# SBMLBioModels: K - L

## K

Khajanchi2019 - Stability Analysis of a Mathematical Model forGlioma-Immune Interaction under OptimalTherapy: BIOMD0000000891v0.0.1

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

##### Details

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:

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

States:

NameDescription
v[macrophage]
w[T-lymphocyte]
u[glioma cell]

Khan2018 - Origins of robustness in translational control via eukaryotic translation initiation factor (eIF) 2: MODEL1911120001v0.0.1

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

##### Details

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

Khanin1998 - Mathematical Model of Blood Coagulation Prothrombin Time Test: MODEL1806120001v0.0.1

Blood coagulation model for prothrombin time test.

##### Details

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

Kholodenko1999 - EGFR signaling: BIOMD0000000048v0.0.1

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

##### Details

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:

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

States:

NameDescription
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]

Kholodenko2000 - Ultrasensitivity and negative feedback bring oscillations in MAPK cascade: BIOMD0000000010v0.0.1

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

##### Details

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:

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

States:

NameDescription
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]

Kierzek2001_LacZ: MODEL4821294342v0.0.1

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

##### Details

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

Kim2007 - Crosstalk between Wnt and ERK pathways: BIOMD0000000149v0.0.1

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

##### Details

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:

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

States:

NameDescription
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]
X27unknown 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]

Kim2007 - Genome-scale metabolic network of Mannheimia succiniciproducens (iTY425): MODEL1507180062v0.0.1

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

##### Details

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

Kim2007_CellularMemory_AsymmetricModel: BIOMD0000000179v0.0.1

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

##### Details

Parameters:

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

States:

NameDescription
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]

Kim2007_CellularMemory_SymmetricModel: BIOMD0000000180v0.0.1

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

##### Details

Parameters:

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

States:

NameDescription
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]

Kim2009 - Genome-scale metabolic network of Acinetobacter baumannii (AbyMBEL891): MODEL1507180029v0.0.1

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

##### Details

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

Kim2010_VvuMBEL943_GSMR: MODEL1011300000v0.0.1

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

##### Details

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

Kim2011_Oscillator_DetailedI: MODEL1012090002v0.0.1

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

##### Details

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

Kim2011_Oscillator_DetailedII: MODEL1012090003v0.0.1

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

##### Details

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

Kim2011_Oscillator_DetailedIII: MODEL1012090004v0.0.1

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

##### Details

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

Kim2011_Oscillator_ExtendedI: MODEL1012090005v0.0.1

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

##### Details

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

Kim2011_Oscillator_ExtendedIII: MODEL1012090006v0.0.1

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

##### Details

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

Kim2011_Oscillator_SimpleI: BIOMD0000000322v0.0.1

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

##### Details

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:

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

States:

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

Kim2011_Oscillator_SimpleIII: BIOMD0000000323v0.0.1

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

##### Details

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:

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

States:

NameDescription
species 2[inhibitor; ribonucleic acid]
species 3[inhibitor; ribonucleic acid]
species 1[inhibitor; ribonucleic acid]

Kim2014 - Tumor model under immune suppression: MODEL1909240002v0.0.1

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

##### Details

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

Kirschner1998_Immunotherapy_Tumour: BIOMD0000000732v0.0.1

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

##### Details

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:

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

States:

NameDescription
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]

Kiselyov2009_InsulinReceptorModel: MODEL1112050000v0.0.1

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

##### Details

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

Klipp2002_MetabolicOptimization_linearPathway(n=2): BIOMD0000000104v0.0.1

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

##### Details

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:

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

States:

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

Koenders2015 - multiple myeloma: BIOMD0000000804v0.0.1

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

##### Details

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:

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

States:

NameDescription
B[osteoblast]
T[myeloma cell]
C[osteoclast]

Koenig2012 Hepatic Glucose Metabolism: MODEL1204270001v0.0.1

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

##### Details

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

Koenig2012 Hepatic Glucose Metabolism in Type 2 Diabetes: MODEL1209260000v0.0.1

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

##### Details

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

Kofahl2004_PheromonePathway: BIOMD0000000032v0.0.1

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

##### Details

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:

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

States:

NameDescription
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]
alphaα-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]
pFar1ubiquitin

Kogan2001_aPTT_coagulation: MODEL1109160001v0.0.1

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

##### Details

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

Kogan2001_aPTT_preincubation: MODEL1109160000v0.0.1

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

##### Details

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

Kogan2013 - A mathematical model for the immunotherapeutic control of the TH1 TH2 imbalance in melanoma: BIOMD0000000881v0.0.1

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

##### Details

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:

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

States:

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

Koivumaki2009_SERCAATPase_long: MODEL1006230105v0.0.1

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

##### Details

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

Koivumaki2009_SERCAATPase_short: MODEL1006230029v0.0.1

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

##### Details

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

Koivumaki2009_SERCAATPase_Standalone: MODEL1006230023v0.0.1

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

##### Details

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

Kok2020 - IFNalpha-induced signaling in Huh7.5 cells: BIOMD0000000959v0.0.1

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

##### Details

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

Kollarovic2016 - Cell fate decision at G1-S transition: BIOMD0000000632v0.0.1

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

##### Details

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:

NameDescription
vb7_k1_0 = 10.0Reaction: CycE + Cdk2 => CycECdk2; CycE, Cdk2, Rate Law: compartment*vb7_k1_0*CycE*Cdk2
vb3_v_0 = 99.84Reaction: => 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 = 0.001143917344Reaction: 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 = 2.16068Reaction: DDR = BaseDNAdamage+DNADamageC+DNADamageS+TAF, Rate Law: missing
k6b = 1.08476678528373Reaction: CycE => ; CycE, Rate Law: compartment*k6b*CycE
k8b = 1.12435827886665Reaction: CycECdk2 => CycE + Cdk2; CycECdk2, Rate Law: compartment*k8b*CycECdk2
va3_k_0 = 0.00547468Reaction: => p53; DDR, DDR, Rate Law: compartment*va3_k_0*DDR
k1=0.0164994Reaction: DNADamageC => ; DNADamageC, Rate Law: compartment*k1*DNADamageC
k2b = 2.43594662809282Reaction: CycECdk2a => CycECdk2; CycECdk2a, Rate Law: compartment*k2b*CycECdk2a
va5_k_0 = 193.258Reaction: => p21; p53, p53, Rate Law: compartment*va5_k_0*p53
k4b = 5987.90902984358Reaction: Cdk2 => ; Cdk2, Rate Law: compartment*k4b*Cdk2
k4a = 0.01460046788944Reaction: p53 => ; p53, Rate Law: compartment*k4a*p53
k1=0.234805Reaction: DNADamageS => ; DNADamageS, Rate Law: compartment*k1*DNADamageS
vb5_v_0 = 9.99936Reaction: => CycE, Rate Law: compartment*vb5_v_0
k6a = 193.258Reaction: p21 => ; p21, Rate Law: compartment*k6a*p21

States:

NameDescription
CycE[G1/S-specific cyclin-E1]
DDRDDR
p21[Cyclin-dependent kinase inhibitor 1]
CycECdk2a[Cyclin-dependent kinase 2; G1/S-specific cyclin-E1]
DNADamageSDNADamageS
DNADamageCDNADamageC
Cdk2[Cyclin-dependent kinase 2]
CycECdk2[Cyclin-dependent kinase 2; G1/S-specific cyclin-E1]
p53[Cellular tumor antigen p53]

Kolodkin2013 - Nuclear receptor-mediated cortisol signalling network: BIOMD0000000576v0.0.1

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

##### Details

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:

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

States:

NameDescription
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]

Kolomeisky2003_MyosinV_Processivity: BIOMD0000000305v0.0.1

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

##### Details

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:

NameDescription
th_1 = -0.01; Force = 0.0; k_1 = 0.7; kT = 4.1164; d = 36.0Reaction: 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 = 0.385Reaction: 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 = 36.0Reaction: 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 = 0.58Reaction: S0 + ATP => S1 + Pi_ + back_step1, Rate Law: k_3*S0*ATP*exp(th_3*Force*d/kT)

States:

NameDescription
S0[myosin V complex]
ATP[ATP; ATP; 3304]
S1[ADP; myosin V complex]
Pi[phosphate(3-); Orthophosphate]
fwd step1fwd_step1
fwd step2fwd_step2
back step1back_step1
ADP[ADP; ADP; 3310]
back step2back_step2

Komarova2003_BoneRemodeling: BIOMD0000000148v0.0.1

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

##### Details

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:

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

States:

NameDescription
x1Osteoclast
x1 barSteady state osteoclast
x2Osteoblast
zBone mass
x2 barSteady state osteoblast

Komarova2005_PTHaction_OsteoclastOsteoblastCoupling: BIOMD0000000279v0.0.1

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

##### Details

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:

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

States:

NameDescription
x1[osteoclast]
x2[osteoblast]
z[mass]

Komarova2005_TheoreticalFramework_BasicArchitecture: BIOMD0000000125v0.0.1

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

##### Details

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:

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

States:

NameDescription
x1[IPR003527]
x2x2
y2y2

Konduru2020 - Genome-scale metabolic reconstruction and in silico analysis of rice leaf blight pathogen, Xanthomonas oryzae: MODEL1912100001v0.0.1

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

##### Details

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:

Kongas2007 - Creatine Kinase in energy metabolic signaling in muscle: BIOMD0000000041v0.0.1

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

##### Details

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:

NameDescription
k1_6=14.6Reaction: 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=34900.0Reaction: 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=18.4Reaction: Pi => P, Rate Law: IMS*k2_5*Pi-CYT*k2_5*P
k1_8=14.6Reaction: PCri => PCr, Rate Law: IMS*k1_8*PCri-CYT*k1_8*PCr
v_4=4600.0Reaction: ATP => ADP + P, Rate Law: CYT*v_4*ATP
k1_7=8.16Reaction: ADPi => ADP, Rate Law: IMS*k1_7*ADPi-CYT*k1_7*ADP
k1_9=8.16Reaction: ATPi => ATP, Rate Law: IMS*k1_9*ATPi-CYT*k1_9*ATP
Ka_1=800.0; Kb_1=20.0; V_1=4600.0Reaction: 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=28800.0Reaction: 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:

NameDescription
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]

Konrath2020_p53_signaling_model: MODEL2004300002v0.0.1

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

##### Details

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:

Koschorreck2008_InsulinClearance: BIOMD0000000345v0.0.1

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

##### Details

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:

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

States:

NameDescription
I2RPen[Insulin:p-6Y-insulin receptor [endosome membrane]]
I2RenI2Ren
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]]

Kosinsky2018 - Radiation and PD-(L)1 treatment combinations: BIOMD0000000863v0.0.1

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

##### Details

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:

NameDescription
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/dReaction: => 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/dReaction: dTeff =>, Rate Law: compartment*kapo*dTeff
k_el = 0.2 1/dReaction: 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/dReaction: => 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/dReaction: => 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/dReaction: TV => ; dTeff, Rate Law: compartment*(n_e*dTeff+d0)*TV
r = 0.4 1/d; TVmax = 2500.0 ulReaction: => TV; TV, Rate Law: compartment*r*TV*(1-TV/TVmax)
alpha = 0.146; tau = 0.02 d; delta = 19.0; radiation_Dose = 0.0Reaction: TV => TVd; U, Rate Law: compartment*TV*(alpha*radiation_Dose+0.2*alpha/(tau*delta^2)*U^2)
mu = 0.1725 1/dReaction: TVd =>, Rate Law: compartment*mu*TVd
delta = 19.0; radiation_Dose = 0.0Reaction: => U, Rate Law: compartment*radiation_Dose*delta
Kpdl = 478.0; kpdl = 1.0 1/dReaction: => PDL1; dTeff, Rate Law: compartment*kpdl*dTeff/(Kpdl+dTeff)
kpdl = 1.0 1/dReaction: PDL1 =>, Rate Law: compartment*kpdl*PDL1
tau = 0.02 dReaction: U =>, Rate Law: compartment*tau*U

States:

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

Kosiuk2015-Geometric analysis of the Goldbeter minimal model for the embryonic cell cycle: BIOMD0000000933v0.0.1

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

##### Details

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:

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

States:

NameDescription
M[0016746]
C[Guanidine]
X[0000652]

Koster1988_Histone_Expression: MODEL5954483266v0.0.1

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

##### Details

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

Kotte2010_Ecoli_Metabolic_Adaption: BIOMD0000000244v0.0.1

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

##### Details

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:

NameDescription
e_CAMPdegr_KcAMP = 0.1; e_CAMPdegr_kcat = 1000.0Reaction: 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 = 1.0E8Reaction: 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 = 0.0017Reaction: => 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 = 0.0Reaction: => 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 = 3.4Reaction: 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 = 0.0Reaction: => 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 = 0.017Reaction: => 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 = 0.0Reaction: 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 = 2.0Reaction: 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 = 0.212Reaction: 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 = 1.33Reaction: 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-7Reaction: => 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 = 0.001Reaction: 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 = 2.0Reaction: => 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 = 0.3Reaction: 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 = 0.164Reaction: 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 = 9.5E7Reaction: 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 = 0.95Reaction: 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-7Reaction: => 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 = 0.0Reaction: OAA => ; ACT, GLC, Rate Law: k_bm_OAA*OAA
e_Akg2mal_kcat = 1530.0; e_Akg2mal_Kakg = 0.548Reaction: 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 = 0.0Reaction: => 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 = 773.0Reaction: 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 = 0.0Reaction: 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 = 0.72Reaction: 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 = 0.038Reaction: 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-9Reaction: => 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 = 0.0085Reaction: EIIA_P => G6P + EIIA; EIICB, GLC, Rate Law: pts_k4*EIICB*EIIA_P*GLC/((pts_KEIIA+EIIA_P)*(pts_Kglc+GLC))
k_bm_ACoA = 0.0Reaction: ACoA => ; ACT, GLC, Rate Law: k_bm_ACoA*ACoA
tf_Cra_n = 2.0; tf_Cra_kfbp = 1.36; tf_Cra_scale = 100.0Reaction: 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 = 0.0Reaction: 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 = 0.0Reaction: => 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 = 127.0Reaction: 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 = 20000.0Reaction: => 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-7Reaction: 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 = 0.0Reaction: => 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 = 0.038Reaction: 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 = 0.0Reaction: 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-7Reaction: => 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 = 116.0Reaction: 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-6Reaction: => 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 = 0.00535Reaction: => 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 = 100000.0Reaction: 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-7Reaction: 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:

NameDescription
Fdp[Fructose-1,6-bisphosphatase 1]
CAMPdegrCAMPdegr
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]
Akg2malAkg2mal
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]
Acoa2actAcoa2act
PfkA[ATP-dependent 6-phosphofructokinase isozyme 2]
BMBM
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]

Kowald2006_SOD: BIOMD0000000108v0.0.1

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

##### Details

Parameters:

NameDescription
k17 = 30000.0Reaction: species_0000011 => species_0000007, Rate Law: compartment_0000001*k17*species_0000011
k18 = 7.0Reaction: species_0000007 => species_0000011 + species_0000009, Rate Law: compartment_0000001*k18*species_0000007
k1 = 6.6E-7Reaction: => species_0000001, Rate Law: compartment_0000001*k1
k13b = 0.0087Reaction: species_0000002 =>, Rate Law: compartment_0000001*k13b*species_0000002
k19 = 88000.0Reaction: species_0000007 =>, Rate Law: compartment_0000001*k19*species_0000007^2
k13a = 0.0087; Cu_I_ZnSOD = 0.0Reaction: => species_0000002, Rate Law: compartment_0000001*k13a*Cu_I_ZnSOD
k3 = 1.6E9; Cu_I_ZnSOD = 0.0Reaction: species_0000001 => species_0000006 + species_0000002, Rate Law: compartment_0000001*k3*species_0000001*Cu_I_ZnSOD
k11 = 2.5E8Reaction: species_0000008 => species_0000011, Rate Law: compartment_0000001*k11*species_0000008
k7 = 3.4E7Reaction: species_0000006 => ; species_0000017, Rate Law: compartment_0000001*k7*species_0000006*species_0000017
k2 = 1.6E9Reaction: species_0000001 + species_0000002 =>, Rate Law: compartment_0000001*k2*species_0000001*species_0000002
HO2star = 0.0; k10 = 1000.0Reaction: species_0000001 =>, Rate Law: k10*HO2star*compartment_0000001
k5 = 20000.0Reaction: species_0000001 + species_0000006 => species_0000008, Rate Law: compartment_0000001*k5*species_0000001*species_0000006
k9 = 1000000.0Reaction: species_0000008 =>, Rate Law: compartment_0000001*k9*species_0000008
k4 = 100000.0Reaction: species_0000001 + species_0000007 => species_0000009, Rate Law: compartment_0000001*k4*species_0000001*species_0000007
k6 = 1.0Reaction: species_0000006 => species_0000008; species_0000002, Rate Law: compartment_0000001*k6*species_0000006*species_0000002
k12 = 0.38Reaction: species_0000009 =>, Rate Law: compartment_0000001*k12*species_0000009

States:

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

Kraan199_Kinetics of Cortisol Metabolism and Excretion.: BIOMD0000000916v0.0.1

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

##### Details

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:

NameDescription
K5 = 1.2; K4 = 1.2Reaction: 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 = 1.2Reaction: 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 = 26.6Reaction: The_FOD_in_the_circulation__X1 => The_FOD_in_the_metabolizing_tissues__X4, Rate Law: compartment*K3*The_FOD_in_the_circulation__X1
K1 = 3.6Reaction: 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:

NameDescription
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]

Kremers2015 - Thrombin Inhibitor Kinetics: MODEL1808210001v0.0.1

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

##### Details

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

Krohn2011 - Cerebral amyloid-β proteostasis regulated by membrane transport protein ABCC1: BIOMD0000000618v0.0.1

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

##### Details

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:

NameDescription
k_sol = 0.34237; n_n = 6.0; k_n = 0.34508Reaction: 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 = 0.34508Reaction: 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 = 0.3586Reaction: A14 = k_sol*A13*M-k_insol*A14*M, Rate Law: k_sol*A13*M-k_insol*A14*M
soluble = 1.04389999999997Reaction: soluble_obs = soluble, Rate Law: missing
insoluble = 0.0Reaction: insoluble_obs = insoluble, Rate Law: missing
k_sol = 0.34237Reaction: A12 = k_sol*A11*M-k_sol*A12*M, Rate Law: k_sol*A11*M-k_sol*A12*M
k_insol = 0.3586Reaction: A18 = k_insol*A17*M-k_insol*A18*M, Rate Law: k_insol*A17*M-k_insol*A18*M

States:

NameDescription
A45A45
A34A34
A35A35
A53A53
A22A22
insoluble obsinsoluble_obs
M[amyloid-beta]
A8A8
A21A21
A26A26
A18A18
A32A32
A25A25
A36A36
A12A12
soluble obssoluble_obs
A7A7
A48A48
A37A37
A54A54
A33A33
A29A29
A16A16
A38A38
A47A47
A41A41
A28A28
A40A40
A20A20
A13A13
A19A19
A43A43
A9A9
A23A23
A42A42
NN
A17A17
A39A39
A24A24
A30A30
A49A49
A14A14
A10A10
A44A44
A11A11
A52A52
A50A50
A46A46
A51A51
A15A15
A27A27
A31A31

Kroll2000_PTH_BoneFormationDesorption: MODEL1006230083v0.0.1

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

##### Details

Kronik2008 - Improving alloreactive CTL immunotherapy for malignant gliomas using a simulation model of their interactive dynamics: BIOMD0000000808v0.0.1

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

##### Details

Parameters:

NameDescription
g_M1 = 1.44Reaction: => M1, Rate Law: compartment*g_M1
a_T_beta = 0.69Reaction: => F_beta; T, Rate Law: compartment*a_T_beta*T
g_beta = 63945.0Reaction: => F_beta, Rate Law: compartment*g_beta
mu_beta = 7.0Reaction: F_beta =>, Rate Law: compartment*mu_beta*F_beta
mu_C = 0.007Reaction: C =>, Rate Law: compartment*mu_C*C
mu_gamma = 0.102Reaction: F_gamma =>, Rate Law: compartment*mu_gamma*F_gamma
mu_M2 = 0.0144Reaction: M2 =>, Rate Law: compartment*mu_M2*M2
mu_M1 = 0.0144Reaction: M1 =>, Rate Law: compartment*mu_M1*M1
K = 1.0E11; r = 3.5E-4Reaction: => T, Rate Law: compartment*r*T*(1-T/K)
v=0.1Reaction: => 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 = 5.0E8Reaction: 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 = 0.8Reaction: => 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 = 3.0E7Reaction: => C, Rate Law: compartment*S
a_gamma_C = 1.02E-4Reaction: => F_gamma; C, Rate Law: compartment*a_gamma_C*C

States:

NameDescription
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]

Kronik2010 - Predicting Outcomes of Prostate Cancer Immunotherapyby Personalized Mathematical Models: MODEL2001130003v0.0.1

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

##### Details

Kubota2012_InsulinAction_AKTpathway: MODEL1204060000v0.0.1

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

##### Details

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

Kuepfer2005 - Genome-scale metabolic network of Saccharomyces cerevisiae (iLL672): MODEL1507180066v0.0.1

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

##### Details

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

Kuharsky2001_BloodCoagulation: MODEL1109150000v0.0.1

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

##### Details

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

Kuhn2009_EndoMesodermNetwork: BIOMD0000000235v0.0.1

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

##### Details

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:

NameDescription
P_dissociation_k=0.0514508771131Reaction: 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=1.0Reaction: 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=1.0Reaction: 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=1.0Reaction: 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=1.0Reaction: 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=1.0Reaction: 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=0.727292522645Reaction: 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=1.0Reaction: 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=0.683876854591Reaction: 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=1.0Reaction: 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=1.0Reaction: 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 = 1.0Reaction: 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=1.0Reaction: 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=0.3Reaction: PROTEIN_M_Gelsolin => none; none, Rate Law: P_protein_deg*PROTEIN_M_Gelsolin
k_PROTEIN_Hex=1.0; c_PROTEIN_Hex=1.0Reaction: 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=1.0Reaction: 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 = 0.0Reaction: 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=0.119Reaction: mRNA_P_HesC => none; none, Rate Law: P_mRNA_deg*mRNA_P_HesC
c_PROTEIN_UbiqHnf6=1.0; k_PROTEIN_UbiqHnf6=1.0Reaction: 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=1.0Reaction: 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=1.0Reaction: 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=1.0Reaction: 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=1.0Reaction: 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=0.567550841749Reaction: 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=1.0Reaction: 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=1.0Reaction: 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=2.0Reaction: none => PROTEIN_M_Gelsolin; mRNA_M_Gelsolin, Rate Law: P_k_translation*mRNA_M_Gelsolin
P_association_k=0.711358710507Reaction: 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=1.0Reaction: 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:

NameDescription
GENE P Erg[NP_999833]
PROTEIN E Sm30[AAA30070]
PROTEIN E SoxB1[NP_999639]
GENE M NotGENE_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]
nonenone
PROTEIN M Msp130[373282]
PROTEIN E SoxC[AAD40687]
PROTEIN M HesC[Hairy enhancer of split]
PROTEIN M Pks[NP_001239013]
PROTEIN M GroPROTEIN_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 MspLPROTEIN_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 L1mRNA_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]

Kumar2011 - Genome-scale metabolic network of Methanosarcina acetivorans (iVS941): MODEL1507180035v0.0.1

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

##### Details

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

Kummer2000 - Oscillations in Calcium Signalling: BIOMD0000000329v0.0.1

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

##### Details

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:

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

States:

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

Kurata2002_SinoatrialNode: MODEL0847712949v0.0.1

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

##### Details

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

Kuroda2001_NO_cGMP_Pathway: MODEL4780181279v0.0.1

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…

##### Details

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

Kuwahara2010_Fimbriation_Switch_28C: MODEL1004010000v0.0.1

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

##### Details

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

Kuwahara2010_Fimbriation_Switch_37C: MODEL1004010001v0.0.1

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

##### Details

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

Kuwahara2010_Fimbriation_Switch_42C: MODEL1004010002v0.0.1

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

##### Details

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

Kuznetsov1994 - Nonlinear dynamics of immunogenic tumors: BIOMD0000000762v0.0.1

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

##### Details

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:

NameDescription
p = 0.1245; g = 2.019E7Reaction: => E; E, T, Rate Law: compartment*p*E*T/(g+T)
a = 0.18Reaction: => T; T, Rate Law: compartment*a*T
m = 3.422E-10Reaction: E => ; T, Rate Law: compartment*m*E*T
d = 0.0412Reaction: E =>, Rate Law: compartment*d*E
s = 13000.0Reaction: => E, Rate Law: compartment*s
n = 1.101E-7Reaction: T => ; E, Rate Law: compartment*n*E*T
b = 2.0E-9; a = 0.18Reaction: T => ; T, Rate Law: compartment*a*b*T^2

States:

NameDescription
T[Neoplastic Cell]
E[effector T cell]

Kuznetsov2016(II) - α-syn aggregation kinetics in Parkinson's Disease: BIOMD0000000615v0.0.1

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

##### Details

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:

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

States:

NameDescription
Asyn[Alpha-synuclein]
Bsyn[Alpha-synuclein]
Bs[Alpha-synuclein]
As[Alpha-synuclein]

Kwang2003 - The influence of RKIP on the ERK signaling pathway: BIOMD0000000647v0.0.1

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

##### Details

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:

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

States:

NameDescription
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]

Kyrtsos2011 - A systems biology model for Alzheimer's disease (Cholesterol in AD): MODEL1504240000v0.0.1

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

##### Details

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

Kyrylov2005_HPAaxis: MODEL0478740924v0.0.1

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

##### Details

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

## L

Lai2007_O2_Transport_Metabolism: BIOMD0000000248v0.0.1

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

##### Details

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:

NameDescription
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 mMReaction: 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 mMReaction: => CTcap, Rate Law: Qm*(CTart-CTcap)
Katpase = 0.3207601 perMinReaction: ATP => ADP, Rate Law: Tissue*Katpase*ATP
Km = 7.0E-4 mM; Vmax = 23.11702 mmol*(60*s)^(-1)*l^(-1); Kadp = 0.058 mMReaction: ADP + CTtis => ATP; Pi, CFtis, Rate Law: Tissue*Vmax*CFtis/(Km+CFtis)*ADP/(Kadp+ADP)
PSm = 5338.8 LperMinReaction: 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 dimensionlessReaction: 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 mMReaction: 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:

NameDescription
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]

Lai2014 - Hemiconcerted MWC model of intact calmodulin with two targets: BIOMD0000000574v0.0.1

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

##### Details

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:

NameDescription
k_R2T_C2 = 10000.0; k_T2R_C2 = 1.15490174876063E7Reaction: 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 = 1.0E7Reaction: 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 = 0.1978714Reaction: 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 = 10000.0Reaction: 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 = 19.7628Reaction: 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 = 670413.817319951Reaction: 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 = 1.16054921831207Reaction: 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 = 624.2Reaction: 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 = 3661.03854357121Reaction: 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 = 1.0E9Reaction: 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 = 0.0309898787056147Reaction: 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 = 624.2Reaction: 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 = 1.0E8Reaction: 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 = 1.0E8Reaction: 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 = 1.0E8Reaction: 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 = 1.0E8Reaction: 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:

NameDescription
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]

Lambeth2002_Glycogenolysis: MODEL6623617994v0.0.1

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

##### Details

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

Landberg2009 - Alkylresorcinol Dose Response: BIOMD0000000948v0.0.1

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

##### Details

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:

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

States:

NameDescription
AR A1[Resorcinol; 5-alkylresorcinol]
AR Dose[5-alkylresorcinol; Resorcinol]
F1F1
F2F2
AR A2[5-alkylresorcinol; Resorcinol]
AR Central[Resorcinol; 5-alkylresorcinol]

Larbat2016.1 - Modeling the diversion of primary carbon flux into secondary metabolism under variable nitrate and light or dark conditions (Base Model): BIOMD0000000857v0.0.1

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

##### Details

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:

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

States:

NameDescription
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]

Larbat2016.2 - Modeling the diversion of primary carbon flux into secondary metabolism under variable nitrate and light or dark conditions (Light Dark Cycles): BIOMD0000000858v0.0.1

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

##### Details

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:

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

States:

NameDescription
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]

Larbat2016.3 - Modeling the diversion of primary carbon flux into secondary metabolism under variable nitrate and light or dark conditions (Light Dark Cycles with Minimum Starch Adaption): BIOMD0000000859v0.0.1

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

##### Details

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:

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

States:

NameDescription
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]

Larsen2004_CalciumSpiking: BIOMD0000000330v0.0.1

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

##### Details

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:

NameDescription
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 = 79.0Reaction: 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 = 0.7Reaction: 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 = 5.82Reaction: 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 = 0.93Reaction: 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 = 79.0Reaction: 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:

NameDescription
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]

Larsen2004_CalciumSpiking_EnzymeBinding: BIOMD0000000331v0.0.1

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

##### Details

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:

NameDescription
k_enz = 3.0; k_rem = 3.0Reaction: 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 = 4.0Reaction: 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 = 2.08Reaction: 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 = 4.5Reaction: 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 = 13.4Reaction: 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 = 0.64Reaction: 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 = 7.0Reaction: 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:

NameDescription
G alpha[Guanine nucleotide-binding protein subunit alpha-11]
ProductEnzCatlysedProduct
Ca ER[endoplasmic reticulum]
Ca cyt[cytoplasm]
PLC[1-phosphatidylinositol 4,5-bisphosphate phosphodiesterase beta-1]
EnzEnzyme
Ca mit[mitochondrion]

Laub1998_SpontaneousOscillations: BIOMD0000000099v0.0.1

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

##### Details

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:

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

States:

NameDescription
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]

Lavigne2021 - Non-spatial model of viral infection dynamics and interferon response of well-mixed viral infection: BIOMD0000001021v0.0.1

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

##### Details

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

Lavoie2020 - F.cylindrus_Genome_scale_model: MODEL2001280001v0.0.1

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

##### Details

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

Lavrentovich2008_Ca_Oscillations: BIOMD0000000184v0.0.1

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

##### Details

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:

NameDescription
kdeg = 0.08 sec_1Reaction: Z =>, Rate Law: compartment*kdeg*Z
kf = 0.5 sec_1Reaction: 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 dimensionlessReaction: 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_1Reaction: X =>, Rate Law: compartment*kout*X
vp = 0.05 uM_sec_1; kp = 0.3 uMReaction: => Z; X, Rate Law: compartment*vp*X^2/(X^2+kp^2)
k2 = 0.1 uM; vM2 = 15.0 uM_sec_1Reaction: X => Y, Rate Law: compartment*vM2*X^2/(X^2+k2^2)
vin = 0.05 uM_sec_1Reaction: => X, Rate Law: compartment*vin

States:

NameDescription
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]

Law2020 - SIR model of COVID-19 transmission in Malyasia with time-varying parameters: BIOMD0000000982v0.0.1

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

##### Details

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

LeBeau1999 - IP3-dependent intracellular calcium oscillations due to agonist stimulation from Cholecytokinin: BIOMD0000000965v0.0.1

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

##### Details

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

Lebeda2008 - BoNT paralysis (3 step model): BIOMD0000000267v0.0.1

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

##### Details

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:

NameDescription
kL=0.013 perminuteReaction: translocate => lytic, Rate Law: kL*translocate*endosome
kT=0.141 perminuteReaction: bound => translocate, Rate Law: kT*bound*extracellular
kB=0.058 perminuteReaction: free => bound, Rate Law: kB*free*extracellular

States:

NameDescription
lytic[Botulinum toxin type A]
free[Botulinum toxin type A]
translocate[Botulinum toxin type A]
bound[Botulinum toxin type A]

Lebeda2008 - BoTN Paralysis (4 step model): BIOMD0000000178v0.0.1

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

##### Details

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:

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

States:

NameDescription
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]

Leber2015 - Mucosal immunity and gut microbiome interaction during C. difficile infection: BIOMD0000000583v0.0.1

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

##### Details

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:

NameDescription
K=1.71079818745428E-4Reaction: E => E_i; Cdiff, E, Cdiff, E, Cdiff, Rate Law: Epithelium*K*E*Cdiff
k2=0.156287382551622; k1=4.5E-10Reaction: 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-10Reaction: 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=10.5Reaction: eDC_LP => eDC_MLN; eDC_LP, eDC_LP, Rate Law: k1*eDC_LP
k1=0.5069887Reaction: iTreg_LP => ; Cdiff, iTreg_LP, iTreg_LP, Rate Law: LP*k1*iTreg_LP
k1=0.0933277452272273Reaction: Commensal_Dead => ; Commensal_Dead, Commensal_Dead, Rate Law: Lumen*k1*Commensal_Dead
A1=0.00478; K=2.33225E-5; A2=0.18Reaction: 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-6Reaction: 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-11Reaction: Cdiff => Cdiff; Commensal_Harmful, Commensal_Beneficial, Cdiff, Commensal_Harmful, Cdiff, Commensal_Harmful, Rate Law: Lumen*K*Cdiff*Commensal_Harmful
k1=2.39665140586358Reaction: Th17_LP => ; iTreg_LP, Th17_LP, Th17_LP, Rate Law: LP*k1*Th17_LP
k1=1.72495199303666E-5Reaction: eDC_MLN => ; iTreg_MLN, eDC_MLN, eDC_MLN, Rate Law: MLN*k1*eDC_MLN
k1=2255.80469507059Reaction: eDC_MLN => Th17_MLN; eDC_MLN, eDC_MLN, Rate Law: MLN*k1*eDC_MLN
k1=53.9130568911728Reaction: tDC_MLN => iTreg_MLN; tDC_MLN, tDC_MLN, Rate Law: k1*tDC_MLN
K=2.35932924820229E-7Reaction: N_Lum => ; Commensal_Beneficial, N_Lum, Commensal_Beneficial, N_Lum, Commensal_Beneficial, Rate Law: Lumen*K*N_Lum*Commensal_Beneficial
k1=1.459Reaction: Th1_MLN => Th1_LP; E_i, Th1_MLN, Th1_MLN, Rate Law: k1*Th1_MLN
k2=26.8747332769592; k1=559.297141527983; K=2.0E-4Reaction: 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=5.5Reaction: iTreg_MLN => iTreg_LP; E_i, iTreg_MLN, iTreg_MLN, Rate Law: k1*iTreg_MLN
k=0.55Reaction: iDC_E + Cdiff => eDC_LP; Commensal_Dead, Commensal_Beneficial, Cdiff, Cdiff, Rate Law: k*Cdiff
k1=2.50454427171444Reaction: Th17_MLN => Th17_LP; E_i, Th17_MLN, Th17_MLN, Rate Law: k1*Th17_MLN
k1=0.99505694359Reaction: 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=0.171190728888258Reaction: 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=2.5Reaction: E_i => E_d; E_i, E_i, Rate Law: Epithelium*k1*E_i
K=4.5E-5; e2=0.092308585205372; e1=2.0Reaction: 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-4Reaction: tDC_MLN => ; iTreg_MLN, tDC_MLN, tDC_MLN, Rate Law: Lumen*k*tDC_MLN
k1=20.0Reaction: M_LP => ; iTreg_LP, M_LP, M_LP, Rate Law: Epithelium*k1*M_LP
k1=1.27393226093773; k2=0.0020401460213434Reaction: 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=3.65Reaction: 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=0.065Reaction: 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-5Reaction: 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=4000.0Reaction: E_d => E; E_d, E_d, Rate Law: Epithelium*k1*E_d

States:

NameDescription
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]

Leber2016 - Expanded model of Tfh-Tfr differentiation - Helicobacter pylori infection: BIOMD0000000625v0.0.1

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

##### Details

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:

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

States:

NameDescription
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]

Leber2016 - Host immune response - H.pylori infection: MODEL1611160002v0.0.1

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

##### Details

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

Leber2016 - Regulatory macrophage differentiation - H.pylori infection: MODEL1611160001v0.0.1

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

##### Details

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

Ledzewicz2013 - On optimal chemotherapy with a strongly targeted agent for a model of tumor immune system interactions with generalized logistic growth: BIOMD0000000919v0.0.1

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

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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:

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

States:

NameDescription
x[Tumor Volume]
yy

Lee2003 - Roles of APC and Axin in Wnt Pathway (without regulatory loop): BIOMD0000000658v0.0.1

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

##### Details

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:

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

States:

NameDescription
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]

Lee2008 - ERK and PI3K signal integration by Myc: BIOMD0000000818v0.0.1

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

##### Details

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:

NameDescription
k_MT = 0.4 1/h; K_MT = 0.01 nmol/lReaction: Myc_ser62 => Myc_thr58; GSK3B, Rate Law: Cell*k_MT*GSK3B*Myc_ser62/(K_MT+Myc_ser62)
kM = 1.0 1/hReaction: => Myc; GF, Rate Law: Cell*kM*GF
K_AP = 0.01 nmol/l; k_ap = 360.0 1/hReaction: AKT => AKTp; PI3K, Rate Law: Cell*k_ap*PI3K*AKT/(K_AP+AKT)
dM = 2.08 1/hReaction: Myc =>, Rate Law: Cell*dM*Myc
k_AD = 72.0 nmol/(h*l); K_AD = 0.01 nmol/lReaction: AKTp => AKT, Rate Law: Cell*k_AD*AKTp/(K_AD+AKTp)
K_MS = 0.01 nmol/l; k_MS = 2.3 1/hReaction: 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/hReaction: 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/hReaction: Myc_ser62 =>, Rate Law: Cell*dMS*Myc_ser62
dMT = 2.08 1/hReaction: Myc_thr58 =>, Rate Law: Cell*dMT*Myc_thr58

States:

NameDescription
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]

Lee2008 - Genome-scale metabolic network of Clostridium acetobutylicum (iJL432): MODEL1507180030v0.0.1

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

##### Details

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

Lee2010 - Genome-scale metabolic network of Zymomonas mobilis (iZmobMBEL601): MODEL1507180031v0.0.1

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

##### Details

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

Lee2012_GeneExpression_BasicDecoyModel: MODEL1202270000v0.0.1

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

##### Details

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

Lee2012_GeneExpression_tTA-doxInteraction: MODEL1202270001v0.0.1

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

##### Details

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

Lee2016 - Blood Coagulation Model: MODEL1806060001v0.0.1

Blood coagulation model derived from Nayak2015.

##### Details

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