PDH_g_Keq=5.02; G6PDH_g_KmNADP=0.0094; G6PDH_g_KmGlc6P=0.058; G6PDH_g_Vmax=8.4; G6PDH_g_Km6PGL=0.04 Reaction: Glc6P_g + NADP_g => _6PGL_g + NADPH_g; Glc6P_g, NADP_g, _6PGL_g, NADPH_g, Rate Law: G6PDH_g_Vmax*Glc6P_g*NADP_g*(1-_6PGL_g*NADPH_g/(G6PDH_g_Keq*Glc6P_g*NADP_g))/(G6PDH_g_KmGlc6P*G6PDH_g_KmNADP*(1+Glc6P_g/G6PDH_g_KmGlc6P+_6PGL_g/G6PDH_g_Km6PGL)*(1+NADP_g/G6PDH_g_KmNADP+NADPH_g/G6PDH_g_KmNADPH))
TR_c_KmTS2=0.0069; TR_c_KmTSH2=0.0018; TR_c_KmNADPH=7.7E-4; TR_c_Vmax=252.0; TR_c_Keq=434.0; TR_c_KmNADP=0.081 Reaction: TS2_c + NADPH_c => NADP_c + TSH2_c; TS2_c, NADPH_c, TSH2_c, NADP_c, Rate Law: TR_c_Vmax*TS2_c*NADPH_c*(1-TSH2_c*NADP_c/(TR_c_Keq*TS2_c*NADPH_c))/(TR_c_KmTS2*TR_c_KmNADPH*(1+TS2_c/TR_c_KmTS2+TSH2_c/TR_c_KmTSH2)*(1+NADPH_c/TR_c_KmNADPH+NADP_c/TR_c_KmNADP))
AK_g_k2=1000.0; AK_g_k1=480.0 Reaction: ADP_g => AMP_g + ATP_g; ADP_g, AMP_g, ATP_g, Rate Law: AK_g_k1*ADP_g^2-AMP_g*ATP_g*AK_g_k2
PyrT_c_Vmax=230.0; PyrT_c_KmPyr=1.96 Reaction: Pyr_c => Pyr_e; Pyr_c, Rate Law: PyrT_c_Vmax*Pyr_c/(PyrT_c_KmPyr*(1+Pyr_c/PyrT_c_KmPyr))
HXK_g_Vmax=1774.68; HXK_g_KiFru6P=2.7; HXK_g_KiFru=0.35; HXK_g_KmADP=0.126; HXK_g_Keq=759.0; HXK_g_KmATP=0.116; HXK_g_KmGlc6P=2.7; HXK_g_KmGlc=0.1 Reaction: ATP_g + Glc_g => Glc6P_g + ADP_g; Fru_g, Fru6P_g, Glc_g, ATP_g, Glc6P_g, ADP_g, Fru_g, Fru6P_g, Rate Law: HXK_g_Vmax*Glc_g*ATP_g*(1-Glc6P_g*ADP_g/(HXK_g_Keq*Glc_g*ATP_g))/(HXK_g_KmGlc*HXK_g_KmATP*(1+Glc_g/HXK_g_KmGlc+Glc6P_g/HXK_g_KmGlc6P)*(1+ATP_g/HXK_g_KmATP+ADP_g/HXK_g_KmADP+Fru_g/HXK_g_KiFru+Fru6P_g/HXK_g_KiFru6P))
G6PDH_c_Vmax=8.4; G6PDH_c_Keq=5.02; G6PDH_c_KmNADP=0.0094; G6PDH_c_KmNADPH=1.0E-4; G6PDH_c_Km6PGL=0.04; G6PDH_c_KmGlc6P=0.058 Reaction: Glc6P_c + NADP_c => NADPH_c + _6PGL_c; Glc6P_c, NADP_c, _6PGL_c, NADPH_c, Rate Law: G6PDH_c_Vmax*Glc6P_c*NADP_c*(1-_6PGL_c*NADPH_c/(G6PDH_c_Keq*Glc6P_c*NADP_c))/(G6PDH_c_KmGlc6P*G6PDH_c_KmNADP*(1+Glc6P_c/G6PDH_c_KmGlc6P+_6PGL_c/G6PDH_c_Km6PGL)*(1+NADP_c/G6PDH_c_KmNADP+NADPH_c/G6PDH_c_KmNADPH))
GAPDH_g_Vmax=720.9; GAPDH_g_Km13BPGA=0.1; GAPDH_g_KmNAD=0.45; GAPDH_g_KmNADH=0.02; GAPDH_g_KmGA3P=0.15; GAPDH_g_Keq=0.066 Reaction: GA3P_g + NAD_g + Pi_g => NADH_g + _13BPGA_g; GA3P_g, NAD_g, _13BPGA_g, NADH_g, Rate Law: GAPDH_g_Vmax*GA3P_g*NAD_g*(1-_13BPGA_g*NADH_g/(GAPDH_g_Keq*GA3P_g*NAD_g))/(GAPDH_g_KmGA3P*GAPDH_g_KmNAD*(1+GA3P_g/GAPDH_g_KmGA3P+_13BPGA_g/GAPDH_g_Km13BPGA)*(1+NAD_g/GAPDH_g_KmNAD+NADH_g/GAPDH_g_KmNADH))
FruT_c_Vmax=69.1; FruT_c_alpha=0.75; FruT_c_KmFru=3.91 Reaction: Fru_e => Fru_c; Fru_e, Fru_c, Rate Law: FruT_c_Vmax*(Fru_e-Fru_c)/(FruT_c_KmFru+Fru_e+Fru_c+FruT_c_alpha*Fru_e*Fru_c/FruT_c_KmFru)
PGL_g_Km6PGL=0.05; PGL_g_Km6PG=0.05; PGL_g_Vmax=5.0; PGL_g_Keq=20000.0; PGL_g_k=0.055 Reaction: _6PGL_g => _6PG_g; _6PGL_g, _6PG_g, Rate Law: glycosome*PGL_g_k*(_6PGL_g-_6PG_g/PGL_g_Keq)+PGL_g_Vmax*_6PGL_g*(1-_6PG_g/(PGL_g_Keq*_6PGL_g))/(PGL_g_Km6PGL*(1+_6PGL_g/PGL_g_Km6PGL+_6PG_g/PGL_g_Km6PG))
TOX_c_k=2.0 Reaction: TSH2_c => TS2_c; TSH2_c, Rate Law: TOX_c_k*TSH2_c
ENO_c_Vmax=598.0; ENO_c_Km2PGA=0.054; ENO_c_Keq=4.17; ENO_c_KmPEP=0.24 Reaction: _2PGA_c => PEP_c; _2PGA_c, PEP_c, Rate Law: ENO_c_Vmax*_2PGA_c*(1-PEP_c/(ENO_c_Keq*_2PGA_c))/(ENO_c_Km2PGA*(1+_2PGA_c/ENO_c_Km2PGA+PEP_c/ENO_c_KmPEP))
PFK_g_Vmax=1708.0; PFK_g_KsATP=0.0393; PFK_g_KmFru6P=0.999; PFK_g_KmADP=1.0; PFK_g_KmATP=0.0648; PFK_g_Ki2=10.7; PFK_g_Ki1=15.8; PFK_g_Keq=1035.0 Reaction: ATP_g + Fru6P_g => Fru16BP_g + ADP_g; Fru6P_g, ATP_g, Fru16BP_g, ADP_g, Rate Law: PFK_g_Vmax*PFK_g_Ki1*Fru6P_g*ATP_g*(1-Fru16BP_g*ADP_g/(PFK_g_Keq*Fru6P_g*ATP_g))/(PFK_g_KmFru6P*PFK_g_KmATP*(Fru16BP_g+PFK_g_Ki1)*(PFK_g_KsATP/PFK_g_KmATP+Fru6P_g/PFK_g_KmFru6P+ATP_g/PFK_g_KmATP+ADP_g/PFK_g_KmADP+Fru16BP_g*ADP_g/(PFK_g_KmADP*PFK_g_Ki2)+Fru6P_g*ATP_g/(PFK_g_KmFru6P*PFK_g_KmATP)))
_6PGDH_g_KmNADP=0.001; _6PGDH_g_KmNADPH=6.0E-4; _6PGDH_g_Keq=47.0; _6PGDH_g_Km6PG=0.0035; _6PGDH_g_KmRul5P=0.03; _6PGDH_g_Vmax=10.6 Reaction: _6PG_g + NADP_g => Rul5P_g + CO2_g + NADPH_g; _6PG_g, NADP_g, Rul5P_g, NADPH_g, Rate Law: _6PGDH_g_Vmax*_6PG_g*NADP_g*(1-Rul5P_g*NADPH_g/(_6PGDH_g_Keq*_6PG_g*NADP_g))/(_6PGDH_g_Km6PG*_6PGDH_g_KmNADP*(1+_6PG_g/_6PGDH_g_Km6PG+Rul5P_g/_6PGDH_g_KmRul5P)*(1+NADP_g/_6PGDH_g_KmNADP+NADPH_g/_6PGDH_g_KmNADPH))
TPI_g_Keq=0.046; TPI_g_KmDHAP=1.2; TPI_g_KmGA3P=0.25; TPI_g_Vmax=999.3 Reaction: DHAP_g => GA3P_g; DHAP_g, GA3P_g, Rate Law: TPI_g_Vmax*DHAP_g*(1-GA3P_g/(TPI_g_Keq*DHAP_g))/(TPI_g_KmDHAP*(1+DHAP_g/TPI_g_KmDHAP+GA3P_g/TPI_g_KmGA3P))
FruT_g_k1=250000.0; FruT_g_k2=250000.0 Reaction: Fru_c => Fru_g; Fru_c, Fru_g, Rate Law: FruT_g_k1*Fru_c-FruT_g_k2*Fru_g
GlcT_c_Vmax=111.7; GlcT_c_KmGlc=1.0; GlcT_c_alpha=0.75 Reaction: Glc_e => Glc_c; Glc_e, Glc_c, Rate Law: GlcT_c_Vmax*(Glc_e-Glc_c)/(GlcT_c_KmGlc+Glc_e+Glc_c+GlcT_c_alpha*Glc_e*Glc_c/GlcT_c_KmGlc)
NADPHu_g_k=2.0 Reaction: NADPH_g => NADP_g; NADPH_g, Rate Law: NADPHu_g_k*NADPH_g
PGAM_c_Km3PGA=0.15; PGAM_c_Vmax=225.0; PGAM_c_Km2PGA=0.16; PGAM_c_Keq=0.17 Reaction: _3PGA_c => _2PGA_c; _3PGA_c, _2PGA_c, Rate Law: PGAM_c_Vmax*_3PGA_c*(1-_2PGA_c/(PGAM_c_Keq*_3PGA_c))/(PGAM_c_Km3PGA*(1+_3PGA_c/PGAM_c_Km3PGA+_2PGA_c/PGAM_c_Km2PGA))
G3PDH_g_KmDHAP=0.1; G3PDH_g_KmNAD=0.4; G3PDH_g_Vmax=465.0; G3PDH_g_Keq=17085.0; G3PDH_g_KmNADH=0.01; G3PDH_g_KmGly3P=2.0 Reaction: NADH_g + DHAP_g => Gly3P_g + NAD_g; DHAP_g, NADH_g, Gly3P_g, NAD_g, Rate Law: G3PDH_g_Vmax*DHAP_g*NADH_g*(1-Gly3P_g*NAD_g/(G3PDH_g_Keq*DHAP_g*NADH_g))/(G3PDH_g_KmDHAP*G3PDH_g_KmNADH*(1+DHAP_g/G3PDH_g_KmDHAP+Gly3P_g/G3PDH_g_KmGly3P)*(1+NADH_g/G3PDH_g_KmNADH+NAD_g/G3PDH_g_KmNAD))
GK_g_Keq=8.37E-4; GK_g_KmATP=0.24; GK_g_KmGly=0.44; GK_g_KmADP=0.56; GK_g_KmGly3P=3.83; GK_g_Vmax=200.0 Reaction: Gly3P_g + ADP_g => Gly_e + ATP_g; Gly3P_g, ADP_g, Gly_e, ATP_g, Rate Law: GK_g_Vmax*Gly3P_g*ADP_g*(1-Gly_e*ATP_g/(GK_g_Keq*Gly3P_g*ADP_g))/(GK_g_KmGly3P*GK_g_KmADP*(1+Gly3P_g/GK_g_KmGly3P+Gly_e/GK_g_KmGly)*(1+ADP_g/GK_g_KmADP+ATP_g/GK_g_KmATP))
GlcT_g_k2=250000.0; GlcT_g_k1=250000.0 Reaction: Glc_c => Glc_g; Glc_c, Glc_g, Rate Law: GlcT_g_k1*Glc_c-GlcT_g_k2*Glc_g
PGL_c_Km6PG=0.05; PGL_c_k=0.055; PGL_c_Vmax=28.0; PGL_c_Km6PGL=0.05; PGL_c_Keq=20000.0 Reaction: _6PGL_c => _6PG_c; _6PGL_c, _6PG_c, Rate Law: PGL_c_k*cytosol*(_6PGL_c-_6PG_c/PGL_c_Keq)+PGL_c_Vmax*_6PGL_c*(1-_6PG_c/(PGL_c_Keq*_6PGL_c))/(PGL_c_Km6PGL*(1+_6PGL_c/PGL_c_Km6PGL+_6PG_c/PGL_c_Km6PG))
HXK_c_KmATP=0.116; HXK_c_KmGlc=0.1; HXK_c_KiFru6P=2.7; HXK_c_Vmax=154.32; HXK_c_KmADP=0.126; HXK_c_KiFru=0.35; HXK_c_Keq=759.0; HXK_c_KmGlc6P=2.7 Reaction: Glc_c + ATP_c => Glc6P_c + ADP_c; Fru_c, Fru6P_c, Glc_c, ATP_c, Glc6P_c, ADP_c, Fru_c, Fru6P_c, Rate Law: HXK_c_Vmax*Glc_c*ATP_c*(1-Glc6P_c*ADP_c/(HXK_c_Keq*Glc_c*ATP_c))/(HXK_c_KmGlc*HXK_c_KmATP*(1+Glc_c/HXK_c_KmGlc+Glc6P_c/HXK_c_KmGlc6P)*(1+ATP_c/HXK_c_KmATP+ADP_c/HXK_c_KmADP+Fru_c/HXK_c_KiFru+Fru6P_c/HXK_c_KiFru6P))
AK_c_k1=480.0; AK_c_k2=1000.0 Reaction: ADP_c => AMP_c + ATP_c; ADP_c, AMP_c, ATP_c, Rate Law: AK_c_k1*ADP_c^2-AMP_c*ATP_c*AK_c_k2
_6PGDH_c_KmNADP=0.001; _6PGDH_c_Keq=47.0; _6PGDH_c_Vmax=10.6; _6PGDH_c_KmNADPH=6.0E-4; _6PGDH_c_Km6PG=0.0035; _6PGDH_c_KmRul5P=0.03 Reaction: NADP_c + _6PG_c => CO2_c + NADPH_c + Rul5P_c; _6PG_c, NADP_c, Rul5P_c, NADPH_c, Rate Law: _6PGDH_c_Vmax*_6PG_c*NADP_c*(1-Rul5P_c*NADPH_c/(_6PGDH_c_Keq*_6PG_c*NADP_c))/(_6PGDH_c_Km6PG*_6PGDH_c_KmNADP*(1+_6PG_c/_6PGDH_c_Km6PG+Rul5P_c/_6PGDH_c_KmRul5P)*(1+NADP_c/_6PGDH_c_KmNADP+NADPH_c/_6PGDH_c_KmNADPH))
PPI_g_KmRul5P=1.4; PPI_g_Vmax=72.0; PPI_g_Keq=5.6; PPI_g_KmRib5P=4.0 Reaction: Rul5P_g => Rib5P_g; Rul5P_g, Rib5P_g, Rate Law: PPI_g_Vmax*Rul5P_g*(1-Rib5P_g/(PPI_g_Keq*Rul5P_g))/(PPI_g_KmRul5P*(1+Rul5P_g/PPI_g_KmRul5P+Rib5P_g/PPI_g_KmRib5P))
HXKfru_c_KmFru=0.35; HXKfru_c_KiGlc6P=2.7; HXKfru_c_KmADP=0.126; HXKfru_c_Keq=631.0; HXKfru_c_KmATP=0.116; HXKfru_c_KmFru6P=2.7; HXKfru_c_Vmax=154.32; HXKfru_c_KiGlc=0.1 Reaction: Fru_c + ATP_c => ADP_c + Fru6P_c; Glc_c, Glc6P_c, Fru_c, ATP_c, Fru6P_c, ADP_c, Glc_c, Glc6P_c, Rate Law: HXKfru_c_Vmax*Fru_c*ATP_c*(1-Fru6P_c*ADP_c/(HXKfru_c_Keq*Fru_c*ATP_c))/(HXKfru_c_KmFru*HXKfru_c_KmATP*(1+Fru_c/HXKfru_c_KmFru+Fru6P_c/HXKfru_c_KmFru6P)*(1+ATP_c/HXKfru_c_KmATP+ADP_c/HXKfru_c_KmADP+Glc_c/HXKfru_c_KiGlc+Glc6P_c/HXKfru_c_KiGlc6P))
PGK_g_Km13BPGA=0.003; PGK_g_Vmax=2862.0; PGK_g_KmADP=0.1; PGK_g_Km3PGA=1.62; PGK_g_KmATP=0.29; PGK_g_Keq=3377.0 Reaction: _13BPGA_g + ADP_g => _3PGA_g + ATP_g; _13BPGA_g, ADP_g, _3PGA_g, ATP_g, Rate Law: PGK_g_Vmax*_13BPGA_g*ADP_g*(1-_3PGA_g*ATP_g/(PGK_g_Keq*_13BPGA_g*ADP_g))/(PGK_g_Km13BPGA*PGK_g_KmADP*(1+_13BPGA_g/PGK_g_Km13BPGA+_3PGA_g/PGK_g_Km3PGA)*(1+ADP_g/PGK_g_KmADP+ATP_g/PGK_g_KmATP))
HXKfru_g_Keq=631.0; HXKfru_g_KmATP=0.116; HXKfru_g_KmFru6P=2.7; HXKfru_g_KiGlc6P=2.7; HXKfru_g_KmADP=0.126; HXKfru_g_KiGlc=0.1; HXKfru_g_Vmax=1774.68; HXKfru_g_KmFru=0.35 Reaction: Fru_g + ATP_g => ADP_g + Fru6P_g; Glc_g, Glc6P_g, Fru_g, ATP_g, Fru6P_g, ADP_g, Glc_g, Glc6P_g, Rate Law: HXKfru_g_Vmax*Fru_g*ATP_g*(1-Fru6P_g*ADP_g/(HXKfru_g_Keq*Fru_g*ATP_g))/(HXKfru_g_KmFru*HXKfru_g_KmATP*(1+Fru_g/HXKfru_g_KmFru+Fru6P_g/HXKfru_g_KmFru6P)*(1+ATP_g/HXKfru_g_KmATP+ADP_g/HXKfru_g_KmADP+Glc_g/HXKfru_g_KiGlc+Glc6P_g/HXKfru_g_KiGlc6P))

States:

Name Description
6PG g [6-phospho-D-gluconic acid]
6PG c [6-phospho-D-gluconic acid]
Rul5P g [D-ribulose 5-phosphate(2-)]
PEP c [phosphoenolpyruvate]
TS2 c [trypanothione]
CO2 g [carbon dioxide]
ATP g [ATP]
Glc c [glucose]
GA3P g [glyceraldehyde 3-phosphate]
Fru16BP g [alpha-D-fructofuranose 1,6-bisphosphate]
Fru g [fructose]
Glc g [glucose]
Glc e [glucose]
TSH2 c [BTO:35490; trypanothione disulfide]
Pyr e [pyruvate]
ADP g [ADP]
13BPGA g [683]
NADP c [NADP(+)]
Fru c [fructose]
DHAP g [glycerone phosphate(2-)]
NAD g [NAD]
NADH g [NADH]
Pyr c [pyruvate]
Fru e [fructose]
CO2 c [carbon dioxide]
6PGL g _6PGL_g
Fru6P g [444848]
2PGA c [59]
Gly3P c [glycerol 1-phosphate]
3PGA c [3-phospho-D-glyceric acid]
NADP g [NADP(+)]
Rib5P g [aldehydo-D-ribose 5-phosphate(2-)]
Pi g [phosphatidylinositol]
Glc6P g [D-glucopyranose 6-phosphate]
ATP c [ATP]
NADPH c [NADPH]
Gly e [glycerol]
6PGL c [6-phosphogluconolactonase3.1.1.17]
Gly3P g [glycerol 1-phosphate]
ADP c [ADP]
AMP g [AMP]
Rul5P c [D-ribulose 5-phosphate(2-)]
3PGA g [3-phospho-D-glyceric acid]
AMP c [AMP]
NADPH g [NADPH]

Observables: none

Kerkhoven2013 - Glycolysis in T.brucei - MODEL AThere are six models (Model A, B, C, C-fruc, D, D-fruc) described in the…

Dynamic models of metabolism can be useful in identifying potential drug targets, especially in unicellular organisms. A model of glycolysis in the causative agent of human African trypanosomiasis, Trypanosoma brucei, has already shown the utility of this approach. Here we add the pentose phosphate pathway (PPP) of T. brucei to the glycolytic model. The PPP is localized to both the cytosol and the glycosome and adding it to the glycolytic model without further adjustments leads to a draining of the essential bound-phosphate moiety within the glycosome. This phosphate "leak" must be resolved for the model to be a reasonable representation of parasite physiology. Two main types of theoretical solution to the problem could be identified: (i) including additional enzymatic reactions in the glycosome, or (ii) adding a mechanism to transfer bound phosphates between cytosol and glycosome. One example of the first type of solution would be the presence of a glycosomal ribokinase to regenerate ATP from ribose 5-phosphate and ADP. Experimental characterization of ribokinase in T. brucei showed that very low enzyme levels are sufficient for parasite survival, indicating that other mechanisms are required in controlling the phosphate leak. Examples of the second type would involve the presence of an ATP:ADP exchanger or recently described permeability pores in the glycosomal membrane, although the current absence of identified genes encoding such molecules impedes experimental testing by genetic manipulation. Confronted with this uncertainty, we present a modeling strategy that identifies robust predictions in the context of incomplete system characterization. We illustrate this strategy by exploring the mechanism underlying the essential function of one of the PPP enzymes, and validate it by confirming the model predictions experimentally. link: http://identifiers.org/pubmed/24339766

Parameters:

Name Description
_3PGAT_g_k=250.0 Reaction: _3PGA_g => _3PGA_c; _3PGA_g, _3PGA_c, _3PGA_g, _3PGA_c, Rate Law: _3PGAT_g_k*_3PGA_g-_3PGAT_g_k*_3PGA_c
GPO_c_Vmax=368.0; GPO_c_KmGly3P=1.7 Reaction: Gly3P_c => DHAP_c; Gly3P_c, Gly3P_c, Rate Law: GPO_c_Vmax*Gly3P_c/(GPO_c_KmGly3P*(1+Gly3P_c/GPO_c_KmGly3P))
GDA_g_k=600.0 Reaction: Gly3P_g + DHAP_c => Gly3P_c + DHAP_g; Gly3P_g, DHAP_c, Gly3P_c, DHAP_g, Gly3P_g, DHAP_c, Gly3P_c, DHAP_g, Rate Law: Gly3P_g*GDA_g_k*DHAP_c-Gly3P_c*GDA_g_k*DHAP_g
ENO_c_Vmax=598.0; ENO_c_Km2PGA=0.054; ENO_c_Keq=4.17; ENO_c_KmPEP=0.24 Reaction: _2PGA_c => PEP_c; _2PGA_c, PEP_c, _2PGA_c, PEP_c, Rate Law: ENO_c_Vmax*_2PGA_c*(1-PEP_c/(ENO_c_Keq*_2PGA_c))/(ENO_c_Km2PGA*(1+_2PGA_c/ENO_c_Km2PGA+PEP_c/ENO_c_KmPEP))
PFK_g_Vmax=1708.0; PFK_g_KsATP=0.0393; PFK_g_KmFru6P=0.999; PFK_g_KmADP=1.0; PFK_g_KmATP=0.0648; PFK_g_Ki2=10.7; PFK_g_Ki1=15.8; PFK_g_Keq=1035.0 Reaction: ATP_g + Fru6P_g => Fru16BP_g + ADP_g; Fru6P_g, ATP_g, Fru16BP_g, ADP_g, Fru6P_g, ATP_g, Fru16BP_g, ADP_g, Rate Law: PFK_g_Vmax*PFK_g_Ki1*Fru6P_g*ATP_g*(1-Fru16BP_g*ADP_g/(PFK_g_Keq*Fru6P_g*ATP_g))/(PFK_g_KmFru6P*PFK_g_KmATP*(Fru16BP_g+PFK_g_Ki1)*(PFK_g_KsATP/PFK_g_KmATP+Fru6P_g/PFK_g_KmFru6P+ATP_g/PFK_g_KmATP+ADP_g/PFK_g_KmADP+Fru16BP_g*ADP_g/(PFK_g_KmADP*PFK_g_Ki2)+Fru6P_g*ATP_g/(PFK_g_KmFru6P*PFK_g_KmATP)))
GlcT_c_Vmax=111.7; GlcT_c_KmGlc=1.0; GlcT_c_alpha=0.75 Reaction: Glc_e => Glc_c; Glc_e, Glc_c, Glc_e, Glc_c, Rate Law: GlcT_c_Vmax*(Glc_e-Glc_c)/(GlcT_c_KmGlc+Glc_e+Glc_c+GlcT_c_alpha*Glc_e*Glc_c/GlcT_c_KmGlc)
TPI_g_Keq=0.046; TPI_g_KmDHAP=1.2; TPI_g_KmGA3P=0.25; TPI_g_Vmax=999.3 Reaction: DHAP_g => GA3P_g; DHAP_g, GA3P_g, DHAP_g, GA3P_g, Rate Law: TPI_g_Vmax*DHAP_g*(1-GA3P_g/(TPI_g_Keq*DHAP_g))/(TPI_g_KmDHAP*(1+DHAP_g/TPI_g_KmDHAP+GA3P_g/TPI_g_KmGA3P))
ALD_g_KmDHAP=0.015; ALD_g_KiGA3P=0.098; ALD_g_KmGA3P=0.067; ALD_g_Vmax=560.0; ALD_g_KmFru16BP=0.009; ALD_g_KiADP=1.51; ALD_g_KiAMP=3.65; ALD_g_Keq=0.084; ALD_g_KiATP=0.68 Reaction: Fru16BP_g => GA3P_g + DHAP_g; ATP_g, ADP_g, AMP_g, Fru16BP_g, GA3P_g, DHAP_g, ATP_g, ADP_g, AMP_g, Fru16BP_g, GA3P_g, DHAP_g, ATP_g, ADP_g, AMP_g, Rate Law: ALD_g_Vmax*Fru16BP_g*(1-GA3P_g*DHAP_g/(Fru16BP_g*ALD_g_Keq))/(ALD_g_KmFru16BP*(1+ATP_g/ALD_g_KiATP+ADP_g/ALD_g_KiADP+AMP_g/ALD_g_KiAMP)*(1+GA3P_g/ALD_g_KmGA3P+DHAP_g/ALD_g_KmDHAP+Fru16BP_g/(ALD_g_KmFru16BP*(1+ATP_g/ALD_g_KiATP+ADP_g/ALD_g_KiADP+AMP_g/ALD_g_KiAMP))+GA3P_g*DHAP_g/(ALD_g_KmGA3P*ALD_g_KmDHAP)+Fru16BP_g*GA3P_g/(ALD_g_KmFru16BP*ALD_g_KiGA3P*(1+ATP_g/ALD_g_KiATP+ADP_g/ALD_g_KiADP+AMP_g/ALD_g_KiAMP))))
ATPu_c_k=50.0 Reaction: ATP_c => ADP_c; ATP_c, ADP_c, ATP_c, ADP_c, Rate Law: ATPu_c_k*ATP_c/ADP_c
HXK_g_Vmax=1774.68; HXK_g_KmGlc6P=12.0; HXK_g_KmADP=0.126; HXK_g_Keq=759.0; HXK_g_KmATP=0.116; HXK_g_KmGlc=0.1 Reaction: ATP_g + Glc_g => Glc6P_g + ADP_g; Glc_g, ATP_g, Glc6P_g, ADP_g, Glc_g, ATP_g, Glc6P_g, ADP_g, Rate Law: HXK_g_Vmax*Glc_g*ATP_g*(1-Glc6P_g*ADP_g/(HXK_g_Keq*Glc_g*ATP_g))/(HXK_g_KmGlc*HXK_g_KmATP*(1+Glc_g/HXK_g_KmGlc+Glc6P_g/HXK_g_KmGlc6P)*(1+ATP_g/HXK_g_KmATP+ADP_g/HXK_g_KmADP))
PYK_c_KmPyr=50.0; PYK_c_KiADP=0.64; PYK_c_Vmax=1020.0; PYK_c_KmADP=0.114; PYK_c_Keq=10800.0; PYK_c_KiATP=0.57; PYK_c_KmATP=15.0; PYK_c_KmPEP=0.34; PYK_c_n=2.5 Reaction: PEP_c + ADP_c => Pyr_c + ATP_c; ADP_c, Pyr_c, ATP_c, PEP_c, ADP_c, Pyr_c, ATP_c, PEP_c, Rate Law: PYK_c_Vmax*ADP_c*(1-Pyr_c*ATP_c/(PYK_c_Keq*PEP_c*ADP_c))*(PEP_c/(PYK_c_KmPEP*(1+ADP_c/PYK_c_KiADP+ATP_c/PYK_c_KiATP)))^PYK_c_n/(PYK_c_KmADP*(1+(PEP_c/(PYK_c_KmPEP*(1+ADP_c/PYK_c_KiADP+ATP_c/PYK_c_KiATP)))^PYK_c_n+Pyr_c/PYK_c_KmPyr)*(1+ADP_c/PYK_c_KmADP+ATP_c/PYK_c_KmATP))
PGAM_c_Km3PGA=0.15; PGAM_c_Vmax=225.0; PGAM_c_Km2PGA=0.16; PGAM_c_Keq=0.17 Reaction: _3PGA_c => _2PGA_c; _3PGA_c, _2PGA_c, _3PGA_c, _2PGA_c, Rate Law: PGAM_c_Vmax*_3PGA_c*(1-_2PGA_c/(PGAM_c_Keq*_3PGA_c))/(PGAM_c_Km3PGA*(1+_3PGA_c/PGAM_c_Km3PGA+_2PGA_c/PGAM_c_Km2PGA))
PGI_g_Vmax=1305.0; PGI_g_Ki6PG=0.14; PGI_g_KmGlc6P=0.4; PGI_g_Keq=0.457; _6PG_g=0.0841958; PGI_g_KmFru6P=0.12 Reaction: Glc6P_g => Fru6P_g; Glc6P_g, Fru6P_g, Glc6P_g, Fru6P_g, Rate Law: PGI_g_Vmax*Glc6P_g*(1-Fru6P_g/(PGI_g_Keq*Glc6P_g))/(PGI_g_KmGlc6P*(1+Glc6P_g/PGI_g_KmGlc6P+Fru6P_g/PGI_g_KmFru6P+_6PG_g/PGI_g_Ki6PG))
G3PDH_g_KmDHAP=0.1; G3PDH_g_KmNAD=0.4; G3PDH_g_Vmax=465.0; G3PDH_g_Keq=17085.0; G3PDH_g_KmNADH=0.01; G3PDH_g_KmGly3P=2.0 Reaction: NADH_g + DHAP_g => Gly3P_g + NAD_g; DHAP_g, NADH_g, Gly3P_g, NAD_g, DHAP_g, NADH_g, Gly3P_g, NAD_g, Rate Law: G3PDH_g_Vmax*DHAP_g*NADH_g*(1-Gly3P_g*NAD_g/(G3PDH_g_Keq*DHAP_g*NADH_g))/(G3PDH_g_KmDHAP*G3PDH_g_KmNADH*(1+DHAP_g/G3PDH_g_KmDHAP+Gly3P_g/G3PDH_g_KmGly3P)*(1+NADH_g/G3PDH_g_KmNADH+NAD_g/G3PDH_g_KmNAD))
GK_g_Keq=8.37E-4; GK_g_KmATP=0.24; GK_g_KmGly=0.44; GK_g_KmADP=0.56; GK_g_KmGly3P=3.83; GK_g_Vmax=200.0 Reaction: Gly3P_g + ADP_g => Gly_e + ATP_g; Gly3P_g, ADP_g, Gly_e, ATP_g, Gly3P_g, ADP_g, Gly_e, ATP_g, Rate Law: GK_g_Vmax*Gly3P_g*ADP_g*(1-Gly_e*ATP_g/(GK_g_Keq*Gly3P_g*ADP_g))/(GK_g_KmGly3P*GK_g_KmADP*(1+Gly3P_g/GK_g_KmGly3P+Gly_e/GK_g_KmGly)*(1+ADP_g/GK_g_KmADP+ATP_g/GK_g_KmATP))
GlcT_g_k2=250000.0; GlcT_g_k1=250000.0 Reaction: Glc_c => Glc_g; Glc_c, Glc_g, Glc_c, Glc_g, Rate Law: GlcT_g_k1*Glc_c-GlcT_g_k2*Glc_g
AK_g_k2=1000.0; AK_g_k1=480.0 Reaction: ADP_g => AMP_g + ATP_g; ADP_g, AMP_g, ATP_g, ADP_g, AMP_g, ATP_g, Rate Law: AK_g_k1*ADP_g^2-AMP_g*ATP_g*AK_g_k2
PyrT_c_Vmax=230.0; PyrT_c_KmPyr=1.96 Reaction: Pyr_c => Pyr_e; Pyr_c, Pyr_c, Rate Law: PyrT_c_Vmax*Pyr_c/(PyrT_c_KmPyr*(1+Pyr_c/PyrT_c_KmPyr))
AK_c_k1=480.0; AK_c_k2=1000.0 Reaction: ADP_c => AMP_c + ATP_c; ADP_c, AMP_c, ATP_c, ADP_c, AMP_c, ATP_c, Rate Law: AK_c_k1*ADP_c^2-AMP_c*ATP_c*AK_c_k2
PGK_g_Km13BPGA=0.003; PGK_g_Vmax=2862.0; PGK_g_KmADP=0.1; PGK_g_Km3PGA=1.62; PGK_g_KmATP=0.29; PGK_g_Keq=3377.0 Reaction: _13BPGA_g + ADP_g => _3PGA_g + ATP_g; _13BPGA_g, ADP_g, _3PGA_g, ATP_g, _13BPGA_g, ADP_g, _3PGA_g, ATP_g, Rate Law: PGK_g_Vmax*_13BPGA_g*ADP_g*(1-_3PGA_g*ATP_g/(PGK_g_Keq*_13BPGA_g*ADP_g))/(PGK_g_Km13BPGA*PGK_g_KmADP*(1+_13BPGA_g/PGK_g_Km13BPGA+_3PGA_g/PGK_g_Km3PGA)*(1+ADP_g/PGK_g_KmADP+ATP_g/PGK_g_KmATP))
GAPDH_g_Vmax=720.9; GAPDH_g_Km13BPGA=0.1; GAPDH_g_KmNAD=0.45; GAPDH_g_KmNADH=0.02; GAPDH_g_KmGA3P=0.15; GAPDH_g_Keq=0.066 Reaction: GA3P_g + NAD_g + Pi_g => NADH_g + _13BPGA_g; GA3P_g, NAD_g, _13BPGA_g, NADH_g, GA3P_g, NAD_g, _13BPGA_g, NADH_g, Rate Law: GAPDH_g_Vmax*GA3P_g*NAD_g*(1-_13BPGA_g*NADH_g/(GAPDH_g_Keq*GA3P_g*NAD_g))/(GAPDH_g_KmGA3P*GAPDH_g_KmNAD*(1+GA3P_g/GAPDH_g_KmGA3P+_13BPGA_g/GAPDH_g_Km13BPGA)*(1+NAD_g/GAPDH_g_KmNAD+NADH_g/GAPDH_g_KmNADH))

States:

Name Description
Fru6P g [444848]
PEP c [phosphoenolpyruvate]
2PGA c [59]
ATP g [ATP]
Gly3P c [glycerol 1-phosphate]
Fru16BP g [alpha-D-fructofuranose 1,6-bisphosphate]
GA3P g [glyceraldehyde 3-phosphate]
3PGA c [3-phospho-D-glyceric acid]
Glc c [glucose]
Glc g [glucose]
Glc e [glucose]
Pi g [phosphatidylinositol]
Glc6P g [D-glucopyranose 6-phosphate]
ATP c [ATP]
Pyr e [pyruvate]
DHAP c [glycerone phosphate(2-)]
13BPGA g [683]
ADP g [ADP]
DHAP g [glycerone phosphate(2-)]
Gly e [glycerol]
NAD g [NAD]
Gly3P g [glycerol 1-phosphate]
ADP c [ADP]
AMP g [AMP]
NADH g [NADH]
Pyr c [pyruvate]
3PGA g [3-phospho-D-glyceric acid]
AMP c [AMP]

Observables: none

MODEL0568648427 @ v0.0.1

# Model of cholesterol regulation (with Boolean Formulae) (2008) This model is described in **Dynamical modeling of th…

BACKGROUND: Qualitative dynamics of small gene regulatory networks have been studied in quite some details both with synchronous and asynchronous analysis. However, both methods have their drawbacks: synchronous analysis leads to spurious attractors and asynchronous analysis lacks computational efficiency, which is a problem to simulate large networks. We addressed this question through the analysis of a major biosynthesis pathway. Indeed the cholesterol synthesis pathway plays a pivotal role in dislypidemia and, ultimately, in cancer through intermediates such as mevalonate, farnesyl pyrophosphate and geranyl geranyl pyrophosphate, but no dynamic model of this pathway has been proposed until now. RESULTS: We set up a computational framework to dynamically analyze large biological networks. This framework associates a classical and computationally efficient synchronous Boolean analysis with a newly introduced method based on Markov chains, which identifies spurious cycles among the results of the synchronous simulation. Based on this method, we present here the results of the analysis of the cholesterol biosynthesis pathway and its physiological regulation by the Sterol Response Element Binding Proteins (SREBPs), as well as the modeling of the action of statins, inhibitor drugs, on this pathway. The in silico experiments show the blockade of the cholesterol endogenous synthesis by statins and its regulation by SREPBs, in full agreement with the known biochemical features of the pathway. CONCLUSION: We believe that the method described here to identify spurious cycles opens new routes to compute large and biologically relevant models, thanks to the computational efficiency of synchronous simulation. Furthermore, to the best of our knowledge, we present here the first dynamic systems biology model of the human cholesterol pathway and several of its key regulatory control elements, hoping it would provide a good basis to perform in silico experiments and confront the resulting properties with published and experimental data. The model of the cholesterol pathway and its regulation, along with Boolean formulae used for simulation are available on our web site http://Bioinformaticsu613.free.fr. Graphical results of the simulation are also shown online. The SBML model is available in the BioModels database http://www.ebi.ac.uk/biomodels/ with submission ID: MODEL0568648427. link: http://identifiers.org/pubmed/19025648

Parameters: none

States: none

Observables: none

The combined effects of optimal control in cancer remission SubhasKhajanchi DibakarGhosh Abstract We investigate a math…

We investigate a mathematical model depicting the nonlinear dynamics of immunogenic tumors as envisioned by Kuznetsov et al. [1]. To understand the dynamics under what circumstances the cancer cells can be eliminated, we implement the theory of optimal control. We design two types of external treatment strategies, one is Adoptive Cellular Immunotherapy and another is interleukin-2. Our aim is to establish the treatment regimens that maximize the effector cell count and minimize the tumor cell burden and the deleterious effects of the total amount of drugs. We derive the existence of an optimal control by using the boundedness of solutions. We characterize the optimality system, in which the state system is coupled with co-states. The uniqueness of an optimal control of our problem is also analyzed. Finally, we demonstrate the numerical illustrations that the optimal regimens reduce the tumor burden under different scenarios. link: http://identifiers.org/doi/10.1016/j.amc.2015.09.012

Parameters:

Name Description
s = 13000.0; e1 = 1.0; p = 0.1245; g = 2.019E7 Reaction: => E; T, Rate Law: compartment*(s*e1+p*E*T/(g+T))
n = 1.101E-7; e2 = 0.0 Reaction: T => ; E, Rate Law: compartment*(n*E*T+e2*T)
m = 3.422E-10; d = 0.0412 Reaction: E => ; T, Rate Law: compartment*(m*E*T+d*E)
b = 2.0E-9; a = 0.18 Reaction: => T, Rate Law: compartment*a*T*(1-b*T)

States:

Name Description
T [Neoplastic Cell]
E [Effector Immune Cell]

Observables: none

This paper describes the synergistic interaction between the growth of malignant gliomas and the immune system interacti…

This paper describes the synergistic interaction between the growth of malignant gliomas and the immune system interactions using a system of coupled ordinary di®erential equations (ODEs). The proposed mathematical model comprises the interaction of glioma cells, macrophages, activated Cytotoxic T-Lymphocytes (CTLs), the immunosuppressive factor TGF- and the immuno-stimulatory factor IFN-. The dynamical behavior of the proposed system both analytically and numerically is investigated from the point of view of stability. By constructing Lyapunov functions, the global behavior of the glioma-free and the interior equilibrium point have been analyzed under some assumptions. Finally, we perform numerical simulations in order to illustrate our analytical ¯ndings by varying the system parameters. link: http://identifiers.org/doi/10.1142/S1793048017500114

Parameters:

Name Description
s1 = 63305.0 Reaction: => T_beta, Rate Law: compartment*s1
alpha4 = 0.1694; k3 = 334450.0 Reaction: C_T => ; G, Rate Law: compartment*alpha4*G/(G+k3)*C_T
mu2 = 6.93 Reaction: T_beta =>, Rate Law: compartment*mu2*T_beta
b2 = 1.02E-4 Reaction: => I_gamma; C_T, Rate Law: compartment*b2*C_T
alpha3 = 0.0194; k2 = 27000.0 Reaction: M => ; G, Rate Law: compartment*alpha3*G/(G+k2)*M
alpha2 = 0.12; k1 = 27000.0; alpha1 = 1.5; e1 = 10000.0 Reaction: G => ; T_beta, M, C_T, Rate Law: compartment*1/(T_beta+e1)*(alpha1*M+alpha2*C_T)*G/(G+k1)
k5 = 2000.0; a2 = 0.0 Reaction: => C_T; G, T_beta, Rate Law: compartment*a2*G/(k5+T_beta)
a1 = 0.1163; e2 = 10000.0; k4 = 10500.0 Reaction: => M; I_gamma, T_beta, Rate Law: compartment*a1*I_gamma/(k4+I_gamma)*1/(T_beta+e2)
mu1 = 0.007 Reaction: C_T =>, Rate Law: compartment*mu1*C_T
r1 = 0.01; G_max = 882650.0 Reaction: => G, Rate Law: compartment*r1*G*(1-G/G_max)
M_max = 1.0; r2 = 0.3307 Reaction: => M, Rate Law: compartment*r2*M*(1-M/M_max)
mu3 = 0.102 Reaction: I_gamma =>, Rate Law: compartment*mu3*I_gamma
b1 = 5.75E-6 Reaction: => T_beta; G, Rate Law: compartment*b1*G

States:

Name Description
C T [C12543]
M [macrophage]
T beta [C30098]
G [glioma cell]
I gamma [Interferon Gamma]

Observables: none

Stability Analysis of a Mathematical Model for Glioma-Immune Interaction under Optimal Therapy Subhas Khajanchi Abstrac…

We investigate a mathematical model using a system of coupled ordinary differential equations, which describes the interplay of malignant glioma cells, macrophages, glioma specific CD8+T cells and the immunotherapeutic drug Adoptive Cellular Immunotherapy (ACI). To better understand under what circumstances the glioma cells can be eliminated, we employ the theory of optimal control. We investigate the dynamics of the system by observing biologically feasible equilibrium points and their stability analysis before administration of the external therapy ACI. We solve an optimal control problem with an objective functional which minimizes the glioma cell burden as well as the side effects of the treatment. We characterize our optimal control in terms of the solutions to the optimality system, in which the state system coupled with the adjoint system. Our model simulation demonstrates that the strength of treatment u1(t) plays an important role to eliminate the glioma cells. Finally, we derive an optimal treatment strategy and then solve it numerically. link: http://identifiers.org/doi/10.1515/ijnsns-2017-0206

Parameters:

Name Description
alpha_3 = 0.0194; k_2 = 0.030584 Reaction: v => ; u, Rate Law: compartment*alpha_3*u*v/(u+k_2)
k_1 = 0.90305; alpha_1 = 0.069943; alpha_2 = 2.74492 Reaction: u => ; v, w, Rate Law: compartment*(alpha_1*v+alpha_2*w)/(u+k_1)*u
k_4 = 0.378918; alpha_4 = 0.01694; mu_1 = 0.0074 Reaction: w => ; u, Rate Law: compartment*(mu_1*w+alpha_4*u*w/(u+k_4))
r_2 = 0.3307 Reaction: => v, Rate Law: compartment*r_2*v*(1-v)
r_1 = 0.4822 Reaction: => u, Rate Law: compartment*r_1*u*(1-u)
gamma_1 = 0.1245; k_3 = 2.8743 Reaction: => w; u, Rate Law: compartment*gamma_1*u*w/(k_3+u)

States:

Name Description
v [macrophage]
w [T-lymphocyte]
u [glioma cell]

Observables: none

This is a ordinary differential equation-based model of the eukaryotic translation initiation factor (eIF2) phosphorylat…

Phosphorylation of eukaryotic translation initiation factor 2 (eIF2) is one of the best studied and most widely used means for regulating protein synthesis activity in eukaryotic cells. This pathway regulates protein synthesis in response to stresses, viral infections, and nutrient depletion, among others. We present analyses of an ordinary differential equation-based model of this pathway, which aim to identify its principal robustness-conferring features. Our analyses indicate that robustness is a distributed property, rather than arising from the properties of any one individual pathway species. However, robustness-conferring properties are unevenly distributed between the different species, and we identify a guanine nucleotide dissociation inhibitor (GDI) complex as a species that likely contributes strongly to the robustness of the pathway. Our analyses make further predictions on the dynamic response to different types of kinases that impinge on eIF2. link: http://identifiers.org/pubmed/29476830

Parameters: none

States: none

Observables: none

Blood coagulation model for prothrombin time test.

A mathematical model for the prothrombin time test is proposed. The time course of clotting factor activation during coagulation was calculated, and the sensitivity of the test to a decrease in the concentrations of coagulation proteins or their activities was studied. The model predicts that only severe coagulation disorders connected with a more than five-fold decrease in the concentrations or activities of the blood coagulation factors can be revealed by the test. link: http://identifiers.org/pubmed/9645916

Parameters: none

States: none

Observables: none

BIOMD0000000048 @ v0.0.1

Kholodenko1999 - EGFR signaling This model has been generated by **the JWS Online project by Jacky Snoep using [PySCeS]…

During the past decade, our knowledge of molecular mechanisms involved in growth factor signaling has proliferated almost explosively. However, the kinetics and control of information transfer through signaling networks remain poorly understood. This paper combines experimental kinetic analysis and computational modeling of the short term pattern of cellular responses to epidermal growth factor (EGF) in isolated hepatocytes. The experimental data show transient tyrosine phosphorylation of the EGF receptor (EGFR) and transient or sustained response patterns in multiple signaling proteins targeted by EGFR. Transient responses exhibit pronounced maxima, reached within 15-30 s of EGF stimulation and followed by a decline to relatively low (quasi-steady-state) levels. In contrast to earlier suggestions, we demonstrate that the experimentally observed transients can be accounted for without requiring receptor-mediated activation of specific tyrosine phosphatases, following EGF stimulation. The kinetic model predicts how the cellular response is controlled by the relative levels and activity states of signaling proteins and under what conditions activation patterns are transient or sustained. EGFR signaling patterns appear to be robust with respect to variations in many elemental rate constants within the range of experimentally measured values. On the other hand, we specify which changes in the kinetic scheme, rate constants, and total amounts of molecular factors involved are incompatible with the experimentally observed kinetics of signal transfer. Quantitation of signaling network responses to growth factors allows us to assess how cells process information controlling their growth and differentiation. link: http://identifiers.org/pubmed/10514507

Parameters:

Name Description
k24f=0.009; k24b=0.0429 Reaction: RShP + GS => RShGS, Rate Law: (k24f*RShP*GS-k24b*RShGS)*compartment
k14f=6.0; k14b=0.06 Reaction: RSh => RShP, Rate Law: (k14f*RSh-k14b*RShP)*compartment
k17f=0.003; k17b=0.1 Reaction: RShP + Grb => RShG, Rate Law: (k17f*RShP*Grb-k17b*RShG)*compartment
k13b=0.6; k13f=0.09 Reaction: Shc + RP => RSh, Rate Law: (k13f*RP*Shc-k13b*RSh)*compartment
K4=50.0; V4=450.0 Reaction: RP => R2, Rate Law: V4*RP/(K4+RP)*compartment
k7f=0.3; k7b=0.006 Reaction: RPLCgP => PLCgP + RP, Rate Law: (k7f*RPLCgP-k7b*RP*PLCgP)*compartment
k21f=0.003; k21b=0.1 Reaction: Grb + ShP => ShG, Rate Law: (k21f*ShP*Grb-k21b*ShG)*compartment
k5b=0.2; k5f=0.06 Reaction: RP + PLCg => RPLCg, Rate Law: (k5f*RP*PLCg-k5b*RPLCg)*compartment
k22b=0.064; k22f=0.03 Reaction: ShG + SOS => ShGS, Rate Law: (k22f*ShG*SOS-k22b*ShGS)*compartment
k6b=0.05; k6f=1.0 Reaction: RPLCg => RPLCgP, Rate Law: (k6f*RPLCg-k6b*RPLCgP)*compartment
k11b=0.0045; k11f=0.03 Reaction: RGS => GS + RP, Rate Law: (k11f*RGS-k11b*RP*GS)*compartment
K8=100.0; V8=1.0 Reaction: PLCgP => PLCg, Rate Law: V8*PLCgP/(K8+PLCgP)*compartment
k3b=0.01; k3f=1.0 Reaction: R2 => RP, Rate Law: (k3f*R2-k3b*RP)*compartment
k20b=2.4E-4; k20f=0.12 Reaction: RShGS => ShGS + RP, Rate Law: (k20f*RShGS-k20b*ShGS*RP)*compartment
k10b=0.06; k10f=0.01 Reaction: RG + SOS => RGS, Rate Law: (k10f*RG*SOS-k10b*RGS)*compartment
k15f=0.3; k15b=9.0E-4 Reaction: RShP => RP + ShP, Rate Law: (k15f*RShP-k15b*ShP*RP)*compartment
K16=340.0; V16=1.7 Reaction: ShP => Shc, Rate Law: V16*ShP/(K16+ShP)*compartment
k2f=0.01; k2b=0.1 Reaction: Ra => R2, Rate Law: (k2f*Ra*Ra-k2b*R2)*compartment
k9b=0.05; k9f=0.003 Reaction: Grb + RP => RG, Rate Law: (k9f*RP*Grb-k9b*RG)*compartment
k25b=0.03; k25f=1.0 Reaction: PLCgP => PLCgl, Rate Law: (k25f*PLCgP-k25b*PLCgl)*compartment
k18f=0.3; k18b=9.0E-4 Reaction: RShG => ShG + RP, Rate Law: (k18f*RShG-k18b*RP*ShG)*compartment
k1f=0.003; k1b=0.06 Reaction: R + EGF => Ra, Rate Law: (k1f*R*EGF-k1b*Ra)*compartment
k23f=0.1; k23b=0.021 Reaction: ShGS => GS + ShP, Rate Law: (k23f*ShGS-k23b*ShP*GS)*compartment
k19b=0.0214; k19f=0.01 Reaction: SOS + RShG => RShGS, Rate Law: (k19f*RShG*SOS-k19b*RShGS)*compartment
k12f=0.0015; k12b=1.0E-4 Reaction: GS => Grb + SOS, Rate Law: (k12f*GS-k12b*Grb*SOS)*compartment

States:

Name Description
Ra [Receptor protein-tyrosine kinase; Pro-epidermal growth factor]
RGS [Receptor protein-tyrosine kinase; Growth factor receptor-bound protein 2; Son of sevenless 1]
Shc [SHC-transforming protein 1]
EGF [Pro-epidermal growth factor]
ShGS [SHC-transforming protein 1; Growth factor receptor-bound protein 2; Son of sevenless 1]
RP [Receptor protein-tyrosine kinase]
RShP [SHC-transforming protein 1; Receptor protein-tyrosine kinase]
RPLCgP [1-phosphatidylinositol 4,5-bisphosphate phosphodiesterase gamma-2; 1-phosphatidylinositol 4,5-bisphosphate phosphodiesterase gamma-1; Receptor protein-tyrosine kinase]
RG [Growth factor receptor-bound protein 2; Receptor protein-tyrosine kinase]
SOS [Son of sevenless 1]
RShGS [Growth factor receptor-bound protein 2; SHC-transforming protein 1; Son of sevenless 1; Receptor protein-tyrosine kinase]
RShG [SHC-transforming protein 1; Growth factor receptor-bound protein 2; Receptor protein-tyrosine kinase]
PLCg [IPR001192; 1-phosphatidylinositol 4,5-bisphosphate phosphodiesterase gamma-1; 1-phosphatidylinositol 4,5-bisphosphate phosphodiesterase gamma-2]
GS [Growth factor receptor-bound protein 2; Son of sevenless 1]
ShP [SHC-transforming protein 1]
Grb [Growth factor receptor-bound protein 2]
PLCgl [IPR001192; 1-phosphatidylinositol 4,5-bisphosphate phosphodiesterase gamma-2; 1-phosphatidylinositol 4,5-bisphosphate phosphodiesterase gamma-1]
RSh [Receptor protein-tyrosine kinase; SHC-transforming protein 1]
ShG [SHC-transforming protein 1; Growth factor receptor-bound protein 2]
RPLCg [1-phosphatidylinositol 4,5-bisphosphate phosphodiesterase gamma-1; 1-phosphatidylinositol 4,5-bisphosphate phosphodiesterase gamma-2; Receptor protein-tyrosine kinase]
PLCgP [IPR001192; 1-phosphatidylinositol 4,5-bisphosphate phosphodiesterase gamma-2; 1-phosphatidylinositol 4,5-bisphosphate phosphodiesterase gamma-1]
R2 [Pro-epidermal growth factor; Receptor protein-tyrosine kinase]
R [Receptor protein-tyrosine kinase]

Observables: none

Kholodenko2000 - Ultrasensitivity and negative feedback bring oscillations in MAPK cascadeThe combination of ultrasensit…

Functional organization of signal transduction into protein phosphorylation cascades, such as the mitogen-activated protein kinase (MAPK) cascades, greatly enhances the sensitivity of cellular targets to external stimuli. The sensitivity increases multiplicatively with the number of cascade levels, so that a tiny change in a stimulus results in a large change in the response, the phenomenon referred to as ultrasensitivity. In a variety of cell types, the MAPK cascades are imbedded in long feedback loops, positive or negative, depending on whether the terminal kinase stimulates or inhibits the activation of the initial level. Here we demonstrate that a negative feedback loop combined with intrinsic ultrasensitivity of the MAPK cascade can bring about sustained oscillations in MAPK phosphorylation. Based on recent kinetic data on the MAPK cascades, we predict that the period of oscillations can range from minutes to hours. The phosphorylation level can vary between the base level and almost 100% of the total protein. The oscillations of the phosphorylation cascades and slow protein diffusion in the cytoplasm can lead to intracellular waves of phospho-proteins. link: http://identifiers.org/pubmed/10712587

Parameters:

Name Description
KK9=15.0; V9=0.5 Reaction: MAPK_PP => MAPK_P, Rate Law: uVol*V9*MAPK_PP/(KK9+MAPK_PP)
KK2=8.0; V2=0.25 Reaction: MKKK_P => MKKK, Rate Law: uVol*V2*MKKK_P/(KK2+MKKK_P)
KK10=15.0; V10=0.5 Reaction: MAPK_P => MAPK, Rate Law: uVol*V10*MAPK_P/(KK10+MAPK_P)
V5=0.75; KK5=15.0 Reaction: MKK_PP => MKK_P, Rate Law: uVol*V5*MKK_PP/(KK5+MKK_PP)
k7=0.025; KK7=15.0 Reaction: MAPK => MAPK_P; MKK_PP, Rate Law: uVol*k7*MKK_PP*MAPK/(KK7+MAPK)
KK8=15.0; k8=0.025 Reaction: MAPK_P => MAPK_PP; MKK_PP, Rate Law: uVol*k8*MKK_PP*MAPK_P/(KK8+MAPK_P)
Ki=9.0; V1=2.5; K1=10.0; n=1.0 Reaction: MKKK => MKKK_P; MAPK_PP, Rate Law: uVol*V1*MKKK/((1+(MAPK_PP/Ki)^n)*(K1+MKKK))
V6=0.75; KK6=15.0 Reaction: MKK_P => MKK, Rate Law: uVol*V6*MKK_P/(KK6+MKK_P)
KK3=15.0; k3=0.025 Reaction: MKK => MKK_P; MKKK_P, Rate Law: uVol*k3*MKKK_P*MKK/(KK3+MKK)
k4=0.025; KK4=15.0 Reaction: MKK_P => MKK_PP; MKKK_P, Rate Law: uVol*k4*MKKK_P*MKK_P/(KK4+MKK_P)

States:

Name Description
MKKK P [RAF proto-oncogene serine/threonine-protein kinase]
MKK [Dual specificity mitogen-activated protein kinase kinase 1]
MAPK [Mitogen-activated protein kinase 1]
MKKK [RAF proto-oncogene serine/threonine-protein kinase]
MAPK PP [Mitogen-activated protein kinase 1]
MKK PP [Dual specificity mitogen-activated protein kinase kinase 1]
MAPK P [Mitogen-activated protein kinase 1]
MKK P [Dual specificity mitogen-activated protein kinase kinase 1]

Observables: none

MODEL4821294342 @ v0.0.1

An approximation to the <a href = "http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=pubmed&dopt=Abstract&li…

The kinetics of prokaryotic gene expression has been modelled by the Monte Carlo computer simulation algorithm of Gillespie, which allowed the study of random fluctuations in the number of protein molecules during gene expression. The model, when applied to the simulation of LacZ gene expression, is in good agreement with experimental data. The influence of the frequencies of transcription and translation initiation on random fluctuations in gene expression has been studied in a number of simulations in which promoter and ribosome binding site effectiveness has been changed in the range of values reported for various prokaryotic genes. We show that the genes expressed from strong promoters produce the protein evenly, with a rate that does not vary significantly among cells. The genes with very weak promoters express the protein in "bursts" occurring at random time intervals. Therefore, if the low level of gene expression results from the low frequency of transcription initiation, huge fluctuations arise. In contrast, the protein can be produced with a low and uniform rate if the gene has a strong promoter and a slow rate of ribosome binding (a weak ribosome binding site). The implications of these findings for the expression of regulatory proteins are discussed. link: http://identifiers.org/pubmed/11062240

Parameters: none

States: none

Observables: none

Kim2007 - Crosstalk between Wnt and ERK pathwaysExperimental studies have shown that both Wnt and the MAPK pathways are…

The Wnt and the extracellular signal regulated-kinase (ERK) pathways are both involved in the pathogenesis of various kinds of cancers. Recently, the existence of crosstalk between Wnt and ERK pathways was reported. Gathering all reported results, we have discovered a positive feedback loop embedded in the crosstalk between the Wnt and ERK pathways. We have developed a plausible model that represents the role of this hidden positive feedback loop in the Wnt/ERK pathway crosstalk based on the integration of experimental reports and employing established basic mathematical models of each pathway. Our analysis shows that the positive feedback loop can generate bistability in both the Wnt and ERK signaling pathways, and this prediction was further validated by experiments. In particular, using the commonly accepted assumption that mutations in signaling proteins contribute to cancerogenesis, we have found two conditions through which mutations could evoke an irreversible response leading to a sustained activation of both pathways. One condition is enhanced production of beta-catenin, the other is a reduction of the velocity of MAP kinase phosphatase(s). This enables that high activities of Wnt and ERK pathways are maintained even without a persistent extracellular signal. Thus, our study adds a novel aspect to the molecular mechanisms of carcinogenesis by showing that mutational changes in individual proteins can cause fundamental functional changes well beyond the pathway they function in by a positive feedback loop embedded in crosstalk. Thus, crosstalk between signaling pathways provides a vehicle through which mutations of individual components can affect properties of the system at a larger scale. link: http://identifiers.org/pubmed/17237813

Parameters:

Name Description
Vmax5 = 45.0; Km8 = 15.0 Reaction: X23 => X22, Rate Law: cytoplasm*Vmax5*X23/(Km8+X23)
Vmax3 = 45.0; Km4 = 15.0 Reaction: X19 => X18, Rate Law: cytoplasm*Vmax3*X19/(Km4+X19)
kcat1 = 1.5; Km3 = 15.0 Reaction: X18 => X19; X17, Rate Law: cytoplasm*kcat1*X17*X18/(Km3+X18)
k19 = 39.0; k18 = 0.15 Reaction: X18 + X25 => X24, Rate Law: cytoplasm*(k18*X18*X25-k19*X24)
k15 = 0.167 Reaction: X12 =>, Rate Law: cytoplasm*k15*X12
k5 = 0.133 Reaction: X3 => X4, Rate Law: cytoplasm*k5*X3
W = 0.0; Vmax1 = 150.0; Ki = 9.0; Km1 = 10.0 Reaction: X16 => X17; X23, Rate Law: cytoplasm*Vmax1*X16*W/(Km1+X16)*Ki/(Ki+X23)
k20 = 0.015 Reaction: X27 =>, Rate Law: cytoplasm*k20*X27
k_plus7 = 1.0; k_minus7 = 50.0 Reaction: X12 + X7 => X6, Rate Law: cytoplasm*(k_plus7*X7*X12-k_minus7*X6)
k9 = 206.0 Reaction: X8 => X9, Rate Law: cytoplasm*k9*X8
Km7 = 15.0; kcat3 = 1.5 Reaction: X22 => X23; X21, Rate Law: cytoplasm*kcat3*X21*X22/(Km7+X22)
Vmax2 = 15.0; Km2 = 8.0 Reaction: X17 => X16, Rate Law: cytoplasm*Vmax2*X17/(Km2+X17)
k1 = 0.182; W = 0.0 Reaction: X1 => X2, Rate Law: cytoplasm*k1*X1*W
V12 = 0.423 Reaction: => X11, Rate Law: cytoplasm*V12
Km5 = 15.0; kcat2 = 1.5 Reaction: X20 => X21; X19, Rate Law: cytoplasm*kcat2*X19*X20/(Km5+X20)
k3 = 0.05 Reaction: X4 => X6 + X5; X2, Rate Law: cytoplasm*k3*X2*X4
k_minus6 = 0.909; k_plus6 = 0.0909 Reaction: X6 + X5 => X4, Rate Law: cytoplasm*(k_plus6*X5*X6-k_minus6*X4)
kcat7 = 1.5; Km13 = 15.0 Reaction: X5 => X28; X23, Rate Law: cytoplasm*kcat7*X23*X5/(Km13+X5)
k4 = 0.267 Reaction: X4 => X3, Rate Law: cytoplasm*k4*X4
k11 = 0.417 Reaction: X10 =>, Rate Law: cytoplasm*k11*X10
Km12 = 15.0; kcat6 = 1.5 Reaction: X18 => X19; X27, Rate Law: cytoplasm*kcat6*X27*X18/(Km12+X18)
k10 = 206.0 Reaction: X9 => X3 + X10, Rate Law: cytoplasm*k10*X9
k_minus17 = 1200.0; k_plus17 = 1.0 Reaction: X11 + X7 => X15, Rate Law: cytoplasm*(k_plus17*X7*X11-k_minus17*X15)
k_plus8 = 1.0; k_minus8 = 120.0 Reaction: X11 + X3 => X8, Rate Law: cytoplasm*(k_plus8*X3*X11-k_minus8*X8)
Vmax6 = 45.0; Km10 = 12.0 Reaction: X26 => X25, Rate Law: cytoplasm*Vmax6*X26/(Km10+X26)
Km14 = 15.0; Vmax7 = 45.0 Reaction: X28 => X5, Rate Law: cytoplasm*Vmax7*X28/(Km14+X28)
kcat4 = 1.5; Km9 = 9.0 Reaction: X24 => X18 + X26; X23, Rate Law: cytoplasm*kcat4*X23*X24/(Km9+X24)
Km11 = 15.0; kcat5 = 0.6; n1 = 2.0 Reaction: => X27; X14, Rate Law: cytoplasm*kcat5*X14^n1/(Km11^n1+X14^n1)
k_plus16 = 1.0; k_minus16 = 30.0 Reaction: X13 + X11 => X14, Rate Law: nucleus*(k_plus16*X11*X13-k_minus16*X14)
k21 = 1.0E-6; k14 = 8.22E-5 Reaction: => X12; X11, X14, Rate Law: nucleus*(k14+k21*(X11+X14))
Km6 = 15.0; Vmax4 = 45.0 Reaction: X21 => X20, Rate Law: cytoplasm*Vmax4*X21/(Km6+X21)
k2 = 0.0182 Reaction: X2 => X1, Rate Law: cytoplasm*k2*X2
k13 = 2.57E-4 Reaction: X11 =>, Rate Law: nucleus*k13*X11

States:

Name Description
X18 [RAF proto-oncogene serine/threonine-protein kinase]
X7 [Adenomatous polyposis coli protein 2]
X20 [Dual specificity mitogen-activated protein kinase kinase 1]
X21 [Dual specificity mitogen-activated protein kinase kinase 1]
X19 [RAF proto-oncogene serine/threonine-protein kinase]
X16 [Ras-related protein R-Ras2]
X11 [Catenin beta-1]
X22 [Mitogen-activated protein kinase 1]
X24 [RAF proto-oncogene serine/threonine-protein kinase; Phosphatidylethanolamine-binding protein 1]
X14 [Catenin beta-1; Lymphoid enhancer-binding factor 1]
X2 [Segment polarity protein dishevelled homolog DVL-1]
X13 [Lymphoid enhancer-binding factor 1]
X5 [Glycogen synthase kinase-3 beta]
X26 [Phosphatidylethanolamine-binding protein 1]
X8 [Adenomatous polyposis coli protein 2; Axin-1; Glycogen synthase kinase-3 beta; Catenin beta-1; beta-catenin destruction complex]
X25 [Phosphatidylethanolamine-binding protein 1]
X9 [Adenomatous polyposis coli protein 2; Axin-1; Glycogen synthase kinase-3 beta; Catenin beta-1; beta-catenin destruction complex]
X12 [Axin-1]
X27 unknown molecule X
X17 [Ras-related protein R-Ras2]
X28 [Glycogen synthase kinase-3 beta]
X6 [Adenomatous polyposis coli protein 2; Axin-1]
X3 [Adenomatous polyposis coli protein 2; Axin-1; Glycogen synthase kinase-3 beta; beta-catenin destruction complex]
X23 [Mitogen-activated protein kinase 1]
X4 [Adenomatous polyposis coli protein 2; Axin-1; Glycogen synthase kinase-3 beta; beta-catenin destruction complex]
X10 [Catenin beta-1]
X15 [Adenomatous polyposis coli protein 2; Catenin beta-1]
X1 [Segment polarity protein dishevelled homolog DVL-1]

Observables: none

Kim2007 - Genome-scale metabolic network of Mannheimia succiniciproducens (iTY425)This model is described in the article…

Mannheimia succiniciproducens MBEL55E isolated from bovine rumen is a capnophilic gram-negative bacterium that efficiently produces succinic acid, an industrially important four carbon dicarboxylic acid. In order to design a metabolically engineered strain which is capable of producing succinic acid with high yield and productivity, it is essential to optimize the whole metabolism at the systems level. Consequently, in silico modeling and simulation of the genome-scale metabolic network was employed for genome-scale analysis and efficient design of metabolic engineering experiments. The genome-scale metabolic network of M. succiniciproducens consisting of 686 reactions and 519 metabolites was constructed based on reannotation and validation experiments. With the reconstructed model, the network structure and key metabolic characteristics allowing highly efficient production of succinic acid were deciphered; these include strong PEP carboxylation, branched TCA cycle, relative weak pyruvate formation, the lack of glyoxylate shunt, and non-PTS for glucose uptake. Constraints-based flux analyses were then carried out under various environmental and genetic conditions to validate the genome-scale metabolic model and to decipher the altered metabolic characteristics. Predictions based on constraints-based flux analysis were mostly in excellent agreement with the experimental data. In silico knockout studies allowed prediction of new metabolic engineering strategies for the enhanced production of succinic acid. This genome-scale in silico model can serve as a platform for the systematic prediction of physiological responses of M. succiniciproducens to various environmental and genetic perturbations and consequently for designing rational strategies for strain improvement. link: http://identifiers.org/pubmed/17405177

Parameters: none

States: none

Observables: none

BIOMD0000000179 @ v0.0.1

This model is from the article: Interlinked mutual inhibitory positive feedbacks induce robust cellular memory effec…

Mutual inhibitory positive feedback (MIPF), or double-negative feedback, is a key regulatory motif of cellular memory with the capability of maintaining switched states for transient stimuli. Such MIPFs are found in various biological systems where they are interlinked in many cases despite a single MIPF can still realize such a memory effect. An intriguing question then arises about the advantage of interlinking MIPFs instead of exploiting an isolated single MIPF to realize the memory effect. We have investigated the advantages of interlinked MIPF systems through mathematical modeling and computer simulations. Our results revealed that interlinking MIPFs expands the parameter range of achieving the memory effect, or the memory region, thereby making the system more robust to parameter perturbations. Moreover, the minimal duration and amplitude of an external stimulus required for off-to-on state transition are increased and, as a result, external noises can more effectively be filtered out. Hence, interlinked MIPF systems can realize more robust cellular memories with respect to both parameter perturbations and external noises. Our study suggests that interlinked MIPF systems might be an evolutionary consequence acquired for a more reliable memory effect by enhancing robustness against noisy cellular environments. link: http://identifiers.org/pubmed/17892872

Parameters:

Name Description
i1 = 0.0 Reaction: => R1, Rate Law: i1
d_R2 = 0.23521 Reaction: R2 =>, Rate Law: d_R2*R2
sP2R2 = 0.47305 Reaction: => P2; R2, Rate Law: sP2R2*R2
sP1_prime_P1 = 0.28687 Reaction: => P1_prime; P1, Rate Law: sP1_prime_P1*P1
i2 = 1.0 Reaction: => R2, Rate Law: i2
d_P2 = 0.22367 Reaction: P2 =>, Rate Law: d_P2*P2
n = 9.0; s1 = 0.4 Reaction: => P1_prime; P2_prime, Rate Law: s1/(1+P2_prime^n)
d_P2_prime = 0.37048 Reaction: P2_prime =>, Rate Law: d_P2_prime*P2_prime
sP3_prime_P2_prime = 0.5; n = 9.0 Reaction: => P3_prime; P2_prime, Rate Law: sP3_prime_P2_prime*P2_prime^n/(1+P2_prime^n)
n = 9.0; s3 = 0.2 Reaction: => P1_prime; P3_prime, Rate Law: s3/(1+P3_prime^n)
d_R1 = 0.23521 Reaction: R1 =>, Rate Law: d_R1*R1
sP1R1 = 0.47305 Reaction: => P1; R1, Rate Law: sP1R1*R1
d_P3_prime = 0.37048 Reaction: P3_prime =>, Rate Law: d_P3_prime*P3_prime
d_P1 = 0.22367 Reaction: P1 =>, Rate Law: d_P1*P1
d_P1_prime = 0.37048 Reaction: P1_prime =>, Rate Law: d_P1_prime*P1_prime
s2 = 0.3; n = 9.0 Reaction: => P2_prime; P1_prime, Rate Law: s2/(1+P1_prime^n)
sP2_prime_P2 = 0.28687 Reaction: => P2_prime; P2, Rate Law: sP2_prime_P2*P2

States:

Name Description
P1 prime [protein; Protein]
P3 prime [protein; Protein]
R1 [messenger RNA; RNA]
P2 [protein; Protein]
R2 [messenger RNA; RNA]
P2 prime [protein; Protein]
P1 [protein; Protein]

Observables: none

BIOMD0000000180 @ v0.0.1

This model is from the article: Interlinked mutual inhibitory positive feedbacks induce robust cellular memory effec…

Mutual inhibitory positive feedback (MIPF), or double-negative feedback, is a key regulatory motif of cellular memory with the capability of maintaining switched states for transient stimuli. Such MIPFs are found in various biological systems where they are interlinked in many cases despite a single MIPF can still realize such a memory effect. An intriguing question then arises about the advantage of interlinking MIPFs instead of exploiting an isolated single MIPF to realize the memory effect. We have investigated the advantages of interlinked MIPF systems through mathematical modeling and computer simulations. Our results revealed that interlinking MIPFs expands the parameter range of achieving the memory effect, or the memory region, thereby making the system more robust to parameter perturbations. Moreover, the minimal duration and amplitude of an external stimulus required for off-to-on state transition are increased and, as a result, external noises can more effectively be filtered out. Hence, interlinked MIPF systems can realize more robust cellular memories with respect to both parameter perturbations and external noises. Our study suggests that interlinked MIPF systems might be an evolutionary consequence acquired for a more reliable memory effect by enhancing robustness against noisy cellular environments. link: http://identifiers.org/pubmed/17892872

Parameters:

Name Description
i1 = 0.0 Reaction: => R1, Rate Law: i1
d_R2 = 0.23521 Reaction: R2 =>, Rate Law: d_R2*R2
sP2R2 = 0.47305 Reaction: => P2; R2, Rate Law: sP2R2*R2
sP1_prime_P1 = 0.28687 Reaction: => P1_prime; P1, Rate Law: sP1_prime_P1*P1
i2 = 1.0 Reaction: => R2, Rate Law: i2
d_P2 = 0.22367 Reaction: P2 =>, Rate Law: d_P2*P2
n = 9.0; s1 = 0.4 Reaction: => P1_prime; P2_prime, Rate Law: s1/(1+P2_prime^n)
d_P2_prime = 0.37048 Reaction: P2_prime =>, Rate Law: d_P2_prime*P2_prime
sP3_prime_P2_prime = 0.5; n = 9.0 Reaction: => P3_prime; P2_prime, Rate Law: sP3_prime_P2_prime*P2_prime^n/(1+P2_prime^n)
n = 9.0; s3 = 0.2 Reaction: => P1_prime; P3_prime, Rate Law: s3/(1+P3_prime^n)
d_P4_prime = 0.37048 Reaction: P4_prime =>, Rate Law: d_P4_prime*P4_prime
sP4_prime_P1_prime = 0.5; n = 9.0 Reaction: => P4_prime; P1_prime, Rate Law: sP4_prime_P1_prime*P1_prime^n/(1+P1_prime^n)
d_R1 = 0.23521 Reaction: R1 =>, Rate Law: d_R1*R1
sP1R1 = 0.47305 Reaction: => P1; R1, Rate Law: sP1R1*R1
d_P3_prime = 0.37048 Reaction: P3_prime =>, Rate Law: d_P3_prime*P3_prime
d_P1 = 0.22367 Reaction: P1 =>, Rate Law: d_P1*P1
d_P1_prime = 0.37048 Reaction: P1_prime =>, Rate Law: d_P1_prime*P1_prime
s2 = 0.3; n = 9.0 Reaction: => P2_prime; P1_prime, Rate Law: s2/(1+P1_prime^n)
sP2_prime_P2 = 0.28687 Reaction: => P2_prime; P2, Rate Law: sP2_prime_P2*P2

States:

Name Description
P1 prime [protein; Protein]
P3 prime [protein; Protein]
R1 [messenger RNA; RNA]
P2 [protein; Protein]
P1 [protein; Protein]
R2 [messenger RNA; RNA]
P2 prime [protein; Protein]
P4 prime [protein; Protein]

Observables: none

Kim2009 - Genome-scale metabolic network of Acinetobacter baumannii (AbyMBEL891)This model is described in the article:…

Acinetobacter baumannii has emerged as a new clinical threat to human health, particularly to ill patients in the hospital environment. Current lack of effective clinical solutions to treat this pathogen urges us to carry out systems-level studies that could contribute to the development of an effective therapy. Here we report the development of a strategy for identifying drug targets by combined genome-scale metabolic network and essentiality analyses. First, a genome-scale metabolic network of A. baumannii AYE, a drug-resistant strain, was reconstructed based on its genome annotation data, and biochemical knowledge from literatures and databases. In order to evaluate the performance of the in silico model, constraints-based flux analysis was carried out with appropriate constraints. Simulations were performed from both reaction (gene)- and metabolite-centric perspectives, each of which identifies essential genes/reactions and metabolites critical to the cell growth. The gene/reaction essentiality enables validation of the model and its comparative study with other known organisms' models. The metabolite essentiality approach was undertaken to predict essential metabolites that are critical to the cell growth. The EMFilter, a framework that filters initially predicted essential metabolites to find the most effective ones as drug targets, was also developed. EMFilter considers metabolite types, number of total and consuming reaction linkage with essential metabolites, and presence of essential metabolites and their relevant enzymes in human metabolism. Final drug target candidates obtained by this system framework are presented along with implications of this approach. link: http://identifiers.org/pubmed/20094653

Parameters: none

States: none

Observables: none

MODEL1011300000 @ v0.0.1

This is a model of the genome scale reconstruction of the Vibrio vulnificus metabolic network, VvuMBEL943, described in…

Although the genomes of many microbial pathogens have been studied to help identify effective drug targets and novel drugs, such efforts have not yet reached full fruition. In this study, we report a systems biological approach that efficiently utilizes genomic information for drug targeting and discovery, and apply this approach to the opportunistic pathogen Vibrio vulnificus CMCP6. First, we partially re-sequenced and fully re-annotated the V. vulnificus CMCP6 genome, and accordingly reconstructed its genome-scale metabolic network, VvuMBEL943. The validated network model was employed to systematically predict drug targets using the concept of metabolite essentiality, along with additional filtering criteria. Target genes encoding enzymes that interact with the five essential metabolites finally selected were experimentally validated. These five essential metabolites are critical to the survival of the cell, and hence were used to guide the cost-effective selection of chemical analogs, which were then screened for antimicrobial activity in a whole-cell assay. This approach is expected to help fill the existing gap between genomics and drug discovery. link: http://identifiers.org/pubmed/21245845

Parameters: none

States: none

Observables: none

MODEL1012090002 @ v0.0.1

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

The construction of synthetic biochemical circuits from simple components illuminates how complex behaviors can arise in chemistry and builds a foundation for future biological technologies. A simplified analog of genetic regulatory networks, in vitro transcriptional circuits, provides a modular platform for the systematic construction of arbitrary circuits and requires only two essential enzymes, bacteriophage T7 RNA polymerase and Escherichia coli ribonuclease H, to produce and degrade RNA signals. In this study, we design and experimentally demonstrate three transcriptional oscillators in vitro. First, a negative feedback oscillator comprising two switches, regulated by excitatory and inhibitory RNA signals, showed up to five complete cycles. To demonstrate modularity and to explore the design space further, a positive-feedback loop was added that modulates and extends the oscillatory regime. Finally, a three-switch ring oscillator was constructed and analyzed. Mathematical modeling guided the design process, identified experimental conditions likely to yield oscillations, and explained the system's robust response to interference by short degradation products. Synthetic transcriptional oscillators could prove valuable for systematic exploration of biochemical circuit design principles and for controlling nanoscale devices and orchestrating processes within artificial cells. link: http://identifiers.org/pubmed/21283141

Parameters: none

States: none

Observables: none

MODEL1012090003 @ v0.0.1

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

The construction of synthetic biochemical circuits from simple components illuminates how complex behaviors can arise in chemistry and builds a foundation for future biological technologies. A simplified analog of genetic regulatory networks, in vitro transcriptional circuits, provides a modular platform for the systematic construction of arbitrary circuits and requires only two essential enzymes, bacteriophage T7 RNA polymerase and Escherichia coli ribonuclease H, to produce and degrade RNA signals. In this study, we design and experimentally demonstrate three transcriptional oscillators in vitro. First, a negative feedback oscillator comprising two switches, regulated by excitatory and inhibitory RNA signals, showed up to five complete cycles. To demonstrate modularity and to explore the design space further, a positive-feedback loop was added that modulates and extends the oscillatory regime. Finally, a three-switch ring oscillator was constructed and analyzed. Mathematical modeling guided the design process, identified experimental conditions likely to yield oscillations, and explained the system's robust response to interference by short degradation products. Synthetic transcriptional oscillators could prove valuable for systematic exploration of biochemical circuit design principles and for controlling nanoscale devices and orchestrating processes within artificial cells. link: http://identifiers.org/pubmed/21283141

Parameters: none

States: none

Observables: none

MODEL1012090004 @ v0.0.1

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

The construction of synthetic biochemical circuits from simple components illuminates how complex behaviors can arise in chemistry and builds a foundation for future biological technologies. A simplified analog of genetic regulatory networks, in vitro transcriptional circuits, provides a modular platform for the systematic construction of arbitrary circuits and requires only two essential enzymes, bacteriophage T7 RNA polymerase and Escherichia coli ribonuclease H, to produce and degrade RNA signals. In this study, we design and experimentally demonstrate three transcriptional oscillators in vitro. First, a negative feedback oscillator comprising two switches, regulated by excitatory and inhibitory RNA signals, showed up to five complete cycles. To demonstrate modularity and to explore the design space further, a positive-feedback loop was added that modulates and extends the oscillatory regime. Finally, a three-switch ring oscillator was constructed and analyzed. Mathematical modeling guided the design process, identified experimental conditions likely to yield oscillations, and explained the system's robust response to interference by short degradation products. Synthetic transcriptional oscillators could prove valuable for systematic exploration of biochemical circuit design principles and for controlling nanoscale devices and orchestrating processes within artificial cells. link: http://identifiers.org/pubmed/21283141

Parameters: none

States: none

Observables: none

MODEL1012090005 @ v0.0.1

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

The construction of synthetic biochemical circuits from simple components illuminates how complex behaviors can arise in chemistry and builds a foundation for future biological technologies. A simplified analog of genetic regulatory networks, in vitro transcriptional circuits, provides a modular platform for the systematic construction of arbitrary circuits and requires only two essential enzymes, bacteriophage T7 RNA polymerase and Escherichia coli ribonuclease H, to produce and degrade RNA signals. In this study, we design and experimentally demonstrate three transcriptional oscillators in vitro. First, a negative feedback oscillator comprising two switches, regulated by excitatory and inhibitory RNA signals, showed up to five complete cycles. To demonstrate modularity and to explore the design space further, a positive-feedback loop was added that modulates and extends the oscillatory regime. Finally, a three-switch ring oscillator was constructed and analyzed. Mathematical modeling guided the design process, identified experimental conditions likely to yield oscillations, and explained the system's robust response to interference by short degradation products. Synthetic transcriptional oscillators could prove valuable for systematic exploration of biochemical circuit design principles and for controlling nanoscale devices and orchestrating processes within artificial cells. link: http://identifiers.org/pubmed/21283141

Parameters: none

States: none

Observables: none

MODEL1012090006 @ v0.0.1

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

The construction of synthetic biochemical circuits from simple components illuminates how complex behaviors can arise in chemistry and builds a foundation for future biological technologies. A simplified analog of genetic regulatory networks, in vitro transcriptional circuits, provides a modular platform for the systematic construction of arbitrary circuits and requires only two essential enzymes, bacteriophage T7 RNA polymerase and Escherichia coli ribonuclease H, to produce and degrade RNA signals. In this study, we design and experimentally demonstrate three transcriptional oscillators in vitro. First, a negative feedback oscillator comprising two switches, regulated by excitatory and inhibitory RNA signals, showed up to five complete cycles. To demonstrate modularity and to explore the design space further, a positive-feedback loop was added that modulates and extends the oscillatory regime. Finally, a three-switch ring oscillator was constructed and analyzed. Mathematical modeling guided the design process, identified experimental conditions likely to yield oscillations, and explained the system's robust response to interference by short degradation products. Synthetic transcriptional oscillators could prove valuable for systematic exploration of biochemical circuit design principles and for controlling nanoscale devices and orchestrating processes within artificial cells. link: http://identifiers.org/pubmed/21283141

Parameters: none

States: none

Observables: none

BIOMD0000000322 @ v0.0.1

This a model from the article: Synthetic in vitro transcriptional oscillators. Kim J, Winfree E Mol. Syst. Biol. 20…

The construction of synthetic biochemical circuits from simple components illuminates how complex behaviors can arise in chemistry and builds a foundation for future biological technologies. A simplified analog of genetic regulatory networks, in vitro transcriptional circuits, provides a modular platform for the systematic construction of arbitrary circuits and requires only two essential enzymes, bacteriophage T7 RNA polymerase and Escherichia coli ribonuclease H, to produce and degrade RNA signals. In this study, we design and experimentally demonstrate three transcriptional oscillators in vitro. First, a negative feedback oscillator comprising two switches, regulated by excitatory and inhibitory RNA signals, showed up to five complete cycles. To demonstrate modularity and to explore the design space further, a positive-feedback loop was added that modulates and extends the oscillatory regime. Finally, a three-switch ring oscillator was constructed and analyzed. Mathematical modeling guided the design process, identified experimental conditions likely to yield oscillations, and explained the system's robust response to interference by short degradation products. Synthetic transcriptional oscillators could prove valuable for systematic exploration of biochemical circuit design principles and for controlling nanoscale devices and orchestrating processes within artificial cells. link: http://identifiers.org/pubmed/21283141

Parameters:

Name Description
parameter_1 = 0.57 Reaction: species_3 => species_3 + species_1, Rate Law: compartment_1*parameter_1*species_3
k1=1.0 Reaction: species_1 =>, Rate Law: compartment_1*k1*species_1
parameter_6 = 1.5 Reaction: species_4 => species_4 + species_1, Rate Law: compartment_1*parameter_6*species_4
parameter_2 = 2.5 Reaction: species_4 => species_4 + species_2, Rate Law: compartment_1*parameter_2*species_4
parameter_5 = 6.5; Shalve=1.0; V=1.0 Reaction: species_1 => species_1 + species_4, Rate Law: compartment_1*V*species_1^parameter_5/(Shalve^parameter_5+species_1^parameter_5)
Shalve=1.0; V=1.0; parameter_4 = 6.5 Reaction: species_2 => species_2 + species_3, Rate Law: compartment_1*V/(Shalve^parameter_4+species_2^parameter_4)

States:

Name Description
species 2 [inhibitor; ribonucleic acid]
species 3 u
species 1 [ribonucleic acid]
species 4 v

Observables: none

BIOMD0000000323 @ v0.0.1

This a model from the article: Synthetic in vitro transcriptional oscillators. Kim J, Winfree E Mol. Syst. Biol. 20…

The construction of synthetic biochemical circuits from simple components illuminates how complex behaviors can arise in chemistry and builds a foundation for future biological technologies. A simplified analog of genetic regulatory networks, in vitro transcriptional circuits, provides a modular platform for the systematic construction of arbitrary circuits and requires only two essential enzymes, bacteriophage T7 RNA polymerase and Escherichia coli ribonuclease H, to produce and degrade RNA signals. In this study, we design and experimentally demonstrate three transcriptional oscillators in vitro. First, a negative feedback oscillator comprising two switches, regulated by excitatory and inhibitory RNA signals, showed up to five complete cycles. To demonstrate modularity and to explore the design space further, a positive-feedback loop was added that modulates and extends the oscillatory regime. Finally, a three-switch ring oscillator was constructed and analyzed. Mathematical modeling guided the design process, identified experimental conditions likely to yield oscillations, and explained the system's robust response to interference by short degradation products. Synthetic transcriptional oscillators could prove valuable for systematic exploration of biochemical circuit design principles and for controlling nanoscale devices and orchestrating processes within artificial cells. link: http://identifiers.org/pubmed/21283141

Parameters:

Name Description
Shalve=1.0; parameter_1 = 1.0; parameter_3 = 5.0 Reaction: species_3 => species_3 + species_2, Rate Law: compartment_1*parameter_1/(Shalve^parameter_3+species_3^parameter_3)
parameter_2 = 0.3 Reaction: species_3 =>, Rate Law: compartment_1*species_3/parameter_2/(1+species_3/parameter_2)

States:

Name Description
species 2 [inhibitor; ribonucleic acid]
species 3 [inhibitor; ribonucleic acid]
species 1 [inhibitor; ribonucleic acid]

Observables: none

its a mathematical model explaining the impact of chemotherapy and immunotherpay together on Tumor cells involving cytok…

We propose a mathematical model describing tumor-immune interactions under immune suppression. These days evidences indicate that the immune suppression related to cancer contributes to its progression. The mathematical model for tumor-immune interactions would provide a new methodology for more sophisticated treatment options of cancer. To do this we have developed a system of 11 ordinary differential equations including the movement, interaction, and activation of NK cells, CD8(+)T-cells, CD4(+)T cells, regulatory T cells, and dendritic cells under the presence of tumor and cytokines and the immune interactions. In addition, we apply two control therapies, immunotherapy and chemotherapy to the model in order to control growth of tumor. Using optimal control theory and numerical simulations, we obtain appropriate treatment strategies according to the ratio of the cost for two therapies, which suggest an optimal timing of each administration for the two types of models, without and with immunosuppressive effects. These results mean that the immune suppression can have an influence on treatment strategies for cancer. link: http://identifiers.org/pubmed/25140193

Parameters: none

States: none

Observables: none

BIOMD0000000732 @ v0.0.1

This a model from the article: Modeling immunotherapy of the tumor-immune interaction. Kirschner D, Panetta JC. J Ma…

A number of lines of evidence suggest that immunotherapy with the cytokine interleukin-2 (IL-2) may boost the immune system to fight tumors. CD4+ T cells, the cells that orchestrate the immune response, use these cytokines as signaling mechanisms for immune-response stimulation as well as lymphocyte stimulation, growth, and differentiation. Because tumor cells begin as 'self', the immune system may not respond in an effective way to eradicate them. Adoptive cellular immunotherapy can potentially restore or enhance these effects. We illustrate through mathematical modeling the dynamics between tumor cells, immune-effector cells, and IL-2. These efforts are able to explain both short tumor oscillations in tumor sizes as well as long-term tumor relapse. We then explore the effects of adoptive cellular immunotherapy on the model and describe under what circumstances the tumor can be eliminated. link: http://identifiers.org/pubmed/9785481

Parameters:

Name Description
s1 = 0.0 1/d; g1 = 2.0E7 l; c = 0.035 1/d; p1 = 0.1245 1/d Reaction: Source => Immune_cells; Tumor, IL2, Rate Law: COMpartment*(s1+c*Tumor+p1*Immune_cells*IL2/g1)
mu3 = 10.0 1/d Reaction: IL2 => Sink, Rate Law: COMpartment*mu3*IL2
g3 = 1000.0; p2 = 5.0; V = 3.2; s2 = 0.0 Reaction: => I; T, E, Rate Law: compartment*(p2/V*T*E/(g3*V+T)+s2)
a = 1.0 1/d; g2 = 100000.0 l Reaction: Tumor => Sink; Immune_cells, Rate Law: COMpartment*a*Immune_cells*Tumor/(g2+Tumor)
r2 = 0.18 1/d; b = 1.0E-9 l Reaction: Source => Tumor, Rate Law: COMpartment*r2*(1-b*Tumor)*Tumor
mu2 = 0.03 Reaction: E =>, Rate Law: compartment*mu2*E
p1 = 0.1245; s1 = 0.0; g1 = 2.0E7; V = 3.2; c = 0.02 Reaction: => E; I, T, Rate Law: compartment*(p1*I/(g1*I)*E+c*T+V*s1)
a = 1.0; V = 3.2; g2 = 100000.0 Reaction: T => ; E, Rate Law: compartment*a*T/(g2*V+T)*E
g3 = 1000.0 l; s2 = 0.0 1/d; p2 = 5.0 1/d Reaction: Source => IL2; Immune_cells, Tumor, Rate Law: COMpartment*(s2+p2*Immune_cells*Tumor/(g3+Tumor))
mu3 = 10.0 Reaction: I =>, Rate Law: compartment*mu3*I
r2 = 0.18; V = 3.2; b = 1.0E-9 Reaction: => T, Rate Law: compartment*r2*T*(1-b/V*T)
mu2 = 0.03 1/d Reaction: Immune_cells => Sink, Rate Law: COMpartment*mu2*Immune_cells

States:

Name Description
Tumor [EFO:0000616]
Source [empty set]
IL2 [Interleukin-2]
I [Interleukin-2]
T [neoplasm]
Immune cells [macrophage; natural killer cell; cytotoxic T-lymphocyte; Immune Cell]
Sink [empty set]
E [Immune Cell]

Observables: none

MODEL1112050000 @ v0.0.1

This a model from the article: Harmonic oscillator model of the insulin and IGF1 receptors' allosteric binding and act…

The insulin and insulin-like growth factor 1 receptors activate overlapping signalling pathways that are critical for growth, metabolism, survival and longevity. Their mechanism of ligand binding and activation displays complex allosteric properties, which no mathematical model has been able to account for. Modelling these receptors' binding and activation in terms of interactions between the molecular components is problematical due to many unknown biochemical and structural details. Moreover, substantial combinatorial complexity originating from multivalent ligand binding further complicates the problem. On the basis of the available structural and biochemical information, we develop a physically plausible model of the receptor binding and activation, which is based on the concept of a harmonic oscillator. Modelling a network of interactions among all possible receptor intermediaries arising in the context of the model (35, for the insulin receptor) accurately reproduces for the first time all the kinetic properties of the receptor, and provides unique and robust estimates of the kinetic parameters. The harmonic oscillator model may be adaptable for many other dimeric/dimerizing receptor tyrosine kinases, cytokine receptors and G-protein-coupled receptors where ligand crosslinking occurs. link: http://identifiers.org/pubmed/19225456

Parameters: none

States: none

Observables: none

Klipp2002_MetabolicOptimization_linearPathway(n=2)The model describes time dependent gene expression as a means to enabl…

A computational approach is used to analyse temporal gene expression in the context of metabolic regulation. It is based on the assumption that cells developed optimal adaptation strategies to changing environmental conditions. Time-dependent enzyme profiles are calculated which optimize the function of a metabolic pathway under the constraint of limited total enzyme amount. For linear model pathways it is shown that wave-like enzyme profiles are optimal for a rapid substrate turnover. For the central metabolism of yeast cells enzyme profiles are calculated which ensure long-term homeostasis of key metabolites under conditions of a diauxic shift. These enzyme profiles are in close correlation with observed gene expression data. Our results demonstrate that optimality principles help to rationalize observed gene expression profiles. link: http://identifiers.org/pubmed/12423338

Parameters:

Name Description
k1=1.0 Reaction: species_0 => species_1; species_2, Rate Law: compartment_0*species_0*species_2*k1
k2=1.0 Reaction: species_1 => species_4; species_3, Rate Law: compartment_0*k2*species_1*species_3

States:

Name Description
species 3 [enzyme]
species 0 [SBO:0000015]
species 1 [metabolite]
species 4 [SBO:0000011]

Observables: none

BIOMD0000000804 @ v0.0.1

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

In Multiple Myeloma Bone Disease healthy bone remodelling is affected by tumour cells by means of paracrine cytokinetic signalling in such a way that osteoclast formation is enhanced and the growth of osteoblast cells inhibited. The participating cytokines are described in the literature. Osteoclast-induced myeloma cell growth is also reported. Based on existing mathematical models for healthy bone remodelling a three-way equilibrium model is presented for osteoclasts, osteoblasts and myeloma cell populations to describe the progress of the illness in a scenario in which there is a secular increase in the cytokinetic interactive effectiveness of paracrine processes. The equilibrium state for the system is obtained. The paracrine interactive effectiveness is explored by parameter variation and the stable region in the parameter space is identified. Then recently-discovered joint myeloma-osteoclast cells are added to the model to describe the populations inside lytic lesions. It transpires that their presence expands the available parameter space for stable equilibrium, thus permitting a detrimental, larger population of osteoclasts and myeloma cells. A possible relapse mechanism for the illness is explored by letting joint cells dissociate. The mathematics then permits the evaluation of the evolution of the cell populations as a function of time during relapse. link: http://identifiers.org/pubmed/26643942

Parameters:

Name Description
bb = 0.02 1/d Reaction: B =>, Rate Law: tme*bb*B
gcb = -0.5 1; hct = 0.0 1; ac = 3.0 1/d; gcc = 0.0 1 Reaction: => C; B, T, Rate Law: tme*ac*C^gcc*B^gcb*(1+hct*T)
bt = 0.1 1/d Reaction: T =>, Rate Law: tme*bt*T
bc = 0.2 1/d Reaction: C =>, Rate Law: tme*bc*C
at = 0.316227766016838 1/d; gtt = 0.5 1; gtc = 0.0 1 Reaction: => T; C, Rate Law: tme*at*C^gtc*T^gtt
gbc = 1.0 1; hbt = 0.0 1; gbb = 0.0 1; ab = 4.0 1/d Reaction: => B; C, T, Rate Law: tme*ab*C^gbc*B^gbb*(1-hbt*T)

States:

Name Description
B [osteoblast]
T [myeloma cell]
C [osteoclast]

Observables: none

MODEL1204270001 @ v0.0.1

# Quantifying the Contribution of the Liver to Glucose Homeostasis: A Detailed Kinetic Model of Human Hepatic Glucose Me…

Despite the crucial role of the liver in glucose homeostasis, a detailed mathematical model of human hepatic glucose metabolism is lacking so far. Here we present a detailed kinetic model of glycolysis, gluconeogenesis and glycogen metabolism in human hepatocytes integrated with the hormonal control of these pathways by insulin, glucagon and epinephrine. Model simulations are in good agreement with experimental data on (i) the quantitative contributions of glycolysis, gluconeogenesis, and glycogen metabolism to hepatic glucose production and hepatic glucose utilization under varying physiological states. (ii) the time courses of postprandial glycogen storage as well as glycogen depletion in overnight fasting and short term fasting (iii) the switch from net hepatic glucose production under hypoglycemia to net hepatic glucose utilization under hyperglycemia essential for glucose homeostasis (iv) hormone perturbations of hepatic glucose metabolism. Response analysis reveals an extra high capacity of the liver to counteract changes of plasma glucose level below 5 mM (hypoglycemia) and above 7.5 mM (hyperglycemia). Our model may serve as an important module of a whole-body model of human glucose metabolism and as a valuable tool for understanding the role of the liver in glucose homeostasis under normal conditions and in diseases like diabetes or glycogen storage diseases. link: http://identifiers.org/pubmed/22761565

Parameters: none

States: none

Observables: none

# Kinetic Modeling of Human Hepatic Glucose Metabolism in Type 2 Diabetes Mellitus Predicts Higher Risk of Hypoglycemic…

A major problem in the insulin therapy of patients with diabetes type 2 (T2DM) is the increased occurrence of hypoglycemic events which, if left untreated, may cause confusion or fainting and in severe cases seizures, coma, and even death. To elucidate the potential contribution of the liver to hypoglycemia in T2DM we applied a detailed kinetic model of human hepatic glucose metabolism to simulate changes in glycolysis, gluconeogenesis, and glycogen metabolism induced by deviations of the hormones insulin, glucagon, and epinephrine from their normal plasma profiles. Our simulations reveal in line with experimental and clinical data from a multitude of studies in T2DM, (i) significant changes in the relative contribution of glycolysis, gluconeogenesis, and glycogen metabolism to hepatic glucose production and hepatic glucose utilization; (ii) decreased postprandial glycogen storage as well as increased glycogen depletion in overnight fasting and short term fasting; and (iii) a shift of the set point defining the switch between hepatic glucose production and hepatic glucose utilization to elevated plasma glucose levels, respectively, in T2DM relative to normal, healthy subjects. Intriguingly, our model simulations predict a restricted gluconeogenic response of the liver under impaired hormonal signals observed in T2DM, resulting in an increased risk of hypoglycemia. The inability of hepatic glucose metabolism to effectively counterbalance a decline of the blood glucose level becomes even more pronounced in case of tightly controlled insulin treatment. Given this Janus face mode of action of insulin, our model simulations underline the great potential that normalization of the plasma glucagon profile may have for the treatment of T2DM. link: http://identifiers.org/pubmed/22977253

Parameters: none

States: none

Observables: none

BIOMD0000000032 @ v0.0.1

This a model from the article: Modelling the dynamics of the yeast pheromone pathway. Kofahl B, Klipp E Yeast[200…

We present a mathematical model of the dynamics of the pheromone pathways in haploid yeast cells of mating type MATa after stimulation with pheromone alpha-factor. The model consists of a set of differential equations and describes the dynamics of signal transduction from the receptor via several steps, including a G protein and a scaffold MAP kinase cascade, up to changes in the gene expression after pheromone stimulation in terms of biochemical changes (complex formations, phosphorylations, etc.). The parameters entering the models have been taken from the literature or adapted to observed time courses or behaviour. Using this model we can follow the time course of the various complex formation processes and of the phosphorylation states of the proteins involved. Furthermore, we can explain the phenotype of more than a dozen well-characterized mutants and also the graded response of yeast cells to varying concentrations of the stimulating pheromone. link: http://identifiers.org/pubmed/15300679

Parameters:

Name Description
k39=18.0 min_inv Reaction: Far1 => Far1PP; Fus3PP, Rate Law: compartment*Far1*Fus3PP*Fus3PP/(100*100+Fus3PP*Fus3PP)*k39
k14=1.0 min_inv_nM_inv Reaction: Fus3 + Ste7 => complexB, Rate Law: compartment*Ste7*Fus3*k14
k43=0.01 min_inv Reaction: complexM => Gbc + Far1PP, Rate Law: compartment*complexM*k43
k9=2000.0 min_inv_nM_inv Reaction: GaGDP + Gbc => Gabc, Rate Law: compartment*GaGDP*Gbc*k9
k2=0.0012 min_inv_nM_inv Reaction: Ste2 => Ste2a; alpha, Rate Law: compartment*Ste2*alpha*k2
k8=0.033 min_inv_nM_inv Reaction: GaGTP => GaGDP; Sst2, Rate Law: compartment*GaGTP*Sst2*k8
k5=0.024 min_inv Reaction: Ste2 =>, Rate Law: compartment*Ste2*k5
k31=250.0 min_inv Reaction: complexK => complexI, Rate Law: compartment*complexK*k31
k40=1.0 min_inv Reaction: Far1PP => Far1, Rate Law: compartment*Far1PP*k40
k27=5.0 min_inv Reaction: complexH => Gbc + Ste7 + Ste5 + Fus3 + Ste20 + Ste11, Rate Law: compartment*complexH*k27
k35=10.0 min_inv Reaction: Ste12a => Ste12 + Fus3PP, Rate Law: compartment*Ste12a*k35
k25=5.0 min_inv Reaction: complexG => Gbc + Ste7 + Ste5 + Fus3 + Ste20 + Ste11, Rate Law: compartment*complexG*k25
k41=0.02 min_inv_nM_inv Reaction: Far1 => Far1U; Cdc28, Rate Law: compartment*Far1*Cdc28*k41
k44=0.01 min_inv Reaction: complexN => Cdc28 + Far1PP, Rate Law: compartment*complexN*k44
k42=0.1 min_inv_nM_inv Reaction: Gbc + Far1PP => complexM, Rate Law: compartment*Gbc*Far1PP*k42
k30=1.0 min_inv Reaction: complexK => complexL + Fus3, Rate Law: compartment*complexK*k30
k21=5.0 min_inv Reaction: complexE => Gbc + Ste7 + Ste5 + Fus3 + Ste20 + Ste11, Rate Law: compartment*complexE*k21
k26=50.0 min_inv Reaction: complexH => complexI, Rate Law: compartment*complexH*k26
k6=0.0036 min_inv_nM_inv Reaction: Gabc => GaGTP + Gbc; Ste2a, Rate Law: compartment*Ste2a*Gabc*k6
k18=5.0 min_inv_nM_inv Reaction: complexD + Ste20 => complexE, Rate Law: compartment*complexD*Ste20*k18
k32=5.0 min_inv Reaction: complexL => Gbc + Ste7 + Ste5 + Ste20 + Ste11, Rate Law: compartment*complexL*k32
k38=0.01 min_inv Reaction: Bar1a => Bar1aex, Rate Law: compartment*Bar1a*k38
k47=1.0 min_inv Reaction: Sst2 => p, Rate Law: compartment*Sst2*k47
k29=10.0 min_inv_nM_inv Reaction: complexL + Fus3 => complexK, Rate Law: compartment*complexL*Fus3*k29
k15=3.0 min_inv Reaction: complexB => Fus3 + Ste7, Rate Law: compartment*complexB*k15
k17=100.0 min_inv Reaction: complexC => Fus3 + Ste11 + Ste7 + Ste5, Rate Law: compartment*complexC*k17
k3=0.6 min_inv Reaction: Ste2a => Ste2, Rate Law: compartment*Ste2a*k3
k19=1.0 min_inv Reaction: complexE => complexD + Ste20, Rate Law: compartment*complexE*k19
k33=50.0 min_inv Reaction: Fus3PP => Fus3, Rate Law: compartment*Fus3PP*k33
k7=0.24 min_inv Reaction: GaGTP => GaGDP, Rate Law: compartment*GaGTP*k7
k12=1.0 min_inv_nM_inv Reaction: Ste11 + Ste5 => complexA, Rate Law: compartment*Ste5*Ste11*k12
k11=5.0 min_inv Reaction: complexD => Gbc + complexC, Rate Law: compartment*complexD*k11
k4=0.24 min_inv Reaction: Ste2a => p, Rate Law: compartment*Ste2a*k4
k46=200.0 nM_min_inv Reaction: p => Sst2; Fus3PP, Rate Law: compartment*Fus3PP^2/(4^2+Fus3PP^2)*k46
k23=5.0 min_inv Reaction: complexF => Gbc + Ste7 + Ste5 + Fus3 + Ste20 + Ste11, Rate Law: compartment*complexF*k23
k24=345.0 min_inv Reaction: complexG => complexH, Rate Law: compartment*complexG*k24
k28=140.0 min_inv Reaction: complexI => complexL + Fus3PP, Rate Law: compartment*complexI*k28
k13=3.0 min_inv Reaction: complexA => Ste11 + Ste5, Rate Law: compartment*complexA*k13
k45=0.1 min_inv_nM_inv Reaction: Cdc28 + Far1PP => complexN, Rate Law: compartment*Far1PP*Cdc28*k45
k10=0.1 min_inv_nM_inv Reaction: Gbc + complexC => complexD, Rate Law: compartment*Gbc*complexC*k10
k34=18.0 min_inv_nM_inv Reaction: Ste12 + Fus3PP => Ste12a, Rate Law: compartment*Ste12*Fus3PP*k34
k1=0.03 min_inv_nM_inv Reaction: alpha => ; Bar1aex, Rate Law: Extracellular*alpha*Bar1aex*k1

States:

Name Description
Gbc [Guanine nucleotide-binding protein subunit beta; Guanine nucleotide-binding protein subunit gamma; 50058]
Ste20 [Serine/threonine-protein kinase STE20]
complexE [Guanine nucleotide-binding protein subunit gamma; Guanine nucleotide-binding protein subunit beta; Guanine nucleotide-binding protein alpha-1 subunit; Mitogen-activated protein kinase FUS3; Serine/threonine-protein kinase STE7; Serine/threonine-protein kinase STE20; Serine/threonine-protein kinase STE11; Protein STE5]
Far1U [Cyclin-dependent kinase inhibitor FAR1]
complexI [Guanine nucleotide-binding protein subunit gamma; Guanine nucleotide-binding protein subunit beta; Guanine nucleotide-binding protein alpha-1 subunit; Serine/threonine-protein kinase STE7; Mitogen-activated protein kinase FUS3; Serine/threonine-protein kinase STE20; Serine/threonine-protein kinase STE11; Protein STE5]
Fus3 [Mitogen-activated protein kinase FUS3]
complexD [Serine/threonine-protein kinase STE11; Guanine nucleotide-binding protein subunit beta; Protein STE5; Serine/threonine-protein kinase STE7; Guanine nucleotide-binding protein alpha-1 subunit; Mitogen-activated protein kinase FUS3; Guanine nucleotide-binding protein subunit gamma]
Far1PP [Cyclin-dependent kinase inhibitor FAR1]
complexK [Guanine nucleotide-binding protein subunit gamma; Guanine nucleotide-binding protein subunit beta; Guanine nucleotide-binding protein alpha-1 subunit; Mitogen-activated protein kinase FUS3; Serine/threonine-protein kinase STE7; Serine/threonine-protein kinase STE20; Serine/threonine-protein kinase STE11; Protein STE5]
Ste7 [Serine/threonine-protein kinase STE7]
Ste5 [Protein STE5]
Ste12 [Protein STE12]
Bar1aex [Barrierpepsin]
complexL [Guanine nucleotide-binding protein subunit gamma; Guanine nucleotide-binding protein subunit beta; Guanine nucleotide-binding protein alpha-1 subunit; Serine/threonine-protein kinase STE7; Serine/threonine-protein kinase STE20; Serine/threonine-protein kinase STE11; Protein STE5]
complexN [Cyclin-dependent kinase inhibitor FAR1; Cyclin-dependent kinase 1]
Cdc28 [Cyclin-dependent kinase 1]
complexC [Mitogen-activated protein kinase FUS3; Serine/threonine-protein kinase STE11; Serine/threonine-protein kinase STE7; Protein STE5; 133390]
GaGTP [Guanine nucleotide-binding protein alpha-1 subunit]
Ste11 [Serine/threonine-protein kinase STE11]
Fus3PP [Mitogen-activated protein kinase FUS3]
Sst2 [Protein SST2]
complexH [Guanine nucleotide-binding protein subunit gamma; Guanine nucleotide-binding protein subunit beta; Mitogen-activated protein kinase FUS3; Guanine nucleotide-binding protein alpha-1 subunit; Serine/threonine-protein kinase STE7; Serine/threonine-protein kinase STE11; Serine/threonine-protein kinase STE20; Protein STE5]
alpha α-factor
Far1 [Cyclin-dependent kinase inhibitor FAR1]
Gabc [Guanine nucleotide-binding protein alpha-1 subunit; Guanine nucleotide-binding protein subunit beta; Guanine nucleotide-binding protein subunit gamma]
Ste2 [Pheromone alpha factor receptorPheromone alpha factor receptor]
complexA [Protein STE5; Serine/threonine-protein kinase STE11]
Ste12a [Protein STE12]
GaGDP [Guanine nucleotide-binding protein alpha-1 subunit]
Ste2a [Pheromone alpha factor receptorPheromone alpha factor receptor]
p Far1ubiquitin

Observables: none

MODEL1109160001 @ v0.0.1

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

Activated partial thromboplastin time (APTT) is a laboratory test for the diagnosis of blood coagulation disorders. The test consists of two stages: The first one is the preincubation of a plasma sample with negatively charged materials (kaolin, ellagic acid etc.) to activate factors XII and XI; the second stage begins after the addition of calcium ions that triggers a chain of calcium-dependent enzymatic reactions resulting in fibrinogen clotting. Mathematical modeling was used for the analysis of the APTT test. The process of coagulation was described by a set of coupled differential equations that were solved by the numerical method. It was found that as little as 2.3 x 10(-9) microM of factor XIIa (1/10000 of its plasma concentration) is enough to cause the complete activation of factor XII and prekallikrein (PK) during the first 20 s of the preincubation phase. By the end of this phase, kallikrein (K) is completely inhibited, residual activity of factor XIIa is 54%, and factor XI is activated by 26%. Once a clot is formed, factor II is activated by 4%, factor X by 5%, factor IX by 90%, and factor XI by 39%. Calculated clotting time using protein concentrations found in the blood of healthy people was 40.5 s. The most pronounced prolongation of APTT is caused by a decrease in factor X concentration. link: http://identifiers.org/pubmed/11248291

Parameters: none

States: none

Observables: none

MODEL1109160000 @ v0.0.1

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

Activated partial thromboplastin time (APTT) is a laboratory test for the diagnosis of blood coagulation disorders. The test consists of two stages: The first one is the preincubation of a plasma sample with negatively charged materials (kaolin, ellagic acid etc.) to activate factors XII and XI; the second stage begins after the addition of calcium ions that triggers a chain of calcium-dependent enzymatic reactions resulting in fibrinogen clotting. Mathematical modeling was used for the analysis of the APTT test. The process of coagulation was described by a set of coupled differential equations that were solved by the numerical method. It was found that as little as 2.3 x 10(-9) microM of factor XIIa (1/10000 of its plasma concentration) is enough to cause the complete activation of factor XII and prekallikrein (PK) during the first 20 s of the preincubation phase. By the end of this phase, kallikrein (K) is completely inhibited, residual activity of factor XIIa is 54%, and factor XI is activated by 26%. Once a clot is formed, factor II is activated by 4%, factor X by 5%, factor IX by 90%, and factor XI by 39%. Calculated clotting time using protein concentrations found in the blood of healthy people was 40.5 s. The most pronounced prolongation of APTT is caused by a decrease in factor X concentration. link: http://identifiers.org/pubmed/11248291

Parameters: none

States: none

Observables: none

This is a mathematical model describing the imbalance between T helper (Th1/Th2) cell types in melanome patients, togeth…

Aggressive cancers develop immune suppression mechanisms, allowing them to evade specific immune responses. Patients with active melanoma are polarized towards a T helper (Th) 2-type immune phenotype, which subverts effective anticancer Th1-type cellular immunity. The pro-inammatory factor, interleukin (IL)-12, can potentially restore Th1 responses in such patients, but still shows limited clinical efficacy and substantial side effects. We developed a model for the Th1/Th2 imbalance in melanoma patients and its regulation via IL-12 treatment. The model focuses on the interactions between the two Th cell types as mediated by their respective key cytokines, interferon (IFN)-γ and IL-10. Theoretical and numerical analysis showed a landscape consisting of a single, globally attracting steady state, which is stable under large ranges of relevant parameter values. Our results suggest that in melanoma, the cellular arm of the immune system cannot reverse tumor immunotolerance naturally, and that immunotherapy may be the only way to overturn tumor dominance. We have shown that given a toxicity threshold for IFNγ, the maximal allowable IL-12 concentration to yield a Th1-polarized state can be estimated. Moreover, our analysis pinpoints the IL-10 secretion rate as a significant factor inuencing the Th1:Th2 balance, suggesting its use as a personal immunomarker for prognosis. link: http://identifiers.org/doi/10.3934/dcdsb.2013.18.1017

Parameters:

Name Description
L = 0.0; q_G = 1.0E-7; b_G = 0.13; f_G = 0.22; a_G = 0.59; e_G = 5.4 Reaction: => G; T_1, I, Rate Law: compartment*q_G*T_1*(a_G+(1-a_G)*b_G/(I+b_G))*(1+e_G*L/(L+f_G))
mu_I = 0.36 Reaction: I =>, Rate Law: compartment*mu_I*I
c_2 = 0.1; L = 0.0; r_T = 1000.0; b_2 = 0.18; d_1 = 0.8 Reaction: => T_2; G, Rate Law: compartment*(c_2+(1-c_2)*d_1/(L+d_1))*r_T*b_2/(b_2+G)
c_1 = 30.0; L = 0.0; r_T = 1000.0; b_1 = 0.35; d_1 = 0.8 Reaction: => T_1; I, Rate Law: compartment*(1+c_1*L/(L+d_1))*r_T*b_1/(b_1+I)
mu_T = 0.001 Reaction: T_1 =>, Rate Law: compartment*mu_T*T_1
c_G = 12.0; L = 0.0; d_G = 0.05; p_G = 0.016 Reaction: => G, Rate Law: compartment*p_G*(1+c_G*L/(L+d_G))
mu_G = 0.6 Reaction: G =>, Rate Law: compartment*mu_G*G
q_I = 1.0E-7 Reaction: => I; T_2, Rate Law: compartment*q_I*T_2
a_I = 0.12; p_I = 0.5; b_I = 0.025 Reaction: => I; G, Rate Law: compartment*p_I*(a_I+(1-a_I)*b_I/(G+b_I))

States:

Name Description
I [Interleukin-10]
T 2 [T-helper 2 cell]
T 1 [T-helper 1 cell]
G [Interferon Gamma]

Observables: none

MODEL1006230105 @ v0.0.1

This a model from the article: Modelling sarcoplasmic reticulum calcium ATPase and its regulation in cardiac myocytes.…

When developing large-scale mathematical models of physiology, some reduction in complexity is necessarily required to maintain computational efficiency. A prime example of such an intricate cell is the cardiac myocyte. For the predictive power of the cardiomyocyte models, it is vital to accurately describe the calcium transport mechanisms, since they essentially link the electrical activation to contractility. The removal of calcium from the cytoplasm takes place mainly by the Na(+)/Ca(2+) exchanger, and the sarcoplasmic reticulum Ca(2+) ATPase (SERCA). In the present study, we review the properties of SERCA, its frequency-dependent and beta-adrenergic regulation, and the approaches of mathematical modelling that have been used to investigate its function. Furthermore, we present novel theoretical considerations that might prove useful for the elucidation of the role of SERCA in cardiac function, achieving a reduction in model complexity, but at the same time retaining the central aspects of its function. Our results indicate that to faithfully predict the physiological properties of SERCA, we should take into account the calcium-buffering effect and reversible function of the pump. This 'uncomplicated' modelling approach could be useful to other similar transport mechanisms as well. link: http://identifiers.org/pubmed/19414452

Parameters: none

States: none

Observables: none

MODEL1006230029 @ v0.0.1

This a model from the article: Modelling sarcoplasmic reticulum calcium ATPase and its regulation in cardiac myocytes.…

When developing large-scale mathematical models of physiology, some reduction in complexity is necessarily required to maintain computational efficiency. A prime example of such an intricate cell is the cardiac myocyte. For the predictive power of the cardiomyocyte models, it is vital to accurately describe the calcium transport mechanisms, since they essentially link the electrical activation to contractility. The removal of calcium from the cytoplasm takes place mainly by the Na(+)/Ca(2+) exchanger, and the sarcoplasmic reticulum Ca(2+) ATPase (SERCA). In the present study, we review the properties of SERCA, its frequency-dependent and beta-adrenergic regulation, and the approaches of mathematical modelling that have been used to investigate its function. Furthermore, we present novel theoretical considerations that might prove useful for the elucidation of the role of SERCA in cardiac function, achieving a reduction in model complexity, but at the same time retaining the central aspects of its function. Our results indicate that to faithfully predict the physiological properties of SERCA, we should take into account the calcium-buffering effect and reversible function of the pump. This 'uncomplicated' modelling approach could be useful to other similar transport mechanisms as well. link: http://identifiers.org/pubmed/19414452

Parameters: none

States: none

Observables: none

MODEL1006230023 @ v0.0.1

This a model from the article: Modelling sarcoplasmic reticulum calcium ATPase and its regulation in cardiac myocytes.…

When developing large-scale mathematical models of physiology, some reduction in complexity is necessarily required to maintain computational efficiency. A prime example of such an intricate cell is the cardiac myocyte. For the predictive power of the cardiomyocyte models, it is vital to accurately describe the calcium transport mechanisms, since they essentially link the electrical activation to contractility. The removal of calcium from the cytoplasm takes place mainly by the Na(+)/Ca(2+) exchanger, and the sarcoplasmic reticulum Ca(2+) ATPase (SERCA). In the present study, we review the properties of SERCA, its frequency-dependent and beta-adrenergic regulation, and the approaches of mathematical modelling that have been used to investigate its function. Furthermore, we present novel theoretical considerations that might prove useful for the elucidation of the role of SERCA in cardiac function, achieving a reduction in model complexity, but at the same time retaining the central aspects of its function. Our results indicate that to faithfully predict the physiological properties of SERCA, we should take into account the calcium-buffering effect and reversible function of the pump. This 'uncomplicated' modelling approach could be useful to other similar transport mechanisms as well. link: http://identifiers.org/pubmed/19414452

Parameters: none

States: none

Observables: none

The proposed ODE model describes dynamics of IFNalpha-induced signaling in Huh7.5 cells for a time scale up to 32 hours…

Tightly interlinked feedback regulators control the dynamics of intracellular responses elicited by the activation of signal transduction pathways. Interferon alpha (IFNα) orchestrates antiviral responses in hepatocytes, yet mechanisms that define pathway sensitization in response to prestimulation with different IFNα doses remained unresolved. We establish, based on quantitative measurements obtained for the hepatoma cell line Huh7.5, an ordinary differential equation model for IFNα signal transduction that comprises the feedback regulators STAT1, STAT2, IRF9, USP18, SOCS1, SOCS3, and IRF2. The model-based analysis shows that, mediated by the signaling proteins STAT2 and IRF9, prestimulation with a low IFNα dose hypersensitizes the pathway. In contrast, prestimulation with a high dose of IFNα leads to a dose-dependent desensitization, mediated by the negative regulators USP18 and SOCS1 that act at the receptor. The analysis of basal protein abundance in primary human hepatocytes reveals high heterogeneity in patient-specific amounts of STAT1, STAT2, IRF9, and USP18. The mathematical modeling approach shows that the basal amount of USP18 determines patient-specific pathway desensitization, while the abundance of STAT2 predicts the patient-specific IFNα signal response. link: http://identifiers.org/pubmed/32696599

Parameters: none

States: none

Observables: none

Kollarovic2016 - Cell fate decision at G1-S transitionThis model is described in the article: [To senesce or not to sen…

Excessive DNA damage can induce an irreversible cell cycle arrest, called senescence, which is generally perceived as an important tumour-suppressor mechanism. However, it is unclear how cells decide whether to senesce or not after DNA damage. By combining experimental data with a parameterized mathematical model we elucidate this cell fate decision at the G1-S transition. Our model provides a quantitative and conceptually new understanding of how human fibroblasts decide whether DNA damage is beyond repair and senesce. Model and data imply that the G1-S transition is regulated by a bistable hysteresis switch with respect to Cdk2 activity, which in turn is controlled by the Cdk2/p21 ratio rather than cyclin abundance. We experimentally confirm the resulting predictions that to induce senescence i) in healthy cells both high initial and elevated background DNA damage are necessary and sufficient, and ii) in already damaged cells much lower additional DNA damage is sufficient. Our study provides a mechanistic explanation of a) how noise in protein abundances allows cells to overcome the G1-S arrest even with substantial DNA damage, potentially leading to neoplasia, and b) how accumulating DNA damage with age increasingly sensitizes cells for senescence. link: http://identifiers.org/pubmed/26830321

Parameters:

Name Description
vb7_k1_0 = 10.0 Reaction: CycE + Cdk2 => CycECdk2; CycE, Cdk2, Rate Law: compartment*vb7_k1_0*CycE*Cdk2
vb3_v_0 = 99.84 Reaction: => Cdk2, Rate Law: compartment*vb3_v_0
vb1_k0_0 = 0.10249; vb1_kb_0 = 0.324616; vb1_h_0 = 4.93142; vb1_ka_0 = 3.40431; vb1_Ki_0 = 0.394586; vb1_k1_0 = 4.00486; vb1_Kmb_0 = 0.00842472; vb1_Kma_0 = 0.001143917344 Reaction: CycECdk2 => CycECdk2a; p21, CycECdk2, p21, CycECdk2a, Rate Law: compartment*CycECdk2*(vb1_k0_0+vb1_k1_0*2*vb1_ka_0*CycECdk2a*vb1_Kmb_0/((vb1_kb_0-vb1_ka_0*CycECdk2a)+vb1_kb_0*vb1_Kma_0+vb1_ka_0*CycECdk2a*vb1_Kmb_0+(((vb1_kb_0-vb1_ka_0*CycECdk2a)+vb1_kb_0*vb1_Kma_0+vb1_ka_0*CycECdk2a*vb1_Kmb_0)^2-4*(vb1_kb_0-vb1_ka_0*CycECdk2a)*vb1_ka_0*CycECdk2a*vb1_Kmb_0)^(1/2)))/(1+(vb1_Ki_0*p21)^vb1_h_0)
TAF = 0.506228; BaseDNAdamage = 2.16068 Reaction: DDR = BaseDNAdamage+DNADamageC+DNADamageS+TAF, Rate Law: missing
k6b = 1.08476678528373 Reaction: CycE => ; CycE, Rate Law: compartment*k6b*CycE
k8b = 1.12435827886665 Reaction: CycECdk2 => CycE + Cdk2; CycECdk2, Rate Law: compartment*k8b*CycECdk2
va3_k_0 = 0.00547468 Reaction: => p53; DDR, DDR, Rate Law: compartment*va3_k_0*DDR
k1=0.0164994 Reaction: DNADamageC => ; DNADamageC, Rate Law: compartment*k1*DNADamageC
k2b = 2.43594662809282 Reaction: CycECdk2a => CycECdk2; CycECdk2a, Rate Law: compartment*k2b*CycECdk2a
va5_k_0 = 193.258 Reaction: => p21; p53, p53, Rate Law: compartment*va5_k_0*p53
k4b = 5987.90902984358 Reaction: Cdk2 => ; Cdk2, Rate Law: compartment*k4b*Cdk2
k4a = 0.01460046788944 Reaction: p53 => ; p53, Rate Law: compartment*k4a*p53
k1=0.234805 Reaction: DNADamageS => ; DNADamageS, Rate Law: compartment*k1*DNADamageS
vb5_v_0 = 9.99936 Reaction: => CycE, Rate Law: compartment*vb5_v_0
k6a = 193.258 Reaction: p21 => ; p21, Rate Law: compartment*k6a*p21

States:

Name Description
CycE [G1/S-specific cyclin-E1]
DDR DDR
p21 [Cyclin-dependent kinase inhibitor 1]
CycECdk2a [Cyclin-dependent kinase 2; G1/S-specific cyclin-E1]
DNADamageS DNADamageS
DNADamageC DNADamageC
Cdk2 [Cyclin-dependent kinase 2]
CycECdk2 [Cyclin-dependent kinase 2; G1/S-specific cyclin-E1]
p53 [Cellular tumor antigen p53]

Observables: none

Kolodkin2013 - Nuclear receptor-mediated cortisol signalling networkThis model is described in the article: [Optimizati…

It is an accepted paradigm that extended stress predisposes an individual to pathophysiology. However, the biological adaptations to minimize this risk are poorly understood. Using a computational model based upon realistic kinetic parameters we are able to reproduce the interaction of the stress hormone cortisol with its two nuclear receptors, the high-affinity glucocorticoid receptor and the low-affinity pregnane X-receptor. We demonstrate that regulatory signals between these two nuclear receptors are necessary to optimize the body's response to stress episodes, attenuating both the magnitude and duration of the biological response. In addition, we predict that the activation of pregnane X-receptor by multiple, low-affinity endobiotic ligands is necessary for the significant pregnane X-receptor-mediated transcriptional response observed following stress episodes. This integration allows responses mediated through both the high and low-affinity nuclear receptors, which we predict is an important strategy to minimize the risk of disease from chronic stress. link: http://identifiers.org/pubmed/23653204

Parameters:

Name Description
k2=270.0; k1=60.0 Reaction: s2 + CBG => CBG_CortOUT; s2, CBG, CBG_CortOUT, Rate Law: blood*(k1*s2*CBG-k2*CBG_CortOUT)
GRGene_GRprotein = 60.0; GeneProteinBinding_diff_limited = 60.0 Reaction: s40 + s87 => s84; s40, s87, s84, Rate Law: default*(GeneProteinBinding_diff_limited*s40*s87-GRGene_GRprotein*s84)
tatMrna_synt = 0.005 Reaction: s28 => s185; TATgene_GRprot_DEX, s28, TATgene_GRprot_DEX, Rate Law: default*tatMrna_synt*s28*TATgene_GRprot_DEX
k1=1000.0; k2=1000.0 Reaction: s2 => s114; s2, s114, Rate Law: k1*s2-k2*s114
cypGene_PXRprotein = 1.0; GeneProteinBinding_diff_limited = 60.0 Reaction: s155 + PXRprot_Ligand2 => CYPgene_PXRprot_Ligand2; s155, PXRprot_Ligand2, CYPgene_PXRprot_Ligand2, Rate Law: default*(GeneProteinBinding_diff_limited*s155*PXRprot_Ligand2-cypGene_PXRprotein*CYPgene_PXRprot_Ligand2)
k2=60000.0; k1=60.0 Reaction: s42 + DEX => PXRprot_DEX; s42, DEX, PXRprot_DEX, Rate Law: default*(k1*s42*DEX-k2*PXRprot_DEX)
Ka=8.55E-4 Reaction: s28 => s185; s178, s28, s178, Rate Law: default*Ka*s28*s178
k1=0.064 Reaction: s185 => s30; s185, Rate Law: default*k1*s185
pxrMrna_synt = 1.1E-4 Reaction: s28 => s32; s109, s28, s109, Rate Law: default*pxrMrna_synt*s28*s109
k1=0.006 Reaction: s32 => s30; s32, Rate Law: default*k1*s32
grMrna_synt = 1.2E-6 Reaction: s28 => s33; s84, s28, s84, Rate Law: default*grMrna_synt*s28*s84
k2=900000.0; k1=60.0 Reaction: Alb + s2 => Alb_CortOUT; Alb, s2, Alb_CortOUT, Rate Law: blood*(k1*Alb*s2-k2*Alb_CortOUT)
k1=0.001 Reaction: s87 => s114 + s30; s87, Rate Law: default*k1*s87
Ka=0.5 Reaction: s36 => TAT_PROT; s185, s36, s185, Rate Law: default*Ka*s36*s185
TATGene_GRprotein = 300.0; GeneProteinBinding_diff_limited = 60.0 Reaction: s178 + s87 => s183; s178, s87, s183, Rate Law: default*(GeneProteinBinding_diff_limited*s178*s87-TATGene_GRprotein*s183)
k1=0.016; k2=0.016 Reaction: Cortisone => s114; Cortisone, s114, Rate Law: default*(k1*Cortisone-k2*s114)
Ka=19.98 Reaction: s36 => s39; s33, s36, s33, Rate Law: default*Ka*s36*s33
Ka=5.52E-5 Reaction: s28 => s32; s46, s28, s46, Rate Law: default*Ka*s28*s46
cypMrna_synt = 0.05 Reaction: s28 => s173; s165, s28, s165, Rate Law: default*cypMrna_synt*s28*s165
k1=100.0; k2=100.0 Reaction: DEXout => DEX; DEXout, DEX, Rate Law: k1*DEXout-k2*DEX
k1=0.012 Reaction: TAT_PROT => s30; TAT_PROT, Rate Law: default*k1*TAT_PROT
Ka=0.00321 Reaction: s28 => s173; s155, s28, s155, Rate Law: default*Ka*s28*s155
PXRGene_GRprotein = 200.0; GeneProteinBinding_diff_limited = 60.0 Reaction: s46 + s87 => s109; s46, s87, s109, Rate Law: default*(GeneProteinBinding_diff_limited*s46*s87-PXRGene_GRprotein*s109)
k1=0.003 Reaction: s42 => s30; s42, Rate Law: default*k1*s42
k1=0.0015 Reaction: s172 => s30; s172, Rate Law: default*k1*s172
Kms1=15000.0; Kms2=15000.0; Vm=0.083; Kms3=23000.0 Reaction: s114 => s10; s172, Ligand2, DEX, s172, s114, Ligand2, DEX, Rate Law: default*s172*Vm*s114/Kms1/(1+s114/Kms1+Ligand2/Kms2+DEX/Kms3)
k2=60.0; k1=60.0 Reaction: s39 + DEX => GRprot_DEX; s39, DEX, GRprot_DEX, Rate Law: default*(k1*s39*DEX-k2*GRprot_DEX)
k2=600000.0; k1=60.0 Reaction: s42 + s114 => s119; s42, s114, s119, Rate Law: default*(k1*s42*s114-k2*s119)
Kms3=15000.0; Kms1=23000.0; Kms2=15000.0; Vm=0.00425 Reaction: DEX => DEX_degr; s172, Ligand2, s114, s172, DEX, Ligand2, s114, Rate Law: default*s172*Vm*DEX/Kms1/(1+DEX/Kms1+Ligand2/Kms2+s114/Kms3)
Ka=10.0 Reaction: s36 => s42; s32, s36, s32, Rate Law: default*Ka*s36*s32
k1=60.0; k2=600.0 Reaction: s114 + s39 => s87; s114, s39, s87, Rate Law: default*(k1*s114*s39-k2*s87)
k1=1000.0 Reaction: CortAdded => s2; CortAdded, Rate Law: blood*k1*CortAdded
Ka=2.5 Reaction: s36 => s172; s173, s36, s173, Rate Law: default*Ka*s36*s173

States:

Name Description
s172 [Cytochrome P450 3A4]
GRgene GRprot DEX [dexamethasone; NR3C1; Glucocorticoid receptor]
CYPgene PXRprot Ligand2 [CYP3A4; Nuclear receptor subfamily 1 group I member 2; SBO:0000280]
s40 [NR3C1; Glucocorticoid receptor]
s109 [cortisol; NR1I2; Glucocorticoid receptor]
Alb CortOUT [cortisol; Serum albumin]
Cortisone [cortisone]
CortAdded [cortisol]
s36 [protein polypeptide chain]
s183 [cortisol; TAT; Glucocorticoid receptor]
TATgene GRprot DEX [dexamethasone; TAT; Glucocorticoid receptor]
s165 [cortisol; CYP3A4; Nuclear receptor subfamily 1 group I member 2]
s10 [empty set]
s87 [cortisol; Glucocorticoid receptor]
Ligand2 [SBO:0000280]
s32 [Nuclear receptor subfamily 1 group I member 2; NR1I2-201]
s46 [Nuclear receptor subfamily 1 group I member 2; NR1I2]
s185 [TAT-201; Tyrosine aminotransferase]
s178 [Tyrosine aminotransferase; TAT]
CYPgene PXRprot DEX [dexamethasone; CYP3A4; Nuclear receptor subfamily 1 group I member 2]
s119 [cortisol; Nuclear receptor subfamily 1 group I member 2]
CBG [Corticosteroid-binding globulin]
s84 [cortisol; NR3C1; Glucocorticoid receptor]
DEXout [dexamethasone]
s2 [cortisol]
s33 [NR3C1-202; Glucocorticoid receptor]
CBG CortOUT [cortisol; Corticosteroid-binding globulin]
s30 [empty set]
PXRprot DEX [dexamethasone; Nuclear receptor subfamily 1 group I member 2]
Alb [Serum albumin]
s42 [Nuclear receptor subfamily 1 group I member 2]
GRprot DEX [dexamethasone; Glucocorticoid receptor]
s114 [cortisol]
s155 [Cytochrome P450 3A4; CYP3A4]
s173 [Cytochrome P450 3A4; CYP3A4-201]
TAT PROT [Tyrosine aminotransferase]
s28 [messenger RNA]
DEX [dexamethasone]
PXRprot Ligand2 [Nuclear receptor subfamily 1 group I member 2; SBO:0000280]
s39 [Glucocorticoid receptor]
DEX degr [empty set]
PXRgene GRprot DEX [dexamethasone; NR1I2; Glucocorticoid receptor]

Observables: none

BIOMD0000000305 @ v0.0.1

This is the 2 state model of Myosin V movement described in the article: **A simple kinetic model describes the process…

Myosin-V is a motor protein responsible for organelle and vesicle transport in cells. Recent single-molecule experiments have shown that it is an efficient processive motor that walks along actin filaments taking steps of mean size close to 36 nm. A theoretical study of myosin-V motility is presented following an approach used successfully to analyze the dynamics of conventional kinesin but also taking some account of step-size variations. Much of the present experimental data for myosin-V can be well described by a two-state chemical kinetic model with three load-dependent rates. In addition, the analysis predicts the variation of the mean velocity and of the randomness-a quantitative measure of the stochastic deviations from uniform, constant-speed motion-with ATP concentration under both resisting and assisting loads, and indicates a substep of size d(0) approximately 13-14 nm (from the ATP-binding state) that appears to accord with independent observations. link: http://identifiers.org/pubmed/12609867

Parameters:

Name Description
th_1 = -0.01; Force = 0.0; k_1 = 0.7; kT = 4.1164; d = 36.0 Reaction: S0 + ATP => S1 + Pi_ + fwd_step1, Rate Law: k_1*S0*ATP*exp((-th_1)*Force*d/kT)
Force = 0.0; k_4 = 6.0E-6; kT = 4.1164; d = 36.0; th_4 = 0.385 Reaction: S1 => S0 + ADP + back_step2, Rate Law: k_4*S1*exp(th_4*Force*d/kT)
Force = 0.0; k_2 = 12.0; th_2 = 0.045; kT = 4.1164; d = 36.0 Reaction: S1 => S0 + ADP + fwd_step2, Rate Law: k_2*S1*exp((-th_2)*Force*d/kT)
Force = 0.0; k_3 = 5.0E-6; kT = 4.1164; d = 36.0; th_3 = 0.58 Reaction: S0 + ATP => S1 + Pi_ + back_step1, Rate Law: k_3*S0*ATP*exp(th_3*Force*d/kT)

States:

Name Description
S0 [myosin V complex]
ATP [ATP; ATP; 3304]
S1 [ADP; myosin V complex]
Pi [phosphate(3-); Orthophosphate]
fwd step1 fwd_step1
fwd step2 fwd_step2
back step1 back_step1
ADP [ADP; ADP; 3310]
back step2 back_step2

Observables: none

BIOMD0000000148 @ v0.0.1

This a model from the article: Mathematical model predicts a critical role for osteoclast autocrine regulation in the…

Bone remodeling occurs asynchronously at multiple sites in the adult skeleton and involves resorption by osteoclasts, followed by formation of new bone by osteoblasts. Disruptions in bone remodeling contribute to the pathogenesis of disorders such as osteoporosis, osteoarthritis, and Paget's disease. Interactions among cells of osteoblast and osteoclast lineages are critical in the regulation of bone remodeling. We constructed a mathematical model of autocrine and paracrine interactions among osteoblasts and osteoclasts that allowed us to calculate cell population dynamics and changes in bone mass at a discrete site of bone remodeling. The model predicted different modes of dynamic behavior: a single remodeling cycle in response to an external stimulus, a series of internally regulated cycles of bone remodeling, or unstable behavior similar to pathological bone remodeling in Paget's disease. Parametric analysis demonstrated that the mode of dynamic behavior in the system depends strongly on the regulation of osteoclasts by autocrine factors, such as transforming growth factor beta. Moreover, simulations demonstrated that nonlinear dynamics of the system may explain the differing effects of immunosuppressants on bone remodeling in vitro and in vivo. In conclusion, the mathematical model revealed that interactions among osteoblasts and osteoclasts result in complex, nonlinear system behavior, which cannot be deduced from studies of each cell type alone. The model will be useful in future studies assessing the impact of cytokines, growth factors, and potential therapies on the overall process of remodeling in normal bone and in pathological conditions such as osteoporosis and Paget's disease. link: http://identifiers.org/pubmed/14499354

Parameters:

Name Description
g11 = 0.5; alpha1 = 3.0; g21 = -0.5 Reaction: => x1; x2, Rate Law: alpha1*x1^g11*x2^g21
flag_resorption = 0.0; k1 = 0.24 Reaction: z => ; x1, x1_bar, Rate Law: flag_resorption*k1*(x1-x1_bar)
g22 = 0.0; g12 = 1.0; alpha2 = 4.0 Reaction: => x2; x1, Rate Law: alpha2*x1^g12*x2^g22
beta2 = 0.02 Reaction: x2 =>, Rate Law: beta2*x2
beta1 = 0.2 Reaction: x1 =>, Rate Law: beta1*x1
beta1 = 0.2; beta2 = 0.02; g22 = 0.0; alpha1 = 3.0; gamma = 0.0; g21 = -0.5; alpha2 = 4.0 Reaction: x1_bar = (beta1/alpha1)^((1-g22)/gamma)*(beta2/alpha2)^(g21/gamma), Rate Law: missing
g11 = 0.5; beta1 = 0.2; beta2 = 0.02; alpha1 = 3.0; g12 = 1.0; gamma = 0.0; alpha2 = 4.0 Reaction: x2_bar = (beta1/alpha1)^(g12/gamma)*(beta2/alpha2)^((1-g11)/gamma), Rate Law: missing
k2 = 0.0017; flag_formation = 0.0 Reaction: => z; x2, x2_bar, Rate Law: flag_formation*k2*(x2-x2_bar)

States:

Name Description
x1 Osteoclast
x1 bar Steady state osteoclast
x2 Osteoblast
z Bone mass
x2 bar Steady state osteoblast

Observables: none

This a model from the article: Mathematical model of paracrine interactions between osteoclasts and osteoblasts pred…

To restore falling plasma calcium levels, PTH promotes calcium liberation from bone. PTH targets bone-forming cells, osteoblasts, to increase expression of the cytokine receptor activator of nuclear factor kappaB ligand (RANKL), which then stimulates osteoclastic bone resorption. Intriguingly, whereas continuous administration of PTH decreases bone mass, intermittent PTH has an anabolic effect on bone, which was proposed to arise from direct effects of PTH on osteoblastic bone formation. However, antiresorptive therapies impair the ability of PTH to increase bone mass, indicating a complex role for osteoclasts in the process. We developed a mathematical model that describes the actions of PTH at a single site of bone remodeling, where osteoclasts and osteoblasts are regulated by local autocrine and paracrine factors. It was assumed that PTH acts only to increase the production of RANKL by osteoblasts. As a result, PTH stimulated osteoclasts upon application, followed by compensatory osteoblast activation due to the coupling of osteoblasts to osteoclasts through local paracrine factors. Continuous PTH administration resulted in net bone loss, because bone resorption preceded bone formation at all times. In contrast, over a wide range of model parameters, short application of PTH resulted in a net increase in bone mass, because osteoclasts were rapidly removed upon PTH withdrawal, enabling osteoblasts to rebuild the bone. In excellent agreement with experimental findings, increase in the rate of osteoclast death abolished the anabolic effect of PTH on bone. This study presents an original concept for the regulation of bone remodeling by PTH, currently the only approved anabolic treatment for osteoporosis. link: http://identifiers.org/pubmed/15860557

Parameters:

Name Description
k1 = 0.24; k2 = 0.0017; y1 = NaN; y2 = NaN Reaction: z = k2*y2-k1*y1, Rate Law: k2*y2-k1*y1
beta2 = 0.02; g22 = 0.0; g12 = 1.0; alpha2 = 4.0 Reaction: x2 = alpha2*x1^g12*x2^g22-beta2*x2, Rate Law: alpha2*x1^g12*x2^g22-beta2*x2
g11 = 0.5; beta1 = 0.2; alpha1 = 3.0; g21 = -0.5 Reaction: x1 = alpha1*x1^g11*x2^g21-beta1*x1, Rate Law: alpha1*x1^g11*x2^g21-beta1*x1

States:

Name Description
x1 [osteoclast]
x2 [osteoblast]
z [mass]

Observables: none

This model according to the paper *A Theoretical Framework for Specificity in Cell Signalling* The model is "basic arch…

Different cellular signal transduction pathways are often interconnected, so that the potential for undesirable crosstalk between pathways exists. Nevertheless, signaling networks have evolved that maintain specificity from signal to cellular response. Here, we develop a framework for the analysis of networks containing two or more interconnected signaling pathways. We define two properties, specificity and fidelity, that all pathways in a network must possess in order to avoid paradoxical situations where one pathway activates another pathway's output, or responds to another pathway's input, more than its own. In unembellished networks that share components, it is impossible for all pathways to have both mutual specificity and mutual fidelity. However, inclusion of either of two related insulating mechanisms–compartmentalization or the action of a scaffold protein–allows both properties to be achieved, provided deactivation rates are fast compared to exchange rates. link: http://identifiers.org/pubmed/16729058

Parameters:

Name Description
a1 = 2.0 Reaction: => x1; x0, Rate Law: compartment_0000001*a1*x0
b1 = 1.0 Reaction: => x1; y0, Rate Law: compartment_0000001*b1*y0
d2y = 1.0 Reaction: y2 =>, Rate Law: compartment_0000001*d2y*y2
d2x = 1.0 Reaction: x2 =>, Rate Law: compartment_0000001*d2x*x2
a2 = 2.0 Reaction: => x2; x1, Rate Law: compartment_0000001*x1*a2
d1 = 1.0 Reaction: x1 =>, Rate Law: compartment_0000001*d1*x1
b2 = 1.0 Reaction: => y2; x1, Rate Law: compartment_0000001*x1*b2

States:

Name Description
x1 [IPR003527]
x2 x2
y2 y2

Observables: none

Genome-scale metabolic reconstruction and in silico analysis of rice leaf blight pathogen, Xanthomonas oryzae

Xanthomonas oryzae pathovar oryzae (Xoo) is a vascular pathogen that causes leaf blight in rice leading to severe yield losses. Since the usage of chemical control methods has not been very promising for the future disease management, it is of high importance to systematically gain new insights about Xoo virulence and pathogenesis, and devise effective strategies to combat the rice disease. To do so, we newly reconstructed a genome-scale metabolic model of Xoo (iXOO673) and validated the model predictions using culture experiments. Comparison of the metabolic architecture of Xoo and other plant pathogens found that Entner-Doudoroff pathway is a more common feature in these bacteria than previously thought, while suggesting some of the unique virulence mechanisms related to Xoo metabolism. Subsequent constraint-based flux analysis allowed us to show that Xoo modulates fluxes through gluconeogenesis, glycogen biosynthesis and degradation pathways, thereby exacerbating the leaf blight in rice exposed to nitrogenous fertilizers, which is remarkably consistent with published experimental literature. Moreover, model-based interrogation of transcriptomic data revealed the metabolic components under the diffusible signal factor (DSF) regulon that are crucial for virulence and survival in Xoo. Finally, we identified promising antibacterial targets for the control of leaf blight in rice by resorting to gene essentiality analysis. link:

Parameters: none

States: none

Observables: none

Kongas2007 - Creatine Kinase in energy metabolic signaling in muscleThis model is described in the article: [Creatine k…

There has been much debate on the mechanism of regulation of mitochondrial ATP synthesis to balance ATP consumption during changing cardiac workloads. A key role of creatine kinase (CK) isoenzymes in this regulation of oxidative phosphorylation and in intracellular energy transport had been proposed, but has in the mean time been disputed for many years. It was hypothesized that high-energy phosphoryl groups are obligatorily transferred via CK; this is termed the phosphocreatine shuttle. The other important role ascribed to the CK system is its ability to buffer ADP concentration in cytosol near sites of ATP hydrolysis.

Almost all of the experiments to determine the role of CK had been done in the steady state, but recently the dynamic response of oxidative phosphorylation to quick changes in cytosolic ATP hydrolysis has been assessed at various levels of inhibition of CK. Steady state models of CK function in energy transfer existed but were unable to explain the dynamic response with CK inhibited.

The aim of this study was to explain the mode of functioning of the CK system in heart, and in particular the role of different CK isoenzymes in the dynamic response to workload steps. For this purpose we used a mathematical model of cardiac muscle cell energy metabolism containing the kinetics of the key processes of energy production, consumption and transfer pathways. The model underscores that CK plays indeed a dual role in the cardiac cells. The buffering role of CK system is due to the activity of myofibrillar CK (MMCK) while the energy transfer role depends on the activity of mitochondrial CK (MiCK). We propose that this may lead to the differences in regulation mechanisms and energy transfer modes in species with relatively low MiCK activity such as rabbit in comparison with species with high MiCK activity such as rat.

The model needed modification to explain the new type of experimental data on the dynamic response of the mitochondria. We submit that building a Virtual Muscle Cell is not possible without continuous experimental tests to improve the model. In close interaction with experiments we are developing a model for muscle energy metabolism and transport mediated by the creatine kinase isoforms which now already can explain many different types of experiments. link: http://identifiers.org/doi/10.1038/npre.2007.1317.1

Parameters:

Name Description
k1_6=14.6 Reaction: Cri => Cr, Rate Law: IMS*k1_6*Cri-CYT*k1_6*Cr
Vb_3=29250.0; Kid_3=4730.0; Kb_3=15500.0; Kic_3=222.4; Vf_3=6966.0; Kia_3=900.0; Kd_3=1670.0; Kib_3=34900.0 Reaction: ATP + Cr => PCr + ADP, Rate Law: CYT*(Vf_3*ATP*Cr/(Kia_3*Kb_3)-Vb_3*ADP*PCr/(Kic_3*Kd_3))/(1+Cr/Kib_3+PCr/Kid_3+ATP*(1/Kia_3+Cr/(Kia_3*Kb_3))+ADP*(1/Kic_3+Cr/(Kic_3*Kib_3)+PCr/(Kid_3*Kic_3*Kd_3/Kid_3)))
k2_5=18.4 Reaction: Pi => P, Rate Law: IMS*k2_5*Pi-CYT*k2_5*P
k1_8=14.6 Reaction: PCri => PCr, Rate Law: IMS*k1_8*PCri-CYT*k1_8*PCr
v_4=4600.0 Reaction: ATP => ADP + P, Rate Law: CYT*v_4*ATP
k1_7=8.16 Reaction: ADPi => ADP, Rate Law: IMS*k1_7*ADPi-CYT*k1_7*ADP
k1_9=8.16 Reaction: ATPi => ATP, Rate Law: IMS*k1_9*ATPi-CYT*k1_9*ATP
Ka_1=800.0; Kb_1=20.0; V_1=4600.0 Reaction: ADPi + Pi => ATPi, Rate Law: IMS*V_1*ADPi*Pi/(Ka_1*Kb_1*(1+ADPi/Ka_1+Pi/Kb_1+ADPi*Pi/(Ka_1*Kb_1)))
Kia_2=750.0; Kb_2=5200.0; Vf_2=2658.0; Vb_2=11160.0; Kic_2=204.8; Kd_2=500.0; Kid_2=1600.0; Kib_2=28800.0 Reaction: ATPi + Cri => ADPi + PCri, Rate Law: IMS*(Vf_2*ATPi*Cri/(Kia_2*Kb_2)-Vb_2*ADPi*PCri/(Kic_2*Kd_2))/(1+Cri/Kib_2+PCri/Kid_2+ATPi*(1/Kia_2+Cri/(Kia_2*Kb_2))+ADPi*(1/Kic_2+Cri/(Kic_2*Kib_2)+PCri/(Kid_2*Kic_2*Kd_2/Kid_2)))

States:

Name Description
PCr [N-phosphocreatine; Phosphocreatine]
ATP [ATP; ATP]
Cr [creatine; Creatine]
Pi [phosphate(3-); Orthophosphate]
P [phosphate(3-); Orthophosphate]
ATPi [ATP; ATP]
ADPi [ADP; ADP]
Cri [creatine; Creatine]
ADP [ADP; ADP]
PCri [N-phosphocreatine; Phosphocreatine]

Observables: none

MODEL2004300002 @ v0.0.1

The ODE model is based on Batchelor et al., Mol. Syst. Biol. 7 (2011) and was extended by introducing explicit descripti…

The transcription factors NF-κB and p53 are key regulators in the genotoxic stress response and are critical for tumor development. Although there is ample evidence for interactions between both networks, a comprehensive understanding of the crosstalk is lacking. Here, we developed a systematic approach to identify potential interactions between the pathways. We perturbed NF-κB signaling by inhibiting IKK2, a critical regulator of NF-κB activity, and monitored the altered response of p53 to genotoxic stress using single cell time lapse microscopy. Fitting subpopulation-specific computational p53 models to this time-resolved single cell data allowed to reproduce in a quantitative manner signaling dynamics and cellular heterogeneity for the unperturbed and perturbed conditions. The approach enabled us to untangle the integrated effects of IKK/ NF-κB perturbation on p53 dynamics and thereby derive potential interactions between both networks. Intriguingly, we find that a simultaneous perturbation of multiple processes is necessary to explain the observed changes in the p53 response. Specifically, we show interference with the activation and degradation of p53 as well as the degradation of Mdm2. Our results highlight the importance of the crosstalk and its potential implications in p53-dependent cellular functions. link:

Parameters: none

States: none

Observables: none

BIOMD0000000345 @ v0.0.1

This model is from the article: Mathematical modeling and analysis of insulin clearance in vivo. Koschorreck M, Gil…

BACKGROUND: Analyzing the dynamics of insulin concentration in the blood is necessary for a comprehensive understanding of the effects of insulin in vivo. Insulin removal from the blood has been addressed in many studies. The results are highly variable with respect to insulin clearance and the relative contributions of hepatic and renal insulin degradation. RESULTS: We present a dynamic mathematical model of insulin concentration in the blood and of insulin receptor activation in hepatocytes. The model describes renal and hepatic insulin degradation, pancreatic insulin secretion and nonspecific insulin binding in the liver. Hepatic insulin receptor activation by insulin binding, receptor internalization and autophosphorylation is explicitly included in the model. We present a detailed mathematical analysis of insulin degradation and insulin clearance. Stationary model analysis shows that degradation rates, relative contributions of the different tissues to total insulin degradation and insulin clearance highly depend on the insulin concentration. CONCLUSION: This study provides a detailed dynamic model of insulin concentration in the blood and of insulin receptor activation in hepatocytes. Experimental data sets from literature are used for the model validation. We show that essential dynamic and stationary characteristics of insulin degradation are nonlinear and depend on the actual insulin concentration. link: http://identifiers.org/pubmed/18477391

Parameters:

Name Description
r5 = 0.0; f1 = -4.78999999985533E-8; r1 = 3.53837 Reaction: R = ((-r1)+r5)-f1, Rate Law: ((-r1)+r5)-f1
i3 = 0.0; i7 = 3.20632409511745E-17; f3 = 0.0 Reaction: I2Ren = ((-i3)-i7)+f3, Rate Law: ((-i3)-i7)+f3
r5 = 0.0; r2 = 0.0; f4 = 0.0 Reaction: Rp = ((-r2)-r5)-f4, Rate Law: ((-r2)-r5)-f4
f6 = 0.0; r7 = 0.0; r4 = 0.0 Reaction: I2Rp = (r4+r7)-f6, Rate Law: (r4+r7)-f6
r3 = 0.0; r1 = 3.53837; f2 = 0.0; r6 = 0.0 Reaction: IR = ((r1-r3)-r6)-f2, Rate Law: ((r1-r3)-r6)-f2
f5 = 0.0; r2 = 0.0; r4 = 0.0; r6 = 0.0 Reaction: IRp = ((r2-r4)+r6)-f5, Rate Law: ((r2-r4)+r6)-f5
r7 = 0.0; f3 = 0.0; r3 = 0.0 Reaction: I2R = (r3-r7)-f3, Rate Law: (r3-r7)-f3
i2 = 0.0; f5 = 0.0; i4 = -1.70974345792274E-17; i6 = 0.0 Reaction: IRPen = (-i2)+i4+i6+f5, Rate Law: (-i2)+i4+i6+f5
Rtotal = 40.0 Reaction: I2RPen = ((((((((((Rtotal-R)-IR)-I2R)-Rp)-IRp)-I2Rp)-Ren)-IRen)-I2Ren)-RPen)-IRPen, Rate Law: missing
i1 = 0.0; i3 = 0.0; i6 = 0.0; f2 = 0.0 Reaction: IRen = (((-i1)+i3)-i6)+f2, Rate Law: (((-i1)+i3)-i6)+f2
i5 = 0.0; i1 = 0.0; f1 = -4.78999999985533E-8 Reaction: Ren = i1+i5+f1, Rate Law: i1+i5+f1
i2 = 0.0; i5 = 0.0; f4 = 0.0 Reaction: RPen = (i2-i5)+f4, Rate Law: (i2-i5)+f4

States:

Name Description
I2RPen [Insulin:p-6Y-insulin receptor [endosome membrane]]
I2Ren I2Ren
I2R [Insulin:Insulin receptor [plasma membrane]]
IRPen [Insulin:p-6Y-insulin receptor [endosome membrane]]
Ren [insulin receptor [endosome membrane]]
IRen [Internalisation of the insulin receptor]
IRp [Insulin:p-6Y-Insulin receptor [plasma membrane]]
IR [Insulin:Insulin receptor [plasma membrane]]
I2Rp [Insulin:p-6Y-Insulin receptor [plasma membrane]]
RPen [p-6Y-insulin receptor [endosome membrane]]
R [Insulin receptor; insulin receptor complex]
Rp [p-6Y-insulin receptor [plasma membrane]]

Observables: none

This is a quantitative systems pharmacology (QSP) model that describes key elements of the cancer immunity cycle and the…

BACKGROUND:Numerous oncology combination therapies involving modulators of the cancer immune cycle are being developed, yet quantitative simulation models predictive of outcome are lacking. We here present a model-based analysis of tumor size dynamics and immune markers, which integrates experimental data from multiple studies and provides a validated simulation framework predictive of biomarkers and anti-tumor response rates, for untested dosing sequences and schedules of combined radiation (RT) and anti PD-(L)1 therapies. METHODS:A quantitative systems pharmacology model, which includes key elements of the cancer immunity cycle and the tumor microenvironment, tumor growth, as well as dose-exposure-target modulation features, was developed to reproduce experimental data of CT26 tumor size dynamics upon administration of RT and/or a pharmacological IO treatment such as an anti-PD-L1 agent. Variability in individual tumor size dynamics was taken into account using a mixed-effects model at the level of tumor-infiltrating T cell influx. RESULTS:The model allowed for a detailed quantitative understanding of the synergistic kinetic effects underlying immune cell interactions as linked to tumor size modulation, under these treatments. The model showed that the ability of T cells to infiltrate tumor tissue is a primary determinant of variability in individual tumor size dynamics and tumor response. The model was further used as an in silico evaluation tool to quantitatively predict, prospectively, untested treatment combination schedules and sequences. We demonstrate that anti-PD-L1 administration prior to, or concurrently with RT reveal further synergistic effects, which, according to the model, may materialize due to more favorable dynamics between RT-induced immuno-modulation and reduced immuno-suppression of T cells through anti-PD-L1. CONCLUSIONS:This study provides quantitative mechanistic explanations of the links between RT and anti-tumor immune responses, and describes how optimized combinations and schedules of immunomodulation and radiation may tip the immune balance in favor of the host, sufficiently to lead to tumor shrinkage or rejection. link: http://identifiers.org/pubmed/29486799

Parameters:

Name Description
n_e = 0.001 1/d; mAb = 0.0; kpro = 3.0 1/d; mu = 0.1725 1/d; S_R = 30.5; K_D = 30.0 nmol/l; Ktcd = 0.2 1/d; kdif = 3.2 1/d; d0 = 0.01 1/d Reaction: => nTeff; PDL1, TVd, TV, dTeff, nTeff, Rate Law: compartment*(1-PDL1/(1+mAb/K_D))*(1-(mu*TVd/(TV+TVd)+n_e*dTeff+d0)^2/((mu*TVd/(TV+TVd)+n_e*dTeff+d0)^2+Ktcd^2)*(TV+TVd)/((mu*TVd/(TV+TVd)+n_e*dTeff+d0)^2/((mu*TVd/(TV+TVd)+n_e*dTeff+d0)^2+Ktcd^2)*(TV+TVd)+S_R))*nTeff*(kpro-kdif)
kapo = 2.0 1/d Reaction: dTeff =>, Rate Law: compartment*kapo*dTeff
k_el = 0.2 1/d Reaction: nTeff =>, Rate Law: compartment*k_el*nTeff
n_e = 0.001 1/d; kLN = 279.0 1/d; mu = 0.1725 1/d; S_L = 8.89; Ktcd = 0.2 1/d; d0 = 0.01 1/d Reaction: => nTeff; TVd, TV, dTeff, Rate Law: compartment*kLN*(mu*TVd/(TV+TVd)+n_e*dTeff+d0)^2/((mu*TVd/(TV+TVd)+n_e*dTeff+d0)^2+Ktcd^2)*(TV+TVd)/((mu*TVd/(TV+TVd)+n_e*dTeff+d0)^2/((mu*TVd/(TV+TVd)+n_e*dTeff+d0)^2+Ktcd^2)*(TV+TVd)+S_L)
n_e = 0.001 1/d; mAb = 0.0; mu = 0.1725 1/d; S_R = 30.5; K_D = 30.0 nmol/l; Ktcd = 0.2 1/d; kdif = 3.2 1/d; d0 = 0.01 1/d Reaction: => dTeff; PDL1, TVd, TV, dTeff, nTeff, Rate Law: compartment*(1-PDL1/(1+mAb/K_D))*(1-(mu*TVd/(TV+TVd)+n_e*dTeff+d0)^2/((mu*TVd/(TV+TVd)+n_e*dTeff+d0)^2+Ktcd^2)*(TV+TVd)/((mu*TVd/(TV+TVd)+n_e*dTeff+d0)^2/((mu*TVd/(TV+TVd)+n_e*dTeff+d0)^2+Ktcd^2)*(TV+TVd)+S_R))*nTeff*kdif
n_e = 0.001 1/d; d0 = 0.01 1/d Reaction: TV => ; dTeff, Rate Law: compartment*(n_e*dTeff+d0)*TV
r = 0.4 1/d; TVmax = 2500.0 ul Reaction: => TV; TV, Rate Law: compartment*r*TV*(1-TV/TVmax)
alpha = 0.146; tau = 0.02 d; delta = 19.0; radiation_Dose = 0.0 Reaction: TV => TVd; U, Rate Law: compartment*TV*(alpha*radiation_Dose+0.2*alpha/(tau*delta^2)*U^2)
mu = 0.1725 1/d Reaction: TVd =>, Rate Law: compartment*mu*TVd
delta = 19.0; radiation_Dose = 0.0 Reaction: => U, Rate Law: compartment*radiation_Dose*delta
Kpdl = 478.0; kpdl = 1.0 1/d Reaction: => PDL1; dTeff, Rate Law: compartment*kpdl*dTeff/(Kpdl+dTeff)
kpdl = 1.0 1/d Reaction: PDL1 =>, Rate Law: compartment*kpdl*PDL1
tau = 0.02 d Reaction: U =>, Rate Law: compartment*tau*U

States:

Name Description
dTeff [effector T cell]
TV [Tumor Volume]
U [C25832]
nTeff [CL:0002420]
PDL1 [C96024]
TVd [C25832; Tumor Volume]

Observables: none

A minimal model describing the embryonic cell division cycle at the molecular level in eukaryotes is analyzed mathematic…

A minimal model describing the embryonic cell division cycle at the molecular level in eukaryotes is analyzed mathematically. It is known from numerical simulations that the corresponding three-dimensional system of ODEs has periodic solutions in certain parameter regimes. We prove the existence of a stable limit cycle and provide a detailed description on how the limit cycle is generated. The limit cycle corresponds to a relaxation oscillation of an auxiliary system, which is singularly perturbed and has the same orbits as the original model. The singular perturbation character of the auxiliary problem is caused by the occurrence of small Michaelis constants in the model. Essential pieces of the limit cycle of the auxiliary problem consist of segments of slow motion close to several branches of a two dimensional critical manifold which are connected by fast jumps. In addition, a new phenomenon of exchange of stability occurs at lines, where the branches of the two-dimensional critical manifold intersect. This novel type of relaxation oscillations is studied by combining standard results from geometric singular perturbation with several suitable blow-up transformations. link: http://identifiers.org/pubmed/26100376

Parameters:

Name Description
epislon = 0.001 Reaction: => M; C, Rate Law: compartment*(6*C/(1+2*C)*(1-M)/((epislon+1)-M)-3/2*M/(epislon+M))

States:

Name Description
M [0016746]
C [Guanidine]
X [0000652]

Observables: none

MODEL5954483266 @ v0.0.1

This model is described in the article: Kinetics of histone gene expression during early development of Xenopus laevis…

Using literature data for transcriptional and translational rate constants, gene copy numbers, DNA concentrations, and stability constants, we have calculated the expected concentrations of histones and histone mRNA during embryogenesis of Xenopus laevis. The results led us to conclude that: (i) for X. laevis the gene copy number of the histone genes is too low to ensure the synthesis of sufficient histones during very early development, inheritance from the oocyte of either histone protein or histone mRNA (but not necessarily both) is necessary; (ii) from the known storage of histones in the oocyte and the rates of histone synthesis determined by Adamson & Woodland (1977), there would be sufficient histones to structure the newly synthesized DNA up to gastrulation but not thereafter (these empirical rates of histone synthesis may be underestimates); (iii) on the other hand, the amount of H3 mRNA recently observed during early embryogenesis (Koster, 1987, Koster et al., 1988) could direct a higher and sufficient synthesis of H3 protein, also after gastrulation. We present a quantitative model that accounts both for the observed H3 mRNA concentration as a function of time during embryogenesis and for the synthesis of sufficient histones to structure the DNA throughout early embryogenesis. The model suggests that X. laevis exhibits a major (i.e. some 14-fold) reduction in transcription of histone genes approximately 11 hours after fertilization. This reduction could be due to a decrease in the number of transcribed histone genes, a decreased rate constant of transcription with continued transcription of all the histone genes, and/or a reduction in the time during the cell cycle in which histone mRNA synthesis takes place. Alternatively, the histone mRNA stability might decrease approximately 16-fold 11 hours after fertilization. link: http://identifiers.org/pubmed/3267765

Parameters: none

States: none

Observables: none

BIOMD0000000244 @ v0.0.1

This is the model described in: **Bacterial adaptation through distributed sensing of metabolic fluxes** Oliver Kott…

The recognition of carbon sources and the regulatory adjustments to recognized changes are of particular importance for bacterial survival in fluctuating environments. Despite a thorough knowledge base of Escherichia coli's central metabolism and its regulation, fundamental aspects of the employed sensing and regulatory adjustment mechanisms remain unclear. In this paper, using a differential equation model that couples enzymatic and transcriptional regulation of E. coli's central metabolism, we show that the interplay of known interactions explains in molecular-level detail the system-wide adjustments of metabolic operation between glycolytic and gluconeogenic carbon sources. We show that these adaptations are enabled by an indirect recognition of carbon sources through a mechanism we termed distributed sensing of intracellular metabolic fluxes. This mechanism uses two general motifs to establish flux-signaling metabolites, whose bindings to transcription factors form flux sensors. As these sensors are embedded in global feedback loop architectures, closed-loop self-regulation can emerge within metabolism itself and therefore, metabolic operation may adapt itself autonomously (not requiring upstream sensing and signaling) to fluctuating carbon sources. link: http://identifiers.org/pubmed/20212527

Parameters:

Name Description
e_CAMPdegr_KcAMP = 0.1; e_CAMPdegr_kcat = 1000.0 Reaction: cAMP => ; CAMPdegr, Rate Law: e_CAMPdegr_kcat*CAMPdegr*cAMP/(cAMP+e_CAMPdegr_KcAMP)
tf_Crp_n = 1.0; tf_Crp_kcamp = 0.895; tf_Crp_scale = 1.0E8 Reaction: Crp => CrpcAMP; cAMP, Rate Law: tf_Crp_scale*((Crp+CrpcAMP)*cAMP^tf_Crp_n/(cAMP^tf_Crp_n+tf_Crp_kcamp^tf_Crp_n)-CrpcAMP)
e_Cya_kcat = 993.0; e_Cya_KEIIA = 0.0017 Reaction: => cAMP; Cya, EIIA_P, Rate Law: e_Cya_kcat*Cya*EIIA_P/(EIIA_P+e_Cya_KEIIA)
SS_Me = 0.0; d_k_degr = 2.8E-5; mu = 0.0 Reaction: => Me; ACT, GLC, Rate Law: (mu+d_k_degr)*SS_Me
e_Pdh_Kglx = 0.218; e_Pdh_Kpyr = 0.128; e_Pdh_n = 2.65; e_Pdh_KpyrI = 0.231; e_Pdh_kcat = 1179.0; e_Pdh_L = 3.4 Reaction: PYR => ACoA; GLX, Pdh, Rate Law: Pdh*e_Pdh_kcat*PYR/e_Pdh_Kpyr*(1+PYR/e_Pdh_Kpyr)^(e_Pdh_n-1)/((1+PYR/e_Pdh_Kpyr)^e_Pdh_n+e_Pdh_L*(1+GLX/e_Pdh_Kglx+PYR/e_Pdh_KpyrI)^e_Pdh_n)
g_fdp_vcra_unbound = 0.0; bm_k_expr = 20000.0; g_fdp_Kcra = 0.00118; g_fdp_vcra_bound = 4.5E-8; mu = 0.0 Reaction: => Fdp; ACT, Cra, GLC, Rate Law: bm_k_expr*mu*((1-Cra/(Cra+g_fdp_Kcra))*g_fdp_vcra_unbound+Cra/(Cra+g_fdp_Kcra)*g_fdp_vcra_bound)
bm_k_expr = 20000.0; g_ppsA_vcra_bound = 3.3E-6; g_ppsA_vcra_unbound = 0.0; mu = 0.0; g_ppsA_Kcra = 0.017 Reaction: => PpsA; ACT, Cra, GLC, Rate Law: bm_k_expr*mu*((1-Cra/(Cra+g_ppsA_Kcra))*g_ppsA_vcra_unbound+Cra/(Cra+g_ppsA_Kcra)*g_ppsA_vcra_bound)
mu = 0.0 Reaction: ACoA => ; ACT, GLC, Rate Law: mu*ACoA
e_Acoa2act_L = 639000.0; e_Acoa2act_Kacoa = 0.022; e_Acoa2act_kcat = 3079.0; e_Acoa2act_Kpyr = 0.022; e_Acoa2act_n = 2.0 Reaction: ACoA => ; Acoa2act, PYR, Rate Law: Acoa2act*e_Acoa2act_kcat*ACoA/e_Acoa2act_Kacoa*(1+ACoA/e_Acoa2act_Kacoa)^(e_Acoa2act_n-1)/((1+ACoA/e_Acoa2act_Kacoa)^e_Acoa2act_n+e_Acoa2act_L/(1+PYR/e_Acoa2act_Kpyr)^e_Acoa2act_n)
e_GltA_kcat = 1614.0; e_GltA_Kakg = 0.63; e_GltA_Koaa = 0.029; e_GltA_Koaaacoa = 0.029; e_GltA_Kacoa = 0.212 Reaction: ACoA + OAA => ICT; AKG, GltA, Rate Law: GltA*e_GltA_kcat*OAA*ACoA/((1+AKG/e_GltA_Kakg)*e_GltA_Koaaacoa*e_GltA_Kacoa+e_GltA_Kacoa*OAA+(1+AKG/e_GltA_Kakg)*e_GltA_Koaa*ACoA+OAA*ACoA)
e_Me_L = 104000.0; e_Me_kcat = 1879.0; e_Me_Kmal = 0.00624; e_Me_Kacoa = 3.64; e_Me_Kcamp = 6.54; e_Me_n = 1.33 Reaction: MAL => PYR; ACoA, Me, cAMP, Rate Law: Me*e_Me_kcat*MAL/e_Me_Kmal*(1+MAL/e_Me_Kmal)^(e_Me_n-1)/((1+MAL/e_Me_Kmal)^e_Me_n+e_Me_L*(1+ACoA/e_Me_Kacoa+cAMP/e_Me_Kcamp)^e_Me_n)
bm_k_expr = 20000.0; g_icd_vcra_unbound = 1.1E-7; mu = 0.0; g_icd_Kcra = 0.00117; g_icd_vcra_bound = 8.5E-7 Reaction: => Icd; ACT, Cra, GLC, Rate Law: bm_k_expr*mu*((1-Cra/(Cra+g_icd_Kcra))*g_icd_vcra_unbound+Cra/(Cra+g_icd_Kcra)*g_icd_vcra_bound)
e_PpsA_Kpyr = 0.00177; e_PpsA_L = 1.0E-79; e_PpsA_kcat = 1.32; e_PpsA_n = 2.0; e_PpsA_Kpep = 0.001 Reaction: PYR => PEP; PpsA, Rate Law: PpsA*e_PpsA_kcat*PYR/e_PpsA_Kpyr*(1+PYR/e_PpsA_Kpyr)^(e_PpsA_n-1)/((1+PYR/e_PpsA_Kpyr)^e_PpsA_n+e_PpsA_L*(1+PEP/e_PpsA_Kpep)^e_PpsA_n)
e_Acoa2act_L = 639000.0; env_M_ACT = 60.05; e_Acoa2act_Kacoa = 0.022; e_Acoa2act_kcat = 3079.0; e_Acoa2act_Kpyr = 0.022; env_uc = 9.5E-7; e_Acoa2act_n = 2.0 Reaction: => ACT; ACoA, Acoa2act, BM, PYR, Rate Law: env_uc*env_M_ACT*BM*Acoa2act*e_Acoa2act_kcat*ACoA/e_Acoa2act_Kacoa*(1+ACoA/e_Acoa2act_Kacoa)^(e_Acoa2act_n-1)/((1+ACoA/e_Acoa2act_Kacoa)^e_Acoa2act_n+e_Acoa2act_L/(1+PYR/e_Acoa2act_Kpyr)^e_Acoa2act_n)
e_Fdp_n = 4.0; e_Fdp_L = 4000000.0; e_Fdp_kcat = 192.0; e_Fdp_Kfbp = 0.003; e_Fdp_Kpep = 0.3 Reaction: FBP => G6P; Fdp, PEP, Rate Law: Fdp*e_Fdp_kcat*FBP/e_Fdp_Kfbp*(1+FBP/e_Fdp_Kfbp)^(e_Fdp_n-1)/((1+FBP/e_Fdp_Kfbp)^e_Fdp_n+e_Fdp_L/(1+PEP/e_Fdp_Kpep)^e_Fdp_n)
tf_PdhR_scale = 100.0; tf_PdhR_n = 1.0; tf_PdhR_kpyr = 0.164 Reaction: PdhR => PdhRPYR; PYR, Rate Law: tf_PdhR_scale*((PdhR+PdhRPYR)*PYR^tf_PdhR_n/(PYR^tf_PdhR_n+tf_PdhR_kpyr^tf_PdhR_n)-PdhRPYR)
e_PfkA_n = 4.0; e_PfkA_Kpep = 0.138; e_PfkA_kcat = 908000.0; e_PfkA_Kg6p = 0.022; e_PfkA_L = 9.5E7 Reaction: G6P => FBP; PEP, PfkA, Rate Law: PfkA*e_PfkA_kcat*G6P/e_PfkA_Kg6p*(1+G6P/e_PfkA_Kg6p)^(e_PfkA_n-1)/((1+G6P/e_PfkA_Kg6p)^e_PfkA_n+e_PfkA_L*(1+PEP/e_PfkA_Kpep)^e_PfkA_n)
e_AceB_kcat = 47.8; e_AceB_Kacoa = 0.755; e_AceB_Kglxacoa = 0.719; e_AceB_Kglx = 0.95 Reaction: ACoA + GLX => MAL; AceB, Rate Law: AceB*e_AceB_kcat*GLX*ACoA/(e_AceB_Kglxacoa*e_AceB_Kacoa+e_AceB_Kacoa*GLX+e_AceB_Kglx*ACoA+GLX*ACoA)
bm_k_expr = 20000.0; g_pfkA_vcra_bound = 6.6E-9; mu = 0.0; g_pfkA_vcra_unbound = 8.2E-7; g_pfkA_Kcra = 6.3E-7 Reaction: => PfkA; ACT, Cra, GLC, Rate Law: bm_k_expr*mu*((1-Cra/(Cra+g_pfkA_Kcra))*g_pfkA_vcra_unbound+Cra/(Cra+g_pfkA_Kcra)*g_pfkA_vcra_bound)
k_bm_OAA = 0.0 Reaction: OAA => ; ACT, GLC, Rate Law: k_bm_OAA*OAA
e_Akg2mal_kcat = 1530.0; e_Akg2mal_Kakg = 0.548 Reaction: AKG => MAL; Akg2mal, Rate Law: Akg2mal*e_Akg2mal_kcat*AKG/(AKG+e_Akg2mal_Kakg)
mu = 0.0; g_gltA_n = 1.07; g_gltA_vcrp_bound = 2.3E-6; bm_k_expr = 20000.0; g_gltA_Kcrp = 0.04; g_gltA_vcrp_unbound = 0.0 Reaction: => GltA; ACT, CrpcAMP, GLC, Rate Law: bm_k_expr*mu*((1-CrpcAMP^g_gltA_n/(CrpcAMP^g_gltA_n+g_gltA_Kcrp^g_gltA_n))*g_gltA_vcrp_unbound+CrpcAMP^g_gltA_n/(CrpcAMP^g_gltA_n+g_gltA_Kcrp^g_gltA_n)*g_gltA_vcrp_bound)
e_Mdh_n = 1.7; e_Mdh_Kmal = 10.1; e_Mdh_kcat = 773.0 Reaction: MAL => OAA; Mdh, Rate Law: Mdh*e_Mdh_kcat*MAL^e_Mdh_n/(MAL^e_Mdh_n+e_Mdh_Kmal^e_Mdh_n)
k_bm_PG3 = 0.0 Reaction: PG3 => ; ACT, GLC, Rate Law: k_bm_PG3*PG3
e_AceA_kcat = 614.0; e_AceA_n = 4.0; e_AceA_L = 50100.0; e_AceA_Kpep = 0.055; e_AceA_Kict = 0.022; e_AceA_Kakg = 0.827; e_AceA_Kpg3 = 0.72 Reaction: ICT => AKG + GLX; AceA, PEP, PG3, Rate Law: AceA*e_AceA_kcat*ICT/e_AceA_Kict*(1+ICT/e_AceA_Kict)^(e_AceA_n-1)/((1+ICT/e_AceA_Kict)^e_AceA_n+e_AceA_L*(1+PEP/e_AceA_Kpep+PG3/e_AceA_Kpg3+AKG/e_AceA_Kakg)^e_AceA_n)
e_AceK_kcat_ki = 3.4E12; e_AceK_Kakg = 0.82; e_AceK_Kict = 0.137; e_AceK_Kicd = 0.043; e_AceK_Kpep = 0.539; e_AceK_L = 1.0E8; e_AceK_Koaa = 0.173; e_AceK_n = 2.0; e_AceK_Kglx = 0.866; e_AceK_Kpg3 = 1.57; e_AceK_Kpyr = 0.038 Reaction: Icd => Icd_P; AKG, AceK, GLX, ICT, OAA, PEP, PG3, PYR, Rate Law: AceK*e_AceK_kcat_ki*Icd/e_AceK_Kicd*(1+Icd/e_AceK_Kicd)^(e_AceK_n-1)/((1+Icd/e_AceK_Kicd)^e_AceK_n+e_AceK_L*(1+ICT/e_AceK_Kict+GLX/e_AceK_Kglx+OAA/e_AceK_Koaa+AKG/e_AceK_Kakg+PEP/e_AceK_Kpep+PG3/e_AceK_Kpg3+PYR/e_AceK_Kpyr)^e_AceK_n)
bm_k_expr = 20000.0; g_pykF_vcra_unbound = 3.9E-7; g_pykF_Kcra = 0.0023; mu = 0.0; g_pykF_vcra_bound = 2.1E-9 Reaction: => PykF; ACT, Cra, GLC, Rate Law: bm_k_expr*mu*((1-Cra/(Cra+g_pykF_Kcra))*g_pykF_vcra_unbound+Cra/(Cra+g_pykF_Kcra)*g_pykF_vcra_bound)
pts_k4 = 2520.0; pts_Kglc = 0.0012; pts_KEIIA = 0.0085 Reaction: EIIA_P => G6P + EIIA; EIICB, GLC, Rate Law: pts_k4*EIICB*EIIA_P*GLC/((pts_KEIIA+EIIA_P)*(pts_Kglc+GLC))
k_bm_ACoA = 0.0 Reaction: ACoA => ; ACT, GLC, Rate Law: k_bm_ACoA*ACoA
tf_Cra_n = 2.0; tf_Cra_kfbp = 1.36; tf_Cra_scale = 100.0 Reaction: Cra => CraFBP; FBP, Rate Law: tf_Cra_scale*((Cra+CraFBP)*FBP^tf_Cra_n/(FBP^tf_Cra_n+tf_Cra_kfbp^tf_Cra_n)-CraFBP)
d_k_degr = 2.8E-5; mu = 0.0 Reaction: Mdh => ; ACT, GLC, Rate Law: (mu+d_k_degr)*Mdh
bm_k_expr = 20000.0; g_mdh_vcrp_bound = 9.1E-6; g_mdh_Kcrp = 0.06; mu = 0.0; g_mdh_vcrp_unbound = 0.0 Reaction: => Mdh; ACT, CrpcAMP, GLC, Rate Law: bm_k_expr*mu*((1-CrpcAMP/(CrpcAMP+g_mdh_Kcrp))*g_mdh_vcrp_unbound+CrpcAMP/(CrpcAMP+g_mdh_Kcrp)*g_mdh_vcrp_bound)
e_Icd_Kict = 1.6E-4; e_Icd_Kpep = 0.334; e_Icd_n = 2.0; e_Icd_kcat = 695.0; e_Icd_L = 127.0 Reaction: ICT => AKG; Icd, PEP, Rate Law: Icd*e_Icd_kcat*ICT/e_Icd_Kict*(1+ICT/e_Icd_Kict)^(e_Icd_n-1)/((1+ICT/e_Icd_Kict)^e_Icd_n+e_Icd_L*(1+PEP/e_Icd_Kpep)^e_Icd_n)
g_akg2mal_vcrp_unbound = 0.0; mu = 0.0; g_akg2mal_n = 0.74; g_akg2mal_Kcrp = 0.091; g_akg2mal_vcrp_bound = 1.4E-6; bm_k_expr = 20000.0 Reaction: => Akg2mal; ACT, CrpcAMP, GLC, Rate Law: bm_k_expr*mu*((1-CrpcAMP^g_akg2mal_n/(CrpcAMP^g_akg2mal_n+g_akg2mal_Kcrp^g_akg2mal_n))*g_akg2mal_vcrp_unbound+CrpcAMP^g_akg2mal_n/(CrpcAMP^g_akg2mal_n+g_akg2mal_Kcrp^g_akg2mal_n)*g_akg2mal_vcrp_bound)
e_Acs_Kact = 0.001; env_M_ACT = 60.05; e_Acs_kcat = 340.0; env_uc = 9.5E-7 Reaction: ACT => ; Acs, BM, Rate Law: env_uc*env_M_ACT*BM*Acs*e_Acs_kcat*ACT/(ACT+e_Acs_Kact)
d_k_degr = 2.8E-5; SS_Ppc = 0.0; mu = 0.0 Reaction: => Ppc; ACT, GLC, Rate Law: (mu+d_k_degr)*SS_Ppc
e_AceK_Kakg = 0.82; e_AceK_Kpep = 0.539; e_AceK_L = 1.0E8; e_AceK_Koaa = 0.173; e_AceK_n = 2.0; e_AceK_Kicd_P = 0.643; e_AceK_Kpg3 = 1.57; e_AceK_kcat_ph = 1.7E9; e_AceK_Kpyr = 0.038 Reaction: Icd_P => Icd; AKG, AceK, OAA, PEP, PG3, PYR, Rate Law: AceK*e_AceK_kcat_ph*Icd_P/e_AceK_Kicd_P*(1+Icd_P/e_AceK_Kicd_P)^(e_AceK_n-1)/((1+Icd_P/e_AceK_Kicd_P)^e_AceK_n+e_AceK_L/(1+OAA/e_AceK_Koaa+AKG/e_AceK_Kakg+PEP/e_AceK_Kpep+PG3/e_AceK_Kpg3+PYR/e_AceK_Kpyr)^e_AceK_n)
k_bm_G6P = 0.0 Reaction: G6P => ; ACT, GLC, Rate Law: k_bm_G6P*G6P
bm_k_expr = 20000.0; g_pdh_vpdhr_bound = 1.3E-9; mu = 0.0; g_pdh_Kpdhr = 0.0034; g_pdh_vpdhr_unbound = 3.6E-7 Reaction: => Pdh; ACT, GLC, PdhR, Rate Law: bm_k_expr*mu*((1-PdhR/(PdhR+g_pdh_Kpdhr))*g_pdh_vpdhr_unbound+PdhR/(PdhR+g_pdh_Kpdhr)*g_pdh_vpdhr_bound)
pts_km1 = 46.3; pts_k1 = 116.0 Reaction: PEP + EIIA => PYR + EIIA_P, Rate Law: pts_k1*PEP*EIIA-pts_km1*PYR*EIIA_P
g_acs_Kcrp = 0.0047; mu = 0.0; g_acs_n = 2.31; bm_k_expr = 20000.0; g_acs_vcrp_unbound = 0.0; g_acs_vcrp_bound = 1.2E-6 Reaction: => Acs; ACT, CrpcAMP, GLC, Rate Law: bm_k_expr*mu*((1-CrpcAMP^g_acs_n/(CrpcAMP^g_acs_n+g_acs_Kcrp^g_acs_n))*g_acs_vcrp_unbound+CrpcAMP^g_acs_n/(CrpcAMP^g_acs_n+g_acs_Kcrp^g_acs_n)*g_acs_vcrp_bound)
bm_k_expr = 20000.0; g_pckA_vcra_unbound = 0.0; g_pckA_vcra_bound = 2.5E-6; mu = 0.0; g_pckA_Kcra = 0.00535 Reaction: => PckA; ACT, Cra, GLC, Rate Law: bm_k_expr*mu*((1-Cra/(Cra+g_pckA_Kcra))*g_pckA_vcra_unbound+Cra/(Cra+g_pckA_Kcra)*g_pckA_vcra_bound)
e_PykF_Kfbp = 0.413; e_PykF_n = 4.0; e_PykF_Kpep = 5.0; e_PykF_kcat = 5749.0; e_PykF_L = 100000.0 Reaction: PEP => PYR; FBP, PykF, Rate Law: PykF*e_PykF_kcat*PEP/e_PykF_Kpep*(1+PEP/e_PykF_Kpep)^(e_PykF_n-1)/((1+PEP/e_PykF_Kpep)^e_PykF_n+e_PykF_L/(1+FBP/e_PykF_Kfbp)^e_PykF_n)
pts_k4 = 2520.0; pts_Kglc = 0.0012; pts_KEIIA = 0.0085; env_M_GLC = 180.156; env_uc = 9.5E-7 Reaction: GLC => ; BM, EIIA_P, EIICB, Rate Law: env_uc*env_M_GLC*BM*pts_k4*EIICB*EIIA_P*GLC/((pts_KEIIA+EIIA_P)*(pts_Kglc+GLC))

States:

Name Description
Fdp [Fructose-1,6-bisphosphatase 1]
CAMPdegr CAMPdegr
EIICB [phosphoenolpyruvate-dependent sugar phosphotransferase system; PTS system mannitol-specific EIICBA component]
ACoA [acetyl-CoA; Acetyl-CoA]
Icd P [Isocitrate dehydrogenase [NADP]]
GltA [Citrate synthase]
cAMP [3',5'-cyclic AMP; 3',5'-Cyclic AMP]
PdhRPYR [pyruvic acid; Pyruvate dehydrogenase complex repressor]
MAL [(R)-malic acid; (R)-Malate]
OAA [oxaloacetic acid; Oxaloacetate]
Pdh [Pyruvate dehydrogenase E1 component]
Crp [cAMP-activated global transcriptional regulator CRP]
PYR [pyruvic acid; Pyruvate]
Akg2mal Akg2mal
PpsA [Phosphoenolpyruvate synthase]
Mdh [Malate dehydrogenase]
G6P [D-glucose 6-phosphate; D-Glucose 6-phosphate]
Cra [Catabolite repressor/activator]
PckA [Phosphoenolpyruvate carboxykinase (ATP)]
Ppc [Phosphoenol pyruvate carboxylase]
PEP [phosphoenolpyruvate; Phosphoenolpyruvate]
CraFBP [keto-D-fructose 1,6-bisphosphate; Catabolite repressor/activator]
Icd [Isocitrate dehydrogenase [NADP]]
GLX [glyoxylic acid; Glyoxylate]
Me [NADP-dependent malic enzyme]
AceK [Isocitrate dehydrogenase kinase/phosphatase]
FBP [keto-D-fructose 1,6-bisphosphate; D-Fructose 1,6-bisphosphate]
GLC [glucose; C00293]
PykF [Pyruvate kinase I]
EIIA [phosphoenolpyruvate-dependent sugar phosphotransferase system; PTS system mannitol-specific EIICBA component]
Cya [Adenylate cyclase]
PG3 [3-phospho-D-glyceric acid; 3-Phospho-D-glycerate]
Acoa2act Acoa2act
PfkA [ATP-dependent 6-phosphofructokinase isozyme 2]
BM BM
IclR [Transcriptional repressor IclR]
PdhR [Pyruvate dehydrogenase complex repressor]
CrpcAMP [3',5'-cyclic AMP; cAMP-activated global transcriptional regulator CRP]
Acs [Acetyl-coenzyme A synthetase]
ACT [acetic acid; Acetate]
EIIA P [phosphoenolpyruvate-dependent sugar phosphotransferase system; PTS system mannitol-specific EIICBA component]
AKG [2-oxoglutarate(2-); 2-Oxoglutarate]
ICT [isocitric acid; Isocitrate]

Observables: none

BIOMD0000000108 @ v0.0.1

This model is according to the paper from Axel Kowald *Alternative pathways as mechanism for the negative effects associ…

One of the most important antioxidant enzymes is superoxide dismutase (SOD), which catalyses the dismutation of superoxide radicals to hydrogen peroxide. The enzyme plays an important role in diseases like trisomy 21 and also in theories of the mechanisms of aging. But instead of being beneficial, intensified oxidative stress is associated with the increased expression of SOD and also studies on bacteria and transgenic animals show that high levels of SOD actually lead to increased lipid peroxidation and hypersensitivity to oxidative stress. Using mathematical models we investigate the question how overexpression of SOD can lead to increased oxidative stress, although it is an antioxidant enzyme. We consider the following possibilities that have been proposed in the literature: (i) Reaction of H(2)O(2) with CuZnSOD leading to hydroxyl radical formation. (ii) Superoxide radicals might reduce membrane damage by acting as radical chain breaker. (iii) While detoxifying superoxide radicals SOD cycles between a reduced and oxidized state. At low superoxide levels the intermediates might interact with other redox partners and increase the superoxide reductase (SOR) activity of SOD. This short-circuiting of the SOD cycle could lead to an increased hydrogen peroxide production. We find that only one of the proposed mechanisms is under certain circumstances able to explain the increased oxidative stress caused by SOD. But furthermore we identified an additional mechanism that is of more general nature and might be a common basis for the experimental findings. We call it the alternative pathway mechanism. link: http://identifiers.org/pubmed/16085106

Parameters:

Name Description
k17 = 30000.0 Reaction: species_0000011 => species_0000007, Rate Law: compartment_0000001*k17*species_0000011
k18 = 7.0 Reaction: species_0000007 => species_0000011 + species_0000009, Rate Law: compartment_0000001*k18*species_0000007
k1 = 6.6E-7 Reaction: => species_0000001, Rate Law: compartment_0000001*k1
k13b = 0.0087 Reaction: species_0000002 =>, Rate Law: compartment_0000001*k13b*species_0000002
k19 = 88000.0 Reaction: species_0000007 =>, Rate Law: compartment_0000001*k19*species_0000007^2
k13a = 0.0087; Cu_I_ZnSOD = 0.0 Reaction: => species_0000002, Rate Law: compartment_0000001*k13a*Cu_I_ZnSOD
k3 = 1.6E9; Cu_I_ZnSOD = 0.0 Reaction: species_0000001 => species_0000006 + species_0000002, Rate Law: compartment_0000001*k3*species_0000001*Cu_I_ZnSOD
k11 = 2.5E8 Reaction: species_0000008 => species_0000011, Rate Law: compartment_0000001*k11*species_0000008
k7 = 3.4E7 Reaction: species_0000006 => ; species_0000017, Rate Law: compartment_0000001*k7*species_0000006*species_0000017
k2 = 1.6E9 Reaction: species_0000001 + species_0000002 =>, Rate Law: compartment_0000001*k2*species_0000001*species_0000002
HO2star = 0.0; k10 = 1000.0 Reaction: species_0000001 =>, Rate Law: k10*HO2star*compartment_0000001
k5 = 20000.0 Reaction: species_0000001 + species_0000006 => species_0000008, Rate Law: compartment_0000001*k5*species_0000001*species_0000006
k9 = 1000000.0 Reaction: species_0000008 =>, Rate Law: compartment_0000001*k9*species_0000008
k4 = 100000.0 Reaction: species_0000001 + species_0000007 => species_0000009, Rate Law: compartment_0000001*k4*species_0000001*species_0000007
k6 = 1.0 Reaction: species_0000006 => species_0000008; species_0000002, Rate Law: compartment_0000001*k6*species_0000006*species_0000002
k12 = 0.38 Reaction: species_0000009 =>, Rate Law: compartment_0000001*k12*species_0000009

States:

Name Description
species 0000008 [hydroxyl]
species 0000002 [IPR001424]
species 0000011 [lipid]
species 0000001 [superoxide; O2.-]
species 0000007 LOO*
species 0000009 [Lipid hydroperoxide; lipid hydroperoxide]
species 0000006 [hydrogen peroxide; Hydrogen peroxide]

Observables: none

A new model is proposed to study the kinetics of [3H]cortisol metabolism by using urinary data only. The model consists…

A new model is proposed to study the kinetics of [3H]cortisol metabolism by using urinary data only. The model consists of 5 pools, in which changes of the fractions of dose are given by a system of 5 ordinary differential equations. After i.v. administration of [3H]cortisol to 8 multiple pituitary deficient (MPD) patients (group I) the urines from each patient were collected in 9-15 portions during the following 3 days. From the urinary data the rate constants of cortisol metabolism were calculated. A published set of urinary data from patients with a normal cortisol metabolism (group II) was used for comparison. The overall half-life of the label in the circulation was 30 min for both groups; the half-life of the label excretion by both groups was 6 h and the time of maximal activity in the main metabolizing pool was 1.8 h in group I and 1.5 h in group II. The 20% of normal cortisol production rate (CPR) in the 8 MPD patients amounted to 7.2 +/- 1.9 mumol/(m2*d). Therefore, the low CPR but normal rate constants, i.e. a normal metabolic clearance rate of cortisol, in the MPD patients suggest a sensitive adjustment of the cortisol response in the target organs. link: http://identifiers.org/pubmed/1567783

Parameters:

Name Description
K5 = 1.2; K4 = 1.2 Reaction: The_FOD_in_the_metabolizing_tissues__X4 => The_FOD_in_the_gallbladder___intestinal_lumen__X5, Rate Law: compartment*(K4*The_FOD_in_the_metabolizing_tissues__X4-K5*The_FOD_in_the_gallbladder___intestinal_lumen__X5)
K2 = 1.2 Reaction: The_FOD_in_the_gallbladder___intestinal_lumen__X5 => The_cumulative_FOD_excreted_in_the_non_urinary_pool__X3, Rate Law: compartment*K2*The_FOD_in_the_gallbladder___intestinal_lumen__X5
K3 = 26.6 Reaction: The_FOD_in_the_circulation__X1 => The_FOD_in_the_metabolizing_tissues__X4, Rate Law: compartment*K3*The_FOD_in_the_circulation__X1
K1 = 3.6 Reaction: The_FOD_in_the_metabolizing_tissues__X4 => The_cumulative_FOD_excreted_in_the_urine__X2, Rate Law: compartment*K1*The_FOD_in_the_metabolizing_tissues__X4

States:

Name Description
The FOD in the gallbladder intestinal lumen X5 [BTO:0000647; gall bladder]
The FOD in the metabolizing tissues X4 [BTO:0003092; liver; BTO:0005937]
The cumulative FOD excreted in the non urinary pool X3 [BTO:0003092]
The FOD in the circulation X1 [BTO:0003092]
The cumulative FOD excreted in the urine X2 [BTO:0003092]

Observables: none

Mathematical model of thrombin inhibition by ATIII, alpha-2-macroglobulin and miscellaneous serpins (a1-antitrypsin, a1-…

The generation of thrombin in time is the combined effect of the processes of prothrombin conversion and thrombin inactivation. Measurement of prothrombin consumption used to provide valuable information on hemostatic disorders, but is no longer used, due to its elaborate nature.Because thrombin generation (TG) curves are easily obtained with modern techniques, we developed a method to extract the prothrombin conversion curve from the TG curve, using a computational model for thrombin inactivation.Thrombin inactivation was modelled computationally by a reaction scheme with antithrombin, α(2) Macroglobulin and fibrinogen, taking into account the presence of the thrombin substrate ZGGR-AMC used to obtain the experimental data. The model was validated by comparison with data obtained from plasma as well as from a reaction mixture containing the same reactants as plasma.The computational model fitted experimental data within the limits of experimental error. Thrombin inactivation curves were predicted within 2 SD in 96% of healthy subjects. Prothrombin conversion was calculated in 24 healthy subjects and validated by comparison with the experimental consumption of prothrombin during TG. The endogenous thrombin potential (ETP) mainly depends on the total amount of prothrombin converted and the thrombin decay capacity, and the peak height is determined by the maximum prothrombin conversion rate and the thrombin decay capacity.Thrombin inactivation can be accurately predicted by the proposed computational model and prothrombin conversion can be extracted from a TG curve using this computational prediction. This additional computational analysis of TG facilitates the analysis of the process of disturbed TG. link: http://identifiers.org/pubmed/25421744

Parameters: none

States: none

Observables: none

Krohn2011 - Cerebral amyloid-β proteostasis regulated by membrane transport protein ABCC1This model is described in the…

In Alzheimer disease (AD), the intracerebral accumulation of amyloid-β (Aβ) peptides is a critical yet poorly understood process. Aβ clearance via the blood-brain barrier is reduced by approximately 30% in AD patients, but the underlying mechanisms remain elusive. ABC transporters have been implicated in the regulation of Aβ levels in the brain. Using a mouse model of AD in which the animals were further genetically modified to lack specific ABC transporters, here we have shown that the transporter ABCC1 has an important role in cerebral Aβ clearance and accumulation. Deficiency of ABCC1 substantially increased cerebral Aβ levels without altering the expression of most enzymes that would favor the production of Aβ from the Aβ precursor protein. In contrast, activation of ABCC1 using thiethylperazine (a drug approved by the FDA to relieve nausea and vomiting) markedly reduced Aβ load in a mouse model of AD expressing ABCC1 but not in such mice lacking ABCC1. Thus, by altering the temporal aggregation profile of Aβ, pharmacological activation of ABC transporters could impede the neurodegenerative cascade that culminates in the dementia of AD. link: http://identifiers.org/pubmed/21881209

Parameters:

Name Description
k_sol = 0.34237; n_n = 6.0; k_n = 0.34508 Reaction: N = k_n*M^n_n-k_sol*N*M, Rate Law: k_n*M^n_n-k_sol*N*M
k_sol = 0.34237; k_insol = 0.3586; I_net = 5.20180590104651; n_n = 6.0; k_n = 0.34508 Reaction: M = ((((((((((((((((((((((((((((((((((((((((((((((((I_net-k_n*n_n*M^n_n)-k_sol*N*M)-k_sol*A7*M)-k_sol*A8*M)-k_sol*A9*M)-k_sol*A10*M)-k_sol*A11*M)-k_sol*A12*M)-k_sol*A13*M)-k_insol*A14*M)-k_insol*A15*M)-k_insol*A16*M)-k_insol*A17*M)-k_insol*A18*M)-k_insol*A19*M)-k_insol*A20*M)-k_insol*A21*M)-k_insol*A22*M)-k_insol*A23*M)-k_insol*A24*M)-k_insol*A25*M)-k_insol*A26*M)-k_insol*A27*M)-k_insol*A28*M)-k_insol*A29*M)-k_insol*A30*M)-k_insol*A31*M)-k_insol*A32*M)-k_insol*A33*M)-k_insol*A34*M)-k_insol*A35*M)-k_insol*A36*M)-k_insol*A37*M)-k_insol*A38*M)-k_insol*A39*M)-k_insol*A40*M)-k_insol*A41*M)-k_insol*A42*M)-k_insol*A43*M)-k_insol*A44*M)-k_insol*A45*M)-k_insol*A46*M)-k_insol*A47*M)-k_insol*A48*M)-k_insol*A49*M)-k_insol*A50*M)-k_insol*A51*M)-k_insol*A52*M)-k_insol*A53*M, Rate Law: ((((((((((((((((((((((((((((((((((((((((((((((((I_net-k_n*n_n*M^n_n)-k_sol*N*M)-k_sol*A7*M)-k_sol*A8*M)-k_sol*A9*M)-k_sol*A10*M)-k_sol*A11*M)-k_sol*A12*M)-k_sol*A13*M)-k_insol*A14*M)-k_insol*A15*M)-k_insol*A16*M)-k_insol*A17*M)-k_insol*A18*M)-k_insol*A19*M)-k_insol*A20*M)-k_insol*A21*M)-k_insol*A22*M)-k_insol*A23*M)-k_insol*A24*M)-k_insol*A25*M)-k_insol*A26*M)-k_insol*A27*M)-k_insol*A28*M)-k_insol*A29*M)-k_insol*A30*M)-k_insol*A31*M)-k_insol*A32*M)-k_insol*A33*M)-k_insol*A34*M)-k_insol*A35*M)-k_insol*A36*M)-k_insol*A37*M)-k_insol*A38*M)-k_insol*A39*M)-k_insol*A40*M)-k_insol*A41*M)-k_insol*A42*M)-k_insol*A43*M)-k_insol*A44*M)-k_insol*A45*M)-k_insol*A46*M)-k_insol*A47*M)-k_insol*A48*M)-k_insol*A49*M)-k_insol*A50*M)-k_insol*A51*M)-k_insol*A52*M)-k_insol*A53*M
k_sol = 0.34237; k_insol = 0.3586 Reaction: A14 = k_sol*A13*M-k_insol*A14*M, Rate Law: k_sol*A13*M-k_insol*A14*M
soluble = 1.04389999999997 Reaction: soluble_obs = soluble, Rate Law: missing
insoluble = 0.0 Reaction: insoluble_obs = insoluble, Rate Law: missing
k_sol = 0.34237 Reaction: A12 = k_sol*A11*M-k_sol*A12*M, Rate Law: k_sol*A11*M-k_sol*A12*M
k_insol = 0.3586 Reaction: A18 = k_insol*A17*M-k_insol*A18*M, Rate Law: k_insol*A17*M-k_insol*A18*M

States:

Name Description
A45 A45
A34 A34
A35 A35
A53 A53
A22 A22
insoluble obs insoluble_obs
M [amyloid-beta]
A8 A8
A21 A21
A26 A26
A18 A18
A32 A32
A25 A25
A36 A36
A12 A12
soluble obs soluble_obs
A7 A7
A48 A48
A37 A37
A54 A54
A33 A33
A29 A29
A16 A16
A38 A38
A47 A47
A41 A41
A28 A28
A40 A40
A20 A20
A13 A13
A19 A19
A43 A43
A9 A9
A23 A23
A42 A42
N N
A17 A17
A39 A39
A24 A24
A30 A30
A49 A49
A14 A14
A10 A10
A44 A44
A11 A11
A52 A52
A50 A50
A46 A46
A51 A51
A15 A15
A27 A27
A31 A31

Observables: none

MODEL1006230083 @ v0.0.1

This a model from the article: Parathyroid hormone temporal effects on bone formation and resorption. Kroll MH. Bull…

Parathyroid hormone (PTH) paradoxically causes net bone loss (resorption) when administered in a continuous fashion, and net bone formation (deposition) when administered intermittently. Currently no pharmacological formulations are available to promote bone formation, as needed for the treatment of osteoporosis. The paradoxical behavior of PTH confuses endocrinologists, thus, a model bone resorption or deposition dependent on the timing of PTH administration would de-mystify this behavior and provide the basis for logical drug formulation. We developed a mathematical model that accounts for net bone loss with continuous PTH administration and net bone formation with intermittent PTH administration, based on the differential effects of PTH on the osteoblastic and osteoclastic populations of cells. Bone, being a major reservoir of body calcium, is under the hormonal control of PTH. The overall effect of PTH is to raise plasma levels of calcium, partly through bone resorption. Osteoclasts resorb bone and liberate calcium, but they lack receptors for PTH. The preosteoblastic precursors and preosteoblasts possess receptors for PTH, upon which the hormone induces differentiation from the precursor to preosteoblast and from the preosteoblast to the osteoblast. The osteoblasts generate IL-6; IL-6 stimulates preosteoclasts to differentiate into osteoclasts. We developed a mathematical model for the differentiation of osteoblastic and osteoclastic populations in bone, using a delay time of 1 hour for differentiation of preosteoblastic precursors into preosteoblasts and 2 hours for the differentiation of preosteoblasts into osteoblasts. The ratio of the number of osteoblasts to osteoclasts indicates the net effect of PTH on bone resorption and deposition; the timing of events producing the maximum ratio would induce net bone deposition. When PTH is pulsed with a frequency of every hour, the preosteoblastic population rises and decreases in nearly a symmetric pattern, with 3.9 peaks every 24 hours, and 4.0 peaks every 24 hours when PTH is administered every 6 hours. Thus, the preosteoblast and osteoblast frequency depends more on the nearly constant value of the PTH, rather than on the frequency of the PTH pulsations. Increasing the time delay gradually increases the mean value for the number of osteoblasts. The osteoblastic population oscillates for all intermittent administrations of PTH and even when the PTH infusion is constant. The maximum ratio of osteoblasts to osteoclasts occurs when PTH is administered in pulses of every 6 hours. The delay features in the model bear most of the responsibility for the occurrence of these oscillations, because without the delay and in the presence of constant PTH infusions, no oscillations occur. However, with a delay, under constant PTH infusions, the model generates oscillations. The osteoblast oscillations express limit cycle behavior. Phase plane analysis show simple and complex attractors. Subsequent to a disturbance in the number of osteoblasts, the osteoblasts quickly regain their oscillatory behavior and cycle back to the original attractor, typical of limit cycle behavior. Further, because the model was constructed with dissipative and nonlinear features, one would expect ensuing oscillations to show limit cycle behavior. The results from our model, increased bone deposition with intermittent PTH administration and increased bone resorption with constant PTH administration, conforms with experimental observations and with an accepted explanation for osteoporosis. link: http://identifiers.org/pubmed/10824426

Parameters: none

States: none

Observables: none

This mathematical model describes interactions between glioma tumors and the immune system that may occur following dire…

Glioblastoma (GBM), a highly aggressive (WHO grade IV) primary brain tumor, is refractory to traditional treatments, such as surgery, radiation or chemotherapy. This study aims at aiding in the design of more efficacious GBM therapies. We constructed a mathematical model for glioma and the immune system interactions, that may ensue upon direct intra-tumoral administration of ex vivo activated alloreactive cytotoxic-T-lymphocytes (aCTL). Our model encompasses considerations of the interactive dynamics of aCTL, tumor cells, major histocompatibility complex (MHC) class I and MHC class II molecules, as well as cytokines, such as TGF-beta and IFN-gamma, which dampen or increase the pro-inflammatory environment, respectively. Computer simulations were used for model verification and for retrieving putative treatment scenarios. The mathematical model successfully retrieved clinical trial results of efficacious aCTL immunotherapy for recurrent anaplastic oligodendroglioma and anaplastic astrocytoma (WHO grade III). It predicted that cellular adoptive immunotherapy failed in GBM because the administered dose was 20-fold lower than required for therapeutic efficacy. Model analysis suggests that GBM may be eradicated by new dose-intensive strategies, e.g., 3 x 10(8) aCTL every 4 days for small tumor burden, or 2 x 10(9) aCTL, infused every 5 days for larger tumor burden. Further analysis pinpoints crucial bio-markers relating to tumor growth rate, tumor size, and tumor sensitivity to the immune system, whose estimation enables regimen personalization. We propose that adoptive cellular immunotherapy was prematurely abandoned. It may prove efficacious for GBM, if dose intensity is augmented, as prescribed by the mathematical model. Re-initiation of clinical trials, using calculated individualized regimens for grade III-IV malignant glioma, is suggested. link: http://identifiers.org/pubmed/17823798

Parameters:

Name Description
g_M1 = 1.44 Reaction: => M1, Rate Law: compartment*g_M1
a_T_beta = 0.69 Reaction: => F_beta; T, Rate Law: compartment*a_T_beta*T
g_beta = 63945.0 Reaction: => F_beta, Rate Law: compartment*g_beta
mu_beta = 7.0 Reaction: F_beta =>, Rate Law: compartment*mu_beta*F_beta
mu_C = 0.007 Reaction: C =>, Rate Law: compartment*mu_C*C
mu_gamma = 0.102 Reaction: F_gamma =>, Rate Law: compartment*mu_gamma*F_gamma
mu_M2 = 0.0144 Reaction: M2 =>, Rate Law: compartment*mu_M2*M2
mu_M1 = 0.0144 Reaction: M1 =>, Rate Law: compartment*mu_M1*M1
K = 1.0E11; r = 3.5E-4 Reaction: => T, Rate Law: compartment*r*T*(1-T/K)
v=0.1 Reaction: => M2, Rate Law: compartment*v
e_T_beta = 10000.0; a_T_beta = 0.69; a_T = 0.12; e_T = 50.0; h_T = 5.0E8 Reaction: T => ; M1, C, F_beta, Rate Law: compartment*a_T*M1/(M1+e_T)*C*T/(h_T+T)*(a_T_beta+e_T_beta*(1-a_T_beta)/(F_beta+e_T_beta))
e_C_beta = 10000.0; a_C_M2 = 4.8E-11; e_C_M2 = 1.0E14; a_C_beta = 0.8 Reaction: => C; M2, T, F_beta, Rate Law: compartment*a_C_M2*M2*T/(M2*T+e_C_M2)*(a_C_beta+e_C_beta*(1-a_C_beta)/(F_beta+e_C_beta))
S = 3.0E7 Reaction: => C, Rate Law: compartment*S
a_gamma_C = 1.02E-4 Reaction: => F_gamma; C, Rate Law: compartment*a_gamma_C*C

States:

Name Description
T [neoplastic cell]
F gamma [Interferon gamma]
M1 [MHC class I protein complex]
M2 [MHC class II protein complex]
C [cytotoxic T cell]
F beta [Transforming Growth Factor-Beta Superfamily]

Observables: none

Predicting Outcomes of Prostate Cancer Immunotherapyby Personalized Mathematical Models Natalie Kronik1¤, Yuri Kogan1,…

Glioblastoma (GBM), a highly aggressive (WHO grade IV) primary brain tumor, is refractory to traditional treatments, such as surgery, radiation or chemotherapy. This study aims at aiding in the design of more efficacious GBM therapies. We constructed a mathematical model for glioma and the immune system interactions, that may ensue upon direct intra-tumoral administration of ex vivo activated alloreactive cytotoxic-T-lymphocytes (aCTL). Our model encompasses considerations of the interactive dynamics of aCTL, tumor cells, major histocompatibility complex (MHC) class I and MHC class II molecules, as well as cytokines, such as TGF-beta and IFN-gamma, which dampen or increase the pro-inflammatory environment, respectively. Computer simulations were used for model verification and for retrieving putative treatment scenarios. The mathematical model successfully retrieved clinical trial results of efficacious aCTL immunotherapy for recurrent anaplastic oligodendroglioma and anaplastic astrocytoma (WHO grade III). It predicted that cellular adoptive immunotherapy failed in GBM because the administered dose was 20-fold lower than required for therapeutic efficacy. Model analysis suggests that GBM may be eradicated by new dose-intensive strategies, e.g., 3 x 10(8) aCTL every 4 days for small tumor burden, or 2 x 10(9) aCTL, infused every 5 days for larger tumor burden. Further analysis pinpoints crucial bio-markers relating to tumor growth rate, tumor size, and tumor sensitivity to the immune system, whose estimation enables regimen personalization. We propose that adoptive cellular immunotherapy was prematurely abandoned. It may prove efficacious for GBM, if dose intensity is augmented, as prescribed by the mathematical model. Re-initiation of clinical trials, using calculated individualized regimens for grade III-IV malignant glioma, is suggested. link: http://identifiers.org/pubmed/17823798

Parameters: none

States: none

Observables: none

MODEL1204060000 @ v0.0.1

This model is from the article: Temporal Coding of Insulin Action through Multiplexing of the AKT Pathway. Kubota H,…

One of the unique characteristics of cellular signaling pathways is that a common signaling pathway can selectively regulate multiple cellular functions of a hormone; however, this selective downstream control through a common signaling pathway is poorly understood. Here we show that the insulin-dependent AKT pathway uses temporal patterns multiplexing for selective regulation of downstream molecules. Pulse and sustained insulin stimulations were simultaneously encoded into transient and sustained AKT phosphorylation, respectively. The downstream molecules, including ribosomal protein S6 kinase (S6K), glucose-6-phosphatase (G6Pase), and glycogen synthase kinase-3β (GSK3β) selectively decoded transient, sustained, and both transient and sustained AKT phosphorylation, respectively. Selective downstream decoding is mediated by the molecules' network structures and kinetics. Our results demonstrate that the AKT pathway can multiplex distinct patterns of blood insulin, such as pulse-like additional and sustained-like basal secretions, and the downstream molecules selectively decode secretion patterns of insulin. link: http://identifiers.org/pubmed/22633957

Parameters: none

States: none

Observables: none

Kuepfer2005 - Genome-scale metabolic network of Saccharomyces cerevisiae (iLL672)This model is described in the article:…

The roles of duplicate genes and their contribution to the phenomenon of enzyme dispensability are a central issue in molecular and genome evolution. A comprehensive classification of the mechanisms that may have led to their preservation, however, is currently lacking. In a systems biology approach, we classify here back-up, regulatory, and gene dosage functions for the 105 duplicate gene families of Saccharomyces cerevisiae metabolism. The key tool was the reconciled genome-scale metabolic model iLL672, which was based on the older iFF708. Computational predictions of all metabolic gene knockouts were validated with the experimentally determined phenotypes of the entire singleton yeast library of 4658 mutants under five environmental conditions. iLL672 correctly identified 96%-98% and 73%-80% of the viable and lethal singleton phenotypes, respectively. Functional roles for each duplicate family were identified by integrating the iLL672-predicted in silico duplicate knockout phenotypes, genome-scale carbon-flux distributions, singleton mutant phenotypes, and network topology analysis. The results provide no evidence for a particular dominant function that maintains duplicate genes in the genome. In particular, the back-up function is not favored by evolutionary selection because duplicates do not occur more frequently in essential reactions than singleton genes. Instead of a prevailing role, multigene-encoded enzymes cover different functions. Thus, at least for metabolism, persistence of the paralog fraction in the genome can be better explained with an array of different, often overlapping functional roles. link: http://identifiers.org/pubmed/16204195

Parameters: none

States: none

Observables: none

MODEL1109150000 @ v0.0.1

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

A mathematical model of the extrinsic or tissue factor (TF) pathway of blood coagulation is formulated and results from a computational study of its behavior are presented. The model takes into account plasma-phase and surface-bound enzymes and zymogens, coagulation inhibitors, and activated and unactivated platelets. It includes both plasma-phase and membrane-phase reactions, and accounts for chemical and cellular transport by flow and diffusion, albeit in a simplified manner by assuming the existence of a thin, well-mixed fluid layer, near the surface, whose thickness depends on flow. There are three main conclusions from these studies. (i) The model system responds in a threshold manner to changes in the availability of particular surface binding sites; an increase in TF binding sites, as would occur with vascular injury, changes the system's production of thrombin dramatically. (ii) The model suggests that platelets adhering to and covering the subendothelium, rather than chemical inhibitors, may play the dominant role in blocking the activity of the TF:VIIa enzyme complex. This, in turn, suggests that a role of the IXa-tenase pathway for activating factor X to Xa is to continue factor Xa production after platelets have covered the TF:VIIa complexes on the subendothelium. (iii) The model gives a kinetic explanation of the reduced thrombin production in hemophilias A and B. link: http://identifiers.org/pubmed/11222273

Parameters: none

States: none

Observables: none

BIOMD0000000235 @ v0.0.1

This a model from the article: Monte Carlo analysis of an ODE Model of the Sea Urchin Endomesoderm Network. Kühn C,…

BACKGROUND: Gene Regulatory Networks (GRNs) control the differentiation, specification and function of cells at the genomic level. The levels of interactions within large GRNs are of enormous depth and complexity. Details about many GRNs are emerging, but in most cases it is unknown to what extent they control a given process, i.e. the grade of completeness is uncertain. This uncertainty stems from limited experimental data, which is the main bottleneck for creating detailed dynamical models of cellular processes. Parameter estimation for each node is often infeasible for very large GRNs. We propose a method, based on random parameter estimations through Monte-Carlo simulations to measure completeness grades of GRNs. RESULTS: We developed a heuristic to assess the completeness of large GRNs, using ODE simulations under different conditions and randomly sampled parameter sets to detect parameter-invariant effects of perturbations. To test this heuristic, we constructed the first ODE model of the whole sea urchin endomesoderm GRN, one of the best studied large GRNs. We find that nearly 48% of the parameter-invariant effects correspond with experimental data, which is 65% of the expected optimal agreement obtained from a submodel for which kinetic parameters were estimated and used for simulations. Randomized versions of the model reproduce only 23.5% of the experimental data. CONCLUSION: The method described in this paper enables an evaluation of network topologies of GRNs without requiring any parameter values. The benefit of this method is exemplified in the first mathematical analysis of the complete Endomesoderm Network Model. The predictions we provide deliver candidate nodes in the network that are likely to be erroneous or miss unknown connections, which may need additional experiments to improve the network topology. This mathematical model can serve as a scaffold for detailed and more realistic models. We propose that our method can be used to assess a completeness grade of any GRN. This could be especially useful for GRNs involved in human diseases, where often the amount of connectivity is unknown and/or many genes/interactions are missing. link: http://identifiers.org/pubmed/19698179

Parameters:

Name Description
P_dissociation_k=0.0514508771131 Reaction: PROTEIN_M_SuHN => PROTEIN_M_Notch2 + PROTEIN_M_SuH, Rate Law: P_dissociation_k*PROTEIN_M_SuHN
c_PROTEIN_Bra=1.0; k_PROTEIN_Bra=1.0 Reaction: GENE_M_Kakapo => mRNA_M_Kakapo; PROTEIN_M_Bra, PROTEIN_E_Bra, Rate Law: k_PROTEIN_Bra*PROTEIN_M_Bra/(c_PROTEIN_Bra+PROTEIN_M_Bra)+k_PROTEIN_Bra*PROTEIN_E_Bra/(c_PROTEIN_Bra+PROTEIN_E_Bra)
k_PROTEIN_Hox=1.0; c_PROTEIN_Bra=1.0; c_PROTEIN_Hox=1.0; k_PROTEIN_Bra=1.0 Reaction: GENE_M_OrCt => mRNA_M_OrCt; PROTEIN_M_Bra, PROTEIN_E_Bra, PROTEIN_M_Hox, Rate Law: (k_PROTEIN_Bra*PROTEIN_M_Bra/(c_PROTEIN_Bra+PROTEIN_M_Bra)+k_PROTEIN_Bra*PROTEIN_E_Bra/(c_PROTEIN_Bra+PROTEIN_E_Bra))*k_PROTEIN_Hox*c_PROTEIN_Hox/(c_PROTEIN_Hox+PROTEIN_M_Hox)
c_PROTEIN_Ets1=1.0; c_PROTEIN_TBr=1.0; k_PROTEIN_Hex=1.0; k_PROTEIN_TBr=1.0; k_PROTEIN_Ets1=1.0; c_PROTEIN_Hex=1.0 Reaction: GENE_P_Erg => mRNA_P_Erg; PROTEIN_P_TBr, PROTEIN_P_Ets1, PROTEIN_P_Hex, Rate Law: k_PROTEIN_TBr*PROTEIN_P_TBr/(c_PROTEIN_TBr+PROTEIN_P_TBr)+k_PROTEIN_Ets1*PROTEIN_P_Ets1/(c_PROTEIN_Ets1+PROTEIN_P_Ets1)+k_PROTEIN_Hex*PROTEIN_P_Hex/(c_PROTEIN_Hex+PROTEIN_P_Hex)
k_PROTEIN_Erg=1.0; c_PROTEIN_Tgif=1.0; c_PROTEIN_Ets1=1.0; k_PROTEIN_Hex=1.0; c_PROTEIN_Erg=1.0; k_PROTEIN_Ets1=1.0; c_PROTEIN_Hex=1.0; k_PROTEIN_Tgif=1.0 Reaction: GENE_M_Tgif => mRNA_M_Tgif; PROTEIN_M_Tgif, PROTEIN_M_Ets1, PROTEIN_M_Erg, PROTEIN_M_Hex, Rate Law: k_PROTEIN_Tgif*PROTEIN_M_Tgif/(c_PROTEIN_Tgif+PROTEIN_M_Tgif)+k_PROTEIN_Ets1*PROTEIN_M_Ets1/(c_PROTEIN_Ets1+PROTEIN_M_Ets1)+k_PROTEIN_Erg*PROTEIN_M_Erg/(c_PROTEIN_Erg+PROTEIN_M_Erg)+k_PROTEIN_Hex*PROTEIN_M_Hex/(c_PROTEIN_Hex+PROTEIN_M_Hex)
c_PROTEIN_GataE=1.0; k_PROTEIN_GataE=1.0 Reaction: GENE_M_Not => mRNA_M_Not; PROTEIN_M_GataE, Rate Law: k_PROTEIN_GataE*PROTEIN_M_GataE/(c_PROTEIN_GataE+PROTEIN_M_GataE)
P_association_k=0.727292522645 Reaction: PROTEIN_E_Notch2 + PROTEIN_E_SuH => PROTEIN_E_SuHN, Rate Law: P_association_k*PROTEIN_E_Notch2*PROTEIN_E_SuH
c_PROTEIN_Hnf6=1.0; k_PROTEIN_nBTCF=1.0; c_PROTEIN_nBTCF=1.0; c_PROTEIN_GroTCF=1.0; k_PROTEIN_GroTCF=1.0; k_PROTEIN_Hnf6=1.0 Reaction: GENE_M_z13 => mRNA_M_z13; PROTEIN_M_nBTCF, PROTEIN_M_GroTCF, PROTEIN_M_Hnf6, Rate Law: k_PROTEIN_nBTCF*PROTEIN_M_nBTCF/(c_PROTEIN_nBTCF+PROTEIN_M_nBTCF)*k_PROTEIN_GroTCF*c_PROTEIN_GroTCF/(c_PROTEIN_GroTCF+PROTEIN_M_GroTCF)*k_PROTEIN_Hnf6*c_PROTEIN_Hnf6/(c_PROTEIN_Hnf6+PROTEIN_M_Hnf6)
P_activation_k=0.683876854591 Reaction: PROTEIN_M_Notch2 => PROTEIN_M_Notch; PROTEIN_M_Delta2, Rate Law: PROTEIN_M_Notch2*PROTEIN_M_Delta2*P_activation_k
k_PROTEIN_SuHN=1.0; c_PROTEIN_Gcm=1.0; c_PROTEIN_nBTCF=1.0; k_PROTEIN_Alx1=1.0; c_PROTEIN_GroTCF=1.0; c_PROTEIN_SuHN=1.0; k_PROTEIN_GroTCF=1.0; k_PROTEIN_Gcm=1.0; k_PROTEIN_FoxA=1.0; k_PROTEIN_nBTCF=1.0; c_PROTEIN_Alx1=1.0; c_PROTEIN_FoxA=1.0 Reaction: GENE_M_Gcm => mRNA_M_Gcm; PROTEIN_M_nBTCF, PROTEIN_M_SuHN, PROTEIN_M_Gcm, PROTEIN_M_GroTCF, PROTEIN_M_FoxA, PROTEIN_M_Alx1, Rate Law: (k_PROTEIN_nBTCF*PROTEIN_M_nBTCF/(c_PROTEIN_nBTCF+PROTEIN_M_nBTCF)+k_PROTEIN_SuHN*PROTEIN_M_SuHN/(c_PROTEIN_SuHN+PROTEIN_M_SuHN)+k_PROTEIN_Gcm*PROTEIN_M_Gcm/(c_PROTEIN_Gcm+PROTEIN_M_Gcm))*k_PROTEIN_GroTCF*c_PROTEIN_GroTCF/(c_PROTEIN_GroTCF+PROTEIN_M_GroTCF)*k_PROTEIN_FoxA*c_PROTEIN_FoxA/(c_PROTEIN_FoxA+PROTEIN_M_FoxA)*k_PROTEIN_Alx1*c_PROTEIN_Alx1/(c_PROTEIN_Alx1+PROTEIN_M_Alx1)
c_PROTEIN_UbiqSoxC=1.0; k_PROTEIN_HesC=1.0; c_PROTEIN_SoxC=1.0; k_PROTEIN_SoxC=1.0; c_PROTEIN_HesC=1.0; k_PROTEIN_UbiqSoxC=1.0 Reaction: GENE_M_SoxC => mRNA_M_SoxC; PROTEIN_M_UbiqSoxC, PROTEIN_M_HesC, PROTEIN_M_SoxC, Rate Law: k_PROTEIN_UbiqSoxC*PROTEIN_M_UbiqSoxC/(c_PROTEIN_UbiqSoxC+PROTEIN_M_UbiqSoxC)*k_PROTEIN_HesC*c_PROTEIN_HesC/(c_PROTEIN_HesC+PROTEIN_M_HesC)*k_PROTEIN_SoxC*c_PROTEIN_SoxC/(c_PROTEIN_SoxC+PROTEIN_M_SoxC)
P_L1_HillK=10.0; P_L1_HillH=8.0; P_L1_theta2=30.0; P_L1_theta1=21.0; P_L1_S1 = 0.0; P_L1_S2 = 1.0 Reaction: PRE_P_L1 => mRNA_P_L1, Rate Law: P_L1_S1*P_L1_HillK*time^P_L1_HillH/(P_L1_theta1^P_L1_HillH+time^P_L1_HillH)+P_L1_S2*P_L1_HillK*(1-time^P_L1_HillH/(P_L1_theta2^P_L1_HillH+time^P_L1_HillH))
c_PROTEIN_Alx1=1.0; c_PROTEIN_Dri=1.0; c_PROTEIN_Ets1=1.0; k_PROTEIN_Alx1=1.0; k_PROTEIN_Hex=1.0; k_PROTEIN_Dri=1.0; k_PROTEIN_Ets1=1.0; c_PROTEIN_Hex=1.0 Reaction: GENE_M_VEGFR => mRNA_M_VEGFR; PROTEIN_M_Alx1, PROTEIN_M_Dri, PROTEIN_M_Ets1, PROTEIN_M_Hex, Rate Law: k_PROTEIN_Alx1*PROTEIN_M_Alx1/(c_PROTEIN_Alx1+PROTEIN_M_Alx1)+k_PROTEIN_Dri*PROTEIN_M_Dri/(c_PROTEIN_Dri+PROTEIN_M_Dri)+k_PROTEIN_Ets1*PROTEIN_M_Ets1/(c_PROTEIN_Ets1+PROTEIN_M_Ets1)+k_PROTEIN_Hex*PROTEIN_M_Hex/(c_PROTEIN_Hex+PROTEIN_M_Hex)
P_protein_deg=0.3 Reaction: PROTEIN_M_Gelsolin => none; none, Rate Law: P_protein_deg*PROTEIN_M_Gelsolin
k_PROTEIN_Hex=1.0; c_PROTEIN_Hex=1.0 Reaction: GENE_M_Snail => mRNA_M_Snail; PROTEIN_M_Hex, Rate Law: k_PROTEIN_Hex*PROTEIN_M_Hex/(c_PROTEIN_Hex+PROTEIN_M_Hex)
k_PROTEIN_Otx=1.0; c_PROTEIN_GataE=1.0; c_PROTEIN_Otx=1.0; k_PROTEIN_GataE=1.0 Reaction: GENE_P_Lim => mRNA_P_Lim; PROTEIN_P_GataE, PROTEIN_P_Otx, Rate Law: k_PROTEIN_GataE*PROTEIN_P_GataE/(c_PROTEIN_GataE+PROTEIN_P_GataE)+k_PROTEIN_Otx*PROTEIN_P_Otx/(c_PROTEIN_Otx+PROTEIN_P_Otx)
P_Gcad_HillK=10.0; P_Gcad_S1 = 1.0; P_Gcad_HillH=8.0; P_Gcad_theta1=1.0; P_Gcad_theta2=20.0; P_Gcad_S2 = 0.0 Reaction: PRE_P_Gcad => mRNA_P_Gcad, Rate Law: P_Gcad_S1*P_Gcad_HillK*time^P_Gcad_HillH/(P_Gcad_theta1^P_Gcad_HillH+time^P_Gcad_HillH)+P_Gcad_S2*P_Gcad_HillK*(1-time^P_Gcad_HillH/(P_Gcad_theta2^P_Gcad_HillH+time^P_Gcad_HillH))
P_mRNA_deg=0.119 Reaction: mRNA_P_HesC => none; none, Rate Law: P_mRNA_deg*mRNA_P_HesC
c_PROTEIN_UbiqHnf6=1.0; k_PROTEIN_UbiqHnf6=1.0 Reaction: GENE_M_Hnf6 => mRNA_M_Hnf6; PROTEIN_M_UbiqHnf6, Rate Law: k_PROTEIN_UbiqHnf6*PROTEIN_M_UbiqHnf6/(c_PROTEIN_UbiqHnf6+PROTEIN_M_UbiqHnf6)
c_PROTEIN_Alx1=1.0; c_PROTEIN_Ets1=1.0; k_PROTEIN_Alx1=1.0; k_PROTEIN_Ets1=1.0 Reaction: GENE_P_Dri => mRNA_P_Dri; PROTEIN_P_Alx1, PROTEIN_P_Ets1, Rate Law: k_PROTEIN_Alx1*PROTEIN_P_Alx1/(c_PROTEIN_Alx1+PROTEIN_P_Alx1)+k_PROTEIN_Ets1*PROTEIN_P_Ets1/(c_PROTEIN_Ets1+PROTEIN_P_Ets1)
c_PROTEIN_GroTFC=1.0; c_PROTEIN_nBTCF=1.0; c_PROTEIN_Otx=1.0; k_PROTEIN_Tgif=1.0; k_PROTEIN_FoxA=1.0; k_PROTEIN_nBTCF=1.0; c_PROTEIN_Bra=1.0; k_PROTEIN_Otx=1.0; c_PROTEIN_Tgif=1.0; k_PROTEIN_GroTFC=1.0; c_PROTEIN_FoxA=1.0; k_PROTEIN_Bra=1.0; c_PROTEIN_GataE=1.0; k_PROTEIN_GataE=1.0 Reaction: GENE_P_FoxA => mRNA_P_FoxA; PROTEIN_P_GataE, PROTEIN_P_nBTCF, PROTEIN_P_Otx, PROTEIN_P_Bra, PROTEIN_P_Tgif, PROTEIN_P_GroTFC, PROTEIN_P_FoxA, Rate Law: (k_PROTEIN_GataE*PROTEIN_P_GataE/(c_PROTEIN_GataE+PROTEIN_P_GataE)+k_PROTEIN_nBTCF*PROTEIN_P_nBTCF/(c_PROTEIN_nBTCF+PROTEIN_P_nBTCF)+k_PROTEIN_Otx*PROTEIN_P_Otx/(c_PROTEIN_Otx+PROTEIN_P_Otx)+k_PROTEIN_Bra*PROTEIN_P_Bra/(c_PROTEIN_Bra+PROTEIN_P_Bra)+k_PROTEIN_Tgif*PROTEIN_P_Tgif/(c_PROTEIN_Tgif+PROTEIN_P_Tgif))*k_PROTEIN_GroTFC*c_PROTEIN_GroTFC/(c_PROTEIN_GroTFC+PROTEIN_P_GroTFC)*k_PROTEIN_FoxA*c_PROTEIN_FoxA/(c_PROTEIN_FoxA+PROTEIN_P_FoxA)
k_PROTEIN_UMANrl=1.0; c_PROTEIN_FoxN23=1.0; c_PROTEIN_HesC=1.0; k_PROTEIN_TBr=1.0; k_PROTEIN_Tgif=1.0; k_PROTEIN_HesC=1.0; c_PROTEIN_Bra=1.0; k_PROTEIN_FoxN23=1.0; c_PROTEIN_Tgif=1.0; c_PROTEIN_TBr=1.0; c_PROTEIN_UMANrl=1.0; k_PROTEIN_Bra=1.0; c_PROTEIN_GataE=1.0; k_PROTEIN_GataE=1.0 Reaction: GENE_M_Nrl => mRNA_M_Nrl; PROTEIN_M_TBr, PROTEIN_M_UMANrl, PROTEIN_M_FoxN23, PROTEIN_M_GataE, PROTEIN_M_HesC, PROTEIN_E_Bra, PROTEIN_M_Tgif, Rate Law: (k_PROTEIN_TBr*PROTEIN_M_TBr/(c_PROTEIN_TBr+PROTEIN_M_TBr)+k_PROTEIN_UMANrl*PROTEIN_M_UMANrl/(c_PROTEIN_UMANrl+PROTEIN_M_UMANrl)+k_PROTEIN_FoxN23*PROTEIN_M_FoxN23/(c_PROTEIN_FoxN23+PROTEIN_M_FoxN23))*k_PROTEIN_GataE*c_PROTEIN_GataE/(c_PROTEIN_GataE+PROTEIN_M_GataE)*k_PROTEIN_HesC*c_PROTEIN_HesC/(c_PROTEIN_HesC+PROTEIN_M_HesC)*k_PROTEIN_Bra*c_PROTEIN_Bra/(c_PROTEIN_Bra+PROTEIN_E_Bra)*k_PROTEIN_Tgif*c_PROTEIN_Tgif/(c_PROTEIN_Tgif+PROTEIN_M_Tgif)
c_PROTEIN_Pmar1=1.0; c_PROTEIN_UbiqHesC=1.0; k_PROTEIN_Pmar1=1.0; k_PROTEIN_UbiqHesC=1.0 Reaction: GENE_M_HesC => mRNA_M_HesC; PROTEIN_M_UbiqHesC, PROTEIN_M_Pmar1, Rate Law: k_PROTEIN_UbiqHesC*PROTEIN_M_UbiqHesC/(c_PROTEIN_UbiqHesC+PROTEIN_M_UbiqHesC)*k_PROTEIN_Pmar1*c_PROTEIN_Pmar1/(c_PROTEIN_Pmar1+PROTEIN_M_Pmar1)
P_inactivation_k=0.567550841749 Reaction: PROTEIN_M_Notch => PROTEIN_M_Notch2, Rate Law: PROTEIN_M_Notch*P_inactivation_k
c_PROTEIN_Tel=1.0; c_PROTEIN_Hnf6=1.0; c_PROTEIN_Dri=1.0; k_PROTEIN_Alx1=1.0; c_PROTEIN_VEGFSignal=1.0; k_PROTEIN_Hex=1.0; k_PROTEIN_Dri=1.0; k_PROTEIN_Tel=1.0; k_PROTEIN_Ets1=1.0; c_PROTEIN_Hex=1.0; k_PROTEIN_Hnf6=1.0; k_PROTEIN_VEGFSignal=1.0; c_PROTEIN_Alx1=1.0; k_PROTEIN_Erg=1.0; c_PROTEIN_Ets1=1.0; c_PROTEIN_Erg=1.0 Reaction: GENE_M_Sm50 => mRNA_M_Sm50; PROTEIN_M_Dri, PROTEIN_M_Hnf6, PROTEIN_M_Ets1, PROTEIN_M_Alx1, PROTEIN_M_Tel, PROTEIN_M_Hex, PROTEIN_M_Erg, PROTEIN_M_VEGFSignal, Rate Law: k_PROTEIN_Dri*PROTEIN_M_Dri/(c_PROTEIN_Dri+PROTEIN_M_Dri)+k_PROTEIN_Hnf6*PROTEIN_M_Hnf6/(c_PROTEIN_Hnf6+PROTEIN_M_Hnf6)+k_PROTEIN_Ets1*PROTEIN_M_Ets1/(c_PROTEIN_Ets1+PROTEIN_M_Ets1)+k_PROTEIN_Alx1*PROTEIN_M_Alx1/(c_PROTEIN_Alx1+PROTEIN_M_Alx1)+k_PROTEIN_Tel*PROTEIN_M_Tel/(c_PROTEIN_Tel+PROTEIN_M_Tel)+k_PROTEIN_Hex*PROTEIN_M_Hex/(c_PROTEIN_Hex+PROTEIN_M_Hex)+k_PROTEIN_Erg*PROTEIN_M_Erg/(c_PROTEIN_Erg+PROTEIN_M_Erg)+k_PROTEIN_VEGFSignal*PROTEIN_M_VEGFSignal/(c_PROTEIN_VEGFSignal+PROTEIN_M_VEGFSignal)
c_PROTEIN_Hnf6=1.0; k_PROTEIN_Alx1=1.0; k_PROTEIN_Hex=1.0; c_PROTEIN_FoxB=1.0; k_PROTEIN_TBr=1.0; k_PROTEIN_Ets1=1.0; k_PROTEIN_FoxB=1.0; c_PROTEIN_Hex=1.0; k_PROTEIN_Hnf6=1.0; c_PROTEIN_Alx1=1.0; k_PROTEIN_Erg=1.0; c_PROTEIN_Ets1=1.0; c_PROTEIN_TBr=1.0; c_PROTEIN_Erg=1.0 Reaction: GENE_M_Msp130 => mRNA_M_Msp130; PROTEIN_M_Hnf6, PROTEIN_M_FoxB, PROTEIN_M_Ets1, PROTEIN_M_Alx1, PROTEIN_M_Hex, PROTEIN_M_TBr, PROTEIN_M_Erg, Rate Law: k_PROTEIN_Hnf6*PROTEIN_M_Hnf6/(c_PROTEIN_Hnf6+PROTEIN_M_Hnf6)+k_PROTEIN_FoxB*PROTEIN_M_FoxB/(c_PROTEIN_FoxB+PROTEIN_M_FoxB)+k_PROTEIN_Ets1*PROTEIN_M_Ets1/(c_PROTEIN_Ets1+PROTEIN_M_Ets1)+k_PROTEIN_Alx1*PROTEIN_M_Alx1/(c_PROTEIN_Alx1+PROTEIN_M_Alx1)+k_PROTEIN_Hex*PROTEIN_M_Hex/(c_PROTEIN_Hex+PROTEIN_M_Hex)+k_PROTEIN_TBr*PROTEIN_M_TBr/(c_PROTEIN_TBr+PROTEIN_M_TBr)+k_PROTEIN_Erg*PROTEIN_M_Erg/(c_PROTEIN_Erg+PROTEIN_M_Erg)
P_k_translation=2.0 Reaction: none => PROTEIN_M_Gelsolin; mRNA_M_Gelsolin, Rate Law: P_k_translation*mRNA_M_Gelsolin
P_association_k=0.711358710507 Reaction: PROTEIN_M_Gro + PROTEIN_M_TCF => PROTEIN_M_GroTCF, Rate Law: P_association_k*PROTEIN_M_Gro*PROTEIN_M_TCF
c_PROTEIN_UbiqGcad=1.0; c_PROTEIN_Snail=1.0; k_PROTEIN_Snail=1.0; k_PROTEIN_UbiqGcad=1.0 Reaction: GENE_P_Gcad => mRNA_P_Gcad; PROTEIN_P_UbiqGcad, PROTEIN_P_Snail, Rate Law: k_PROTEIN_UbiqGcad*PROTEIN_P_UbiqGcad/(c_PROTEIN_UbiqGcad+PROTEIN_P_UbiqGcad)*k_PROTEIN_Snail*c_PROTEIN_Snail/(c_PROTEIN_Snail+PROTEIN_P_Snail)

States:

Name Description
GENE P Erg [NP_999833]
PROTEIN E Sm30 [AAA30070]
PROTEIN E SoxB1 [NP_999639]
GENE M Not GENE_M_Not
GENE P FoxA [578584]
mRNA P Gcad [G-cadherin]
PROTEIN E SuHN [575174]
GENE M Tgif [NP_001009815]
mRNA P Hnf6 [AAQ81630]
PROTEIN E SuH [575174]
GENE M Nrl [753578]
PROTEIN M Hnf6 [AAQ81630]
PROTEIN E Pks [NP_001239013]
GENE M SoxC [AAD40687]
PROTEIN M Sm27 [3914393]
PROTEIN M Pmar1 [AAL38537]
PROTEIN P Notch [XP_797451]
GENE M Snail [NP_999825]
PROTEIN M SoxB1 [NP_999639]
PROTEIN E Nrl [753578]
none none
PROTEIN M Msp130 [373282]
PROTEIN E SoxC [AAD40687]
PROTEIN M HesC [Hairy enhancer of split]
PROTEIN M Pks [NP_001239013]
PROTEIN M Gro PROTEIN_M_Gro
GENE M Gcm [NP_999826]
PROTEIN E Snail [NP_999825]
GENE M Msp130 [373282]
GENE P Dri [373505]
PROTEIN M Nrl [753578]
PROTEIN M MspL PROTEIN_M_MspL
GENE M Sm50 [NP_999775]
PROTEIN E OrCt [XP_003731785]
mRNA P Hex [100892136]
GENE M z13 [Zinc finger and BTB domain-containing protein 17]
GENE M Hnf6 [AAQ81630]
PROTEIN E Sm50 [NP_999775]
GENE M HesC [Hairy enhancer of split]
mRNA P Gelsolin [ABY58156]
mRNA P L1 mRNA_P_L1
PROTEIN M Gelsolin [ABY58156]
PROTEIN P Notch2 [XP_797451]
mRNA P HesC [Hairy enhancer of split]
PROTEIN M Hex [100892136]
GENE M OrCt [XP_003731785]
GENE M VEGFR [Vascular endothelial growth factor receptor 1]
PROTEIN M Notch2 [XP_797451]
mRNA P Lim [373522]
PROTEIN E Pmar1 [AAL38537]
PROTEIN M Snail [NP_999825]
PROTEIN E Otx [AAB33568]
GENE M Kakapo [765824]
PROTEIN M Notch [XP_797451]
mRNA P Msp130 [373282]

Observables: none

Kumar2011 - Genome-scale metabolic network of Methanosarcina acetivorans (iVS941)This model is described in the article:…

BACKGROUND: Methanogens are ancient organisms that are key players in the carbon cycle accounting for about one billion tones of biological methane produced annually. Methanosarcina acetivorans, with a genome size of ~5.7 mb, is the largest sequenced archaeon methanogen and unique amongst the methanogens in its biochemical characteristics. By following a systematic workflow we reconstruct a genome-scale metabolic model for M. acetivorans. This process relies on previously developed computational tools developed in our group to correct growth prediction inconsistencies with in vivo data sets and rectify topological inconsistencies in the model. RESULTS: The generated model iVS941 accounts for 941 genes, 705 reactions and 708 metabolites. The model achieves 93.3% prediction agreement with in vivo growth data across different substrates and multiple gene deletions. The model also correctly recapitulates metabolic pathway usage patterns of M. acetivorans such as the indispensability of flux through methanogenesis for growth on acetate and methanol and the unique biochemical characteristics under growth on carbon monoxide. CONCLUSIONS: Based on the size of the genome-scale metabolic reconstruction and extent of validated predictions this model represents the most comprehensive up-to-date effort to catalogue methanogenic metabolism. The reconstructed model is available in spreadsheet and SBML formats to enable dissemination. link: http://identifiers.org/pubmed/21324125

Parameters: none

States: none

Observables: none

Kummer2000 - Oscillations in Calcium SignallingSimplified (3-variable) calcium oscillation model Kummer et al. (2000) B…

We present a new model for calcium oscillations based on experiments in hepatocytes. The model considers feedback inhibition on the initial agonist receptor complex by calcium and activated phospholipase C, as well as receptor type-dependent self-enhanced behavior of the activated G(alpha) subunit. It is able to show simple periodic oscillations and periodic bursting, and it is the first model to display chaotic bursting in response to agonist stimulations. Moreover, our model offers a possible explanation for the differences in dynamic behavior observed in response to different agonists in hepatocytes. link: http://identifiers.org/pubmed/10968983

Parameters:

Name Description
V=4.88; Km=1.18 Reaction: a => ; c, Rate Law: compartment*V*c*a/(Km+a)
V=1.52; Km=0.19 Reaction: a => ; b, Rate Law: compartment*V*b*a/(Km+a)
Km=29.09; V=32.24 Reaction: b =>, Rate Law: compartment*V*b/(Km+b)
V=153.0; Km=0.16 Reaction: c =>, Rate Law: compartment*V*c/(Km+c)
v=0.212 Reaction: => a, Rate Law: compartment*v
constant=1.24 Reaction: => b; a, Rate Law: compartment*constant*a
constant=2.9 Reaction: => a; a, Rate Law: compartment*constant*a
constant=13.58 Reaction: => c; a, Rate Law: compartment*constant*a

States:

Name Description
c [calcium(2+)]
b [1-phosphatidylinositol 4,5-bisphosphate phosphodiesterase beta-1]
a [Guanine nucleotide-binding protein subunit alpha-11]

Observables: none

MODEL0847712949 @ v0.0.1

This a model from the article: Dynamical description of sinoatrial node pacemaking: improved mathematical model for pr…

We developed an improved mathematical model for a single primary pacemaker cell of the rabbit sinoatrial node. Original features of our model include 1) incorporation of the sustained inward current (I(st)) recently identified in primary pacemaker cells, 2) reformulation of voltage- and Ca(2+)-dependent inactivation of the L-type Ca(2+) channel current (I(Ca,L)), 3) new expressions for activation kinetics of the rapidly activating delayed rectifier K(+) channel current (I(Kr)), and 4) incorporation of the subsarcolemmal space as a diffusion barrier for Ca(2+). We compared the simulated dynamics of our model with those of previous models, as well as with experimental data, and examined whether the models could accurately simulate the effects of modulating sarcolemmal ionic currents or intracellular Ca(2+) dynamics on pacemaker activity. Our model represents significant improvements over the previous models, because it can 1) simulate whole cell voltage-clamp data for I(Ca,L), I(Kr), and I(st); 2) reproduce the waveshapes of spontaneous action potentials and ionic currents during action potential clamp recordings; and 3) mimic the effects of channel blockers or Ca(2+) buffers on pacemaker activity more accurately than the previous models. link: http://identifiers.org/pubmed/12384487

Parameters: none

States: none

Observables: none

MODEL4780181279 @ v0.0.1

This model of sGC is based on the paper by [Kuroda S. et al. J Neurosci. (2001) 21(15):5693-702](http://www.ncbi.nlm.nih…

Because multiple molecular signal transduction pathways regulate cerebellar long-term depression (LTD), which is thought to be a possible molecular and cellular basis of cerebellar learning, the systematic relationship between cerebellar LTD and the currently known signal transduction pathways remains obscure. To address this issue, we built a new diagram of signal transduction pathways and developed a computational model of kinetic simulation for the phosphorylation of AMPA receptors, known as a key step for expressing cerebellar LTD. The phosphorylation of AMPA receptors in this model consists of an initial phase and an intermediate phase. We show that the initial phase is mediated by the activation of linear cascades of protein kinase C (PKC), whereas the intermediate phase is mediated by a mitogen-activated protein (MAP) kinase-dependent positive feedback loop pathway that is responsible for the transition from the transient phosphorylation of the AMPA receptors to the stable phosphorylation of the AMPA receptors. These phases are dually regulated by the PKC and protein phosphatase pathways. Both phases also require nitric oxide (NO), although NO per se does not show any ability to induce LTD; this is consistent with a permissive role as reported experimentally (Lev-Ram et al., 1997). Therefore, the kinetic simulation is a powerful tool for understanding and exploring the behaviors of complex signal transduction pathways involved in cerebellar LTD. link: http://identifiers.org/pubmed/11466441

Parameters: none

States: none

Observables: none

MODEL1004010000 @ v0.0.1

This the detailed model for 28°C from the article: Temperature Control of Fimbriation Circuit Switch in Uropathogenic…

Uropathogenic Escherichia coli (UPEC) represent the predominant cause of urinary tract infections (UTIs). A key UPEC molecular virulence mechanism is type 1 fimbriae, whose expression is controlled by the orientation of an invertible chromosomal DNA element-the fim switch. Temperature has been shown to act as a major regulator of fim switching behavior and is overall an important indicator as well as functional feature of many urologic diseases, including UPEC host-pathogen interaction dynamics. Given this panoptic physiological role of temperature during UTI progression and notable empirical challenges to its direct in vivo studies, in silico modeling of corresponding biochemical and biophysical mechanisms essential to UPEC pathogenicity may significantly aid our understanding of the underlying disease processes. However, rigorous computational analysis of biological systems, such as fim switch temperature control circuit, has hereto presented a notoriously demanding problem due to both the substantial complexity of the gene regulatory networks involved as well as their often characteristically discrete and stochastic dynamics. To address these issues, we have developed an approach that enables automated multiscale abstraction of biological system descriptions based on reaction kinetics. Implemented as a computational tool, this method has allowed us to efficiently analyze the modular organization and behavior of the E. coli fimbriation switch circuit at different temperature settings, thus facilitating new insights into this mode of UPEC molecular virulence regulation. In particular, our results suggest that, with respect to its role in shutting down fimbriae expression, the primary function of FimB recombinase may be to effect a controlled down-regulation (rather than increase) of the ON-to-OFF fim switching rate via temperature-dependent suppression of competing dynamics mediated by recombinase FimE. Our computational analysis further implies that this down-regulation mechanism could be particularly significant inside the host environment, thus potentially contributing further understanding toward the development of novel therapeutic approaches to UPEC-caused UTIs. link: http://identifiers.org/pubmed/20361050

Parameters: none

States: none

Observables: none

MODEL1004010001 @ v0.0.1

This the detailed model for 37°C from the article: Temperature Control of Fimbriation Circuit Switch in Uropathogenic…

Uropathogenic Escherichia coli (UPEC) represent the predominant cause of urinary tract infections (UTIs). A key UPEC molecular virulence mechanism is type 1 fimbriae, whose expression is controlled by the orientation of an invertible chromosomal DNA element-the fim switch. Temperature has been shown to act as a major regulator of fim switching behavior and is overall an important indicator as well as functional feature of many urologic diseases, including UPEC host-pathogen interaction dynamics. Given this panoptic physiological role of temperature during UTI progression and notable empirical challenges to its direct in vivo studies, in silico modeling of corresponding biochemical and biophysical mechanisms essential to UPEC pathogenicity may significantly aid our understanding of the underlying disease processes. However, rigorous computational analysis of biological systems, such as fim switch temperature control circuit, has hereto presented a notoriously demanding problem due to both the substantial complexity of the gene regulatory networks involved as well as their often characteristically discrete and stochastic dynamics. To address these issues, we have developed an approach that enables automated multiscale abstraction of biological system descriptions based on reaction kinetics. Implemented as a computational tool, this method has allowed us to efficiently analyze the modular organization and behavior of the E. coli fimbriation switch circuit at different temperature settings, thus facilitating new insights into this mode of UPEC molecular virulence regulation. In particular, our results suggest that, with respect to its role in shutting down fimbriae expression, the primary function of FimB recombinase may be to effect a controlled down-regulation (rather than increase) of the ON-to-OFF fim switching rate via temperature-dependent suppression of competing dynamics mediated by recombinase FimE. Our computational analysis further implies that this down-regulation mechanism could be particularly significant inside the host environment, thus potentially contributing further understanding toward the development of novel therapeutic approaches to UPEC-caused UTIs. link: http://identifiers.org/pubmed/20361050

Parameters: none

States: none

Observables: none

MODEL1004010002 @ v0.0.1

This the detailed model for 42°C from the article: Temperature Control of Fimbriation Circuit Switch in Uropathogenic…

Uropathogenic Escherichia coli (UPEC) represent the predominant cause of urinary tract infections (UTIs). A key UPEC molecular virulence mechanism is type 1 fimbriae, whose expression is controlled by the orientation of an invertible chromosomal DNA element-the fim switch. Temperature has been shown to act as a major regulator of fim switching behavior and is overall an important indicator as well as functional feature of many urologic diseases, including UPEC host-pathogen interaction dynamics. Given this panoptic physiological role of temperature during UTI progression and notable empirical challenges to its direct in vivo studies, in silico modeling of corresponding biochemical and biophysical mechanisms essential to UPEC pathogenicity may significantly aid our understanding of the underlying disease processes. However, rigorous computational analysis of biological systems, such as fim switch temperature control circuit, has hereto presented a notoriously demanding problem due to both the substantial complexity of the gene regulatory networks involved as well as their often characteristically discrete and stochastic dynamics. To address these issues, we have developed an approach that enables automated multiscale abstraction of biological system descriptions based on reaction kinetics. Implemented as a computational tool, this method has allowed us to efficiently analyze the modular organization and behavior of the E. coli fimbriation switch circuit at different temperature settings, thus facilitating new insights into this mode of UPEC molecular virulence regulation. In particular, our results suggest that, with respect to its role in shutting down fimbriae expression, the primary function of FimB recombinase may be to effect a controlled down-regulation (rather than increase) of the ON-to-OFF fim switching rate via temperature-dependent suppression of competing dynamics mediated by recombinase FimE. Our computational analysis further implies that this down-regulation mechanism could be particularly significant inside the host environment, thus potentially contributing further understanding toward the development of novel therapeutic approaches to UPEC-caused UTIs. link: http://identifiers.org/pubmed/20361050

Parameters: none

States: none

Observables: none

This mathematical model describes the response of cytotoxic T lymphocytes to the growth of an immunogenic tumor, with th…

We present a mathematical model of the cytotoxic T lymphocyte response to the growth of an immunogenic tumor. The model exhibits a number of phenomena that are seen in vivo, including immunostimulation of tumor growth, "sneaking through" of the tumor, and formation of a tumor "dormant state". The model is used to describe the kinetics of growth and regression of the B-lymphoma BCL1 in the spleen of mice. By comparing the model with experimental data, numerical estimates of parameters describing processes that cannot be measured in vivo are derived. Local and global bifurcations are calculated for realistic values of the parameters. For a large set of parameters we predict that the course of tumor growth and its clinical manifestation have a recurrent profile with a 3- to 4-month cycle, similar to patterns seen in certain leukemias. link: http://identifiers.org/pubmed/8186756

Parameters:

Name Description
p = 0.1245; g = 2.019E7 Reaction: => E; E, T, Rate Law: compartment*p*E*T/(g+T)
a = 0.18 Reaction: => T; T, Rate Law: compartment*a*T
m = 3.422E-10 Reaction: E => ; T, Rate Law: compartment*m*E*T
d = 0.0412 Reaction: E =>, Rate Law: compartment*d*E
s = 13000.0 Reaction: => E, Rate Law: compartment*s
n = 1.101E-7 Reaction: T => ; E, Rate Law: compartment*n*E*T
b = 2.0E-9; a = 0.18 Reaction: T => ; T, Rate Law: compartment*a*b*T^2

States:

Name Description
T [Neoplastic Cell]
E [effector T cell]

Observables: none

Kuznetsov2016(II) - α-syn aggregation kinetics in Parkinson'sThis theoretical model uses 2-step Finke-Watzky (FW) kineti…

The aim of this paper is to develop a minimal model describing events leading to the onset of Parkinson's disease (PD). The model accounts for α-synuclein (α-syn) production in the soma, transport toward the synapse, misfolding, and aggregation. The production and aggregation of polymeric α-syn is simulated using a minimalistic 2-step Finke-Watzky model. We utilized the developed model to analyze what changes in a healthy neuron are likely to lead to the onset of α-syn aggregation. We checked the effects of interruption of α-syn transport toward the synapse, entry of misfolded (infectious) α-syn into the somatic and synaptic compartments, increasing the rate of α-syn synthesis in the soma, and failure of α-syn degradation machinery. Our model suggests that failure of α-syn degradation machinery is probably the most likely cause for the onset of α-syn aggregation leading to PD. link: http://identifiers.org/pubmed/27211070

Parameters:

Name Description
TAh1 = 72000.0 Reaction: Asyn =>, Rate Law: default_compartment*Asyn*ln(2)/TAh1/default_compartment
Vsyn = 4.19E-15; nA = 2.91E-20 Reaction: => Asyn; As, Rate Law: default_compartment*nA*As/Vsyn/default_compartment
nA = 2.91E-20; Vs = 4.19E-15 Reaction: As =>, Rate Law: default_compartment*nA*As/Vs/default_compartment
qA = 4.17E-8 Reaction: => As, Rate Law: default_compartment*qA/default_compartment
k2 = 2.0E-9 Reaction: Asyn => ; Bsyn, Rate Law: default_compartment*k2*Asyn*Bsyn/default_compartment
QBsyn = 0.0 Reaction: => Bsyn, Rate Law: default_compartment*QBsyn/default_compartment
k1 = 3.0E-7 Reaction: As =>, Rate Law: default_compartment*k1*As/default_compartment
QBs = 0.0 Reaction: => Bs, Rate Law: default_compartment*QBs/default_compartment
TBh1 = 720000.0 Reaction: Bs =>, Rate Law: default_compartment*Bs*ln(2)/TBh1/default_compartment

States:

Name Description
Asyn [Alpha-synuclein]
Bsyn [Alpha-synuclein]
Bs [Alpha-synuclein]
As [Alpha-synuclein]

Observables: none

Kwang2003 - The influence of RKIP on the ERK signaling pathwayThis model is described in the article: [Mathematical Mod…

This paper investigates the influence of the Raf Kinase Inhibitor Pro- tein (RKIP) on the Extracellular signal Regulated Kinase (ERK) signaling pathway through mathematical modeling and simulation. Using nonlinear ordi- nary differential equations to represent biochemical reactions in the pathway, we suggest a technique for parameter estimation, utilizing time series data of proteins involved in the signaling pathway. The mathematical model allows the simulation the sensitivity of the ERK pathway to variations of initial RKIP and ERK-PP (phosphorylated ERK) concentrations along with time. Throughout the simulation study, we can qualitatively validate the proposed mathematical model compared with experimental results. link: http://identifiers.org/doi/10.1007/3-540-36481-1_11

Parameters:

Name Description
k8 = 0.071 Reaction: MEKPP_ERK => MEKPP + ERKPP, Rate Law: cytoplasm*k8*MEKPP_ERK
k10 = 0.00122 Reaction: RKIPP_RP => RP + RKIPP, Rate Law: cytoplasm*k10*RKIPP_RP
k4 = 0.00245 Reaction: Raf1_RKIP_ERKPP => Raf1_RKIP + ERKPP, Rate Law: cytoplasm*k4*Raf1_RKIP_ERKPP
k6 = 0.8 Reaction: ERK + MEKPP => MEKPP_ERK, Rate Law: cytoplasm*k6*ERK*MEKPP
k2 = 0.0072 Reaction: Raf1_RKIP => Raf1 + RKIP, Rate Law: cytoplasm*k2*Raf1_RKIP
k1 = 0.53 Reaction: Raf1 + RKIP => Raf1_RKIP, Rate Law: cytoplasm*k1*Raf1*RKIP
k7 = 0.0075 Reaction: MEKPP_ERK => ERK + MEKPP, Rate Law: cytoplasm*k7*MEKPP_ERK
k5 = 0.0315 Reaction: Raf1_RKIP_ERKPP => Raf1 + ERK + RKIPP, Rate Law: cytoplasm*k5*Raf1_RKIP_ERKPP
k9 = 0.92 Reaction: RKIPP + RP => RKIPP_RP, Rate Law: cytoplasm*k9*RKIPP*RP
k3 = 0.625 Reaction: Raf1_RKIP + ERKPP => Raf1_RKIP_ERKPP, Rate Law: cytoplasm*k3*Raf1_RKIP*ERKPP
k11 = 0.87 Reaction: RKIPP_RP => RP + RKIP, Rate Law: cytoplasm*k11*RKIPP_RP

States:

Name Description
Raf1 RKIP ERKPP [Mitogen-activated protein kinase 3; RAF proto-oncogene serine/threonine-protein kinase; Raf Kinase Inhibitor; protein complex]
ERKPP [Mitogen-activated protein kinase 3]
RKIPP RP [Raf Kinase Inhibitor]
Raf1 RKIP [RAF proto-oncogene serine/threonine-protein kinase; Raf Kinase Inhibitor; protein complex]
Raf1 [RAF proto-oncogene serine/threonine-protein kinase]
RP [Phosphatase]
MEKPP [Dual specificity mitogen-activated protein kinase kinase 1]
MEKPP ERK [Mitogen-activated protein kinase 3; Dual specificity mitogen-activated protein kinase kinase 1; protein complex]
RKIP [Raf Kinase Inhibitor]
ERK [Mitogen-activated protein kinase 3]
RKIPP [Raf Kinase Inhibitor]

Observables: none

Kyrtsos2011 - A systems biology model for Alzheimer's disease (Cholesterol in AD)Encoded non-curated model. Issues: - C…

Alzheimer's disease (AD) is the most prevalent neurodegenerative disorder in the US, affecting over 1 in 8 people over the age of 65. There are several well-known pathological changes in the brains of AD patients, namely: the presence of diffuse beta amyloid plaques derived from the amyloid precursor protein (APP), hyper-phosphorylated tau protein, neuroinflammation and mitochondrial dysfunction. Recent studies have shown that cholesterol levels in both the plasma and the brain may play a role in disease pathogenesis, however, this exact role is not well understood. Additional proteins of interest have also been identified (ApoE, LRP-1, IL-1) as possible contributors to AD pathogenesis. To help understand these roles better, a systems biology mathematical model was developed. Basic principles from graph theory and control analysis were used to study the effect of altered cholesterol, ApoE, LRP and APP on the system as a whole. Negative feedback regulation and the rate of cholesterol transfer between astrocytes and neurons were identified as key modulators in the level of beta amyloid. Experiments were run concurrently to test whether decreasing plasma and brain cholesterol levels with simvastatin altered the expression levels of beta amyloid, ApoE, and LRP-1, to ascertain the edge directions in the network model and to better understand whether statin treatment served as a viable treatment option for AD patients. The work completed herein represents the first attempt to create a systems-level mathematical model to study AD that looks at intercellular interactions, as well as interactions between metabolic and inflammatory pathways. link: http://hdl.handle.net/1903/11919

Parameters: none

States: none

Observables: none

MODEL0478740924 @ v0.0.1

This a model from the article: Modeling robust oscillatory behavior of the hypothalamic-pituitary-adrenal axis. Kyry…

A mathematical model of the hypothalamic-pituitary-adrenal (HPA) axis of the human endocrine system is proposed. This new model provides an improvement over previous models by introducing two nonlinear factors with physiological relevance: 1) a limit to gland size; 2) rejection of negative hormone concentrations. The result is that the new model is by far the most robust; e.g., it can tolerate at least -50% and +100% perturbations to any of its parameters. This high degree of robustness allows one, for the first time, to model features of the system such as circadian rhythm and response to hormone injections. In addition, relative to its closest predecessor, the model is simpler; it contains only about half of the parameters, and yet achieves more functions. The new model provides opportunities for teaching endocrinology within a biological or medical school context; it may also have applications in modeling and studying HPA axis disorders, for example, related to gland size dynamics, abnormal hormone levels, or stress influences. link: http://identifiers.org/pubmed/16366221

Parameters: none

States: none

Observables: none

L


BIOMD0000000248 @ v0.0.1

This file describes the SBML version of the mathematical model in the following journal article: Linking Pulmonary Oxyge…

The energy demand imposed by physical exercise on the components of the oxygen transport and utilization system requires a close link between cellular and external respiration in order to maintain ATP homeostasis. Invasive and non-invasive experimental approaches have been used to elucidate mechanisms regulating the balance between oxygen supply and consumption during exercise. Such approaches suggest that the mechanism controlling the various subsystems coupling internal to external respiration are part of a highly redundant and hierarchical multi-scale system. In this work, we present a "systems biology" framework that integrates experimental and theoretical approaches able to provide simultaneously reliable information on the oxygen transport and utilization processes occurring at the various steps in the pathway of oxygen from air to mitochondria, particularly at the onset of exercise. This multi-disciplinary framework provides insights into the relationship between cellular oxygen consumption derived from measurements of muscle oxygenation during exercise and pulmonary oxygen uptake by indirect calorimetry. With a validated model, muscle oxygen dynamic responses is simulated and quantitatively related to cellular metabolism under a variety of conditions. link: http://identifiers.org/pubmed/17380394

Parameters:

Name Description
KMb = 308.642 permM; PSm = 5338.8 LperMin; Wmc = 0.8064 dimensionless; Km = 7.0E-4 mM; Vmax = 23.11702 mmol*(60*s)^(-1)*l^(-1); CmcMb = 0.5 mM; Kadp = 0.058 mM Reaction: CFtis = (PSm*(CFcap-CFtis)/Tissue-Vmax*CFtis/(Km+CFtis)*ADP/(Kadp+ADP))/(1+Wmc*CmcMb*KMb/(1+KMb*CFtis)^2), Rate Law: (PSm*(CFcap-CFtis)/Tissue-Vmax*CFtis/(Km+CFtis)*ADP/(Kadp+ADP))/(1+Wmc*CmcMb*KMb/(1+KMb*CFtis)^2)
Qm = 3.118 LperMin; CTart = 9.199981 mM Reaction: => CTcap, Rate Law: Qm*(CTart-CTcap)
Katpase = 0.3207601 perMin Reaction: ATP => ADP, Rate Law: Tissue*Katpase*ATP
Km = 7.0E-4 mM; Vmax = 23.11702 mmol*(60*s)^(-1)*l^(-1); Kadp = 0.058 mM Reaction: ADP + CTtis => ATP; Pi, CFtis, Rate Law: Tissue*Vmax*CFtis/(Km+CFtis)*ADP/(Kadp+ADP)
PSm = 5338.8 LperMin Reaction: CTcap => CTtis; CFcap, CFtis, Rate Law: PSm*(CFcap-CFtis)
PSm = 5338.8 LperMin; KHb = 7800.7 mM; CrbcHb = 5.18 mM; Qm = 3.118 LperMin; nH = 2.7 dimensionless; CTart = 9.199981 mM; Hct = 0.45 dimensionless Reaction: CFcap = (Qm*(CTart-CTcap)-PSm*(CFcap-CFtis))*1/Capillary/(1+4*Hct*CrbcHb*KHb*nH*CFcap^(nH-1)/(1+KHb*CFcap^nH)^2), Rate Law: (Qm*(CTart-CTcap)-PSm*(CFcap-CFtis))*1/Capillary/(1+4*Hct*CrbcHb*KHb*nH*CFcap^(nH-1)/(1+KHb*CFcap^nH)^2)
Kb = 1.11 mM; VrCK = 3008.65837589001 mmol*(60*s)^(-1)*l^(-1); Kp = 3.8 mM; Kia = 0.135 mM; Kib = 3.9 mM; VfCK = 6000.0 mmol*(60*s)^(-1)*l^(-1); Kiq = 3.5 mM Reaction: ADP + PCr => ATP + Cr, Rate Law: Tissue*(VfCK*ADP*PCr/(Kb*Kia)-VrCK*Cr*ATP/(Kiq*Kp))/((Kia+ADP)/Kia+ATP/Kiq+PCr/Kib+ADP*PCr/(Kb*Kia)+Cr*ATP/(Kiq*Kp))

States:

Name Description
PCr [N-phosphocreatine; Phosphocreatine]
Cr [creatine; Creatine]
ATP [ATP; ATP]
ADP [ADP; ADP]
CFtis [dioxygen; Oxygen]
CFcap [dioxygen; Oxygen]
CTcap [oxyhemoglobin; dioxygen; Oxyhemoglobin; Oxygen; hemoglobin complex]
CTtis [myoglobin; dioxygen; Myoglobin; Oxygen]

Observables: none

Lai2014 - Hemiconcerted MWC model of intact calmodulin with two targetsThis model is described in the article: [Modulat…

Calmodulin is a calcium-binding protein ubiquitous in eukaryotic cells, involved in numerous calcium-regulated biological phenomena, such as synaptic plasticity, muscle contraction, cell cycle, and circadian rhythms. It exibits a characteristic dumbell shape, with two globular domains (N- and C-terminal lobe) joined by a linker region. Each lobe can take alternative conformations, affected by the binding of calcium and target proteins. Calmodulin displays considerable functional flexibility due to its capability to bind different targets, often in a tissue-specific fashion. In various specific physiological environments (e.g. skeletal muscle, neuron dendritic spines) several targets compete for the same calmodulin pool, regulating its availability and affinity for calcium. In this work, we sought to understand the general principles underlying calmodulin modulation by different target proteins, and to account for simultaneous effects of multiple competing targets, thus enabling a more realistic simulation of calmodulin-dependent pathways. We built a mechanistic allosteric model of calmodulin, based on an hemiconcerted framework: each calmodulin lobe can exist in two conformations in thermodynamic equilibrium, with different affinities for calcium and different affinities for each target. Each lobe was allowed to switch conformation on its own. The model was parameterised and validated against experimental data from the literature. In spite of its simplicity, a two-state allosteric model was able to satisfactorily represent several sets of experiments, in particular the binding of calcium on intact and truncated calmodulin and the effect of different skMLCK peptides on calmodulin's saturation curve. The model can also be readily extended to include multiple targets. We show that some targets stabilise the low calcium affinity T state while others stabilise the high affinity R state. Most of the effects produced by calmodulin targets can be explained as modulation of a pre-existing dynamic equilibrium between different conformations of calmodulin's lobes, in agreement with linkage theory and MWC-type models. link: http://identifiers.org/pubmed/25611683

Parameters:

Name Description
k_R2T_C2 = 10000.0; k_T2R_C2 = 1.15490174876063E7 Reaction: cam_RT_ACD_0 => cam_RR_ACD_0; cam_RT_ACD_0, cam_RR_ACD_0, Rate Law: cytosol*(k_T2R_C2*cam_RT_ACD_0-k_R2T_C2*cam_RR_ACD_0)
koff_CR = 0.1978714; kon_CR = 1.0E7 Reaction: ca + cam_RR_AD_tbp => cam_RR_ACD_tbp; ca, cam_RR_AD_tbp, cam_RR_ACD_tbp, Rate Law: cytosol*(kon_CR*ca*cam_RR_AD_tbp-koff_CR*cam_RR_ACD_tbp)
kon_DR = 1.0E7; koff_DR = 0.1978714 Reaction: ca + cam_RR_ABC_0 => cam_RR_ABCD_0; ca, cam_RR_ABC_0, cam_RR_ABCD_0, Rate Law: cytosol*(kon_DR*ca*cam_RR_ABC_0-koff_DR*cam_RR_ABCD_0)
k_T2R_N1 = 144.13897072379; k_R2T_N1 = 10000.0 Reaction: cam_TR_BC_0 => cam_RR_BC_0; cam_TR_BC_0, cam_RR_BC_0, Rate Law: cytosol*(k_T2R_N1*cam_TR_BC_0-k_R2T_N1*cam_RR_BC_0)
kon_AR = 1.0E9; koff_AR = 19.7628 Reaction: ca + cam_RR_BC_0 => cam_RR_ABC_0; ca, cam_RR_BC_0, cam_RR_ABC_0, Rate Law: cytosol*(kon_AR*ca*cam_RR_BC_0-koff_AR*cam_RR_ABC_0)
k_R2T_N2 = 10000.0; k_T2R_N2 = 670413.817319951 Reaction: cam_TR_ABC_0 => cam_RR_ABC_0; cam_TR_ABC_0, cam_RR_ABC_0, Rate Law: cytosol*(k_T2R_N2*cam_TR_ABC_0-k_R2T_N2*cam_RR_ABC_0)
k_R2T_C = 10000.0; k_T2R_C = 1.16054921831207 Reaction: cam_RT_0_0 => cam_RR_0_0; cam_RT_0_0, cam_RR_0_0, Rate Law: cytosol*(k_T2R_C*cam_RT_0_0-k_R2T_C*cam_RR_0_0)
kon_DT = 1.0E7; koff_DT = 624.2 Reaction: ca + cam_RT_0_0 => cam_RT_D_0; ca, cam_RT_0_0, cam_RT_D_0, Rate Law: cytosol*(kon_DT*ca*cam_RT_0_0-koff_DT*cam_RT_D_0)
k_R2T_C1 = 10000.0; k_T2R_C1 = 3661.03854357121 Reaction: cam_RT_BC_0 => cam_RR_BC_0; cam_RT_BC_0, cam_RR_BC_0, Rate Law: cytosol*(k_T2R_C1*cam_RT_BC_0-k_R2T_C1*cam_RR_BC_0)
koff_BR = 19.7628; kon_BR = 1.0E9 Reaction: ca + cam_RR_C_0 => cam_RR_BC_0; ca, cam_RR_C_0, cam_RR_BC_0, Rate Law: cytosol*(kon_BR*ca*cam_RR_C_0-koff_BR*cam_RR_BC_0)
k_R2T_N = 10000.0; k_T2R_N = 0.0309898787056147 Reaction: cam_TT_0_0 => cam_RT_0_0; cam_TT_0_0, cam_RT_0_0, Rate Law: cytosol*(k_T2R_N*cam_TT_0_0-k_R2T_N*cam_RT_0_0)
kon_CT = 1.0E7; koff_CT = 624.2 Reaction: ca + cam_RT_0_0 => cam_RT_C_0; ca, cam_RT_0_0, cam_RT_C_0, Rate Law: cytosol*(kon_CT*ca*cam_RT_0_0-koff_CT*cam_RT_C_0)
koff_tbp_RT = 1.0E8; kon_tbp = 1.0E8 Reaction: tbp + cam_RT_0_0 => cam_RT_0_tbp; tbp, cam_RT_0_0, cam_RT_0_tbp, Rate Law: cytosol*(kon_tbp*tbp*cam_RT_0_0-koff_tbp_RT*cam_RT_0_tbp)
koff_rbp_RR = 0.005; kon_rbp = 1.0E8 Reaction: rbp + cam_RR_BC_0 => cam_RR_BC_rbp; rbp, cam_RR_BC_0, cam_RR_BC_rbp, Rate Law: cytosol*(kon_rbp*rbp*cam_RR_BC_0-koff_rbp_RR*cam_RR_BC_rbp)
koff_rbp_RT = 60000.0; kon_rbp = 1.0E8 Reaction: rbp + cam_RT_0_0 => cam_RT_0_rbp; rbp, cam_RT_0_0, cam_RT_0_rbp, Rate Law: cytosol*(kon_rbp*rbp*cam_RT_0_0-koff_rbp_RT*cam_RT_0_rbp)
koff_tbp_RR = 0.1; kon_tbp = 1.0E8 Reaction: tbp + cam_RR_BC_0 => cam_RR_BC_tbp; tbp, cam_RR_BC_0, cam_RR_BC_tbp, Rate Law: cytosol*(kon_tbp*tbp*cam_RR_BC_0-koff_tbp_RR*cam_RR_BC_tbp)

States:

Name Description
cam RR ABC 0 [Calmodulin]
cam RR ACD 0 [Calmodulin]
cam RR AD tbp [Neurogranin; Calmodulin]
cam RR ABC tbp [Neurogranin; Calmodulin]
cam RR ABCD tbp [Neurogranin; Calmodulin]
cam RR ABD 0 [Calmodulin]
cam RR ABCD rbp [IPR020636; Calmodulin]
cam RR ABD tbp [Neurogranin; Calmodulin]
cam RR BCD rbp [IPR020636; Calmodulin]
cam RR ABCD 0 [Calmodulin]
cam RR BC 0 [Calmodulin]
cam RR BCD 0 [Calmodulin]
cam RT 0 0 [Calmodulin]
cam RR ACD rbp [IPR020636; Calmodulin]
cam RR ABC rbp [IPR020636; Calmodulin]
cam RT 0 rbp [IPR020636; Calmodulin]
cam RR ABD rbp [IPR020636; Calmodulin]
cam RR ACD tbp [Neurogranin; Calmodulin]
cam RT 0 tbp [Neurogranin; Calmodulin]
cam RR BCD tbp [Neurogranin; Calmodulin]

Observables: none

MODEL6623617994 @ v0.0.1

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

A dynamic model of the glycogenolytic pathway to lactate in skeletal muscle was constructed with mammalian kinetic parameters obtained from the literature. Energetic buffers relevant to muscle were included. The model design features stoichiometric constraints, mass balance, and fully reversible thermodynamics as defined by the Haldane relation. We employed a novel method of validating the thermodynamics of the model by allowing the closed system to come to equilibrium; the combined mass action ratio of the pathway equaled the product of the individual enzymes' equilibrium constants. Adding features physiologically relevant to muscle-a fixed glycogen concentration, efflux of lactate, and coupling to an ATPase–alowed for a steady-state flux far from equilibrium. The main result of our analysis is that coupling of the glycogenolytic network to the ATPase transformed the entire complex into an ATPase driven system. This steady-state system was most sensitive to the external ATPase activity and not to internal pathway mechanisms. The control distribution among the internal pathway enzymes-although small compared to control by ATPase-depended on the flux level and fraction of glycogen phosphorylase a. This model of muscle glycogenolysis thus has unique features compared to models developed for other cell types. link: http://identifiers.org/pubmed/12220081

Parameters: none

States: none

Observables: none

Pharmacokinetic model of alkylresorcinols. Both plasma AR concentrations and urinary metabolites in 24-h samples showed…

Alkylresorcinols (ARs), phenolic lipids almost exclusively present in the outer parts of wheat and rye grains in commonly consumed foods, have been proposed as specific dietary biomarkers of whole-grain wheat and rye intakes.The objective was to assess the dose response of plasma ARs and the excretion of 2 recently discovered AR metabolites in 24-h urine samples in relation to AR intake and to establish a pharmacokinetic model for predicting plasma AR concentration.Sixteen subjects were given rye bran flakes containing 11, 22, or 44 mg total ARs 3 times daily during week-long intervention periods separated by 1-wk washout periods in a nonblinded randomized crossover design. Blood samples were collected at baseline, after the 1-wk run-in period, and after each treatment and washout period. Two 24-h urine samples were collected at baseline and after each treatment period.Plasma AR concentrations and daily excretion of 2 urinary AR metabolites increased with increasing AR dose (P < 0.001). Recovery of urinary metabolites in 24-h samples decreased with increasing doses from approximately 90% to approximately 45% in the range tested. A one-compartment model with 2 absorption compartments with different lag times and absorption rate constants adequately predicted plasma AR concentrations at the end of each intervention period.Both plasma AR concentrations and urinary metabolites in 24-h samples showed a dose-response relation to increased AR intake, which strongly supports the hypothesis that ARs and their metabolites may be useful as biomarkers of whole-grain wheat and rye intakes. link: http://identifiers.org/pubmed/19056600

Parameters:

Name Description
CL_V = 20.0 Reaction: AR_Central =>, Rate Law: Central*CL_V*AR_Central
k_a_1 = 0.3 Reaction: AR_A1 => AR_Central, Rate Law: k_a_1*AR_A1
Lag_time_2 = 4.7 Reaction: F2 = piecewise(0, time < Lag_time_2, 0.048), Rate Law: missing
Lag_time_1 = 0.9; Lag_time_2 = 4.7 Reaction: F1 = piecewise(0, time < Lag_time_1, piecewise(0.1, (time >= Lag_time_1) && (time < Lag_time_2), 0.052)), Rate Law: missing
base = 0.32 Reaction: => AR_Central, Rate Law: Central*base
k_a_2 = 1.8 Reaction: AR_A2 => AR_Central, Rate Law: k_a_2*AR_A2

States:

Name Description
AR A1 [Resorcinol; 5-alkylresorcinol]
AR Dose [5-alkylresorcinol; Resorcinol]
F1 F1
F2 F2
AR A2 [5-alkylresorcinol; Resorcinol]
AR Central [Resorcinol; 5-alkylresorcinol]

Observables: none

This is a global mathematical model describing metabolic partitioning of carbon resources in plants between growth and d…

In plants, the partitioning of carbon resources between growth and defense is detrimental for their development. From a metabolic viewpoint, growth is mainly related to primary metabolism including protein, amino acid and lipid synthesis, whereas defense is based notably on the biosynthesis of a myriad of secondary metabolites. Environmental factors, such as nitrate fertilization, impact the partitioning of carbon resources between growth and defense. Indeed, experimental data showed that a shortage in the nitrate fertilization resulted in a reduction of the plant growth, whereas some secondary metabolites involved in plant defense, such as phenolic compounds, accumulated. Interestingly, sucrose, a key molecule involved in the transport and partitioning of carbon resources, appeared to be under homeostatic control. Based on the inflow/outflow properties of sucrose homeostatic regulation we propose a global model on how the diversion of the primary carbon flux into the secondary phenolic pathways occurs at low nitrate concentrations. The model can account for the accumulation of starch during the light phase and the sucrose remobilization by starch degradation during the night. Day-length sensing mechanisms for variable light-dark regimes are discussed, showing that growth is proportional to the length of the light phase. The model can describe the complete starch consumption during the night for plants adapted to a certain light/dark regime when grown on sufficient nitrate and can account for an increased accumulation of starch observed under nitrate limitation. link: http://identifiers.org/pubmed/27164436

Parameters:

Name Description
k10 = 10.0 Reaction: trioseP => starch, Rate Law: compartment*k10*trioseP
k37 = 0.1 Reaction: starch => sucr; Estarch, Rate Law: compartment*k37*starch*Estarch
k8 = 1.0E-6; k7 = 9.8 Reaction: Ephe =>, Rate Law: compartment*k7*Ephe/(k8+Ephe)
k4 = 1.0 Reaction: trioseP => sucr; EtrioseP, Rate Law: compartment*k4*EtrioseP*trioseP
k26 = 0.5 Reaction: => Enitrate, Rate Law: compartment*k26
k29 = 10.1; f_act_trioseP = 0.999999999998 Reaction: => trioseP; ECO2, Rate Law: compartment*k29*f_act_trioseP*ECO2
k11 = 0.2 Reaction: => N; Next, Enitrate, Rate Law: compartment*k11*Next*Enitrate
k14 = 0.2; k15 = 0.2 Reaction: sucr =>, Rate Law: compartment*(k14+k15)*sucr
k36 = 1.0E-4; k35 = 10.0 Reaction: Estarch => ; sucr, Rate Law: compartment*k35*sucr*Estarch/(k36+Estarch)
k3 = 1.0E-5; k2 = 1.0 Reaction: EtrioseP => ; sucr, Rate Law: compartment*k2*sucr*EtrioseP/(k3+EtrioseP)
f_act_pcf = 0.833333333333333; k5 = 8.0 Reaction: sucr =>, Rate Law: compartment*k5*sucr*f_act_pcf
k34 = 9.8 Reaction: => Estarch, Rate Law: compartment*k34
k9 = 1.0; f_I_phe = 0.0384615384615385 Reaction: sucr => ; Ephe, Rate Law: compartment*k9*sucr*Ephe*f_I_phe
k1 = 1.0 Reaction: => EtrioseP, Rate Law: compartment*k1
k12 = 1.5 Reaction: N =>, Rate Law: compartment*k12*N
k6 = 10.0; f_I_E_phe_outfl = 0.995024875621891 Reaction: => Ephe; sucr, Rate Law: compartment*k6*sucr*f_I_E_phe_outfl
g = 1.0; k11 = 0.2 Reaction: Next => ; Enitrate, Rate Law: compartment*g*k11*Next*Enitrate
k30 = 0.0 Reaction: => ECO2, Rate Law: compartment*k30
k32 = 1.0E-5; k31 = 0.0 Reaction: ECO2 => ; trioseP, Rate Law: compartment*k31*trioseP*ECO2/(k32+ECO2)
k27 = 0.1; k28 = 1.0E-6 Reaction: Enitrate => ; N, Rate Law: compartment*k27*N*Enitrate/(k28+Enitrate)

States:

Name Description
Next [nitrate; extracellular region]
sucr [sucrose]
ECO2 [C49887; carbon dioxide]
N [nitrate]
Enitrate [nitrate; C49887]
starch [starch]
Estarch [starch; C49887]
Ephe [C49887; phenol]
trioseP [CHEBI:27137; phosphorylated]
EtrioseP [C49887; CHEBI:27137]

Observables: none

This is a global mathematical model describing metabolic partitioning of carbon resources in plants between growth and d…

In plants, the partitioning of carbon resources between growth and defense is detrimental for their development. From a metabolic viewpoint, growth is mainly related to primary metabolism including protein, amino acid and lipid synthesis, whereas defense is based notably on the biosynthesis of a myriad of secondary metabolites. Environmental factors, such as nitrate fertilization, impact the partitioning of carbon resources between growth and defense. Indeed, experimental data showed that a shortage in the nitrate fertilization resulted in a reduction of the plant growth, whereas some secondary metabolites involved in plant defense, such as phenolic compounds, accumulated. Interestingly, sucrose, a key molecule involved in the transport and partitioning of carbon resources, appeared to be under homeostatic control. Based on the inflow/outflow properties of sucrose homeostatic regulation we propose a global model on how the diversion of the primary carbon flux into the secondary phenolic pathways occurs at low nitrate concentrations. The model can account for the accumulation of starch during the light phase and the sucrose remobilization by starch degradation during the night. Day-length sensing mechanisms for variable light-dark regimes are discussed, showing that growth is proportional to the length of the light phase. The model can describe the complete starch consumption during the night for plants adapted to a certain light/dark regime when grown on sufficient nitrate and can account for an increased accumulation of starch observed under nitrate limitation. link: http://identifiers.org/pubmed/27164436

Parameters:

Name Description
k10 = 10.0 Reaction: trioseP => starch, Rate Law: compartment*k10*trioseP
f_act_pcf = 0.833277759253084; k5 = 5.5 Reaction: sucr =>, Rate Law: compartment*k5*sucr*f_act_pcf
k37 = 0.1 Reaction: starch => sucr; Estarch, Rate Law: compartment*k37*starch*Estarch
k8 = 1.0E-6; k7 = 9.8 Reaction: Ephe =>, Rate Law: compartment*k7*Ephe/(k8+Ephe)
k29 = 10.1; f_act_trioseP = 0.999999999997999 Reaction: => trioseP; ECO2, Rate Law: compartment*k29*f_act_trioseP*ECO2
k9 = 1.0; f_I_phe = 0.00398565165404544 Reaction: sucr => ; Ephe, Rate Law: compartment*k9*sucr*Ephe*f_I_phe
k26 = 0.5 Reaction: => Enitrate, Rate Law: compartment*k26
k11 = 0.2 Reaction: => N; Next, Enitrate, Rate Law: compartment*k11*Next*Enitrate
k14 = 0.2; k15 = 0.2 Reaction: sucr =>, Rate Law: compartment*(k14+k15)*sucr
k4 = 5.0 Reaction: trioseP => sucr; EtrioseP, Rate Law: compartment*k4*EtrioseP*trioseP
k36 = 1.0E-4; k35 = 10.0 Reaction: Estarch => ; sucr, Rate Law: compartment*k35*sucr*Estarch/(k36+Estarch)
k3 = 1.0E-5; k2 = 1.0 Reaction: EtrioseP => ; sucr, Rate Law: compartment*k2*sucr*EtrioseP/(k3+EtrioseP)
k34 = 9.8 Reaction: => Estarch, Rate Law: compartment*k34
k1 = 1.0 Reaction: => EtrioseP, Rate Law: compartment*k1
k6 = 10.0; f_I_E_phe_outfl = 0.995026855774837 Reaction: => Ephe; sucr, Rate Law: compartment*k6*sucr*f_I_E_phe_outfl
k12 = 15.0 Reaction: N =>, Rate Law: compartment*k12*N
g = 1.0; k11 = 0.2 Reaction: Next => ; Enitrate, Rate Law: compartment*g*k11*Next*Enitrate
k30 = 0.0 Reaction: => ECO2, Rate Law: compartment*k30
k32 = 1.0E-5; k31 = 0.0 Reaction: ECO2 => ; trioseP, Rate Law: compartment*k31*trioseP*ECO2/(k32+ECO2)
k27 = 0.1; k28 = 1.0E-6 Reaction: Enitrate => ; N, Rate Law: compartment*k27*N*Enitrate/(k28+Enitrate)

States:

Name Description
Next [nitrate; extracellular region]
sucr [sucrose]
ECO2 [C49887; carbon dioxide]
N [nitrate]
Enitrate [nitrate; C49887]
starch [starch]
Ephe [phenol; C49887]
Estarch [starch; C49887]
trioseP [CHEBI:27137; phosphorylated]
EtrioseP [C49887; CHEBI:27137]

Observables: none

This is a global mathematical model describing metabolic partitioning of carbon resources in plants between growth and d…

In plants, the partitioning of carbon resources between growth and defense is detrimental for their development. From a metabolic viewpoint, growth is mainly related to primary metabolism including protein, amino acid and lipid synthesis, whereas defense is based notably on the biosynthesis of a myriad of secondary metabolites. Environmental factors, such as nitrate fertilization, impact the partitioning of carbon resources between growth and defense. Indeed, experimental data showed that a shortage in the nitrate fertilization resulted in a reduction of the plant growth, whereas some secondary metabolites involved in plant defense, such as phenolic compounds, accumulated. Interestingly, sucrose, a key molecule involved in the transport and partitioning of carbon resources, appeared to be under homeostatic control. Based on the inflow/outflow properties of sucrose homeostatic regulation we propose a global model on how the diversion of the primary carbon flux into the secondary phenolic pathways occurs at low nitrate concentrations. The model can account for the accumulation of starch during the light phase and the sucrose remobilization by starch degradation during the night. Day-length sensing mechanisms for variable light-dark regimes are discussed, showing that growth is proportional to the length of the light phase. The model can describe the complete starch consumption during the night for plants adapted to a certain light/dark regime when grown on sufficient nitrate and can account for an increased accumulation of starch observed under nitrate limitation. link: http://identifiers.org/pubmed/27164436

Parameters:

Name Description
k29 = 10.1; k40 = 0.0568 Reaction: => M1, Rate Law: compartment*k29*k40
k30 = 0.1 Reaction: => ECO2, Rate Law: compartment*k30
k8 = 1.0E-6; k7 = 9.8 Reaction: Ephe =>, Rate Law: compartment*k7*Ephe/(k8+Ephe)
k37 = 0.1 Reaction: starch => sucr; Estarch, Rate Law: compartment*k37*starch*Estarch
k29 = 10.1; k44 = 1000.0; K_I_L = 1.0E-4 Reaction: M1 => M2, Rate Law: compartment*k44*K_I_L*M1/(K_I_L+k29)
f_I = 1.0; k49 = 0.001; k10 = 10.0 Reaction: trioseP => starch, Rate Law: compartment*k10*trioseP*f_I/(k49+trioseP)
k26 = 0.5 Reaction: => Enitrate, Rate Law: compartment*k26
k11 = 0.2 Reaction: => N; Next, Enitrate, Rate Law: compartment*k11*Next*Enitrate
k14 = 0.2; k15 = 0.2 Reaction: sucr =>, Rate Law: compartment*(k14+k15)*sucr
k34 = 9.8 Reaction: => Estarch, Rate Law: compartment*k34
K_M_M2 = 1.0E-6; k29 = 10.1; k40 = 0.0568 Reaction: M2 =>, Rate Law: compartment*k29*k40*M2/(K_M_M2+M2)
k32 = 1.0E-6; k31 = 2.0 Reaction: ECO2 => ; trioseP, Rate Law: compartment*k31*trioseP*ECO2/(k32+ECO2)
k53 = 2.5E-4 Reaction: => ETP; starch, Rate Law: compartment*k53*starch
g = 1.0; k11 = 0.2 Reaction: Next => ; Enitrate, Rate Law: compartment*g*k11*Next*Enitrate
f_act_pcf = 0.833333333333333; k5 = 2.492 Reaction: sucr =>, Rate Law: compartment*k5*sucr*f_act_pcf
k29 = 10.1; f_act_trioseP = 0.999999999998 Reaction: => trioseP; ECO2, Rate Law: compartment*k29*f_act_trioseP*ECO2
k4 = 5.0 Reaction: trioseP => sucr; EtrioseP, Rate Law: compartment*k4*EtrioseP*trioseP
k9 = 1.0; f_I_phe = 0.00398406374501992 Reaction: sucr => ; Ephe, Rate Law: compartment*k9*sucr*Ephe*f_I_phe
k36 = 1.0E-4; k35 = 10.0 Reaction: Estarch => ; sucr, Rate Law: compartment*k35*sucr*Estarch/(k36+Estarch)
k3 = 1.0E-5; k2 = 1.0 Reaction: EtrioseP => ; sucr, Rate Law: compartment*k2*sucr*EtrioseP/(k3+EtrioseP)
k1 = 1.0 Reaction: => EtrioseP, Rate Law: compartment*k1
k6 = 10.0; f_I_E_phe_outfl = 0.995024875621891 Reaction: => Ephe; sucr, Rate Law: compartment*k6*sucr*f_I_E_phe_outfl
k12 = 15.0 Reaction: N =>, Rate Law: compartment*k12*N
k54 = 0.00625; k55 = 1.0E-4 Reaction: ETP =>, Rate Law: compartment*k54*ETP/(k55+ETP)
k27 = 0.1; k28 = 1.0E-6 Reaction: Enitrate => ; N, Rate Law: compartment*k27*N*Enitrate/(k28+Enitrate)

States:

Name Description
ETP [C49887]
Next [nitrate; extracellular region]
M2 [0000568; C61366]
Enitrate [nitrate; C49887]
Estarch [C49887; starch]
Ephe [C49887; phenol]
trioseP [CHEBI:27137; phosphorylated]
EtrioseP [C49887; CHEBI:27137]
sucr [sucrose]
ECO2 [carbon dioxide; C49887]
N [nitrate]
M1 [0000568; C63905]
starch [starch]

Observables: none

BIOMD0000000330 @ v0.0.1

This model is from the article: On the encoding and decoding of calcium signals in hepatocytes Ann Zahle Larsen, L…

Many different agonists use calcium as a second messenger. Despite intensive research in intracellular calcium signalling it is an unsolved riddle how the different types of information represented by the different agonists, is encoded using the universal carrier calcium. It is also still not clear how the information encoded is decoded again into the intracellular specific information at the site of enzymes and genes. After the discovery of calcium oscillations, one likely mechanism is that information is encoded in the frequency, amplitude and waveform of the oscillations. This hypothesis has received some experimental support. However, the mechanism of decoding of oscillatory signals is still not known. Here, we study a mechanistic model of calcium oscillations, which is able to reproduce both spiking and bursting calcium oscillations. We use the model to study the decoding of calcium signals on the basis of co-operativity of calcium binding to various proteins. We show that this co-operativity offers a simple way to decode different calcium dynamics into different enzyme activities. link: http://identifiers.org/pubmed/14871603

Parameters:

Name Description
K21 = 1.5; K15 = 0.16; K17 = 0.05; k12 = 0.76; k13 = 0.0; K19 = 2.0; k10 = 0.93; k14 = 149.0; K11 = 2.667; k16 = 20.9; k20 = 1.5; k18 = 79.0 Reaction: Ca_cyt = (((((Ca_ER-Ca_cyt)*k10*Ca_cyt*PLC^4/(PLC^4+K11^4)+k12*PLC+k13*G_alpha)-k14*Ca_cyt/(Ca_cyt+K15))-k16*Ca_cyt/(Ca_cyt+K17))-k18*Ca_cyt^8/(K19^8+Ca_cyt^8))+(Ca_mit-Ca_cyt)*k20*Ca_cyt/(Ca_cyt+K21), Rate Law: (((((Ca_ER-Ca_cyt)*k10*Ca_cyt*PLC^4/(PLC^4+K11^4)+k12*PLC+k13*G_alpha)-k14*Ca_cyt/(Ca_cyt+K15))-k16*Ca_cyt/(Ca_cyt+K17))-k18*Ca_cyt^8/(K19^8+Ca_cyt^8))+(Ca_mit-Ca_cyt)*k20*Ca_cyt/(Ca_cyt+K21)
k1 = 0.35; k3 = 1.0E-4; k5 = 1.24; K4 = 0.783; k2 = 0.0; K6 = 0.7 Reaction: G_alpha = ((k1+k2*G_alpha)-k3*G_alpha*PLC/(G_alpha+K4))-k5*G_alpha*Ca_cyt/(G_alpha+K6), Rate Law: ((k1+k2*G_alpha)-k3*G_alpha*PLC/(G_alpha+K4))-k5*G_alpha*Ca_cyt/(G_alpha+K6)
K9 = 29.09; k8 = 32.24; k7 = 5.82 Reaction: PLC = k7*G_alpha-k8*PLC/(PLC+K9), Rate Law: k7*G_alpha-k8*PLC/(PLC+K9)
K17 = 0.05; K11 = 2.667; k16 = 20.9; k10 = 0.93 Reaction: Ca_ER = (-(Ca_ER-Ca_cyt))*k10*Ca_cyt*PLC^4/(PLC^4+K11^4)+k16*Ca_cyt/(Ca_cyt+K17), Rate Law: (-(Ca_ER-Ca_cyt))*k10*Ca_cyt*PLC^4/(PLC^4+K11^4)+k16*Ca_cyt/(Ca_cyt+K17)
K21 = 1.5; k20 = 1.5; K19 = 2.0; k18 = 79.0 Reaction: Ca_mit = k18*Ca_cyt^8/(K19^8+Ca_cyt^8)-(Ca_mit-Ca_cyt)*k20*Ca_cyt/(Ca_cyt+K21), Rate Law: k18*Ca_cyt^8/(K19^8+Ca_cyt^8)-(Ca_mit-Ca_cyt)*k20*Ca_cyt/(Ca_cyt+K21)

States:

Name Description
G alpha [Guanine nucleotide-binding protein subunit alpha-11]
Ca ER [endoplasmic reticulum; calcium(2+); Calcium cation]
Ca cyt [calcium(2+); Calcium cation; cytoplasm]
PLC [1-phosphatidylinositol 4,5-bisphosphate phosphodiesterase beta-1]
Ca mit [calcium(2+); Calcium cation; mitochondrion]

Observables: none

BIOMD0000000331 @ v0.0.1

This a model from the article: On the encoding and decoding of calcium signals in hepatocytes Ann Zahle Larsen, Lar…

Many different agonists use calcium as a second messenger. Despite intensive research in intracellular calcium signalling it is an unsolved riddle how the different types of information represented by the different agonists, is encoded using the universal carrier calcium. It is also still not clear how the information encoded is decoded again into the intracellular specific information at the site of enzymes and genes. After the discovery of calcium oscillations, one likely mechanism is that information is encoded in the frequency, amplitude and waveform of the oscillations. This hypothesis has received some experimental support. However, the mechanism of decoding of oscillatory signals is still not known. Here, we study a mechanistic model of calcium oscillations, which is able to reproduce both spiking and bursting calcium oscillations. We use the model to study the decoding of calcium signals on the basis of co-operativity of calcium binding to various proteins. We show that this co-operativity offers a simple way to decode different calcium dynamics into different enzyme activities. link: http://identifiers.org/pubmed/14871603

Parameters:

Name Description
k_enz = 3.0; k_rem = 3.0 Reaction: Product = k_enz*Enz-k_rem*Product, Rate Law: k_enz*Enz-k_rem*Product
k_act = 5.0; KM = 0.62; k_inact = 0.4; p = 4.0 Reaction: Enz = k_act*Ca_cyt^p/(KM^p+Ca_cyt^p)-k_inact*Enz, Rate Law: k_act*Ca_cyt^p/(KM^p+Ca_cyt^p)-k_inact*Enz
K9 = 29.09; k8 = 32.24; k7 = 2.08 Reaction: PLC = k7*G_alpha-k8*PLC/(PLC+K9), Rate Law: k7*G_alpha-k8*PLC/(PLC+K9)
k20 = 0.81; K19 = 3.5; k18 = 79.0; K21 = 4.5 Reaction: Ca_mit = k18*Ca_cyt^8/(K19^8+Ca_cyt^8)-(Ca_mit-Ca_cyt)*k20*Ca_cyt/(Ca_cyt+K21), Rate Law: k18*Ca_cyt^8/(K19^8+Ca_cyt^8)-(Ca_mit-Ca_cyt)*k20*Ca_cyt/(Ca_cyt+K21)
K11 = 3.0; K15 = 0.16; K17 = 0.05; k10 = 0.7; K19 = 3.5; k14 = 153.0; k16 = 7.0; k20 = 0.81; k12 = 2.8; k18 = 79.0; K21 = 4.5; k13 = 13.4 Reaction: Ca_cyt = (((((Ca_ER-Ca_cyt)*k10*Ca_cyt*PLC^4/(PLC^4+K11^4)+k12*PLC+k13*G_alpha)-k14*Ca_cyt/(Ca_cyt+K15))-k16*Ca_cyt/(Ca_cyt+K17))-k18*Ca_cyt^8/(K19^8+Ca_cyt^8))+(Ca_mit-Ca_cyt)*k20*Ca_cyt/(Ca_cyt+K21), Rate Law: (((((Ca_ER-Ca_cyt)*k10*Ca_cyt*PLC^4/(PLC^4+K11^4)+k12*PLC+k13*G_alpha)-k14*Ca_cyt/(Ca_cyt+K15))-k16*Ca_cyt/(Ca_cyt+K17))-k18*Ca_cyt^8/(K19^8+Ca_cyt^8))+(Ca_mit-Ca_cyt)*k20*Ca_cyt/(Ca_cyt+K21)
k1 = 0.01; k5 = 4.88; K4 = 0.09; k2 = 1.65; K6 = 1.18; k3 = 0.64 Reaction: G_alpha = ((k1+k2*G_alpha)-k3*G_alpha*PLC/(G_alpha+K4))-k5*G_alpha*Ca_cyt/(G_alpha+K6), Rate Law: ((k1+k2*G_alpha)-k3*G_alpha*PLC/(G_alpha+K4))-k5*G_alpha*Ca_cyt/(G_alpha+K6)
K11 = 3.0; K17 = 0.05; k10 = 0.7; k16 = 7.0 Reaction: Ca_ER = (-(Ca_ER-Ca_cyt))*k10*Ca_cyt*PLC^4/(PLC^4+K11^4)+k16*Ca_cyt/(Ca_cyt+K17), Rate Law: (-(Ca_ER-Ca_cyt))*k10*Ca_cyt*PLC^4/(PLC^4+K11^4)+k16*Ca_cyt/(Ca_cyt+K17)

States:

Name Description
G alpha [Guanine nucleotide-binding protein subunit alpha-11]
Product EnzCatlysedProduct
Ca ER [endoplasmic reticulum]
Ca cyt [cytoplasm]
PLC [1-phosphatidylinositol 4,5-bisphosphate phosphodiesterase beta-1]
Enz Enzyme
Ca mit [mitochondrion]

Observables: none

BIOMD0000000099 @ v0.0.1

A network of interacting proteins has been found that can account for the spontaneous oscillations in adenylyl cyclase a…

This is model according to the paper "A Molecular Network That Produces Spontaneous Oscillations in Excitalbe Cells of Dictyostelium. Figure 3 has been reproduced by Copasi 4.0.20(development) ". However four of the parameters have been changed, see details in notes.

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

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

To cite BioModels Database, please use:

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

Parameters:

Name Description
parameter_0 = 1.4 Reaction: => species_4; species_6, Rate Law: compartment_1*parameter_0*species_6
parameter_13 = 4.5 Reaction: species_5 => ; species_2, Rate Law: compartment_1*parameter_13*species_5*species_2
parameter_3 = 1.5 Reaction: species_2 =>, Rate Law: compartment_1*parameter_3*species_2
parameter_2 = 2.5 Reaction: => species_2; species_1, Rate Law: compartment_1*parameter_2*species_1
parameter_12 = 33.0 Reaction: => species_5; species_0, Rate Law: compartment_1*parameter_12*species_0
parameter_8 = 0.29 Reaction: => species_1; species_4, Rate Law: compartment_1*parameter_8*species_4
parameter_10 = 0.6 Reaction: => species_0; species_4, Rate Law: compartment_0*parameter_10*species_4
parameter_1 = 0.9 Reaction: species_4 =>, Rate Law: compartment_1*parameter_1*species_4
parameter_6 = 2.0 Reaction: => species_3, Rate Law: compartment_1*parameter_6
parameter_7 = 1.3 Reaction: species_3 => ; species_6, Rate Law: compartment_1*parameter_7*species_3*species_6
parameter_4 = 0.6 Reaction: => species_6; species_5, Rate Law: compartment_1*parameter_4*species_5
parameter_5 = 0.8 Reaction: species_6 => ; species_2, Rate Law: compartment_1*parameter_5*species_6*species_2
parameter_9 = 1.0 Reaction: species_1 => ; species_3, Rate Law: compartment_1*parameter_9*species_1*species_3
parameter_11 = 3.1 Reaction: species_0 =>, Rate Law: compartment_0*parameter_11*species_0

States:

Name Description
species 2 [cAMP-dependent protein kinase catalytic subunit; IPR002373]
species 6 [IPR008349; Mitogen-activated protein kinase 1]
species 3 [IPR000396]
species 0 [3',5'-cyclic AMP; 3',5'-Cyclic AMP]
species 1 [3',5'-cyclic AMP; 3',5'-Cyclic AMP]
species 4 [IPR008172]
species 5 [Cyclic AMP receptor 1; IPR000848]

Observables: none

This ordinary differential equation model is described in the following article: "Autocrine and paracrine interferon sig…

The innate immune response, particularly the interferon response, represents a first line of defence against viral infections. The interferon molecules produced from infected cells act through autocrine and paracrine signalling to turn host cells into an antiviral state. Although the molecular mechanisms of IFN signalling have been well characterized, how the interferon response collectively contribute to the regulation of host cells to stop or suppress viral infection during early infection remain unclear. Here, we use mathematical models to delineate the roles of the autocrine and the paracrine signalling, and show that their impacts on viral spread are dependent on how infection proceeds. In particular, we found that when infection is well-mixed, the paracrine signalling is not as effective; by contrast, when infection spreads in a spatial manner, a likely scenario during initial infection in tissue, the paracrine signalling can impede the spread of infection by decreasing the number of susceptible cells close to the site of infection. Furthermore, we argue that the interferon response can be seen as a parallel to population-level epidemic prevention strategies such as 'contact tracing' or 'ring vaccination'. Thus, our results here may have implications for the outbreak control at the population scale more broadly. link: http://identifiers.org/pubmed/33622135

Parameters: none

States: none

Observables: none

This is an automatically generated .xml file describing a genome-scale model of the metabolism of a polar diatom, Fragil…

Diatoms are major primary producers in polar environments where they can actively grow under extremely variable conditions. Integrative modeling using a genome-scale model (GSM) is a powerful approach to decipher the complex interactions between components of diatom metabolism and can provide insights into metabolic mechanisms underlying their evolutionary success in polar ecosystems. We developed the first GSM for a polar diatom, Fragilariopsis cylindrus, which enabled us to study its metabolic robustness using sensitivity analysis. We find that the predicted growth rate was robust to changes in all model parameters (i.e., cell biochemical composition) except the carbon uptake rate. Constraints on total cellular carbon buffer the effect of changes in the input parameters on reaction fluxes and growth rate. We also show that single reaction deletion of 20% to 32% of active (nonzero flux) reactions and single gene deletion of 44% to 55% of genes associated with active reactions affected the growth rate, as well as the production fluxes of total protein, lipid, carbohydrate, DNA, RNA, and pigments by less than 1%, which was due to the activation of compensatory reactions (e.g., analogous enzymes and alternative pathways) with more highly connected metabolites involved in the reactions that were robust to deletion. Interestingly, including highly divergent alleles unique for F. cylindrus increased its metabolic robustness to cellular perturbations even more. Overall, our results underscore the high robustness of metabolism in F. cylindrus, a feature that likely helps to maintain cell homeostasis under polar conditions. link: http://identifiers.org/pubmed/32079178

Parameters: none

States: none

Observables: none

BIOMD0000000184 @ v0.0.1

The model reproduces the time profile of cytoplasmic Calcium as depicted in Fig 3 of the paper. Model successfully repro…

Astrocytes exhibit oscillations and waves of Ca2+ ions within their cytosol and it appears that this behavior helps facilitate the astrocyte's interaction with its environment, including its neighboring neurons. Often changes in the oscillatory behavior are initiated by an external stimulus such as glutamate, recently however, it has been observed that oscillations are also initiated spontaneously. We propose here a mathematical model of how spontaneous Ca2+ oscillations arise in astrocytes. This model uses the calcium-induced calcium release and inositol cross-coupling mechanisms coupled with a receptor-independent method for producing inositol (1,4,5)-trisphosphate as the heart of the model. By computationally mimicking experimental constraints we have found that this model provides results that are qualitatively similar to experiment. link: http://identifiers.org/pubmed/18275973

Parameters:

Name Description
kdeg = 0.08 sec_1 Reaction: Z =>, Rate Law: compartment*kdeg*Z
kf = 0.5 sec_1 Reaction: Y => X, Rate Law: ER*kf*(Y-X)
k_CaI = 0.15 uM; k_CaA = 0.15 uM; m = 2.2 dimensionless; kip3 = 0.1 uM; vM3 = 40.0 sec_1; n = 2.02 dimensionless Reaction: Y => X; Z, Rate Law: ER*4*vM3*k_CaA^n*X^n/((X^n+k_CaA^n)*(X^n+k_CaI^n))*Z^m/(Z^m+kip3^m)*(Y-X)
kout = 0.5 sec_1 Reaction: X =>, Rate Law: compartment*kout*X
vp = 0.05 uM_sec_1; kp = 0.3 uM Reaction: => Z; X, Rate Law: compartment*vp*X^2/(X^2+kp^2)
k2 = 0.1 uM; vM2 = 15.0 uM_sec_1 Reaction: X => Y, Rate Law: compartment*vM2*X^2/(X^2+k2^2)
vin = 0.05 uM_sec_1 Reaction: => X, Rate Law: compartment*vin

States:

Name Description
Y [calcium(2+); Calcium cation]
Z [1D-myo-inositol 1,4,5-trisphosphate; D-myo-Inositol 1,4,5-trisphosphate]
X [calcium(2+); Calcium cation]

Observables: none

The susceptible-infectious-removed (SIR) model offers the simplest framework to study transmission dynamics of COVID-19,…

The susceptible-infectious-removed (SIR) model offers the simplest framework to study transmission dynamics of COVID-19, however, it does not factor in its early depleting trend observed during a lockdown. We modified the SIR model to specifically simulate the early depleting transmission dynamics of COVID-19 to better predict its temporal trend in Malaysia. The classical SIR model was fitted to observed total (I total), active (I) and removed (R) cases of COVID-19 before lockdown to estimate the basic reproduction number. Next, the model was modified with a partial time-varying force of infection, given by a proportionally depleting transmission coefficient, [Formula: see text] and a fractional term, z. The modified SIR model was then fitted to observed data over 6&#160;weeks during the lockdown. Model fitting and projection were validated using the mean absolute percent error (MAPE). The transmission dynamics of COVID-19 was interrupted immediately by the lockdown. The modified SIR model projected the depleting temporal trends with lowest MAPE for I total, followed by I, I daily and R. During lockdown, the dynamics of COVID-19 depleted at a rate of 4.7% each day with a decreased capacity of 40%. For 7-day and 14-day projections, the modified SIR model accurately predicted I total, I and R. The depleting transmission dynamics for COVID-19 during lockdown can be accurately captured by time-varying SIR model. Projection generated based on observed data is useful for future planning and control of COVID-19. link: http://identifiers.org/pubmed/33303925

Parameters: none

States: none

Observables: none

The properties of inositol 1,4,5-trisphosphate (IP3)-dependent intracellular calcium oscillations in pancreatic acinar c…

The properties of inositol 1,4,5-trisphosphate (IP3)-dependent intracellular calcium oscillations in pancreatic acinar cells depend crucially on the agonist used to stimulate them. Acetylcholine or carbachol (CCh) cause high-frequency (10-12-s period) calcium oscillations that are superimposed on a raised baseline, while cholecystokinin (CCK) causes long-period (>100-s period) baseline spiking. We show that physiological concentrations of CCK induce rapid phosphorylation of the IP3 receptor, which is not true of physiological concentrations of CCh. Based on this and other experimental data, we construct a mathematical model of agonist-specific intracellular calcium oscillations in pancreatic acinar cells. Model simulations agree with previous experimental work on the rates of activation and inactivation of the IP3 receptor by calcium (DuFour, J.-F., I.M. Arias, and T.J. Turner. 1997. J. Biol. Chem. 272:2675-2681), and reproduce both short-period, raised baseline oscillations, and long-period baseline spiking. The steady state open probability curve of the model IP3 receptor is an increasing function of calcium concentration, as found for type-III IP3 receptors by Hagar et al. (Hagar, R.E., A.D. Burgstahler, M.H. Nathanson, and B.E. Ehrlich. 1998. Nature. 396:81-84). We use the model to predict the effect of the removal of external calcium, and this prediction is confirmed experimentally. We also predict that, for type-III IP3 receptors, the steady state open probability curve will shift to lower calcium concentrations as the background IP3 concentration increases. We conclude that the differences between CCh- and CCK-induced calcium oscillations in pancreatic acinar cells can be explained by two principal mechanisms: (a) CCK causes more phosphorylation of the IP3 receptor than does CCh, and the phosphorylated receptor cannot pass calcium current; and (b) the rate of calcium ATPase pumping and the rate of calcium influx from the outside the cell are greater in the presence of CCh than in the presence of CCK. link: http://identifiers.org/pubmed/10352035

Parameters: none

States: none

Observables: none

Lebeda2008 - BoNT paralysis (3 step model)The onset of paralysis of skeletal muscles induced by BoNT/A at the isolated…

Experimental studies have demonstrated that botulinum neurotoxin serotype A (BoNT/A) causes flaccid paralysis by a multi-step mechanism. Following its binding to specific receptors at peripheral cholinergic nerve endings, BoNT/A is internalized by receptor-mediated endocytosis. Subsequently its zinc-dependent catalytic domain translocates into the neuroplasm where it cleaves a vesicle-docking protein, SNAP-25, to block neurally evoked cholinergic neurotransmission. We tested the hypothesis that mathematical models having a minimal number of reactions and reactants can simulate published data concerning the onset of paralysis of skeletal muscles induced by BoNT/A at the isolated rat neuromuscular junction (NMJ) and in other systems. Experimental data from several laboratories were simulated with two different models that were represented by sets of coupled, first-order differential equations. In this study, the 3-step sequential model developed by Simpson (J Pharmacol Exp Ther 212:16-21,1980) was used to estimate upper limits of the times during which anti-toxins and other impermeable inhibitors of BoNT/A can exert an effect. The experimentally determined binding reaction rate was verified to be consistent with published estimates for the rate constants for BoNT/A binding to and dissociating from its receptors. Because this 3-step model was not designed to reproduce temporal changes in paralysis with different toxin concentrations, a new BoNT/A species and rate (k(S)) were added at the beginning of the reaction sequence to create a 4-step scheme. This unbound initial species is transformed at a rate determined by k(S) to a free species that is capable of binding. By systematically adjusting the values of k(S), the 4-step model simulated the rapid decline in NMJ function (k(S) >or= 0.01), the less rapid onset of paralysis in mice following i.m. injections (k (S) = 0.001), and the slow onset of the therapeutic effects of BoNT/A (k(S) < 0.001) in man. This minimal modeling approach was not only verified by simulating experimental results, it helped to quantitatively define the time available for an inhibitor to have some effect (t(inhib)) and the relation between this time and the rate of paralysis onset. The 4-step model predicted that as the rate of paralysis becomes slower, the estimated upper limits of (t(inhib)) for impermeable inhibitors become longer. More generally, this modeling approach may be useful in studying the kinetics of other toxins or viruses that invade host cells by similar mechanisms, e.g., receptor-mediated endocytosis. link: http://identifiers.org/pubmed/18551355

Parameters:

Name Description
kL=0.013 perminute Reaction: translocate => lytic, Rate Law: kL*translocate*endosome
kT=0.141 perminute Reaction: bound => translocate, Rate Law: kT*bound*extracellular
kB=0.058 perminute Reaction: free => bound, Rate Law: kB*free*extracellular

States:

Name Description
lytic [Botulinum toxin type A]
free [Botulinum toxin type A]
translocate [Botulinum toxin type A]
bound [Botulinum toxin type A]

Observables: none

Lebeda2008 - BoTN Paralysis (4 step model)The onset of paralysis of skeletal muscles induced by BoNT/A at the isolated…

Experimental studies have demonstrated that botulinum neurotoxin serotype A (BoNT/A) causes flaccid paralysis by a multi-step mechanism. Following its binding to specific receptors at peripheral cholinergic nerve endings, BoNT/A is internalized by receptor-mediated endocytosis. Subsequently its zinc-dependent catalytic domain translocates into the neuroplasm where it cleaves a vesicle-docking protein, SNAP-25, to block neurally evoked cholinergic neurotransmission. We tested the hypothesis that mathematical models having a minimal number of reactions and reactants can simulate published data concerning the onset of paralysis of skeletal muscles induced by BoNT/A at the isolated rat neuromuscular junction (NMJ) and in other systems. Experimental data from several laboratories were simulated with two different models that were represented by sets of coupled, first-order differential equations. In this study, the 3-step sequential model developed by Simpson (J Pharmacol Exp Ther 212:16-21,1980) was used to estimate upper limits of the times during which anti-toxins and other impermeable inhibitors of BoNT/A can exert an effect. The experimentally determined binding reaction rate was verified to be consistent with published estimates for the rate constants for BoNT/A binding to and dissociating from its receptors. Because this 3-step model was not designed to reproduce temporal changes in paralysis with different toxin concentrations, a new BoNT/A species and rate (k(S)) were added at the beginning of the reaction sequence to create a 4-step scheme. This unbound initial species is transformed at a rate determined by k(S) to a free species that is capable of binding. By systematically adjusting the values of k(S), the 4-step model simulated the rapid decline in NMJ function (k(S) >or= 0.01), the less rapid onset of paralysis in mice following i.m. injections (k (S) = 0.001), and the slow onset of the therapeutic effects of BoNT/A (k(S) < 0.001) in man. This minimal modeling approach was not only verified by simulating experimental results, it helped to quantitatively define the time available for an inhibitor to have some effect (t(inhib)) and the relation between this time and the rate of paralysis onset. The 4-step model predicted that as the rate of paralysis becomes slower, the estimated upper limits of (t(inhib)) for impermeable inhibitors become longer. More generally, this modeling approach may be useful in studying the kinetics of other toxins or viruses that invade host cells by similar mechanisms, e.g., receptor-mediated endocytosis. link: http://identifiers.org/pubmed/18551355

Parameters:

Name Description
kL=0.013 perminute Reaction: translocate => lytic, Rate Law: kL*translocate*endosome
kS=1.5E-4 perminute Reaction: bulk => free, Rate Law: kS*bulk*extracellular
kT=0.141 perminute Reaction: bound => translocate, Rate Law: kT*bound*extracellular
kB=0.058 perminute Reaction: free => bound, Rate Law: kB*free*extracellular

States:

Name Description
lytic [Botulinum toxin type A]
free [Botulinum toxin type A]
bulk [Botulinum toxin type A]
BoNT [Botulinum toxin type A]
translocate [Botulinum toxin type A]
bound [Botulinum toxin type A]

Observables: none

Leber2015 - Mucosal immunity and gut microbiome interaction during C. difficile infectionThis model is described in the…

Clostridium difficile infections are associated with the use of broad-spectrum antibiotics and result in an exuberant inflammatory response, leading to nosocomial diarrhea, colitis and even death. To better understand the dynamics of mucosal immunity during C. difficile infection from initiation through expansion to resolution, we built a computational model of the mucosal immune response to the bacterium. The model was calibrated using data from a mouse model of C. difficile infection. The model demonstrates a crucial role of T helper 17 (Th17) effector responses in the colonic lamina propria and luminal commensal bacteria populations in the clearance of C. difficile and colonic pathology, whereas regulatory T (Treg) cells responses are associated with the recovery phase. In addition, the production of anti-microbial peptides by inflamed epithelial cells and activated neutrophils in response to C. difficile infection inhibit the re-growth of beneficial commensal bacterial species. Computational simulations suggest that the removal of neutrophil and epithelial cell derived anti-microbial inhibitions, separately and together, on commensal bacterial regrowth promote recovery and minimize colonic inflammatory pathology. Simulation results predict a decrease in colonic inflammatory markers, such as neutrophilic influx and Th17 cells in the colonic lamina propria, and length of infection with accelerated commensal bacteria re-growth through altered anti-microbial inhibition. Computational modeling provides novel insights on the therapeutic value of repopulating the colonic microbiome and inducing regulatory mucosal immune responses during C. difficile infection. Thus, modeling mucosal immunity-gut microbiota interactions has the potential to guide the development of targeted fecal transplantation therapies in the context of precision medicine interventions. link: http://identifiers.org/pubmed/26230099

Parameters:

Name Description
K=1.71079818745428E-4 Reaction: E => E_i; Cdiff, E, Cdiff, E, Cdiff, Rate Law: Epithelium*K*E*Cdiff
k2=0.156287382551622; k1=4.5E-10 Reaction: Commensal_Beneficial => Commensal_Dead; N_Lum, E_i, Commensal_Beneficial, N_Lum, E_i, Commensal_Dead, Commensal_Beneficial, N_Lum, E_i, Commensal_Dead, Rate Law: Lumen*(k1*Commensal_Beneficial*N_Lum*E_i-k2*Commensal_Dead)
m3=0.102702503781515; m2=594.896546415159; K=6.27092296294148E-10 Reaction: Cdiff => ; M_LP, N_Lum, Commensal_Harmful, Cdiff, M_LP, N_Lum, Commensal_Harmful, Cdiff, M_LP, N_Lum, Commensal_Harmful, Rate Law: Lumen*K*Cdiff*((M_LP+m2*N_Lum)-m3*Commensal_Harmful)
k1=10.5 Reaction: eDC_LP => eDC_MLN; eDC_LP, eDC_LP, Rate Law: k1*eDC_LP
k1=0.5069887 Reaction: iTreg_LP => ; Cdiff, iTreg_LP, iTreg_LP, Rate Law: LP*k1*iTreg_LP
k1=0.0933277452272273 Reaction: Commensal_Dead => ; Commensal_Dead, Commensal_Dead, Rate Law: Lumen*k1*Commensal_Dead
A1=0.00478; K=2.33225E-5; A2=0.18 Reaction: Commensal_Harmful => ; N_LP, E_i, Commensal_Harmful, N_LP, E_i, Commensal_Harmful, N_LP, E_i, Rate Law: Lumen*K*Commensal_Harmful*(N_LP*A1+E_i*A2)
k3=62.5911647602982; v=1.59920673150176E-6; k1=1.1E-5; k2=2.3381277077344E-6 Reaction: E => E_d; N_Lum, Th17_LP, M_LP, E, N_Lum, Th17_LP, M_LP, E, N_Lum, Th17_LP, M_LP, Rate Law: Epithelium*v*E*(k1*N_Lum+k2*Th17_LP+k3*M_LP)
K=5.0E-11 Reaction: Cdiff => Cdiff; Commensal_Harmful, Commensal_Beneficial, Cdiff, Commensal_Harmful, Cdiff, Commensal_Harmful, Rate Law: Lumen*K*Cdiff*Commensal_Harmful
k1=2.39665140586358 Reaction: Th17_LP => ; iTreg_LP, Th17_LP, Th17_LP, Rate Law: LP*k1*Th17_LP
k1=1.72495199303666E-5 Reaction: eDC_MLN => ; iTreg_MLN, eDC_MLN, eDC_MLN, Rate Law: MLN*k1*eDC_MLN
k1=2255.80469507059 Reaction: eDC_MLN => Th17_MLN; eDC_MLN, eDC_MLN, Rate Law: MLN*k1*eDC_MLN
k1=53.9130568911728 Reaction: tDC_MLN => iTreg_MLN; tDC_MLN, tDC_MLN, Rate Law: k1*tDC_MLN
K=2.35932924820229E-7 Reaction: N_Lum => ; Commensal_Beneficial, N_Lum, Commensal_Beneficial, N_Lum, Commensal_Beneficial, Rate Law: Lumen*K*N_Lum*Commensal_Beneficial
k1=1.459 Reaction: Th1_MLN => Th1_LP; E_i, Th1_MLN, Th1_MLN, Rate Law: k1*Th1_MLN
k2=26.8747332769592; k1=559.297141527983; K=2.0E-4 Reaction: iDC_E + Cdiff => tDC_LP; Commensal_Beneficial, Commensal_Dead, E, E_i, Cdiff, Commensal_Beneficial, Commensal_Dead, E, E_i, Cdiff, Commensal_Beneficial, Commensal_Dead, E, E_i, Rate Law: K*Cdiff*(k1*Commensal_Beneficial/Commensal_Dead+k2*E/(E_i+100))
k1=5.5 Reaction: iTreg_MLN => iTreg_LP; E_i, iTreg_MLN, iTreg_MLN, Rate Law: k1*iTreg_MLN
k=0.55 Reaction: iDC_E + Cdiff => eDC_LP; Commensal_Dead, Commensal_Beneficial, Cdiff, Cdiff, Rate Law: k*Cdiff
k1=2.50454427171444 Reaction: Th17_MLN => Th17_LP; E_i, Th17_MLN, Th17_MLN, Rate Law: k1*Th17_MLN
k1=0.99505694359 Reaction: Th1_LP => ; iTreg_LP, Commensal_Dead, Th1_LP, Th1_LP, Rate Law: LP*k1*Th1_LP
k3=0.129717307334483; v=5.29827880572231E-5; k1=0.120935308788409; k2=0.171190728888258 Reaction: N_LP => N_Lum; Cdiff, E_d, Th17_LP, iTreg_LP, N_LP, Cdiff, E_d, Th17_LP, iTreg_LP, N_LP, Cdiff, E_d, Th17_LP, iTreg_LP, Rate Law: v*N_LP*(Cdiff*(k1*E_d+k2*Th17_LP)-k3*iTreg_LP)
k1=2.5 Reaction: E_i => E_d; E_i, E_i, Rate Law: Epithelium*k1*E_i
K=4.5E-5; e2=0.092308585205372; e1=2.0 Reaction: M0 => M_LP; Th17_LP, Cdiff, iTreg_LP, M0, Th17_LP, Cdiff, iTreg_LP, M0, Th17_LP, Cdiff, iTreg_LP, Rate Law: K*M0*((e1*Th17_LP+Cdiff)-e2*iTreg_LP)
k=9.5E-4 Reaction: tDC_MLN => ; iTreg_MLN, tDC_MLN, tDC_MLN, Rate Law: Lumen*k*tDC_MLN
k1=20.0 Reaction: M_LP => ; iTreg_LP, M_LP, M_LP, Rate Law: Epithelium*k1*M_LP
k1=1.27393226093773; k2=0.0020401460213434 Reaction: Th17_LP => iTreg_LP; Cdiff, Th17_LP, Cdiff, iTreg_LP, Th17_LP, Cdiff, iTreg_LP, Rate Law: LP*(k1*Th17_LP-k2*Cdiff*iTreg_LP)
k1=3.65 Reaction: tDC_LP => tDC_MLN; tDC_LP, tDC_LP, Rate Law: Lumen*k1*tDC_LP
k1=0.006; k3=1.16013457036959E-6; k2=0.0106698310809694; v=0.065 Reaction: E_i => E_d; N_Lum, Th17_LP, M_LP, E_i, N_Lum, Th17_LP, M_LP, E_i, N_Lum, Th17_LP, M_LP, Rate Law: Epithelium*v*E_i*(k1*N_Lum+k2*Th17_LP+k3*M_LP)
k1=0.0648415756801505; K=0.0430096; k2=9.65568121975566E-5 Reaction: eDC_MLN => Th1_MLN; Commensal_Dead, Commensal_Beneficial, E, eDC_MLN, Commensal_Dead, Commensal_Beneficial, E, eDC_MLN, Commensal_Dead, Commensal_Beneficial, E, Rate Law: MLN*K*eDC_MLN*Commensal_Dead/(k1*Commensal_Beneficial+k2*E)
k1=4000.0 Reaction: E_d => E; E_d, E_d, Rate Law: Epithelium*k1*E_d

States:

Name Description
eDC LP [dendritic cell; lamina propria]
Cdiff [Clostridioides difficile]
iTreg LP [regulatory T-lymphocyte; lamina propria]
Commensal Beneficial [Bacteria]
Commensal Harmful [Bacteria]
E i [epithelial cell]
eDC MLN [mesenteric lymph node; dendritic cell]
M0 [macrophage]
M LP [lamina propria; macrophage]
Th1 MLN [mesenteric lymph node; Th1 cell]
N Lum [neutrophil; Lumen of intestine]
E [epithelial cell]
Th1 LP [Th1 cell; lamina propria]
Th17 LP [Th17 cell; lamina propria]
E d [epithelial cell]
tDC MLN [dendritic cell; mesenteric lymph node]
Th17 MLN [mesenteric lymph node; Th17 cell]
N LP [lamina propria; neutrophil]
iDC E [dendritic cell; epithelium]
tDC LP [dendritic cell; lamina propria]
iTreg MLN [mesenteric lymph node; regulatory T-lymphocyte]
Commensal Dead [Bacteria]

Observables: none

Leber2016 - Expanded model of Tfh-Tfr differentiation - Helicobacter pylori infection The parameters used in the model…

T follicular helper (Tfh) cells are a highly plastic subset of CD4+ T cells specialized in providing B cell help and promoting inflammatory and effector responses during infectious and immune-mediate diseases. Helicobacter pylori is the dominant member of the gastric microbiota and exerts both beneficial and harmful effects on the host. Chronic inflammation in the context of H. pylori has been linked to an upregulation in T helper (Th)1 and Th17 CD4+ T cell phenotypes, controlled in part by the cytokine, interleukin-21. This study investigates the differentiation and regulation of Tfh cells, major producers of IL-21, in the immune response to H. pylori challenge. To better understand the conditions influencing the promotion and inhibition of a chronically elevated Tfh population, we used top-down and bottom-up approaches to develop computational models of Tfh and T follicular regulatory (Tfr) cell differentiation. Stability analysis was used to characterize the presence of two bi-stable steady states in the calibrated Tfh/Tfr models. Stochastic simulation was used to illustrate the ability of the parameter set to dictate two distinct behavioral patterns. Furthermore, sensitivity analysis helped identify the importance of various parameters on the establishment of Tfh and Tfr cell populations. The core network model was expanded into a more comprehensive and predictive model by including cytokine production and signaling pathways. From the expanded network, the interaction between TGFB-Induced Factor Homeobox 1 (Tgif1) and the retinoid X receptor (RXR) was displayed to exert control over the determination of the Tfh response. Model simulations predict that Tgif1 and RXR respectively induce and curtail Tfh responses. This computational hypothesis was validated experimentally by assaying Tgif1, RXR and Tfh in stomachs of mice infected with H. pylori. link: http://identifiers.org/pubmed/26947272

Parameters:

Name Description
sigma1=3.0403; alpha=0.0539319; sigma2=2.92243 Reaction: => CXCR5; Tfh, Tfr, Blimp1, Rate Law: compartment*(sigma1*Tfh+sigma2*Tfr)/(alpha+Blimp1)
k1=0.03 Reaction: nTreg =>, Rate Law: compartment*k1*nTreg
sigma=0.01787 Reaction: => ICOS; Tfh, Rate Law: compartment*sigma*Tfh
sigma=0.1 Reaction: => FoxP3; nTreg, Rate Law: compartment*sigma*nTreg
k1=0.08465 Reaction: RXR =>, Rate Law: compartment*k1*RXR
sigma=10.0 Reaction: => STAT5; IL2, Rate Law: compartment*sigma*IL2
v=100.0 Reaction: => NaiveCD4, Rate Law: compartment*v
alpha=0.1; gamma=0.364318 Reaction: NaiveCD4 => Tfh; Bcl6, IL10, Rate Law: compartment*gamma*NaiveCD4*Bcl6/(alpha+IL10)
gamma1=0.0555708; gamma2=0.111444 Reaction: nTreg => Tfr; Bcl6, CXCR5, Rate Law: compartment*(gamma1*nTreg*Bcl6+gamma2*nTreg*CXCR5)
alpha=3.04985; sigma=0.05 Reaction: => RXR; TGFb, Tgif1, Rate Law: compartment*sigma*TGFb/(alpha+Tgif1)
sigma2=0.1; sigma1=0.1253 Reaction: => STAT3; IL6, IL21, Rate Law: compartment*(sigma1*IL6+sigma2*IL21)
k1=0.69675 Reaction: IL6 =>, Rate Law: compartment*k1*IL6
sigma=0.0677 Reaction: => IL10; Tfr, Rate Law: compartment*sigma*Tfr
v=10.0 Reaction: => nTreg, Rate Law: compartment*v
sigma=0.014555 Reaction: => IL4; Tfh, Rate Law: compartment*sigma*Tfh
sigma=0.06005 Reaction: => IL21; Tfh, Rate Law: compartment*sigma*Tfh
k1=0.16373 Reaction: Bcl6 =>, Rate Law: compartment*k1*Bcl6
alpha2=1.36752; sigma2=3.2195; alpha1=0.20001; alpha3=0.1253; sigma1=3.24417 Reaction: => Bcl6; ICOS, STAT3, Blimp1, STAT5, RXR, Rate Law: compartment*(sigma1*ICOS+sigma2*STAT3)/((alpha1+Blimp1)*(alpha2+STAT5)*(alpha3+RXR))
sigma=3.59995; alpha=2.386 Reaction: => Blimp1; Tfr, Bcl6, Rate Law: compartment*sigma*Tfr/(alpha+Bcl6)
k1=0.1 Reaction: FoxP3 =>, Rate Law: compartment*k1*FoxP3
sigma1=0.9901; alpha1=0.43475 Reaction: => IL6; IL4, Rate Law: compartment*sigma1/(alpha1+IL4)
k1=0.1106 Reaction: Blimp1 =>, Rate Law: compartment*k1*Blimp1
v=0.1 Reaction: => IL2, Rate Law: compartment*v
k1=0.035655 Reaction: NaiveCD4 =>, Rate Law: compartment*k1*NaiveCD4

States:

Name Description
NaiveCD4 [T-cell surface glycoprotein CD4]
CXCR5 [C-X-C chemokine receptor type 5]
Bcl6 [B-cell lymphoma 6 protein homolog]
IL21 [Interleukin-21]
TGFb [TGF-beta receptor type-1]
Tgif1 [Homeobox protein TGIF1]
Blimp1 [PR domain zinc finger protein 1]
STAT3 [Signal transducer and activator of transcription 3]
ICOS [Inducible T-cell costimulator]
FoxP3 [Forkhead box protein P3]
Tfr [naive regulatory T cell]
RXR [Retinoic acid receptor RXR-alpha]
IL2 [Interleukin-2]
STAT5 [Signal transducer and activator of transcription 5B]
IL4 [Interleukin-4]
nTreg [naive regulatory T cell]
Tfh [T follicular helper cell]
IL6 [Interleukin-6]
IL10 [Interleukin-10]

Observables: none

The model is first model of tissue level cellular immune responses to H. pylori in the publication, "Modeling the role o…

Immune responses to Helicobacter pylori are orchestrated through complex balances of host-bacterial interactions, including inflammatory and regulatory immune responses across scales that can lead to the development of the gastric disease or the promotion of beneficial systemic effects. While inflammation in response to the bacterium has been reasonably characterized, the regulatory pathways that contribute to preventing inflammatory events during H. pylori infection are incompletely understood. To aid in this effort, we have generated a computational model incorporating recent developments in the understanding of H. pylori-host interactions. Sensitivity analysis of this model reveals that a regulatory macrophage population is critical in maintaining high H. pylori colonization without the generation of an inflammatory response. To address how this myeloid cell subset arises, we developed a second model describing an intracellular signaling network for the differentiation of macrophages. Modeling studies predicted that LANCL2 is a central regulator of inflammatory and effector pathways and its activation promotes regulatory responses characterized by IL-10 production while suppressing effector responses. The predicted impairment of regulatory macrophage differentiation by the loss of LANCL2 was simulated based on multiscale linkages between the tissue-level gastric mucosa and the intracellular models. The simulated deletion of LANCL2 resulted in a greater clearance of H. pylori, but also greater IFN? responses and damage to the epithelium. The model predictions were validated within a mouse model of H. pylori colonization in wild-type (WT), LANCL2 whole body KO and myeloid-specific LANCL2-/- (LANCL2Myeloid) mice, which displayed similar decreases in H. pylori burden, CX3CR1+ IL-10-producing macrophages, and type 1 regulatory (Tr1) T cells. This study shows the importance of LANCL2 in the induction of regulatory responses in macrophages and T cells during H. pylori infection. link: http://identifiers.org/doi/10.1371/journal.pone.0167440

Parameters: none

States: none

Observables: none

The model is the second model of the publication "Modeling the role of lanthionine synthetase C-like 2 (LANCL2) in the m…

Immune responses to Helicobacter pylori are orchestrated through complex balances of host-bacterial interactions, including inflammatory and regulatory immune responses across scales that can lead to the development of the gastric disease or the promotion of beneficial systemic effects. While inflammation in response to the bacterium has been reasonably characterized, the regulatory pathways that contribute to preventing inflammatory events during H. pylori infection are incompletely understood. To aid in this effort, we have generated a computational model incorporating recent developments in the understanding of H. pylori-host interactions. Sensitivity analysis of this model reveals that a regulatory macrophage population is critical in maintaining high H. pylori colonization without the generation of an inflammatory response. To address how this myeloid cell subset arises, we developed a second model describing an intracellular signaling network for the differentiation of macrophages. Modeling studies predicted that LANCL2 is a central regulator of inflammatory and effector pathways and its activation promotes regulatory responses characterized by IL-10 production while suppressing effector responses. The predicted impairment of regulatory macrophage differentiation by the loss of LANCL2 was simulated based on multiscale linkages between the tissue-level gastric mucosa and the intracellular models. The simulated deletion of LANCL2 resulted in a greater clearance of H. pylori, but also greater IFN? responses and damage to the epithelium. The model predictions were validated within a mouse model of H. pylori colonization in wild-type (WT), LANCL2 whole body KO and myeloid-specific LANCL2-/- (LANCL2Myeloid) mice, which displayed similar decreases in H. pylori burden, CX3CR1+ IL-10-producing macrophages, and type 1 regulatory (Tr1) T cells. This study shows the importance of LANCL2 in the induction of regulatory responses in macrophages and T cells during H. pylori infection. link: http://identifiers.org/doi/10.1371/journal.pone.0167440

Parameters: none

States: none

Observables: none

On optimal chemotherapy with a strongly targeted agent for a model of tumor-immune system interactions with generalized…

In this paper, a mathematical model for chemotherapy that takes tumor immune-system interactions into account is considered for a strongly targeted agent. We use a classical model originally formulated by Stepanova, but replace exponential tumor growth with a generalised logistic growth model function depending on a parameter v. This growth function interpolates between a Gompertzian model (in the limit v → 0) and an exponential model (in the limit v → ∞). The dynamics is multi-stable and equilibria and their stability will be investigated depending on the parameter v. Except for small values of v, the system has both an asymptotically stable microscopic (benign) equilibrium point and an asymptotically stable macroscopic (malignant) equilibrium point. The corresponding regions of attraction are separated by the stable manifold of a saddle. The optimal control problem of moving an initial condition that lies in the malignant region into the benign region is formulated and the structure of optimal singular controls is determined. link: http://identifiers.org/pubmed/23906150

Parameters:

Name Description
alpha = 0.1181 Reaction: => y, Rate Law: compartment*alpha
v = 1.0; mu_C = 0.5599; x_inf = 780.0 Reaction: => x, Rate Law: compartment*mu_C*x*(1-(x/x_inf)^v)
delta = 0.37451 Reaction: y =>, Rate Law: compartment*delta*y
beta = 0.00264; mu_I = 0.00484 Reaction: => y; x, Rate Law: compartment*mu_I*(1-beta*x)*x*y
gamma = 1.0 Reaction: x => ; y, Rate Law: compartment*gamma*x*y

States:

Name Description
x [Tumor Volume]
y y

Observables: none

Lee2003 - Roles of APC and Axin in Wnt Pathway (without regulatory loop) This model is described in the article: [The…

Wnt signaling plays an important role in both oncogenesis and development. Activation of the Wnt pathway results in stabilization of the transcriptional coactivator beta-catenin. Recent studies have demonstrated that axin, which coordinates beta-catenin degradation, is itself degraded. Although the key molecules required for transducing a Wnt signal have been identified, a quantitative understanding of this pathway has been lacking. We have developed a mathematical model for the canonical Wnt pathway that describes the interactions among the core components: Wnt, Frizzled, Dishevelled, GSK3beta, APC, axin, beta-catenin, and TCF. Using a system of differential equations, the model incorporates the kinetics of protein-protein interactions, protein synthesis/degradation, and phosphorylation/dephosphorylation. We initially defined a reference state of kinetic, thermodynamic, and flux data from experiments using Xenopus extracts. Predictions based on the analysis of the reference state were used iteratively to develop a more refined model from which we analyzed the effects of prolonged and transient Wnt stimulation on beta-catenin and axin turnover. We predict several unusual features of the Wnt pathway, some of which we tested experimentally. An insight from our model, which we confirmed experimentally, is that the two scaffold proteins axin and APC promote the formation of degradation complexes in very different ways. We can also explain the importance of axin degradation in amplifying and sharpening the Wnt signal, and we show that the dependence of axin degradation on APC is an essential part of an unappreciated regulatory loop that prevents the accumulation of beta-catenin at decreased APC concentrations. By applying control analysis to our mathematical model, we demonstrate the modular design, sensitivity, and robustness of the Wnt pathway and derive an explicit expression for tumor suppression and oncogenicity. link: http://identifiers.org/pubmed/14551908

Parameters:

Name Description
k4 = 0.267 Reaction: APC_axin_GSK3 => APC__axin__GSK3, Rate Law: Cytoplasm*k4*APC_axin_GSK3
k11 = 0.417 Reaction: B_catenin =>, Rate Law: Cytoplasm*k11*B_catenin
k12 = 0.423 Reaction: => B_catenin_0, Rate Law: Nucleus*k12
k15 = 0.167 Reaction: Axin =>, Rate Law: Cytoplasm*k15*Axin
k5 = 0.133 Reaction: APC__axin__GSK3 => APC_axin_GSK3, Rate Law: Cytoplasm*k5*APC__axin__GSK3
k10 = 206.0 Reaction: B_catenin__APC__axin__GSK3 => B_catenin + APC__axin__GSK3, Rate Law: Cytoplasm*k10*B_catenin__APC__axin__GSK3
k_16 = 15000.0; k16 = 500.0 Reaction: B_catenin_0 + TCF => B_catenin_TCF, Rate Law: Nucleus*(k16*B_catenin_0*TCF-k_16*B_catenin_TCF)
k9 = 206.0 Reaction: B_catenin_APC__axin__GSK3 => B_catenin__APC__axin__GSK3, Rate Law: Cytoplasm*k9*B_catenin_APC__axin__GSK3
k7 = 500.0; k_7 = 25000.0 Reaction: APC + Axin => APC_axin, Rate Law: Cytoplasm*(k7*APC*Axin-k_7*APC_axin)
k14 = 8.22E-5 Reaction: => Axin, Rate Law: Cytoplasm*k14
k6 = 0.0909; k_6 = 0.909 Reaction: GSK3 + APC_axin => APC_axin_GSK3, Rate Law: Cytoplasm*(k6*GSK3*APC_axin-k_6*APC_axin_GSK3)
t0 = 40.0; lambda = 0.05 Reaction: W = piecewise(0, time < t0, exp((-1)*lambda*(time-t0))), Rate Law: missing
k3 = 0.05 Reaction: APC_axin_GSK3 => GSK3 + APC_axin; Dsh_a, Rate Law: Cytoplasm*k3*Dsh_a*APC_axin_GSK3
k1 = 0.182 Reaction: Dsh_i => Dsh_a; W, Rate Law: Cytoplasm*k1*Dsh_i*W
k_8 = 60000.0; k8 = 500.0 Reaction: APC__axin__GSK3 + B_catenin_0 => B_catenin_APC__axin__GSK3, Rate Law: k8*APC__axin__GSK3*B_catenin_0-k_8*B_catenin_APC__axin__GSK3
k_17 = 600000.0; k17 = 500.0 Reaction: APC + B_catenin_0 => B_catenin_APC, Rate Law: k17*APC*B_catenin_0-k_17*B_catenin_APC
k2 = 0.0182 Reaction: Dsh_a => Dsh_i, Rate Law: Cytoplasm*k2*Dsh_a
k13 = 2.57E-4 Reaction: B_catenin_0 =>, Rate Law: Nucleus*k13*B_catenin_0

States:

Name Description
APC axin GSK3 [Axin-1; Glycogen synthase kinase-3 beta; Adenomatous polyposis coli homolog]
W [stimulation]
B catenin APC axin GSK3 [Axin-1; Catenin beta-1; Adenomatous polyposis coli homolog; Glycogen synthase kinase-3 beta]
APC axin [Axin-1; Adenomatous polyposis coli homolog]
TCF [trichloroacetic acid]
GSK3 [Glycogen synthase kinase-3 beta]
Dsh a [Segment polarity protein dishevelled homolog DVL-2]
Dsh i [Segment polarity protein dishevelled homolog DVL-2]
B catenin 0 [Catenin beta-1]
B catenin APC axin GSK3 [Adenomatous polyposis coli homolog; Catenin beta-1; Axin-1; Glycogen synthase kinase-3 beta]
APC axin GSK3 [Axin-1; Adenomatous polyposis coli homolog; Glycogen synthase kinase-3 beta]
APC [Adenomatous polyposis coli homolog]
B catenin [Catenin beta-1]
B catenin TCF [trichloroacetic acid; Catenin beta-1]
B catenin APC [Catenin beta-1; Adenomatous polyposis coli homolog]
Axin [Axin-1]

Observables: none

Mechanisitc model of PI3K and ERK signal integration by Myc. ERK and PI3K regulated Myc satbility by phosphorylating the…

The transcription factor Myc plays a central role in regulating cell-fate decisions, including proliferation, growth, and apoptosis. To maintain a normal cell physiology, it is critical that the control of Myc dynamics is precisely orchestrated. Recent studies suggest that such control of Myc can be achieved at the post-translational level via protein stability modulation. Myc is regulated by two Ras effector pathways: the extracellular signal-regulated kinase (Erk) and phosphatidylinositol 3-kinase (PI3K) pathways. To gain quantitative insight into Myc dynamics, we have developed a mathematical model to analyze post-translational regulation of Myc via sequential phosphorylation by Erk and PI3K. Our results suggest that Myc integrates Erk and PI3K signals to result in various cellular responses by differential stability control of Myc protein isoforms. Such signal integration confers a flexible dynamic range for the system output, governed by stability change. In addition, signal integration may require saturation of the input signals, leading to sensitive signal integration to the temporal features of the input signals, insensitive response to their amplitudes, and resistance to input fluctuations. We further propose that these characteristics of the protein stability control module in Myc may be commonly utilized in various cell types and classes of proteins. link: http://identifiers.org/pubmed/18463697

Parameters:

Name Description
k_MT = 0.4 1/h; K_MT = 0.01 nmol/l Reaction: Myc_ser62 => Myc_thr58; GSK3B, Rate Law: Cell*k_MT*GSK3B*Myc_ser62/(K_MT+Myc_ser62)
kM = 1.0 1/h Reaction: => Myc; GF, Rate Law: Cell*kM*GF
K_AP = 0.01 nmol/l; k_ap = 360.0 1/h Reaction: AKT => AKTp; PI3K, Rate Law: Cell*k_ap*PI3K*AKT/(K_AP+AKT)
dM = 2.08 1/h Reaction: Myc =>, Rate Law: Cell*dM*Myc
k_AD = 72.0 nmol/(h*l); K_AD = 0.01 nmol/l Reaction: AKTp => AKT, Rate Law: Cell*k_AD*AKTp/(K_AD+AKTp)
K_MS = 0.01 nmol/l; k_MS = 2.3 1/h Reaction: Myc => Myc_ser62; ERK, Rate Law: Cell*k_MS*ERK*Myc/(K_MS+Myc)
K_GP = 0.01 nmol/l; k_GP = 360.0 1/h Reaction: GSK3B => GSK3Bp; AKTp, Rate Law: Cell*k_GP*AKTp*GSK3B/(K_GP+GSK3B)
K_GD = 0.01 nmol/l; k_GD = 72.0 nmol/(h*l) Reaction: GSK3Bp => GSK3B, Rate Law: Cell*k_GD*GSK3Bp/(K_GD+GSK3Bp)
dMS = 0.35 1/h Reaction: Myc_ser62 =>, Rate Law: Cell*dMS*Myc_ser62
dMT = 2.08 1/h Reaction: Myc_thr58 =>, Rate Law: Cell*dMT*Myc_thr58

States:

Name Description
AKT [RAC-alpha serine/threonine-protein kinase]
AKTp [RAC-alpha serine/threonine-protein kinase]
Myc ser62 [Myc proto-oncogene protein]
Myc [Myc proto-oncogene protein]
GSK3Bp [Glycogen synthase kinase-3 beta]
Myc thr58 [Myc proto-oncogene protein]
Myc total [Myc proto-oncogene protein]
GSK3B [Glycogen synthase kinase-3 beta]

Observables: none

Lee2008 - Genome-scale metabolic network of Clostridium acetobutylicum (iJL432)This model is described in the article:…

To understand the metabolic characteristics of Clostridium acetobutylicum and to examine the potential for enhanced butanol production, we reconstructed the genome-scale metabolic network from its annotated genomic sequence and analyzed strategies to improve its butanol production. The generated reconstructed network consists of 502 reactions and 479 metabolites and was used as the basis for an in silico model that could compute metabolic and growth performance for comparison with fermentation data. The in silico model successfully predicted metabolic fluxes during the acidogenic phase using classical flux balance analysis. Nonlinear programming was used to predict metabolic fluxes during the solventogenic phase. In addition, essential genes were predicted via single gene deletion studies. This genome-scale in silico metabolic model of C. acetobutylicum should be useful for genome-wide metabolic analysis as well as strain development for improving production of biochemicals, including butanol. link: http://identifiers.org/pubmed/18758767

Parameters: none

States: none

Observables: none

Lee2010 - Genome-scale metabolic network of Zymomonas mobilis (iZmobMBEL601)This model is described in the article: [Th…

BACKGROUND: Zymomonas mobilis ZM4 is a Gram-negative bacterium that can efficiently produce ethanol from various carbon substrates, including glucose, fructose, and sucrose, via the Entner-Doudoroff pathway. However, systems metabolic engineering is required to further enhance its metabolic performance for industrial application. As an important step towards this goal, the genome-scale metabolic model of Z. mobilis is required to systematically analyze in silico the metabolic characteristics of this bacterium under a wide range of genotypic and environmental conditions. RESULTS: The genome-scale metabolic model of Z. mobilis ZM4, ZmoMBEL601, was reconstructed based on its annotated genes, literature, physiological and biochemical databases. The metabolic model comprises 579 metabolites and 601 metabolic reactions (571 biochemical conversion and 30 transport reactions), built upon extensive search of existing knowledge. Physiological features of Z. mobilis were then examined using constraints-based flux analysis in detail as follows. First, the physiological changes of Z. mobilis as it shifts from anaerobic to aerobic environments (i.e. aerobic shift) were investigated. Then the intensities of flux-sum, which is the cluster of either all ingoing or outgoing fluxes through a metabolite, and the maximum in silico yields of ethanol for Z. mobilis and Escherichia coli were compared and analyzed. Furthermore, the substrate utilization range of Z. mobilis was expanded to include pentose sugar metabolism by introducing metabolic pathways to allow Z. mobilis to utilize pentose sugars. Finally, double gene knock-out simulations were performed to design a strategy for efficiently producing succinic acid as another example of application of the genome-scale metabolic model of Z. mobilis. CONCLUSION: The genome-scale metabolic model reconstructed in this study was able to successfully represent the metabolic characteristics of Z. mobilis under various conditions as validated by experiments and literature information. This reconstructed metabolic model will allow better understanding of Z. mobilis metabolism and consequently designing metabolic engineering strategies for various biotechnological applications. link: http://identifiers.org/pubmed/21092328

Parameters: none

States: none

Observables: none

MODEL1202270000 @ v0.0.1

This model is from the article: A regulatory role for repeated decoy transcription factor binding sites in target gene…

Tandem repeats of DNA that contain transcription factor (TF) binding sites could serve as decoys, competitively binding to TFs and affecting target gene expression. Using a synthetic system in budding yeast, we demonstrate that repeated decoy sites inhibit gene expression by sequestering a transcriptional activator and converting the graded dose-response of target promoters to a sharper, sigmoidal-like response. On the basis of both modeling and chromatin immunoprecipitation measurements, we attribute the altered response to TF binding decoy sites more tightly than promoter binding sites. Tight TF binding to arrays of contiguous repeated decoy sites only occurs when the arrays are mostly unoccupied. Finally, we show that the altered sigmoidal-like response can convert the graded response of a transcriptional positive-feedback loop to a bimodal response. Together, these results show how changing numbers of repeated TF binding sites lead to qualitative changes in behavior and raise new questions about the stability of TF/promoter binding. link: http://identifiers.org/pubmed/22453733

Parameters: none

States: none

Observables: none

This model is from the article: A regulatory role for repeated decoy transcription factor binding sites in target gene…

Tandem repeats of DNA that contain transcription factor (TF) binding sites could serve as decoys, competitively binding to TFs and affecting target gene expression. Using a synthetic system in budding yeast, we demonstrate that repeated decoy sites inhibit gene expression by sequestering a transcriptional activator and converting the graded dose-response of target promoters to a sharper, sigmoidal-like response. On the basis of both modeling and chromatin immunoprecipitation measurements, we attribute the altered response to TF binding decoy sites more tightly than promoter binding sites. Tight TF binding to arrays of contiguous repeated decoy sites only occurs when the arrays are mostly unoccupied. Finally, we show that the altered sigmoidal-like response can convert the graded response of a transcriptional positive-feedback loop to a bimodal response. Together, these results show how changing numbers of repeated TF binding sites lead to qualitative changes in behavior and raise new questions about the stability of TF/promoter binding. link: http://identifiers.org/pubmed/22453733

Parameters: none

States: none

Observables: none

MODEL1806060001 @ v0.0.1

Blood coagulation model derived from Nayak2015.

Essentials Baseline coagulation activity can be detected in non-bleeding state by in vivo biomarker levels. A detailed mathematical model of coagulation was developed to describe the non-bleeding state. Optimized model described in vivo biomarkers with recombinant activated factor VII treatment. Sensitivity analysis predicted prothrombin fragment 1 + 2 and D-dimer are regulated differently.Background Prothrombin fragment 1 + 2 (F1 + 2 ), thrombin-antithrombin III complex (TAT) and D-dimer can be detected in plasma from non-bleeding hemostatically normal subjects or hemophilic patients. They are often used as safety or pharmacodynamic biomarkers for hemostatis-modulating therapies in the clinic, and provide insights into in vivo coagulation activity. Objectives To develop a quantitative systems pharmacology (QSP) model of the blood coagulation network to describe in vivo biomarkers, including F1 + 2 , TAT, and D-dimer, under non-bleeding conditions. Methods The QSP model included intrinsic and extrinsic coagulation pathways, platelet activation state-dependent kinetics, and a two-compartment pharmacokinetics model for recombinant activated factor VII (rFVIIa). Literature data on F1 + 2 and D-dimer at baseline and changes with rFVIIa treatment were used for parameter optimization. Multiparametric sensitivity analysis (MPSA) was used to understand key proteins that regulate F1 + 2 , TAT and D-dimer levels. Results The model was able to describe tissue factor (TF)-dependent baseline levels of F1 + 2 , TAT and D-dimer in a non-bleeding state, and their increases in hemostatically normal subjects and hemophilic patients treated with different doses of rFVIIa. The amount of TF required is predicted to be very low in a non-bleeding state. The model also predicts that these biomarker levels will be similar in hemostatically normal subjects and hemophilic patients. MPSA revealed that F1 + 2 and TAT levels are highly correlated, and that D-dimer is more sensitive to the perturbation of coagulation protein concentrations. Conclusions A QSP model for non-bleeding baseline coagulation activity was established with data from clinically relevant in vivo biomarkers at baseline and changes in response to rFVIIa treatment. This model will provide future mechanistic insights into this system. link: http://identifiers.org/pubmed/27666750

Parameters: none

States: none

Observables: none

Authors developed a microfluidic gut-liver co-culture chip that aims to reproduce the first-pass metabolism of oral drug…

Accurate prediction of first-pass metabolism is essential for improving the time and cost efficiency of drug development process. Here, we have developed a microfluidic gut-liver co-culture chip that aims to reproduce the first-pass metabolism of oral drugs. This chip consists of two separate layers for gut (Caco-2) and liver (HepG2) cell lines, where cells can be co-cultured in both 2D and 3D forms. Both cell lines were maintained well in the chip, verified by confocal microscopy and measurement of hepatic enzyme activity. We investigated the PK profile of paracetamol in the chip, and corresponding PK model was constructed, which was used to predict PK profiles for different chip design parameters. Simulation results implied that a larger absorption surface area and a higher metabolic capacity are required to reproduce the in vivo PK profile of paracetamol more accurately. Our study suggests the possibility of reproducing the human PK profile on a chip, contributing to accurate prediction of pharmacological effect of drugs. link: http://identifiers.org/pubmed/29116458

Parameters:

Name Description
V_basol = 380.0; Mp_g_HepG2 = 0.59; Mp_s_HepG2 = 0.35; P_para = 103.8; Ai = 0.33 Reaction: C_para__Basolateral___HepG2_ = ((P_para*Ai*(C_para_Caco_2-C_para__Basolateral___HepG2_)-Mp_s_HepG2*C_para__Basolateral___HepG2_*V_basol)-Mp_g_HepG2*C_para__Basolateral___HepG2_*V_basol)/V_basol, Rate Law: ((P_para*Ai*(C_para_Caco_2-C_para__Basolateral___HepG2_)-Mp_s_HepG2*C_para__Basolateral___HepG2_*V_basol)-Mp_g_HepG2*C_para__Basolateral___HepG2_*V_basol)/V_basol
P_sulf = 49.9; V_basol = 380.0; Mp_s_HepG2 = 0.35; Ai = 0.33 Reaction: C_sulf__Basolateral___HepG2_ = (P_sulf*Ai*(C_sulf_Caco_2-C_sulf__Basolateral___HepG2_)+Mp_s_HepG2*C_para__Basolateral___HepG2_*V_basol)/V_basol, Rate Law: (P_sulf*Ai*(C_sulf_Caco_2-C_sulf__Basolateral___HepG2_)+Mp_s_HepG2*C_para__Basolateral___HepG2_*V_basol)/V_basol
P_glu = 58.9; V_basol = 380.0; Mp_g_HepG2 = 0.59; Ai = 0.33 Reaction: C_glu__Basolateral___HepG2_ = (P_glu*Ai*(C_glu_Caco_2-C_glu__Basolateral___HepG2_)+Mp_g_HepG2*C_para__Basolateral___HepG2_*V_basol)/V_basol, Rate Law: (P_glu*Ai*(C_glu_Caco_2-C_glu__Basolateral___HepG2_)+Mp_g_HepG2*C_para__Basolateral___HepG2_*V_basol)/V_basol
P_para = 103.8; V_api = 500.0; Ai = 0.33 Reaction: C_para_Apical = (-1)*P_para*Ai*(C_para_Apical-C_para_Caco_2)/V_api, Rate Law: (-1)*P_para*Ai*(C_para_Apical-C_para_Caco_2)/V_api
P_sulf = 49.9; Mp_s_caco = 14.9; V_caco = 0.33; Ai = 0.33 Reaction: C_sulf_Caco_2 = ((P_sulf*Ai*(C_sulf_Apical-C_sulf_Caco_2)-P_sulf*Ai*(C_sulf_Caco_2-C_sulf__Basolateral___HepG2_))+Mp_s_caco*C_para_Caco_2*V_caco)/V_caco, Rate Law: ((P_sulf*Ai*(C_sulf_Apical-C_sulf_Caco_2)-P_sulf*Ai*(C_sulf_Caco_2-C_sulf__Basolateral___HepG2_))+Mp_s_caco*C_para_Caco_2*V_caco)/V_caco
P_glu = 58.9; Mp_g_caco = 17.6; V_caco = 0.33; Ai = 0.33 Reaction: C_glu_Caco_2 = ((P_glu*Ai*(C_glu_Apical-C_glu_Caco_2)-P_glu*Ai*(C_glu_Caco_2-C_glu__Basolateral___HepG2_))+Mp_g_caco*C_para_Caco_2*V_caco)/V_caco, Rate Law: ((P_glu*Ai*(C_glu_Apical-C_glu_Caco_2)-P_glu*Ai*(C_glu_Caco_2-C_glu__Basolateral___HepG2_))+Mp_g_caco*C_para_Caco_2*V_caco)/V_caco
P_glu = 58.9; V_api = 500.0; Ai = 0.33 Reaction: C_glu_Apical = (-1)*P_glu*Ai*(C_glu_Apical-C_glu_Caco_2)/V_api, Rate Law: (-1)*P_glu*Ai*(C_glu_Apical-C_glu_Caco_2)/V_api
P_sulf = 49.9; V_api = 500.0; Ai = 0.33 Reaction: C_sulf_Apical = (-1)*P_sulf*Ai*(C_sulf_Apical-C_sulf_Caco_2)/V_api, Rate Law: (-1)*P_sulf*Ai*(C_sulf_Apical-C_sulf_Caco_2)/V_api
Mp_s_caco = 14.9; Mp_g_caco = 17.6; V_caco = 0.33; P_para = 103.8; Ai = 0.33 Reaction: C_para_Caco_2 = (((P_para*Ai*(C_para_Apical-C_para_Caco_2)-P_para*Ai*(C_para_Caco_2-C_para__Basolateral___HepG2_))-Mp_s_caco*C_para_Caco_2*V_caco)-Mp_g_caco*C_para_Caco_2*V_caco)/V_caco, Rate Law: (((P_para*Ai*(C_para_Apical-C_para_Caco_2)-P_para*Ai*(C_para_Caco_2-C_para__Basolateral___HepG2_))-Mp_s_caco*C_para_Caco_2*V_caco)-Mp_g_caco*C_para_Caco_2*V_caco)/V_caco

States:

Name Description
C para Caco 2 [paracetamol; D00217]
C glu Basolateral HepG2 [D00217; paracetamol; Glucuronide]
C sulf Apical [paracetamol sulfate]
C sulf Caco 2 [paracetamol sulfate]
C glu Apical [paracetamol; D00217; Glucuronide]
C sulf Basolateral HepG2 [paracetamol sulfate]
C para Basolateral HepG2 [paracetamol; D00217]
C para Apical [D00217; paracetamol]
C glu Caco 2 [Glucuronide; paracetamol; D00217]

Observables: none

Elucidating the interactions between the adhesive and transcriptional functions of beta-catenin in normal and cancerous…

Wnt signalling is involved in a wide range of physiological and pathological processes. The presence of an extracellular Wnt stimulus induces cytoplasmic stabilisation and nuclear translocation of beta-catenin, a protein that also plays an essential role in cadherin-mediated adhesion. Two main hypotheses have been proposed concerning the balance between beta-catenin's adhesive and transcriptional functions: either beta-catenin's fate is determined by competition between its binding partners, or Wnt induces folding of beta-catenin into a conformation allocated preferentially to transcription. The experimental data supporting each hypotheses remain inconclusive. In this paper we present a new mathematical model of the Wnt pathway that incorporates beta-catenin's dual function. We use this model to carry out a series of in silico experiments and compare the behaviour of systems governed by each hypothesis. Our analytical results and model simulations provide further insight into the current understanding of Wnt signalling and, in particular, reveal differences in the response of the two modes of interaction between adhesion and signalling in certain in silico settings. We also exploit our model to investigate the impact of the mutations most commonly observed in human colorectal cancer. Simulations show that the amount of functional APC required to maintain a normal phenotype increases with increasing strength of the Wnt signal, a result which illustrates that the environment can substantially influence both tumour initiation and phenotype. link: http://identifiers.org/pubmed/17382967

Parameters: none

States: none

Observables: none

BIOMD0000000103 @ v0.0.1

This model represents the non-competitive binding of XIAP to Casapase-3 and Caspase-9. In other words, XIAP mediated fee…

The intrinsic, or mitochondrial, pathway of caspase activation is essential for apoptosis induction by various stimuli including cytotoxic stress. It depends on the cellular context, whether cytochrome c released from mitochondria induces caspase activation gradually or in an all-or-none fashion, and whether caspase activation irreversibly commits cells to apoptosis. By analyzing a quantitative kinetic model, we show that inhibition of caspase-3 (Casp3) and Casp9 by inhibitors of apoptosis (IAPs) results in an implicit positive feedback, since cleaved Casp3 augments its own activation by sequestering IAPs away from Casp9. We demonstrate that this positive feedback brings about bistability (i.e., all-or-none behaviour), and that it cooperates with Casp3-mediated feedback cleavage of Casp9 to generate irreversibility in caspase activation. Our calculations also unravel how cell-specific protein expression brings about the observed qualitative differences in caspase activation (gradual versus all-or-none and reversible versus irreversible). Finally, known regulators of the pathway are shown to efficiently shift the apoptotic threshold stimulus, suggesting that the bistable caspase cascade computes multiple inputs into an all-or-none caspase output. As cellular inhibitory proteins (e.g., IAPs) frequently inhibit consecutive intermediates in cellular signaling cascades (e.g., Casp3 and Casp9), the feedback mechanism described in this paper is likely to be a widespread principle on how cells achieve ultrasensitivity, bistability, and irreversibility. link: http://identifiers.org/pubmed/16978046

Parameters:

Name Description
k6 = 5.0E-5 Reaction: C3 + C9_star => C3_star + C9_star, Rate Law: cytosol*k6*C3*C9_star
d = 1.0; a = 1.0; k1 = 0.002; kb1 = 0.1 Reaction: C9X_C3_star + A => AC9X_C3_star, Rate Law: cytosol*(a*k1*C9X_C3_star*A-d*kb1*AC9X_C3_star)
d = 1.0; a = 1.0; k15 = 0.003; k15b = 0.001 Reaction: C3_star + C9_starX => C9_starX_C3_star, Rate Law: cytosol*(a*k15*C3_star*C9_starX-d*k15b*C9_starX_C3_star)
k17 = 0.001; k17prod = 0.02 Reaction: => C9, Rate Law: cytosol*(k17prod-k17*C9)
k20 = 0.001 Reaction: AC9X =>, Rate Law: cytosol*k20*AC9X
k1 = 0.002; kb1 = 0.1 Reaction: A + C9 => AC9, Rate Law: cytosol*(k1*A*C9-kb1*AC9)
k3 = 3.5E-4 Reaction: C3 + AC9 => C3_star + AC9, Rate Law: cytosol*k3*C3*AC9
k28 = 0.001 Reaction: AC9_starX =>, Rate Law: cytosol*k28*AC9_starX
k31 = 0.001 Reaction: C9_starX_C3_star =>, Rate Law: cytosol*k31*C9_starX_C3_star
k9 = 0.001; k9b = 0.001 Reaction: C9 + X => C9X, Rate Law: cytosol*(k9*C9*X-k9b*C9X)
d = 1.0; a = 1.0; k9 = 0.001; k9b = 0.001 Reaction: C9 + C3_starX => C9X_C3_star, Rate Law: cytosol*(a*k9*C9*C3_starX-d*k9b*C9X_C3_star)
k25 = 0.001 Reaction: C9_starX =>, Rate Law: cytosol*k25*C9_starX
k22prod = 0.2; k22 = 0.001 Reaction: => C3, Rate Law: cytosol*(k22prod-k22*C3)
k14b = 0.1; k14 = 0.002 Reaction: C9_starX + A => AC9_starX, Rate Law: cytosol*(k14*C9_starX*A-k14b*AC9_starX)
k29 = 0.001 Reaction: C9X_C3_star =>, Rate Law: cytosol*k29*C9X_C3_star
k8b = 0.1; k8 = 0.002 Reaction: C9_star + A => AC9_star, Rate Law: cytosol*(k8*C9_star*A-k8b*AC9_star)
k21 = 0.001 Reaction: AC9 =>, Rate Law: cytosol*k21*AC9
k16prod = 0.02; k16 = 0.001 Reaction: => A, Rate Law: cytosol*(k16prod-k16*A)
k13 = 0.002; k13b = 0.1 Reaction: C9X + A => AC9X, Rate Law: cytosol*(k13*C9X*A-k13b*AC9X)
k5 = 2.0E-4 Reaction: AC9 + C3_star => AC9_star + C3_star, Rate Law: cytosol*k5*AC9*C3_star
k2 = 5.0E-6 Reaction: C3 + C9 => C3_star + C9, Rate Law: cytosol*k2*C3*C9
k4 = 2.0E-4 Reaction: C9 + C3_star => C9_star + C3_star, Rate Law: cytosol*k4*C9*C3_star
k23 = 0.001 Reaction: C3_star =>, Rate Law: cytosol*k23*C3_star
k19 = 0.001 Reaction: C9X =>, Rate Law: cytosol*k19*C9X
k12b = 0.001; k12 = 0.001 Reaction: AC9_star + X => AC9_starX, Rate Law: cytosol*(k12*AC9_star*X-k12b*AC9_starX)
k18 = 0.001; k18prod = 0.04 Reaction: => X, Rate Law: cytosol*(k18prod-k18*X)
k10 = 0.001; k10b = 0.001 Reaction: AC9 + X => AC9X, Rate Law: cytosol*(k10*AC9*X-k10b*AC9X)
k26 = 0.001 Reaction: C9_star =>, Rate Law: cytosol*k26*C9_star
k30 = 0.001 Reaction: AC9_starX_C3_star =>, Rate Law: cytosol*k30*AC9_starX_C3_star
k11b = 0.001; k11 = 0.001 Reaction: C9_star + X => C9_starX, Rate Law: cytosol*(k11*C9_star*X-k11b*C9_starX)
k32 = 0.001 Reaction: AC9_starX_C3_star =>, Rate Law: cytosol*k32*AC9_starX_C3_star
k27 = 0.001 Reaction: AC9_star =>, Rate Law: cytosol*k27*AC9_star
k15 = 0.003; k15b = 0.001 Reaction: C3_star + X => C3_starX, Rate Law: cytosol*(k15*C3_star*X-k15b*C3_starX)
k24 = 0.001 Reaction: C3_starX =>, Rate Law: cytosol*k24*C3_starX
k7 = 0.0035 Reaction: C3 + AC9_star => C3_star + AC9_star, Rate Law: cytosol*k7*C3*AC9_star

States:

Name Description
C3 star [Caspase-3]
A [Apoptotic protease-activating factor 1]
C3 [Caspase-3]
X [E3 ubiquitin-protein ligase XIAP]
AC9 star [Caspase-9; Apoptotic protease-activating factor 1]
C9 starX [E3 ubiquitin-protein ligase XIAP; Caspase-9]
C9X [E3 ubiquitin-protein ligase XIAP; Caspase-9]
AC9X C3 star [E3 ubiquitin-protein ligase XIAP; Caspase-9; Apoptotic protease-activating factor 1]
AC9X [E3 ubiquitin-protein ligase XIAP; Caspase-9; Apoptotic protease-activating factor 1]
C9 starX C3 star [Caspase-3; E3 ubiquitin-protein ligase XIAP; Caspase-9]
C9 [Caspase-9]
C9X C3 star [E3 ubiquitin-protein ligase XIAP; Caspase-9]
C9 star [Caspase-9]
AC9 starX [E3 ubiquitin-protein ligase XIAP; Caspase-9; Apoptotic protease-activating factor 1]
C3 starX [E3 ubiquitin-protein ligase XIAP; Caspase-3]
AC9 starX C3 star [Caspase-3; Caspase-9; E3 ubiquitin-protein ligase XIAP; Apoptotic protease-activating factor 1]
AC9 [Caspase-9; Apoptotic protease-activating factor 1]

Observables: none

BIOMD0000000102 @ v0.0.1

The model reproduces active Caspase-3 time profile corresponding to the total Apaf-1 value of 20 nM as depicted in Fig 2…

The intrinsic, or mitochondrial, pathway of caspase activation is essential for apoptosis induction by various stimuli including cytotoxic stress. It depends on the cellular context, whether cytochrome c released from mitochondria induces caspase activation gradually or in an all-or-none fashion, and whether caspase activation irreversibly commits cells to apoptosis. By analyzing a quantitative kinetic model, we show that inhibition of caspase-3 (Casp3) and Casp9 by inhibitors of apoptosis (IAPs) results in an implicit positive feedback, since cleaved Casp3 augments its own activation by sequestering IAPs away from Casp9. We demonstrate that this positive feedback brings about bistability (i.e., all-or-none behaviour), and that it cooperates with Casp3-mediated feedback cleavage of Casp9 to generate irreversibility in caspase activation. Our calculations also unravel how cell-specific protein expression brings about the observed qualitative differences in caspase activation (gradual versus all-or-none and reversible versus irreversible). Finally, known regulators of the pathway are shown to efficiently shift the apoptotic threshold stimulus, suggesting that the bistable caspase cascade computes multiple inputs into an all-or-none caspase output. As cellular inhibitory proteins (e.g., IAPs) frequently inhibit consecutive intermediates in cellular signaling cascades (e.g., Casp3 and Casp9), the feedback mechanism described in this paper is likely to be a widespread principle on how cells achieve ultrasensitivity, bistability, and irreversibility. link: http://identifiers.org/pubmed/16978046

Parameters:

Name Description
k17 = 0.001 sec_inverse; k17prod = 0.02 nM_per_sec Reaction: => C9, Rate Law: cytosol*(k17prod-k17*C9)
k14 = 0.002 per_nM_per_sec; k14b = 0.1 sec_inverse Reaction: C9_starX + A => AC9_starX, Rate Law: cytosol*(k14*C9_starX*A-k14b*AC9_starX)
k26 = 0.001 sec_inverse Reaction: C9_star =>, Rate Law: cytosol*k26*C9_star
k19 = 0.001 sec_inverse Reaction: C9X =>, Rate Law: cytosol*k19*C9X
k8b = 0.1 sec_inverse; k8 = 0.002 per_nM_per_sec Reaction: C9_star + A => AC9_star, Rate Law: cytosol*(k8*C9_star*A-k8b*AC9_star)
k1 = 0.002 per_nM_per_sec; kb1 = 0.1 sec_inverse Reaction: A + C9 => AC9, Rate Law: cytosol*(k1*A*C9-kb1*AC9)
k12 = 0.001 per_nM_per_sec; k12b = 0.001 sec_inverse Reaction: AC9_star + X => AC9_starX, Rate Law: cytosol*(k12*AC9_star*X-k12b*AC9_starX)
k2 = 5.0E-6 per_nM_per_sec Reaction: C3 + C9 => C3_star + C9, Rate Law: cytosol*k2*C3*C9
k13 = 0.002 per_nM_per_sec; k13b = 0.1 sec_inverse Reaction: C9X + A => AC9X, Rate Law: cytosol*(k13*C9X*A-k13b*AC9X)
k6 = 5.0E-5 per_nM_per_sec Reaction: C3 + C9_star => C3_star + C9_star, Rate Law: cytosol*k6*C3*C9_star
k18prod = 0.04 nM_per_sec; k18 = 0.001 sec_inverse Reaction: => X, Rate Law: cytosol*(k18prod-k18*X)
k7 = 0.0035 per_nM_per_sec Reaction: C3 + AC9_star => C3_star + AC9_star, Rate Law: cytosol*k7*C3*AC9_star
k4 = 2.0E-4 per_nM_per_sec Reaction: C9 + C3_star => C9_star + C3_star, Rate Law: cytosol*k4*C9*C3_star
k16prod = 0.02 nM_per_sec; k16 = 0.001 sec_inverse Reaction: => A, Rate Law: cytosol*(k16prod-k16*A)
k5 = 2.0E-4 per_nM_per_sec Reaction: AC9 + C3_star => AC9_star + C3_star, Rate Law: cytosol*k5*AC9*C3_star
k24 = 0.001 sec_inverse Reaction: C3_starX =>, Rate Law: cytosol*k24*C3_starX
k21 = 0.001 sec_inverse Reaction: AC9 =>, Rate Law: cytosol*k21*AC9
k9b = 0.001 sec_inverse; k9 = 0.001 per_nM_per_sec Reaction: C9 + X => C9X, Rate Law: cytosol*(k9*C9*X-k9b*C9X)
k27 = 0.001 sec_inverse Reaction: AC9_star =>, Rate Law: cytosol*k27*AC9_star
k20 = 0.001 sec_inverse Reaction: AC9X =>, Rate Law: cytosol*k20*AC9X
k3 = 3.5E-4 per_nM_per_sec Reaction: C3 + AC9 => C3_star + AC9, Rate Law: cytosol*k3*C3*AC9
k28 = 0.001 sec_inverse Reaction: AC9_starX =>, Rate Law: cytosol*k28*AC9_starX
k23 = 0.001 sec_inverse Reaction: C3_star =>, Rate Law: cytosol*k23*C3_star
k22prod = 0.2 nM_per_sec; k22 = 0.001 sec_inverse Reaction: => C3, Rate Law: cytosol*(k22prod-k22*C3)
k15b = 0.001 sec_inverse; k15 = 0.003 per_nM_per_sec Reaction: C3_star + X => C3_starX, Rate Law: cytosol*(k15*C3_star*X-k15b*C3_starX)
k10 = 0.001 per_nM_per_sec; k10b = 0.001 sec_inverse Reaction: AC9 + X => AC9X, Rate Law: cytosol*(k10*AC9*X-k10b*AC9X)
k25 = 0.001 sec_inverse Reaction: C9_starX =>, Rate Law: cytosol*k25*C9_starX
k11b = 0.001 sec_inverse; k11 = 0.001 per_nM_per_sec Reaction: C9_star + X => C9_starX, Rate Law: cytosol*(k11*C9_star*X-k11b*C9_starX)

States:

Name Description
C3 star [Caspase-3]
A [Apoptotic protease-activating factor 1]
C3 [Caspase-3]
X [E3 ubiquitin-protein ligase XIAP]
AC9 star [Apoptotic protease-activating factor 1; Caspase-9]
C9 starX [Caspase-9; E3 ubiquitin-protein ligase XIAP]
C9X [Caspase-9; E3 ubiquitin-protein ligase XIAP]
AC9X [Apoptotic protease-activating factor 1; Caspase-9; E3 ubiquitin-protein ligase XIAP]
C9 [Caspase-9]
C9 star [Caspase-9]
AC9 starX [Apoptotic protease-activating factor 1; Caspase-9; E3 ubiquitin-protein ligase XIAP]
C3 starX [Caspase-3; E3 ubiquitin-protein ligase XIAP]
AC9 [Apoptotic protease-activating factor 1; Caspase-9]

Observables: none

BIOMD0000000245 @ v0.0.1

This the model from the article: A biochemically structured model for Saccharomyces cerevisiae. Lei F, Rotbøll M, Jø…

A biochemically structured model for the aerobic growth of Saccharomyces cerevisiae on glucose and ethanol is presented. The model focuses on the pyruvate and acetaldehyde branch points where overflow metabolism occurs when the growth changes from oxidative to oxido-reductive. The model is designed to describe the onset of aerobic alcoholic fermentation during steady-state as well as under dynamical conditions, by triggering an increase in the glycolytic flux using a key signalling component which is assumed to be closely related to acetaldehyde. An investigation of the modelled process dynamics in a continuous cultivation revealed multiple steady states in a region of dilution rates around the transition between oxidative and oxido-reductive growth. A bifurcation analysis using the two external variables, the dilution rate, D, and the inlet concentration of glucose, S(f), as parameters, showed that a fold bifurcation occurs close to the critical dilution rate resulting in multiple steady-states. The region of dilution rates within which multiple steady states may occur depends strongly on the substrate feed concentration. Consequently a single steady state may prevail at low feed concentrations, whereas multiple steady states may occur over a relatively wide range of dilution rates at higher feed concentrations. link: http://identifiers.org/pubmed/11434967

Parameters:

Name Description
X_AcDH = 0.0075 dimensionless; k_11 = 0.02 gram per liter per hour Reaction: AcDH => ; x, Rate Law: k_11*X_AcDH*x*env
X_AcDH = 0.0075 dimensionless Reaction: AcDH = x*X_AcDH, Rate Law: missing
D = 0.1 per hour Reaction: s_pyr =>, Rate Law: s_pyr*D*env
K_9e = 13.0 gram per liter; k_9c = 0.00399 gram per liter per hour; k_9 = 0.008 gram per liter per hour; k_9e = 0.0751 gram per liter per hour; K_9 = 1.0E-6 gram per liter; K_9i = 25.0 liter per gram; X_a = 0.1 dimensionless Reaction: a => AcDH; x, s_glu, s_EtOH, Rate Law: ((k_9*s_glu/(s_glu+K_9)+k_9e*s_EtOH/(s_EtOH+K_9e))/(K_9i*s_glu+1)+k_9c*s_glu/(s_glu+K_9))*X_a*x*env
k_1e = 47.1 gram per liter per hour; K_1e = 0.12 gram per liter; K_1l = 0.94 gram per liter; k_1h = 0.584 gram per liter per hour; X_a = 0.1 dimensionless; k_1l = 1.43 gram per liter per hour; K_1h = 0.0116 gram per liter; K_1i = 14.2 liter per gram Reaction: s_glu => s_pyr + Red; s_acetald, x, Rate Law: (k_1l*s_glu/(s_glu+K_1l)+k_1h*s_glu/(s_glu+K_1h)+k_1e*s_acetald*s_glu/(s_glu*(K_1i*s_acetald+1)+K_1e))*x*X_a*env
K_5e = 0.1 gram per liter; K_5i = 440.0 liter per gram; k_8 = 0.589 gram per liter per hour; X_a = 0.1 dimensionless Reaction: s_acetate => x + CO2 + Red; x, s_glu, Rate Law: k_8*s_acetate/((s_acetate+K_5e)*(1+K_5i*s_glu))*x*X_a*env
K_5e = 0.1 gram per liter; K_5 = 0.0102 gram per liter; K_5i = 440.0 liter per gram; k_5e = 0.775 gram per liter per hour; k_5 = 0.0104 gram per liter per hour; X_a = 0.1 dimensionless Reaction: s_acetate => CO2 + Red; x, s_glu, Rate Law: (k_5*s_acetate/(s_acetate+K_5)+k_5e*s_acetate/((s_acetate+K_5e)*(1+K_5i*s_glu)))*x*X_a*env
K_10 = 0.0023 gram per liter; k_10 = 0.392 gram per liter per hour; K_10e = 0.0018 gram per liter; k_10e = 0.00339 gram per liter per hour; X_a = 0.1 dimensionless Reaction: a => ; x, s_glu, s_EtOH, Rate Law: (k_10*s_glu/(s_glu+K_10)+k_10e*s_EtOH/(s_EtOH+K_10e))*X_a*x*env
K_6e = 0.057 gram per liter; k_6r = 0.0125 dimensionless; k_6 = 2.82 gram per liter per hour; K_6 = 0.034 gram per liter; X_a = 0.1 dimensionless Reaction: s_acetald + Red => s_EtOH; x, Rate Law: k_6*(s_acetald-k_6r*s_EtOH)/(s_acetald+K_6+K_6e*s_EtOH)*x*X_a*env
X_a = 0.1 dimensionless Reaction: a = x*X_a, Rate Law: missing
K_3 = 5.0E-7 gram per liter; k_3 = 5.81 gram per liter per hour; X_a = 0.1 dimensionless Reaction: s_pyr => s_acetald + CO2; x, Rate Law: k_3*s_pyr^4/(s_pyr^4+K_3)*x*X_a*env
k_2 = 0.501 gram per liter per hour; K_2i = 0.101 liter per gram; K_2 = 2.0E-5 gram per liter; X_a = 0.1 dimensionless Reaction: s_pyr => CO2 + Red; x, s_glu, Rate Law: k_2*s_pyr/((s_pyr+K_2)*(K_2i*s_glu+1))*x*X_a*env
k_7 = 1.203 gram per liter per hour; K_7 = 0.0101 gram per liter; X_a = 0.1 dimensionless Reaction: s_glu => x + CO2 + Red; x, Rate Law: k_7*s_glu/(s_glu+K_7)*x*X_a*env
X_AcDH = 0.0075 dimensionless; K_4 = 2.64E-4 gram per liter; k_4 = 4.8 gram per liter per hour; X_a = 0.1 dimensionless Reaction: s_acetald => s_acetate + Red; x, s_EtOH, Rate Law: k_4*s_acetald/(s_acetald+K_4)*x*X_a*X_AcDH*env

States:

Name Description
s acetald [acetaldehyde; Acetaldehyde]
Red [NADH; NADH]
x BM
CO2 [carbon dioxide; CO2]
a BM(active)
S f [glucose; C00293]
s EtOH [ethanol; Ethanol]
s glu [glucose; C00293]
s pyr [pyruvate; Pyruvate]
AcDH BM(AcDH)
s acetate [CHEBI_40480; Acetate]

Observables: none

MODEL1109150002 @ v0.0.1

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

A mathematical model has been developed to simulate the generation of thrombin by the tissue factor pathway. The model gives reasonable predictions of published experimental results without the adjustment of any parameter values. The model also accounts explicitly for the effects of serine protease inhibitors on thrombin generation. Simulations to define the optimum affinity profile of an inhibitor in this system indicate that for an inhibitor simultaneously potent against VIIa, IXa, and Xa, inhibition of thrombin generation decreases dramatically as the affinity for thrombin increases. Additional simulations show that the reason for this behavior is the sequestration of the inhibitor by small amounts of thrombin generated early in the reaction. This model is also useful for predicting the potency of compounds that inhibit thrombosis in rats. We believe that this is the first mathematical model of blood coagulation that considers the effects of exogenous inhibitors. Such a model, or extensions thereof, should be useful for evaluating targets for therapeutic intervention in the processes of blood coagulation. link: http://identifiers.org/pubmed/7592704

Parameters: none

States: none

Observables: none

MODEL1109150001 @ v0.0.1

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

A mathematical model has been developed to simulate the generation of thrombin by the tissue factor pathway. The model gives reasonable predictions of published experimental results without the adjustment of any parameter values. The model also accounts explicitly for the effects of serine protease inhibitors on thrombin generation. Simulations to define the optimum affinity profile of an inhibitor in this system indicate that for an inhibitor simultaneously potent against VIIa, IXa, and Xa, inhibition of thrombin generation decreases dramatically as the affinity for thrombin increases. Additional simulations show that the reason for this behavior is the sequestration of the inhibitor by small amounts of thrombin generated early in the reaction. This model is also useful for predicting the potency of compounds that inhibit thrombosis in rats. We believe that this is the first mathematical model of blood coagulation that considers the effects of exogenous inhibitors. Such a model, or extensions thereof, should be useful for evaluating targets for therapeutic intervention in the processes of blood coagulation. link: http://identifiers.org/pubmed/7592704

Parameters: none

States: none

Observables: none

BIOMD0000000171 @ v0.0.1

# Leloup and Goldbeter, 1998 This model was created after the article by Leloup and Goldbeter, *J Biol Rhythms* 1998,…

The authors present a model for circadian oscillations of the Period (PER) and Timeless (TIM) proteins in Drosophila. The model for the circadian clock is based on multiple phosphorylation of PER and TIM and on the negative feedback exerted by a nuclear PER-TIM complex on the transcription of the per and tim genes. Periodic behavior occurs in a large domain of parameter space in the form of limit cycle oscillations. These sustained oscillations occur in conditions corresponding to continuous darkness or to entrainment by light-dark cycles and are in good agreement with experimental observations on the temporal variations of PER and TIM and of per and tim mRNAs. Birhythmicity (coexistence of two periodic regimes) and aperiodic oscillations (chaos) occur in a restricted range of parameter values. The results are compared to the predictions of a model based on the sole regulation by PER. Both the formation of a complex between PER and TIM and protein phosphorylation are found to favor oscillatory behavior. Determining how the period depends on several key parameters allows us to test possible molecular explanations proposed for the altered period in the per(l) and per(s) mutants. The extended model further allows the construction of phase-response curves based on the light-induced triggering of TIM degradation. These curves, established as a function of both the duration and magnitude of the effect of a light pulse, match the phase-response curves obtained experimentally in the wild type and per(s) mutant of Drosophila. link: http://identifiers.org/pubmed/9486845

Parameters:

Name Description
K_2T=2.0 nanomoleperlitre; V_2T=1.0 nanoMperHour Reaction: T1 => T0, Rate Law: V_2T*T1/(K_2T+T1)*cytoplasm
k_sP=0.9 perhour Reaction: => P0; M_P, Rate Law: k_sP*M_P*cytoplasm
K_4P=2.0 nanomoleperlitre; V_4P=1.0 nanoMperHour Reaction: P2 => P1, Rate Law: V_4P*P2/(K_4P+P2)*cytoplasm
kd_C=0.01 perhour Reaction: C =>, Rate Law: kd_C*C*cytoplasm
K_4T=2.0 nanomoleperlitre; V_4T=1.0 nanoMperHour Reaction: T2 => T1, Rate Law: V_4T*T2/(K_4T+T2)*cytoplasm
v_mT=0.7 nanoMperHour; K_mT=0.2 nanomoleperlitre; kd = 0.01 perhour Reaction: M_T =>, Rate Law: (v_mT/(K_mT+M_T)+kd)*M_T*cytoplasm
v_dP=2.0 nanoMperHour; K_dP=0.2 nanomoleperlitre Reaction: P2 =>, Rate Law: v_dP*P2/(K_dP+P2)*cytoplasm
K_mP=0.2 nanomoleperlitre; v_mP=0.8 nanoMperHour; kd = 0.01 perhour Reaction: M_P =>, Rate Law: (v_mP/(K_mP+M_P)+kd)*M_P*cytoplasm
K_3P=2.0 nanomoleperlitre; V_3P=8.0 nanoMperHour Reaction: P1 => P2, Rate Law: V_3P*P1/(K_3P+P1)*cytoplasm
kd = 0.01 perhour Reaction: P1 =>, Rate Law: kd*P1*cytoplasm
k_sT=0.9 perhour Reaction: => T0; M_T, Rate Law: k_sT*M_T*cytoplasm
V_1P=8.0 nanoMperHour; K_1P=2.0 nanomoleperlitre Reaction: P0 => P1, Rate Law: V_1P*P0/(K_1P+P0)*cytoplasm
K_dT=0.2 nanomoleperlitre; v_dT = 2.0 nanoMperHour Reaction: T2 =>, Rate Law: v_dT*T2/(K_dT+T2)*cytoplasm
Ki_P=1.0 nanomoleperlitre; v_sP=0.8 nanomolperhour; n = 4.0 dimensionless Reaction: => M_P; CN, Rate Law: v_sP*Ki_P^n/(Ki_P^n+CN^n)
K_2P=2.0 nanomoleperlitre; V_2P=1.0 nanoMperHour Reaction: P1 => P0, Rate Law: V_2P*P1/(K_2P+P1)*cytoplasm
kd_CN=0.01 perhour Reaction: CN =>, Rate Law: kd_CN*CN*nucleus
v_sT=1.0 nanomolperhour; n = 4.0 dimensionless; Ki_T=1.0 nanomoleperlitre Reaction: => M_T; CN, Rate Law: v_sT*Ki_T^n/(Ki_T^n+CN^n)
k3=1.2 pernMperHour; k4=0.6 perhour Reaction: P2 + T2 => C, Rate Law: (k3*T2*P2-k4*C)*cytoplasm
K_1T=2.0 nanomoleperlitre; V_1T=8.0 nanoMperHour Reaction: T0 => T1, Rate Law: V_1T*T0/(K_1T+T0)*cytoplasm
k1=1.2 perhour; k2=0.2 perhour Reaction: C => CN, Rate Law: k1*C*cytoplasm-k2*CN*nucleus
V_3T=8.0 nanoMperHour; K_3T=2.0 nanomoleperlitre Reaction: T1 => T2, Rate Law: V_3T*T1/(K_3T+T1)*cytoplasm

States:

Name Description
M P [messenger RNA; (5')ppPur-mRNA]
T0 [Protein timeless]
C [Period circadian protein; Protein timeless; protein complex]
Pt [Period circadian protein]
P2 [Period circadian protein; Phosphoprotein]
P1 [Period circadian protein; Phosphoprotein]
M T [messenger RNA; (5')ppPur-mRNA]
P0 [Period circadian protein]
CN [Period circadian protein; Protein timeless; protein complex]
Tt [Protein timeless]
T1 [Protein timeless; Phosphoprotein]
T2 [Protein timeless]

Observables: none

BIOMD0000000298 @ v0.0.1

This a model from the article: Limit cycle models for circadian rhythms based on transcriptional regulation in Droso…

We examine theoretical models for circadian oscillations based on transcriptional regulation in Drosophila and Neurospora. For Drosophila, the molecular model is based on the negative feedback exerted on the expression of the per and tim genes by the complex formed between the PER and TIM proteins. For Neurospora, similarly, the model relies on the feedback exerted on the expression of the frq gene by its protein product FRQ. In both models, sustained rhythmic variations in protein and mRNA levels occur in continuous darkness, in the form of limit cycle oscillations. The effect of light on circadian rhythms is taken into account in the models by considering that it triggers degradation of the TIM protein in Drosophila, and frq transcription in Neurospora. When incorporating the control exerted by light at the molecular level, we show that the models can account for the entrainment of circadian rhythms by light-dark cycles and for the damping of the oscillations in constant light, though such damping occurs more readily in the Drosophila model. The models account for the phase shifts induced by light pulses and allow the construction of phase response curves. These compare well with experimental results obtained in Drosophila. The model for Drosophila shows that when applied at the appropriate phase, light pulses of appropriate duration and magnitude can permanently or transiently suppress circadian rhythmicity. We investigate the effects of the magnitude of light-induced changes on oscillatory behavior. Finally, we discuss the common and distinctive features of circadian oscillations in the two organisms. link: http://identifiers.org/pubmed/10643740

Parameters:

Name Description
V2T = 1.0; kd = 0.01; V3T = 8.0; K3T = 2.0; K2T = 2.0; K4T = 2.0; V1T = 8.0; K1T = 2.0; V4T = 1.0 Reaction: T1 = (V1T*T0/(K1T+T0)+V4T*T2/(K4T+T2))-(V2T*T1/(K2T+T1)+V3T*T1/(K3T+T1)+kd*T1), Rate Law: (V1T*T0/(K1T+T0)+V4T*T2/(K4T+T2))-(V2T*T1/(K2T+T1)+V3T*T1/(K3T+T1)+kd*T1)
kd = 0.01; V3T = 8.0; K3T = 2.0; K4T = 2.0; k4 = 0.6; vdT = 3.0; k3 = 1.2; V4T = 1.0; KdT = 0.2 Reaction: T2 = (V3T*T1/(K3T+T1)+k4*C)-(V4T*T2/(K4T+T2)+k3*P2*T2+vdT*T2/(KdT+T2)+kd*T2), Rate Law: (V3T*T1/(K3T+T1)+k4*C)-(V4T*T2/(K4T+T2)+k3*P2*T2+vdT*T2/(KdT+T2)+kd*T2)
V2T = 1.0; kd = 0.01; ksT = 0.9; K2T = 2.0; V1T = 8.0; K1T = 2.0 Reaction: T0 = (ksT*MT+V2T*T1/(K2T+T1))-(V1T*T0/(K1T+T0)+kd*T0), Rate Law: (ksT*MT+V2T*T1/(K2T+T1))-(V1T*T0/(K1T+T0)+kd*T0)
kd = 0.01; n = 4.0; KIP = 1.0; vmP = 1.0; KmP = 0.2; vsP = 1.1 Reaction: MP = vsP*KIP^n/(KIP^n+CN^n)-(vmP*MP/(KmP+MP)+kd*MP), Rate Law: vsP*KIP^n/(KIP^n+CN^n)-(vmP*MP/(KmP+MP)+kd*MP)
k2 = 0.2; k1 = 0.8; kdN = 0.01 Reaction: CN = k1*C-(k2*CN+kdN*CN), Rate Law: k1*C-(k2*CN+kdN*CN)
kd = 0.01; n = 4.0; vsT = 1.0; KIT = 1.0; KmT = 0.2; vmT = 0.7 Reaction: MT = vsT*KIT^n/(KIT^n+CN^n)-(vmT*MT/(KmT+MT)+kd*MT), Rate Law: vsT*KIT^n/(KIT^n+CN^n)-(vmT*MT/(KmT+MT)+kd*MT)
kd = 0.01; V1P = 8.0; V2P = 1.0; K2P = 2.0; K1P = 2.0; ksP = 0.9 Reaction: P0 = (ksP*MP+V2P*P1/(K2P+P1))-(V1P*P0/(K1P+P0)+kd*P0), Rate Law: (ksP*MP+V2P*P1/(K2P+P1))-(V1P*P0/(K1P+P0)+kd*P0)
V4P = 1.0; kd = 0.01; V1P = 8.0; V2P = 1.0; K1P = 2.0; K2P = 2.0; K3P = 2.0; K4P = 2.0; V3P = 8.0 Reaction: P1 = (V1P*P0/(K1P+P0)+V4P*P2/(K4P+P2))-(V2P*P1/(K2P+P1)+V3P*P1/(K3P+P1)+kd*P1), Rate Law: (V1P*P0/(K1P+P0)+V4P*P2/(K4P+P2))-(V2P*P1/(K2P+P1)+V3P*P1/(K3P+P1)+kd*P1)
k2 = 0.2; k1 = 0.8; k4 = 0.6; k3 = 1.2; kdC = 0.01 Reaction: C = (k3*P2*T2+k2*CN)-(k4*C+k1*C+kdC*C), Rate Law: (k3*P2*T2+k2*CN)-(k4*C+k1*C+kdC*C)
V4P = 1.0; kd = 0.01; KdP = 0.2; K3P = 2.0; k4 = 0.6; K4P = 2.0; V3P = 8.0; k3 = 1.2; vdP = 2.2 Reaction: P2 = (V3P*P1/(K3P+P1)+k4*C)-(V4P*P2/(K4P+P2)+k3*P2*T2+vdP*P2/(KdP+P2)+kd*P2), Rate Law: (V3P*P1/(K3P+P1)+k4*C)-(V4P*P2/(K4P+P2)+k3*P2*T2+vdP*P2/(KdP+P2)+kd*P2)

States:

Name Description
CN [Period circadian protein; Protein timeless]
MP [Period circadian protein; messenger RNA; (5')ppPur-mRNA]
T0 [Protein timeless]
C [Protein timeless; Period circadian protein]
T1 [Protein timeless; Phosphoprotein]
T2 [Protein timeless; Phosphoprotein]
P2 [Period circadian protein; Phosphoprotein]
P1 [Period circadian protein; Phosphoprotein]
P0 [Period circadian protein]
MT [Protein timeless; messenger RNA; (5')ppPur-mRNA]

Observables: none

BIOMD0000000299 @ v0.0.1

This a model from the article: Limit cycle models for circadian rhythms based on transcriptional regulation in Drosoph…

We examine theoretical models for circadian oscillations based on transcriptional regulation in Drosophila and Neurospora. For Drosophila, the molecular model is based on the negative feedback exerted on the expression of the per and tim genes by the complex formed between the PER and TIM proteins. For Neurospora, similarly, the model relies on the feedback exerted on the expression of the frq gene by its protein product FRQ. In both models, sustained rhythmic variations in protein and mRNA levels occur in continuous darkness, in the form of limit cycle oscillations. The effect of light on circadian rhythms is taken into account in the models by considering that it triggers degradation of the TIM protein in Drosophila, and frq transcription in Neurospora. When incorporating the control exerted by light at the molecular level, we show that the models can account for the entrainment of circadian rhythms by light-dark cycles and for the damping of the oscillations in constant light, though such damping occurs more readily in the Drosophila model. The models account for the phase shifts induced by light pulses and allow the construction of phase response curves. These compare well with experimental results obtained in Drosophila. The model for Drosophila shows that when applied at the appropriate phase, light pulses of appropriate duration and magnitude can permanently or transiently suppress circadian rhythmicity. We investigate the effects of the magnitude of light-induced changes on oscillatory behavior. Finally, we discuss the common and distinctive features of circadian oscillations in the two organisms. link: http://identifiers.org/pubmed/10643740

Parameters:

Name Description
n = 4.0; Km = 0.5; vm = 0.505; KI = 1.0; vs = 1.6 Reaction: M = vs*KI^n/(KI^n+FN^n)-vm*M/(Km+M), Rate Law: vs*KI^n/(KI^n+FN^n)-vm*M/(Km+M)
Kd = 0.13; k2 = 0.6; ks = 0.5; vd = 1.4; k1 = 0.5 Reaction: FC = (ks*M+k2*FN)-(vd*FC/(Kd+FC)+k1*FC), Rate Law: (ks*M+k2*FN)-(vd*FC/(Kd+FC)+k1*FC)
k2 = 0.6; k1 = 0.5 Reaction: FN = k1*FC-k2*FN, Rate Law: k1*FC-k2*FN

States:

Name Description
FN [Frequency clock protein]
M [Frequency clock protein; messenger RNA; (5')ppPur-mRNA]
FC [Frequency clock protein]

Observables: none

BIOMD0000000021 @ v0.0.1

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

In Drosophila, circadian oscillations in the levels of two proteins, PER and TIM, result from the negative feedback exerted by a PER-TIM complex on the expression of the per and tim genes which code for these two proteins. On the basis of these experimental observations, we have recently proposed a theoretical model for circadian oscillations of the PER and TIM proteins in Drosophila. Here we show that for constant environmental conditions this model is capable of generating autonomous chaotic oscillations. For other parameter values, the model can also display birhythmicity, i.e. the coexistence between two stable regimes of limit cycle oscillations. We analyse the occurrence of chaos and birhythmicity by means of bifurcation diagrams and locate the different domains of complex oscillatory behavior in parameter space. The relative smallness of these domains raises doubts as to the possible physiological significance of chaos and birhythmicity in regard to circadian rhythm generation. Beyond the particular context of circadian rhythms we discuss the results in the light of other mechanisms underlying chaos and birhythmicity in regulated biological systems. Copyright 1999 Academic Press. link: http://identifiers.org/pubmed/10366496

Parameters:

Name Description
k3=1.2; k4=0.6 Reaction: P2 + T2 => CC, Rate Law: Cell*k3*P2*T2-Cell*k4*CC
k_dC=0.01 Reaction: CC =>, Rate Law: Cell*k_dC*CC
k_d=0.01 Reaction: P1 =>, Rate Law: Cell*k_d*P1
k_dN=0.01 Reaction: Cn =>, Rate Law: compartment_0000002*k_dN*Cn
V_dT = 2.0; K_dT=0.2; k_d=0.01 Reaction: T2 =>, Rate Law: Cell*k_d*T2+Cell*V_dT*T2/(K_dT+T2)
V_2T=1.0; K_2T=2.0 Reaction: T1 => T0, Rate Law: Cell*V_2T*T1/(K_2T+T1)
V_3P=8.0; K_3P=2.0 Reaction: P1 => P2, Rate Law: Cell*V_3P*P1/(K_3P+P1)
V_1T=8.0; K_1T=2.0 Reaction: T0 => T1, Rate Law: Cell*V_1T*T0/(K_1T+T0)
k1=0.6; k2=0.2 Reaction: CC => Cn, Rate Law: Cell*k1*CC-compartment_0000002*k2*Cn
V_2P=1.0; K_2P=2.0 Reaction: P1 => P0, Rate Law: Cell*V_2P*P1/(K_2P+P1)
V_mP=0.7; K_mP=0.2; k_d=0.01 Reaction: Mp =>, Rate Law: Cell*k_d*Mp+Cell*V_mP*Mp/(K_mP+Mp)
K_IT=1.0; n=4.0; V_sT=1.0 Reaction: => Mt; Cn, Rate Law: Cell*V_sT*K_IT^n/(K_IT^n+Cn^n)
v_sP=1.0; K_IP=1.0; n=4.0 Reaction: => Mp; Cn, Rate Law: Cell*v_sP*K_IP^n/(K_IP^n+Cn^n)
k_sP=0.9 Reaction: => P0; Mp, Rate Law: Cell*k_sP*Mp
V_1P=8.0; K1_P=2.0 Reaction: P0 => P1, Rate Law: Cell*V_1P*P0/(K1_P+P0)
V_dP=2.0; K_dP=0.2; k_d=0.01 Reaction: P2 =>, Rate Law: Cell*k_d*P2+Cell*V_dP*P2/(K_dP+P2)
V_mT = 0.7; K_mT=0.2; k_d=0.01 Reaction: Mt =>, Rate Law: Cell*k_d*Mt+Cell*V_mT*Mt/(K_mT+Mt)
k_sT=0.9 Reaction: => T0; Mt, Rate Law: Cell*k_sT*Mt
K_4P=2.0; V_4P=1.0 Reaction: P2 => P1, Rate Law: Cell*V_4P*P2/(K_4P+P2)
K_3T=2.0; V_3T=8.0 Reaction: T1 => T2, Rate Law: Cell*V_3T*T1/(K_3T+T1)
V_4T=1.0; K_4T=2.0 Reaction: T2 => T1, Rate Law: Cell*V_4T*T2/(K_4T+T2)

States:

Name Description
Cn [Protein timeless; Period circadian protein]
T1 [Protein timeless]
Mp [messenger RNA; RNA]
T2 [Protein timeless]
T0 [Protein timeless]
CC [Protein timeless; Period circadian protein]
P2 [Period circadian protein]
P1 [Period circadian protein]
Mt [messenger RNA; RNA]
P0 [Period circadian protein]

Observables: none

BIOMD0000000073 @ v0.0.1

This model is according to the paper *Toward a detailed computational model for the mammalian circadian clock* . In thi…

We present a computational model for the mammalian circadian clock based on the intertwined positive and negative regulatory loops involving the Per, Cry, Bmal1, Clock, and Rev-Erb alpha genes. In agreement with experimental observations, the model can give rise to sustained circadian oscillations in continuous darkness, characterized by an antiphase relationship between Per/Cry/Rev-Erbalpha and Bmal1 mRNAs. Sustained oscillations correspond to the rhythms autonomously generated by suprachiasmatic nuclei. For other parameter values, damped oscillations can also be obtained in the model. These oscillations, which transform into sustained oscillations when coupled to a periodic signal, correspond to rhythms produced by peripheral tissues. When incorporating the light-induced expression of the Per gene, the model accounts for entrainment of the oscillations by light-dark cycles. Simulations show that the phase of the oscillations can then vary by several hours with relatively minor changes in parameter values. Such a lability of the phase could account for physiological disorders related to circadian rhythms in humans, such as advanced or delayed sleep phase syndrome, whereas the lack of entrainment by light-dark cycles can be related to the non-24h sleep-wake syndrome. The model uncovers the possible existence of multiple sources of oscillatory behavior. Thus, in conditions where the indirect negative autoregulation of Per and Cry expression is inoperative, the model indicates the possibility that sustained oscillations might still arise from the negative autoregulation of Bmal1 expression. link: http://identifiers.org/pubmed/12775757

Parameters:

Name Description
Vs=1.5; K=0.7; n=4.0 Reaction: => species_7; species_3, Rate Law: cell*Vs*species_3^n/(K^n+species_3^n)
V=0.5; Km=0.3 Reaction: species_2 =>, Rate Law: cell*V*species_2/(Km+species_2)
V=0.2; Km=0.1 Reaction: species_13 => species_3, Rate Law: cell*V*species_13/(Km+species_13)
k1=0.4; k2=0.2 Reaction: species_1 => species_3, Rate Law: cell*(k1*species_1-k2*species_3)
Vs=1.1; K=0.6; n=4.0 Reaction: => species_5; species_3, Rate Law: cell*Vs*species_3^n/(K^n+species_3^n)
k=0.12 Reaction: => species_1; species_0, Rate Law: cell*k*species_0
V=0.1; Km=0.1 Reaction: species_14 => species_12, Rate Law: cell*V*species_14/(Km+species_14)
vsb=1.0; m=2.0; K=2.2 Reaction: => species_0; species_3, Rate Law: cell*vsb*K^m/(K^m+species_3^m)
k=1.6 Reaction: => species_4; species_5, Rate Law: cell*k*species_5
k1=0.12 Reaction: species_4 =>, Rate Law: cell*k1*species_4
k1=0.01 Reaction: species_11 =>, Rate Law: cell*k1*species_11
k=0.6 Reaction: => species_8; species_7, Rate Law: cell*k*species_7
V=0.3; Km=0.1 Reaction: species_9 => species_8, Rate Law: cell*V*species_9/(Km+species_9)
V=0.7; Km=0.3 Reaction: species_11 =>, Rate Law: cell*V*species_11/(Km+species_11)
V=0.5; Km=0.1 Reaction: species_3 => species_13, Rate Law: cell*V*species_3/(Km+species_3)
Km=0.31; V=1.1 Reaction: species_7 =>, Rate Law: cell*V*species_7/(Km+species_7)
V=1.0; Km=0.4 Reaction: species_5 =>, Rate Law: cell*V*species_5/(Km+species_5)
V=0.4; Km=0.1 Reaction: species_12 => species_14, Rate Law: cell*V*species_12/(Km+species_12)
V=0.8; Km=0.4 Reaction: species_0 =>, Rate Law: cell*V*species_0/(Km+species_0)
k1=0.5; k2=0.1 Reaction: species_12 + species_3 => species_15, Rate Law: cell*(k1*species_12*species_3-k2*species_15)
V=0.6; Km=0.1 Reaction: species_4 => species_6, Rate Law: cell*V*species_4/(Km+species_4)
V=0.8; Km=0.3 Reaction: species_15 =>, Rate Law: cell*V*species_15/(Km+species_15)
V=0.6; Km=0.3 Reaction: species_13 =>, Rate Law: cell*V*species_13/(Km+species_13)

States:

Name Description
species 9 [Period circadian protein homolog 1; Period circadian protein homolog 2; Period circadian protein homolog 3]
species 2 [Aryl hydrocarbon receptor nuclear translocator-like protein 1]
species 6 [Cryptochrome-1; Cryptochrome-2]
species 10 [Period circadian protein homolog 1; Cryptochrome-1; Period circadian protein homolog 2; Cryptochrome-1; Period circadian protein homolog 3; Cryptochrome-1]
species 11 [Period circadian protein homolog 1; Cryptochrome-1; Period circadian protein homolog 2; Cryptochrome-2; Period circadian protein homolog 3; Cryptochrome-2]
species 1 [Aryl hydrocarbon receptor nuclear translocator-like protein 1]
species 4 [Cryptochrome-1; Cryptochrome-2]
species 14 [Period circadian protein homolog 1; Cryptochrome-1; Period circadian protein homolog 1; Cryptochrome-2; Period circadian protein homolog 3; Cryptochrome-2]
species 3 [Aryl hydrocarbon receptor nuclear translocator-like protein 1]
species 0 [messenger RNA]
species 8 [Period circadian protein homolog 1; Period circadian protein homolog 2; Period circadian protein homolog 3]
species 12 [Period circadian protein homolog 1; Cryptochrome-1; Period circadian protein homolog 3; Cryptochrome-1; Period circadian protein homolog 3; Cryptochrome-2]
species 7 [messenger RNA]
species 5 [messenger RNA]
species 15 In
species 13 [Aryl hydrocarbon receptor nuclear translocator-like protein 1]

Observables: none

BIOMD0000000074 @ v0.0.1

This is model in continous darkness (DD) described in the article *Toward a detailed computational model for the mammali…

We present a computational model for the mammalian circadian clock based on the intertwined positive and negative regulatory loops involving the Per, Cry, Bmal1, Clock, and Rev-Erb alpha genes. In agreement with experimental observations, the model can give rise to sustained circadian oscillations in continuous darkness, characterized by an antiphase relationship between Per/Cry/Rev-Erbalpha and Bmal1 mRNAs. Sustained oscillations correspond to the rhythms autonomously generated by suprachiasmatic nuclei. For other parameter values, damped oscillations can also be obtained in the model. These oscillations, which transform into sustained oscillations when coupled to a periodic signal, correspond to rhythms produced by peripheral tissues. When incorporating the light-induced expression of the Per gene, the model accounts for entrainment of the oscillations by light-dark cycles. Simulations show that the phase of the oscillations can then vary by several hours with relatively minor changes in parameter values. Such a lability of the phase could account for physiological disorders related to circadian rhythms in humans, such as advanced or delayed sleep phase syndrome, whereas the lack of entrainment by light-dark cycles can be related to the non-24h sleep-wake syndrome. The model uncovers the possible existence of multiple sources of oscillatory behavior. Thus, in conditions where the indirect negative autoregulation of Per and Cry expression is inoperative, the model indicates the possibility that sustained oscillations might still arise from the negative autoregulation of Bmal1 expression. link: http://identifiers.org/pubmed/12775757

Parameters:

Name Description
V=0.2; Km=0.1 Reaction: species_2 => species_1, Rate Law: compartment_0*V*species_2/(Km+species_2)
m=2.0; K=1.0; vsb=1.8 Reaction: => species_0; species_18, Rate Law: compartment_0*vsb*K^m/(K^m+species_18^m)
k=1.2 Reaction: => species_8; species_7, Rate Law: compartment_0*k*species_7
k1=1.0; k2=0.2 Reaction: species_12 + species_3 => species_15, Rate Law: compartment_0*(k1*species_12*species_3-k2*species_15)
V=3.4; Km=0.3 Reaction: species_9 =>, Rate Law: compartment_0*V*species_9/(Km+species_9)
Vs=2.4; K=0.6; n=2.0 Reaction: => species_7; species_3, Rate Law: compartment_0*Vs*species_3^n/(K^n+species_3^n)
V=4.4; Km=0.3 Reaction: species_17 =>, Rate Law: compartment_0*V*species_17/(Km+species_17)
V=2.2; Km=0.3 Reaction: species_7 =>, Rate Law: compartment_0*V*species_7/(Km+species_7)
Km=1.006; V=9.6 Reaction: species_8 => species_9, Rate Law: compartment_0*V*species_8/(Km+species_8)
Vs=1.6; K=0.6; n=2.0 Reaction: => species_16; species_3, Rate Law: compartment_0*Vs*species_3^n/(K^n+species_3^n)
Km=1.006; V=2.4 Reaction: species_10 => species_11, Rate Law: compartment_0*V*species_10/(Km+species_10)
Km=1.006; V=1.2 Reaction: species_4 => species_6, Rate Law: compartment_0*V*species_4/(Km+species_4)
V=1.6; Km=0.4 Reaction: species_16 =>, Rate Law: compartment_0*V*species_16/(Km+species_16)
Km=1.006; V=1.4 Reaction: species_1 => species_2, Rate Law: compartment_0*V*species_1/(Km+species_1)
k2=0.4; k1=0.8 Reaction: species_1 => species_3, Rate Law: compartment_0*(k1*species_1-k2*species_3)
k=1.7 Reaction: => species_17; species_16, Rate Law: compartment_0*k*species_16
V=1.3; Km=0.4 Reaction: species_0 =>, Rate Law: compartment_0*V*species_0/(Km+species_0)
Vs=2.2; K=0.6; n=2.0 Reaction: => species_5; species_3, Rate Law: compartment_0*Vs*species_3^n/(K^n+species_3^n)
V=0.4; Km=0.1 Reaction: species_13 => species_3, Rate Law: compartment_0*V*species_13/(Km+species_13)
V=2.0; Km=0.4 Reaction: species_5 =>, Rate Law: compartment_0*V*species_5/(Km+species_5)
V=3.0; Km=0.3 Reaction: species_2 =>, Rate Law: compartment_0*V*species_2/(Km+species_2)
V=0.6; Km=0.1 Reaction: species_9 => species_8, Rate Law: compartment_0*V*species_9/(Km+species_9)
V=0.8; Km=0.3 Reaction: species_18 =>, Rate Law: compartment_0*V*species_18/(Km+species_18)
k=3.2 Reaction: => species_4; species_5, Rate Law: compartment_0*k*species_5
k=0.32 Reaction: => species_1; species_0, Rate Law: compartment_0*k*species_0
k1=0.02 Reaction: species_2 =>, Rate Law: compartment_0*k1*species_2
V=1.6; Km=0.3 Reaction: species_15 =>, Rate Law: compartment_0*V*species_15/(Km+species_15)
V=1.4; Km=0.3 Reaction: species_6 =>, Rate Law: compartment_0*V*species_6/(Km+species_6)

States:

Name Description
species 9 [Period circadian protein homolog 1; Period circadian protein homolog 2; Period circadian protein homolog 3]
species 2 [Aryl hydrocarbon receptor nuclear translocator-like protein 1]
species 6 [Cryptochrome-1; Cryptochrome-2]
species 10 [Period circadian protein homolog 1; Cryptochrome-1; Period circadian protein homolog 3; Cryptochrome-2]
species 11 [Period circadian protein homolog 1; Cryptochrome-1; Period circadian protein homolog 3; Cryptochrome-2]
species 1 [Aryl hydrocarbon receptor nuclear translocator-like protein 1]
species 18 [Rev-erb alpha]
species 4 [Cryptochrome-1; Cryptochrome-2]
species 16 [messenger RNA]
species 14 [Period circadian protein homolog 1; Cryptochrome-1; Period circadian protein homolog 2; Cryptochrome-1; Period circadian protein homolog 3; Cryptochrome-2]
species 3 [Aryl hydrocarbon receptor nuclear translocator-like protein 1]
species 0 [messenger RNA]
species 8 [Period circadian protein homolog 1; Period circadian protein homolog 2; Period circadian protein homolog 3]
species 17 [Rev-erb alpha]
species 12 [Period circadian protein homolog 1; Cryptochrome-1; Period circadian protein homolog 3; Cryptochrome-2]
species 7 [messenger RNA]
species 5 [messenger RNA]
species 15 In
species 13 [Aryl hydrocarbon receptor nuclear translocator-like protein 1]

Observables: none

BIOMD0000000078 @ v0.0.1

This model is described in the paper *Toward a detailed computational model for the mammalian circadian clock* . In thi…

We present a computational model for the mammalian circadian clock based on the intertwined positive and negative regulatory loops involving the Per, Cry, Bmal1, Clock, and Rev-Erb alpha genes. In agreement with experimental observations, the model can give rise to sustained circadian oscillations in continuous darkness, characterized by an antiphase relationship between Per/Cry/Rev-Erbalpha and Bmal1 mRNAs. Sustained oscillations correspond to the rhythms autonomously generated by suprachiasmatic nuclei. For other parameter values, damped oscillations can also be obtained in the model. These oscillations, which transform into sustained oscillations when coupled to a periodic signal, correspond to rhythms produced by peripheral tissues. When incorporating the light-induced expression of the Per gene, the model accounts for entrainment of the oscillations by light-dark cycles. Simulations show that the phase of the oscillations can then vary by several hours with relatively minor changes in parameter values. Such a lability of the phase could account for physiological disorders related to circadian rhythms in humans, such as advanced or delayed sleep phase syndrome, whereas the lack of entrainment by light-dark cycles can be related to the non-24h sleep-wake syndrome. The model uncovers the possible existence of multiple sources of oscillatory behavior. Thus, in conditions where the indirect negative autoregulation of Per and Cry expression is inoperative, the model indicates the possibility that sustained oscillations might still arise from the negative autoregulation of Bmal1 expression. link: http://identifiers.org/pubmed/12775757

Parameters:

Name Description
V=0.5; Km=0.3 Reaction: species_2 =>, Rate Law: cell*V*species_2/(Km+species_2)
V=0.2; Km=0.1 Reaction: species_13 => species_3, Rate Law: cell*V*species_13/(Km+species_13)
k1=0.4; k2=0.2 Reaction: species_4 + species_8 => species_10, Rate Law: cell*(k1*species_4*species_8-k2*species_10)
Vs=1.1; K=0.6; n=4.0 Reaction: => species_5; species_3, Rate Law: cell*Vs*species_3^n/(K^n+species_3^n)
k=0.12 Reaction: => species_1; species_0, Rate Law: cell*k*species_0
V=0.1; Km=0.1 Reaction: species_6 => species_4, Rate Law: cell*V*species_6/(Km+species_6)
vsb=1.0; m=2.0; K=2.2 Reaction: => species_0; species_3, Rate Law: cell*vsb*K^m/(K^m+species_3^m)
k=1.6 Reaction: => species_4; species_5, Rate Law: cell*k*species_5
k1=0.12 Reaction: species_4 =>, Rate Law: cell*k1*species_4
k1=0.01 Reaction: species_7 =>, Rate Law: cell*k1*species_7
k=0.6 Reaction: => species_8; species_7, Rate Law: cell*k*species_7
V=0.3; Km=0.1 Reaction: species_9 => species_8, Rate Law: cell*V*species_9/(Km+species_9)
V=0.7; Km=0.3 Reaction: species_14 =>, Rate Law: cell*V*species_14/(Km+species_14)
parameter_0000082 = NaN; K=0.7; n=4.0 Reaction: => species_7; species_3, Rate Law: cell*parameter_0000082*species_3^n/(K^n+species_3^n)
V=0.5; Km=0.1 Reaction: species_3 => species_13, Rate Law: cell*V*species_3/(Km+species_3)
Km=0.31; V=1.1 Reaction: species_7 =>, Rate Law: cell*V*species_7/(Km+species_7)
V=1.0; Km=0.4 Reaction: species_5 =>, Rate Law: cell*V*species_5/(Km+species_5)
V=0.4; Km=0.1 Reaction: species_8 => species_9, Rate Law: cell*V*species_8/(Km+species_8)
k1=0.5; k2=0.1 Reaction: species_12 + species_3 => species_15, Rate Law: cell*(k1*species_12*species_3-k2*species_15)
V=0.8; Km=0.4 Reaction: species_0 =>, Rate Law: cell*V*species_0/(Km+species_0)
V=0.6; Km=0.1 Reaction: species_4 => species_6, Rate Law: cell*V*species_4/(Km+species_4)
V=0.8; Km=0.3 Reaction: species_15 =>, Rate Law: cell*V*species_15/(Km+species_15)
V=0.6; Km=0.3 Reaction: species_13 =>, Rate Law: cell*V*species_13/(Km+species_13)

States:

Name Description
species 9 [Period circadian protein homolog 3; Period circadian protein homolog 2; Period circadian protein homolog 1]
species 2 [Aryl hydrocarbon receptor nuclear translocator-like protein 1]
species 6 [Cryptochrome-2; Cryptochrome-1]
species 10 [Period circadian protein homolog 3; Cryptochrome-2; Period circadian protein homolog 1; Cryptochrome-2; Period circadian protein homolog 1; Cryptochrome-1]
species 11 [Period circadian protein homolog 3; Cryptochrome-2; Period circadian protein homolog 1; Cryptochrome-1]
species 1 [Aryl hydrocarbon receptor nuclear translocator-like protein 1]
species 4 [Cryptochrome-2; Cryptochrome-1]
species 14 [Period circadian protein homolog 3; Cryptochrome-2; Period circadian protein homolog 2; Cryptochrome-2; Period circadian protein homolog 1; Cryptochrome-1]
species 3 [Aryl hydrocarbon receptor nuclear translocator-like protein 1]
species 0 [messenger RNA]
species 8 [Period circadian protein homolog 3; Period circadian protein homolog 2; Period circadian protein homolog 1]
species 12 [Period circadian protein homolog 3; Cryptochrome-2; Period circadian protein homolog 1; Cryptochrome-2; Period circadian protein homolog 1; Cryptochrome-1]
species 7 [messenger RNA]
species 5 [messenger RNA]
species 15 In
species 13 [Aryl hydrocarbon receptor nuclear translocator-like protein 1]

Observables: none

BIOMD0000000083 @ v0.0.1

This is model is according to the paper*Toward a detailed computational model for the mammalian circadian clock* In thi…

We present a computational model for the mammalian circadian clock based on the intertwined positive and negative regulatory loops involving the Per, Cry, Bmal1, Clock, and Rev-Erb alpha genes. In agreement with experimental observations, the model can give rise to sustained circadian oscillations in continuous darkness, characterized by an antiphase relationship between Per/Cry/Rev-Erbalpha and Bmal1 mRNAs. Sustained oscillations correspond to the rhythms autonomously generated by suprachiasmatic nuclei. For other parameter values, damped oscillations can also be obtained in the model. These oscillations, which transform into sustained oscillations when coupled to a periodic signal, correspond to rhythms produced by peripheral tissues. When incorporating the light-induced expression of the Per gene, the model accounts for entrainment of the oscillations by light-dark cycles. Simulations show that the phase of the oscillations can then vary by several hours with relatively minor changes in parameter values. Such a lability of the phase could account for physiological disorders related to circadian rhythms in humans, such as advanced or delayed sleep phase syndrome, whereas the lack of entrainment by light-dark cycles can be related to the non-24h sleep-wake syndrome. The model uncovers the possible existence of multiple sources of oscillatory behavior. Thus, in conditions where the indirect negative autoregulation of Per and Cry expression is inoperative, the model indicates the possibility that sustained oscillations might still arise from the negative autoregulation of Bmal1 expression. link: http://identifiers.org/pubmed/12775757

Parameters:

Name Description
k6 = 0.4; k5 = 0.8 Reaction: Bc => Bn, Rate Law: cell*(k5*Bc-k6*Bn)
Kdp = 0.1; V4B = 0.4 Reaction: Bnp => Bn, Rate Law: cell*V4B*Bnp/(Kdp+Bnp)
Kp = 1.006; V3PC = 2.4 Reaction: PCn => PCnp, Rate Law: cell*V3PC*PCn/(Kp+PCn)
Kdp = 0.1; V2C = 0.2 Reaction: Ccp => Cc, Rate Law: cell*V2C*Ccp/(Kdp+Ccp)
Kd = 0.3; vdCC = 1.4 Reaction: Ccp =>, Rate Law: cell*vdCC*Ccp/(Kd+Ccp)
vmB = 1.3; KmB = 0.4 Reaction: Mb =>, Rate Law: cell*vmB*Mb/(KmB+Mb)
Kdp = 0.1; V2B = 0.2 Reaction: Bcp => Bc, Rate Law: cell*V2B*Bcp/(Kdp+Bcp)
k4 = 0.4; k3 = 0.8 Reaction: Cc + Pc => PCc, Rate Law: cell*(k3*Cc*Pc-k4*PCc)
KmC = 0.4; vmC = 2.0 Reaction: Mc =>, Rate Law: cell*vmC*Mc/(KmC+Mc)
kdnC = 0.02 Reaction: Cc =>, Rate Law: cell*kdnC*Cc
vdBN = 3.0; Kd = 0.3 Reaction: Bnp =>, Rate Law: cell*vdBN*Bnp/(Kd+Bnp)
Kdp = 0.1; V4PC = 0.2 Reaction: PCnp => PCn, Rate Law: cell*V4PC*PCnp/(Kdp+PCnp)
Kp = 1.006; V1P = 9.6 Reaction: Pc => Pcp, Rate Law: cell*V1P*Pc/(Kp+Pc)
Kp = 1.006; V1PC = 2.4 Reaction: PCc => PCcp, Rate Law: cell*V1PC*PCc/(Kp+PCc)
Kd = 0.3; vdRC = 4.4 Reaction: Rc =>, Rate Law: cell*vdRC*Rc/(Kd+Rc)
Kd = 0.3; vdBC = 3.0 Reaction: Bcp =>, Rate Law: cell*vdBC*Bcp/(Kd+Bcp)
Kp = 1.006; V1C = 1.2 Reaction: Cc => Ccp, Rate Law: cell*V1C*Cc/(Kp+Cc)
kdmb = 0.02 Reaction: Mb =>, Rate Law: cell*kdmb*Mb
KmP = 0.3; vmP = 2.2 Reaction: Mp =>, Rate Law: cell*vmP*Mp/(KmP+Mp)
Kd = 0.3; vdIN = 1.6 Reaction: In =>, Rate Law: cell*vdIN*In/(Kd+In)
m = 2.0; K=1.0; vsB = 1.8 Reaction: => Mb; Rn, Rate Law: cell*vsB*K^m/(K^m+Rn^m)
k2 = 0.4; k1 = 0.8 Reaction: PCc => PCn, Rate Law: cell*(k1*PCc-k2*PCn)
kdmc = 0.02 Reaction: Mc =>, Rate Law: cell*kdmc*Mc
kdn = 0.02 Reaction: Bn =>, Rate Law: cell*kdn*Bn
Kdp = 0.1; V2P = 0.6 Reaction: Pcp => Pc, Rate Law: cell*V2P*Pcp/(Kdp+Pcp)
vdRN = 0.8; Kd = 0.3 Reaction: Rn =>, Rate Law: cell*vdRN*Rn/(Kd+Rn)
k9 = 0.8; k10 = 0.4 Reaction: Rc => Rn, Rate Law: cell*(k9*Rc-k10*Rn)
Kp = 1.006; V1B = 1.4 Reaction: Bc => Bcp, Rate Law: cell*V1B*Bc/(Kp+Bc)
parameter_0000097 = 3.0; n = 2.0; KAP = 0.6 Reaction: => Mp; Bn, Rate Law: cell*parameter_0000097*Bn^n/(KAP^n+Bn^n)
vmR = 1.6; kmR = 0.4 Reaction: Mr =>, Rate Law: cell*vmR*Mr/(kmR+Mr)
kdmr = 0.02 Reaction: Mr =>, Rate Law: cell*kdmr*Mr
Kp = 1.006; V3B = 1.4 Reaction: Bn => Bnp, Rate Law: cell*V3B*Bn/(Kp+Bn)
ksB = 0.32 Reaction: => Bc; Mb, Rate Law: cell*ksB*Mb
vdPCC = 1.4; Kd = 0.3 Reaction: PCcp =>, Rate Law: cell*vdPCC*PCcp/(Kd+PCcp)
k7 = 1.0; k8 = 0.2 Reaction: PCn + Bn => In, Rate Law: cell*(k7*PCn*Bn-k8*In)
Kd = 0.3; VdPC = 3.4 Reaction: Pcp =>, Rate Law: cell*VdPC*Pcp/(Kd+Pcp)
Kdp = 0.1; V2PC = 0.2 Reaction: PCcp => PCc, Rate Law: cell*V2PC*PCcp/(Kdp+PCcp)
ksP = 1.2 Reaction: => Pc; Mp, Rate Law: cell*ksP*Mp
vsC = 2.2; KAC = 0.6; n = 2.0 Reaction: => Mc; Bn, Rate Law: cell*vsC*Bn^n/(KAC^n+Bn^n)
h = 2.0; vsR = 1.6; KAR = 0.6 Reaction: => Mr; Bn, Rate Law: cell*vsR*Bn^h/(KAR^h+Bn^h)
Kd = 0.3; vdPCN = 1.4 Reaction: PCnp =>, Rate Law: cell*vdPCN*PCnp/(Kd+PCnp)
ksR = 1.7 Reaction: => Rc; Mr, Rate Law: cell*ksR*Mr
ksC = 3.2 Reaction: => Cc; Mc, Rate Law: cell*ksC*Mc
kdmp = 0.02 Reaction: Mp =>, Rate Law: cell*kdmp*Mp

States:

Name Description
Ccp [Cryptochrome-2; Cryptochrome-1]
PCc [Cryptochrome-1; Period circadian protein homolog 1; Cryptochrome-2; Period circadian protein homolog 3]
Bnp [Aryl hydrocarbon receptor nuclear translocator-like protein 1]
PCcp [Period circadian protein homolog 3; Period circadian protein homolog 1; Cryptochrome-1; Cryptochrome-2]
Mb [Aryl hydrocarbon receptor nuclear translocator-like protein 1; messenger RNA]
Mr [Rev-erb alpha; messenger RNA]
Pc [Period circadian protein homolog 2; Period circadian protein homolog 1; Period circadian protein homolog 3]
Bcp [Aryl hydrocarbon receptor nuclear translocator-like protein 1]
Rc [Rev-erb alpha]
Bn [Aryl hydrocarbon receptor nuclear translocator-like protein 1]
Cc [Cryptochrome-2; Cryptochrome-1]
Pcp [Period circadian protein homolog 1; Period circadian protein homolog 2; Period circadian protein homolog 3]
Mp [Period circadian protein homolog 3; Period circadian protein homolog 2; Period circadian protein homolog 1; messenger RNA]
Bc [Aryl hydrocarbon receptor nuclear translocator-like protein 1]
PCnp [Period circadian protein homolog 3; Cryptochrome-2; Cryptochrome-1; Period circadian protein homolog 1]
PCn [Cryptochrome-2; Cryptochrome-1; Period circadian protein homolog 3; Period circadian protein homolog 1]
Rn [Rev-erb alpha]
In In
Mc [Cryptochrome-1; Cryptochrome-2; messenger RNA]

Observables: none

We extend the study of a computational model recently proposed for the mammalian circadian clock (Proc. Natl Acad. Sci.…

We extend the study of a computational model recently proposed for the mammalian circadian clock (Proc. Natl Acad. Sci. USA 100 (2003) 7051). The model, based on the intertwined positive and negative regulatory loops involving the Per, Cry, Bmal1, and Clock genes, can give rise to sustained circadian oscillations in conditions of continuous darkness. These limit cycle oscillations correspond to circadian rhythms autonomously generated by suprachiasmatic nuclei and by some peripheral tissues. By using different sets of parameter values producing circadian oscillations, we compare the effect of the various parameters and show that both the occurrence and the period of the oscillations are generally most sensitive to parameters related to synthesis or degradation of Bmal1 mRNA and BMAL1 protein. The mechanism of circadian oscillations relies on the formation of an inactive complex between PER and CRY and the activators CLOCK and BMAL1 that enhance Per and Cry expression. Bifurcation diagrams and computer simulations nevertheless indicate the possible existence of a second source of oscillatory behavior. Thus, sustained oscillations might arise from the sole negative autoregulation of Bmal1 expression. This second oscillatory mechanism may not be functional in physiological conditions, and its period need not necessarily be circadian. When incorporating the light-induced expression of the Per gene, the model accounts for entrainment of the oscillations by light-dark (LD) cycles. Long-term suppression of circadian oscillations by a single light pulse can occur in the model when a stable steady state coexists with a stable limit cycle. The phase of the oscillations upon entrainment in LD critically depends on the parameters that govern the level of CRY protein. Small changes in the parameters governing CRY levels can shift the peak in Per mRNA from the L to the D phase, or can prevent entrainment. The results are discussed in relation to physiological disorders of the sleep-wake cycle linked to perturbations of the human circadian clock, such as the familial advanced sleep phase syndrome or the non-24h sleep-wake syndrome. link: http://identifiers.org/pubmed/15363675

Parameters: none

States: none

Observables: none

This a model from the article: Modeling the interactions between osteoblast and osteoclast activities in bone remode…

We propose a mathematical model explaining the interactions between osteoblasts and osteoclasts, two cell types specialized in the maintenance of the bone integrity. Bone is a dynamic, living tissue whose structure and shape continuously evolves during life. It has the ability to change architecture by removal of old bone and replacement with newly formed bone in a localized process called remodeling. The model described here is based on the idea that the relative proportions of immature and mature osteoblasts control the degree of osteoclastic activity. In addition, osteoclasts control osteoblasts differentially depending on their stage of differentiation. Despite the tremendous complexity of the bone regulatory system and its fragmentary understanding, we obtain surprisingly good correlations between the model simulations and the experimental observations extracted from the literature. The model results corroborate all behaviors of the bone remodeling system that we have simulated, including the tight coupling between osteoblasts and osteoclasts, the catabolic effect induced by continuous administration of PTH, the catabolic action of RANKL, as well as its reversal by soluble antagonist OPG. The model is also able to simulate metabolic bone diseases such as estrogen deficiency, vitamin D deficiency, senescence and glucocorticoid excess. Conversely, possible routes for therapeutic interventions are tested and evaluated. Our model confirms that anti-resorptive therapies are unable to partially restore bone loss, whereas bone formation therapies yield better results. The model enables us to determine and evaluate potential therapies based on their efficacy. In particular, the model predicts that combinations of anti-resorptive and anabolic therapies provide significant benefits compared with monotherapy, especially for certain type of skeletal disease. Finally, the model clearly indicates that increasing the size of the pool of preosteoblasts is an essential ingredient for the therapeutic manipulation of bone formation. This model was conceived as the first step in a bone turnover modeling platform. These initial modeling results are extremely encouraging and lead us to proceed with additional explorations into bone turnover and skeletal remodeling. link: http://identifiers.org/pubmed/15234198

Parameters:

Name Description
D_C = 0.0021; D_A = 0.7; Phi_L = NaN; Phi_C = NaN Reaction: C = D_C*Phi_L-D_A*Phi_C*C, Rate Law: D_C*Phi_L-D_A*Phi_C*C
D_B = NaN; D_R = 7.0E-4; Phi_C = NaN Reaction: R = D_R*Phi_C-D_B*R/Phi_C, Rate Law: D_R*Phi_C-D_B*R/Phi_C
D_B = NaN; Phi_C = NaN; k_B = 0.189 Reaction: B = D_B*R/Phi_C-k_B*B, Rate Law: D_B*R/Phi_C-k_B*B

States:

Name Description
B [osteoblast]
C [osteoclast]
R [osteoblast]

Observables: none

MODEL1006230039 @ v0.0.1

This a model from the article: Metabotropic receptor activation, desensitization and sequestration-I: modelling calciu…

A mathematical account is given of the processes governing the time courses of calcium ions (Ca2+), inositol 1,4,5-trisphosphate (IP(3)) and phosphatidylinositol 4,5-bisphosphate (PIP(2)) in single cells following the application of external agonist to metabotropic receptors. A model is constructed that incorporates the regulation of metabotropic receptor activity, the G-protein cascade and the Ca2+ dynamics in the cytosol. It is subsequently used to reproduce observations on the extent of desensitization and sequestration of the P(2)Y(2) receptor following its activation by uridine triphosphate (UTP). The theory predicts the dependence on agonist concentration of the change in the number of receptors in the membrane as well as the time course of disappearance of receptors from the plasmalemma, upon exposure to agonist. In addition, the extent of activation and desensitization of the receptor, using the calcium transients in cells initiated by exposure to agonist, is also predicted. Model predictions show the significance of membrane PIP(2) depletion and resupply on the time course of IP(3) and Ca2+ levels. Results of the modelling also reveal the importance of receptor recycling and PIP(2) resupply for maintaining Ca2+ and IP(3) levels during sustained application of agonist. link: http://identifiers.org/pubmed/12782119

Parameters: none

States: none

Observables: none

MODEL0479926177 @ v0.0.1

This a model from the article: Modelling fluctuation phenomena in the plasma cortisol secretion system in normal man.…

A system of three non-linear differential equations with exponential feedback terms is proposed to model the self-regulating cortisol secretion system and explain the fluctuation patterns observed in clinical data. It is shown that the model exhibits bifurcation and chaos patterns for a certain range of parametric values. This helps us to explain clinical observations and characterize different dynamic behaviors of the self-regulative system. link: http://identifiers.org/pubmed/1668715

Parameters: none

States: none

Observables: none

BIOMD0000000878 @ v0.0.1

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

This paper presents a nonlinear mathematical model of the glucose-insulin feedback system, which has been extended to incorporate the beta-cells' function on maintaining and regulating plasma insulin level in man. Initially, a gastrointestinal absorption term for glucose is utilized to effect the glucose absorption by the intestine and the subsequent release of glucose into the bloodstream, taking place at a given initial rate and falling off exponentially with time. An analysis of the model is carried out by the singular perturbation technique in order to derive boundary conditions on the system parameters which identify, in particular, the existence of limit cycles in our model system consistent with the oscillatory patterns often observed in clinical data. We then utilize a sinusoidal term to incorporate the temporal absorption of glucose in order to study the responses in the patients under ambulatory-fed conditions. A numerical investigation is carried out in this case to construct a bifurcation diagram to identify the ranges of parametric values for which chaotic behavior can be expected, leading to interesting biological interpretations. link: http://identifiers.org/pubmed/11226623

Parameters:

Name Description
r_5 = 0.1; r_6 = 0.1; y_hat = 1.24; z_hat = 2.57039578276886 Reaction: => z; y, z, Rate Law: COMpartment*(r_5*(y-y_hat)*(z_hat-z)+r_6*z*(z_hat-z))
epsilon = 0.1; r_4 = 0.1 Reaction: y => ; x, Rate Law: COMpartment*epsilon*r_4*x
r_7 = 0.05 Reaction: z =>, Rate Law: COMpartment*r_7*z
r_1 = 0.2; c_1 = 0.1 Reaction: => x; y, z, Rate Law: COMpartment*z*(r_1*y+c_1)
r_2 = 0.1 Reaction: x => ; z, Rate Law: COMpartment*z*r_2*x
epsilon = 0.1; c_2 = 0.1; r_3 = 0.1 Reaction: => y; z, Rate Law: COMpartment*(epsilon*r_3/z+epsilon*c_2)

States:

Name Description
x [Insulin]
z [pancreatic beta cell]
y [C2831]

Observables: none

MODEL1201140003 @ v0.0.1

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

This paper presents a nonlinear mathematical model of the glucose-insulin feedback system, which has been extended to incorporate the beta-cells' function on maintaining and regulating plasma insulin level in man. Initially, a gastrointestinal absorption term for glucose is utilized to effect the glucose absorption by the intestine and the subsequent release of glucose into the bloodstream, taking place at a given initial rate and falling off exponentially with time. An analysis of the model is carried out by the singular perturbation technique in order to derive boundary conditions on the system parameters which identify, in particular, the existence of limit cycles in our model system consistent with the oscillatory patterns often observed in clinical data. We then utilize a sinusoidal term to incorporate the temporal absorption of glucose in order to study the responses in the patients under ambulatory-fed conditions. A numerical investigation is carried out in this case to construct a bifurcation diagram to identify the ranges of parametric values for which chaotic behavior can be expected, leading to interesting biological interpretations. link: http://identifiers.org/pubmed/11226623

Parameters: none

States: none

Observables: none

This model is based on the publication: "CAR T cell therapy in B-cell acute lymphoblastic leukaemia: Insights from mathe…

Immunotherapies use components of the patient immune system to selectively target can- cer cells. The use of chimeric antigenic receptor (CAR) T cells to treat B-cell malignancies –leukaemias and lymphomas–is one of the most successful examples, with many patients experiencing long-lasting full responses to this therapy. This treatment works by extract- ing the patient’s T cells and transducing them with the CAR, enabling them to recognize and target cells carrying the antigen CD19 + , which is expressed in these haematological cancers. Here we put forward a mathematical model describing the time response of leukaemias to the injection of CAR T cells. The model accounts for mature and progenitor B-cells, leukaemic cells, CAR T cells and side effects by including the main biological processes involved. The model explains the early post-injection dynamics of the different compart- ments and the fact that the number of CAR T cells injected does not critically affect the treatment outcome. An explicit formula is found that gives the maximum CAR T cell ex- pansion in vivo and the severity of side effects. Our mathematical model captures other known features of the response to this immunotherapy. It also predicts that CD19 + cancer relapses could be the result of competition between leukaemic and CAR T cells, analogous to predator-prey dynamics. We discuss this in the light of the available evidence and the possibility of controlling relapses by early re-challenging of the leukaemia cells with stored CAR T cells. link: http://identifiers.org/doi/10.1016/j.cnsns.2020.105570

Parameters: none

States: none

Observables: none

This model is based on the publication: "CAR T cell therapy in B-cell acute lymphoblastic leukaemia: Insights from mathe…

Immunotherapies use components of the patient immune system to selectively target can- cer cells. The use of chimeric antigenic receptor (CAR) T cells to treat B-cell malignancies –leukaemias and lymphomas–is one of the most successful examples, with many patients experiencing long-lasting full responses to this therapy. This treatment works by extract- ing the patient’s T cells and transducing them with the CAR, enabling them to recognize and target cells carrying the antigen CD19 + , which is expressed in these haematological cancers. Here we put forward a mathematical model describing the time response of leukaemias to the injection of CAR T cells. The model accounts for mature and progenitor B-cells, leukaemic cells, CAR T cells and side effects by including the main biological processes involved. The model explains the early post-injection dynamics of the different compart- ments and the fact that the number of CAR T cells injected does not critically affect the treatment outcome. An explicit formula is found that gives the maximum CAR T cell ex- pansion in vivo and the severity of side effects. Our mathematical model captures other known features of the response to this immunotherapy. It also predicts that CD19 + cancer relapses could be the result of competition between leukaemic and CAR T cells, analogous to predator-prey dynamics. We discuss this in the light of the available evidence and the possibility of controlling relapses by early re-challenging of the leukaemia cells with stored CAR T cells. link: http://identifiers.org/doi/10.1016/j.cnsns.2020.105570

Parameters: none

States: none

Observables: none

This model of the use of chimeric antigen receptor (CAR)-T cell therapy in the treatment of solid tumours is described i…

Chimeric antigen receptor (CAR)-T cell-based therapies have achieved substantial success against B-cell malignancies, which has led to a growing scientific and clinical interest in extending their use to solid cancers. However, results for solid tumours have been limited up to now, in part due to the immunosuppressive tumour microenvironment, which is able to inactivate CAR-T cell clones. In this paper we put forward a mathematical model describing the competition of CAR-T and tumour cells, taking into account their immunosuppressive capacity. Using the mathematical model, we show that the use of large numbers of CAR-T cells targetting the solid tumour antigens could overcome the immunosuppressive potential of cancer. To achieve such high levels of CAR-T cells we propose, and study computationally, the manufacture and injection of CAR-T cells targetting two antigens: CD19 and a tumour-associated antigen. We study in silico the resulting dynamics of the disease after the injection of this product and find that the expansion of the CAR-T cell population in the blood and lymphopoietic organs could lead to the massive production of an army of CAR-T cells targetting the solid tumour, and potentially overcoming its immune suppression capabilities. This strategy could benefit from the combination with PD-1 inhibitors and low tumour loads. Our computational results provide theoretical support for the treatment of different types of solid tumours using T cells engineered with combination treatments of dual CARs with on- and off-tumour activity and anti-PD-1 drugs after completion of classical cytoreductive treatments. link: http://identifiers.org/pubmed/33572301

Parameters: none

States: none

Observables: none

This model of the use of chimeric antigen receptor (CAR)-T cell therapy in the treatment of solid tumours is described i…

Chimeric antigen receptor (CAR)-T cell-based therapies have achieved substantial success against B-cell malignancies, which has led to a growing scientific and clinical interest in extending their use to solid cancers. However, results for solid tumours have been limited up to now, in part due to the immunosuppressive tumour microenvironment, which is able to inactivate CAR-T cell clones. In this paper we put forward a mathematical model describing the competition of CAR-T and tumour cells, taking into account their immunosuppressive capacity. Using the mathematical model, we show that the use of large numbers of CAR-T cells targetting the solid tumour antigens could overcome the immunosuppressive potential of cancer. To achieve such high levels of CAR-T cells we propose, and study computationally, the manufacture and injection of CAR-T cells targetting two antigens: CD19 and a tumour-associated antigen. We study in silico the resulting dynamics of the disease after the injection of this product and find that the expansion of the CAR-T cell population in the blood and lymphopoietic organs could lead to the massive production of an army of CAR-T cells targetting the solid tumour, and potentially overcoming its immune suppression capabilities. This strategy could benefit from the combination with PD-1 inhibitors and low tumour loads. Our computational results provide theoretical support for the treatment of different types of solid tumours using T cells engineered with combination treatments of dual CARs with on- and off-tumour activity and anti-PD-1 drugs after completion of classical cytoreductive treatments. link: http://identifiers.org/pubmed/33572301

Parameters: none

States: none

Observables: none

BIOMD0000000011 @ v0.0.1

# MAPK cascade in solution (no scaffold) DescriptionThis model describes a basic 3- stage Mitogen Activated Prote…

In addition to preventing crosstalk among related signaling pathways, scaffold proteins might facilitate signal transduction by preforming multimolecular complexes that can be rapidly activated by incoming signal. In many cases, such as mitogen-activated protein kinase (MAPK) cascades, scaffold proteins are necessary for full activation of a signaling pathway. To date, however, no detailed biochemical model of scaffold action has been suggested. Here we describe a quantitative computer model of MAPK cascade with a generic scaffold protein. Analysis of this model reveals that formation of scaffold-kinase complexes can be used effectively to regulate the specificity, efficiency, and amplitude of signal propagation. In particular, for any generic scaffold there exists a concentration value optimal for signal amplitude. The location of the optimum is determined by the concentrations of the kinases rather than their binding constants and in this way is scaffold independent. This effect and the alteration of threshold properties of the signal propagation at high scaffold concentrations might alter local signaling properties at different subcellular compartments. Different scaffold levels and types might then confer specialized properties to tune evolutionarily conserved signaling modules to specific cellular contexts. link: http://identifiers.org/pubmed/10823939

Parameters:

Name Description
a3=3.3 Reaction: MEK + RAFp => MEKRAFp, Rate Law: a3*MEK*RAFp
a7=20.0 Reaction: MAPK + MEKpp => MAPKMEKpp, Rate Law: a7*MAPK*MEKpp
a5=3.3 Reaction: MEKp + RAFp => MEKpRAFp, Rate Law: a5*MEKp*RAFp
k5=0.1 Reaction: MEKpRAFp => MEKpp + RAFp, Rate Law: k5*MEKpRAFp
k3=0.1 Reaction: MEKRAFp => MEKp + RAFp, Rate Law: k3*MEKRAFp
k10=0.1 Reaction: MAPKppMAPKPH => MAPKp + MAPKPH, Rate Law: k10*MAPKppMAPKPH
a2=0.5 Reaction: RAFp + RAFPH => RAFpRAFPH, Rate Law: a2*RAFp*RAFPH
a6=10.0 Reaction: MEKPH + MEKpp => MEKppMEKPH, Rate Law: a6*MEKPH*MEKpp
a9=20.0 Reaction: MAPKp + MEKpp => MAPKpMEKpp, Rate Law: a9*MAPKp*MEKpp
k4=0.1 Reaction: MEKpMEKPH => MEK + MEKPH, Rate Law: k4*MEKpMEKPH
k7=0.1 Reaction: MAPKMEKpp => MAPKp + MEKpp, Rate Law: k7*MAPKMEKpp
d6=0.8 Reaction: MEKppMEKPH => MEKPH + MEKpp, Rate Law: d6*MEKppMEKPH
d2=0.5 Reaction: RAFpRAFPH => RAFp + RAFPH, Rate Law: d2*RAFpRAFPH
a4=10.0 Reaction: MEKp + MEKPH => MEKpMEKPH, Rate Law: a4*MEKp*MEKPH
k9=0.1 Reaction: MAPKpMEKpp => MAPKpp + MEKpp, Rate Law: k9*MAPKpMEKpp
d10=0.4 Reaction: MAPKppMAPKPH => MAPKPH + MAPKpp, Rate Law: d10*MAPKppMAPKPH
a1=1.0 Reaction: RAF + RAFK => RAFRAFK, Rate Law: a1*RAF*RAFK
d3=0.42 Reaction: MEKRAFp => MEK + RAFp, Rate Law: d3*MEKRAFp
d1=0.4 Reaction: RAFRAFK => RAF + RAFK, Rate Law: d1*RAFRAFK
d5=0.4 Reaction: MEKpRAFp => MEKp + RAFp, Rate Law: d5*MEKpRAFp
k8=0.1 Reaction: MAPKpMAPKPH => MAPK + MAPKPH, Rate Law: k8*MAPKpMAPKPH
d8=0.4 Reaction: MAPKpMAPKPH => MAPKp + MAPKPH, Rate Law: d8*MAPKpMAPKPH
d9=0.6 Reaction: MAPKpMEKpp => MAPKp + MEKpp, Rate Law: d9*MAPKpMEKpp
a10=5.0 Reaction: MAPKPH + MAPKpp => MAPKppMAPKPH, Rate Law: a10*MAPKPH*MAPKpp
d4=0.8 Reaction: MEKpMEKPH => MEKp + MEKPH, Rate Law: d4*MEKpMEKPH
k2=0.1 Reaction: RAFpRAFPH => RAF + RAFPH, Rate Law: k2*RAFpRAFPH
k1=0.1 Reaction: RAFRAFK => RAFK + RAFp, Rate Law: k1*RAFRAFK
d7=0.6 Reaction: MAPKMEKpp => MAPK + MEKpp, Rate Law: d7*MAPKMEKpp
k6=0.1 Reaction: MEKppMEKPH => MEKp + MEKPH, Rate Law: k6*MEKppMEKPH
a8=5.0 Reaction: MAPKp + MAPKPH => MAPKpMAPKPH, Rate Law: a8*MAPKp*MAPKPH

States:

Name Description
MAPKPH [Dual specificity protein phosphatase 1-B]
RAFK [IPR003577]
RAFpRAFPH [RAF proto-oncogene serine/threonine-protein kinase]
MEKppMEKPH [Dual specificity mitogen-activated protein kinase kinase 1]
MEKpp [Dual specificity mitogen-activated protein kinase kinase 1]
MAPKp [Mitogen-activated protein kinase 1]
MEKpMEKPH [Dual specificity mitogen-activated protein kinase kinase 1]
MAPK [Mitogen-activated protein kinase 1]
MEKpRAFp [RAF proto-oncogene serine/threonine-protein kinase; Dual specificity mitogen-activated protein kinase kinase 1]
MAPKpMAPKPH [Mitogen-activated protein kinase 1; Dual specificity protein phosphatase 1-B]
MAPKMEKpp [Mitogen-activated protein kinase 1; Dual specificity mitogen-activated protein kinase kinase 1]
MAPKppMAPKPH [Mitogen-activated protein kinase 1; Dual specificity protein phosphatase 1-B]
MEKPH MEK phosphatase
MEKp [Dual specificity mitogen-activated protein kinase kinase 1]
RAFp [RAF proto-oncogene serine/threonine-protein kinase]
MEK [Dual specificity mitogen-activated protein kinase kinase 1]
MAPKpMEKpp [Dual specificity mitogen-activated protein kinase kinase 1; Mitogen-activated protein kinase 1]
RAF [RAF proto-oncogene serine/threonine-protein kinase]
RAFPH RAF phosphatase
RAFRAFK [RAF proto-oncogene serine/threonine-protein kinase; IPR003577]
MAPKpp [Mitogen-activated protein kinase 1]
MEKRAFp [RAF proto-oncogene serine/threonine-protein kinase; Dual specificity mitogen-activated protein kinase kinase 1]

Observables: none

BIOMD0000000014 @ v0.0.1

# MAPK cascade on a scaffold CitationLevchenko, A., Bruck, J., Sternberg, P.W. (2000) .Scaffold proteins may biph…

In addition to preventing crosstalk among related signaling pathways, scaffold proteins might facilitate signal transduction by preforming multimolecular complexes that can be rapidly activated by incoming signal. In many cases, such as mitogen-activated protein kinase (MAPK) cascades, scaffold proteins are necessary for full activation of a signaling pathway. To date, however, no detailed biochemical model of scaffold action has been suggested. Here we describe a quantitative computer model of MAPK cascade with a generic scaffold protein. Analysis of this model reveals that formation of scaffold-kinase complexes can be used effectively to regulate the specificity, efficiency, and amplitude of signal propagation. In particular, for any generic scaffold there exists a concentration value optimal for signal amplitude. The location of the optimum is determined by the concentrations of the kinases rather than their binding constants and in this way is scaffold independent. This effect and the alteration of threshold properties of the signal propagation at high scaffold concentrations might alter local signaling properties at different subcellular compartments. Different scaffold levels and types might then confer specialized properties to tune evolutionarily conserved signaling modules to specific cellular contexts. link: http://identifiers.org/pubmed/10823939

Parameters:

Name Description
d3=0.42 Reaction: K_K_2_0_3_1 => K_2_0 + K_3_1, Rate Law: d3*K_K_2_0_3_1
a3=3.3 Reaction: K_2_0 + K_3_1 => K_K_2_0_3_1, Rate Law: a3*K_2_0*K_3_1
a7=20.0 Reaction: K_1_0 + K_2_2 => K_K_1_0_2_2, Rate Law: a7*K_1_0*K_2_2
k3=0.1 Reaction: S_m1_0_1 => S_m1_1_1, Rate Law: k3*S_m1_0_1
k1a=100.0 Reaction: RAFK + S_2_1_0 => S_RAFK_2_1_0, Rate Law: k1a*RAFK*S_2_1_0
a2=0.5 Reaction: RAFP + K_3_1 => K_RAFP_3_1, Rate Law: a2*RAFP*K_3_1
a9=20.0 Reaction: K_1_1 + K_2_2 => K_K_1_1_2_2, Rate Law: a9*K_1_1*K_2_2
kon=10.0 Reaction: K_1_0 + S_m1_1_m1 => S_0_1_m1, Rate Law: kon*K_1_0*S_m1_1_m1
k4=0.1 Reaction: K_MEKP_2_1 => MEKP + K_2_0, Rate Law: k4*K_MEKP_2_1
koff=0.5 Reaction: S_m1_0_1 => K_2_0 + S_m1_m1_1, Rate Law: koff*S_m1_0_1
d9=0.6 Reaction: K_K_1_1_2_2 => K_1_1 + K_2_2, Rate Law: d9*K_K_1_1_2_2
d2=0.5 Reaction: K_RAFP_3_1 => RAFP + K_3_1, Rate Law: d2*K_RAFP_3_1
k2=0.1 Reaction: K_RAFP_3_1 => RAFP + K_3_0, Rate Law: k2*K_RAFP_3_1
k1=0.1 Reaction: S_RAFK_2_2_0 => RAFK + S_2_2_1, Rate Law: k1*S_RAFK_2_2_0
d1a=0.0 Reaction: S_RAFK_2_0_0 => RAFK + S_2_0_0, Rate Law: d1a*S_RAFK_2_0_0
kpoff=0.05 Reaction: S_m1_0_1 => K_3_1 + S_m1_0_m1, Rate Law: kpoff*S_m1_0_1
k9a=0.1 Reaction: S_1_2_m1 => S_2_2_m1, Rate Law: k9a*S_1_2_m1
d7=0.6 Reaction: K_K_1_0_2_2 => K_1_0 + K_2_2, Rate Law: d7*K_K_1_0_2_2
k5a=0.1 Reaction: S_1_1_1 => S_1_2_1, Rate Law: k5a*S_1_1_1
k9=0.1 Reaction: K_K_1_1_2_2 => K_1_2 + K_2_2, Rate Law: k9*K_K_1_1_2_2
kpon=0.0 Reaction: K_3_1 + S_m1_0_m1 => S_m1_0_1, Rate Law: kpon*K_3_1*S_m1_0_m1

States:

Name Description
K 1 2 [Mitogen-activated protein kinase 1]
S 0 m1 m1 [Mitogen-activated protein kinase 1]
S m1 1 m1 [Dual specificity mitogen-activated protein kinase kinase 1]
K K 1 1 2 2 [Dual specificity mitogen-activated protein kinase kinase 1; Mitogen-activated protein kinase 1]
RAFK [IPR003577]
S 1 1 1 [RAF proto-oncogene serine/threonine-protein kinase; Dual specificity mitogen-activated protein kinase kinase 1; Mitogen-activated protein kinase 1]
S RAFK m1 m1 0 [RAF proto-oncogene serine/threonine-protein kinase]
S RAFK m1 0 0 [RAF proto-oncogene serine/threonine-protein kinase; Dual specificity mitogen-activated protein kinase kinase 1]
S 1 2 0 [RAF proto-oncogene serine/threonine-protein kinase; Dual specificity mitogen-activated protein kinase kinase 1; Mitogen-activated protein kinase 1]
S 2 2 0 [RAF proto-oncogene serine/threonine-protein kinase; Dual specificity mitogen-activated protein kinase kinase 1; Mitogen-activated protein kinase 1]
K 2 0 [Dual specificity mitogen-activated protein kinase kinase 1]
RAFP RAF phosphatase
S m1 0 0 [RAF proto-oncogene serine/threonine-protein kinase; Dual specificity mitogen-activated protein kinase kinase 1]
K 2 2 [Dual specificity mitogen-activated protein kinase kinase 1]
S 0 m1 0 [RAF proto-oncogene serine/threonine-protein kinase; Mitogen-activated protein kinase 1]
S m1 0 1 [RAF proto-oncogene serine/threonine-protein kinase; Dual specificity mitogen-activated protein kinase kinase 1]
K 1 0 [Mitogen-activated protein kinase 1]
S 1 2 1 [RAF proto-oncogene serine/threonine-protein kinase; Dual specificity mitogen-activated protein kinase kinase 1; Mitogen-activated protein kinase 1]
S 2 2 1 [RAF proto-oncogene serine/threonine-protein kinase; Dual specificity mitogen-activated protein kinase kinase 1; Mitogen-activated protein kinase 1]
K K 2 0 3 1 [RAF proto-oncogene serine/threonine-protein kinase; Dual specificity mitogen-activated protein kinase kinase 1]
S 1 2 m1 [Dual specificity mitogen-activated protein kinase kinase 1; Mitogen-activated protein kinase 1]

Observables: none

This is a phenotypic model of a kinetic proofreading mechanism used to describe dynamics governing interactions between…

T cell activation is a crucial checkpoint in adaptive immunity, and this activation depends on the binding parameters that govern the interactions between T cell receptors (TCRs) and peptide-MHC complexes (pMHC complexes). Despite extensive experimental studies, the relationship between the TCR-pMHC binding parameters and T cell activation remains controversial. To make sense of conflicting experimental data, a variety of verbal and mathematical models have been proposed. However, it is currently unclear which model or models are consistent or inconsistent with experimental data. A key problem is that a direct comparison between the models has not been carried out, in part because they have been formulated in different frameworks. For this Analysis article, we reformulated published models of T cell activation into phenotypic models, which allowed us to directly compare them. We find that a kinetic proofreading model that is modified to include limited signalling is consistent with the majority of published data. This model makes the intriguing prediction that the stimulation hierarchy of two different pMHC complexes (or two different TCRs that are specific for the same pMHC complex) may reverse at different pMHC concentrations. link: http://identifiers.org/pubmed/25145757

Parameters: none

States: none

Observables: none

This model is built by COPASI 4.24(Build197), based on paper: A mathematical model of the effects of aging on naive T-c…

The human adaptive immune response is known to weaken in advanced age, resulting in increased severity of pathogen-born illness, poor vaccine efficacy, and a higher prevalence of cancer in the elderly. Age-related erosion of the T cell compartment has been implicated as a likely cause, but the underlying mechanisms driving this immunosenescence have not been quantitatively modeled and systematically analyzed. T cell receptor diversity, or the extent of pathogen-derived antigen responsiveness of the T cell pool, is known to diminish with age, but inherent experimental difficulties preclude accurate analysis on the full organismal level. In this paper, we formulate a mechanistic mathematical model of T cell population dynamics on the immunoclonal subpopulation level, which provides quantitative estimates of diversity. We define different estimates for diversity that depend on the individual number of cells in a specific immunoclone. We show that diversity decreases with age primarily due to diminished thymic output of new T cells and the resulting overall loss of small immunoclones. link: http://identifiers.org/pubmed/31201663

Parameters:

Name Description
gamma = 1.8E10 Reaction: => N, Rate Law: compartment*gamma
K = 1.0E10; myu_1 = 0.04; myu_0 = 0.18 Reaction: myu = myu_0+myu_1*N^2/(N^2+K^2), Rate Law: missing
p = 0.17 Reaction: => N, Rate Law: compartment*p*N

States:

Name Description
myu myu
N [Natural Killer T-Cell]

Observables: none

BIOMD0000000718 @ v0.0.1

This a model from the article: A Quantitative Study of the Division Cycle of Caulobacter crescentus Stalked Cells. S…