bungay3

The SBML for this model was obtained from the BioModels database (BioModels ID: BIOMD0000000334) Biomodels notes: Thrombin generation model. Factors are denoted by their numbers, with _l and _f suffixes depending on whether they are lipid-bound or fluid phase. Vesicle concentration is derived from LIPID (concentration of head groups) using the formula [vesicle] * 4*10nm^2*pi / 0.74nm^2 per head group. The model was integrated and simulated using Copasi 4.6.32 and plotted using Matplotlib to reproduce figure 4 of the article. JWS Online curation: This model was curated by reproducing the figures as described in the BioModels Notes. No additional changes were made.

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A mathematical model of lipid-mediated thrombin generation.

  • Sharene D Bungay
  • Patricia A Gentry
  • Rodney D Gentry
Math Med Biol 2003; 20 (1): 105-129
Abstract
Thrombin is an enzyme that is generated in both vascular and non-vascular systems. In blood coagulation, a fundamental process in all species, thrombin induces the formation of a fibrin clot. A dynamical model of thrombin generation in the presence of lipid surfaces is presented. This model also includes the self-regulating thrombin feedback reactions, the thrombomodulin-protein C-protein S inhibitory system, tissue factor pathway inhibitor (TFPI), and the inhibitor, antithrombin (AT). The dynamics of this complex system were found to be highly lipid dependent, as would be expected from experimental studies. Simulations of this model indicate that a threshold lipid level is required to generate physiologically relevant amounts of thrombin. The dependence of the onset, the peak levels, and the duration of thrombin generation on lipid was saturable. The lipid concentration affects the way in which the inhibitors modulate thrombin production. A novel feature of this model is the inclusion of the dynamical protein C pathway, initiated by thrombin feedback. This inhibitory system exerts its effects on the lipid surface, where its substrates are formed. The maximum impact of TFPI occurs at intermediate vesicle concentrations. Inhibition by AT is only indirectly affected by the lipid since AT irreversibly binds only to solution phase proteins. In a system with normal plasma concentrations of the proteins involved in thrombin formation, the combination of these three inhibitors is sufficient both to effectively stop thrombin generation prior to the exhaustion of its precursor, prothrombin, and to inhibit all thrombin formed. This model can be used to predict thrombin generation under extreme lipid conditions that are difficult to implement experimentally and to examine thrombin generation in non-vascular systems.

Unit definitions have no effect on the numerical analysis of the model. It remains the responsibility of the modeler to ensure the internal numerical consistency of the model. If units are provided, however, the consistency of the model units will be checked.

Name Definition
1e-09 mole
Id Name Spatial dimensions Size
compartment Cell 3.0 1.0
Id Name Initial quantity Compartment Fixed
APC_PS_VIIIa_l APC_PS_VIIIa_l 0.0 compartment (Cell)
APC_PS_Va_l APC_PS_Va_l 0.0 compartment (Cell)
APC_PS_l APC_PS_l 0.0 compartment (Cell)
APC_f APC_f 0.0 compartment (Cell)
APC_l APC_l 0.0 compartment (Cell)
AT_f AT_f 3400.0 compartment (Cell)
II_f II_f 1400.0 compartment (Cell)
II_l II_l 0.0 compartment (Cell)
IIa_AT_f IIa_AT_f 0.0 compartment (Cell)
IIa_TM_PC_l IIa_TM_PC_l 0.0 compartment (Cell)
IIa_TM_l IIa_TM_l 0.0 compartment (Cell)
IIa_f IIa_f 0.0 compartment (Cell)
IX_f IX_f 90.0 compartment (Cell)
IX_l IX_l 0.0 compartment (Cell)
IXa_AT_f IXa_AT_f 0.0 compartment (Cell)
IXa_VIIIa_X_l IXa_VIIIa_X_l 0.0 compartment (Cell)
IXa_VIIIa_l IXa_VIIIa_l 0.0 compartment (Cell)
IXa_f IXa_f 0.0 compartment (Cell)
IXa_l IXa_l 0.0 compartment (Cell)
LIPID LIPID 849079.0 compartment (Cell)
PC_f PC_f 60.0 compartment (Cell)
PC_l PC_l 0.0 compartment (Cell)
PS_f PS_f 300.0 compartment (Cell)
PS_l PS_l 0.0 compartment (Cell)
TFPI_Xa_TF_VIIa_l TFPI_Xa_TF_VIIa_l 0.0 compartment (Cell)
TFPI_Xa_l TFPI_Xa_l 0.0 compartment (Cell)
TFPI_f TFPI_f 2.5 compartment (Cell)
TF_VII_Xa_l TF_VII_Xa_l 0.0 compartment (Cell)
TF_VII_l TF_VII_l 0.0 compartment (Cell)
TF_VIIa_IX_l TF_VIIa_IX_l 0.0 compartment (Cell)
TF_VIIa_IXa_l TF_VIIa_IXa_l 0.0 compartment (Cell)
TF_VIIa_X_l TF_VIIa_X_l 0.0 compartment (Cell)
TF_VIIa_Xa_l TF_VIIa_Xa_l 0.0 compartment (Cell)
TF_VIIa_l TF_VIIa_l 0.0 compartment (Cell)
TF_l TF_l 0.005 compartment (Cell)
TM_l TM_l 1.0 compartment (Cell)
VIII_IIa_l VIII_IIa_l 0.0 compartment (Cell)
VIII_Xa_l VIII_Xa_l 0.0 compartment (Cell)
VIII_f VIII_f 0.7 compartment (Cell)
VIII_l VIII_l 0.0 compartment (Cell)
VIII_mIIa_l VIII_mIIa_l 0.0 compartment (Cell)
VIIIa_f VIIIa_f 0.0 compartment (Cell)
VIIIa_l VIIIa_l 0.0 compartment (Cell)
VIIIai_f VIIIai_f 0.0 compartment (Cell)
VIIIai_l VIIIai_l 0.0 compartment (Cell)
VII_Xa_l VII_Xa_l 0.0 compartment (Cell)
VII_f VII_f 10.0 compartment (Cell)
VII_l VII_l 0.0 compartment (Cell)
VIIa_f VIIa_f 0.1 compartment (Cell)
VIIa_l VIIa_l 0.0 compartment (Cell)
V_IIa_l V_IIa_l 0.0 compartment (Cell)
V_Xa_l V_Xa_l 0.0 compartment (Cell)
V_f V_f 20.0 compartment (Cell)
V_l V_l 0.0 compartment (Cell)
V_mIIa_l V_mIIa_l 0.0 compartment (Cell)
Va_f Va_f 0.0 compartment (Cell)
Va_l Va_l 0.0 compartment (Cell)
Vai_f Vai_f 0.0 compartment (Cell)
Vai_l Vai_l 0.0 compartment (Cell)
XI_IIa_l XI_IIa_l 0.0 compartment (Cell)
XI_f XI_f 30.0 compartment (Cell)
XIa_IX_l XIa_IX_l 0.0 compartment (Cell)
XIa_l XIa_l 0.0 compartment (Cell)
X_f X_f 170.0 compartment (Cell)
X_l X_l 0.0 compartment (Cell)
Xa_AT_f Xa_AT_f 0.0 compartment (Cell)
Xa_Va_II_l Xa_Va_II_l 0.0 compartment (Cell)
Xa_Va_l Xa_Va_l 0.0 compartment (Cell)
Xa_Va_mIIa_l Xa_Va_mIIa_l 0.0 compartment (Cell)
Xa_f Xa_f 0.0 compartment (Cell)
Xa_l Xa_l 0.0 compartment (Cell)
mIIa_AT_l mIIa_AT_l 0.0 compartment (Cell)
mIIa_f mIIa_f 0.0 compartment (Cell)
mIIa_l mIIa_l 0.0 compartment (Cell)

Initial assignments are expressions that are evaluated at time=0. It is not recommended to create initial assignments for all model entities. Restrict the use of initial assignments to cases where a value is expressed in terms of values or sizes of other model entities. Note that it is not permitted to have both an initial assignment and an assignment rule for a single model entity.

Definition
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
LB1 Factor II lipid binding II_f + {100.0}LIPID > II_l

compartment * (konII * II_f * LIPID / nva - koffII * II_l)
LB10 Factor IXa lipid binding IXa_f + {100.0}LIPID > IXa_l

compartment * (konIXa * IXa_f * LIPID / nva - koffIXa * IXa_l)
LB11 Factor X lipid binding X_f + {100.0}LIPID > X_l

compartment * (konX * X_f * LIPID / nva - koffX * X_l)
LB12 Factor Xa lipid binding Xa_f + {100.0}LIPID > Xa_l

konXa * Xa_f * LIPID / nva - koffXa * Xa_l
LB13 APC lipid binding APC_f + {100.0}LIPID > APC_l

compartment * (konAPC * APC_f * LIPID / nva - koffAPC * APC_l)
LB14 PS lipid binding PS_f + {100.0}LIPID > PS_l

compartment * (konPS * PS_f * LIPID / nva - koffPS * PS_l)
LB15 Factor VIIIai lipid binding VIIIai_f + {100.0}LIPID > VIIIai_l

compartment * (konVIIIai * VIIIai_f * LIPID / nva - koffVIIIai * VIIIai_l)
LB16 Factor Vai lipid binding Vai_f + {100.0}LIPID > Vai_l

compartment * (konVai * Vai_f * LIPID / nva - koffVai * Vai_l)
LB17 PC lipid binding PC_f + {100.0}LIPID > PC_l

compartment * (konPC * PC_f * LIPID / nva - koffPC * PC_l)
LB2 Factor mIIa lipid binding mIIa_f + {100.0}LIPID > mIIa_l

compartment * (konmIIa * mIIa_f * LIPID / nva - koffmIIa * mIIa_l)
LB3 Factor V lipid binding V_f + {100.0}LIPID > V_l

compartment * (konV * V_f * LIPID / nva - koffV * V_l)
LB4 Factor Va lipid binding Va_f + {100.0}LIPID > Va_l

compartment * (konVa * Va_f * LIPID / nva - koffVa * Va_l)
LB5 Factor VII lipid binding VII_f + {100.0}LIPID > VII_l

compartment * (konVII * VII_f * LIPID / nva - koffVII * VII_l)
LB6 Factor VIIa lipid binding VIIa_f + {100.0}LIPID > VIIa_l

compartment * (konVIIa * VIIa_f * LIPID / nva - koffVIIa * VIIa_l)
LB7 Factor VIII lipid binding VIII_f + {100.0}LIPID > VIII_l

compartment * (konVIII * VIII_f * LIPID / nva - koffVIII * VIII_l)
LB8 Factor VIIIa lipid binding VIIIa_f + {100.0}LIPID > VIIIa_l

compartment * (konVIIIa * VIIIa_f * LIPID / nva - koffVIIIa * VIIIa_l)
LB9 Factor IX lipid binding IX_f + {100.0}LIPID > IX_l

compartment * (konIX * IX_f * LIPID / nva - koffIX * IX_l)
R1 TF_VIIa binding VIIa_l + TF_l > TF_VIIa_l

compartment * (k1 * TF_l * VIIa_l - k2 * TF_VIIa_l)
R10 Xa_VIII binding Xa_l + VIII_l > VIII_Xa_l

k24 * VIII_l * Xa_l - k25 * VIII_Xa_l
R10b Factor VIII activation VIII_Xa_l > Xa_l + VIIIa_l

compartment * k26 * VIII_Xa_l
R11 IIa_f + V_l > V_IIa_l

compartment * (k27 * V_l * IIa_f - k28 * V_IIa_l)
R11b V_IIa_l > IIa_f + Va_l

compartment * k29 * V_IIa_l
R12 IIa_f + VIII_l > VIII_IIa_l

compartment * (k30 * VIII_l * IIa_f - k31 * VIII_IIa_l)
R12b VIII_IIa_l > IIa_f + VIIIa_l

compartment * k32 * VIII_IIa_l
R13 II_l + Xa_Va_l > Xa_Va_II_l

compartment * (k33 * Xa_Va_l * II_l - k34 * Xa_Va_II_l)
R14 mIIa_l + Xa_Va_l > Xa_Va_mIIa_l

compartment * (k35 * Xa_Va_l * mIIa_l - k36 * Xa_Va_mIIa_l)
R15 Xa_Va_II_l > Xa_Va_mIIa_l

compartment * k37 * Xa_Va_II_l
R15b Xa_Va_mIIa_l > IIa_f + Xa_Va_l

compartment * k38 * Xa_Va_mIIa_l
R16 Xa_l + VII_l > VII_Xa_l

compartment * (k39 * VII_l * Xa_l - k40 * VII_Xa_l)
R16b VII_Xa_l > Xa_l + VIIa_l

compartment * k41 * VII_Xa_l
R17 IIa_f + XI_f > XI_IIa_l

compartment * (k42 * XI_f * IIa_f - k43 * XI_IIa_l)
R17b XI_IIa_l > IIa_f + XIa_l

compartment * k44 * XI_IIa_l
R18 VIIIa_l + APC_PS_l > APC_PS_VIIIa_l

compartment * (k45 * APC_PS_l * VIIIa_l - k46 * APC_PS_VIIIa_l)
R18b APC_PS_VIIIa_l > VIIIai_l + APC_PS_l

compartment * k47 * APC_PS_VIIIa_l
R19 Va_l + APC_PS_l > APC_PS_Va_l

compartment * (k48 * APC_PS_l * Va_l - k49 * APC_PS_Va_l)
R19b APC_PS_Va_l > Vai_l + APC_PS_l

compartment * k50 * APC_PS_Va_l
R2 TF_VII binding VII_l + TF_l > TF_VII_l

compartment * (k3 * TF_l * VII_l - k4 * TF_VII_l)
R20 Xa_f + TFPI_f > TFPI_Xa_l

compartment * (k51 * TFPI_f * Xa_f - k52 * TFPI_Xa_l)
R21 TF_VIIa_l + TFPI_Xa_l > TFPI_Xa_TF_VIIa_l

compartment * (k53 * TFPI_Xa_l * TF_VIIa_l - k54 * TFPI_Xa_TF_VIIa_l)
R22 AT_f + IXa_f > IXa_AT_f

compartment * k55 * IXa_f * AT_f
R23 AT_f + Xa_f > Xa_AT_f

compartment * k56 * Xa_f * AT_f
R24 AT_f + IIa_f > IIa_AT_f

compartment * k57 * IIa_f * AT_f
R25 mIIa_l + V_l > V_mIIa_l

compartment * (k58 * V_l * mIIa_l - k59 * V_mIIa_l)
R25b V_mIIa_l > mIIa_l + Va_l

compartment * k60 * V_mIIa_l
R26 mIIa_l + VIII_l > VIII_mIIa_l

compartment * (k61 * VIII_l * mIIa_l - k62 * VIII_mIIa_l)
R26b VIII_mIIa_l > mIIa_l + VIIIa_l

compartment * k63 * VIII_mIIa_l
R27 TM_l + IIa_f > IIa_TM_l

compartment * (k64 * IIa_f * TM_l - k65 * IIa_TM_l)
R28 PC_l + IIa_TM_l > IIa_TM_PC_l

compartment * (k66 * IIa_TM_l * PC_l - k67 * IIa_TM_PC_l)
R28b IIa_TM_PC_l > APC_l + IIa_TM_l

compartment * k68 * IIa_TM_PC_l
R29 AT_f + mIIa_f > mIIa_AT_l

compartment * k69 * mIIa_f * AT_f
R3 IX_TF_VIIa binding IX_l + TF_VIIa_l > TF_VIIa_IX_l

compartment * (k5 * TF_VIIa_l * IX_l - k6 * TF_VIIa_IX_l)
R30 PS_l + APC_l > APC_PS_l

compartment * (k70 * APC_l * PS_l - k71 * APC_PS_l)
R31 IX_l + XIa_l > XIa_IX_l

compartment * (k72 * XIa_l * IX_l - k73 * XIa_IX_l)
R31b XIa_IX_l > IXa_l + XIa_l

compartment * k74 * XIa_IX_l
R3b Factor IX activation TF_VIIa_IX_l > TF_VIIa_l + IXa_l

compartment * k7 * TF_VIIa_IX_l
R4 X_TF_VIIa complex formation X_l + TF_VIIa_l > TF_VIIa_X_l

compartment * (k8 * TF_VIIa_l * X_l - k9 * TF_VIIa_X_l)
R4b Factor X activation TF_VIIa_X_l > TF_VIIa_Xa_l

compartment * k10 * TF_VIIa_X_l
R4c Factor Xa release TF_VIIa_Xa_l > Xa_l + TF_VIIa_l

compartment * k75 * TF_VIIa_Xa_l
R5 Xa_TF_VII binding Xa_l + TF_VII_l > TF_VII_Xa_l

compartment * (k11 * TF_VII_l * Xa_l - k12 * TF_VII_Xa_l)
R5b TF_VII activation TF_VII_Xa_l > Xa_l + TF_VIIa_l

compartment * k13 * TF_VII_Xa_l
R6 VIIIa_IXa binding VIIIa_l + IXa_l > IXa_VIIIa_l

compartment * (k14 * IXa_l * VIIIa_l - k15 * IXa_VIIIa_l)
R7 Va_Xa binding Va_l + Xa_l > Xa_Va_l

compartment * (k16 * Xa_l * Va_l - k17 * Xa_Va_l)
R8 X_IXa_VIIIa complex formation X_l + IXa_VIIIa_l > IXa_VIIIa_X_l

compartment * (k18 * IXa_VIIIa_l * X_l - k19 * IXa_VIIIa_X_l)
R8b Factor X activation IXa_VIIIa_X_l > Xa_l + IXa_VIIIa_l

compartment * k20 * IXa_VIIIa_X_l
R9 V_Xa binding Xa_l + V_l > V_Xa_l

compartment * (k21 * V_l * Xa_l - k22 * V_Xa_l)
R9b Factor V activation V_Xa_l > Xa_l + Va_l

compartment * k23 * V_Xa_l

Global parameters

Id Value
k1 0.5
k10 1.5
k11 0.05
k12 44.8
k13 15.2
k14 0.1
k15 0.2
k16 1.0
k17 1.0
k18 0.1
k19 10.7
k2 0.005
k20 8.3
k21 0.1
k22 1.0
k23 0.043
k24 0.1
k25 2.1
k26 0.023
k27 0.1
k28 6.94
k29 0.23
k3 0.005
k30 0.1
k31 13.8
k32 0.9
k33 0.1
k34 100.0
k35 0.1
k36 66.0
k37 13.0
k38 15.0
k39 0.05
k4 0.005
k40 44.8
k41 15.2
k42 0.1
k43 10.0
k44 1.43
k45 0.1
k46 1.6
k47 0.4
k48 0.1
k49 1.6
k5 0.01
k50 0.4
k51 0.016
k52 0.00033
k53 0.01
k54 0.0011
k55 0.00000049
k56 0.0000023
k57 0.0000683
k58 0.1
k59 6.94
k6 2.09
k60 1.035
k61 0.1
k62 13.8
k63 0.9
k64 1.0
k65 0.5
k66 0.1
k67 6.4
k68 3.6
k69 0.00000683
k7 0.34
k70 0.1
k71 0.5
k72 0.01
k73 1.417
k74 0.183
k75 1.0
k8 0.1
k9 32.5
koffAPC 3.5
koffII 1.0
koffIX 0.115
koffIXa 0.115
koffPC 11.5
koffPS 0.2
koffV 0.145
koffVII 0.66
koffVIII 0.1
koffVIIIa 0.335
koffVIIIai 0.335
koffVIIa 0.227
koffVa 0.17
koffVai 0.17
koffX 1.9
koffXa 3.3
koffmIIa 0.475
konAPC 0.05
konII 0.0043
konIX 0.05
konIXa 0.05
konPC 0.05
konPS 0.05
konV 0.05
konVII 0.05
konVIII 0.05
konVIIIa 0.05
konVIIIai 0.05
konVIIa 0.05
konVa 0.057
konVai 0.057
konX 0.01
konXa 0.029
konmIIa 0.05
nva 100.0

Local parameters

Id Value Reaction

Assignment rules

Definition

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments