SBMLBioModels: W - Ç

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W


This a model from the article: Complex bursting in pancreatic islets: a potential glycolytic mechanism. Wierschem K,…

The electrical activity of insulin-secreting pancreatic islets of Langerhans is characterized by bursts of action potentials. Most often this bursting is periodic, but in some cases it is modulated by an underlying slower rhythm. We suggest that the modulatory rhythm for this complex bursting pattern is due to oscillations in glycolysis, while the bursting itself is generated by some other slow process. To demonstrate this hypothesis, we couple a minimal model of glycolytic oscillations to a minimal model for activity-dependent bursting in islets. We show that the combined model can reproduce several complex bursting patterns from mouse islets published in the literature, and we illustrate how these complex oscillations are produced through the use of a fast/slow analysis. link: http://identifiers.org/pubmed/15178199

Parameters: none

States: none

Observables: none

BIOMD0000000233 @ v0.0.1

This a model from the article: The smallest chemical reaction system with bistability Thomas Wilhelm BMC Systems B…

Bistability underlies basic biological phenomena, such as cell division, differentiation, cancer onset, and apoptosis. So far biologists identified two necessary conditions for bistability: positive feedback and ultrasensitivity.Biological systems are based upon elementary mono- and bimolecular chemical reactions. In order to definitely clarify all necessary conditions for bistability we here present the corresponding minimal system. According to our definition, it contains the minimal number of (i) reactants, (ii) reactions, and (iii) terms in the corresponding ordinary differential equations (decreasing importance from i-iii). The minimal bistable system contains two reactants and four irreversible reactions (three bimolecular, one monomolecular).We discuss the roles of the reactions with respect to the necessary conditions for bistability: two reactions comprise the positive feedback loop, a third reaction filters out small stimuli thus enabling a stable 'off' state, and the fourth reaction prevents explosions. We argue that prevention of explosion is a third general necessary condition for bistability, which is so far lacking discussion in the literature.Moreover, in addition to proving that in two-component systems three steady states are necessary for bistability (five for tristability, etc.), we also present a simple general method to design such systems: one just needs one production and three different degradation mechanisms (one production, five degradations for tristability, etc.). This helps modelling multistable systems and it is important for corresponding synthetic biology projects.The presented minimal bistable system finally clarifies the often discussed question for the necessary conditions for bistability. The three necessary conditions are: positive feedback, a mechanism to filter out small stimuli and a mechanism to prevent explosions. This is important for modelling bistability with simple systems and for synthetically designing new bistable systems. Our simple model system is also well suited for corresponding teaching purposes. link: http://identifiers.org/pubmed/19737387

Parameters:

Name Description
k3=1.0 Reaction: X + Y => P + Y, Rate Law: k3*X*Y
k4=1.5 Reaction: X => P, Rate Law: k4*X
k2=1.0 Reaction: X => X + Y, Rate Law: k2*X^2
k1=8.0 Reaction: S + Y => X, Rate Law: k1*S*Y

States:

Name Description
Y Y
S S
X X
P P

Observables: none

The paper describes a basic model of immune-induced cancer dormancy and immune evasion. Created by COPASI 4.25 (Build…

Cancer dormancy, a state in which cancer cells persist in a host without significant growth, is a natural forestallment of progression to manifest disease and is thus of great clinical interest. Experimental work in mice suggests that in immune-induced dormancy, the longer a cancer remains dormant in a host, the more resistant the cancer cells become to cytotoxic T-cell-mediated killing. In this work, mathematical models are used to analyse the possible causative mechanisms of cancer escape from immune-induced dormancy. Using a data-driven approach, both decaying efficacy in immune predation and immune recruitment are analysed with results suggesting that decline in recruitment is a stronger determinant of escape than increased resistance to predation. Using a mechanistic approach, the existence of an immune-resistant cancer cell subpopulation is considered, and the effects on cancer dormancy and potential immunoediting mechanisms of cancer escape are analysed and discussed. The immunoediting mechanism assumes that the immune system selectively prunes the cancer of immune-sensitive cells, which is shown to cause an initially heterogeneous population to become a more homogeneous, and more resistant, population. The fact that this selection may result in the appearance of decreasing efficacy in T-cell cytotoxic effect with time in dormancy is also demonstrated. This work suggests that through actions that temporarily delay cancer growth through the targeted removal of immune-sensitive subpopulations, the immune response may actually progress the cancer to a more aggressive state. link: http://identifiers.org/pubmed/24511375

Parameters:

Name Description
y = 0.2 1; Ie = 100.0 1; u = 0.001 1 Reaction: => I; C, Rate Law: tumor_microenvironment*y*I*(1-I/(Ie+u*C*I))
a0 = 1.05E-4 1 Reaction: C => ; I, Rate Law: tumor_microenvironment*a0*C*I
a = 0.2 1; K = 1.0E10 1 Reaction: => C, Rate Law: tumor_microenvironment*a*C*(1-C/K)

States:

Name Description
I [Effector Immune Cell]
C [malignant cell]

Observables: none

The paper describes a model of immune-induced cancer dormancy and immune evasion with resistance. Created by COPASI 4.…

Cancer dormancy, a state in which cancer cells persist in a host without significant growth, is a natural forestallment of progression to manifest disease and is thus of great clinical interest. Experimental work in mice suggests that in immune-induced dormancy, the longer a cancer remains dormant in a host, the more resistant the cancer cells become to cytotoxic T-cell-mediated killing. In this work, mathematical models are used to analyse the possible causative mechanisms of cancer escape from immune-induced dormancy. Using a data-driven approach, both decaying efficacy in immune predation and immune recruitment are analysed with results suggesting that decline in recruitment is a stronger determinant of escape than increased resistance to predation. Using a mechanistic approach, the existence of an immune-resistant cancer cell subpopulation is considered, and the effects on cancer dormancy and potential immunoediting mechanisms of cancer escape are analysed and discussed. The immunoediting mechanism assumes that the immune system selectively prunes the cancer of immune-sensitive cells, which is shown to cause an initially heterogeneous population to become a more homogeneous, and more resistant, population. The fact that this selection may result in the appearance of decreasing efficacy in T-cell cytotoxic effect with time in dormancy is also demonstrated. This work suggests that through actions that temporarily delay cancer growth through the targeted removal of immune-sensitive subpopulations, the immune response may actually progress the cancer to a more aggressive state. link: http://identifiers.org/pubmed/24511375

Parameters:

Name Description
y = 0.2 1; Ie = 100.0 1; u = 0.001 1 Reaction: => I; C, R, Rate Law: tumor_microenvironment*y*I*(1-I/(Ie+u*(C+0.001*R)*I))
a0 = 1.0E-4 1 Reaction: C => ; I, Rate Law: tumor_microenvironment*a0*C*I
a = 0.2 1; K = 1.0E10 1 Reaction: => C; R, Rate Law: tumor_microenvironment*a*C*(1-(C+R)/K)
K = 1.0E10 1; b = 0.2 1 Reaction: => R; C, Rate Law: tumor_microenvironment*b*R*(1-(R+C)/K)
b0 = 1.0E-4 1 Reaction: R => ; I, Rate Law: tumor_microenvironment*b0*R*I

States:

Name Description
I [Effector Immune Cell]
C [malignant cell]
R [malignant cell]

Observables: none

Mathematical model of blood coagulation to simulate factor IIa, Va and Xa concentration profiles. Publication also illus…

A simulation model for the production of thrombin in plasma is presented. Values of the reaction rate constants as determined in purified systems are used and the model is tested by comparison of simulations of factor Xa, factor Va and thrombin generation curves with experimental data obtained in thromboplastin-activated plasma. Simulations of the effect of hirudin indicate that factor V is predominantly activated by thrombin and not by factor Xa. The model predicts a threshold value for the factor Xa production which, if exceeded, results in explosive and complete activation of prothrombinase. The dependence of this threshold value on different negative feedback reactions, e.g. the inactivation of thrombin and factor Xa by antithrombin III (+ heparin), is investigated. The threshold value, for control plasma in the range of 1-10 pM total factor Xa production, can be raised two orders of magnitude by accelerated inactivation of factor Xa and prothrombinase but is hardly affected by a tenfold increase in the rate of thrombin inactivation or by increased production of activated protein C. This latter effect, however, results in a more gradual input-response relation between factor Xa input and the extent of prothrombinase activation. link: http://identifiers.org/pubmed/1794746

Parameters: none

States: none

Observables: none

BIOMD0000000791 @ v0.0.1

The paper describes a model of antitumor vaccine therapy. Created by COPASI 4.25 (Build 207) This model is described i…

TGF-β is an immunoregulatory protein that contributes to inadequate antitumor immune responses in cancer patients. Recent experimental data suggests that TGF-β inhibition alone, provides few clinical benefits, yet it can significantly amplify the anti-tumor immune response when combined with a tumor vaccine. We develop a mathematical model in order to gain insight into the cooperative interaction between anti-TGF-β and vaccine treatments. The mathematical model follows the dynamics of the tumor size, TGF-β concentration, activated cytotoxic effector cells, and regulatory T cells. Using numerical simulations and stability analysis, we study the following scenarios: a control case of no treatment, anti-TGF-β treatment, vaccine treatment, and combined anti-TGF-β vaccine treatments. We show that our model is capable of capturing the observed experimental results, and hence can be potentially used in designing future experiments involving this approach to immunotherapy. link: http://identifiers.org/pubmed/22438084

Parameters:

Name Description
c2 = 300.0 1; a1 = 0.3 1/d Reaction: => B; T, Rate Law: tme*tgfb(a1, T, c2)
d0 = 1.0E-5 1/d Reaction: T => ; V, Rate Law: tme*induced(d0, T, V)
d1 = 1.0E-5 1/d Reaction: V =>, Rate Law: tme*d1*V
f = 0.62 1/d; c3 = 300.0 1 Reaction: => E; T, B, Rate Law: tme*es(f, E, T, c3, B)
r = 0.01 1/d Reaction: E => R, Rate Law: tme*r*E
a0 = 0.1946 1/d; c0 = 0.002710027100271 1 Reaction: => T, Rate Law: tme*tg(a0, T, c0)
c1 = 100.0 1; d0 = 1.0E-5 1/d Reaction: T => ; E, B, Rate Law: tme*imm(d0, E, T, c1, B)
d = 7.0E-4 1/d Reaction: B =>, Rate Law: tme*d*B

States:

Name Description
B [Transforming growth factor beta-1]
T [malignant cell]
V [effector T cell]
E [effector T cell]
R [regulatory T cell]

Observables: none

Winter2017 - Brain Energy Metabolism with PPPThis model is described in the article: [Mathematical analysis of the infl…

Blood oxygen level-dependent functional magnetic resonance imaging (BOLD-fMRI) is a standard clinical tool for the detection of brain activation. In Alzheimer’s disease (AD), task-related and resting state fMRI have been used to detect brain dysfunction. It has been shown that the shape of the BOLD response is affected in early AD. To correctly interpret these changes, the mechanisms responsible for the observed behaviour need to be known. The parameters of the canonical hemodynamic response function (HRF) commonly used in the analysis of fMRI data have no direct biological interpretation and cannot be used to answer this question. We here present a model that allows relating AD-specific changes in the BOLD shape to changes in the underlying energy metabolism. According to our findings, the classic view that differences in the BOLD shape are only attributed to changes in strength and duration of the stimulus does not hold. Instead, peak height, peak timing and full width at half maximum are sensitive to changes in the reaction rate of several metabolic reactions. Our systems-theoretic approach allows the use of patient-specific clinical data to predict dementia- driven changes in the HRF, which can be used to improve the results of fMRI analyses in AD patients. link: http://identifiers.org/doi/10.1177/0271678X17693024

Parameters:

Name Description
nh_O2__Aubert = 2.73; Hb_OP = 8.6; PScap=10.0; K_O2__Aubert = 0.0361 Reaction: species_23 => species_20, Rate Law: PScap/compartment_3*(K_O2__Aubert*(Hb_OP/(species_23/compartment_1)-1)^((-1)/nh_O2__Aubert)-species_20/compartment_3)*compartment_1
Vmax=2.44278E-4; K_P2=0.192807; Keq=1652870.0; K_P1=0.168333; K_S2=5.85387E-4; K_S1=1.73625E-4 Reaction: X5P_astrocytes + R5P_astrocytes => species_10 + S7P_astrocytes, Rate Law: compartment_3*Vmax*1/(K_S1*K_S2)*(X5P_astrocytes/compartment_3*R5P_astrocytes/compartment_3-species_10/compartment_3*S7P_astrocytes/compartment_3/Keq)/(((1+X5P_astrocytes/compartment_3/K_S1)*(1+R5P_astrocytes/compartment_3/K_S2)+(1+species_10/compartment_3/K_P1)*(1+S7P_astrocytes/compartment_3/K_P2))-1)
_sf = 0.75; Vmax_cg_GLC__wrt_capillaries___Aubert = 0.422727272727273; K_T_GLC_cg__Aubert = 9.0 Reaction: species_25 => species_4, Rate Law: Vmax_cg_GLC__wrt_capillaries___Aubert*_sf*(species_25/compartment_1/(species_25/compartment_1+K_T_GLC_cg__Aubert)-species_4/compartment_3/(species_4/compartment_3+K_T_GLC_cg__Aubert))*compartment_1
v_stim = 0.0 Reaction: Na__extracellular_space => Na__neurons, Rate Law: v_stim*compartment_2
Vmax_eg_GLU__wrt_extracellular_space = 0.026; K_m_GLU = 0.05 Reaction: GLU_extracellular_space => GLU_astrocytes + Na__astrocytes, Rate Law: Vmax_eg_GLU__wrt_extracellular_space*GLU_extracellular_space/compartment_4/(GLU_extracellular_space/compartment_4+K_m_GLU)*compartment_4
v_stim = 0.0; K_m_GLU = 0.05; R_Na_GLU = 0.075 Reaction: GLU_neurons => GLU_extracellular_space, Rate Law: v_stim*R_Na_GLU*GLU_neurons/compartment_2/(GLU_neurons/compartment_2+K_m_GLU)*compartment_2
k2=15.0; k1=2000.0 Reaction: species_15 + species_11 => species_18 + NAD_neurons, Rate Law: compartment_2*(k1*species_15/compartment_2*species_11/compartment_2-k2*species_18/compartment_2*NAD_neurons/compartment_2)
k_PGK=3.0 Reaction: species_10 + ADP_astrocytes + NAD_astrocytes => species_13 + species_14 + species_5, Rate Law: compartment_3*k_PGK*species_10/compartment_3*ADP_astrocytes/compartment_3*NAD_astrocytes/compartment_3/(species_13/compartment_3)
Vmax=4.93027E-4; K_P2=0.192807; Keq=1652870.0; K_P1=0.168333; K_S2=5.85387E-4; K_S1=1.73625E-4 Reaction: X5P_neurons + R5P_neurons => species_9 + S7P_neurons, Rate Law: compartment_2*Vmax*1/(K_S1*K_S2)*(X5P_neurons/compartment_2*R5P_neurons/compartment_2-species_9/compartment_2*S7P_neurons/compartment_2/Keq)/(((1+X5P_neurons/compartment_2/K_S1)*(1+R5P_neurons/compartment_2/K_S2)+(1+species_9/compartment_2/K_P1)*(1+S7P_neurons/compartment_2/K_P2))-1)
K_P1=0.603002; Keq=0.0777764; Vmax=1.37124E-4; K_S2=0.168333; K_P2=0.109681; K_S1=0.0799745 Reaction: species_8 + species_10 => X5P_astrocytes + E4P_astrocytes, Rate Law: compartment_3*Vmax*1/(K_S1*K_S2)*(species_8/compartment_3*species_10/compartment_3-X5P_astrocytes/compartment_3*E4P_astrocytes/compartment_3/Keq)/(((1+species_8/compartment_3/K_S1)*(1+species_10/compartment_3/K_S2)+(1+X5P_astrocytes/compartment_3/K_P1)*(1+E4P_astrocytes/compartment_3/K_P2))-1)
Vmax=0.0080394; K_S1=0.168333; K_S2=0.192807; K_P1=0.0799745; K_P2=0.109681; Keq=0.323922 Reaction: species_10 + S7P_astrocytes => species_8 + E4P_astrocytes, Rate Law: compartment_3*Vmax*1/(K_S1*K_S2)*(species_10/compartment_3*S7P_astrocytes/compartment_3-species_8/compartment_3*E4P_astrocytes/compartment_3/Keq)/(((1+species_10/compartment_3/K_S1)*(1+S7P_astrocytes/compartment_3/K_S2)+(1+species_8/compartment_3/K_P1)*(1+E4P_astrocytes/compartment_3/K_P2))-1)
k_PGK=10.0 Reaction: species_9 + ADP_neurons + NAD_neurons => species_11 + species_12 + species_3, Rate Law: compartment_2*k_PGK*species_9/compartment_2*ADP_neurons/compartment_2*NAD_neurons/compartment_2/(species_11/compartment_2)
_sf = 0.75; K_T_GLC_en__Aubert = 9.0; Vmax_en_GLC__wrt_neurons___Aubert = 11767.5 Reaction: species_27 => species_1, Rate Law: Vmax_en_GLC__wrt_neurons___Aubert*_sf*(species_27/compartment_4/(species_27/compartment_4+K_T_GLC_en__Aubert)-species_1/compartment_2/(species_1/compartment_2+K_T_GLC_en__Aubert))*compartment_4
Sm_g = 10500.0; K_m_Na_pump = 0.4243; k_pump = 3.17E-7 Reaction: species_5 + Na__astrocytes => ADP_astrocytes, Rate Law: compartment_3*Sm_g/compartment_3*k_pump*species_5/compartment_3*Na__astrocytes/compartment_3*(1+species_5/compartment_3/K_m_Na_pump)^(-1)
K_m_ATP_ATPase = 0.001; VmaxATPase=0.035 Reaction: species_5 => ADP_astrocytes, Rate Law: compartment_3*VmaxATPase*species_5/compartment_3/(species_5/compartment_3+K_m_ATP_ATPase)
K_m_F6P=0.18; k_PFK=0.2; parameter_5 = 1.0; parameter_6 = 4.0 Reaction: species_8 + species_5 => species_10 + ADP_astrocytes, Rate Law: compartment_3*k_PFK*species_5/compartment_3*(1+(species_5/compartment_3/parameter_5)^parameter_6)^(-1)*species_8/compartment_3/(species_8/compartment_3+K_m_F6P)
k_HK=0.022; K_I_G6P=0.02 Reaction: species_3 + species_1 => species_2 + ADP_neurons; species_2, Rate Law: compartment_2*k_HK*species_3/compartment_2*(1+species_2/compartment_2/K_I_G6P)^(-1)
K_P1=0.603002; K_S1=0.0537179; Vmax=0.00775925; Keq=39.2574 Reaction: Ru5P_astrocytes => X5P_astrocytes, Rate Law: compartment_3*Vmax*1/K_S1*(Ru5P_astrocytes/compartment_3-X5P_astrocytes/compartment_3/Keq)/((1+Ru5P_astrocytes/compartment_3/K_S1+1+X5P_astrocytes/compartment_3/K_P1)-1)
k1=4.23283E-4 Reaction: NADPH_neurons => NADP_neurons, Rate Law: k1*NADPH_neurons
v_max_mito=0.1; beta=20.0; parameter_18 = 0.0632; parameter_16 = 0.00107; alpha=5.0; parameter_17 = 0.0029658 Reaction: species_15 + species_16 + species_11 + ADP_neurons => species_3 + species_24 + NAD_neurons, Rate Law: v_max_mito*species_15/compartment_2/(species_15/compartment_2+parameter_18)*ADP_neurons/compartment_2/(ADP_neurons/compartment_2+parameter_16)*species_16/compartment_2/(species_16/compartment_2+parameter_17)*(1-1/(1+exp((-alpha)*(species_3/compartment_2/(ADP_neurons/compartment_2)-beta))))*compartment_2
K_P2=0.0537179; K_S2=3.11043E-6; K_P1=5.0314E-4; Keq=4.0852E7; K_S1=3.23421E-5; Vmax=1.31677 Reaction: P6G_astrocytes + NADP_astrocytes => Ru5P_astrocytes + NADPH_astrocytes, Rate Law: compartment_3*Vmax*1/(K_S1*K_S2)*(P6G_astrocytes/compartment_3*NADP_astrocytes/compartment_3-Ru5P_astrocytes/compartment_3*NADPH_astrocytes/compartment_3/Keq)/(((1+P6G_astrocytes/compartment_3/K_S1)*(1+NADP_astrocytes/compartment_3/K_S2)+(1+Ru5P_astrocytes/compartment_3/K_P1)*(1+NADPH_astrocytes/compartment_3/K_P2))-1)
k1=2.09722E-4 Reaction: NADPH_astrocytes => NADP_astrocytes, Rate Law: k1*NADPH_astrocytes
Vmax_ne_LAC__wrt_neurons___Aubert = 0.2175; K_T_LAC_ne__Aubert = 0.5 Reaction: species_28 => species_18, Rate Law: Vmax_ne_LAC__wrt_neurons___Aubert*(species_28/compartment_4/(species_28/compartment_4+K_T_LAC_ne__Aubert)-species_18/compartment_2/(species_18/compartment_2+K_T_LAC_ne__Aubert))*compartment_4
k_PK=44.0 Reaction: species_12 + ADP_neurons => species_3 + species_15, Rate Law: compartment_2*k_PK*species_12/compartment_2*ADP_neurons/compartment_2
k2=32.0; k1=780.0 Reaction: species_17 + species_13 => species_19 + NAD_astrocytes, Rate Law: compartment_3*(k1*species_17/compartment_3*species_13/compartment_3-k2*species_19/compartment_3*NAD_astrocytes/compartment_3)
Vmax_eg_GLC__wrt_astrocytes___Aubert_ = 1275.0; _sf = 0.75; K_T_GLC_eg__Aubert = 9.0 Reaction: species_27 => species_4, Rate Law: Vmax_eg_GLC__wrt_astrocytes___Aubert_*_sf*(species_27/compartment_4/(species_27/compartment_4+K_T_GLC_eg__Aubert)-species_4/compartment_3/(species_4/compartment_3+K_T_GLC_eg__Aubert))*compartment_4
Vmax_ge_LAC__wrt_astrocytes___Aubert = 0.057; K_T_LAC_ge__Aubert = 0.5 Reaction: species_19 => species_28, Rate Law: Vmax_ge_LAC__wrt_astrocytes___Aubert*(species_19/compartment_3/(species_19/compartment_3+K_T_LAC_ge__Aubert)-species_28/compartment_4/(species_28/compartment_4+K_T_LAC_ge__Aubert))*compartment_3
F_in = 0.012 Reaction: O2_artery => species_23, Rate Law: 2*F_in/compartment_1*(O2_artery/artery-species_23/compartment_1)*artery
K_P2=5.0314E-4; Keq=22906.4; K_P1=0.0180932; Vmax=0.29057; K_S1=6.91392E-5; K_S2=1.31616E-5 Reaction: species_6 + NADP_astrocytes => G6L_astrocytes + NADPH_astrocytes, Rate Law: compartment_3*Vmax*1/(K_S1*K_S2)*(species_6/compartment_3*NADP_astrocytes/compartment_3-G6L_astrocytes/compartment_3*NADPH_astrocytes/compartment_3/Keq)/(((1+species_6/compartment_3/K_S1)*(1+NADP_astrocytes/compartment_3/K_S2)+(1+G6L_astrocytes/compartment_3/K_P1)*(1+NADPH_astrocytes/compartment_3/K_P2))-1)
nh_O2__Aubert = 2.73; Hb_OP = 8.6; PS_cap_neuron__wrt_capillaries___Aubert = 40.5; K_O2__Aubert = 0.0361 Reaction: species_23 => species_16, Rate Law: PS_cap_neuron__wrt_capillaries___Aubert/compartment_2*(K_O2__Aubert*(Hb_OP/(species_23/compartment_1)-1)^((-1)/nh_O2__Aubert)-species_16/compartment_2)*compartment_1
k_HK=0.01; K_I_G6P=0.02 Reaction: species_5 + species_4 => species_6 + ADP_astrocytes; species_6, Rate Law: compartment_3*k_HK*species_5/compartment_3*(1+species_6/compartment_3/K_I_G6P)^(-1)
Sm_n = 40500.0; K_m_Na_pump = 0.4243; k_pump = 3.17E-7 Reaction: species_3 + Na__neurons => ADP_neurons, Rate Law: compartment_2*Sm_n/compartment_2*k_pump*species_3/compartment_2*Na__neurons/compartment_2*(1+species_3/compartment_2/K_m_Na_pump)^(-1)
K_P1=0.603002; Keq=0.0777764; K_S2=0.168333; K_P2=0.109681; K_S1=0.0799745; Vmax=2.76758E-4 Reaction: species_7 + species_9 => X5P_neurons + E4P_neurons, Rate Law: compartment_2*Vmax*1/(K_S1*K_S2)*(species_7/compartment_2*species_9/compartment_2-X5P_neurons/compartment_2*E4P_neurons/compartment_2/Keq)/(((1+species_7/compartment_2/K_S1)*(1+species_9/compartment_2/K_S2)+(1+X5P_neurons/compartment_2/K_P1)*(1+E4P_neurons/compartment_2/K_P2))-1)
k1=0.5; k2=0.01 Reaction: species_21 + ADP_neurons => species_3 + Cr_neurons, Rate Law: compartment_2*(k1*species_21/compartment_2*ADP_neurons/compartment_2-k2*species_3/compartment_2*Cr_neurons/compartment_2)
Vmax=0.00165901; K_S1=0.0537179; K_P1=0.778461; Keq=35.4534 Reaction: Ru5P_neurons => R5P_neurons, Rate Law: compartment_2*Vmax*1/K_S1*(Ru5P_neurons/compartment_2-R5P_neurons/compartment_2/Keq)/((1+Ru5P_neurons/compartment_2/K_S1+1+R5P_neurons/compartment_2/K_P1)-1)
K_S1=0.168333; K_S2=0.192807; K_P1=0.0799745; K_P2=0.109681; Vmax=0.0162259; Keq=0.323922 Reaction: species_9 + S7P_neurons => species_7 + E4P_neurons, Rate Law: compartment_2*Vmax*1/(K_S1*K_S2)*(species_9/compartment_2*S7P_neurons/compartment_2-species_7/compartment_2*E4P_neurons/compartment_2/Keq)/(((1+species_9/compartment_2/K_S1)*(1+S7P_neurons/compartment_2/K_S2)+(1+species_7/compartment_2/K_P1)*(1+E4P_neurons/compartment_2/K_P2))-1)
K_T_GLC_ce__Aubert = 9.0; _sf = 0.75; Vmax_ce_GLC__wrt_capillaries___Aubert = 4.29090909090909 Reaction: species_25 => species_27, Rate Law: Vmax_ce_GLC__wrt_capillaries___Aubert*_sf*(species_25/compartment_1/(species_25/compartment_1+K_T_GLC_ce__Aubert)-species_27/compartment_4/(species_27/compartment_4+K_T_GLC_ce__Aubert))*compartment_1
Vmax=0.586458; K_P2=5.0314E-4; Keq=22906.4; K_P1=0.0180932; K_S1=6.91392E-5; K_S2=1.31616E-5 Reaction: species_2 + NADP_neurons => G6L_neurons + NADPH_neurons, Rate Law: compartment_2*Vmax*1/(K_S1*K_S2)*(species_2/compartment_2*NADP_neurons/compartment_2-G6L_neurons/compartment_2*NADPH_neurons/compartment_2/Keq)/(((1+species_2/compartment_2/K_S1)*(1+NADP_neurons/compartment_2/K_S2)+(1+G6L_neurons/compartment_2/K_P1)*(1+NADPH_neurons/compartment_2/K_P2))-1)
k_PK=20.0 Reaction: species_14 + ADP_astrocytes => species_5 + species_17, Rate Law: compartment_3*k_PK*species_14/compartment_3*ADP_astrocytes/compartment_3
beta=20.0; parameter_18 = 0.0632; parameter_16 = 0.00107; alpha=5.0; v_max_mito=0.01; parameter_17 = 0.0029658 Reaction: species_17 + ADP_astrocytes + species_20 + species_13 => species_5 + species_24 + NAD_astrocytes, Rate Law: v_max_mito*species_17/compartment_3/(species_17/compartment_3+parameter_18)*ADP_astrocytes/compartment_3/(ADP_astrocytes/compartment_3+parameter_16)*species_20/compartment_3/(species_20/compartment_3+parameter_17)*(1-1/(1+exp((-alpha)*(species_5/compartment_3/(ADP_astrocytes/compartment_3)-beta))))*compartment_3
k1=931.69; k2=2273.32 Reaction: species_6 => species_8, Rate Law: compartment_3*(k1*species_6/compartment_3-k2*species_8/compartment_3)
K_m_F6P=0.18; parameter_5 = 1.0; parameter_6 = 4.0; k_PFK=0.44 Reaction: species_7 + species_3 => species_9 + ADP_neurons, Rate Law: compartment_2*k_PFK*species_3/compartment_2*(1+(species_3/compartment_2/parameter_5)^parameter_6)^(-1)*species_7/compartment_2/(species_7/compartment_2+K_m_F6P)
V_gn_max_GLU = 0.3; parameter_14 = 0.01532; K_m_GLU = 0.05 Reaction: GLU_astrocytes + species_5 => GLU_neurons + ADP_astrocytes, Rate Law: V_gn_max_GLU*GLU_astrocytes/compartment_3/(GLU_astrocytes/compartment_3+K_m_GLU)*species_5/compartment_3/(species_5/compartment_3+parameter_14)*compartment_3
k1=1000.0; k2=920.0 Reaction: ADP_astrocytes => species_5 + AMP_astrocytes, Rate Law: compartment_3*(k1*(ADP_astrocytes/compartment_3)^2-k2*species_5/compartment_3*AMP_astrocytes/compartment_3)
K_P2=5.0314E-4; K_S2=3.11043E-6; Keq=4.0852E7; K_P1=0.0537179; K_S1=3.23421E-5; Vmax=2.65764 Reaction: P6G_neurons + NADP_neurons => Ru5P_neurons + NADPH_neurons, Rate Law: compartment_2*Vmax*1/(K_S1*K_S2)*(P6G_neurons/compartment_2*NADP_neurons/compartment_2-Ru5P_neurons/compartment_2*NADPH_neurons/compartment_2/Keq)/(((1+P6G_neurons/compartment_2/K_S1)*(1+NADP_neurons/compartment_2/K_S2)+(1+Ru5P_neurons/compartment_2/K_P1)*(1+NADPH_neurons/compartment_2/K_P2))-1)
Vmax_ec_LAC__wrt_extracellular_space___Aubert = 0.0058725; K_T_LAC_ec__Aubert = 0.5 Reaction: species_28 => species_26, Rate Law: Vmax_ec_LAC__wrt_extracellular_space___Aubert*(species_28/compartment_4/(species_28/compartment_4+K_T_LAC_ec__Aubert)-species_26/compartment_1/(species_26/compartment_1+K_T_LAC_ec__Aubert))*compartment_4
gNA=0.0039; RT = 2577340.0; Vm = -70.0; Sm_g = 10500.0; F = 96500.0 Reaction: Na__extracellular_space => Na__astrocytes, Rate Law: Sm_g*gNA/(compartment_3*F)*(RT/F*ln(Na__extracellular_space/compartment_4/(Na__astrocytes/compartment_3))-Vm)*compartment_3

States:

Name Description
species 9 [6-phospho-D-gluconic acid]
species 27 [D-glucose]
species 18 [(S)-lactic acid]
species 4 [D-glucose]
species 16 [dioxygen]
species 28 [(S)-lactic acid]
GLU extracellular space [L-glutamic acid]
species 20 [dioxygen]
NADPH neurons [NADPH]
ADP neurons [ADP]
NADP astrocytes [NADP]
Na astrocytes [sodium(1+)]
species 8 [D-fructose 6-phosphate]
NADPH astrocytes [NADPH]
CO2 artery [carbon dioxide]
Ru5P neurons [ribulose 5-phosphate]
species 5 [ATP]
species 15 [pyruvic acid]
species 12 [phosphoenolpyruvate]
GLU astrocytes [L-glutamic acid]
O2 artery [dioxygen]
species 6 [6-phospho-D-gluconic acid]
E4P neurons [D-erythrose 4-phosphate]
NADP neurons [NADP]
species 10 [6-phospho-D-gluconic acid]
NAD neurons [NAD]
species 11 [NADH]
Na extracellular space [sodium(1+)]
species 19 [(S)-lactic acid]
Ru5P astrocytes [ribulose 5-phosphate]
E4P astrocytes [D-erythrose 4-phosphate]
Na neurons [sodium(1+)]
S7P astrocytes [sedoheptulose 7-phosphate]
AMP neurons [AMP]
Cr neurons [creatine]
species 3 [ATP]
species 23 [dioxygen]
species 7 [D-fructose 6-phosphate]
GLU neurons [L-glutamic acid]
ADP astrocytes [ADP]
GLC artery [D-glucose]

Observables: none

BIOMD0000000683 @ v0.0.1

This a model from the article: Specific therapy regimes could lead to long-term immunological control of HIV. Wodarz…

We use mathematical models to study the relationship between HIV and the immune system during the natural course of infection and in the context of different antiviral treatment regimes. The models suggest that an efficient cytotoxic T lymphocyte (CTL) memory response is required to control the virus. We define CTL memory as long-term persistence of CTL precursors in the absence of antigen. Infection and depletion of CD4(+) T helper cells interfere with CTL memory generation, resulting in persistent viral replication and disease progression. We find that antiviral drug therapy during primary infection can enable the development of CTL memory. In chronically infected patients, specific treatment schedules, either including deliberate drug holidays or antigenic boosts of the immune system, can lead to a re-establishment of CTL memory. Whether such treatment regimes would lead to long-term immunologic control deserves investigation under carefully controlled conditions. link: http://identifiers.org/pubmed/10588728

Parameters:

Name Description
lamda = 1.0 Reaction: => x, Rate Law: COMpartment*lamda
d = 0.1 Reaction: x =>, Rate Law: COMpartment*d*x
c = 0.1 Reaction: => w; x, y, Rate Law: COMpartment*c*x*y*w
b = 0.01 Reaction: w =>, Rate Law: COMpartment*b*w
a = 0.2 Reaction: y =>, Rate Law: COMpartment*a*y
q = 0.5; c = 0.1 Reaction: w => z; y, Rate Law: COMpartment*c*q*y*w
s = 1.0; beta = 1.5 Reaction: x => y; y, Rate Law: COMpartment*s*beta*x*y
p = 1.0 Reaction: y => ; z, Rate Law: COMpartment*p*y*z
h = 0.1 Reaction: z =>, Rate Law: COMpartment*h*z

States:

Name Description
w [cytotoxic T-lymphocyte; precursor]
x [CD4-Positive T-Lymphocyte; uninfected]
z [effector T cell; cytotoxic T-lymphocyte]
y [CD4-Positive T-Lymphocyte; HIV infection]

Observables: none

This a model from the article: A dynamical perspective of CTL cross-priming and regulation: implications for cancer im…

Cytotoxic T lymphocytes (CTL) responses are required to fight many diseases such as viral infections and tumors. At the same time, they can cause disease when induced inappropriately. Which factors regulate CTL and decide whether they should remain silent or react is open to debate. The phenomenon called cross-priming has received attention in this respect. That is, CTL expansion occurs if antigen is recognized on the surface of professional antigen presenting cells (APCs). This is in contrast to direct presentation where antigen is seen on the surface of the target cells (e.g. infected cells or tumor cells). Here we introduce a mathematical model, which takes the phenomenon of cross-priming into account. We propose a new mechanism of regulation which is implicit in the dynamics of the CTL: According to the model, the ability of a CTL response to become established depends on the ratio of cross-presentation to direct presentation of the antigen. If this ratio is relatively high, CTL responses are likely to become established. If this ratio is relatively low, tolerance is the likely outcome. The behavior of the model includes a parameter region where the outcome depends on the initial conditions. We discuss our results with respect to the idea of self/non-self discrimination and the danger signal hypothesis. We apply the model to study the role of CTL in cancer initiation, cancer evolution/progression, and therapeutic vaccination against cancers. link: http://identifiers.org/pubmed/12706524

Parameters: none

States: none

Observables: none

BIOMD0000000684 @ v0.0.1

This a model from the article: Evolution of immunological memory and the regulation of competition between pathogens.…

Memory is a central characteristic of immune responses. It is defined as an elevated number of specific immune cells that remain after resolution of infection and can protect the host against reinfection. The evolution of immunological memory is subject to debate. The advantages of memory discussed so far include protection from reinfection, control of chronic infection, and the transfer of immune function to the next generation. Mathematical models are used to identify a new force that can drive the evolution of immunological memory: the duration of memory can regulate the degree of competition between different pathogens. While a long duration of memory provides lasting protection against reinfection, it may also allow an inferior pathogen species to persist. This can be detrimental for the host if the inferior pathogen is more virulent. On the other hand, a shorter duration of memory ensures that an inferior pathogen species is excluded. This can be beneficial for the host if the inferior pathogen is more virulent. Thus, while in the absence of pathogen diversity memory is always expected to evolve to a long duration, under specific circumstances, memory can evolve toward shorter durations in the presence of pathogen diversity. link: http://identifiers.org/pubmed/13678598

Parameters: none

States: none

Observables: none

This a model from the article: Dynamics of killer T cell inflation in viral infections. Wodarz D, Sierro S, Klenerma…

Upon acute viral infection, a typical cytotoxic T lymphocyte (CTL) response is characterized by a phase of expansion and contraction after which it settles at a relatively stable memory level. Recently, experimental data from mice infected with murine cytomegalovirus (MCMV) showed different and unusual dynamics. After acute infection had resolved, some antigen specific CTL started to expand over time despite the fact that no replicative virus was detectable. This phenomenon has been termed as "CTL memory inflation". In order to examine the dynamics of this system further, we developed a mathematical model analysing the impact of innate and adaptive immune responses. According to this model, a potentially important contributor to CTL inflation is competition between the specific CTL response and an innate natural killer (NK) cell response. Inflation occurs most readily if the NK cell response is more efficient than the CTL at reducing virus load during acute infection, but thereafter maintains a chronic virus load which is sufficient to induce CTL proliferation. The model further suggests that weaker NK cell mediated protection can correlate with more pronounced CTL inflation dynamics over time. We present experimental data from mice infected with MCMV which are consistent with the theoretical predictions. This model provides valuable information and may help to explain the inflation of CMV specific CD8+T cells seen in humans as they age. link: http://identifiers.org/pubmed/17251133

Parameters: none

States: none

Observables: none

This a model from the article: Dynamics of killer T cell inflation in viral infections. Wodarz D, Sierro S, Klenerma…

Upon acute viral infection, a typical cytotoxic T lymphocyte (CTL) response is characterized by a phase of expansion and contraction after which it settles at a relatively stable memory level. Recently, experimental data from mice infected with murine cytomegalovirus (MCMV) showed different and unusual dynamics. After acute infection had resolved, some antigen specific CTL started to expand over time despite the fact that no replicative virus was detectable. This phenomenon has been termed as "CTL memory inflation". In order to examine the dynamics of this system further, we developed a mathematical model analysing the impact of innate and adaptive immune responses. According to this model, a potentially important contributor to CTL inflation is competition between the specific CTL response and an innate natural killer (NK) cell response. Inflation occurs most readily if the NK cell response is more efficient than the CTL at reducing virus load during acute infection, but thereafter maintains a chronic virus load which is sufficient to induce CTL proliferation. The model further suggests that weaker NK cell mediated protection can correlate with more pronounced CTL inflation dynamics over time. We present experimental data from mice infected with MCMV which are consistent with the theoretical predictions. This model provides valuable information and may help to explain the inflation of CMV specific CD8+T cells seen in humans as they age. link: http://identifiers.org/pubmed/17251133

Parameters:

Name Description
alpha = 0.2 Reaction: => z_a; m_8, Rate Law: COMpartment*alpha*m_8
d = 0.1 Reaction: x =>, Rate Law: COMpartment*d*x
a1 = 0.2 Reaction: y_1 =>, Rate Law: COMpartment*a1*y_1
a0 = 0.1 Reaction: y_0 =>, Rate Law: COMpartment*a0*y_0
phi = 0.1 Reaction: L => y_0, Rate Law: COMpartment*phi*L
u = 1.0 Reaction: v =>, Rate Law: COMpartment*u*v
lambda = 10.0 Reaction: => x, Rate Law: COMpartment*lambda
ci = 12.0 Reaction: => z_i; y_0, y_1, Rate Law: COMpartment*ci*(y_0+y_1)*z_i
k = 1.0 Reaction: => v; y_1, Rate Law: COMpartment*k*y_1
ca = 15.5 Reaction: => z_a; y_0, y_1, Rate Law: COMpartment*ca*(y_0+y_1)*z_a
r = 1.0 Reaction: m_3 => m_4, Rate Law: COMpartment*r*m_3
beta = 0.1 Reaction: x => y_0; v, Rate Law: COMpartment*beta*v*x
pa = 1.0E-6 Reaction: y_0 => ; z_a, Rate Law: COMpartment*pa*z_a*y_0
bi = 0.1 Reaction: z_i =>, Rate Law: COMpartment*bi*z_i
gamma = 0.5 Reaction: x => L; v, Rate Law: COMpartment*gamma*v*x
eta = 0.01 Reaction: y_0 => y_1, Rate Law: COMpartment*eta*y_0
ba = 0.1 Reaction: z_a =>, Rate Law: COMpartment*ba*z_a
xi = 0.01 Reaction: => z_i, Rate Law: COMpartment*xi
p_i = 1.0 Reaction: y_0 => ; z_i, Rate Law: COMpartment*p_i*z_i*y_0

States:

Name Description
v [cytomegalovirus infection; virion]
m 2 [naive T cell]
m 6 [naive T cell]
m 7 [naive T cell]
m 5 [naive T cell]
z a [cytotoxic T-lymphocyte; cytotoxic T cell]
x [cell; Susceptibility; cell]
y 0 [cytomegalovirus infection; infected cell]
L [cytomegalovirus infection; infected cell]
m 1 [naive T cell]
m 4 [naive T cell]
y 1 [cytomegalovirus infection; infected cell]
m 3 [naive T cell]
m 0 [naive T cell]
m 8 [naive T cell]
z i [natural killer cell; natural killer cell]

Observables: none

This a model from the article: Dynamics of killer T cell inflation in viral infections. Wodarz D, Sierro S, Klenerma…

Upon acute viral infection, a typical cytotoxic T lymphocyte (CTL) response is characterized by a phase of expansion and contraction after which it settles at a relatively stable memory level. Recently, experimental data from mice infected with murine cytomegalovirus (MCMV) showed different and unusual dynamics. After acute infection had resolved, some antigen specific CTL started to expand over time despite the fact that no replicative virus was detectable. This phenomenon has been termed as "CTL memory inflation". In order to examine the dynamics of this system further, we developed a mathematical model analysing the impact of innate and adaptive immune responses. According to this model, a potentially important contributor to CTL inflation is competition between the specific CTL response and an innate natural killer (NK) cell response. Inflation occurs most readily if the NK cell response is more efficient than the CTL at reducing virus load during acute infection, but thereafter maintains a chronic virus load which is sufficient to induce CTL proliferation. The model further suggests that weaker NK cell mediated protection can correlate with more pronounced CTL inflation dynamics over time. We present experimental data from mice infected with MCMV which are consistent with the theoretical predictions. This model provides valuable information and may help to explain the inflation of CMV specific CD8+T cells seen in humans as they age. link: http://identifiers.org/pubmed/17251133

Parameters:

Name Description
alpha = 0.2 Reaction: => z_a; m_8_0, Rate Law: COMpartment*alpha*m_8_0
d = 0.1 Reaction: L_0 =>, Rate Law: COMpartment*d*L_0
a1 = 0.2 Reaction: y_1 =>, Rate Law: COMpartment*a1*y_1
a0 = 0.1 Reaction: y_0 =>, Rate Law: COMpartment*a0*y_0
phi = 0.1 Reaction: L_0 => y_0, Rate Law: COMpartment*phi*L_0
u = 1.0 Reaction: v_0 =>, Rate Law: COMpartment*u*v_0
lambda = 10.0 Reaction: => x_0, Rate Law: COMpartment*lambda
k = 1.0 Reaction: => v_0; y_1, Rate Law: COMpartment*k*y_1
ca = 15.5 Reaction: => z_a; y_0, y_1, Rate Law: COMpartment*ca*(y_0+y_1)*z_a
r = 1.0 Reaction: m_0_0 => m_1_0, Rate Law: COMpartment*r*m_0_0
beta = 0.1 Reaction: x_0 => y_0; v_0, Rate Law: COMpartment*beta*v_0*x_0
pa = 1.0E-6 Reaction: y_0 => ; z_a, Rate Law: COMpartment*pa*z_a*y_0
gamma = 0.5 Reaction: x_0 => L_0; v_0, Rate Law: COMpartment*gamma*v_0*x_0
eta = 0.01 Reaction: y_0 => y_1, Rate Law: COMpartment*eta*y_0
ba = 0.1 Reaction: z_a =>, Rate Law: COMpartment*ba*z_a

States:

Name Description
m 2 0 [naive T cell]
z a [cytotoxic T-lymphocyte; cytotoxic T cell]
y 0 [cytomegalovirus infection; infected cell]
m 4 0 [naive T cell]
m 7 0 [naive T cell]
m 3 0 [naive T cell]
m 0 0 [naive T cell]
m 8 0 [naive T cell]
y 1 [cytomegalovirus infection; infected cell]
m 6 0 [naive T cell]
L 0 [cytomegalovirus infection; infected cell]
v 0 [virion; cytomegalovirus infection]
m 1 0 [naive T cell]
x 0 [cell; Susceptibility; cell]
m 5 0 [naive T cell]

Observables: none

BIOMD0000000663 @ v0.0.1

Wodarz2007 - HIV/CD4 T-cell interactionA deterministic model illustrating how CD4 T-cells can influence HIV infection.…

Recent experimental data have shown that HIV-specific CD4 T cells provide a very important target for HIV replication. We use mathematical models to explore the effect of specific CD4 T cell infection on the dynamics of virus spread and immune responses. Infected CD4 T cells can provide antigen for their own stimulation. We show that such autocatalytic cell division can significantly enhance virus spread, and can also provide an additional reservoir for virus persistence during anti-viral drug therapy. In addition, the initial number of HIV-specific CD4 T cells is an important determinant of acute infection dynamics. A high initial number of HIV-specific CD4 T cells can lead to a sudden and fast drop of the population of HIV-specific CD4 T cells which results quickly in their extinction. On the other hand, a low initial number of HIV-specific CD4 T cells can lead to a prolonged persistence of HIV-specific CD4 T cell help at higher levels. The model suggests that boosting the population of HIV-specific CD4 T cells can increase the amount of virus-induced immune impairment, lead to less efficient anti-viral effector responses, and thus speed up disease progression, especially if effector responses such as CTL have not been sufficiently boosted at the same time. link: http://identifiers.org/pubmed/17379260

Parameters:

Name Description
r = 1.0 Reaction: => x; v, Rate Law: compartment*r*v*x
d = 0.1 Reaction: x =>, Rate Law: compartment*d*x
a = 0.2 Reaction: y =>, Rate Law: compartment*a*y
r = 1.0; k = 10.0 Reaction: y => ; v, x, Rate Law: compartment*r*y*v*(x+y)/k
u = 0.5 Reaction: v =>, Rate Law: compartment*u*v
eta = 1.0 Reaction: => v; y, Rate Law: compartment*eta*y
Beta = 0.2 Reaction: x => y; v, Rate Law: compartment*Beta*v*x

States:

Name Description
v [Human Immunodeficiency Virus]
x [Human Immunodeficiency Virus; infected cell; T-lymphocyte]
y [T-lymphocyte]

Observables: none

BIOMD0000000774 @ v0.0.1

The paper describes a basic model of effect of cellular de-differentiation on the dynamics and evolution of tissue and t…

Tissues are maintained by adult stem cells that self-renew and also differentiate into functioning tissue cells. Homeostasis is achieved by a set of complex mechanisms that involve regulatory feedback loops. Similarly, tumors are believed to be maintained by a minority population of cancer stem cells, while the bulk of the tumor is made up of more differentiated cells, and there is indication that some of the feedback loops that operate in tissues continue to be functional in tumors. Mathematical models of such tissue hierarchies, including feedback loops, have been analyzed in a variety of different contexts. Apart from stem cells giving rise to differentiated cells, it has also been observed that more differentiated cells can de-differentiate into stem cells, both in healthy tissue and tumors, aspects of which have also been investigated mathematically. This paper analyses the effect of de-differentiation on the basic and evolutionary dynamics of cells in the context of tissue hierarchy models that include negative feedback regulation of the cell populations. The models predict that in the presence of de-differentiation, the fixation probability of a neutral mutant is lower than in its absence. Therefore, if de-differentiation occurs, a mutant with identical parameters compared to the wild-type cell population behaves like a disadvantageous mutant. Similarly, the process of de-differentiation is found to lower the fixation probability of an advantageous mutant. These results indicate that the presence of de-differentiation can lower the rates of tumor initiation and progression in the context of the models considered here. link: http://identifiers.org/pubmed/29605227

Parameters:

Name Description
a = 0.0025 1 Reaction: D =>, Rate Law: tme*a*D
p = 0.7 1; r = 0.01 1 Reaction: => S, Rate Law: tme*r*S*(2*p-1)
g = 0.00346534653465347 1 Reaction: D => S, Rate Law: tme*g*D

States:

Name Description
S [stem cell]
D [cell]

Observables: none

The paper describes a model of effect of cellular de-differentiation on the dynamics and evolution of tissue and tumor c…

Tissues are maintained by adult stem cells that self-renew and also differentiate into functioning tissue cells. Homeostasis is achieved by a set of complex mechanisms that involve regulatory feedback loops. Similarly, tumors are believed to be maintained by a minority population of cancer stem cells, while the bulk of the tumor is made up of more differentiated cells, and there is indication that some of the feedback loops that operate in tissues continue to be functional in tumors. Mathematical models of such tissue hierarchies, including feedback loops, have been analyzed in a variety of different contexts. Apart from stem cells giving rise to differentiated cells, it has also been observed that more differentiated cells can de-differentiate into stem cells, both in healthy tissue and tumors, aspects of which have also been investigated mathematically. This paper analyses the effect of de-differentiation on the basic and evolutionary dynamics of cells in the context of tissue hierarchy models that include negative feedback regulation of the cell populations. The models predict that in the presence of de-differentiation, the fixation probability of a neutral mutant is lower than in its absence. Therefore, if de-differentiation occurs, a mutant with identical parameters compared to the wild-type cell population behaves like a disadvantageous mutant. Similarly, the process of de-differentiation is found to lower the fixation probability of an advantageous mutant. These results indicate that the presence of de-differentiation can lower the rates of tumor initiation and progression in the context of the models considered here. link: http://identifiers.org/pubmed/29605227

Parameters:

Name Description
a = 0.0025 1 Reaction: D =>, Rate Law: tme*a*D
r2_0 = 0.02 1; q_0 = 0.396039603960396 1; p2_0 = 0.4 1 Reaction: => S; T, Rate Law: tme*2*r2_0*T*q_0*(1-p2_0)
p1_0 = 0.7 1; r1_0 = 0.01 1 Reaction: => S, Rate Law: tme*(2*p1_0-1)*r1_0*S
r1_0 = 0.01 1; p1_0 = 0.7 1 Reaction: => T; S, Rate Law: tme*2*r1_0*S*(1-p1_0)
r2_0 = 0.02 1; p2_0 = 0.4 1 Reaction: => T, Rate Law: tme*(2*p2_0-1)*r2_0*T

States:

Name Description
S [stem cell]
T [cell]
D [cell]

Observables: none

Wodke2013 - Genome-scale constraint-based model of M.pneumoniae energy metabolism (iJW145)A new genome-scale metabolic r…

Mycoplasma pneumoniae, a threatening pathogen with a minimal genome, is a model organism for bacterial systems biology for which substantial experimental information is available. With the goal of understanding the complex interactions underlying its metabolism, we analyzed and characterized the metabolic network of M. pneumoniae in great detail, integrating data from different omics analyses under a range of conditions into a constraint-based model backbone. Iterating model predictions, hypothesis generation, experimental testing, and model refinement, we accurately curated the network and quantitatively explored the energy metabolism. In contrast to other bacteria, M. pneumoniae uses most of its energy for maintenance tasks instead of growth. We show that in highly linear networks the prediction of flux distributions for different growth times allows analysis of time-dependent changes, albeit using a static model. By performing an in silico knock-out study as well as analyzing flux distributions in single and double mutant phenotypes, we demonstrated that the model accurately represents the metabolism of M. pneumoniae. The experimentally validated model provides a solid basis for understanding its metabolic regulatory mechanisms. link: http://identifiers.org/pubmed/23549481

Parameters: none

States: none

Observables: none

Wolf2000 - Cellular interaction on glycolytic oscillations in yeastA two-cell model of glycolysis.This model is describe…

On the basis of a detailed model of yeast glycolysis, the effect of intercellular dynamics is analysed theoretically. The model includes the main steps of anaerobic glycolysis, and the production of ethanol and glycerol. Transmembrane diffusion of acetaldehyde is included, since it has been hypothesized that this substance mediates the interaction. Depending on the kinetic parameter, the single-cell model shows both stationary and oscillatory behaviour. This agrees with experimental data with respect to metabolite concentrations and phase shifts. The inclusion of intercellular coupling leads to a variety of dynamical modes, such as synchronous oscillations, and different kinds of asynchronous behavior. These oscillations can co-exist, leading to bi- and tri-rhythmicity. The corresponding parameter regions have been identified by a bifurcation analysis. The oscillatory dynamics of synchronized cell populations are investigated by calculating the phase responses to acetaldehyde pulses. Simulations are performed with respect to the synchronization of two subpopulations that are oscillating out of phase before mixing. The effect of the various process on synchronization is characterized quantitatively. While continuous exchange of acetaldehyde might synchronize the oscillations for appropriate sets of parameter values, the calculated synchronization time is longer than that observed experimentally. It is concluded either that addition to the transmembrane exchange of acetaldehyde, other processes may contribute to intercellular coupling, or that intracellular regulator feedback plays a role in the acceleration of the synchronization. for appropriate sets of parameter values, the calculated synchronization time is longer than that observed experimentally. It is concluded either that addition to the transmembrane exchange of acetaldehyde, other processes may contribute to intercellular coupling, or that intracellular regulator feedback plays a role in the acceleration of the synchronization. link: http://identifiers.org/pubmed/10702114

Parameters:

Name Description
q = 4.0; k1 = 100.0; K_I = 0.52 Reaction: S1__Cell_1_ + A3__Cell_1_ => S2__Cell_1_, Rate Law: Cell_1*k1*S1__Cell_1_*A3__Cell_1_*(1+(A3__Cell_1_/K_I)^q)^(-1)
k5 = 1.28 Reaction: A3__Cell_1_ =>, Rate Law: Cell_1*k5*A3__Cell_1_
j_cell_2 = 0.0; J_cell_1 = 1.3; phi = 0.1 Reaction: => S4_ex, Rate Law: Compartment*phi/2*(J_cell_1+j_cell_2)
J0 = 3.0 Reaction: => S1__Cell_1_, Rate Law: Cell_1*J0
k2 = 6.0 Reaction: S2__Cell_2_ + N1__Cell_2_ => S3__Cell_2_ + N2__Cell_2_, Rate Law: Cell_2*k2*S2__Cell_2_*N1__Cell_2_
J_cell_1 = 1.3 Reaction: S4__Cell_1_ =>, Rate Law: Cell_1*J_cell_1
j_cell_2 = 0.0 Reaction: S4__Cell_2_ =>, Rate Law: Cell_2*j_cell_2
k = 1.5 Reaction: S4_ex =>, Rate Law: Compartment*k*S4_ex
k3 = 16.0 Reaction: S3__Cell_2_ + A2__Cell_2_ => S4__Cell_2_ + A3__Cell_2_, Rate Law: Cell_2*k3*S3__Cell_2_*A2__Cell_2_
k6 = 12.0 Reaction: S2__Cell_1_ + N2__Cell_1_ =>, Rate Law: Cell_1*k6*S2__Cell_1_*N2__Cell_1_
k4 = 100.0 Reaction: S4__Cell_2_ + N2__Cell_2_ =>, Rate Law: Cell_2*k4*S4__Cell_2_*N2__Cell_2_

States:

Name Description
S2 Cell 1 [Glyceraldehyde 3-phosphate; Glycerone phosphate]
S1 Cell 1 [glucose; D-Glucose]
S3 Cell 1 [Glyceric acid 1,3-biphosphate; 3-Phospho-D-glyceroyl phosphate]
S4 Cell 1 [Pyruvate; Acetaldehyde]
N1 Cell 1 [NAD(+); NAD+]
S4 Cell 2 [Acetaldehyde; Pyruvate]
S2 Cell 2 [Glyceraldehyde 3-phosphate; Glycerone phosphate]
N1 Cell 2 [NAD+; NAD(+)]
N2 Cell 1 [NADH; NADH]
A3 Cell 2 [ATP; ATP]
A2 Cell 1 [ADP; ADP]
A2 Cell 2 [ADP; ADP]
N2 Cell 2 [NADH; NADH]
S3 Cell 2 [Glyceric acid 1,3-biphosphate; 3-Phospho-D-glyceroyl phosphate]
A3 Cell 1 [ATP; ATP]
S4 ex S4_ex
S1 Cell 2 [glucose; D-Glucose]

Observables: none

BIOMD0000000206 @ v0.0.1

Model reproduces the dynamics of ATP and NADH as depicted in Fig 4 of the paper. Model successfully tested on Jarnac and…

Under certain well-defined conditions, a population of yeast cells exhibits glycolytic oscillations that synchronize through intercellular acetaldehyde. This implies that the dynamic phenomenon of the oscillation propagates within and between cells. We here develop a method to establish by which route dynamics propagate through a biological reaction network. Application of the method to yeast demonstrates how the oscillations and the synchronization signal can be transduced. That transduction is not so much through the backbone of glycolysis, as via the Gibbs energy and redox coenzyme couples (ATP/ADP, and NADH/NAD), and via both intra- and intercellular acetaldehyde. link: http://identifiers.org/pubmed/10692304

Parameters:

Name Description
ntot = 1.0 mM; k31 = 323.8 mM_1_min_1; k33 = 57823.1 mM_1_min_1; k32 = 76411.1 mM_1_min_1; atot = 4.0 mM; k34 = 23.7 mM_1_min_1 Reaction: s3 + na => s4 + at, Rate Law: compartment*(k31*k32*s3*na*(atot-at)-k33*k34*s4*at*(ntot-na))/(k33*(ntot-na)+k32*(atot-at))
k9 = 80.0 min_1 Reaction: s6o =>, Rate Law: compartment*k9*s6o
k8 = 85.7 mM_1_min_1; ntot = 1.0 mM Reaction: s3 => na, Rate Law: compartment*k8*s3*(ntot-na)
k1 = 550.0 mM_1_min_1; n = 4.0 dimensionless; ki = 1.0 mM Reaction: s1 + at => s2, Rate Law: compartment*k1*s1*at/(1+(at/ki)^n)
ntot = 1.0 mM; k6 = 2000.0 mM_1_min_1 Reaction: s6 => na, Rate Law: compartment*k6*s6*(ntot-na)
k4 = 80.0 mM_1_min_1; atot = 4.0 mM Reaction: s4 => s5 + at, Rate Law: compartment*k4*s4*(atot-at)
k2 = 9.8 min_1 Reaction: s2 => s3, Rate Law: compartment*k2*s2
k0 = 50.0 mM_min_1 Reaction: => s1, Rate Law: compartment*k0
k10 = 375.0 min_1 Reaction: s6 => s6o, Rate Law: compartment*k10*(s6-s6o)
k7 = 28.0 min_1 Reaction: at =>, Rate Law: compartment*k7*at
k5 = 9.7 min_1 Reaction: s5 => s6, Rate Law: compartment*k5*s5

States:

Name Description
s1 [glucose; C00293]
na [NAD(+); NAD+]
s5 [Pyruvate; pyruvic acid; pyruvate]
s6 [acetaldehyde; Acetaldehyde]
s6o [acetaldehyde; Acetaldehyde]
at [ATP; ATP]
s2 [keto-D-fructose 1,6-bisphosphate; beta-D-Fructose 1,6-bisphosphate]
s4 [3-phospho-D-glyceric acid; 3-Phospho-D-glycerate]
s3 [dihydroxyacetone phosphate; D-glyceraldehyde 3-phosphate; Glycerone phosphate; D-Glyceraldehyde 3-phosphate]

Observables: none

BIOMD0000000090 @ v0.0.1

This model by Jana Wolf et al. 2001 is the first mechanistic model of respiratory oscillations in Saccharomyces cerevisa…

Autonomous metabolic oscillations were observed in aerobic continuous culture of Saccharomyces cerevisiae. Experimental investigation of the underlying mechanism revealed that several pathways and regulatory couplings are involved. Here a hypothetical mechanism including the sulfate assimilation pathway, ethanol degradation and respiration is transformed into a mathematical model. Simulations confirm the ability of the model to produce limit cycle oscillations which reproduce most of the characteristic features of the system. link: http://identifiers.org/pubmed/11423122

Parameters:

Name Description
k_v13 = 4.0 Reaction: eth_ex => eth, Rate Law: c0*k_v13
Ac = 2.0 Reaction: A2c = Ac-A3c, Rate Law: missing
k12 = 5.0 Reaction: A3c => A2c, Rate Law: c1*k12*A3c
k7 = 10.0 Reaction: eth + N1 => aco + N2, Rate Law: c1*k7*eth*N1
k3 = 0.2 Reaction: aps + A3c => pap + A2c, Rate Law: c1*k3*aps*A3c
k9 = 10.0 Reaction: S1 + N1 => S2 + N2, Rate Law: c2*k9*S1*N1
k15 = 5.0 Reaction: aco => oah, Rate Law: c1*k15*aco
k18 = 1.0 Reaction: oah =>, Rate Law: c1*k18*oah
n = 4.0; k_v0 = 1.6; Kc = 0.1 Reaction: sul_ex => sul; cys, Rate Law: c0*k_v0/(1+(cys/Kc)^n)
k4 = 0.2 Reaction: pap + N2 => hyd + N1, Rate Law: c1*k4*pap*N2
k17 = 0.02 Reaction: hyd =>, Rate Law: c1*k17*hyd
a = 0.1; k11 = 10.0; Kh = 0.5; Ka = 1.0; m = 4.0 Reaction: Ho + A2m => Hm + A3m; hyd, N2, oxy, Rate Law: c2*3*k11*N2*oxy/((a*N2+oxy)*(1+(hyd/Kh)^m))*A2m/(Ka+A2m)
k16 = 10.0 Reaction: A2c + A3m => A2m + A3c, Rate Law: c2*k16*A3m*A2c
k_v10 = 80.0 Reaction: oxy_ex => oxy, Rate Law: c0*k_v10
k14 = 10.0 Reaction: oxy => oxy_ex, Rate Law: c2*k14*oxy
k6 = 0.12 Reaction: cys =>, Rate Law: c1*k6*cys
S = 2.0 Reaction: S2 = S-S1, Rate Law: missing
k2 = 0.2 Reaction: sul + A3c => aps + PPi, Rate Law: c1*k2*sul*A3c
a = 0.1; k11 = 10.0; Kh = 0.5; m = 4.0 Reaction: C2 + oxy => C1 + H2O; hyd, N2, Rate Law: c2*k11*N2*oxy/((a*N2+oxy)*(1+(hyd/Kh)^m))
k8 = 10.0 Reaction: S2 + aco => S1, Rate Law: c2*k8*aco*S2
k5 = 0.1 Reaction: hyd + oah => cys, Rate Law: c1*k5*hyd*oah
Am = 2.0 Reaction: A2m = Am-A3m, Rate Law: missing
N = 2.0 Reaction: N1 = N-N2, Rate Law: missing

States:

Name Description
sul ex [sulfate]
N1 [NAD(+)]
A3c [ATP]
cys [L-cysteine]
pap [3'-phospho-5'-adenylyl sulfate]
N2 [NADH]
C1 [mitochondrial respiratory chain]
hyd [hydrogen sulfide]
oxy [dioxygen]
oxy ex [dioxygen]
S1 [mitochondrial tricarboxylic acid cycle enzyme complex]
C2 [mitochondrial respiratory chain]
A2m [ADP]
aps [5'-adenylyl sulfate]
eth [ethanol]
aco [acetyl-CoA]
A2c [ADP]
PPi [diphosphate(4-)]
A3m [ATP]
eth ex [ethanol]
S2 [mitochondrial tricarboxylic acid cycle enzyme complex]
sul [sulfate]
Ho [proton]
oah [O-acetyl-L-homoserine]
Hm [proton]
H2O [water]

Observables: none

Wollbold2014 - Effects of reactive oxygen speciesThis model is described in the article: [Anti-inflammatory effects of…

BACKGROUND: Recent findings suggest that in pancreatic acinar cells stimulated with bile acid, a pro-apoptotic effect of reactive oxygen species (ROS) dominates their effect on necrosis and spreading of inflammation. The first effect presumably occurs via cytochrome C release from the inner mitochondrial membrane. A pro-necrotic effect - similar to the one of Ca2+ - can be strong opening of mitochondrial pores leading to breakdown of the membrane potential, ATP depletion, sustained Ca2+ increase and premature activation of digestive enzymes. To explain published data and to understand ROS effects during the onset of acute pancreatitis, a model using multi-valued logic is constructed. Formal concept analysis (FCA) is used to validate the model against data as well as to analyze and visualize rules that capture the dynamics. RESULTS: Simulations for two different levels of bile stimulation and for inhibition or addition of antioxidants reproduce the qualitative behaviour shown in the experiments. Based on reported differences of ROS production and of ROS induced pore opening, the model predicts a more uniform apoptosis/necrosis ratio for higher and lower bile stimulation in liver cells than in pancreatic acinar cells. FCA confirms that essential dynamical features of the data are captured by the model. For instance, high necrosis always occurs together with at least a medium level of apoptosis. At the same time, FCA helps to reveal subtle differences between data and simulations. The FCA visualization underlines the protective role of ROS against necrosis. CONCLUSIONS: The analysis of the model demonstrates how ROS and decreased antioxidant levels contribute to apoptosis. Studying the induction of necrosis via a sustained Ca2+ increase, we implemented the commonly accepted hypothesis of ATP depletion after strong bile stimulation. Using an alternative model, we demonstrate that this process is not necessary to generate the dynamics of the measured variables. Opening of plasma membrane channels could also lead to a prolonged increase of Ca2+ and to necrosis. Finally, the analysis of the model suggests a direct experimental testing for the model-based hypothesis of a self-enhancing cycle of cytochrome C release and ROS production by interruption of the mitochondrial electron transport chain. link: http://identifiers.org/pubmed/25315877

Parameters: none

States: none

Observables: none

MODEL1807230002 @ v0.0.1

Whole-genome metabolic reconstructions for the model organism Caenorhabditis elegans.

Metabolism is one of the attributes of life and supplies energy and building blocks to organisms. Therefore, understanding metabolism is crucial for the understanding of complex biological phenomena. Despite having been in the focus of research for centuries, our picture of metabolism is still incomplete. Metabolomics, the systematic analysis of all small molecules in a biological system, aims to close this gap. In order to facilitate such investigations a blueprint of the metabolic network is required. Recently, several metabolic network reconstructions for the model organism Caenorhabditis elegans have been published, each having unique features. We have established the WormJam Community to merge and reconcile these (and other unpublished models) into a single consensus metabolic reconstruction. In a series of workshops and annotation seminars this model was refined with manual correction of incorrect assignments, metabolite structure and identifier curation as well as addition of new pathways. The WormJam consensus metabolic reconstruction represents a rich data source not only for in silico network-based approaches like flux balance analysis, but also for metabolomics, as it includes a database of metabolites present in C. elegans, which can be used for annotation. Here we present the process of model merging, correction and curation and give a detailed overview of the model. In the future it is intended to expand the model toward different tissues and put special emphasizes on lipid metabolism and secondary metabolism including ascaroside metabolism in accordance to their central role in C. elegans physiology. link: http://identifiers.org/pubmed/30488036

Parameters: none

States: none

Observables: none

MODEL1006230034 @ v0.0.1

This a model from the article: Oxidative ATP synthesis in skeletal muscle is controlled by substrate feedback. Wu F,…

Data from (31)P-nuclear magnetic resonance spectroscopy of human forearm flexor muscle were analyzed based on a previously developed model of mitochondrial oxidative phosphorylation (PLoS Comp Bio 1: e36, 2005) to test the hypothesis that substrate level (concentrations of ADP and inorganic phosphate) represents the primary signal governing the rate of mitochondrial ATP synthesis and maintaining the cellular ATP hydrolysis potential in skeletal muscle. Model-based predictions of cytoplasmic concentrations of phosphate metabolites (ATP, ADP, and P(i)) matched data obtained from 20 healthy volunteers and indicated that as work rate is varied from rest to submaximal exercise commensurate increases in the rate of mitochondrial ATP synthesis are effected by changes in concentrations of available ADP and P(i). Additional data from patients with a defect of complex I of the respiratory chain and a patient with a deficiency in the mitochondrial adenine nucleotide translocase were also predicted the by the model by making the appropriate adjustments to the activities of the affected proteins associates with the defects, providing both further validation of the biophysical model of the control of oxidative phosphorylation and insight into the impact of these diseases on the ability of the cell to maintain its energetic state. link: http://identifiers.org/pubmed/16837647

Parameters: none

States: none

Observables: none

BIOMD0000000124 @ v0.0.1

The model is described in the paper by Wu and Chang (2006). Diethyl pyrocarbonate, a histidine-modifying agent, directly…

The ATP-sensitive K(+) (K(ATP)) channels are composed of sulfonylurea receptor and inwardly rectifying K(+) channel (Kir6.2) subunit. These channels are regulated by intracellular ADP/ATP ratio and play a role in cellular metabolism. Diethyl pyrocarbonate (DEPC), a histidine-specific alkylating reagent, is known to modify the histidine residues of the structure of proteins. The objective of this study was to determine whether DEPC modifies K(ATP)-channel activity in pituitary GH(3) cells. Steady-state fluctuation analyses of macroscopic K(+) current at -120 mV produced power spectra that could be fitted with a single Lorentzian curve in these cells. The time constants in the presence of DEPC were increased. Consistent with fluctuation analyses, the mean open time of K(ATP)-channels was significantly increased during exposure to DEPC. However, DEPC produced no change in single-channel conductance, despite the ability of this compound to enhance K(ATP)-channel activity in a concentration-dependent manner with an EC(50) value of 16 microM. DEPC-stimulated K(ATP)-channel activity was attenuated by pretreatment with glibenclamide. In current-clamp configuration, DEPC decreased the firing of action potentials in GH(3) cells. A further application of glibenclamide reversed DEPC-induced inhibition of spontaneous action potentials. Intracellullar Ca(2+) measurements revealed the ability of DEPC to decrease Ca(2+) oscillations in GH(3) cells. Simulation studies also demonstrated that the increased conductance of K(ATP)-channels used to mimic DEPC actions reduced the frequency of spontaneous action potentials and fluctuation of intracellular Ca(2+). The results indicate that chemical modification with DEPC enhances K(ATP)-channel activity and influences functional activities of pituitary GH(3) cells. link: http://identifiers.org/pubmed/16375866

Parameters:

Name Description
jer = NaN; vcytver = 5.0; fer = 0.01 Reaction: => cer, Rate Law: (-fer)*vcytver*jer*cell
jmem = NaN; fcyt = 0.01; jer = NaN Reaction: => c, Rate Law: cell*fcyt*(jmem+jer)

States:

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

Observables: none

MODEL1006230090 @ v0.0.1

This a model from the article: Computer modeling of mitochondrial tricarboxylic acid cycle, oxidative phosphorylation,…

A computational model of mitochondrial metabolism and electrophysiology is introduced and applied to analysis of data from isolated cardiac mitochondria and data on phosphate metabolites in striated muscle in vivo. This model is constructed based on detailed kinetics and thermodynamically balanced reaction mechanisms and a strict accounting of rapidly equilibrating biochemical species. Since building such a model requires introducing a large number of adjustable kinetic parameters, a correspondingly large amount of independent data from isolated mitochondria respiring on different substrates and subject to a variety of protocols is used to parameterize the model and ensure that it is challenged by a wide range of data corresponding to diverse conditions. The developed model is further validated by both in vitro data on isolated cardiac mitochondria and in vivo experimental measurements on human skeletal muscle. The validated model is used to predict the roles of NAD and ADP in regulating the tricarboxylic acid cycle dehydrogenase fluxes, demonstrating that NAD is the more important regulator. Further model predictions reveal that a decrease of cytosolic pH value results in decreases in mitochondrial membrane potential and a corresponding drop in the ability of the mitochondria to synthesize ATP at the hydrolysis potential required for cellular function. link: http://identifiers.org/pubmed/17591785

Parameters: none

States: none

Observables: none

MODEL2003030003 @ v0.0.1

<notes xmlns="http://www.sbml.org/sbml/level2/version4"> <body xmlns="http://www.w3.org/1…

Our objective was to determine the pharmacokinetics, bioavailability and lymph node uptake of the monoclonal antibody bevacizumab, labeled with the near-infrared (IR) dye 800CW, after intravenous (IV) and subcutaneous (SC) administration in mice. Fluorescence imaging and enzyme-linked immunosorbent assay (ELISA) assays were developed and validated to measure the concentration of bevacizumab in plasma. The bevacizumab-IRDye conjugate remained predominantly intact in plasma and in lymph node homogenate samples over a 24-h period, as determined by sodium dodecyl sulfate polyacrylamide gel electrophoresis and size exclusion chromatography. The plasma concentration vs. time plots obtained by fluorescence and ELISA measurements were similar; however, unlike ELISA, fluorescent imaging was only able to quantitate concentrations for 24 h after administration. At a low dose of 0.45 mg/kg, the plasma clearance of bevacizumab was 6.96 mL/h/kg after IV administration; this clearance is higher than that reported after higher doses. Half-lives of bevacizumab after SC and IV administration were 4.6 and 3.9 days, respectively. After SC administration, bevacizumab-IRDye800CW was present in the axillary lymph nodes that drain the SC site; lymph node uptake of bevacizumab-IRDye 800CW was negligible after IV administration. Bevacizumab exhibited complete bioavailability after SC administration. Using a compartmental pharmacokinetic model, the fraction absorbed through the lymphatics after SC administration was estimated to be about 1%. This is the first report evaluating the use of fluorescent imaging to determine the pharmacokinetics, lymphatic uptake, and bioavailability of a near-infrared dye-labeled antibody conjugate. link: http://identifiers.org/pubmed/22391791

Parameters: none

States: none

Observables: none

X


BIOMD0000000160 @ v0.0.1

The model reproduces the oscillations for mRNA and protein species as depicted in Fig 3 of the plot. The model differs s…

Circadian rhythms of gene activity, metabolism, physiology and behaviour are observed in all the eukaryotes and some prokaryotes. In this study, we present a model to represent the transcriptional regulatory network essential for the circadian rhythmicity in Drosophila. The model incorporates the transcriptional feedback loops revealed so far in the network of the circadian clock (PER/TIM and VRI/PDP1 loops). Conventional Hill functions are not assumed to describe the regulation of genes, instead of the explicit reactions of binding and unbinding processes of transcription factors to promoters are modelled. The model simulates sustained circadian oscillations in mRNA and protein concentrations in constant darkness in agreement with experimental observations. It also simulates entrainment by light-dark cycles, disappearance of the rhythmicity in constant light and the shape of phase response curves resembling that of the experimental results. The model is robust over a wide range of parameter variations. In addition, the simulated E-box mutation, per(S) and per(L) mutants are similar to that observed in the experiments. The deficiency between the simulated mRNA levels and experimental observations in per(01), tim(01) and clk(Jrk) mutants suggests some difference on the part of the model from reality. link: http://identifiers.org/pubmed/17157878

Parameters:

Name Description
tccctimp = 11.0; npt = 5.0; tcdvpmt = 0.028 Reaction: => timm; prct, timp, Rate Law: wholeCell*((1-(1-prct)^npt)*tccctimp+(1-prct)^npt*tcdvpmt)*timp
dtimm = 0.053 Reaction: timm =>, Rate Law: wholeCell*timm*dtimm
ubcctimp = 0.262 Reaction: prct =>, Rate Law: wholeCell*prct*ubcctimp
bccpt = 51.0 Reaction: CC + PT => CCPT, Rate Law: wholeCell*CC*PT*bccpt
dccpt = 15.06 Reaction: CCPT =>, Rate Law: wholeCell*CCPT*dccpt
ubpt = 2.93 Reaction: PT => PER + TIM, Rate Law: wholeCell*PT*ubpt
ubcc = 0.89 Reaction: CC => CLK + CYC, Rate Law: wholeCell*CC*ubcc
dper = 0.62 Reaction: PER =>, Rate Law: wholeCell*PER*dper
dvrim = 0.07 Reaction: vrim =>, Rate Law: wholeCell*vrim*dvrim
ubccpt = 7.89 Reaction: CCPT => CC + PT, Rate Law: wholeCell*CCPT*ubccpt
tcpdpclkp = 125.54; tcvriclkp = 0.053; tcclkp = 1.42 Reaction: => clkm; prvc, clkp, prpc, Rate Law: wholeCell*(prvc*tcvriclkp+prpc*tcpdpclkp+((1-prvc)-prpc)*tcclkp)*clkp
tcdvpmt = 0.028; npdp = 6.0; tcccpdpp = 9.831 Reaction: => pdpm; prcpdp, pdpp, Rate Law: wholeCell*((1-(1-prcpdp)^npdp)*tcccpdpp+(1-prcpdp)^npdp*tcdvpmt)*pdpp
dtim = 0.62 Reaction: TIM =>, Rate Law: wholeCell*TIM*dtim
dperm = 0.053 Reaction: perm =>, Rate Law: wholeCell*perm*dperm
ubccvrip = 0.276 Reaction: prcv =>, Rate Law: wholeCell*ubccvrip*prcv
dclkm = 0.643 Reaction: clkm =>, Rate Law: wholeCell*clkm*dclkm
dpt = 0.279 Reaction: PT =>, Rate Law: wholeCell*PT*dpt
dpdpm = 0.06 Reaction: pdpm =>, Rate Law: wholeCell*pdpm*dpdpm
bvriclkp = 1.858 Reaction: => prvc; prpc, VRI, Rate Law: wholeCell*((1-prvc)-prpc)*bvriclkp*VRI
bcctimp = 0.069 Reaction: => prct; CC, Rate Law: wholeCell*(1-prct)*bcctimp*CC
ubccperp = 0.262 Reaction: prcper =>, Rate Law: wholeCell*prcper*ubccperp
bccperp = 0.069 Reaction: => prcper; CC, Rate Law: wholeCell*(1-prcper)*bccperp*CC
bccvrip = 0.1 Reaction: => prcv; CC, Rate Law: wholeCell*(1-prcv)*bccvrip*CC
bpdpclkp = 1.155 Reaction: => prpc; prvc, PDP, Rate Law: wholeCell*((1-prvc)-prpc)*bpdpclkp*PDP
dclk = 0.2 Reaction: CLK =>, Rate Law: wholeCell*CLK*dclk
dpdp = 0.156 Reaction: PDP =>, Rate Law: wholeCell*PDP*dpdp
dvri = 1.226 Reaction: VRI =>, Rate Law: wholeCell*VRI*dvri
tlvri = 14.68 Reaction: => VRI; vrim, Rate Law: wholeCell*vrim*tlvri
tcccvrip = 16.86; tcdvpmt = 0.028; nvri = 4.0 Reaction: => vrim; prcv, vrip, Rate Law: wholeCell*((1-(1-prcv)^nvri)*tcccvrip+(1-prcv)^nvri*tcdvpmt)*vrip
tlpdp = 1.87 Reaction: => PDP; pdpm, Rate Law: wholeCell*pdpm*tlpdp
tltim = 36.0 Reaction: => TIM; timm, Rate Law: wholeCell*timm*tltim
dcc = 0.184 Reaction: CC =>, Rate Law: wholeCell*CC*dcc
tlper = 36.0 Reaction: => PER; perm, Rate Law: wholeCell*perm*tlper
ubvriclkp = 1.043 Reaction: prvc =>, Rate Law: wholeCell*prvc*ubvriclkp
ubccpdpp = 0.145 Reaction: prcpdp =>, Rate Law: wholeCell*ubccpdpp*prcpdp
npt = 5.0; tcdvpmt = 0.028; tcccperp = 11.0 Reaction: => perm; prcper, perp, Rate Law: wholeCell*((1-(1-prcper)^npt)*tcccperp+(1-prcper)^npt*tcdvpmt)*perp
ubpdpclkp = 0.952 Reaction: prpc =>, Rate Law: wholeCell*prpc*ubpdpclkp
bccpdpp = 0.062 Reaction: => prcpdp; CC, Rate Law: wholeCell*(1-prcpdp)*bccpdpp*CC
bcc = 2.349 Reaction: CLK + CYC => CC, Rate Law: wholeCell*CLK*bcc*CYC
tlclk = 35.0 Reaction: => CLK; clkm, Rate Law: wholeCell*clkm*tlclk
bpt = 1.1 Reaction: PER + TIM => PT, Rate Law: wholeCell*PER*TIM*bpt

States:

Name Description
prvc VRIbindingclkp
timm timm
PT [Protein timeless; Period circadian protein]
TIM [Protein timeless]
CC [Protein cycle; Circadian locomoter output cycles protein kaput]
CYC [Protein cycle]
PER [Period circadian protein]
prcv CCbindingvri
prpc PDPbindingclkp
prcper CCbindingPer
vrim vrim
prcpdp CCbindingpdp
PDP [PAR domain protein 1-betaPAR-domain protein 1, isoform G]
prct CCbindingtim
pdpm pdpm
VRI [GH23983pVrille, isoform AVrille, isoform DVrille, isoform F]
CLK [Circadian locomoter output cycles protein kaput]
perm perm
clkm clkm
CCPT [Protein timeless; Period circadian protein; Protein cycle; Circadian locomoter output cycles protein kaput]

Observables: none

System of ODEs to describe the dynamics of several activated factors of blood coagulation. Publication introduces a plat…

In order to confirm which process is the most important in the blood coagulation cascade, a dynamic model of the function of platelets in blood coagulation is provided based on biochemical experiments. A series of conclusions based on qualitative analysis and mathematical simulation are drawn about the influence of the activation rate of factor VIII and factor IX on the generation of thrombin (IIa). It is evident that the pro-coagulation stimulus must exceed a threshold value to initiate the coagulation cascade. The value is related to the rate of platelet activation, the binding constant d2. The stability of the fixed value is also related to the pro-coagulation stimulus. This article also evaluates the influence of the stimulus strength and the activated rate parameter of platelets on thrombin. The proportion of platelets activated at any given time is designated c. To each c, we obtain a maximum concentration of thrombin. It is evident that when the level of factor IX is below 1% of normal levels, the rate of thrombin generation reduces dramatically resulting in severe bleeding tendency. link: http://identifiers.org/pubmed/12376045

Parameters: none

States: none

Observables: none

BIOMD0000000075 @ v0.0.1

Xu2003 - Phosphoinositide turnoverThe model reproduces the percentage change of PIP_PM, PIP2_PM and IP3_Cyt as depicted…

We studied the bradykinin-induced changes in phosphoinositide composition of N1E-115 neuroblastoma cells using a combination of biochemistry, microscope imaging, and mathematical modeling. Phosphatidylinositol-4,5-bisphosphate (PIP2) decreased over the first 30 s, and then recovered over the following 2-3 min. However, the rate and amount of inositol-1,4,5-trisphosphate (InsP3) production were much greater than the rate or amount of PIP2 decline. A mathematical model of phosphoinositide turnover based on this data predicted that PIP2 synthesis is also stimulated by bradykinin, causing an early transient increase in its concentration. This was subsequently confirmed experimentally. Then, we used single-cell microscopy to further examine phosphoinositide turnover by following the translocation of the pleckstrin homology domain of PLCdelta1 fused to green fluorescent protein (PH-GFP). The observed time course could be simulated by incorporating binding of PIP2 and InsP3 to PH-GFP into the model that had been used to analyze the biochemistry. Furthermore, this analysis could help to resolve a controversy over whether the translocation of PH-GFP from membrane to cytosol is due to a decrease in PIP2 on the membrane or an increase in InsP3 in cytosol; by computationally clamping the concentrations of each of these compounds, the model shows how both contribute to the dynamics of probe translocation. link: http://identifiers.org/pubmed/12771127

Parameters:

Name Description
KMOLE = 0.00166112956810631 aAvogadro; kf_IP3PH_IP3_PHGFP = 10.0 µl/(mol*s); kr_IP3PH_IP3_PHGFP = 20.0 1/s Reaction: IP3_Cyt + PH_GFP_Cyt => IP3_PHGFP_Cyt, Rate Law: Cytosol*(kf_IP3PH_IP3_PHGFP*0.00166112956810631*IP3_Cyt*0.00166112956810631*PH_GFP_Cyt+(-kr_IP3PH_IP3_PHGFP*0.00166112956810631*IP3_PHGFP_Cyt))*1*1/KMOLE
kf_PIP2PH_PIP2_PH = 0.12 µl/(mol*s); kr_PIP2PH_PIP2_PH = 0.24 1/s Reaction: PH_GFP_Cyt + PIP2_PM => PIP2_PHGFP_PM, Rate Law: (kf_PIP2PH_PIP2_PH*0.00166112956810631*PH_GFP_Cyt*PIP2_PM+(-kr_PIP2PH_PIP2_PH*PIP2_PHGFP_PM))*PM
Ratestim_PIPsyn_PIPSyn = 0.0 1/s; Ratebasal_PIPsyn_PIPSyn = 0.0 1/s Reaction: PI_PM => PIP_PM, Rate Law: PM*(Ratebasal_PIPsyn_PIPSyn+Ratestim_PIPsyn_PIPSyn)*PI_PM
k_PIP2PHhyd=0.0 Reaction: PIP2_PHGFP_PM => PH_GFP_Cyt + IP3_Cyt + DAG_PM; PLC_act_PM, Rate Law: k_PIP2PHhyd*PLC_act_PM*PIP2_PHGFP_PM*PM
kIP3deg=0.08; KMOLE = 0.00166112956810631 aAvogadro; IP3_basal=0.16 Reaction: IP3_Cyt =>, Rate Law: Cytosol*kIP3deg*(0.00166112956810631*IP3_Cyt+(-IP3_basal))*1*1/KMOLE
KfPLCact=5.0E-4; signal_PLCact = 0.0 1; krPLCact=0.1 Reaction: PLC_PM => PLC_act_PM; stim_PM, Rate Law: PM*(KfPLCact*PLC_PM*stim_PM*signal_PLCact+(-krPLCact*PLC_act_PM))
k_PIP2hyd=2.4 Reaction: PIP2_PM => DAG_PM + IP3_Cyt; PLC_act_PM, Rate Law: k_PIP2hyd*PIP2_PM*PLC_act_PM*PM
Rate_PIP2SynStim_PIP2Syn = 0.0 1/s; Rate_PIP2Synbasal_PIP2Syn = 0.0 1/s Reaction: PIP_PM => PIP2_PM, Rate Law: PM*(Rate_PIP2Synbasal_PIP2Syn+Rate_PIP2SynStim_PIP2Syn)*PIP_PM

States:

Name Description
PH GFP Cyt [IPR001849; IPR011584]
IP3 Cyt [1D-myo-inositol 1,4,5-trisphosphate]
PI PM [phosphatidylinositol]
PLC act PM [1-phosphatidylinositol 4,5-bisphosphate phosphodiesterase epsilon-1; 1-phosphatidylinositol 4,5-bisphosphate phosphodiesterase]
PIP2 PM [1-phosphatidyl-1D-myo-inositol 4,5-bisphosphate]
IP3 PHGFP Cyt [IPR001849; 1D-myo-inositol 1,4,5-trisphosphate; IPR011584]
DAG PM [diglyceride]
PIP2 PHGFP PM [1-phosphatidyl-1D-myo-inositol 4,5-bisphosphate; IPR011584; IPR001849]
PLC PM [1-phosphatidylinositol 4,5-bisphosphate phosphodiesterase epsilon-1]
PIP PM [phosphatidylinositol 3-phosphate]

Observables: none

System of ODEs to describe the behaviour of the activated factors of the extrinsic pathway of blood coagulation with the…

Blood coagulation is a complex physiological process. With the development of biochemistry and molecular biology, especially the discovery of the tissue factor pathway inhibitor (TFPI) and further research, the researches of tissue factor (TF) and TFPI have been the hot topics now. Based on this result, we provide a new concept of blood coagulation system and provide a dynamic model to describe the role of TFPI of this pathway. Through stability analysis of the equilibrium point and numerical simulations, we obtain some important conclusions. All these results may have great significance for lesions of cardiac vessels and cerebral vessels, haemophilia, DIC, thrombosis formation and malignancy. link: http://identifiers.org/pubmed/15767116

Parameters: none

States: none

Observables: none

Y


Mathematical modeling of immune modulation by glucocorticoids Konstantin Yakimchuk https://doi.org/10.1016/j.biosystems.…

The cellular and molecular mechanisms of immunomodulatory actions of glucocorticoids (GC) remain to be identified. Using our experimental findings, a mathematical model based on a system of ordinary differential equations for characterization of the regulation of anti-tumor immune activity by the both direct and indirect GC effects was generated to study the effects of GC treatment on effector CD8+ T cells, GC-generated tolerogenic dendritic cells (DC), regulatory T cells and the growth of lymphoma cells. In addition, we compared the data from in vivo and in silico experiments. The mathematical simulations indicated that treatment with GCs may suppress anti-tumor immune response in a dose-dependent manner. Our in silico results were in line with our earlier experimental findings of inhibitory effects of GCs on T, NK and dendritic cells. The model simulations were in line with earlier experimental observations of inhibitory effects of GCs on T and NK cells and DCs. The results of this study might be useful for predicting clinical outcomes in patients receiving GC therapy. link: http://identifiers.org/pubmed/31734335

Parameters: none

States: none

Observables: none

BIOMD0000000093 @ v0.0.1

NCBS Curation Comments This model shows the control mechanism of Jak-Stat pathway, here SOCS1 (Suppressor of cytokine s…

Suppressor of cytokine signaling-1 (SOCS1) was identified as the negative regulator of Janus kinase (JAK) and signal transducer and activator of transcription (STAT) signal transduction pathway. However, the kinetics and control mechanism of the pathway have not yet been fully understood. We have developed the computer simulation of the JAK/STAT pathway. Without nuclear phosphatase, SOCS1's binding to JAK did not cause the decrease in nuclear phosphorylated STAT1. However, without SH2 domain-containing tyrosine phosphatase 2 (SHP-2) or cytoplasmic phosphatase, it did. So nuclear phosphatase is considered to be the most important in this system. By changing parameters of the model, dynamical characteristics and control mechanism were investigated. link: http://identifiers.org/pubmed/12527385

Parameters:

Name Description
kf=0.04 nM_inv_sec_inv; kb=0.2 sec_inv Reaction: IFNRJ => IFNRJ2, Rate Law: cytoplasm*(kf*IFNRJ*IFNRJ-kb*IFNRJ2)
ka=0.01 nmol*l^(-1)*s^(-1); kb=400.0 nM Reaction: => mRNAn; STAT1n_star_STAT1n_star, Rate Law: nucleus*ka*STAT1n_star_STAT1n_star/(kb+STAT1n_star_STAT1n_star)
kf=0.001 nM_inv_sec_inv; kb=0.2 sec_inv Reaction: SHP2 + IFNRJ2_star => IFNRJ2_star_SHP2, Rate Law: cytoplasm*(kf*IFNRJ2_star*SHP2-kb*IFNRJ2_star_SHP2)
kb=0.8 sec_inv; kf=0.008 nM_inv_sec_inv Reaction: IFNRJ2_star_SOCS1 + STAT1c => IFNRJ2_star_SOCS1_STAT1c, Rate Law: cytoplasm*(kf*STAT1c*IFNRJ2_star_SOCS1-kb*IFNRJ2_star_SOCS1_STAT1c)
kf=0.005 sec_inv Reaction: STAT1n_star_STAT1n_star_PPN => STAT1n_STAT1n_star + PPN, Rate Law: nucleus*kf*STAT1n_star_STAT1n_star_PPN
kf=0.005 nM_inv_sec_inv; kb=0.5 sec_inv Reaction: STAT1c_star + IFNRJ2_star => IFNRJ2_star_STAT1c_star, Rate Law: cytoplasm*(kf*IFNRJ2_star*STAT1c_star-kb*IFNRJ2_star_STAT1c_star)
kf=0.4 sec_inv Reaction: IFNRJ2_star_STAT1c => STAT1c_star + IFNRJ2_star, Rate Law: cytoplasm*kf*IFNRJ2_star_STAT1c
kf=2.0E-7 nM_inv_sec_inv; kb=0.2 sec_inv Reaction: STAT1n_star + STAT1n => STAT1n_STAT1n_star, Rate Law: nucleus*(kf*STAT1n*STAT1n_star-kb*STAT1n_STAT1n_star)
kf=0.05 sec_inv Reaction: STAT1n => STAT1c, Rate Law: nucleus*kf*STAT1n
kf=0.003 sec_inv Reaction: IFNRJ2_star_SHP2_SOCS1_STAT1c => IFNRJ2 + SOCS1 + STAT1c + SHP2, Rate Law: cytoplasm*kf*IFNRJ2_star_SHP2_SOCS1_STAT1c
kf=5.0E-4 sec_inv Reaction: IFNRJ2_star_SHP2_SOCS1 => IFNRJ2_star_SHP2, Rate Law: cytoplasm*kf*IFNRJ2_star_SHP2_SOCS1
kf=0.02 nM_inv_sec_inv; kb=0.02 sec_inv Reaction: R + IFN => IFNR, Rate Law: cytoplasm*(kf*IFN*R-kb*IFNR)
kf=0.001 sec_inv Reaction: mRNAn => mRNAc, Rate Law: nucleus*kf*mRNAn
kb=0.05 sec_inv; kf=0.1 nM_inv_sec_inv Reaction: JAK + IFNR => IFNRJ, Rate Law: cytoplasm*(kf*IFNR*JAK-kb*IFNRJ)
kf=0.02 nM_inv_sec_inv; kb=0.1 sec_inv Reaction: IFNRJ2_star_STAT1c + SOCS1 => IFNRJ2_star_SOCS1_STAT1c, Rate Law: cytoplasm*(kf*SOCS1*IFNRJ2_star_STAT1c-kb*IFNRJ2_star_SOCS1_STAT1c)
kf=0.01 sec_inv Reaction: => SOCS1; mRNAc, Rate Law: cytoplasm*kf*mRNAc

States:

Name Description
IFNRJ2 star SHP2 SOCS1 STAT1c [Signal transducer and activator of transcription 1; Suppressor of cytokine signaling 1; Tyrosine-protein phosphatase non-receptor type 11; Tyrosine-protein kinase JAK1; Ciliary neurotrophic factor receptor subunit alpha; Interferon alpha-1]
SHP2 [Tyrosine-protein phosphatase non-receptor type 11; IPR000980]
mRNAc [messenger RNA; RNA]
IFNRJ [Tyrosine-protein kinase JAK1; Ciliary neurotrophic factor receptor subunit alpha; Interferon alpha-1]
STAT1c star PPX [Signal transducer and activator of transcription 1]
IFNRJ2 star SHP2 [Tyrosine-protein phosphatase non-receptor type 11; Tyrosine-protein kinase JAK1; Ciliary neurotrophic factor receptor subunit alpha; Interferon alpha-1]
STAT1n STAT1n star [Signal transducer and activator of transcription 1]
IFNRJ2 star SOCS1 STAT1c [Signal transducer and activator of transcription 1; Suppressor of cytokine signaling 1; Tyrosine-protein kinase JAK1; Ciliary neurotrophic factor receptor subunit alpha; Interferon alpha-1]
IFNRJ2 star [Tyrosine-protein kinase JAK1; Ciliary neurotrophic factor receptor subunit alpha; Interferon alpha-1]
IFNR [Ciliary neurotrophic factor receptor subunit alpha; Interferon alpha-1]
IFNRJ2 star SHP2 SOCS1 [Suppressor of cytokine signaling 1; Tyrosine-protein phosphatase non-receptor type 11; Tyrosine-protein kinase JAK1; Ciliary neurotrophic factor receptor subunit alpha; Interferon alpha-1]
STAT1c [Signal transducer and activator of transcription 1; IPR001217]
STAT1c STAT1c star [Signal transducer and activator of transcription 1]
STAT1n [Signal transducer and activator of transcription 1]
mRNAn [messenger RNA; RNA]
JAK [Tyrosine-protein kinase JAK1; IPR009127]
IFNRJ2 star SOCS1 [Suppressor of cytokine signaling 1; Tyrosine-protein kinase JAK1; Ciliary neurotrophic factor receptor subunit alpha; Interferon alpha-1]
IFNRJ2 star STAT1c [Signal transducer and activator of transcription 1; Tyrosine-protein kinase JAK1; Ciliary neurotrophic factor receptor subunit alpha; Interferon alpha-1]
STAT1n star [Signal transducer and activator of transcription 1]
STAT1n star STAT1n star PPN [Signal transducer and activator of transcription 1]
STAT1c star [Signal transducer and activator of transcription 1]
PPN PPN
STAT1n star STAT1n star [Signal transducer and activator of transcription 1]
IFN [Interferon alpha-1]
STAT1c star STAT1c star [Signal transducer and activator of transcription 1]
IFNRJ2 [Tyrosine-protein kinase JAK1; Ciliary neurotrophic factor receptor subunit alpha; Interferon alpha-1]
PPX PPX
RJ [Tyrosine-protein kinase JAK1; Ciliary neurotrophic factor receptor subunit alpha]
IFNRJ2 star SHP2 STAT1c [Signal transducer and activator of transcription 1; Tyrosine-protein phosphatase non-receptor type 11; Tyrosine-protein kinase JAK1; Ciliary neurotrophic factor receptor subunit alpha; Interferon alpha-1]
SOCS1 [Suppressor of cytokine signaling 1; IPR001496]
IFNRJ2 star STAT1c star [Signal transducer and activator of transcription 1; Tyrosine-protein kinase JAK1; Ciliary neurotrophic factor receptor subunit alpha; Interferon alpha-1]
R [Ciliary neurotrophic factor receptor subunit alpha]
STAT1c star STAT1c star PPX [Signal transducer and activator of transcription 1]

Observables: none

BIOMD0000000094 @ v0.0.1

NCBS Curation Comments: This model shows the control mechanism of Jak-Stat pathway, here SOCS1 (Suppressor of cytokine…

Suppressor of cytokine signaling-1 (SOCS1) was identified as the negative regulator of Janus kinase (JAK) and signal transducer and activator of transcription (STAT) signal transduction pathway. However, the kinetics and control mechanism of the pathway have not yet been fully understood. We have developed the computer simulation of the JAK/STAT pathway. Without nuclear phosphatase, SOCS1's binding to JAK did not cause the decrease in nuclear phosphorylated STAT1. However, without SH2 domain-containing tyrosine phosphatase 2 (SHP-2) or cytoplasmic phosphatase, it did. So nuclear phosphatase is considered to be the most important in this system. By changing parameters of the model, dynamical characteristics and control mechanism were investigated. link: http://identifiers.org/pubmed/12527385

Parameters:

Name Description
kf=0.04 nM_inv_sec_inv; kb=0.2 sec_inv Reaction: IFNRJ => IFNRJ2, Rate Law: cytoplasm*(kf*IFNRJ*IFNRJ-kb*IFNRJ2)
kf=0.001 nM_inv_sec_inv; kb=0.2 sec_inv Reaction: IFNRJ2_star_SOCS1 + SHP2 => IFNRJ2_star_SHP2_SOCS1, Rate Law: cytoplasm*(kf*SHP2*IFNRJ2_star_SOCS1-kb*IFNRJ2_star_SHP2_SOCS1)
kb=0.8 sec_inv; kf=0.008 nM_inv_sec_inv Reaction: IFNRJ2_star_SHP2_SOCS1 + STAT1c => IFNRJ2_star_SHP2_SOCS1_STAT1c, Rate Law: cytoplasm*(kf*STAT1c*IFNRJ2_star_SHP2_SOCS1-kb*IFNRJ2_star_SHP2_SOCS1_STAT1c)
kf=0.005 sec_inv Reaction: STAT1n_star_STAT1n_star_PPN => STAT1n_STAT1n_star + PPN, Rate Law: nucleus*kf*STAT1n_star_STAT1n_star_PPN
kf=0.005 nM_inv_sec_inv; kb=0.5 sec_inv Reaction: STAT1c_star + IFNRJ2_star => IFNRJ2_star_STAT1c_star, Rate Law: cytoplasm*(kf*IFNRJ2_star*STAT1c_star-kb*IFNRJ2_star_STAT1c_star)
kf=0.4 sec_inv Reaction: IFNRJ2_star_STAT1c => STAT1c_star + IFNRJ2_star, Rate Law: cytoplasm*kf*IFNRJ2_star_STAT1c
kf=0.05 sec_inv Reaction: STAT1n => STAT1c, Rate Law: nucleus*kf*STAT1n
kf=2.0E-7 nM_inv_sec_inv; kb=0.2 sec_inv Reaction: STAT1c_star + STAT1c => STAT1c_STAT1c_star, Rate Law: cytoplasm*(kf*STAT1c*STAT1c_star-kb*STAT1c_STAT1c_star)
kf=0.003 sec_inv Reaction: IFNRJ2_star_SHP2_SOCS1_STAT1c => IFNRJ2 + SOCS1 + STAT1c + SHP2, Rate Law: nucleus*kf*IFNRJ2_star_SHP2_SOCS1_STAT1c
kf=5.0E-4 sec_inv Reaction: mRNAc =>, Rate Law: cytoplasm*kf*mRNAc
kf=0.02 nM_inv_sec_inv; kb=0.02 sec_inv Reaction: R + IFN => IFNR, Rate Law: cytoplasm*(kf*IFN*R-kb*IFNR)
kf=0.001 sec_inv Reaction: mRNAn => mRNAc, Rate Law: nucleus*kf*mRNAn
kb=0.05 sec_inv; kf=0.1 nM_inv_sec_inv Reaction: JAK + IFNR => IFNRJ, Rate Law: cytoplasm*(kf*IFNR*JAK-kb*IFNRJ)
kf=0.02 nM_inv_sec_inv; kb=0.1 sec_inv Reaction: IFNRJ2_star + SOCS1 => IFNRJ2_star_SOCS1, Rate Law: cytoplasm*(kf*SOCS1*IFNRJ2_star-kb*IFNRJ2_star_SOCS1)
kf=0.01 sec_inv Reaction: => SOCS1; mRNAc, Rate Law: cytoplasm*kf*mRNAc

States:

Name Description
IFNRJ2 star SHP2 SOCS1 STAT1c [Tyrosine-protein phosphatase non-receptor type 11; Signal transducer and activator of transcription 1; Suppressor of cytokine signaling 1; Tyrosine-protein kinase JAK1; Interferon gamma receptor 1; Interferon alpha-1]
mRNAc [messenger RNA; RNA]
SHP2 [Tyrosine-protein phosphatase non-receptor type 11]
IFNRJ2 star SOCS1 STAT1c [Signal transducer and activator of transcription 1; Suppressor of cytokine signaling 1; Tyrosine-protein kinase JAK1; Interferon gamma receptor 1; Interferon alpha-1]
STAT1n STAT1n star [Signal transducer and activator of transcription 1]
IFNRJ2 star SHP2 [Tyrosine-protein phosphatase non-receptor type 11; Tyrosine-protein kinase JAK1; Interferon gamma receptor 1; Interferon alpha-1]
STAT1c star PPX [Signal transducer and activator of transcription 1]
IFNRJ [Tyrosine-protein kinase JAK1; Interferon gamma receptor 1; Interferon alpha-1]
IFNRJ2 star [Tyrosine-protein kinase JAK1; Interferon gamma receptor 1; Interferon alpha-1]
IFNR [Interferon gamma receptor 1; Interferon alpha-1]
IFNRJ2 star SHP2 SOCS1 [Tyrosine-protein phosphatase non-receptor type 11; Suppressor of cytokine signaling 1; Tyrosine-protein kinase JAK1; Interferon gamma receptor 1; Interferon alpha-1]
STAT1c [Signal transducer and activator of transcription 1; IPR001217]
STAT1n star PPN [Signal transducer and activator of transcription 1]
STAT1n [Signal transducer and activator of transcription 1]
STAT1c STAT1c star [Signal transducer and activator of transcription 1]
mRNAn [messenger RNA; RNA]
JAK [Tyrosine-protein kinase JAK1; IPR009127]
IFNRJ2 star SOCS1 [Suppressor of cytokine signaling 1; Tyrosine-protein kinase JAK1; Interferon gamma receptor 1; Interferon alpha-1]
IFNRJ2 star STAT1c [Signal transducer and activator of transcription 1; Tyrosine-protein kinase JAK1; Interferon gamma receptor 1; Interferon alpha-1]
STAT1n star [Signal transducer and activator of transcription 1]
STAT1n star STAT1n star PPN [Signal transducer and activator of transcription 1]
PPN PPN
STAT1c star [Signal transducer and activator of transcription 1]
STAT1c star STAT1c star [Signal transducer and activator of transcription 1]
IFNRJ2 [Tyrosine-protein kinase JAK1; Interferon gamma receptor 1; Interferon alpha-1]
PPX PPX
RJ [Tyrosine-protein kinase JAK1; Interferon gamma receptor 1]
IFNRJ2 star SHP2 STAT1c [Tyrosine-protein phosphatase non-receptor type 11; Signal transducer and activator of transcription 1; Tyrosine-protein kinase JAK1; Interferon gamma receptor 1; Interferon alpha-1]
SOCS1 [Suppressor of cytokine signaling 1; IPR001496]
R [Interferon gamma receptor 1; IPR008355]
IFNRJ2 star STAT1c star [Tyrosine-protein kinase JAK1; Signal transducer and activator of transcription 1; Interferon alpha-1; Interferon gamma receptor 1]
STAT1c star STAT1c star PPX [Signal transducer and activator of transcription 1]

Observables: none

MODEL1006230032 @ v0.0.1

This a model from the article: Constancy and variability of contractile efficiency as a function of calcium and cross-…

We simulated myocardial Ca2+ (Ca) and cross-bridge (CB) kinetics to get insight into the experimentally observed constancy and variability of cardiac contractile efficiency in generating total mechanical energy under various inotropic and pathological conditions. The simulation consisted of a Ca transient, Ca association and dissociation rate constants of troponin C, and CB on and off rate constants. We evaluated sarcomere isometric twitch contractions at a constant muscle length. We assumed that each CB cycle hydrolyzes one ATP and that the force-length area (FLA) quantifies the total mechanical energy generated by CB cycles in a twitch contraction. FLA is a linear version of pressure-volume area, which quantifies the total mechanical energy of cardiac twitch contraction and correlates linearly with cardiac oxygen consumption (H. Suga, Physiol. Rev. 70: 247-277, 1990). The simulation shows that the contractile efficiency varies with changes in the Ca transient and Ca and CB kinetics except when they simultaneously speed up or slow down proportionally. These results point to possible mechanisms underlying the constancy and variability of cardiac contractile efficiency. link: http://identifiers.org/pubmed/8967394

Parameters: none

States: none

Observables: none

MiRNAs, which are a family of small non-coding RNAs, regulate a broad array of physiological and developmental processes…

MiRNAs, which are a family of small non-coding RNAs, regulate a broad array of physiological and developmental processes. However, their regulatory roles have remained largely mysterious. E2F is a positive regulator of cell cycle progression and also a potent inducer of apoptosis. Positive feedback loops in the regulation of Rb-E2F pathway are predicted and shown experimentally. Recently, it has been discovered that E2F induce a cluster of miRNAs called miR449. In turn, E2F is inhibited by miR449 through regulating different transcripts, thus forming negative feedback loops in the interaction network. Here, based on the integration of experimental evidence and quantitative data, we studied Rb-E2F pathway coupling the positive feedback loops and negative feedback loops mediated by miR449. Therefore, a mathematical model is constructed based in part on the model proposed in Yao-Lee et al. (2008) and nonlinear dynamical behaviors including the stability and bifurcations of the model are discussed. A comparison is given to reveal the implication of the fundamental differences of Rb-E2F pathway between regulation and deregulation of miR449. Coherent with the experiments it predicts that miR449 plays a critical role in regulating the cell cycle progression and provides a twofold safety mechanism to avoid excessive E2F-induced proliferation by cell cycle arrest and apoptosis. Moreover, numerical simulation and bifurcation analysis shows that the mechanisms of the negative regulation of miR449 to three different transcripts are quite distinctive which needs to be verified experimentally. This study may help us to analyze the whole cell cycle process mediated by other miRNAs more easily. A better knowledge of the dynamical behaviors of miRNAs mediated networks is also of interest for bio-engineering and artificial control. link: http://identifiers.org/pubmed/23028477

Parameters:

Name Description
kdRE = 0.03 Reaction: RE =>, Rate Law: compartment*kdRE*RE
JP = 0.01; kP = 3.6 Reaction: PRB => RB; PRB, Rate Law: compartment*kP*PRB/(JP+PRB)
kdP = 0.06 Reaction: PRB =>, Rate Law: compartment*kdP*PRB
ksM = 1.0; JS = 0.5 Reaction: => Myc; S, Rate Law: compartment*ksM*S/(JS+S)
JE = 0.15; ksCE = 0.35 Reaction: => CycE; E2F, Rate Law: compartment*ksCE*E2F/(JE+E2F)
kdR = 0.06 Reaction: RB =>, Rate Law: compartment*kdR*RB
JM = 0.15; ksCD2 = 0.03 Reaction: => CycD; Myc, Rate Law: compartment*ksCD2*Myc/(JM+Myc)
JCD = 0.92; kdCD2 = 1.0 Reaction: miR449 + CycD => ; miR449, Rate Law: compartment*kdCD2*miR449*CycD/(JCD+CycD)
kdM2 = 0.6; JM = 0.15 Reaction: miR449 + Myc => ; miR449, Rate Law: compartment*kdM2*miR449*Myc/(JM+Myc)
kdE = 0.25 Reaction: E2F =>, Rate Law: compartment*kdE*E2F
JM = 0.15; JE = 0.15; ksE1 = 0.4 Reaction: => E2F; Myc, Rate Law: compartment*ksE1*Myc/(JM+Myc)*E2F/(JE+E2F)
kdM1 = 0.7 Reaction: Myc =>, Rate Law: compartment*kdM1*Myc
kRE = 180.0 Reaction: E2F + RB => RE, Rate Law: compartment*kRE*E2F*RB
JCD = 0.92; kP1 = 18.0 Reaction: RE => E2F + PRB; CycD, Rate Law: compartment*kP1*CycD*RE/(JCD+RE)
ksR = 0.18 Reaction: => RB, Rate Law: compartment*ksR
kdCD1 = 1.5 Reaction: CycD => ; S, Rate Law: compartment*kdCD1*CycD
ksmiR = 1.4; JE = 0.15 Reaction: => miR449; E2F, Rate Law: compartment*ksmiR*E2F/(JE+E2F)
kdmiR = 0.02 Reaction: miR449 =>, Rate Law: compartment*kdmiR*miR449
ksCD1 = 0.45; JS = 0.5 Reaction: => CycD; S, Rate Law: compartment*ksCD1*S/(JS+S)
kdCE1 = 1.5 Reaction: CycE =>, Rate Law: compartment*kdCE1*CycE
JCE = 0.92; kP2 = 18.0 Reaction: RE => E2F + PRB; CycE, Rate Law: compartment*kP2*CycE*RE/(JCE+RE)
JM = 0.15; ksE2 = 0.003 Reaction: => E2F; Myc, Rate Law: compartment*ksE2*Myc/(JM+Myc)
kdCE2 = 0.7; JCE = 0.92 Reaction: miR449 + CycE => ; miR449, Rate Law: compartment*kdCE2*miR449*CycE/(JCE+CycE)

States:

Name Description
E2F [Transcription factor E2F1]
CycE [G1/S-specific cyclin-E1; Cyclin-dependent kinase 2]
CycD [Cyclin-dependent kinase 6; Cyclin-dependent kinase 4; G1/S-specific cyclin-D2; G1/S-specific cyclin-D3; G1/S-specific cyclin-D1]
Myc [Myc proto-oncogene protein]
RE [Transcription factor E2F1; Retinoblastoma-associated protein]
miR449 [MIMAT0001541]
RB [Retinoblastoma-associated protein]
PRB [Retinoblastoma-associated protein; Phosphorylated Peptide]

Observables: none

MODEL1006230072 @ v0.0.1

This a model from the article: Reconstruction of sino-atrial node pacemaker potential based on the voltage clamp exper…

The pacemaker activity of the S-A node cell was explained by reconstructing the pacemaker potential using a Hodgkin-Huxley type mathematical model which was based on the reported voltage clamp data. In this model four dynamic currents, the sodium current iNa, the slow inward current, is, the potassium current, iK, and the hyperpolarization-activated current, ih, in addition to a time-dependent leak current, i1 were included. The model simulated the spontaneous action potential the current voltage relationship, and the voltage clamp experiment in normal Tyrode solution of the rabbit S-A node. Furthermore, the changes of activity induced by the potassium current blocker Ba2+, by applying constant current, acetylcholine, and epinephrine were also reconstructed. It was strongly suggested that the pacemaker depolarization in the S-A node cell is mainly due to a gradual increase of iS during diastole, and that the contribution of iK is much less compared to the potassium current iK2 in the Purkinje fiber pacemaker depolarization. The rising phase of the action potential was due to iS and the plateau phase is determined by both the inactivation of iS and activation of iK. link: http://identifiers.org/pubmed/7265560

Parameters: none

States: none

Observables: none

MODEL1006230040 @ v0.0.1

This a model from the article: Population-based analysis of methadone distribution and metabolism using an age-depende…

Limited pharmacokinetic (PK) and pharmacodynamic (PD) data are available to use in methadone dosing recommendations in pediatric patients for either opioid abstinence or analgesia. Considering the extreme inter-individual variability of absorption and metabolism of methadone, population-based PK would be useful to provide insight into the relationship between dose, blood concentrations, and clinical effects of methadone. To address this need, an age-dependent physiologically based pharmacokinetic (PBPK) model has been constructed to systematically study methadone metabolism and PK. The model will facilitate the design of cost-effective studies that will evaluate methadone PK and PD relationships, and may be useful to guide methadone dosing in children. The PBPK model, which includes whole-body multi-organ distribution, plasma protein binding, metabolism, and clearance, is parameterized based on a database of pediatric PK parameters and data collected from clinical experiments. The model is further tailored and verified based on PK data from individual adults, then scaled appropriately to apply to children aged 0-24 months. Based on measured variability in CYP3A enzyme expression levels and plasma orosomucoid (ORM2) concentrations, a Monte-Carlo-based simulation of methadone kinetics in a pediatric population was performed. The simulation predicts extreme variability in plasma concentrations and clearance kinetics for methadone in the pediatric population, based on standard dosing protocols. In addition, it is shown that when doses are designed for individuals based on prior protein expression information, inter-individual variability in methadone kinetics may be greatly reduced. link: http://identifiers.org/pubmed/16758333

Parameters: none

States: none

Observables: none

BIOMD0000000106 @ v0.0.1

This model is according to the paper *Dynamic Simulation on the Arachidonic Acid Metabolic Network* . Figure 2A has bee…

Drug molecules not only interact with specific targets, but also alter the state and function of the associated biological network. How to design drugs and evaluate their functions at the systems level becomes a key issue in highly efficient and low-side-effect drug design. The arachidonic acid metabolic network is the network that produces inflammatory mediators, in which several enzymes, including cyclooxygenase-2 (COX-2), have been used as targets for anti-inflammatory drugs. However, neither the century-old nonsteriodal anti-inflammatory drugs nor the recently revocatory Vioxx have provided completely successful anti-inflammatory treatment. To gain more insights into the anti-inflammatory drug design, the authors have studied the dynamic properties of arachidonic acid (AA) metabolic network in human polymorphous leukocytes. Metabolic flux, exogenous AA effects, and drug efficacy have been analyzed using ordinary differential equations. The flux balance in the AA network was found to be important for efficient and safe drug design. When only the 5-lipoxygenase (5-LOX) inhibitor was used, the flux of the COX-2 pathway was increased significantly, showing that a single functional inhibitor cannot effectively control the production of inflammatory mediators. When both COX-2 and 5-LOX were blocked, the production of inflammatory mediators could be completely shut off. The authors have also investigated the differences between a dual-functional COX-2 and 5-LOX inhibitor and a mixture of these two types of inhibitors. Their work provides an example for the integration of systems biology and drug discovery. link: http://identifiers.org/pubmed/17381237

Parameters:

Name Description
ks = 500.0; k24 = 70.0; K24 = 500.0 Reaction: x2 => x3; x24, Rate Law: cell*K24*x24*x2/(x2+k24*(1+x3/ks))
ki10 = 0.01 Reaction: x21 => ; x10, Rate Law: cell*ki10*x10*x21
kd8 = 0.1 Reaction: x8 =>, Rate Law: cell*kd8*x8
ki5 = 0.1 Reaction: x20 => ; x6, Rate Law: cell*ki5*x6*x20
kd3 = 0.01 Reaction: x3 =>, Rate Law: kd3*x3*cell
kd12 = 0.07 Reaction: x12 =>, Rate Law: cell*x12*kd12
K16 = 1000.0; ks = 500.0; k16 = 70.0 Reaction: x1 => x2; x16, Rate Law: cell*K16*x16*x1/(x1+k16*(1+x2/ks))
kd11 = 0.001 Reaction: x11 =>, Rate Law: kd11*x11*cell
ki9 = 0.175 Reaction: x21 => ; x12, Rate Law: cell*ki9*x12*x21
kd9 = 0.001 Reaction: x9 =>, Rate Law: kd9*x9*cell
a24 = 0.15; KI24 = 2.3E-5 Reaction: => x16; x7, Rate Law: cell*a24*x7*x7/(x7*x7+KI24*KI24)
KI23 = 0.053 Reaction: => x21; x13, Rate Law: cell*KI23*x13*x21
kd2 = 0.05 Reaction: x2 =>, Rate Law: kd2*cell*x2
ki6 = 0.01 Reaction: x21 => ; x2, Rate Law: cell*ki6*x21*x2
K22 = 125.0; k22 = 20.0 Reaction: x22 => ; x12, Rate Law: cell*K22*x22*x12/((x12+k22)*129)
kd16 = 0.01 Reaction: x16 =>, Rate Law: cell*kd16*x16
ks = 500.0; ki3 = 30.0; K18 = 1000.0; k18 = 50.0 Reaction: x1 => x6; x18, x7, Rate Law: cell*K18*x18*x1/(x1+k18*(1+x7/ki3+x6/ks))
ks = 500.0; K19 = 3000.0; ki2 = 30.0; k19 = 160.0; ki1 = 0.3 Reaction: x6 => x7; x1, x19, x3, Rate Law: cell*K19*x19*x6/(x6+k19*(1+x1/ki1+x3/ki2+x7/ks))
K22 = 125.0; ks = 500.0; k22 = 20.0 Reaction: x12 => x13; x22, Rate Law: cell*K22*x22*x12/(x12+k22*(1+x13/ks))
ks = 500.0; K23 = 150.0; ki14 = 0.2; ki15 = 0.86; k23 = 3.9 Reaction: x13 => x14; x11, x23, x5, Rate Law: cell*K23*x23*x13/(x13+k23*(1+x5/ki14+x11/ki15+x14/ks))
ks = 500.0; k20 = 4.0; K20 = 1599.0 Reaction: x6 => x8; x20, Rate Law: cell*K20*x20*x6/(x6+k20*(1+x8/ks))
ki4 = 0.6 Reaction: x20 => ; x2, Rate Law: ki4*x2*x20*cell
K15 = 3600.0; KI21 = 500.0; lin = 12.0; ks = 500.0; k15 = 2600.0; KI22 = 500.0; KI19 = 500.0; KI20 = 200.0 Reaction: => x1; x11, x13, x15, x2, x4, Rate Law: cell*K15*x15*lin*(1+x4/KI19+x2/KI20+x13/KI21+x11/KI22)/(lin+k15*(1+x1/ks))
k21 = 5.0; ks = 500.0; ki8 = 4.0; ki7 = 30.0; ki11 = 15.0; K21 = 5000.0; ki12 = 6.3 Reaction: x1 => x10; x11, x3, x5, x7, x21, Rate Law: cell*K21*x21*x1/(x1+k21*(1+x5/ki7+x3/ki8+x7/ki11+x11/ki12+x10/ks))
kd13 = 0.01 Reaction: x13 =>, Rate Law: cell*kd13*x13
ki17 = 10.0 Reaction: x17 => ; x2, Rate Law: cell*ki17*x2*x17
ks = 500.0; ki18 = 10.0; ki16 = 10.0; k17 = 50.0; K17 = 1000.0 Reaction: x1 => x4; x17, x3, Rate Law: cell*K17*x17*x1/(x1+k17*(1+x4/ki18+x3/ki16+x4/ks))

States:

Name Description
x5 [12(S)-HETE; 12(S)-HETE]
x16 [Arachidonate 15-lipoxygenase]
x4 [12(S)-HPETE; 12(S)-HPETE]
x6 [prostaglandin H2; Prostaglandin H2]
x2 [15(S)-HPETE; 15(S)-HPETE]
x14 [20-hydroxy-leukotriene B4]
x20 [Thromboxane-A synthase]
x17 [Arachidonate 12-lipoxygenase, 12S-type]
x3 [15(S)-HETE; (15S)-15-Hydroxy-5,8,11-cis-13-trans-eicosatetraenoate]
x9 [thromboxane B2; Thromboxane B2]
x1 [arachidonic acid; Arachidonate]
x8 [thromboxane A2; Thromboxane A2]
x13 [leukotriene B4]
x7 [prostaglandin E2; Prostaglandin E2]
x11 [5(S)-HETE; 5(S)-HETE]
x21 [Arachidonate 5-lipoxygenase]
x22 [Leukotriene A-4 hydrolase]
x10 [5(S)-HPETE; 5(S)-HPETE]
x12 [leukotriene A4]

Observables: none

MODEL8236480549 @ v0.0.1

This is the arachidonic acid metabolic network model for human endothelial cells (EC) described in the article: **Find…

Drugs against multiple targets may overcome the many limitations of single targets and achieve a more effective and safer control of the disease. Numerous high-throughput experiments have been performed in this emerging field. However, systematic identification of multiple drug targets and their best intervention requires knowledge of the underlying disease network and calls for innovative computational methods that exploit the network structure and dynamics. Here, we develop a robust computational algorithm for finding multiple target optimal intervention (MTOI) solutions in a disease network. MTOI identifies potential drug targets and suggests optimal combinations of the target intervention that best restore the network to a normal state, which can be customer designed. We applied MTOI to an inflammation-related network. The well-known side effects of the traditional non-steriodal anti-inflammatory drugs and the recently recalled Vioxx were correctly accounted for in our network model. A number of promising MTOI solutions were found to be both effective and safer. link: http://identifiers.org/pubmed/18985027

Parameters: none

States: none

Observables: none

MODEL8236520494 @ v0.0.1

This is the arachidonic acid metabolic network model for human platelet cells (PLT) described in the article: **Findin…

Drugs against multiple targets may overcome the many limitations of single targets and achieve a more effective and safer control of the disease. Numerous high-throughput experiments have been performed in this emerging field. However, systematic identification of multiple drug targets and their best intervention requires knowledge of the underlying disease network and calls for innovative computational methods that exploit the network structure and dynamics. Here, we develop a robust computational algorithm for finding multiple target optimal intervention (MTOI) solutions in a disease network. MTOI identifies potential drug targets and suggests optimal combinations of the target intervention that best restore the network to a normal state, which can be customer designed. We applied MTOI to an inflammation-related network. The well-known side effects of the traditional non-steriodal anti-inflammatory drugs and the recently recalled Vioxx were correctly accounted for in our network model. A number of promising MTOI solutions were found to be both effective and safer. link: http://identifiers.org/pubmed/18985027

Parameters: none

States: none

Observables: none

MODEL8236441887 @ v0.0.1

This is the arachidonic acid metabolic network model for human polymorphonuclear leukocyte (PMN) described in the articl…

Drugs against multiple targets may overcome the many limitations of single targets and achieve a more effective and safer control of the disease. Numerous high-throughput experiments have been performed in this emerging field. However, systematic identification of multiple drug targets and their best intervention requires knowledge of the underlying disease network and calls for innovative computational methods that exploit the network structure and dynamics. Here, we develop a robust computational algorithm for finding multiple target optimal intervention (MTOI) solutions in a disease network. MTOI identifies potential drug targets and suggests optimal combinations of the target intervention that best restore the network to a normal state, which can be customer designed. We applied MTOI to an inflammation-related network. The well-known side effects of the traditional non-steriodal anti-inflammatory drugs and the recently recalled Vioxx were correctly accounted for in our network model. A number of promising MTOI solutions were found to be both effective and safer. link: http://identifiers.org/pubmed/18985027

Parameters: none

States: none

Observables: none

The paper describes a model of tumor growth with angiogenesis. Created by COPASI 4.26 (Build 213) This model is de…

BACKGROUND: Cancer arises when within a single cell multiple malfunctions of control systems occur, which are, broadly, the system that promote cell growth and the system that protect against erratic growth. Additional systems within the cell must be corrupted so that a cancer cell, to form a mass of any real size, produces substances that promote the growth of new blood vessels. Multiple mutations are required before a normal cell can become a cancer cell by corruption of multiple growth-promoting systems. METHODS: We develop a simple mathematical model to describe the solid cancer growth dynamics inducing angiogenesis in the absence of cancer controlling mechanisms. RESULTS: The initial conditions supplied to the dynamical system consist of a perturbation in form of pulse: The origin of cancer cells from normal cells of an organ of human body. Thresholds of interacting parameters were obtained from the steady states analysis. The existence of two equilibrium points determine the strong dependency of dynamical trajectories on the initial conditions. The thresholds can be used to control cancer. CONCLUSIONS: Cancer can be settled in an organ if the following combination matches: better fitness of cancer cells, decrease in the efficiency of the repairing systems, increase in the capacity of sprouting from existing vascularization, and higher capacity of mounting up new vascularization. However, we show that cancer is rarely induced in organs (or tissues) displaying an efficient (numerically and functionally) reparative or regenerative mechanism. link: http://identifiers.org/pubmed/22300422

Parameters:

Name Description
b1 = 0.01 1/d Reaction: C => ; T, Rate Law: tme*b1*T*C
u1 = 0.01 1/d Reaction: C =>, Rate Law: tme*u1*C
u3 = 0.05 1/d Reaction: T =>, Rate Law: tme*u3*T
a3 = 0.2 1/d; k3 = 5.0 1 Reaction: => T; A, Rate Law: tme*a3*T*T*(1-T/k3)
b2 = 0.01 1/d Reaction: T => ; C, Rate Law: tme*b2*C*T
a1 = 0.1 1/d; k1 = 10.0 1 Reaction: => C, Rate Law: tme*a1*C*(1-C/k1)
u5 = 0.01 1/d Reaction: A =>, Rate Law: tme*u5*A
k2 = 20.0 1; a2 = 0.1 1/d Reaction: => E, Rate Law: tme*a2*E*(1-E/k2)
k4 = 1.0 1; e = 0.01 1/d Reaction: => A; T, Rate Law: tme*e*T*A*(1-A/k4)
d = 0.1 1/d Reaction: P => A, Rate Law: tme*d*P
y = 0.01 1/d Reaction: E => P; T, Rate Law: tme*y*T*E
u4 = 0.01 1/d Reaction: P =>, Rate Law: tme*u4*P
u2 = 0.05 1/d Reaction: E =>, Rate Law: tme*u2*E

States:

Name Description
A [cell]
T [malignant cell]
C [cell]
P [cell]
E [endothelial cell]

Observables: none

BIOMD0000000318 @ v0.0.1

This is the model described in the article: **A bistable Rb-E2F switch underlies the restriction point** Guang Yao,…

The restriction point (R-point) marks the critical event when a mammalian cell commits to proliferation and becomes independent of growth stimulation. It is fundamental for normal differentiation and tissue homeostasis, and seems to be dysregulated in virtually all cancers. Although the R-point has been linked to various activities involved in the regulation of G1-S transition of the mammalian cell cycle, the underlying mechanism remains unclear. Using single-cell measurements, we show here that the Rb-E2F pathway functions as a bistable switch to convert graded serum inputs into all-or-none E2F responses. Once turned ON by sufficient serum stimulation, E2F can memorize and maintain this ON state independently of continuous serum stimulation. We further show that, at critical concentrations and duration of serum stimulation, bistable E2F activation correlates directly with the ability of a cell to traverse the R-point. link: http://identifiers.org/pubmed/18364697

Parameters:

Name Description
kM=1.0 uM per hr; S = 1.0 dimensionless; KS=0.5 dimensionless Reaction: => MC, Rate Law: cell*kM*S/(KS+S)
Kp=0.01 uM; kkRBUP=3.6 uM per hr Reaction: RP => RB, Rate Law: cell*kkRBUP*RP/(Kp+RP)
dCD=1.5 per hr Reaction: CD =>, Rate Law: cell*dCD*CD
KD=0.92 uM; kkRBPP=18.0 per hr; KE=0.92 uM Reaction: RE => EF + RP; CD, CE, Rate Law: cell*(kkRBPP*CD*RE/(KD+RE)+kkRBPP*CE*RE/(KE+RE))
dCE=1.5 per hr Reaction: CE =>, Rate Law: cell*dCE*CE
S = 1.0 dimensionless; kkCDS=0.45 uM per hr; KS=0.5 dimensionless Reaction: => CD, Rate Law: cell*kkCDS*S/(KS+S)
KMC=0.15 uM; kkCD=0.03 uM per hr Reaction: => CD; MC, Rate Law: cell*kkCD*MC/(KMC+MC)
dEF=0.25 per hr Reaction: EF =>, Rate Law: cell*dEF*EF
dRE=0.03 per hr Reaction: RE =>, Rate Law: cell*dRE*RE
dRP=0.06 per hr Reaction: RP =>, Rate Law: cell*dRP*RP
KD=0.92 uM; kkRBP2=18.0 per hr; KE=0.92 uM; kkRBP=18.0 per hr Reaction: RB => RP; CD, CE, Rate Law: cell*(kkRBP*CD*RB/(KD+RB)+kkRBP2*CE*RB/(KE+RB))
dRB=0.06 per hr Reaction: RB =>, Rate Law: cell*dRB*RB
kkEF=0.4 uM per hr; KMC=0.15 uM; KEF=0.15 uM; kkb=0.003 uM per hr Reaction: => EF; MC, Rate Law: cell*(kkEF*MC*EF/((KMC+MC)*(KEF+EF))+kkb*MC/(KMC+MC))
kkRE=180.0 per_uM per hr Reaction: EF + RB => RE, Rate Law: cell*kkRE*RB*EF
dMC=0.7 per hr Reaction: MC =>, Rate Law: cell*dMC*MC
kkCE=0.35 uM per hr; KEF=0.15 uM Reaction: => CE; EF, Rate Law: cell*kkCE*EF/(KEF+EF)
kkRB=0.18 uM per hr Reaction: => RB, Rate Law: cell*kkRB

States:

Name Description
RP [Phosphoprotein; Retinoblastoma-associated protein; MOD:00046]
CE [cyclin-dependent protein kinase holoenzyme complex; G1/S-specific cyclin-E1; G1/S-specific cyclin-E2; cyclin-dependent protein serine/threonine kinase activity]
RE [Retinoblastoma-associated protein; Transcription factor E2F1]
RB [Retinoblastoma-associated protein]
MC [Myc proto-oncogene protein]
EF [Transcription factor E2F1]
CD [cyclin-dependent protein kinase holoenzyme complex; IPR015451; cyclin-dependent protein serine/threonine kinase activity]

Observables: none

MODEL1611150001 @ v0.0.1

Yao2016_Calcium_SignalingThis model is described in the article: [Distinct cellular states determine calcium signaling…

The heterogeneity in mammalian cells signaling response is largely a result of preexisting cell to cell variability. It is unknown whether cell to cell variability rises from biochemical stochastic fluctuations or distinct cellular states. Here, we utilize calcium response to adenosine trisphosphate as a model for investigating the structure of heterogeneity within a population of cells and analyze whether distinct cellular response states coexist. We use a functional definition of cellular state that is based on a mechanistic dynamical systems model of calcium signaling. Using Bayesian parameter inference, we obtain high confidence parameter value distributions for several hundred cells, each fitted individually. Clustering the inferred parameter distributions revealed three major distinct cellular states within the population. The existence of distinct cellular states raises the possibility that the observed variability in response is a result of structured heterogeneity between cells. The inferred parameter distribution predicts, and experiments confirm that variability in IP3R response explains the majority of calcium heterogeneity. Our work shows how mechanistic models and single cell parameter fitting can uncover hidden population structure and demonstrate the need for parameter inference at the single cell level. link: http://identifiers.org/doi/10.15252/msb.20167137

Parameters: none

States: none

Observables: none

Yapo2017 - A2AR/cAMP/PKA signalling in D2 dopamine receptor expressing medium-spiny neuronsThis model is described in th…

Brief dopamine events are critical actors of reward-mediated learning in the striatum; the intracellular cAMP-protein kinase A (PKA) response of striatal medium spiny neurons to such events was studied dynamically using a combination of biosensor imaging in mouse brain slices and in silico simulations. Both D1 and D2 medium spiny neurons can sense brief dopamine transients in the sub-micromolar range. While dopamine transients profoundly change cAMP levels in both types of medium spiny neurons, the PKA-dependent phosphorylation level remains unaffected in D2 neurons. At the level of PKA-dependent phosphorylation, D2 unresponsiveness depends on protein phosphatase-1 (PP1) inhibition by DARPP-32. Simulations suggest that D2 medium spiny neurons could detect transient dips in dopamine level.The phasic release of dopamine in the striatum determines various aspects of reward and action selection, but the dynamics of the dopamine effect on intracellular signalling remains poorly understood. We used genetically encoded FRET biosensors in striatal brain slices to quantify the effect of transient dopamine on cAMP or PKA-dependent phosphorylation levels, and computational modelling to further explore the dynamics of this signalling pathway. Medium-sized spiny neurons (MSNs), which express either D1 or D2 dopamine receptors, responded to dopamine by an increase or a decrease in cAMP, respectively. Transient dopamine showed similar sub-micromolar efficacies on cAMP in both D1 and D2 MSNs, thus challenging the commonly accepted notion that dopamine efficacy is much higher on D2 than on D1 receptors. However, in D2 MSNs, the large decrease in cAMP level triggered by transient dopamine did not translate to a decrease in PKA-dependent phosphorylation level, owing to the efficient inhibition of protein phosphatase 1 by DARPP-32. Simulations further suggested that D2 MSNs can also operate in a 'tone-sensing' mode, allowing them to detect transient dips in basal dopamine. Overall, our results show that D2 MSNs may sense much more complex patterns of dopamine than previously thought. link: http://identifiers.org/pubmed/28782235

Parameters: none

States: none

Observables: none

Yapo2017- cAMP/PKA signalling in D1 dopamine receptor expressing medium-spiny neuronsThis model is described in the arti…

Brief dopamine events are critical actors of reward-mediated learning in the striatum; the intracellular cAMP-protein kinase A (PKA) response of striatal medium spiny neurons to such events was studied dynamically using a combination of biosensor imaging in mouse brain slices and in silico simulations. Both D1 and D2 medium spiny neurons can sense brief dopamine transients in the sub-micromolar range. While dopamine transients profoundly change cAMP levels in both types of medium spiny neurons, the PKA-dependent phosphorylation level remains unaffected in D2 neurons. At the level of PKA-dependent phosphorylation, D2 unresponsiveness depends on protein phosphatase-1 (PP1) inhibition by DARPP-32. Simulations suggest that D2 medium spiny neurons could detect transient dips in dopamine level.The phasic release of dopamine in the striatum determines various aspects of reward and action selection, but the dynamics of the dopamine effect on intracellular signalling remains poorly understood. We used genetically encoded FRET biosensors in striatal brain slices to quantify the effect of transient dopamine on cAMP or PKA-dependent phosphorylation levels, and computational modelling to further explore the dynamics of this signalling pathway. Medium-sized spiny neurons (MSNs), which express either D1 or D2 dopamine receptors, responded to dopamine by an increase or a decrease in cAMP, respectively. Transient dopamine showed similar sub-micromolar efficacies on cAMP in both D1 and D2 MSNs, thus challenging the commonly accepted notion that dopamine efficacy is much higher on D2 than on D1 receptors. However, in D2 MSNs, the large decrease in cAMP level triggered by transient dopamine did not translate to a decrease in PKA-dependent phosphorylation level, owing to the efficient inhibition of protein phosphatase 1 by DARPP-32. Simulations further suggested that D2 MSNs can also operate in a 'tone-sensing' mode, allowing them to detect transient dips in basal dopamine. Overall, our results show that D2 MSNs may sense much more complex patterns of dopamine than previously thought. link: http://identifiers.org/pubmed/28782235

Parameters: none

States: none

Observables: none

MODEL4028801312 @ v0.0.1

This a model from the article: Understanding the slow depletion of memory CD4+ T cells in HIV infection. Yates A, St…

The asymptomatic phase of HIV infection is characterised by a slow decline of peripheral blood CD4(+) T cells. Why this decline is slow is not understood. One potential explanation is that the low average rate of homeostatic proliferation or immune activation dictates the pace of a "runaway" decline of memory CD4(+) T cells, in which activation drives infection, higher viral loads, more recruitment of cells into an activated state, and further infection events. We explore this hypothesis using mathematical models.Using simple mathematical models of the dynamics of T cell homeostasis and proliferation, we find that this mechanism fails to explain the time scale of CD4(+) memory T cell loss. Instead it predicts the rapid attainment of a stable set point, so other mechanisms must be invoked to explain the slow decline in CD4(+) cells.A runaway cycle in which elevated CD4(+) T cell activation and proliferation drive HIV production and vice versa cannot explain the pace of depletion during chronic HIV infection. We summarize some alternative mechanisms by which the CD4(+) memory T cell homeostatic set point might slowly diminish. While none are mutually exclusive, the phenomenon of viral rebound, in which interruption of antiretroviral therapy causes a rapid return to pretreatment viral load and T cell counts, supports the model of virus adaptation as a major force driving depletion. link: http://identifiers.org/pubmed/17518516

Parameters: none

States: none

Observables: none

This model is based on: Reinforcement learning-based control of tumor growth under anti-angiogenic therapy Authors: Pa…

BACKGROUND AND OBJECTIVES:In recent decades, cancer has become one of the most fatal and destructive diseases which is threatening humans life. Accordingly, different types of cancer treatment are studied with the main aim to have the best treatment with minimum side effects. Anti-angiogenic is a molecular targeted therapy which can be coupled with chemotherapy and radiotherapy. Although this method does not eliminate the whole tumor, but it can keep the tumor size in a given state by preventing the formation of new blood vessels. In this paper, a novel model-free method based on reinforcement learning (RL) framework is used to design a closed-loop control of anti-angiogenic drug dosing administration. METHODS:A Q-learning algorithm is developed for the drug dosing closed-loop control. This controller is designed using two different values of the maximum drug dosage to reduce the tumor volume up to a desired value. The mathematical model of tumor growth under anti-angiogenic inhibitor is used to simulate a real patient. RESULTS:The effectiveness of the proposed method is shown through in silico simulation and its robustness to patient parameters variation is demonstrated. It is demonstrated that the tumor reaches its minimal volume in 84 days with maximum drug inlet of 30 mg/kg/day. Also, it is shown that the designed controller is robust with respect to  ± 20% of tumor growth parameters changes. CONCLUSION:The proposed closed-loop reinforcement learning-based controller for cancer treatment using anti-angiogenic inhibitor provides an effective and novel result such that with a clinically valid and safe dosage of drug, the volume reduces up to 1mm3 in a reasonable short period compared to the literature. link: http://identifiers.org/pubmed/31046990

Parameters:

Name Description
a = 1.0; lambda_2 = 0.0 1/d Reaction: endothelial_volume_x_2 =>, Rate Law: compartment*lambda_2*endothelial_volume_x_2*a
a = 1.0; e = 0.66 kg/mg*d Reaction: endothelial_volume_x_2 => ; concentration_of_administrated_inhibitor_x_3, Rate Law: compartment*e*endothelial_volume_x_2*concentration_of_administrated_inhibitor_x_3*a
lambda_1 = 0.192 1/d; a = 1.0 Reaction: tumor_volume_x_1 => ; endothelial_volume_x_2, Rate Law: compartment*lambda_1*tumor_volume_x_1*ln(tumor_volume_x_1/endothelial_volume_x_2)*a
lambda_3 = 1.3 1/d; a = 1.0 Reaction: concentration_of_administrated_inhibitor_x_3 =>, Rate Law: compartment*lambda_3*concentration_of_administrated_inhibitor_x_3*a
u = 0.0 mg/kg/d Reaction: => concentration_of_administrated_inhibitor_x_3, Rate Law: compartment*u
a = 1.0; b = 5.85 1/d Reaction: => endothelial_volume_x_2; tumor_volume_x_1, Rate Law: compartment*b*tumor_volume_x_1*a
a = 1.0; d = 0.00873 1/(mm^2*day) Reaction: endothelial_volume_x_2 => ; tumor_volume_x_1, Rate Law: compartment*d*endothelial_volume_x_2*tumor_volume_x_1^(2/3)*a

States:

Name Description
tumor volume x 1 [Tumor Volume]
endothelial volume x 2 [dTDP-5-dimethyl-L-lyxose]
concentration of administrated inhibitor x 3 [Concentration; Inhibitor]

Observables: none

The iCHO2291 model was reconstructed by updating the previously published iCHO1766 model in a 6-step procedure: 1) ident…

Chinese hamster ovary (CHO) cells are most prevalently used for producing recombinant therapeutics in biomanufacturing. Recently, more rational and systems approaches have been increasingly exploited to identify key metabolic bottlenecks and engineering targets for cell line engineering and process development based on the CHO genome-scale metabolic model which mechanistically characterizes cell culture behaviours. However, it is still challenging to quantify plausible intracellular fluxes and discern metabolic pathway usages considering various clonal traits and bioprocessing conditions. Thus, we newly incorporated enzyme kinetic information into the updated CHO genome-scale model (iCHO2291) and added enzyme capacity constraints within the flux balance analysis framework (ecFBA) to significantly reduce the flux variability in biologically meaningful manner, as such improving the accuracy of intracellular flux prediction. Interestingly, ecFBA could capture the overflow metabolism under the glucose excess condition where the usage of oxidative phosphorylation is limited by the enzyme capacity. In addition, its applicability was successfully demonstrated via a case study where the clone- and media-specific lactate metabolism was deciphered, suggesting that the lactate-pyruvate cycling could be beneficial for CHO cells to efficiently utilize the mitochondrial redox capacity. In summary, iCHO2296 with ecFBA can be used to confidently elucidate cell cultures and effectively identify key engineering targets, thus guiding bioprocess optimization and cell engineering efforts as a part of digital twin model for advanced biomanufacturing in future. link: http://identifiers.org/pubmed/32330653

Parameters: none

States: none

Observables: none

BIOMD0000000072 @ v0.0.1

The paper describes both wild-type and mutant cells of G protein cycle by using different values of G protein deactivati…

The yeast mating response is one of the best understood heterotrimeric G protein signaling pathways. Yet, most descriptions of this system have been qualitative. We have quantitatively characterized the heterotrimeric G protein cycle in yeast based on direct in vivo measurements. We used fluorescence resonance energy transfer to monitor the association state of cyan fluorescent protein (CFP)-Galpha and Gbetagamma-yellow fluorescent protein (YFP), and we found that receptor-mediated G protein activation produced a loss of fluorescence resonance energy transfer. Quantitative time course and dose-response data were obtained for both wild-type and mutant cells possessing an altered pheromone response. These results paint a quantitative portrait of how regulators such as Sst2p and the C-terminal tail of alpha-factor receptor modulate the kinetics and sensitivity of G protein signaling. We have explored critical features of the dynamics including the rapid rise and subsequent decline of active G proteins during the early response, and the relationship between the G protein activation dose-response curve and the downstream dose-response curves for cell-cycle arrest and transcriptional induction. Fitting the data to a mathematical model produced estimates of the in vivo rates of heterotrimeric G protein activation and deactivation in yeast. link: http://identifiers.org/pubmed/12960402

Parameters:

Name Description
k1=1.0 Reaction: Gd + Gbg => G, Rate Law: cell*k1*Gd*Gbg
k1=1.0E-5 Reaction: G => Ga + Gbg; RL, Rate Law: cell*k1*RL*G
k1=0.11 Reaction: Ga => Gd, Rate Law: cell*k1*Ga
k1=3.32E-18; k2=0.01 Reaction: L + R => RL, Rate Law: cell*(k1*L*R-k2*RL)
v=4.0 Reaction: => R, Rate Law: cell*v
k1=4.0E-4 Reaction: R =>, Rate Law: cell*k1*R
k1=0.004 Reaction: RL =>, Rate Law: cell*k1*RL

States:

Name Description
Ga [IPR001019; GTP; GTP; IPR001019]
Gbg [G-protein beta/gamma-subunit complex]
Gd [IPR001019; GDP; GDP; IPR001019]
RL [receptor complex; Mating hormone A-factor 1; Pheromone alpha factor receptorPheromone alpha factor receptor; Mating hormone A-factor 2; Pheromone alpha factor receptorPheromone alpha factor receptor]
L [Mating hormone A-factor 1; Mating hormone A-factor 2; IPR006742]
G [heterotrimeric G-protein complex]
R [Pheromone alpha factor receptorPheromone alpha factor receptor]

Observables: none

BIOMD0000000065 @ v0.0.1

This a model from the article: Feedback regulation in the lactose operon: a mathematical modeling study and comparison…

A mathematical model for the regulation of induction in the lac operon in Escherichia coli is presented. This model takes into account the dynamics of the permease facilitating the internalization of external lactose; internal lactose; beta-galactosidase, which is involved in the conversion of lactose to allolactose, glucose and galactose; the allolactose interactions with the lac repressor; and mRNA. The final model consists of five nonlinear differential delay equations with delays due to the transcription and translation process. We have paid particular attention to the estimation of the parameters in the model. We have tested our model against two sets of beta-galactosidase activity versus time data, as well as a set of data on beta-galactosidase activity during periodic phosphate feeding. In all three cases we find excellent agreement between the data and the model predictions. Analytical and numerical studies also indicate that for physiologically realistic values of the external lactose and the bacterial growth rate, a regime exists where there may be bistable steady-state behavior, and that this corresponds to a cusp bifurcation in the model dynamics. link: http://identifiers.org/pubmed/12719218

Parameters:

Name Description
gamma_L = 0.0; mu = 0.0226 Reaction: L =>, Rate Law: cell*L*(gamma_L+mu)
tau_B = 2.0; tau_P = 0.83; alpha_P = 10.0; mu = 0.0226 Reaction: => I3; M, Rate Law: cell*alpha_P*M*exp(-1*mu*(tau_B+tau_P))
tau_M = 0.1 Reaction: I1 => M, Rate Law: cell*I1/tau_M
mu = 0.0226; gamma_P = 0.65 Reaction: P =>, Rate Law: cell*P*(gamma_P+mu)
gamma_B = 8.33E-4; mu = 0.0226 Reaction: B =>, Rate Law: cell*B*(gamma_B+mu)
tau_M = 0.1; K = 7200.0; mu = 0.0226; K_1 = 25200.0; alpha_M = 9.97E-4 Reaction: => I1; A, Rate Law: cell*alpha_M*(K_1*exp(mu*tau_M*-2)*A^2+1)/(K+K_1*exp(-2*mu*tau_M)*A^2)
mu = 0.0226; gamma_M = 0.411 Reaction: M =>, Rate Law: cell*M*(gamma_M+mu)
gamma_A = 0.52; mu = 0.0226 Reaction: A =>, Rate Law: cell*A*(gamma_A+mu)
K_Le = 0.26; alpha_L = 2880.0 Reaction: => L; P, L_e, Rate Law: cell*alpha_L*P*L_e/(K_Le+L_e)
alpha_A = 17600.0; K_L = 0.97 Reaction: L => A; B, Rate Law: cell*alpha_A*B*L/(K_L+L)
K_A = 1.95; beta_A = 21500.0 Reaction: A => ; B, Rate Law: cell*beta_A*B*A/(K_A+A)
tau_B = 2.0; mu = 0.0226; alpha_B = 0.0166 Reaction: => I2; M, Rate Law: cell*alpha_B*M*exp(-mu*tau_B)
tau_B = 2.0 Reaction: I2 => B, Rate Law: cell*I2/tau_B
tau_B = 2.0; tau_P = 0.83 Reaction: I3 => P, Rate Law: cell*I3/(tau_B+tau_P)
K_L1 = 1.81; beta_L1 = 2650.0 Reaction: L => ; P, Rate Law: cell*beta_L1*P*L/(K_L1+L)
gamma_0 = 7.25E-7 Reaction: => M, Rate Law: cell*gamma_0

States:

Name Description
B [Beta-galactosidase]
A [allolactose]
I1 PartialmRNA
M [messenger RNA]
P [Lactose permease]
I2 PartialBetagalactosidase
I3 PartialPermease
L [lactose; Lactose]

Observables: none

Yilmaz2016 - Genome scale metabolic model - Caenorhabditis elegans (iCEL1273)This model is described in the article: [A…

Caenorhabditis elegans is a powerful model to study metabolism and how it relates to nutrition, gene expression, and life history traits. However, while numerous experimental techniques that enable perturbation of its diet and gene function are available, a high-quality metabolic network model has been lacking. Here, we reconstruct an initial version of the C. elegans metabolic network. This network model contains 1,273 genes, 623 enzymes, and 1,985 metabolic reactions and is referred to as iCEL1273. Using flux balance analysis, we show that iCEL1273 is capable of representing the conversion of bacterial biomass into C. elegans biomass during growth and enables the predictions of gene essentiality and other phenotypes. In addition, we demonstrate that gene expression data can be integrated with the model by comparing metabolic rewiring in dauer animals versus growing larvae. iCEL1273 is available at a dedicated website (wormflux.umassmed.edu) and will enable the unraveling of the mechanisms by which different macro- and micronutrients contribute to the animal's physiology. link: http://identifiers.org/pubmed/27211857

Parameters: none

States: none

Observables: none

iCEL1314 is a genome-scale metabolic network model of Caenorhabditis elegans. This model is based on a previous model na…

Metabolism is a highly compartmentalized process that provides building blocks for biomass generation during development, homeostasis and wound healing, and energy to support cellular and organismal processes. In metazoans, different cells and tissues specialize in different aspects of metabolism. However, studying the compartmentalization of metabolism in different cell types in a whole animal and for a particular stage of life is difficult. Here, we present MERGE (MEtabolic models Reconciled with Gene Expression), a computational pipeline that we used to predict tissue-relevant metabolic function at the network-, pathway-, reaction-, and metabolite-level based on single-cell RNA-sequencing (scRNA-seq) data from the nematode Caenorhabditis elegans. Our analysis recapitulated known tissue functions in C. elegans, captured metabolic properties that are shared with similar tissues in human, and also provided predictions for novel metabolic functions. MERGE is versatile and applicable to other systems. We envision this work as a starting point for the development of metabolic network models for individual cells as scRNA-seq continues to provide higher resolution gene expression data. link: http://identifiers.org/doi/10.15252/msb.20209649

Parameters: none

States: none

Observables: none

Mathematical modeling of mutant transferrin-CRM107 molecular conjugates for cancer therapy. Yoon DJ1, Chen KY1, Lopes AM…

The transferrin (Tf) trafficking pathway is a promising mechanism for use in targeted cancer therapy due to the overexpression of transferrin receptors (TfRs) on cancerous cells. We have previously developed a mathematical model of the Tf/TfR trafficking pathway to improve the efficiency of Tf as a drug carrier. By using diphtheria toxin (DT) as a model toxin, we found that mutating the Tf protein to change its iron release rate improves cellular association and efficacy of the drug. Though this is an improvement upon using wild-type Tf as the targeting ligand, conjugated toxins like DT are unfortunately still highly cytotoxic at off-target sites. In this work, we address this hurdle in cancer research by developing a mathematical model to predict the efficacy and selectivity of Tf conjugates that use an alternative toxin. For this purpose, we have chosen to study a mutant of DT, cross-reacting material 107 (CRM107). First, we developed a mathematical model of the Tf-DT trafficking pathway by extending our Tf/TfR model to include intracellular trafficking via DT and DT receptors. Using this mathematical model, we subsequently investigated the efficacy of several conjugates in cancer cells: DT and CRM107 conjugated to wild-type Tf, as well as to our engineered mutant Tf proteins (K206E/R632A Tf and K206E/R534A Tf). We also investigated the selectivity of mutant Tf-CRM107 against non-neoplastic cells. Through the use of our mathematical model, we predicted that (i) mutant Tf-CRM107 exhibits a greater cytotoxicity than wild-type Tf-CRM107 against cancerous cells, (ii) this improvement was more drastic with CRM107 conjugates than with DT conjugates, and (iii) mutant Tf-CRM107 conjugates were selective against non-neoplastic cells. These predictions were validated with in vitro cytotoxicity experiments, demonstrating that mutant Tf-CRM107 conjugates is indeed a more suitable therapeutic agent. Validation from in vitro experiments also confirmed that such whole-cell kinetic models can be useful in cancer therapeutic design. link: http://identifiers.org/pubmed/28065783

Parameters: none

States: none

Observables: none

MODEL8459127548 @ v0.0.1

This the model from the article: A quantitative model for mRNA translation in Saccharomyces cerevisiae. You T, Coghi…

Messenger RNA (mRNA) translation is an essential step in eukaryotic gene expression that contributes to the regulation of this process. We describe a deterministic model based on ordinary differential equations that describe mRNA translation in Saccharomyces cerevisiae. This model, which was parameterized using published data, was developed to examine the kinetic behaviour of translation initiation factors in response to amino acid availability. The model predicts that the abundance of the eIF1-eIF3-eIF5 complex increases under amino acid starvation conditions, suggesting a possible auxiliary role for these factors in modulating translation initiation in addition to the known mechanisms involving eIF2. Our analyses of the robustness of the mRNA translation model suggest that individual cells within a randomly generated population are sensitive to external perturbations (such as changes in amino acid availability) through Gcn2 signalling. However, the model predicts that individual cells exhibit robustness against internal perturbations (such as changes in the abundance of translation initiation factors and kinetic parameters). Gcn2 appears to enhance this robustness within the system. These findings suggest a trade-off between the robustness and performance of this biological network. The model also predicts that individual cells exhibit considerable heterogeneity with respect to their absolute translation rates, due to random internal perturbations. Therefore, averaging the kinetic behaviour of cell populations probably obscures the dynamic robustness of individual cells. This highlights the importance of single-cell measurements for evaluating network properties. link: http://identifiers.org/pubmed/20306461

Parameters: none

States: none

Observables: none

This is a mathematical model investigating interactions among malignant tumor cells, CD4+ T cells, anti-tumor cytokines…

Blockade of immune checkpoints has recently been shown as a revolutionary strategy in the fight against cancers. Based on recent mouse experiments and clinical trials, large tumors can be completely suppressed with an additional blockade of immune checkpoints. We construct mathematical models capturing key interactions among malignant tumor cells, CD4+ T cells, anti-tumor cytokines, and immune checkpoint inhibitor of CTLA-4 to explore the importance of immune checkpoints on regression of tumor. Our study shows that blockade of immune checkpoints plays essential roles in immune responses. Continuous and one day pulse immune therapies by either T cells, anti-tumor cytokines, anti-CTLA-4 or a joint therapy are administered to exam the effectiveness of immune therapies. Our investigation indicates anti-tumor cytokine is potentially a key factor in determining the future of the malignant tumor. The malignant tumor can be suppressed thoroughly with reasonable dosages of anti-tumor cytokines if pre-radiation along with anti-CTLA-4 therapy are implemented. link: http://identifiers.org/doi/10.1016/j.amc.2019.06.037

Parameters: none

States: none

Observables: none

Yugi2014 - Insulin induced signalling (PFKL phosphorylation) - model 1Insulin induces phosphorylation and activation of…

Cellular homeostasis is regulated by signals through multiple molecular networks that include protein phosphorylation and metabolites. However, where and when the signal flows through a network and regulates homeostasis has not been explored. We have developed a reconstruction method for the signal flow based on time-course phosphoproteome and metabolome data, using multiple databases, and have applied it to acute action of insulin, an important hormone for metabolic homeostasis. An insulin signal flows through a network, through signaling pathways that involve 13 protein kinases, 26 phosphorylated metabolic enzymes, and 35 allosteric effectors, resulting in quantitative changes in 44 metabolites. Analysis of the network reveals that insulin induces phosphorylation and activation of liver-type phosphofructokinase 1, thereby controlling a key reaction in glycolysis. We thus provide a versatile method of reconstruction of signal flow through the network using phosphoproteome and metabolome data. link: http://identifiers.org/pubmed/25131207

Parameters:

Name Description
k_akg = -3.544494721 substance Reaction: s7 => s15, Rate Law: -k_akg
k_f26bp = -0.083430336 substance Reaction: s9 => s18, Rate Law: -k_f26bp
k_cit = -0.351935646 substance Reaction: s10 => s19, Rate Law: -k_cit
K_PFKL_cit = 41.30426029 dimensionless; K_PFKL_f6p = 0.014114844 dimensionless; K_PFKL_PHOS_S775 = 6.283705757 dimensionless; K_PFKL_mal = 9.544729149 dimensionless; K_PFKL_akg = 24661.01154 dimensionless; K_PFKL_f26bp = 1.282443082 dimensionless; Vf_PFKL = 695063.7194 dimensionless; K_PFKL_pep = 0.633518366 dimensionless; K_PFKL_icit = 1784.508205 dimensionless Reaction: s22 => s4; s1, s5, s6, s7, s8, s9, s10, s13, s9, s7, s5, s10, s6, s8, s13, s22, Rate Law: s9/(K_PFKL_f26bp+s9)*K_PFKL_akg/(K_PFKL_akg+s7)*K_PFKL_pep/(K_PFKL_pep+s5)*K_PFKL_cit/(K_PFKL_cit+s10)*K_PFKL_icit/(K_PFKL_icit+s6)*K_PFKL_mal/(K_PFKL_mal+s8)*s13/(K_PFKL_PHOS_S775+s13)*Vf_PFKL*s22/(K_PFKL_f6p+s22)
k_icit = -0.038210156 substance Reaction: s6 => s17, Rate Law: -k_icit
k_mal = 1.005530417 substance Reaction: s8 => s14, Rate Law: -k_mal
k_ALDO = 0.008187906 dimensionless Reaction: s4 => s11; s12, s4, Rate Law: k_ALDO*s4
K_FBPase_cit = 0.0211646 dimensionless; K_FBPase_f16bp = 0.104089638 dimensionless; Vf_FBPase = 9.932861302 dimensionless; K_FBPase_f26bp = 17.51744342 dimensionless Reaction: s4 => s22; s2, s9, s10, s9, s10, s4, Rate Law: K_FBPase_f26bp/(K_FBPase_f26bp+s9)*s10/(K_FBPase_cit+s10)*Vf_FBPase*s4/(K_FBPase_f16bp+s4)
k_f6p = -0.930115636 dimensionless Reaction: s3 => s21, Rate Law: -k_f6p
k_pep = 43.99195576 substance Reaction: s5 => s16, Rate Law: -k_pep
k_pfkl_s775 = -0.011384308 substance Reaction: s13 => s20, Rate Law: -k_pfkl_s775

States:

Name Description
s8 [malic acid]
s5 [phosphoenolpyruvate]
s7 [2-oxoglutaric acid]
s14 sa8_degraded
s18 sa9_degraded
s20 sa13_degraded
s17 sa6_degraded
s13 [ATP-dependent 6-phosphofructokinase, liver type; phosphorylated]
s4 [keto-D-fructose 1,6-bisphosphate]
s19 sa10_degraded
s9 [beta-D-fructofuranose 2,6-bisphosphate]
s16 sa5_degraded
s10 [citric acid]
s6 [isocitric acid]
s21 sa3_degraded
s22 [D-fructose 6-phosphate(2-)]
s11 sa4_degraded
s15 sa7_degraded
s3 [keto-D-fructose 6-phosphate]

Observables: none

Yugi2014 - Insulin induced signalling (PFKL phosphorylation) - model 2Insulin induces phosphorylation and activation of…

Cellular homeostasis is regulated by signals through multiple molecular networks that include protein phosphorylation and metabolites. However, where and when the signal flows through a network and regulates homeostasis has not been explored. We have developed a reconstruction method for the signal flow based on time-course phosphoproteome and metabolome data, using multiple databases, and have applied it to acute action of insulin, an important hormone for metabolic homeostasis. An insulin signal flows through a network, through signaling pathways that involve 13 protein kinases, 26 phosphorylated metabolic enzymes, and 35 allosteric effectors, resulting in quantitative changes in 44 metabolites. Analysis of the network reveals that insulin induces phosphorylation and activation of liver-type phosphofructokinase 1, thereby controlling a key reaction in glycolysis. We thus provide a versatile method of reconstruction of signal flow through the network using phosphoproteome and metabolome data. link: http://identifiers.org/pubmed/25131207

Parameters:

Name Description
k1=1.00000000282413E-5 dimensionless Reaction: s26 => s23; s26, Rate Law: k1*s26
k_cit = -0.351935646 substance Reaction: s10 => s19, Rate Law: -k_cit
k1=0.00105342379833469 dimensionless Reaction: s34 => s35; s31, s34, s35, s31, Rate Law: k1*(s34-s35)*s31
k_f6p = -0.930115636 dimensionless Reaction: s3 => s21, Rate Law: -k_f6p
k1=0.00752464611370891 dimensionless Reaction: s32 => s33; s31, s32, s33, s31, Rate Law: k1*(s32-s33)*s31
k1=0.28442597446931 dimensionless Reaction: s27 => s25; s27, Rate Law: k1*s27
k1=0.419682384304397 dimensionless Reaction: s30 => s31; s29, s30, s31, s29, Rate Law: k1*(s30-s31)*s29
k1=7.78160761103111 dimensionless; k2=1.61147523779118 dimensionless; insulin = 1.0 dimensionless Reaction: s23 => s25; s23, s25, Rate Law: k1*insulin*s23-k2*s25
k1=1.95497593092361 dimensionless Reaction: s33 => s32; s35, s33, s35, Rate Law: k1*s33*s35
k_akg = -3.544494721 substance Reaction: s7 => s15, Rate Law: -k_akg
k1=7.70618517548016 dimensionless Reaction: s29 => s28; s29, Rate Law: k1*s29
k1=26.8316707654711 dimensionless Reaction: s1 => s13; s33, s1, s13, s33, Rate Law: k1*(s1-s13)*s33
k_f26bp = -0.083430336 substance Reaction: s9 => s18, Rate Law: -k_f26bp
k1=0.00145811601430322 substance Reaction: s35 => s34; s35, Rate Law: k1*s35
K_PFKL_cit = 41.30426029 dimensionless; K_PFKL_f6p = 0.014114844 dimensionless; K_PFKL_PHOS_S775 = 6.283705757 dimensionless; K_PFKL_mal = 9.544729149 dimensionless; K_PFKL_akg = 24661.01154 dimensionless; K_PFKL_f26bp = 1.282443082 dimensionless; Vf_PFKL = 695063.7194 dimensionless; K_PFKL_pep = 0.633518366 dimensionless; K_PFKL_icit = 1784.508205 dimensionless Reaction: s22 => s4; s1, s5, s6, s7, s8, s9, s10, s13, s9, s7, s5, s10, s6, s8, s13, s22, Rate Law: s9/(K_PFKL_f26bp+s9)*K_PFKL_akg/(K_PFKL_akg+s7)*K_PFKL_pep/(K_PFKL_pep+s5)*K_PFKL_cit/(K_PFKL_cit+s10)*K_PFKL_icit/(K_PFKL_icit+s6)*K_PFKL_mal/(K_PFKL_mal+s8)*s13/(K_PFKL_PHOS_S775+s13)*Vf_PFKL*s22/(K_PFKL_f6p+s22)
insulin = 1.0 dimensionless; k1=0.363030286526969 dimensionless; k2=0.408127912886804 dimensionless Reaction: s26 => s27; s26, s27, Rate Law: k1*insulin*s26-k2*s27
k_icit = -0.038210156 substance Reaction: s6 => s17, Rate Law: -k_icit
k_ALDO = 0.008187906 dimensionless Reaction: s4 => s11; s12, s4, Rate Law: k_ALDO*s4
k_mal = 1.005530417 substance Reaction: s8 => s14, Rate Law: -k_mal
k1=9.93311225447353 dimensionless Reaction: s23 => s26; s31, s23, s31, Rate Law: k1*s23*s31
K_FBPase_cit = 0.0211646 dimensionless; K_FBPase_f16bp = 0.104089638 dimensionless; Vf_FBPase = 9.932861302 dimensionless; K_FBPase_f26bp = 17.51744342 dimensionless Reaction: s4 => s22; s2, s9, s10, s9, s10, s4, Rate Law: K_FBPase_f26bp/(K_FBPase_f26bp+s9)*s10/(K_FBPase_cit+s10)*Vf_FBPase*s4/(K_FBPase_f16bp+s4)
k1=0.00792717614041237 substance Reaction: s25 => s38; s25, Rate Law: k1*s25
k1=0.0166525139097609 dimensionless Reaction: s13 => s1; s13, Rate Law: k1*s13
k1=1.00277786609339E-5 dimensionless Reaction: s26 => s37; s26, Rate Law: k1*s26
k1=0.0948960328385619 dimensionless Reaction: s27 => s36; s27, Rate Law: k1*s27
k1=0.0477985900779305 dimensionless Reaction: s24 => s23; s24, s23, Rate Law: k1*(s24-s23)
k1=0.124330492920416 dimensionless Reaction: s31 => s30; s31, Rate Law: k1*s31
k_pep = 43.99195576 substance Reaction: s5 => s16, Rate Law: -k_pep
k1=3.88248960751442E-5 dimensionless Reaction: s25 => s27; s31, s25, s31, Rate Law: k1*s25*s31
k1=0.00919578911309774 dimensionless Reaction: s28 => s29; s25, s28, s29, s25, Rate Law: k1*(s28-s29)*s25

States:

Name Description
s8 [malic acid]
s23 [Insulin receptor]
s14 sa8_degraded
s37 sa27_degraded
s24 [Insulin receptor]
s35 [protein; phosphorylated]
s5 [phosphoenolpyruvate]
s7 [2-oxoglutaric acid]
s18 sa9_degraded
s31 [Serine/threonine-protein kinase mTOR; phosphorylated]
s34 [protein]
s9 [beta-D-fructofuranose 2,6-bisphosphate]
s10 [citric acid]
s19 sa10_degraded
s38 sa26_degraded
s36 sa28_degraded
s6 [isocitric acid]
s32 [Ribosomal protein S6 kinase beta-1]
s22 [D-fructose 6-phosphate(2-)]
s11 sa4_degraded
s15 sa7_degraded
s3 [keto-D-fructose 6-phosphate]
s1 [ATP-dependent 6-phosphofructokinase, liver type]
s17 sa6_degraded
s25 [Insulin receptor; protein]
s13 [ATP-dependent 6-phosphofructokinase, liver type; phosphorylated]
s33 [phosphorylated; Ribosomal protein S6 kinase beta-1]
s4 [keto-D-fructose 1,6-bisphosphate]
s16 sa5_degraded
s30 [Serine/threonine-protein kinase mTOR]
s26 [Insulin receptor; protein]
s21 sa3_degraded
s28 [RAC-alpha serine/threonine-protein kinase]
s29 [RAC-alpha serine/threonine-protein kinase; phosphorylated]
s27 [Insulin receptor; protein]

Observables: none

Yuraszeck2010 - Vulnerabilities in the Tau Network in Tau PathophysiologyThis model is described in the article: [Vulne…

The multifactorial nature of disease motivates the use of systems-level analyses to understand their pathology. We used a systems biology approach to study tau aggregation, one of the hallmark features of Alzheimer's disease. A mathematical model was constructed to capture the current state of knowledge concerning tau's behavior and interactions in cells. The model was implemented in silico in the form of ordinary differential equations. The identifiability of the model was assessed and parameters were estimated to generate two cellular states: a population of solutions that corresponds to normal tau homeostasis and a population of solutions that displays aggregation-prone behavior. The model of normal tau homeostasis was robust to perturbations, and disturbances in multiple processes were required to achieve an aggregation-prone state. The aggregation-prone state was ultrasensitive to perturbations in diverse subsets of networks. Tau aggregation requires that multiple cellular parameters are set coordinately to a set of values that drive pathological assembly of tau. This model provides a foundation on which to build and increase our understanding of the series of events that lead to tau aggregation and may ultimately be used to identify critical intervention points that can direct the cell away from tau aggregation to aid in the treatment of tau-mediated (or related) aggregation diseases including Alzheimer's. link: http://identifiers.org/pubmed/21085645

Parameters:

Name Description
k80 = 0.551509 Reaction: TauH4R_CHIP_Hsc70 => TauH4RUb + Hsc70 + CHIP; TauH4R_CHIP_Hsc70, Rate Law: Brain*k80*TauH4R_CHIP_Hsc70
k61 = 19.76984 Reaction: TauH_4R + MT => TauH4RMT; TauH_4R, MT, Rate Law: Brain*k61*TauH_4R*MT
k51 = 7.118684 Reaction: Tau04R => Tau0_4R; Tau04R, Rate Law: Brain*k51*Tau04R
k52 = 15.0 Reaction: Tau0_4R => Tau04R; Tau0_4R, Rate Law: Brain*k52*Tau0_4R
k82 = 0.644848 Reaction: TauH4R_CHIP_Hsc70_Bag2 => TauH4R_Hsc70 + CHIP + Bag2; TauH4R_CHIP_Hsc70_Bag2, Rate Law: Brain*k82*TauH4R_CHIP_Hsc70_Bag2
k91 = 0.005429 Reaction: Ap => TauH3RUb + Ap; Ap, Rate Law: Brain*k91*Ap
k76 = 0.283991 Reaction: TauH4R_Hsc70 + Hsp90 => TauH4R_Hsp90 + Hsc70; TauH4R_Hsc70, Hsp90, Rate Law: Brain*k76*TauH4R_Hsc70*Hsp90
k55 = 1.540886 Reaction: TauN4R => TauN_4R; TauN4R, Rate Law: Brain*k55*TauN4R
k83 = 0.006502 Reaction: TauH4RUb + _26S + ATP => ADP + _26S; TauH4RUb, _26S, ATP, Rate Law: Brain*k83*TauH4RUb*_26S*ATP
k18 = 3.940468 Reaction: TauH3R => TauH_3R; TauH3R, Rate Law: Brain*k18*TauH3R
k31 = 3.991539; k32 = 7.130081 Reaction: TauH3RMT => TauN3RMT; TauH3RMT, Rate Law: Brain*k31*TauH3RMT/(k32+TauH3RMT)
k50 = 5.760257; k49 = 0.003379 Reaction: TauH4R => TauN4R; TauH4R, Rate Law: Brain*k49*TauH4R/(k50+TauH4R)
k35 = 0.146177 Reaction: TauH3R_Hsc70 + Hsp90 => TauH3R_Hsp90 + Hsc70; TauH3R_Hsc70, Hsp90, Rate Law: Brain*k35*TauH3R_Hsc70*Hsp90
k74 = 1.61E-4 Reaction: TauH4R + Hsc70 => TauH4R_Hsc70; TauH4R, Hsc70, Rate Law: Brain*k74*TauH4R*Hsc70
k8 = 0.608448; k9 = 5.760257 Reaction: TauH3R_Hsp90 => Tau03R_Hsp90; TauH3R_Hsp90, Rate Law: Brain*k8*TauH3R_Hsp90/(k9+TauH3R_Hsp90)
k34 = 1.11E-4 Reaction: TauH3R_Hsc70 => TauH3R + Hsc70; TauH3R_Hsc70, Rate Law: Brain*k34*TauH3R_Hsc70
k58 = 0.067355 Reaction: TauN4RMT => TauN_4R + MT; TauN4RMT, Rate Law: Brain*k58*TauN4RMT
k37 = 1.07 Reaction: TauH3R_Hsc70 + CHIP => TauH3R_CHIP_Hsc70; TauH3R_Hsc70, CHIP, Rate Law: Brain*k37*TauH3R_Hsc70*CHIP
k63 = 0.211664 Reaction: Tau04R + _20S + ATP => ADP + _20S; Tau04R, _20S, ATP, Rate Law: Brain*k63*Tau04R*_20S*ATP
k70 = 0.073055; k71 = 16.56551 Reaction: TauN4RMT + ATP => TauH4RMT + ADP; TauN4RMT, ATP, Rate Law: Brain*k70*TauN4RMT*ATP/(k71+TauN4RMT)
k40 = 0.050949 Reaction: TauH3R_CHIP_Hsc70_Bag2 => TauH3R_Hsc70 + CHIP + Bag2; TauH3R_CHIP_Hsc70_Bag2, Rate Law: Brain*k40*TauH3R_CHIP_Hsc70_Bag2
k29 = 0.006017; k30 = 16.56551 Reaction: TauN3RMT + ATP => TauH3RMT + ADP; TauN3RMT, ATP, Rate Law: Brain*k29*TauN3RMT*ATP/(k30+TauN3RMT)
k36 = 0.006298 Reaction: Tau03R_Hsp90 => Hsp90 + Tau03R; Tau03R_Hsp90, Rate Law: Brain*k36*Tau03R_Hsp90
k38 = 0.029266 Reaction: TauH3R_CHIP_Hsc70 => TauH3RUb + Hsc70 + CHIP; TauH3R_CHIP_Hsc70, Rate Law: Brain*k38*TauH3R_CHIP_Hsc70
k90 = 0.095 Reaction: TauH3RUb + Ap => Ap; TauH3RUb, Ap, Rate Law: Brain*k90*TauH3RUb*Ap
k66 = 0.028914; k67 = 0.1452 Reaction: Tau04RMT + ATP => TauN4RMT + ADP; Tau04RMT, ATP, Rate Law: Brain*k66*Tau04RMT*ATP/(k67+Tau04RMT)
k72 = 0.014352; k73 = 7.130081 Reaction: TauH4RMT => TauN4RMT; TauH4RMT, Rate Law: Brain*k72*TauH4RMT/(k73+TauH4RMT)
k79 = 0.346673 Reaction: TauH4R_Hsc70 + CHIP => TauH4R_CHIP_Hsc70; TauH4R_Hsc70, CHIP, Rate Law: Brain*k79*TauH4R_Hsc70*CHIP
k23 = 0.075176 Reaction: TauN3R + _20S + ATP => ADP + _20S; TauN3R, _20S, ATP, Rate Law: Brain*k23*TauN3R*_20S*ATP
k33 = 0.009267 Reaction: TauH3R + Hsc70 => TauH3R_Hsc70; TauH3R, Hsc70, Rate Law: Brain*k33*TauH3R*Hsc70
k7 = 21.91138; k6 = 0.142099 Reaction: TauN3R + ATP => TauH3R + ADP; TauN3R, ATP, Rate Law: Brain*k6*TauN3R*ATP/(k7+TauN3R)
k41 = 0.279 Reaction: TauH3RUb + _26S + ATP => ADP + _26S; TauH3RUb, _26S, ATP, Rate Law: Brain*k41*TauH3RUb*_26S*ATP
k20 = 19.76984 Reaction: TauH_3R + MT => TauH3RMT; TauH_3R, MT, Rate Law: Brain*k20*TauH_3R*MT
k21 = 7.248652 Reaction: TauH3RMT => TauH_3R + MT; TauH3RMT, Rate Law: Brain*k21*TauH3RMT
k87 = 0.0012 Reaction: Nucleus3 => TauH3RUb; Nucleus3, Rate Law: Brain*k87*Nucleus3
k62 = 2.416217 Reaction: TauH4RMT => TauH_4R + MT; TauH4RMT, Rate Law: Brain*k62*TauH4RMT
k44 = 27.5668; k43 = 3.68998 Reaction: Tau04R + ATP => TauN4R + ADP; Tau04R, ATP, Rate Law: Brain*k43*Tau04R*ATP/(k44+Tau04R)
k75 = 8.57E-5 Reaction: TauH4R_Hsc70 => TauH4R + Hsc70; TauH4R_Hsc70, Rate Law: Brain*k75*TauH4R_Hsc70
k19 = 8.052152 Reaction: TauH_3R => TauH3R; TauH_3R, Rate Law: Brain*k19*TauH_3R
k60 = 8.052152 Reaction: TauH_4R => TauH4R; TauH_4R, Rate Law: Brain*k60*TauH_4R
k81 = 5.59E-5 Reaction: TauH4R_CHIP_Hsc70 + Bag2 => TauH4R_CHIP_Hsc70_Bag2; TauH4R_CHIP_Hsc70, Bag2, Rate Law: Brain*k81*TauH4R_CHIP_Hsc70*Bag2
k78 = 0.004562 Reaction: Tau04R_Hsp90 => Hsp90 + Tau04R; Tau04R_Hsp90, Rate Law: Brain*k78*Tau04R_Hsp90
k86 = 5.0E-6 Reaction: TauH3RUb => Nucleus3; TauH3RUb, Rate Law: Brain*k86*TauH3RUb^2
k42 = 0.025365 Reaction: => Tau04R, Rate Law: Brain*k42
k56 = 9.220426 Reaction: TauN_4R => TauN4R; TauN_4R, Rate Law: Brain*k56*TauN_4R
k77 = 1.185806; k9 = 5.760257 Reaction: TauH4R_Hsp90 => Tau04R_Hsp90; TauH4R_Hsp90, Rate Law: Brain*k77*TauH4R_Hsp90/(k9+TauH4R_Hsp90)
k45 = 0.216599; k46 = 7.99621 Reaction: TauN4R => Tau04R; TauN4R, Rate Law: Brain*k45*TauN4R/(k46+TauN4R)
k64 = 0.074306 Reaction: TauN4R + _20S + ATP => ADP + _20S; TauN4R, _20S, ATP, Rate Law: Brain*k64*TauN4R*_20S*ATP
k59 = 3.940468 Reaction: TauH4R => TauH_4R; TauH4R, Rate Law: Brain*k59*TauH4R
k3 = 27.5668 Reaction: Tau03R + ATP => TauN3R + ADP; Tau03R, ATP, Rate Law: Brain*k3*Tau03R*ATP/(k3+Tau03R)
k39 = 1.163756 Reaction: TauH3R_CHIP_Hsc70 + Bag2 => TauH3R_CHIP_Hsc70_Bag2; TauH3R_CHIP_Hsc70, Bag2, Rate Law: Brain*k39*TauH3R_CHIP_Hsc70*Bag2
k57 = 50.66157 Reaction: TauN_4R + MT => TauN4RMT; TauN_4R, MT, Rate Law: Brain*k57*TauN_4R*MT
k22 = 0.173127 Reaction: Tau03R + _20S + ATP => ADP + _20S; Tau03R, _20S, ATP, Rate Law: Brain*k22*Tau03R*_20S*ATP
k48 = 21.91138; k47 = 2.801964 Reaction: TauN4R + ATP => TauH4R + ADP; TauN4R, ATP, Rate Law: Brain*k47*TauN4R*ATP/(k48+TauN4R)

States:

Name Description
TauH3RMT [Tubulin alpha-1A chain; Microtubule-associated protein tau; conformational transition]
Hsc70 [Heat shock cognate 71 kDa protein]
TauH 3R [Microtubule-associated protein tau; conformational transition]
TauN3RMT [Tubulin alpha-1A chain; Microtubule-associated protein tau; phosphorylated]
TauH4RUb [Microtubule-associated protein tau; conformational transition; ubiquinated]
TauN4RMT [Tubulin alpha-1A chain; Microtubule-associated protein tau; phosphorylated]
TauH3R Hsp90 [Hsp90 co-chaperone Cdc37; Microtubule-associated protein tau; conformational transition]
TauH4RMT [Tubulin alpha-1A chain; Microtubule-associated protein tau; conformational transition]
TauH4R Hsp90 [Hsp90 co-chaperone Cdc37; Microtubule-associated protein tau; conformational transition]
Tau04R [Microtubule-associated protein tau]
Tau04R Hsp90 [Hsp90 co-chaperone Cdc37; Microtubule-associated protein tau]
CHIP [E3 ubiquitin-protein ligase CHIP]
Bag2 [BAG family molecular chaperone regulator 2]
26S [proteasome complex]
Tau03R Hsp90 [Hsp90 co-chaperone Cdc37; Microtubule-associated protein tau]
TauH 4R [Microtubule-associated protein tau; conformational transition]
TauH4R CHIP Hsc70 Bag2 [Heat shock cognate 71 kDa protein; E3 ubiquitin-protein ligase CHIP; BAG family molecular chaperone regulator 2; Microtubule-associated protein tau; conformational transition]
TauH4R Hsc70 [Heat shock cognate 71 kDa protein; Microtubule-associated protein tau; conformational transition]
TauN 4R [Microtubule-associated protein tau; conformational transition; phosphorylated]
TauH4R CHIP Hsc70 [Heat shock cognate 71 kDa protein; E3 ubiquitin-protein ligase CHIP; Microtubule-associated protein tau; conformational transition]
TauH3R CHIP Hsc70 Bag2 [Heat shock cognate 71 kDa protein; E3 ubiquitin-protein ligase CHIP; BAG family molecular chaperone regulator 2; Microtubule-associated protein tau; conformational transition]
TauN4R [Microtubule-associated protein tau; phosphorylated]
TauH3R Hsc70 [Heat shock cognate 71 kDa protein; Microtubule-associated protein tau; conformational transition]
ADP [ADP]
20S [proteasome core complex]
TauH3RUb [Microtubule-associated protein tau; conformational transition; ubiquinated]
TauH3R CHIP Hsc70 [Heat shock cognate 71 kDa protein; E3 ubiquitin-protein ligase CHIP; Microtubule-associated protein tau; conformational transition]

Observables: none

Z


MODEL6963432821 @ v0.0.1

This the model from the article without the time delays: A Delayed Nonlinear PBPK Model for Genistein Dosimetry in Rat…

Genistein is an endocrine-active compound (EAC) found in soy products. It has been linked to beneficial effects such as mammary tumor growth suppression and adverse endocrine-related effects such as reduced birth weight in rats and humans. In its conjugated form, genistein is excreted in the bile, which is a significant factor in its pharmacokinetics. Experimental data suggest that genistein induces a concentration-dependent suppression of biliary excretion. In this article, we describe a physiologically based pharmacokinetic (PBPK) model that focuses on biliary excretion with the goal of accurately simulating the observed suppression. The mathematical model is a system of nonlinear differential equations with state-dependent delay to describe biliary excretion. The model was analyzed to examine local existence and uniqueness of a solution to the equations. Furthermore, unknown parameters were estimated, and the mathematical model was compared against published experimental data. link: http://identifiers.org/pubmed/17024552

Parameters: none

States: none

Observables: none

Model listing the reactions of the intrinsic pathway as listed in Zarnitsina1996. Publication model is a spatio-termpora…

We developed and analyzed the mathematical model of the intrinsic pathway based on the current biochemical data on the kinetics of blood coagulation individual stages. The model includes eight differential equations describing the spatio-temporal dynamics of activation of factors XI, IX, X, II, I, VIII, V, and protein C. The assembly of tenase and prothrombinase complexes is considered as a function of calcium concentration. The spatial dynamics of coagulation was analyzed for the one-dimensional case. We examined the formation of active factors, their spreading, and growth of the clot from the site of injury in the direction perpendicular to the vessel wall, into the blood thickness. We assumed that the site of injury (in the model one boundary of the space segment under examination) becomes a source of the continuous influx of factor XIa. In the first part, we described the model, selected the parameters, etc. In the second part, we compared the model with experimental data obtained in the homogeneous system and analyzed the spatial dynamics of the clot growth. link: http://identifiers.org/pubmed/8948047

Parameters: none

States: none

Observables: none

BIOMD0000000159 @ v0.0.1

The model reproduces the time profile of p53 and Mdm2 as depicted in Fig 6B of the plot for model 1. Results obtained on…

Understanding the dynamics and variability of protein circuitry requires accurate measurements in living cells as well as theoretical models. To address this, we employed one of the best-studied protein circuits in human cells, the negative feedback loop between the tumor suppressor p53 and the oncogene Mdm2. We measured the dynamics of fluorescently tagged p53 and Mdm2 over several days in individual living cells. We found that isogenic cells in the same environment behaved in highly variable ways following DNA-damaging gamma irradiation: some cells showed undamped oscillations for at least 3 days (more than 10 peaks). The amplitude of the oscillations was much more variable than the period. Sister cells continued to oscillate in a correlated way after cell division, but lost correlation after about 11 h on average. Other cells showed low-frequency fluctuations that did not resemble oscillations. We also analyzed different families of mathematical models of the system, including a novel checkpoint mechanism. The models point to the possible source of the variability in the oscillations: low-frequency noise in protein production rates, rather than noise in other parameters such as degradation rates. This study provides a view of the extensive variability of the behavior of a protein circuit in living human cells, both from cell to cell and in the same cell over time. link: http://identifiers.org/pubmed/16773083

Parameters:

Name Description
beta_x = 0.3; psi = 1.0 Reaction: => x, Rate Law: compartment*beta_x*psi
beta_y = 0.4; psi = 1.0 Reaction: => y0; x, Rate Law: compartment*beta_y*x*psi
alpha_xy = 3.2 Reaction: x => ; y, Rate Law: compartment*alpha_xy*y*x
alpha_x = 0.0 Reaction: x =>, Rate Law: compartment*alpha_x*x
alpha_y = 0.1 Reaction: y =>, Rate Law: compartment*alpha_y*y
alpha_0 = 0.1 Reaction: y0 => y, Rate Law: compartment*alpha_0*y0

States:

Name Description
x [Cellular tumor antigen p53]
y0 precursor Mdm2
y [E3 ubiquitin-protein ligase Mdm2]

Observables: none

BIOMD0000000158 @ v0.0.1

The model reproduces time profile of p53 and Mdm2 as depicted in Fig 6B of the paper for Model 2. Results obtained using…

Understanding the dynamics and variability of protein circuitry requires accurate measurements in living cells as well as theoretical models. To address this, we employed one of the best-studied protein circuits in human cells, the negative feedback loop between the tumor suppressor p53 and the oncogene Mdm2. We measured the dynamics of fluorescently tagged p53 and Mdm2 over several days in individual living cells. We found that isogenic cells in the same environment behaved in highly variable ways following DNA-damaging gamma irradiation: some cells showed undamped oscillations for at least 3 days (more than 10 peaks). The amplitude of the oscillations was much more variable than the period. Sister cells continued to oscillate in a correlated way after cell division, but lost correlation after about 11 h on average. Other cells showed low-frequency fluctuations that did not resemble oscillations. We also analyzed different families of mathematical models of the system, including a novel checkpoint mechanism. The models point to the possible source of the variability in the oscillations: low-frequency noise in protein production rates, rather than noise in other parameters such as degradation rates. This study provides a view of the extensive variability of the behavior of a protein circuit in living human cells, both from cell to cell and in the same cell over time. link: http://identifiers.org/pubmed/16773083

Parameters:

Name Description
alpha_y = 0.6 Reaction: y =>, Rate Law: compartment*alpha_y*y
alpha_x = 0.0 Reaction: x =>, Rate Law: compartment*alpha_x*x
alpha_xy = 3.15 Reaction: x => ; y, Rate Law: compartment*alpha_xy*y*x
alpha_0 = 55.0 Reaction: y0 => y, Rate Law: compartment*alpha_0*y0
beta_y = 0.85; psi = 1.0 Reaction: => y0; x, Rate Law: compartment*beta_y*x*psi
fx = 0.0; psi = 1.0 Reaction: => x, Rate Law: compartment*fx*psi

States:

Name Description
x [Cellular tumor antigen p53]
y0 precursor Mdm2
y [E3 ubiquitin-protein ligase Mdm2]

Observables: none

BIOMD0000000154 @ v0.0.1

The model reproduces Fig 6B of the paper for model 3. The model was reproduced using XPP. To the extent possible under…

Understanding the dynamics and variability of protein circuitry requires accurate measurements in living cells as well as theoretical models. To address this, we employed one of the best-studied protein circuits in human cells, the negative feedback loop between the tumor suppressor p53 and the oncogene Mdm2. We measured the dynamics of fluorescently tagged p53 and Mdm2 over several days in individual living cells. We found that isogenic cells in the same environment behaved in highly variable ways following DNA-damaging gamma irradiation: some cells showed undamped oscillations for at least 3 days (more than 10 peaks). The amplitude of the oscillations was much more variable than the period. Sister cells continued to oscillate in a correlated way after cell division, but lost correlation after about 11 h on average. Other cells showed low-frequency fluctuations that did not resemble oscillations. We also analyzed different families of mathematical models of the system, including a novel checkpoint mechanism. The models point to the possible source of the variability in the oscillations: low-frequency noise in protein production rates, rather than noise in other parameters such as degradation rates. This study provides a view of the extensive variability of the behavior of a protein circuit in living human cells, both from cell to cell and in the same cell over time. link: http://identifiers.org/pubmed/16773083

Parameters:

Name Description
alpha_y = 24.0 Reaction: y =>, Rate Law: compartment*alpha_y*y
alpha_x = 0.0 Reaction: x =>, Rate Law: compartment*alpha_x*x
alpha_xy = 120.0 Reaction: x => ; y, Rate Law: compartment*alpha_xy*y*x
beta_y = 24.0; psi = 1.0; tau = 3.3 Reaction: => y; x, Rate Law: compartment*beta_y*psi*delay(x, tau)
psi = 1.0; beta_x = 2.3 Reaction: => x, Rate Law: compartment*beta_x*psi

States:

Name Description
x [Cellular tumor antigen p53]
y [E3 ubiquitin-protein ligase Mdm2]

Observables: none

BIOMD0000000157 @ v0.0.1

The model reproduces time profile of p53 and Mdm2 as depicted in Fig 6B of the paper for Model 4. Results obtained using…

Understanding the dynamics and variability of protein circuitry requires accurate measurements in living cells as well as theoretical models. To address this, we employed one of the best-studied protein circuits in human cells, the negative feedback loop between the tumor suppressor p53 and the oncogene Mdm2. We measured the dynamics of fluorescently tagged p53 and Mdm2 over several days in individual living cells. We found that isogenic cells in the same environment behaved in highly variable ways following DNA-damaging gamma irradiation: some cells showed undamped oscillations for at least 3 days (more than 10 peaks). The amplitude of the oscillations was much more variable than the period. Sister cells continued to oscillate in a correlated way after cell division, but lost correlation after about 11 h on average. Other cells showed low-frequency fluctuations that did not resemble oscillations. We also analyzed different families of mathematical models of the system, including a novel checkpoint mechanism. The models point to the possible source of the variability in the oscillations: low-frequency noise in protein production rates, rather than noise in other parameters such as degradation rates. This study provides a view of the extensive variability of the behavior of a protein circuit in living human cells, both from cell to cell and in the same cell over time. link: http://identifiers.org/pubmed/16773083

Parameters:

Name Description
alpha_0 = 0.8 Reaction: y0 => y, Rate Law: compartment*alpha_0*y0
beta_x = 0.9; psi = 1.0 Reaction: => x, Rate Law: compartment*beta_x*psi
alpha_k = 1.7; k = 1.0E-4 Reaction: x => ; y, Rate Law: compartment*alpha_k*y*x/(x+k)
alpha_x = 0.0 Reaction: x =>, Rate Law: compartment*alpha_x*x
alpha_y = 0.8 Reaction: y =>, Rate Law: compartment*alpha_y*y
beta_y = 1.1; psi = 1.0 Reaction: => y0; x, Rate Law: compartment*beta_y*x*psi

States:

Name Description
x [Cellular tumor antigen p53]
y0 precursor Mdm2
y [E3 ubiquitin-protein ligase Mdm2]

Observables: none

BIOMD0000000156 @ v0.0.1

The model reproduces time profile of p53 and Mdm2 as depicted in Fig 6B of the paper for Model 5. Results obtained using…

Understanding the dynamics and variability of protein circuitry requires accurate measurements in living cells as well as theoretical models. To address this, we employed one of the best-studied protein circuits in human cells, the negative feedback loop between the tumor suppressor p53 and the oncogene Mdm2. We measured the dynamics of fluorescently tagged p53 and Mdm2 over several days in individual living cells. We found that isogenic cells in the same environment behaved in highly variable ways following DNA-damaging gamma irradiation: some cells showed undamped oscillations for at least 3 days (more than 10 peaks). The amplitude of the oscillations was much more variable than the period. Sister cells continued to oscillate in a correlated way after cell division, but lost correlation after about 11 h on average. Other cells showed low-frequency fluctuations that did not resemble oscillations. We also analyzed different families of mathematical models of the system, including a novel checkpoint mechanism. The models point to the possible source of the variability in the oscillations: low-frequency noise in protein production rates, rather than noise in other parameters such as degradation rates. This study provides a view of the extensive variability of the behavior of a protein circuit in living human cells, both from cell to cell and in the same cell over time. link: http://identifiers.org/pubmed/16773083

Parameters:

Name Description
alpha_xy = 3.7 Reaction: x => ; y, Rate Law: compartment*alpha_xy*y*x
Theta = 2.0; psi = 1.0 Reaction: => x, Rate Law: compartment*Theta*x*psi
alpha_0 = 1.1 Reaction: y0 => y, Rate Law: compartment*alpha_0*y0
beta_y = 1.5; psi = 1.0 Reaction: => y0; x, Rate Law: compartment*beta_y*x*psi
alpha_y = 0.9 Reaction: y =>, Rate Law: compartment*alpha_y*y

States:

Name Description
x [Cellular tumor antigen p53]
y0 precursor Mdm2
y [E3 ubiquitin-protein ligase Mdm2]

Observables: none

BIOMD0000000155 @ v0.0.1

The model reproduces Fig 6B of the paper for model 6. The model was reproduced using XPP. To the extent possible under…

Understanding the dynamics and variability of protein circuitry requires accurate measurements in living cells as well as theoretical models. To address this, we employed one of the best-studied protein circuits in human cells, the negative feedback loop between the tumor suppressor p53 and the oncogene Mdm2. We measured the dynamics of fluorescently tagged p53 and Mdm2 over several days in individual living cells. We found that isogenic cells in the same environment behaved in highly variable ways following DNA-damaging gamma irradiation: some cells showed undamped oscillations for at least 3 days (more than 10 peaks). The amplitude of the oscillations was much more variable than the period. Sister cells continued to oscillate in a correlated way after cell division, but lost correlation after about 11 h on average. Other cells showed low-frequency fluctuations that did not resemble oscillations. We also analyzed different families of mathematical models of the system, including a novel checkpoint mechanism. The models point to the possible source of the variability in the oscillations: low-frequency noise in protein production rates, rather than noise in other parameters such as degradation rates. This study provides a view of the extensive variability of the behavior of a protein circuit in living human cells, both from cell to cell and in the same cell over time. link: http://identifiers.org/pubmed/16773083

Parameters:

Name Description
alpha_y = 0.7 Reaction: y =>, Rate Law: compartment*alpha_y*y
beta_y = 1.0; tau = 0.9; psi = 1.0 Reaction: => y; x, Rate Law: compartment*beta_y*psi*delay(x, tau)
n = 4.0; beta_x = 0.9; S = 0.0; psi = 1.0 Reaction: => x, Rate Law: compartment*beta_x*S^n/(S^n+1)*psi
alpha_xy = 1.4 Reaction: x => ; y, Rate Law: compartment*alpha_xy*y*x

States:

Name Description
x [Cellular tumor antigen p53]
y [E3 ubiquitin-protein ligase Mdm2]

Observables: none

BIOMD0000000095 @ v0.0.1

The model reproduces the circadian charecteristics as given in Table 1 for the PRR7-PRR9-Y model. The model makes use of…

In plants, as in animals, the core mechanism to retain rhythmic gene expression relies on the interaction of multiple feedback loops. In recent years, molecular genetic techniques have revealed a complex network of clock components in Arabidopsis. To gain insight into the dynamics of these interactions, new components need to be integrated into the mathematical model of the plant clock. Our approach accelerates the iterative process of model identification, to incorporate new components, and to systematically test different proposed structural hypotheses. Recent studies indicate that the pseudo-response regulators PRR7 and PRR9 play a key role in the core clock of Arabidopsis. We incorporate PRR7 and PRR9 into an existing model involving the transcription factors TIMING OF CAB (TOC1), LATE ELONGATED HYPOCOTYL (LHY) and CIRCADIAN CLOCK ASSOCIATED (CCA1). We propose candidate models based on experimental hypotheses and identify the computational models with the application of an optimization routine. Validation is accomplished through systematic analysis of various mutant phenotypes. We introduce and apply sensitivity analysis as a novel tool for analyzing and distinguishing the characteristics of proposed architectures, which also allows for further validation of the hypothesized structures. link: http://identifiers.org/pubmed/17102803

Parameters:

Name Description
p1 = 7.5408 Hour_inv Reaction: => cLc; cLm, Rate Law: cytoplasm*p1*cLm
k10 = 16.4042 nM; m12 = 3.4563 nM_per_hour Reaction: cYm =>, Rate Law: nucleus*m12*cYm/(k10+cYm)
ld = 0.0 dimensionless; q1 = 13.1446 Hour_inv Reaction: => cLm; cPn, Rate Law: nucleus*ld*q1*cPn
g10 = 17.7951 nM; n7 = 4.4383 nM_per_hour; k = 1.5212 dimensionless Reaction: => cP9m; cLn, Rate Law: nucleus*n7*cLn^k/(g10^k+cLn^k)
r5 = 31.0081 Hour_inv Reaction: cXc => cXn, Rate Law: cytoplasm*r5*cXc
n3 = 1.7236 nM_per_hour; g4 = 5.6552 nM; d = 4.0627 dimensionless Reaction: => cXm; cTn, Rate Law: nucleus*n3*cTn^d/(g4^d+cTn^d)
k18 = 48.4999 nM; m20 = 0.5315 nM_per_hour Reaction: cP9c =>, Rate Law: cytoplasm*m20*cP9c/(k18+cP9c)
m4 = 7.1601 nM_per_hour; k4 = 4.7728 nM Reaction: cTm =>, Rate Law: nucleus*m4*cTm/(k4+cTm)
ld = 0.0 dimensionless; k6 = 55.3798 nM; m7 = 1.6789 nM_per_hour; lmax = 1.0 dimensionless; m8 = 11.3548 nM_per_hour Reaction: cTn =>, Rate Law: nucleus*((lmax-ld)*m7+m8)*cTn/(k6+cTn)
m21 = 8.5942 nM_per_hour; k19 = 57.4671 nM Reaction: cP9n =>, Rate Law: nucleus*m21*cP9n/(k19+cP9n)
p6 = 2.0248 Hour_inv Reaction: => cP7c; cP7m, Rate Law: cytoplasm*p6*cP7m
r8 = 37.3301 Hour_inv Reaction: cYn => cYc, Rate Law: nucleus*r8*cYn
ld = 0.0 dimensionless; p5 = 0.5 nM_per_hour; lmax = 1.0 dimensionless Reaction: => cPn, Rate Law: nucleus*(lmax-ld)*p5
r3 = 14.7607 Hour_inv Reaction: cTc => cTn, Rate Law: cytoplasm*r3*cTc
r12 = 15.4577 Hour_inv Reaction: cP9n => cP9c, Rate Law: nucleus*r12*cP9n
r6 = 12.5039 Hour_inv Reaction: cXn => cXc, Rate Law: nucleus*r6*cXn
p4 = 2.8599 Hour_inv Reaction: => cYc; cYm, Rate Law: cytoplasm*p4*cYm
r1 = 9.9378 Hour_inv Reaction: cLc => cLn, Rate Law: cytoplasm*r1*cLc
g5 = 1.5091 nM; g6 = 20.7577 nM; q2 = 12.7437 Hour_inv; n4 = 1.8828 nM_per_hour; e = 3.5723 dimensionless; ld = 0.0 dimensionless; f = 2.0127 dimensionless; n5 = 1.506 nM_per_hour Reaction: => cYm; cTn, cLn, cPn, Rate Law: nucleus*(ld*q2*cPn+(ld*n4+n5)*g5^e/(g5^e+cTn^e))*g6^f/(g6^f+cLn^f)
k13 = 1.2 nM; m15 = 1.2 nM_per_hour Reaction: cPn =>, Rate Law: nucleus*m15*cPn/(k13+cPn)
n2 = 13.5067 nM_per_hour; b = 1.5408 dimensionless; g2 = 8.733 nM; c = 1.4723 dimensionless; g3 = 17.9887 nM Reaction: => cTm; cYn, cLn, Rate Law: nucleus*n2*cYn^b/(g2^b+cYn^b)*g3^c/(g3^c+cLn^c)
k16 = 8.7977 nM; m18 = 7.8275 nM_per_hour Reaction: cP7n =>, Rate Law: nucleus*m18*cP7n/(k16+cP7n)
k8 = 9.5343 nM; m10 = 35.1982 nM_per_hour Reaction: cXc =>, Rate Law: cytoplasm*m10*cXc/(k8+cXc)
p3 = 3.1473 Hour_inv Reaction: => cXc; cXm, Rate Law: cytoplasm*p3*cXm
ld = 0.0 dimensionless; q3 = 1.0 Hour_inv Reaction: cPn =>, Rate Law: nucleus*q3*ld*cPn
k12 = 9.0406 nM; m14 = 7.5549 nM_per_hour Reaction: cYn =>, Rate Law: nucleus*m14*cYn/(k12+cYn)
r7 = 5.735 Hour_inv Reaction: cYc => cYn, Rate Law: cytoplasm*r7*cYc
r9 = 3.2996 Hour_inv Reaction: cP7c => cP7n, Rate Law: cytoplasm*r9*cP7c
r10 = 30.7684 Hour_inv Reaction: cP7n => cP7c, Rate Law: nucleus*r10*cP7n
r2 = 9.6442 Hour_inv Reaction: cLn => cLc, Rate Law: nucleus*r2*cLn
ld = 0.0 dimensionless; k5 = 3.0204 nM; m5 = 1.5511 nM_per_hour; lmax = 1.0 dimensionless; m6 = 1.4189 nM_per_hour Reaction: cTc =>, Rate Law: cytoplasm*((lmax-ld)*m5+m6)*cTc/(k5+cTc)
m16 = 10.1357 nM_per_hour; k14 = 14.0306 nM Reaction: cP7m =>, Rate Law: nucleus*m16*cP7m/(k14+cP7m)
g7 = 4.6434 nM; h = 3.3286 dimensionless; a = 1.8775 dimensionless; g1 = 11.7992 nM; n1 = 1.0988 nM_per_hour; g8 = 4.7985 nM; i = 3.5898 dimensionless Reaction: => cLm; cXn, cP7n, cP9n, Rate Law: nucleus*n1*cXn^a/(g1^a+cXn^a)*g7^h/(g7^h+cP7n^h)*g8^i/(g8^i+cP9n^i)
p2 = 1.4452 Hour_inv Reaction: => cTc; cTm, Rate Law: cytoplasm*p2*cTm
p7 = 1.0929 Hour_inv Reaction: => cP9c; cP9m, Rate Law: cytoplasm*p7*cP9m
m19 = 10.1288 nM_per_hour; k17 = 16.0706 nM Reaction: cP9m =>, Rate Law: nucleus*m19*cP9m/(k17+cP9m)
k1 = 4.1029 nM; m1 = 3.7622 nM_per_hour Reaction: cLm =>, Rate Law: nucleus*m1*cLm/(k1+cLm)
m13 = 9.1535 nM_per_hour; k11 = 55.7326 nM Reaction: cYc =>, Rate Law: cytoplasm*m13*cYc/(k11+cYc)
r11 = 9.7804 Hour_inv Reaction: cP9c => cP9n, Rate Law: cytoplasm*r11*cP9c
k7 = 29.3208 nM; m9 = 5.7847 nM_per_hour Reaction: cXm =>, Rate Law: nucleus*m9*cXm/(k7+cXm)
k15 = 19.799 nM; m17 = 7.2481 nM_per_hour Reaction: cP7c =>, Rate Law: cytoplasm*m17*cP7c/(k15+cP7c)
g9 = 4.8052 nM; n6 = 4.6039 nM_per_hour; j = 1.269 dimensionless Reaction: => cP7m; cLn, Rate Law: nucleus*n6*cLn^j/(g9^j+cLn^j)
k2 = 29.5681 nM; m2 = 22.5198 nM_per_hour Reaction: cLc =>, Rate Law: cytoplasm*m2*cLc/(k2+cLc)
r4 = 0.2559 Hour_inv Reaction: cTn => cTc, Rate Law: nucleus*r4*cTn
k3 = 18.6335 nM; m3 = 4.5545 nM_per_hour Reaction: cLn =>, Rate Law: nucleus*m3*cLn/(k3+cLn)
m11 = 7.0274 nM_per_hour; k9 = 45.1336 nM Reaction: cXn =>, Rate Law: nucleus*m11*cXn/(k9+cXn)

States:

Name Description
cXm [messenger RNA; RNA]
cTc [Two-component response regulator-like APRR1; IPR010402]
cP9c [Two-component response regulator-like APRR9]
cP7m [messenger RNA; RNA]
cTn [Two-component response regulator-like APRR1; IPR010402]
cP7c [Two-component response regulator-like APRR7]
cXc cXc
cP9n [Two-component response regulator-like APRR9]
cXn [transcription factor complex]
cYm [messenger RNA; RNA]
cLn [Protein LHY]
cYn [transcription factor complex]
cP9m [messenger RNA; RNA]
cPn cPn
cP7n [Two-component response regulator-like APRR7]
cYc cYc
cLc [Protein LHY]
cLm [messenger RNA; RNA]
cTm [messenger RNA; RNA]

Observables: none

BIOMD0000000096 @ v0.0.1

The model reproduces the time profile of cYm and cTm under light-dark cycles as depicted in Fig 4 and Fig 5 respectively…

In plants, as in animals, the core mechanism to retain rhythmic gene expression relies on the interaction of multiple feedback loops. In recent years, molecular genetic techniques have revealed a complex network of clock components in Arabidopsis. To gain insight into the dynamics of these interactions, new components need to be integrated into the mathematical model of the plant clock. Our approach accelerates the iterative process of model identification, to incorporate new components, and to systematically test different proposed structural hypotheses. Recent studies indicate that the pseudo-response regulators PRR7 and PRR9 play a key role in the core clock of Arabidopsis. We incorporate PRR7 and PRR9 into an existing model involving the transcription factors TIMING OF CAB (TOC1), LATE ELONGATED HYPOCOTYL (LHY) and CIRCADIAN CLOCK ASSOCIATED (CCA1). We propose candidate models based on experimental hypotheses and identify the computational models with the application of an optimization routine. Validation is accomplished through systematic analysis of various mutant phenotypes. We introduce and apply sensitivity analysis as a novel tool for analyzing and distinguishing the characteristics of proposed architectures, which also allows for further validation of the hypothesized structures. link: http://identifiers.org/pubmed/17102803

Parameters:

Name Description
m18 = 8.671 nM_per_hour; k16 = 42.4837 nM Reaction: cP7n =>, Rate Law: nucleus*m18*cP7n/(k16+cP7n)
k4 = 4.0551 nM; m4 = 8.5185 nM_per_hour Reaction: cTm =>, Rate Law: nucleus*m4*cTm/(k4+cTm)
m21 = 0.028 nM_per_hour; k19 = 26.5795 nM Reaction: cP9n =>, Rate Law: nucleus*m21*cP9n/(k19+cP9n)
r5 = 27.818 Hour_inv Reaction: cXc => cXn, Rate Law: cytoplasm*r5*cXc
g1 = 16.3389 nM; a = 2.2802 dimensionless; n1 = 2.3023 nM_per_hour; g7 = 0.4444 nM; g8 = 11.0459 nM; h = 2.2116 dimensionless; i = 1.1065 dimensionless Reaction: => cLm; cXn, cP7n, cP9n, Rate Law: nucleus*n1*cXn^a/(g1^a+cXn^a)*g7^h/(g7^h+cP7n^h)*g8^i/(g8^i+cP9n^i)
r4 = 33.6178 Hour_inv Reaction: cTn => cTc, Rate Law: nucleus*r4*cTn
r9 = 31.0318 Hour_inv Reaction: cP7c => cP7n, Rate Law: cytoplasm*r9*cP7c
p1 = 1.2294 Hour_inv Reaction: => cLc; cLm, Rate Law: cytoplasm*p1*cLm
k10 = 16.1162 nM; m12 = 8.4753 nM_per_hour Reaction: cYm =>, Rate Law: nucleus*m12*cYm/(k10+cYm)
k15 = 49.4094 nM; m17 = 5.4062 nM_per_hour Reaction: cP7c =>, Rate Law: cytoplasm*m17*cP7c/(k15+cP7c)
ld = 1.0 dimensionless; q1 = 7.9798 Hour_inv Reaction: => cLm; cPn, Rate Law: nucleus*ld*q1*cPn
k17 = 18.6089 nM; m19 = 6.1155 nM_per_hour Reaction: cP9m =>, Rate Law: nucleus*m19*cP9m/(k17+cP9m)
r8 = 25.8963 Hour_inv Reaction: cYn => cYc, Rate Law: nucleus*r8*cYn
r11 = 34.6266 Hour_inv Reaction: cP9c => cP9n, Rate Law: cytoplasm*r11*cP9c
p3 = 8.583 Hour_inv Reaction: => cXc; cXm, Rate Law: cytoplasm*p3*cXm
g3 = 11.5922 nM; g2 = 16.7487 nM; c = 1.6808 dimensionless; b = 3.1075 dimensionless; n2 = 7.5433 nM_per_hour Reaction: => cTm; cYn, cLn, Rate Law: nucleus*n2*cYn^b/(g2^b+cYn^b)*g3^c/(g3^c+cLn^c)
k13 = 1.2 nM; m15 = 1.2 nM_per_hour Reaction: cPn =>, Rate Law: nucleus*m15*cPn/(k13+cPn)
p7 = 10.4532 Hour_inv Reaction: => cP9c; cP9m, Rate Law: cytoplasm*p7*cP9m
p5 = 0.5 nM_per_hour; ld = 1.0 dimensionless; lmax = 1.0 dimensionless Reaction: => cPn, Rate Law: nucleus*(lmax-ld)*p5
k5 = 16.9133 nM; m6 = 10.899 nM_per_hour; ld = 1.0 dimensionless; m5 = 9.3024 nM_per_hour; lmax = 1.0 dimensionless Reaction: cTc =>, Rate Law: cytoplasm*((lmax-ld)*m5+m6)*cTc/(k5+cTc)
g6 = 7.8469 nM; n4 = 1.5293 nM_per_hour; e = 1.4943 dimensionless; f = 1.9491 dimensionless; n5 = 2.6296 nM_per_hour; q2 = 2.5505 Hour_inv; ld = 1.0 dimensionless; g5 = 0.5061 nM Reaction: => cYm; cTn, cLn, cPn, Rate Law: nucleus*(ld*q2*cPn+(ld*n4+n5)*g5^e/(g5^e+cTn^e))*g6^f/(g6^f+cLn^f)
m7 = 0.7527 nM_per_hour; m8 = 13.7459 nM_per_hour; ld = 1.0 dimensionless; k6 = 43.7049 nM; lmax = 1.0 dimensionless Reaction: cTn =>, Rate Law: nucleus*((lmax-ld)*m7+m8)*cTn/(k6+cTn)
r10 = 0.4557 Hour_inv Reaction: cP7n => cP7c, Rate Law: nucleus*r10*cP7n
p4 = 14.6828 Hour_inv Reaction: => cYc; cYm, Rate Law: cytoplasm*p4*cYm
ld = 1.0 dimensionless; q3 = 1.0 Hour_inv Reaction: cPn =>, Rate Law: nucleus*q3*ld*cPn
k8 = 13.4324 nM; m10 = 9.2511 nM_per_hour Reaction: cXc =>, Rate Law: cytoplasm*m10*cXc/(k8+cXc)
r1 = 31.5166 Hour_inv Reaction: cLc => cLn, Rate Law: cytoplasm*r1*cLc
p2 = 1.0494 Hour_inv Reaction: => cTc; cTm, Rate Law: cytoplasm*p2*cTm
r7 = 9.1917 Hour_inv Reaction: cYc => cYn, Rate Law: cytoplasm*r7*cYc
k3 = 29.0823 nM; m3 = 12.7853 nM_per_hour Reaction: cLn =>, Rate Law: nucleus*m3*cLn/(k3+cLn)
k9 = 14.605 nM; m11 = 7.9066 nM_per_hour Reaction: cXn =>, Rate Law: nucleus*m11*cXn/(k9+cXn)
d = 1.0164 dimensionless; g4 = 11.3625 nM; n3 = 0.6703 nM_per_hour Reaction: => cXm; cTn, Rate Law: nucleus*n3*cTn^d/(g4^d+cTn^d)
m2 = 10.4609 nM_per_hour; k2 = 32.7881 nM Reaction: cLc =>, Rate Law: cytoplasm*m2*cLc/(k2+cLc)
m20 = 3.4152 nM_per_hour; k18 = 16.2407 nM Reaction: cP9c =>, Rate Law: cytoplasm*m20*cP9c/(k18+cP9c)
r6 = 4.2863 Hour_inv Reaction: cXn => cXc, Rate Law: nucleus*r6*cXn
m16 = 9.531 nM_per_hour; k14 = 50.9418 nM Reaction: cP7m =>, Rate Law: nucleus*m16*cP7m/(k14+cP7m)
k11 = 48.5862 nM; m13 = 6.8544 nM_per_hour Reaction: cYc =>, Rate Law: cytoplasm*m13*cYc/(k11+cYc)
j = 2.5579 dimensionless; g9 = 14.5219 nM; n6 = 11.3117 nM_per_hour Reaction: => cP7m; cLn, Rate Law: nucleus*n6*cLn^j/(g9^j+cLn^j)
k1 = 22.3951 nM; m1 = 8.0568 nM_per_hour Reaction: cLm =>, Rate Law: nucleus*m1*cLm/(k1+cLm)
p6 = 6.7738 Hour_inv Reaction: => cP7c; cP7m, Rate Law: cytoplasm*p6*cP7m
r3 = 29.4222 Hour_inv Reaction: cTc => cTn, Rate Law: cytoplasm*r3*cTc
m9 = 2.6345 nM_per_hour; k7 = 8.6873 nM Reaction: cXm =>, Rate Law: nucleus*m9*cXm/(k7+cXm)
r2 = 9.1138 Hour_inv Reaction: cLn => cLc, Rate Law: nucleus*r2*cLn
m14 = 3.2581 nM_per_hour; k12 = 23.2876 nM Reaction: cYn =>, Rate Law: nucleus*m14*cYn/(k12+cYn)
r12 = 22.838 Hour_inv Reaction: cP9n => cP9c, Rate Law: nucleus*r12*cP9n
k = 3.3953 dimensionless; g10 = 5.6855 nM; n8 = 2.0738 nM; ld = 1.0 dimensionless; n7 = 0.0833 nM_per_hour; q4 = 7.4548 Hour_inv Reaction: => cP9m; cPn, cLn, Rate Law: (ld*q4*cPn+n7*ld+n8)*cLn^k/(g10^k+cLn^k)

States:

Name Description
cXm [messenger RNA; RNA]
cTc [Two-component response regulator-like APRR1; IPR010402]
cP9c [Two-component response regulator-like APRR9]
cP7m [messenger RNA; RNA]
cTn [Two-component response regulator-like APRR1]
cXc cXc
cP7c [Two-component response regulator-like APRR7]
cP9n [Two-component response regulator-like APRR9]
cXn [transcription factor complex]
cYm [messenger RNA; RNA]
cLn [Protein LHY]
cYn [transcription factor complex]
cPn cPn
cP9m [messenger RNA; RNA]
cP7n [Two-component response regulator-like APRR7]
cYc cYc
cLc [Protein LHY]
cLm [messenger RNA; RNA]
cTm [messenger RNA; RNA]

Observables: none

BIOMD0000000097 @ v0.0.1

The model reproduces the time profile of TOC1 and Y mRNA for a 8:16 cycle as depicted in Fig7A and 7B. A simple algorith…

In plants, as in animals, the core mechanism to retain rhythmic gene expression relies on the interaction of multiple feedback loops. In recent years, molecular genetic techniques have revealed a complex network of clock components in Arabidopsis. To gain insight into the dynamics of these interactions, new components need to be integrated into the mathematical model of the plant clock. Our approach accelerates the iterative process of model identification, to incorporate new components, and to systematically test different proposed structural hypotheses. Recent studies indicate that the pseudo-response regulators PRR7 and PRR9 play a key role in the core clock of Arabidopsis. We incorporate PRR7 and PRR9 into an existing model involving the transcription factors TIMING OF CAB (TOC1), LATE ELONGATED HYPOCOTYL (LHY) and CIRCADIAN CLOCK ASSOCIATED (CCA1). We propose candidate models based on experimental hypotheses and identify the computational models with the application of an optimization routine. Validation is accomplished through systematic analysis of various mutant phenotypes. We introduce and apply sensitivity analysis as a novel tool for analyzing and distinguishing the characteristics of proposed architectures, which also allows for further validation of the hypothesized structures. link: http://identifiers.org/pubmed/17102803

Parameters:

Name Description
m1 = 6.8248 nM_per_hour; k1 = 13.0594 nM Reaction: cLm =>, Rate Law: nucleus*m1*cLm/(k1+cLm)
r12 = 27.2451 Hour_inv Reaction: cP9n => cP9c, Rate Law: nucleus*r12*cP9n
r3 = 51.1965 Hour_inv Reaction: cTc => cTn, Rate Law: cytoplasm*r3*cTc
r9 = 24.5689 Hour_inv Reaction: cP7c => cP7n, Rate Law: cytoplasm*r9*cP7c
m19 = 1.9234 nM_per_hour; k17 = 9.8065 nM Reaction: cP9m =>, Rate Law: nucleus*m19*cP9m/(k17+cP9m)
p4 = 6.0042 Hour_inv Reaction: => cYc; cYm, Rate Law: cytoplasm*p4*cYm
r1 = 25.6818 Hour_inv Reaction: cLc => cLn, Rate Law: cytoplasm*r1*cLc
m7 = 1.1032 nM_per_hour; m8 = 2.2006 nM_per_hour; k6 = 56.7596 nM; ld = 1.0 dimensionless; lmax = 1.0 dimensionless Reaction: cTn =>, Rate Law: nucleus*((lmax-ld)*m7+m8)*cTn/(k6+cTn)
r8 = 27.9229 Hour_inv Reaction: cYn => cYc, Rate Law: nucleus*r8*cYn
r7 = 35.7842 Hour_inv Reaction: cYc => cYn, Rate Law: cytoplasm*r7*cYc
r2 = 3.9781 Hour_inv Reaction: cLn => cLc, Rate Law: nucleus*r2*cLn
r10 = 0.5024 Hour_inv Reaction: cP7n => cP7c, Rate Law: nucleus*r10*cP7n
r6 = 4.5034 Hour_inv Reaction: cXn => cXc, Rate Law: nucleus*r6*cXn
m21 = 0.0193 nM_per_hour; k19 = 21.6441 nM Reaction: cP9n =>, Rate Law: nucleus*m21*cP9n/(k19+cP9n)
g5 = 1.5987 nM; e = 2.4146 dimensionless; n4 = 1.7832 nM_per_hour; n5 = 7.4615 nM_per_hour; f = 2.1349 dimensionless; ld = 1.0 dimensionless; g6 = 16.489 nM Reaction: => cYm; cTn, cLn, cPn, Rate Law: nucleus*(ld*n4+n5)*g5^e/(g5^e+cTn^e)*g6^f/(g6^f+cLn^f)
p1 = 0.6926 Hour_inv Reaction: => cLc; cLm, Rate Law: cytoplasm*p1*cLm
k15 = 32.939 nM; m17 = 3.6143 nM_per_hour Reaction: cP7c =>, Rate Law: cytoplasm*m17*cP7c/(k15+cP7c)
k18 = 25.9739 nM; m20 = 3.7484 nM_per_hour Reaction: cP9c =>, Rate Law: cytoplasm*m20*cP9c/(k18+cP9c)
p3 = 6.9124 Hour_inv Reaction: => cXc; cXm, Rate Law: cytoplasm*p3*cXm
k13 = 1.2 nM; m15 = 1.2 nM_per_hour Reaction: cPn =>, Rate Law: nucleus*m15*cPn/(k13+cPn)
m11 = 23.5996 nM_per_hour; k9 = 15.0626 nM Reaction: cXn =>, Rate Law: nucleus*m11*cXn/(k9+cXn)
p5 = 0.5 nM_per_hour; ld = 1.0 dimensionless; lmax = 1.0 dimensionless Reaction: => cPn, Rate Law: nucleus*(lmax-ld)*p5
r11 = 25.7542 Hour_inv Reaction: cP9c => cP9n, Rate Law: cytoplasm*r11*cP9c
n3 = 2.4751 nM_per_hour; g4 = 20.5277 nM; d = 1.3058 dimensionless Reaction: => cXm; cTn, Rate Law: nucleus*n3*cTn^d/(g4^d+cTn^d)
m14 = 8.1796 nM_per_hour; k12 = 21.8348 nM Reaction: cYn =>, Rate Law: nucleus*m14*cYn/(k12+cYn)
ld = 1.0 dimensionless; q3 = 1.0 Hour_inv Reaction: cPn =>, Rate Law: nucleus*q3*ld*cPn
g2 = 16.6598 nM; g3 = 13.4112 nM; n2 = 11.6086 nM_per_hour; c = 1.4509 dimensionless; b = 4.2126 dimensionless Reaction: => cTm; cYn, cLn, Rate Law: nucleus*n2*cYn^b/(g2^b+cYn^b)*g3^c/(g3^c+cLn^c)
m10 = 8.5523 nM_per_hour; k8 = 12.528 nM Reaction: cXc =>, Rate Law: cytoplasm*m10*cXc/(k8+cXc)
r4 = 8.9147 Hour_inv Reaction: cTn => cTc, Rate Law: nucleus*r4*cTn
g9 = 20.3795 nM; n6 = 11.0924 nM_per_hour; j = 1.7615 dimensionless Reaction: => cP7m; cLn, Rate Law: nucleus*n6*cLn^j/(g9^j+cLn^j)
m3 = 13.7795 nM_per_hour; k3 = 33.514 nM Reaction: cLn =>, Rate Law: nucleus*m3*cLn/(k3+cLn)
m13 = 7.5959 nM_per_hour; k11 = 26.9638 nM Reaction: cYc =>, Rate Law: cytoplasm*m13*cYc/(k11+cYc)
p7 = 1.5323 Hour_inv Reaction: => cP9c; cP9m, Rate Law: cytoplasm*p7*cP9m
ld = 1.0 dimensionless; q1 = 13.4334 Hour_inv Reaction: => cLm; cPn, Rate Law: nucleus*ld*q1*cPn
k2 = 30.5639 nM; m2 = 9.4099 nM_per_hour Reaction: cLc =>, Rate Law: cytoplasm*m2*cLc/(k2+cLc)
p6 = 9.8416 Hour_inv Reaction: => cP7c; cP7m, Rate Law: cytoplasm*p6*cP7m
m6 = 9.5754 nM_per_hour; k5 = 34.2078 nM; ld = 1.0 dimensionless; m5 = 7.2129 nM_per_hour; lmax = 1.0 dimensionless Reaction: cTc =>, Rate Law: cytoplasm*((lmax-ld)*m5+m6)*cTc/(k5+cTc)
m12 = 5.9504 nM_per_hour; k10 = 11.5688 nM Reaction: cYm =>, Rate Law: nucleus*m12*cYm/(k10+cYm)
k16 = 24.451 nM; m18 = 6.7455 nM_per_hour Reaction: cP7n =>, Rate Law: nucleus*m18*cP7n/(k16+cP7n)
m9 = 4.2193 nM_per_hour; k7 = 14.9114 nM Reaction: cXm =>, Rate Law: nucleus*m9*cXm/(k7+cXm)
p2 = 0.5403 Hour_inv Reaction: => cTc; cTm, Rate Law: cytoplasm*p2*cTm
h = 1.4176 dimensionless; g7 = 0.2778 nM; n1 = 3.2016 nM_per_hour; g8 = 0.9187 nM; g1 = 9.041 nM; i = 2.0074 dimensionless; a = 1.2497 dimensionless Reaction: => cLm; cXn, cP7n, cP9n, Rate Law: nucleus*n1*cXn^a/(g1^a+cXn^a)*g7^h/(g7^h+cP7n^h)*g8^i/(g8^i+cP9n^i)
r5 = 29.4607 Hour_inv Reaction: cXc => cXn, Rate Law: cytoplasm*r5*cXc
k4 = 1.3722 nM; m4 = 12.1232 nM_per_hour Reaction: cTm =>, Rate Law: nucleus*m4*cTm/(k4+cTm)
k14 = 51.261 nM; m16 = 9.3186 nM_per_hour Reaction: cP7m =>, Rate Law: nucleus*m16*cP7m/(k14+cP7m)
n7 = 0.1031 nM_per_hour; k = 3.8877 dimensionless; g10 = 5.8418 nM; ld = 1.0 dimensionless; q4 = 6.274 Hour_inv; n8 = 3.5262 nM Reaction: => cP9m; cPn, cLn, Rate Law: nucleus*(ld*q4*cPn+n7*ld+n8)*cLn^k/(g10^k+cLn^k)

States:

Name Description
cXm [messenger RNA; RNA]
cTc [Two-component response regulator-like APRR1; IPR010402]
cP9c [Two-component response regulator-like APRR9]
cP7m [messenger RNA; RNA]
cTn [Two-component response regulator-like APRR1; IPR010402]
cXc cXc
cP7c [Two-component response regulator-like APRR7]
cP9n [Two-component response regulator-like APRR9]
cXn [transcription factor complex]
cYm [messenger RNA; RNA]
cLn [Protein LHY]
cYn [transcription factor complex]
cPn cPn
cP9m [messenger RNA; RNA]
cP7n [Two-component response regulator-like APRR7]
cYc cYc
cLc [Protein LHY]
cLm [messenger RNA; RNA]
cTm [messenger RNA; RNA]

Observables: none

MODEL6962035527 @ v0.0.1

This the model describing the action potentials of the peripheral rabbit sinoatrial node from the article: Mathematica…

Mathematical models of the action potential in the periphery and center of the rabbit sinoatrial (SA) node have been developed on the basis of published experimental data. Simulated action potentials are consistent with those recorded experimentally: the model-generated peripheral action potential has a more negative takeoff potential, faster upstroke, more positive peak value, prominent phase 1 repolarization, greater amplitude, shorter duration, and more negative maximum diastolic potential than the model-generated central action potential. In addition, the model peripheral cell shows faster pacemaking. The models behave qualitatively the same as tissue from the periphery and center of the SA node in response to block of tetrodotoxin-sensitive Na(+) current, L- and T-type Ca(2+) currents, 4-aminopyridine-sensitive transient outward current, rapid and slow delayed rectifying K(+) currents, and hyperpolarization-activated current. A one-dimensional model of a string of SA node tissue, incorporating regional heterogeneity, coupled to a string of atrial tissue has been constructed to simulate the behavior of the intact SA node. In the one-dimensional model, the spontaneous action potential initiated in the center propagates to the periphery at approximately 0.06 m/s and then into the atrial muscle at 0.62 m/s. link: http://identifiers.org/pubmed/10899081

Parameters: none

States: none

Observables: none

Its a mechanistic model explaining the impact of p53 om apoptosis decision. This model represents schema 1 of manuscript…

The transcription factor p53 plays a central role in maintaining genomic integrity. Recent experiments in MCF7 cells have shown that p53 protein level rises and falls in distinct pulses in response to DNA damage. The amplitudes of and intervals between pulses seem to be independent of the extent of damage, and some cells generate regular pulses of p53 over many days. Identifying the molecular mechanisms responsible for such interesting behavior is an important and challenging problem. This paper describes four dual-feedback mechanisms that combine both positive and negative feedback loops, which have been identified in the signaling network responsible for p53 regulation. Mathematical models of all four mechanisms are analyzed to determine if they are consistent with experimental observations and to characterize subtle differences among the possible mechanisms. In addition, a novel molecular mechanism is proposed whereby p53 pulses may induce, at first, cell cycle arrest and, if sustained, cell death. The proposal accounts for basic features of p53-mediated responses to DNA damage and suggests new experiments to probe the dynamics of p53 signaling. link: http://identifiers.org/pubmed/17245126

Parameters: none

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Observables: none

Its a mechanistic model explaining the impact of p53 on apoptosis decision. This model represents schema 2 of manuscript…

The transcription factor p53 plays a central role in maintaining genomic integrity. Recent experiments in MCF7 cells have shown that p53 protein level rises and falls in distinct pulses in response to DNA damage. The amplitudes of and intervals between pulses seem to be independent of the extent of damage, and some cells generate regular pulses of p53 over many days. Identifying the molecular mechanisms responsible for such interesting behavior is an important and challenging problem. This paper describes four dual-feedback mechanisms that combine both positive and negative feedback loops, which have been identified in the signaling network responsible for p53 regulation. Mathematical models of all four mechanisms are analyzed to determine if they are consistent with experimental observations and to characterize subtle differences among the possible mechanisms. In addition, a novel molecular mechanism is proposed whereby p53 pulses may induce, at first, cell cycle arrest and, if sustained, cell death. The proposal accounts for basic features of p53-mediated responses to DNA damage and suggests new experiments to probe the dynamics of p53 signaling. link: http://identifiers.org/pubmed/17245126

Parameters: none

States: none

Observables: none

It's a mechanistic model explaining the impact of p53 on apoptosis decision. This model represents schema 3 of manuscrip…

The transcription factor p53 plays a central role in maintaining genomic integrity. Recent experiments in MCF7 cells have shown that p53 protein level rises and falls in distinct pulses in response to DNA damage. The amplitudes of and intervals between pulses seem to be independent of the extent of damage, and some cells generate regular pulses of p53 over many days. Identifying the molecular mechanisms responsible for such interesting behavior is an important and challenging problem. This paper describes four dual-feedback mechanisms that combine both positive and negative feedback loops, which have been identified in the signaling network responsible for p53 regulation. Mathematical models of all four mechanisms are analyzed to determine if they are consistent with experimental observations and to characterize subtle differences among the possible mechanisms. In addition, a novel molecular mechanism is proposed whereby p53 pulses may induce, at first, cell cycle arrest and, if sustained, cell death. The proposal accounts for basic features of p53-mediated responses to DNA damage and suggests new experiments to probe the dynamics of p53 signaling. link: http://identifiers.org/pubmed/17245126

Parameters: none

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Observables: none

Zhang2009 - Genome-scale metabolic network of Thermotoga maritimaThis model is described in the article: [Three-dimensi…

Metabolic pathways have traditionally been described in terms of biochemical reactions and metabolites. With the use of structural genomics and systems biology, we generated a three-dimensional reconstruction of the central metabolic network of the bacterium Thermotoga maritima. The network encompassed 478 proteins, of which 120 were determined by experiment and 358 were modeled. Structural analysis revealed that proteins forming the network are dominated by a small number (only 182) of basic shapes (folds) performing diverse but mostly related functions. Most of these folds are already present in the essential core (approximately 30%) of the network, and its expansion by nonessential proteins is achieved with relatively few additional folds. Thus, integration of structural data with networks analysis generates insight into the function, mechanism, and evolution of biological networks. link: http://identifiers.org/pubmed/19762644

Parameters: none

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Observables: none

Does not reproduce publication figure 3

Existing experimental data have shown hypoxia to be an important factor affecting the proliferation of mesenchymal stromal cells (MSCs), but the contrasting observations made at various hypoxic levels raise the questions of whether hypoxia accelerates proliferation, and how. On the other hand, in order to meet the increasing demand of MSCs, an optimised bioreactor control strategy is needed to enhance in vitro production.A comprehensive, single-cell mathematical model has been constructed in this work, which combines cellular oxygen sensing with hypoxia-mediated cell cycle progression to predict cell cycle commitment as a proxy to proliferation rate. With oxygen levels defined for in vitro cell culture, the model predicts enhanced proliferation under intermediate (2-8%) and mild (8-15%) hypoxia and cell quiescence under severe (< 2%) hypoxia. Global sensitivity analysis and quasi-Monte Carlo simulation revealed that within a certain range (+/- 100%), model parameters affect (with varying significance) the minimum commitment time, but the existence of a range of optimal oxygen tension could be preserved with the hypothesized effects of Hif2α and reactive oxygen species (ROS). It appears that Hif2α counteracts Hif1α and ROS-mediated protein deactivation under intermediate hypoxia and normoxia (20%), respectively, to regulate the response of cell cycle commitment to oxygen tension.Overall, this modelling study offered an integrative framework to capture several interacting mechanisms and allowed in silico analysis of their individual and collective roles in shaping the hypoxia-mediated commitment to cell cycle. The model offers a starting point to the establishment of a suitable mechanism that can satisfactorily explain the different existing experimental observations from different studies, and warrants future extension and dedicated experimental validation to eventually support bioreactor optimisation. link: http://identifiers.org/pubmed/29606139

Parameters: none

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Observables: none

This is an auto-generated model with COBRA Matlab toolbox.

The availability of genome sequences, annotations and knowledge of the biochemistry underlying metabolic transformations has led to the generation of metabolic network reconstructions for a wide range of organisms in bacteria, archaea, and eukaryotes. When modeled using mathematical representations, a reconstruction can simulate underlying genotype-phenotype relationships. Accordingly, genome-scale metabolic models (GEMs) can be used to predict the response of organisms to genetic and environmental variations. A bottom-up reconstruction procedure typically starts by generating a draft model from existing annotation data on a target organism. For model species, this part of the process can be straightforward, due to the abundant organism-specific biochemical data. However, the process becomes complicated for non-model less-annotated species. In this paper, we present a draft liver reconstruction, ReCodLiver0.9, of Atlantic cod (Gadus morhua), a non-model teleost fish, as a practicable guide for cases with comparably few resources. Although the reconstruction is considered a draft version, we show that it already has utility in elucidating metabolic response mechanisms to environmental toxicants by mapping gene expression data of exposure experiments to the resulting model. link: http://identifiers.org/doi/10.3389/fmolb.2020.591406

Parameters: none

States: none

Observables: none

This is an auto-generated model with COBRA Matlab toolbox.

The availability of genome sequences, annotations and knowledge of the biochemistry underlying metabolic transformations has led to the generation of metabolic network reconstructions for a wide range of organisms in bacteria, archaea, and eukaryotes. When modeled using mathematical representations, a reconstruction can simulate underlying genotype-phenotype relationships. Accordingly, genome-scale metabolic models (GEMs) can be used to predict the response of organisms to genetic and environmental variations. A bottom-up reconstruction procedure typically starts by generating a draft model from existing annotation data on a target organism. For model species, this part of the process can be straightforward, due to the abundant organism-specific biochemical data. However, the process becomes complicated for non-model less-annotated species. In this paper, we present a draft liver reconstruction, ReCodLiver0.9, of Atlantic cod (Gadus morhua), a non-model teleost fish, as a practicable guide for cases with comparably few resources. Although the reconstruction is considered a draft version, we show that it already has utility in elucidating metabolic response mechanisms to environmental toxicants by mapping gene expression data of exposure experiments to the resulting model. link: http://identifiers.org/doi/10.3389/fmolb.2020.591406

Parameters: none

States: none

Observables: none

This is an auto-generated model with COBRA Matlab toolbox. The gadMorTrinigy de novo Trinity transcript assembly and pep…

The availability of genome sequences, annotations and knowledge of the biochemistry underlying metabolic transformations has led to the generation of metabolic network reconstructions for a wide range of organisms in bacteria, archaea, and eukaryotes. When modeled using mathematical representations, a reconstruction can simulate underlying genotype-phenotype relationships. Accordingly, genome-scale metabolic models (GEMs) can be used to predict the response of organisms to genetic and environmental variations. A bottom-up reconstruction procedure typically starts by generating a draft model from existing annotation data on a target organism. For model species, this part of the process can be straightforward, due to the abundant organism-specific biochemical data. However, the process becomes complicated for non-model less-annotated species. In this paper, we present a draft liver reconstruction, ReCodLiver0.9, of Atlantic cod (Gadus morhua), a non-model teleost fish, as a practicable guide for cases with comparably few resources. Although the reconstruction is considered a draft version, we show that it already has utility in elucidating metabolic response mechanisms to environmental toxicants by mapping gene expression data of exposure experiments to the resulting model. link: http://identifiers.org/doi/10.3389/fmolb.2020.591406

Parameters: none

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Observables: none

Background - The coronavirus disease 2019 (COVID-19) is rapidly spreading in China and more than 30 countries over last…

Background:The coronavirus disease 2019 (COVID-19) is rapidly spreading in China and more than 30 countries over last two months. COVID-19 has multiple characteristics distinct from other infectious diseases, including high infectivity during incubation, time delay between real dynamics and daily observed number of confirmed cases, and the intervention effects of implemented quarantine and control measures. Methods:We develop a Susceptible, Un-quanrantined infected, Quarantined infected, Confirmed infected (SUQC) model to characterize the dynamics of COVID-19 and explicitly parameterize the intervention effects of control measures, which is more suitable for analysis than other existing epidemic models. Results:The SUQC model is applied to the daily released data of the confirmed infections to analyze the outbreak of COVID-19 in Wuhan, Hubei (excluding Wuhan), China (excluding Hubei) and four first-tier cities of China. We found that, before January 30, 2020, all these regions except Beijing had a reproductive number R &gt; 1, and after January 30, all regions had a reproductive number R &lt; 1, indicating that the quarantine and control measures are effective in preventing the spread of COVID-19. The confirmation rate of Wuhan estimated by our model is 0.0643, substantially lower than that of Hubei excluding Wuhan (0.1914), and that of China excluding Hubei (0.2189), but it jumps to 0.3229 after February 12 when clinical evidence was adopted in new diagnosis guidelines. The number of unquarantined infected cases in Wuhan on February 12, 2020 is estimated to be 3,509 and declines to 334 on February 21, 2020. After fitting the model with data as of February 21, 2020, we predict that the end time of COVID-19 in Wuhan and Hubei is around late March, around mid March for China excluding Hubei, and before early March 2020 for the four tier-one cities. A total of 80,511 individuals are estimated to be infected in China, among which 49,510 are from Wuhan, 17,679 from Hubei (excluding Wuhan), and the rest 13,322 from other regions of China (excluding Hubei). Note that the estimates are from a deterministic ODE model and should be interpreted with some uncertainty. Conclusions:We suggest that rigorous quarantine and control measures should be kept before early March in Beijing, Shanghai, Guangzhou and Shenzhen, and before late March in Hubei. The model can also be useful to predict the trend of epidemic and provide quantitative guide for other countries at high risk of outbreak, such as South Korea, Japan, Italy and Iran. Supplementary Materials:The supplementary materials can be found online with this article at 10.1007/s40484-020-0199-0. link: http://identifiers.org/pubmed/32219006

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Observables: none

Blood coagulation model investigating effects of Xa-inhibitors (Rivaroxaban and Apixaban). Model is an extension of Pohl…

Factor Xa (FXa) emerged as a promising target for effective anticoagulation and several FXa inhibitors are now available for the prevention of venous thromboembolism. However, in previously reported pharmacokinetic/pharmacodynamic (PK/PD) models, the complex coagulation processes and detailed information of drug action are usually unclear, which makes it difficult to predict clinical outcome at the drug discovery stage. In this study, a large-scale systems pharmacology model was developed based on several published models and clinical data. It takes into account all pathways of the coagulation network, and captures drug-specific features: plasma pharmacokinetics and drug-target binding kinetics (BKs). We aimed to predict the anticoagulation effects of FXa inhibitors in healthy subjects, and to use this model to compare the effects of compounds with different binding properties. Our model predicts the clotting time and anti-FXa effects and could thus serve as a predictive tool for the anticoagulant potential of a new compound. link: http://identifiers.org/pubmed/26783501

Parameters: none

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Observables: none

Zhou2015 - Circadian clock with immune regulator NPR1Arabidopsis clock model modified from P2012 (Pokhilko et al., 2013…

Recent studies have shown that in addition to the transcriptional circadian clock, many organisms, including Arabidopsis, have a circadian redox rhythm driven by the organism's metabolic activities. It has been hypothesized that the redox rhythm is linked to the circadian clock, but the mechanism and the biological significance of this link have only begun to be investigated. Here we report that the master immune regulator NPR1 (non-expressor of pathogenesis-related gene 1) of Arabidopsis is a sensor of the plant's redox state and regulates transcription of core circadian clock genes even in the absence of pathogen challenge. Surprisingly, acute perturbation in the redox status triggered by the immune signal salicylic acid does not compromise the circadian clock but rather leads to its reinforcement. Mathematical modelling and subsequent experiments show that NPR1 reinforces the circadian clock without changing the period by regulating both the morning and the evening clock genes. This balanced network architecture helps plants gate their immune responses towards the morning and minimize costs on growth at night. Our study demonstrates how a sensitive redox rhythm interacts with a robust circadian clock to ensure proper responsiveness to environmental stimuli without compromising fitness of the organism. link: http://identifiers.org/pubmed/26098366

Parameters:

Name Description
n4 = 0.04; L = 1.0; n7 = 0.1; g9 = 0.3; parameter_7 = 2.0; e = 2.0; g8 = 0.04; parameter_2 = 0.4; q3 = 3.0 Reaction: => cP9_m; cP, cL, cEC, cT, cEC, cL, cP, cT, Rate Law: def*parameter_2^parameter_7/(parameter_2^parameter_7+cT^parameter_7)*(L*q3*cP+(n4+n7*cL^e/(cL^e+g9^e))*g8/(cEC+g8))
n13 = 2.0; parameter_7 = 2.0; parameter_3 = 0.4; g2 = 0.01; e = 2.0; g6 = 0.3 Reaction: => cLUX_m; cT, cEC, cL, cEC, cL, cT, Rate Law: def*parameter_3^parameter_7/(parameter_3^parameter_7+cT^parameter_7)*n13*g2/(cEC+g2)*g6^e/(cL^e+g6^e)/def
p17 = 17.0 Reaction: cE3 + cG => cEG; cE3, cG, Rate Law: def*p17*cE3*cG/def
p16 = 0.62 Reaction: => cE3; cE3_m, cE3_m, Rate Law: def*p16*cE3_m/def
m16 = 0.5 Reaction: cNI_m => ; cNI_m, Rate Law: def*m16*cNI_m/def
m29 = 0.3 Reaction: species_4 => ; species_4, Rate Law: default*m29*species_4/def
p1 = 0.13; L = 1.0; p2 = 0.27 Reaction: => cL; cL_m, cL_m, Rate Law: def*cL_m*(p1*L+p2)
parameter_29 = 1.0; parameter_28 = 0.2; parameter_9 = 2.0; parameter_18 = 1.0; parameter_16 = 0.2 Reaction: => species_2; species_1, species_1, Rate Law: default*parameter_28*parameter_16^parameter_9/((0.5*((parameter_29+species_1+parameter_18)-((parameter_29+species_1+parameter_18)^2-4*parameter_29*species_1)^(1/2)))^parameter_9+parameter_16^parameter_9)/def
L = 1.0; m11 = 1.0 Reaction: cP => ; cP, Rate Law: def*m11*cP*L
p8 = 0.6 Reaction: => cP9; cP9_m, cP9_m, Rate Law: def*p8*cP9_m/def
p17 = 17.0; p29 = 0.1; m19 = 0.9; p28 = 2.0 Reaction: cG => ; cE3n, cE3n, cG, Rate Law: def*((m19*cG+p28*cG)-p29*p28*cG/(p29+m19+p17*cE3n))/def
m30 = 1.0 Reaction: species_3 => ; species_2, species_2, species_3, Rate Law: default*m30*species_3*species_2/def
m32 = 0.2; parameter_26 = 0.1; m19 = 0.9; m10 = 0.1; p29 = 0.1; d = 2.0; p17 = 17.0; L = 1.0; p24 = 11.0; p18 = 4.0; p28 = 2.0; m9 = 0.2; g7 = 1.0 Reaction: cEC => ; cCOP1n, cCOP1d, cG, cE3n, cEG, cCOP1d, cCOP1n, cE3n, cEC, cEG, cG, Rate Law: def*(m10*cCOP1n*cEC+m9*cCOP1d*cEC+m32*cEC*(1+p24*L*(p28*cG/(p29+m19+p17*cE3n)+(p18*cEG+p17*cE3n*p28*cG/(p29+m19+p17*cE3n))/(m10*cCOP1n+m9*cCOP1d+parameter_26))^d/((p28*cG/(p29+m19+p17*cE3n)+(p18*cEG+p17*cE3n*p28*cG/(p29+m19+p17*cE3n))/(m10*cCOP1n+m9*cCOP1d+parameter_26))^d+g7^d)))
parameter_7 = 2.0; g12 = 0.1; n10 = 0.3; e = 2.0; n11 = 0.6; b = 2.0; parameter_12 = 0.6; g13 = 1.0 Reaction: => cNI_m; cT, cLm, cP7, cLm, cP7, cT, Rate Law: def*parameter_12^parameter_7/(parameter_12^parameter_7+cT^parameter_7)*(n10*cLm^e/(cLm^e+g12^e)+n11*cP7^b/(cP7^b+g13^b))/def
L = 1.0; p7 = 0.3 Reaction: => cP; cP, Rate Law: def*p7*(1-L)*(1-cP)
g11 = 0.7; parameter_7 = 2.0; g10 = 0.5; n9 = 0.6; e = 2.0; f = 2.0; n8 = 0.5; F_PRR7 = 1.0; parameter_6 = 0.1 Reaction: => cP7_m; cL, cLm, cP9, cT, cL, cLm, cP9, cT, Rate Law: def*F_PRR7*parameter_6^parameter_7/(parameter_6^parameter_7+cT^parameter_7)*(n8*(cLm+cL)^e/((cLm+cL)^e+g10^e)+n9*cP9^f/(cP9^f+g11^f))/def
g16 = 0.3; e = 2.0; n3 = 0.29 Reaction: => cE3_m; cL, cL, Rate Law: def*n3*g16^e/(cL^e+g16^e)/def
L = 1.0; m33 = 13.0; m31 = 0.1 Reaction: cCOP1d => ; cCOP1d, Rate Law: def*m31*(1+m33*(1-L))*cCOP1d
p3 = 0.1; c = 2.0; g3 = 0.6 Reaction: => cLm; cL, cL, Rate Law: def*p3*cL^c/(cL^c+g3^c)/def
p23 = 0.37 Reaction: => cE4; cE4_m, cE4_m, Rate Law: def*p23*cE4_m/def
m23 = 0.5; L = 1.0; m15 = 0.7 Reaction: cP7 => ; cP7, Rate Law: def*(m15+m23*(1-L))*cP7
p27 = 0.8 Reaction: => cLUX; cLUX_m, cLUX_m, Rate Law: def*p27*cLUX_m/def
p4 = 0.5 Reaction: => cT; cT_m, cT_m, Rate Law: def*p4*cT_m/def
m20 = 0.6 Reaction: cZTL => ; cZTL, Rate Law: def*m20*cZTL/def
L = 1.0; m7 = 0.1; p5 = 1.0; m6 = 0.2; m8 = 0.5 Reaction: cT => ; cZTL, cZG, cT, cZG, cZTL, Rate Law: def*((m6+m7*(1-L))*cT*(p5*cZTL+cZG)+m8*cT)
p17 = 17.0; p26 = 0.3; m19 = 0.9; p28 = 2.0; m10 = 0.1; p29 = 0.1; m9 = 0.2; p21 = 1.0; p25 = 2.0 Reaction: cE3n => ; cCOP1n, cCOP1d, cE4, cLUX, cG, cE3n, cCOP1d, cCOP1n, cE3n, cE4, cG, cLUX, Rate Law: def*(((m10*cE3n*cCOP1n+m9*cE3n*cCOP1d+p25*cE4*cE3n)-p21*p25*cE4*cE3n/(p26*cLUX+p21+m9*cCOP1d+m10*cCOP1n))+p17*cE3n*p28*cG/(p29+m19+p17*cE3n))/def
m14 = 0.4 Reaction: cP7_m => ; cP7_m, Rate Law: def*m14*cP7_m/def
m13 = 0.32; L = 1.0; m22 = 0.1 Reaction: cP9 => ; cP9, Rate Law: def*(m13+m22*(1-L))*cP9
p9 = 0.8 Reaction: => cP7; cP7_m, cP7_m, Rate Law: def*p9*cP7_m/def
a = 2.0; n1 = 2.6; L = 1.0; g1 = 0.1; F_LHY = 1.0; q1 = 1.0 Reaction: => cL_m; cNI, cP, cP7, cP9, cT, cNI, cP, cP7, cP9, cT, Rate Law: def*F_LHY*(L*q1*cP+n1*g1^a/((cP9+cP7+cNI+cT)^a+g1^a))
m12 = 1.0 Reaction: cP9_m => ; cP9_m, Rate Law: def*m12*cP9_m/def
m5 = 0.3 Reaction: cT_m => ; cT_m, Rate Law: def*m5*cT_m/def
p11 = 0.5 Reaction: => cG; cG_m, cG_m, Rate Law: def*p11*cG_m/def
m37 = 0.4 Reaction: species_1 => ; species_1, Rate Law: default*m37*species_1/def
m21 = 0.08 Reaction: cZG => ; cZG, Rate Law: def*m21*cZG/def
m10 = 0.1; m9 = 0.2; p26 = 0.3; p21 = 1.0; m35 = 0.3; p25 = 2.0 Reaction: cE4 => ; cE3n, cLUX, cCOP1d, cCOP1n, cCOP1d, cCOP1n, cE3n, cE4, cLUX, Rate Law: def*((m35*cE4+p25*cE4*cE3n)-p21*p25*cE4*cE3n/(p26*cLUX+p21+m9*cCOP1d+m10*cCOP1n))/def
m26 = 0.5 Reaction: cE3_m => ; cE3_m, Rate Law: def*m26*cE3_m/def
m3 = 0.2; p3 = 0.1; c = 2.0; g3 = 0.6 Reaction: cL => ; cL, Rate Law: def*(m3*cL+p3*cL^c/(cL^c+g3^c))/def
parameter_27 = 0.1 Reaction: => species_3, Rate Law: default*parameter_27/def
parameter_10 = 2.0; L = 1.0; parameter_21 = 0.5; parameter_15 = 0.3; parameter_25 = 0.2 Reaction: => species_4; species_4, species_3, species_3, species_4, Rate Law: default*(parameter_25+parameter_21*L)*(1-species_4)*parameter_15^parameter_10/(parameter_15^parameter_10+species_3^parameter_10)/def
parameter_14 = 0.5; n2 = 0.35; g5 = 0.2; parameter_11 = 2.0; g4 = 0.006; F_TOC1 = 1.0; e = 2.0 Reaction: => cT_m; cEC, cL, species_3, cEC, cL, species_3, Rate Law: def*F_TOC1*n2/(1+(cL/(g5*(1+(species_3/parameter_14)^parameter_11)))^e)*g4/(cEC+g4)/def
L = 1.0; n14 = 0.1; n6 = 20.0 Reaction: cCOP1n => cCOP1d; cP, cCOP1n, cP, Rate Law: def*(n6*L*cP*cCOP1n+n14*cCOP1n)
m4 = 0.2 Reaction: cLm => ; cLm, Rate Law: def*m4*cLm/def
p6 = 0.2 Reaction: cCOP1c => cCOP1n; cCOP1c, Rate Law: def*p6*cCOP1c/def
p14 = 0.14 Reaction: => cZTL, Rate Law: def*p14/def
m34 = 0.6 Reaction: cLUX_m => ; cLUX_m, Rate Law: def*m34*cLUX_m/def
m10 = 0.1; m9 = 0.2; p26 = 0.3; p21 = 1.0; p25 = 2.0 Reaction: => cEC; cLUX, cE4, cE3n, cCOP1d, cCOP1n, cCOP1d, cCOP1n, cE3n, cE4, cLUX, Rate Law: def*p26*cLUX*p25*cE4*cE3n/(p26*cLUX+p21+m9*cCOP1d+m10*cCOP1n)/def
m10 = 0.1; m9 = 0.2; m36 = 0.3; p26 = 0.3; p21 = 1.0; p25 = 2.0 Reaction: cLUX => ; cE4, cE3n, cCOP1d, cCOP1n, cCOP1d, cCOP1n, cE3n, cE4, cLUX, Rate Law: def*(m36*cLUX+p26*cLUX*p25*cE4*cE3n/(p26*cLUX+p21+m9*cCOP1d+m10*cCOP1n))/def
parameter_13 = 0.3; parameter_7 = 2.0; parameter_24 = 0.5; e = 2.0; parameter_17 = 0.1 Reaction: => species_1; cT, cL, cL, cT, Rate Law: default*parameter_13^parameter_7/(parameter_13^parameter_7+cT^parameter_7)*parameter_24*cL^e/(cL^e+parameter_17^e)/def
m18 = 3.4 Reaction: cG_m => ; cG_m, Rate Law: def*m18*cG_m/def
g14 = 0.02; L = 1.0; parameter_7 = 2.0; q2 = 1.56; g15 = 0.4; e = 2.0; n12 = 9.0; parameter_1 = 0.6 Reaction: => cG_m; cT, cP, cEC, cL, cEC, cL, cP, cT, Rate Law: def*parameter_1^parameter_7/(parameter_1^parameter_7+cT^parameter_7)*(L*q2*cP+n12*g14/(cEC+g14)*g15^e/(cL^e+g15^e))
L = 1.0; m27 = 0.1; p15 = 2.0 Reaction: cCOP1c => ; cCOP1c, Rate Law: def*m27*cCOP1c*(1+p15*L)
m9 = 0.2 Reaction: cE3 => ; cCOP1c, cCOP1c, cE3, Rate Law: def*m9*cE3*cCOP1c/def
parameter_20 = 0.2 Reaction: species_2 => ; species_2, Rate Law: default*parameter_20*species_2/def
L = 1.0; m2 = 0.24; m1 = 0.54 Reaction: cL_m => ; cL_m, Rate Law: def*(m2+(m1-m2)*L)*cL_m
n5 = 0.4 Reaction: => cCOP1c, Rate Law: def*n5/def
L = 1.0; p12 = 10.0; p13 = 0.1 Reaction: cG + cZTL => cZG; cG, cZG, cZTL, Rate Law: def*(p12*L*cZTL*cG-p13*(1-L)*cZG)
parameter_7 = 2.0; parameter_8 = 2.0; e = 2.0; g6 = 0.3; parameter_4 = 0.03; parameter_5 = 0.4 Reaction: => cE4_m; cT, cEC, cL, cEC, cL, cT, Rate Law: def*parameter_5^parameter_7/(parameter_5^parameter_7+cT^parameter_7)*parameter_8*parameter_4/(cEC+parameter_4)*g6^e/(cL^e+g6^e)/def
p17 = 17.0; parameter_26 = 0.1; p18 = 4.0; m19 = 0.9; p28 = 2.0; m10 = 0.1; p29 = 0.1; m9 = 0.2 Reaction: cEG => ; cCOP1c, cE3n, cG, cCOP1n, cCOP1d, cCOP1c, cCOP1d, cCOP1n, cE3n, cEG, cG, Rate Law: def*((m10*cEG*cCOP1c+p18*cEG)-parameter_26*(p18*cEG+p17*cE3n*p28*cG/(p29+m19+p17*cE3n))/(m10*cCOP1n+m9*cCOP1d+parameter_26))/def
L = 1.0; m24 = 0.5; m17 = 0.5 Reaction: cNI => ; cNI, Rate Law: def*(m17+m24*(1-L))*cNI
p10 = 0.54 Reaction: => cNI; cNI_m, cNI_m, Rate Law: def*p10*cNI_m/def
p20 = 0.1; p19 = 1.0 Reaction: cE3 => cE3n; cE3, cE3n, Rate Law: def*(p19*cE3-p20*cE3n)/def

States:

Name Description
cE4 cE4
cNI cNI
cLUX cLUX
cP9 cP9
cP9 m cP9_m
cZTL cZTL
species 1 cABAR_m
species 4 cs
cCOP1n cCOP1n
cNI m cNI_m
cEG cEG
cG m cG_m
cE4 m cE4_m
cCOP1d cCOP1d
cP cP
cE3n cE3n
cP7 cP7
cZG cZG
cE3 m cE3_m
species 2 cPP2C
cEC cEC
cG cG
cL m cL_m
cE3 cE3
cP7 m cP7_m
cLUX m cLUX_m
cT m cT_m
cCOP1c cCOP1c
species 3 cSnRK2
cLm cLm
cT cT
cL cL

Observables: none

BIOMD0000000166 @ v0.0.1

This a model from the article: A theoretical study on activation of transcription factor modulated by intracellular…

This work presents both deterministic and stochastic models of genetic expression modulated by intracellular calcium (Ca2+) oscillations, based on macroscopic differential equations and chemical Langevin equations, respectively. In deterministic case, the oscillations of intracellular Ca2+ decrease the effective Ca2+ threshold for the activation of transcriptional activator (TF-A). The average activation of TF-A increases with the increase of the average amplitude of intracellular Ca2+ oscillations, but decreases with the increase of the period of intracellular Ca2+ oscillations, which are qualitatively consistent with the experimental results on the gene expression in lymphocytes. In stochastic case, it is found that a large internal fluctuation of the biochemical reaction can enhance gene expression efficiency specifically at a low level of external stimulations or at a small rate of TF-A dimer phosphorylation activated by Ca2+, which reduces the threshold of the average intracellular Ca2+ concentration for gene expression. link: http://identifiers.org/pubmed/17560007

Parameters:

Name Description
kf = NaN; Kd = NaN Reaction: => X, Rate Law: kf*X^2/(X^2+Kd)
Rbas=0.1 Reaction: => X, Rate Law: Rbas
Vm2=30.0; K2=0.5; n=2.0 Reaction: Z => Y, Rate Law: Vm2*Z^n/(K2^n+Z^n)
k1=0.7 Reaction: Y => Z, Rate Law: k1*Y
k=10.0 Reaction: Z =>, Rate Law: k*Z
kd=1.0 Reaction: X =>, Rate Law: kd*X
K_A=0.46; m=2.0; Kr=1.7; Vm3=325.0; p=4.0 Reaction: Y => Z, Rate Law: Vm3*Y^m/(Kr^m+Y^m)*Z^p/(K_A^p+Z^p)
v1=5.7; beta=0.3 Reaction: => Z, Rate Law: v1*beta
v0=1.0 Reaction: => Z, Rate Law: v0

States:

Name Description
Z [calcium atom; Calcium cation]
Y [calcium atom; Calcium cation]
X TF_A

Observables: none

Zhu2015 - Combined gemcitabine and birinapant in pancreatic cancer cells - basic PD modelMathematical model to illustrat…

Combination chemotherapy is standard treatment for pancreatic cancer. However, current drugs lack efficacy for most patients, and selection and evaluation of new combination regimens is empirical and time-consuming. The efficacy of gemcitabine, a standard-of-care agent, combined with birinapant, a pro-apoptotic antagonist of Inhibitor of Apoptosis Proteins (IAPs), was investigated in pancreatic cancer cells. PANC-1 cells were treated with vehicle, gemcitabine (6, 10, 20 nM), birinapant (50, 200, 500 nM), and combinations of the two drugs. Temporal changes in cell numbers, cell cycle distribution, and apoptosis were measured. A basic pharmacodynamic (PD) model based on cell numbers, and a mechanism-based PD model integrating all measurements, were developed. The basic PD model indicated that synergistic effects occurred in both cell proliferation and death processes. The mechanism-based model captured key features of drug action: temporary cell cycle arrest in S phase induced by gemcitabine alone, apoptosis induced by birinapant alone, and prolonged cell cycle arrest and enhanced apoptosis induced by the combination. A drug interaction term Ψ was employed in the models to signify interactions of the combination when data were limited. When more experimental information was utilized, Ψ values approaching 1 indicated that specific mechanisms of interactions were captured better. PD modeling identified the potential benefit of combining gemcitabine and birinapant, and characterized the key interaction pathways. An optimal treatment schedule of pretreatment with gemcitabine for 24-48 h was suggested based on model predictions and was verified experimentally. This approach provides a generalizable modeling platform for exploring combinations of cytostatic and cytotoxic agents in cancer cell culture studies. link: http://identifiers.org/pubmed/26252969

Parameters:

Name Description
C_g = 0.0; Psi_i = 1.0; Hi_g = 3.57; Imax_g = 0.991; IC50_g = 20.8 Reaction: Inh_g = Imax_g*C_g^Hi_g/((Psi_i*IC50_g)^Hi_g+C_g^Hi_g), Rate Law: missing
ModelValue_4 = 3.85E-4 Reaction: Rd = (1+Sti_g4)*(1+Sti_b4)*ModelValue_4*Ra-ModelValue_4*Rd, Rate Law: (1+Sti_g4)*(1+Sti_b4)*ModelValue_4*Ra-ModelValue_4*Rd
ktau_g = 0.086 Reaction: Sti_g => Sti_g1, Rate Law: Pancreas*ktau_g*Sti_g
ktau_b = 0.611 Reaction: Sti_b => Sti_b1, Rate Law: Pancreas*ktau_b*Sti_b
Hi_b = 1.06; C_b = 0.0; IC50_b = 145.0; Imax_b = 0.375; Psi_i = 1.0 Reaction: Inh_b = Imax_b*C_b^Hi_b/((Psi_i*IC50_b)^Hi_b+C_b^Hi_b), Rate Law: missing
Psi_s = 1.0; Smax_g = 4.09; C_g = 0.0; Hs_g = 5.0; SC50_g = 14.0 Reaction: Sti_g = Smax_g*C_g^Hs_g/((Psi_s*SC50_g)^Hs_g+C_g^Hs_g), Rate Law: missing
ModelValue_4 = 3.85E-4; ModelValue_3 = 0.0209; ModelValue_2 = 5490000.0 Reaction: Ra = (1-Inh_g)*(1-Inh_b)*ModelValue_3*Ra*(1-Ra/ModelValue_2)-(1+Sti_g4)*(1+Sti_b4)*ModelValue_4*Ra, Rate Law: (1-Inh_g)*(1-Inh_b)*ModelValue_3*Ra*(1-Ra/ModelValue_2)-(1+Sti_g4)*(1+Sti_b4)*ModelValue_4*Ra
Psi_s = 1.0; C_b = 0.0; SC50_b = 168.0; Smax_b = 17.5; Hs_b = 0.984 Reaction: Sti_b = Smax_b*C_b^Hs_b/((Psi_s*SC50_b)^Hs_b+C_b^Hs_b), Rate Law: missing

States:

Name Description
Ra [PANC-1 cell; Adhesion]
Sti b4 [delay]
Sti g1 [delay]
Sti g2 [delay]
Inh b [Chemotherapy; Inhibition of Cancer Cell Growth; Chemotherapy]
Sti g4 [delay]
Rd [PANC-1 cell; Detached; cell death]
Sti g [Chemotherapy; Positive Regulation of Cell Death; Chemotherapy]
Sti g3 [delay]
Inh g [Chemotherapy; Inhibition of Cancer Cell Growth; Chemotherapy]
Sti b2 [delay]
Sti b3 [delay]
Sti b1 [delay]
Sti b [Chemotherapy; Positive Regulation of Cell Death; Chemotherapy]

Observables: none

Zhu2015 - combined gemcitabine and birinapant in pancreatic cancer cells - mechanistic PD modelMechanistic mathematical…

Combination chemotherapy is standard treatment for pancreatic cancer. However, current drugs lack efficacy for most patients, and selection and evaluation of new combination regimens is empirical and time-consuming. The efficacy of gemcitabine, a standard-of-care agent, combined with birinapant, a pro-apoptotic antagonist of Inhibitor of Apoptosis Proteins (IAPs), was investigated in pancreatic cancer cells. PANC-1 cells were treated with vehicle, gemcitabine (6, 10, 20 nM), birinapant (50, 200, 500 nM), and combinations of the two drugs. Temporal changes in cell numbers, cell cycle distribution, and apoptosis were measured. A basic pharmacodynamic (PD) model based on cell numbers, and a mechanism-based PD model integrating all measurements, were developed. The basic PD model indicated that synergistic effects occurred in both cell proliferation and death processes. The mechanism-based model captured key features of drug action: temporary cell cycle arrest in S phase induced by gemcitabine alone, apoptosis induced by birinapant alone, and prolonged cell cycle arrest and enhanced apoptosis induced by the combination. A drug interaction term Ψ was employed in the models to signify interactions of the combination when data were limited. When more experimental information was utilized, Ψ values approaching 1 indicated that specific mechanisms of interactions were captured better. PD modeling identified the potential benefit of combining gemcitabine and birinapant, and characterized the key interaction pathways. An optimal treatment schedule of pretreatment with gemcitabine for 24-48 h was suggested based on model predictions and was verified experimentally. This approach provides a generalizable modeling platform for exploring combinations of cytostatic and cytotoxic agents in cancer cell culture studies. link: http://identifiers.org/pubmed/26252969

Parameters:

Name Description
Inh_g = 0.874253042562929; Sti_apo_b = 0.0; Inh_b = 0.135321100917431; k1 = 0.357; k_apo = 0.00394; Sti_apo_g = 0.0; k_other = 2.97E-4; Sti_other_b = 2.75; k2 = 0.114; Sti_other_g = 1.34928284767356E-5; Inh_1 = 0.642088110341617 Reaction: S = (((1-Inh_1)*(1-Inh_b)*k1*G1-(1-Inh_g)*k2*S)-(1+Sti_apo_g)*(1+Sti_apo_b)*k_apo*S)-(1+Sti_other_g)*(1+Sti_other_b)*k_other*S, Rate Law: (((1-Inh_1)*(1-Inh_b)*k1*G1-(1-Inh_g)*k2*S)-(1+Sti_apo_g)*(1+Sti_apo_b)*k_apo*S)-(1+Sti_other_g)*(1+Sti_other_b)*k_other*S
Sti_apo_b = 0.0; k_apo = 0.00394; Sti_apo_g = 0.0; f1 = 0.467 Reaction: R_apo = (1+Sti_apo_g)*(1+Sti_apo_b)*k_apo*(G1+S+G2)-(1+Sti_apo_g)*(1+Sti_apo_b)*f1*k_apo*R_apo, Rate Law: (1+Sti_apo_g)*(1+Sti_apo_b)*k_apo*(G1+S+G2)-(1+Sti_apo_g)*(1+Sti_apo_b)*f1*k_apo*R_apo
k_other = 2.97E-4; Sti_other_b = 2.75; Sti_other_g = 1.34928284767356E-5 Reaction: R_other = (1+Sti_other_g)*(1+Sti_other_b)*k_other*(G1+S+G2)-k_other*R_other, Rate Law: (1+Sti_other_g)*(1+Sti_other_b)*k_other*(G1+S+G2)-k_other*R_other
Inh_g = 0.874253042562929; Sti_apo_b = 0.0; Inh_3 = 0.483492347087237; k3 = 0.222; Inh_b = 0.135321100917431; k_apo = 0.00394; Sti_apo_g = 0.0; k_other = 2.97E-4; Sti_other_b = 2.75; k2 = 0.114; Sti_other_g = 1.34928284767356E-5 Reaction: G2 = (((1-Inh_g)*k2*S-(1-Inh_3)*(1-Inh_b)*k3*G2)-(1+Sti_apo_g)*(1+Sti_apo_b)*k_apo*G2)-(1+Sti_other_g)*(1+Sti_other_b)*k_other*G2, Rate Law: (((1-Inh_g)*k2*S-(1-Inh_3)*(1-Inh_b)*k3*G2)-(1+Sti_apo_g)*(1+Sti_apo_b)*k_apo*G2)-(1+Sti_other_g)*(1+Sti_other_b)*k_other*G2
Sti_apo_b = 0.0; k_apo = 0.00394; k_other = 2.97E-4; Sti_other_g = 1.34928284767356E-5; Inh_3 = 0.483492347087237; k3 = 0.222; Inh_b = 0.135321100917431; k1 = 0.357; Sti_apo_g = 0.0; Sti_other_b = 2.75; Inh_1 = 0.642088110341617 Reaction: G1 = ((2*(1-Inh_3)*(1-Inh_b)*k3*G2-(1-Inh_1)*(1-Inh_b)*k1*G1)-(1+Sti_apo_g)*(1+Sti_apo_b)*k_apo*G1)-(1+Sti_other_g)*(1+Sti_other_b)*k_other*G1, Rate Law: ((2*(1-Inh_3)*(1-Inh_b)*k3*G2-(1-Inh_1)*(1-Inh_b)*k1*G1)-(1+Sti_apo_g)*(1+Sti_apo_b)*k_apo*G1)-(1+Sti_other_g)*(1+Sti_other_b)*k_other*G1

States:

Name Description
R total [collection of specimens]
S [PANC-1 cell; S Phase Process; S phase]
G1 [PANC-1 cell; G1 Phase Process; G1 phase]
G2 [M phase; G2 phase; PANC-1 cell; G2 Phase Process]
R apo [PANC-1 cell; Apoptosis]
R other [PANC-1 cell]
R live [collection of specimens; Cell Proliferation]

Observables: none

Zhuang2011 - Ecoli FBA with membrane economicsGenome-scale metabolic model of Escherichia coli able to simulate respiro-…

The simultaneous utilization of efficient respiration and inefficient fermentation even in the presence of abundant oxygen is a puzzling phenomenon commonly observed in bacteria, yeasts, and cancer cells. Despite extensive research, the biochemical basis for this phenomenon remains obscure. We hypothesize that the outcome of a competition for membrane space between glucose transporters and respiratory chain (which we refer to as economics of membrane occupancy) proteins influences respiration and fermentation. By incorporating a sole constraint based on this concept in the genome-scale metabolic model of Escherichia coli, we were able to simulate respiro-fermentation. Further analysis of the impact of this constraint revealed differential utilization of the cytochromes and faster glucose uptake under anaerobic conditions than under aerobic conditions. Based on these simulations, we propose that bacterial cells manage the composition of their cytoplasmic membrane to maintain optimal ATP production by switching between oxidative and substrate-level phosphorylation. These results suggest that the membrane occupancy constraint may be a fundamental governing constraint of cellular metabolism and physiology, and establishes a direct link between cell morphology and physiology. link: http://identifiers.org/pubmed/21694717

Parameters: none

States: none

Observables: none

BIOMD0000000163 @ v0.0.1

The model reproduces the time profiles of Total Smad2 in the nucleus as well as the cytoplasm as depicted in 2D and also…

BACKGROUND: Investigation of dynamics and regulation of the TGF-beta signaling pathway is central to the understanding of complex cellular processes such as growth, apoptosis, and differentiation. In this study, we aim at using systems biology approach to provide dynamic analysis on this pathway. METHODOLOGY/PRINCIPAL FINDINGS: We proposed a constraint-based modeling method to build a comprehensive mathematical model for the Smad dependent TGF-beta signaling pathway by fitting the experimental data and incorporating the qualitative constraints from the experimental analysis. The performance of the model generated by constraint-based modeling method is significantly improved compared to the model obtained by only fitting the quantitative data. The model agrees well with the experimental analysis of TGF-beta pathway, such as the time course of nuclear phosphorylated Smad, the subcellular location of Smad and signal response of Smad phosphorylation to different doses of TGF-beta. CONCLUSIONS/SIGNIFICANCE: The simulation results indicate that the signal response to TGF-beta is regulated by the balance between clathrin dependent endocytosis and non-clathrin mediated endocytosis. This model is useful to be built upon as new precise experimental data are emerging. The constraint-based modeling method can also be applied to quantitative modeling of other signaling pathways. link: http://identifiers.org/pubmed/17895977

Parameters:

Name Description
ki_EE = 0.33 Reaction: T1R_Surf => T1R_EE, Rate Law: V_cyt*ki_EE*T1R_Surf
Kimp_Smads_Complex_c = 0.16 Reaction: Smads_Complex_c => Smads_Complex_n, Rate Law: V_cyt*Kimp_Smads_Complex_c*Smads_Complex_c
k_Smads_Complex_c = 6.85E-5 Reaction: Smad2c + Smad4c => Smads_Complex_c; LRC_EE, Rate Law: V_cyt*k_Smads_Complex_c*Smad2c*Smad4c*LRC_EE
v_T1R = 0.0103 Reaction: => T1R_Surf, Rate Law: V_cyt*v_T1R
Klid = 0.02609 Reaction: LRC_Cave => ; Smads_Complex_n, Rate Law: V_cyt*Klid*LRC_Cave*Smads_Complex_n
Kexp_Smad2n = 1.0 Reaction: Smad2n => Smad2c, Rate Law: V_nuc*Kexp_Smad2n*Smad2n
Kexp_Smad4n = 0.5 Reaction: Smad4n => Smad4c, Rate Law: V_nuc*Kexp_Smad4n*Smad4n
Kdeg_T1R_EE = 0.005 Reaction: T1R_EE =>, Rate Law: V_cyt*Kdeg_T1R_EE*T1R_EE
v_T2R = 0.02869 Reaction: => T2R_Surf, Rate Law: V_cyt*v_T2R
kr_Cave = 0.03742 Reaction: LRC_Cave => T1R_Surf + TGF_beta + T2R_Surf, Rate Law: V_cyt*kr_Cave*LRC_Cave
Kdeg_T2R_EE = 0.025 Reaction: T2R_EE =>, Rate Law: V_cyt*Kdeg_T2R_EE*T2R_EE
ki_Cave = 0.33 Reaction: T1R_Surf => T1R_Cave, Rate Law: V_cyt*ki_Cave*T1R_Surf
Kcd = 0.005 Reaction: LRC_EE =>, Rate Law: V_cyt*Kcd*LRC_EE
Kimp_Smad2c = 0.16 Reaction: Smad2c => Smad2n, Rate Law: V_cyt*Kimp_Smad2c*Smad2c
k_LRC = 2197.0 Reaction: TGF_beta + T2R_Surf + T1R_Surf => LRC_Surf, Rate Law: V_cyt*k_LRC*TGF_beta*T2R_Surf*T1R_Surf
Kdiss_Smads_Complex_n = 0.1174 Reaction: Smads_Complex_n => Smad4n + Smad2n, Rate Law: V_nuc*Kdiss_Smads_Complex_n*Smads_Complex_n
kr_EE = 0.033 Reaction: T2R_EE => T2R_Surf + TGF_beta, Rate Law: V_cyt*kr_EE*T2R_EE
Kimp_Smad4c = 0.08 Reaction: Smad4c => Smad4n, Rate Law: V_cyt*Kimp_Smad4c*Smad4c

States:

Name Description
Smads Complex n [Mothers against decapentaplegic homolog 4; Mothers against decapentaplegic homolog 2]
T1R Surf [Activin receptor type-1C]
T1R EE [Activin receptor type-1C]
LRC Surf [TGF-beta receptor type-2; Activin receptor type-1C; Transforming growth factor beta-1]
LRC EE [TGF-beta receptor type-2; Activin receptor type-1C; Transforming growth factor beta-1]
Smad2n [Mothers against decapentaplegic homolog 2]
Smads Complex c [Mothers against decapentaplegic homolog 4; Mothers against decapentaplegic homolog 2]
Smad4c [Mothers against decapentaplegic homolog 4]
T2R EE [TGF-beta receptor type-2]
TGF beta [Transforming growth factor beta-1]
Smad4n [Mothers against decapentaplegic homolog 4]
T1R Cave [Activin receptor type-1C]
T2R Cave [TGF-beta receptor type-2]
Smad2c [Mothers against decapentaplegic homolog 2]
LRC Cave [TGF-beta receptor type-2; Activin receptor type-1C; Transforming growth factor beta-1]
T2R Surf [TGF-beta receptor type-2]

Observables: none

BIOMD0000000342 @ v0.0.1

This model is from the article: Quantitative analysis of transient and sustained transforming growth factor-β signalin…

Mammalian cells can decode the concentration of extracellular transforming growth factor-β (TGF-β) and transduce this cue into appropriate cell fate decisions. How variable TGF-β ligand doses quantitatively control intracellular signaling dynamics and how continuous ligand doses are translated into discontinuous cellular fate decisions remain poorly understood. Using a combined experimental and mathematical modeling approach, we discovered that cells respond differently to continuous and pulsating TGF-β stimulation. The TGF-β pathway elicits a transient signaling response to a single pulse of TGF-β stimulation, whereas it is capable of integrating repeated pulses of ligand stimulation at short time interval, resulting in sustained phospho-Smad2 and transcriptional responses. Additionally, the TGF-β pathway displays different sensitivities to ligand doses at different time scales. While ligand-induced short-term Smad2 phosphorylation is graded, long-term Smad2 phosphorylation is switch-like to a small change in TGF-β levels. Correspondingly, the short-term Smad7 gene expression is graded, while long-term PAI-1 gene expression is switch-like, as is the long-term growth inhibitory response. Our results suggest that long-term switch-like signaling responses in the TGF-β pathway might be critical for cell fate determination. link: http://identifiers.org/pubmed/21613981

Parameters:

Name Description
kexp_Smad4 = 0.359 per min Reaction: Smad4n => Smad4c, Rate Law: Vnuc*kexp_Smad4*Smad4n
kon_Smads = 0.198472 second order rate constant; koff_Smads = 1.0 per min Reaction: PSmad2_Smad4_n => PSmad2n + Smad4n, Rate Law: Vnuc*(koff_Smads*PSmad2_Smad4_n-kon_Smads*PSmad2n*Smad4n)
ki = 0.333 per min Reaction: LRC_surf => LRC_endo, Rate Law: Vcyt*ki*LRC_surf
k_T1R = 0.0167 nM per min Reaction: AA => T1R_surf, Rate Law: Vcyt*k_T1R
kdeg_T1R = 0.00256 per min Reaction: T1R_endo => empty_degraded, Rate Law: Vcyt*kdeg_T1R*T1R_endo
kdepho_Smad2 = 0.394 per min Reaction: PSmad2n => Smad2n, Rate Law: Vnuc*kdepho_Smad2*PSmad2n
kr = 0.0333 per min Reaction: T1R_endo => T1R_surf, Rate Law: Vcyt*kr*T1R_endo
kimp_Smads = 0.889 per min Reaction: PSmad2_Smad4_c => PSmad2_Smad4_n, Rate Law: Vcyt*kimp_Smads*PSmad2_Smad4_c
kexp_Smad2 = 0.763 per min Reaction: PSmad2n => PSmad2c, Rate Law: Vnuc*kexp_Smad2*PSmad2n
klid = 0.0233678 per min; totalNuclearPSmad2 = 0.0 nanomolar Reaction: LRC_surf => empty_degraded, Rate Law: Vcyt*klid*LRC_surf*totalNuclearPSmad2
k_T2R = 0.0190076 nM per min Reaction: AA => T2R_surf, Rate Law: Vcyt*k_T2R
kdiss_LRC = 0.0438111 per min Reaction: LRC_endo => T1R_endo + T2R_endo + TGF_beta_endo, Rate Law: Vcyt*kdiss_LRC*LRC_endo
kon_ns = 0.0505413 per min; koff_ns = 2.03306 per min Reaction: TGF_beta_ex => TGF_beta_ns, Rate Law: Vmed*(kon_ns*TGF_beta_ex-koff_ns*TGF_beta_ns)
kimp_Smad4 = 0.156 per min Reaction: Smad4c => Smad4n, Rate Law: Vcyt*kimp_Smad4*Smad4c
kimp_Smad2 = 0.156 per min Reaction: Smad2c => Smad2n, Rate Law: Vcyt*kimp_Smad2*Smad2c
kdeg_LRC = 0.00256 per min Reaction: LRC_endo => empty_degraded, Rate Law: Vcyt*kdeg_LRC*LRC_endo
kdeg_TGF_beta = 0.347 per min Reaction: TGF_beta_endo => empty_degraded, Rate Law: Vcyt*kdeg_TGF_beta*TGF_beta_endo
kpho_Smad2 = 0.0488268 second order rate constant Reaction: Smad2c => PSmad2c; LRC_endo, Rate Law: Vcyt*kpho_Smad2*Smad2c*LRC_endo
kdeg_T2R = 0.0132 per min Reaction: T2R_endo => empty_degraded, Rate Law: Vcyt*kdeg_T2R*T2R_endo
ka_LRC = 117.897 third order rate constant Reaction: TGF_beta_ex + T2R_surf + T1R_surf => LRC_surf, Rate Law: Vcyt*ka_LRC*TGF_beta_ex*T2R_surf*T1R_surf

States:

Name Description
PSmad2 Smad4 c [Mothers against decapentaplegic homolog 2; Mothers against decapentaplegic homolog 4; Phosphoprotein]
LRC endo [early endosome; receptor complex; Transforming growth factor beta-1; TGF-beta receptor type-1; Transforming growth factor beta-1; TGF-beta receptor type-2]
PSmad2c [Mothers against decapentaplegic homolog 2; Phosphoprotein]
PSmad2 Smad4 n [Mothers against decapentaplegic homolog 2; Mothers against decapentaplegic homolog 4; Phosphoprotein]
empty degraded empty_degraded
LRC surf [cell surface; receptor complex; Transforming growth factor beta-1; TGF-beta receptor type-1; Transforming growth factor beta-1; TGF-beta receptor type-2]
TGF beta ns [Transforming growth factor beta-1]
Smad2n [Mothers against decapentaplegic homolog 2]
T1R endo [TGF-beta receptor type-1; early endosome]
PSmad2n [Mothers against decapentaplegic homolog 2; Phosphoprotein]
PSmad2 PSmad2 c [Mothers against decapentaplegic homolog 2; Phosphoprotein]
Smad4c [Mothers against decapentaplegic homolog 4]
T2R surf [TGF-beta receptor type-2; cell surface]
TGF beta endo [Transforming growth factor beta-1; early endosome]
PSmad2 PSmad2 n [Mothers against decapentaplegic homolog 2; Phosphoprotein]
T2R endo [TGF-beta receptor type-2; early endosome]
Smad4n [Mothers against decapentaplegic homolog 4]
AA AA
Smad2c [Mothers against decapentaplegic homolog 2]
T1R surf [TGF-beta receptor type-1; cell surface]
TGF beta ex [Transforming growth factor beta-1; culture medium]

Observables: none

The main objective of this paper is to address the following question: are the containment measures imposed by most of t…

The main objective of this paper is to address the following question: are the containment measures imposed by most of the world governments effective and sufficient to stop the epidemic of COVID-19 beyond the lock-down period? In this paper, we propose a mathematical model which allows us to investigate and analyse this problem. We show by means of the reproductive number, ${&amp;#92;cal R}_0$ that the containment measures appear to have slowed the growth of the outbreak. Nevertheless, these measures remain only effective as long as a very large fraction of population, p, greater than the critical value $1-1/{&amp;#92;cal R}_0$ remains confined. Using French current data, we give some simulation experiments with five scenarios including: (i) the validation of model with p estimated to 93%, (ii) the study of the effectiveness of containment measures, (iii) the study of the effectiveness of the large-scale testing, (iv) the study of the social distancing and wearing masks measures and (v) the study taking into account the combination of the large-scale test of detection of infected individuals and the social distancing with linear progressive easing of restrictions. The latter scenario was shown to be effective at overcoming the outbreak if the transmission rate decreases to 75% and the number of tests of detection is multiplied by three. We also noticed that if the measures studied in our five scenarios are taken separately then the second wave might occur at least as far as the parameter values remain unchanged. link: http://identifiers.org/pubmed/32958091

Parameters: none

States: none

Observables: none

MODEL7519354389 @ v0.0.1

This a model from the article: Modeling specificity in the yeast MAPK signaling networks Zou X, Peng T, Pan Z J. The…

Cells sense several kinds of stimuli and trigger corresponding responses through signaling pathways. As a result, cells must process and integrate multiple signals in parallel to maintain specificity and avoid erroneous cross-talk. In this study, we focus our theoretical effort on understanding specificity of a model network system in yeast, Saccharomyces cerevisiae, which contains three mitogen-activated protein kinase (MAPK) signal transduction cascades that share multiple signaling components. The cellular response to the pheromone, the filamentous growth and osmotic pressure stimuli in yeast is described and an integrative mathematical model for the three MAPK cascades is developed using available literature and experimental data. The theoretical framework for analyzing the specificity of signaling networks [Bardwell, L., Zou, X.F., Nie, Q., Komarova, N.L., 2007. Mathematical models of specificity in cell signaling. Biophys. J. 92, 3425-3441] is extended to include multiple interacting pathways with shared components. Simulations are also performed with any one stimulus, with any two simultaneous stimuli, and with the simultaneous application of the three stimuli. The interactions between the three pathways are systematically investigated. Moreover, the specificity and fidelity of this model system are calculated using our newly developed concept under different stimuli or with specific mutants. Our simulated and calculated results demonstrate that the yeast MAPK signaling network can achieve specificity and fidelity by filtering out spurious cross-talk between the relevant pathways through different mechanisms, such as scaffolding, cross-inhibiting, and feedback control. Proof that Pbs2 and Hog1 are essential for the maintenance of signaling specificity is presented. Our studies provide novel insights into integration of relevant signaling pathways in a biological system and the mechanisms conferring specificity in cellular signaling networks. link: http://identifiers.org/pubmed/17977559

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Zou2012 - Genome-scale metabolic network of Ketogulonicigenium vulgare (iWZ663)This model is described in the article:…

Ketogulonicigenium vulgare WSH001 is an industrial strain commonly used in the vitamin C producing industry. In order to acquire a comprehensive understanding of its physiological characteristics, a genome-scale metabolic model of K. vulgare WSH001, iWZ663, including 830 reactions, 649 metabolites, and 663 genes, was reconstructed by genome annotation and literature mining. This model was capable of predicting quantitatively the growth of K. vulgare under L-sorbose fermentation conditions and the results agreed well with experimental data. Furthermore, phenotypic features, such as the defect in sulfate metabolism hampering the syntheses of L-cysteine, L-methionine, coenzyme A (CoA), and glutathione, were investigated and provided an explanation for the poor growth of K. vulgare in monoculture. The model presented here provides a validated platform that can be used to understand and manipulate the phenotype of K. vulgare to further improve 2-KLG production efficiency. link: http://identifiers.org/pubmed/22728423

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This is an SBML version of the reaction network used in the article: Metabolic pathway analysis of yeast strengthens t…

Central carbon metabolism of the yeast Saccharomyces cerevisiae was analyzed using metabolic pathway analysis tools. Elementary flux modes for three substrates (glucose, galactose, and ethanol) were determined using the catabolic reactions occurring in yeast. Resultant elementary modes were used for gene deletion phenotype analysis and for the analysis of robustness of the central metabolism and network functionality. Control-effective fluxes, determined by calculating the efficiency of each mode, were used for the prediction of transcript ratios of metabolic genes in different growth media (glucose-ethanol and galactose-ethanol). A high correlation was obtained between the theoretical and experimental expression levels of 38 genes when ethanol and glucose media were considered. Such analysis was shown to be a bridge between transcriptomics and fluxomics. Control-effective flux distribution was found to be promising in in silico predictions by incorporating functionality and regulation into the metabolic network structure. link: http://identifiers.org/pubmed/15083505

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