Dunster2016  Nondimensional Coagulation Model
Model Identifier
BIOMD0000000925
Short description
We undertake a mathematical investigation of a model for the generation of thrombin, an enzyme central to haemostatic blood coagulation, as well as to thrombotic disorders, that is the end product of a complicated protein cascade with multiple feedbacks that ensures its production in the right place at the right time. In a laboratory setting, its central role is reflected in thrombin evolution over time being used as a measure of the ability of a patient's blood to clot. Here, we present a model for the generation of thrombin (based on earlier work) and analyse it using the method of matched asymptotic expansions to derive a sequence of simplified models that characterize the roles of distinct interactions over various timescales. In particular, we are able through the asymptotic analysis to provide simplified models that are an excellent substitute for the full model (capturing the explosive growth and decay of thrombin) and approximations for the key experimental measurements used to describe thrombin's characteristic evolution over time. The asymptotic results are validated against numerical simulations.
Format
SBML
(L2V4)
Related Publication
 Mathematical modelling of thrombin generation: asymptotic analysis and pathway characterization
 J. L. Dunster, J. R. King
 IMA Journal of Applied Mathematics , 2/ 2017 , Volume 82 , Issue 1 , pages: 6096 , DOI: 10.1093/imamat/hxw007
 Department of Mathematics and Statistics, Institute for Cardiovascular and Metabolic Research, School of Biological Sciences, University of Reading, Reading, UK.
 We undertake a mathematical investigation of a model for the generation of thrombin, an enzyme central to haemostatic blood coagulation, as well as to thrombotic disorders, that is the end product of a complicated protein cascade with multiple feedbacks that ensures its production in the right place at the right time. In a laboratory setting, its central role is reflected in thrombin evolution over time being used as a measure of the ability of a patient's blood to clot. Here, we present a model for the generation of thrombin (based on earlier work) and analyse it using the method of matched asymptotic expansions to derive a sequence of simplified models that characterize the roles of distinct interactions over various timescales. In particular, we are able through the asymptotic analysis to provide simplified models that are an excellent substitute for the full model (capturing the explosive growth and decay of thrombin) and approximations for the key experimental measurements used to describe thrombin's characteristic evolution over time. The asymptotic results are validated against numerical simulations.
Contributors
Submitter of the first revision: Matthew Roberts
Submitter of this revision: Ahmad Zyoud
Modellers: Matthew Roberts, Ahmad Zyoud
Submitter of this revision: Ahmad Zyoud
Modellers: Matthew Roberts, Ahmad Zyoud
Metadata information
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hasTaxon (1 statement)
isVersionOf (1 statement)
hasProperty (1 statement)
occursIn (1 statement)
isDescribedBy (1 statement)
BioModels Database
MODEL1808140001
BioModels Database MODEL1808140001
BioModels Database BIOMD0000000925
BioModels Database MODEL1808140001
BioModels Database BIOMD0000000925
hasTaxon (1 statement)
isVersionOf (1 statement)
hasProperty (1 statement)
occursIn (1 statement)
isDescribedBy (1 statement)
Curation status
Curated
Modelling approach(es)
Tags
Connected external resources
Name  Description  Size  Actions 

Model files 

Dunster2016_Nondimensional_Model_Curated.xml  SBML L2V4 representation of Dunster2016  Nondimensional Coagulation Model_CuratedFigure 4  178.02 KB  Preview  Download 
Additional files 

Dunster2016_Dimensional_Model.cps  Model COPASI file for dimensional model.  97.54 KB  Preview  Download 
Dunster2016_Nondimensional_Model (1).xml  SBML L2V4 representation of Dunster2016  Nondimensional Coagulation Model_Orignal  32.31 KB  Preview  Download 
Dunster2016_Nondimensional_Model.cps  Curated (nondimensional) model COPASI file. Figure 4 simulation results reproduced.  85.55 KB  Preview  Download 
Dunster2016_Nondimensional_Model1.sedml  sedml L1V2 representation of Dunster2016  Nondimensional Coagulation Model_CuratedFigure 4  14.96 KB  Preview  Download 
Dunster2016_Nondimensional_Model_Curated.cps  COPASI version 4.27 (Build 217) representation of Dunster2016  Nondimensional Coagulation Model_CuratedFigure 4  295.14 KB  Preview  Download 
 Model originally submitted by : Matthew Roberts
 Submitted: Aug 14, 2018 2:32:35 PM
 Last Modified: Mar 26, 2020 2:50:50 PM
Revisions

Version: 4
 Submitted on: Mar 26, 2020 2:50:50 PM
 Submitted by: Ahmad Zyoud
 With comment: Automatically added model identifier BIOMD0000000925

Version: 2
 Submitted on: Aug 14, 2018 2:32:35 PM
 Submitted by: Matthew Roberts
 With comment: Edited model metadata online.
(*) You might be seeing discontinuous revisions as only public revisions are displayed here. Any private revisions of this model will only be shown to the submitter and their collaborators.
Legends
: Variable used inside SBML models
: Variable used inside SBML models
Species
Species  Initial Concentration/Amount 

Xa L  0.0 mmol 
Xa  0.0 mmol 
Va Xa L  0.0 mmol 
Va  0.0 mmol 
PC  92.0 mmol 
IIa ATIII  0.0 mmol 
II  17.0 mmol 
Fibrin  0.0 mmol 
Xa ATIII  0.0 mmol 
IIa  0.0 mmol 
Reactions
Reactions  Rate  Parameters 

Xa_L = 0.5*((k_tilde_x+l_tilde_x+Xa)((k_tilde_x+l_tilde_x+Xa)^24*l_tilde_x*Xa)^(0.5))  []  k_tilde_x = 385.0; l_tilde_x = 7.69 
Xa = ((k_tilde_1a*gamma_tilde_1a*exp((gamma_tilde_1a)*time)+k_tilde_3c*k_tilde_3a*APC*Va_Xa/(Va_Xa+1))k_tilde_1b*Xa)k_tilde_3a*Xa*Va  ((k_tilde_1a*gamma_tilde_1a*exp((gamma_tilde_1a)*time)+k_tilde_3c*k_tilde_3a*APC*Va_Xa/(Va_Xa+1))k_tilde_1b*Xa)k_tilde_3a*Xa*Va  gamma_tilde_1a = 0.77; k_tilde_3a = 150.0; k_tilde_1a = 150.0; k_tilde_3c = 1.0; k_tilde_1b = 0.19 
Va_Xa_L = 0.5*((k_tilde_b+l_tilde_b+Va_Xa)((k_tilde_b+l_tilde_b+Va_Xa)^24*l_tilde_b*Va_Xa)^(0.5))  []  k_tilde_b = 5.0E4; l_tilde_b = 0.05 
Va = ((IIa*V/(V+k_tilde_2am*(1+Fibrinogen))+k_tilde_2b*Xa*V/(V+1+II)+k_tilde_3b/q_tilde_3a*Va_Xa)APC*Va/(Va+1))Xa*Va  ((IIa*V/(V+k_tilde_2am*(1+Fibrinogen))+k_tilde_2b*Xa*V/(V+1+II)+k_tilde_3b/q_tilde_3a*Va_Xa)APC*Va/(Va+1))Xa*Va  q_tilde_3a = 1.0; k_tilde_2am = 7.2; k_tilde_2b = 0.013; k_tilde_3b = 0.038 
PC = (k_tilde_5a)*PC  (k_tilde_5a)*PC  k_tilde_5a = 0.0011 
IIa_ATIII = IIa  IIa  [] 
II = (q_tilde_4a)*Xa_L*II/(V+1+II)k_tilde_4b*Va_Xa_L*II/(II+k_tilde_4bm)  (q_tilde_4a)*Xa_L*II/(V+1+II)k_tilde_4b*Va_Xa_L*II/(II+k_tilde_4bm)  k_tilde_4b = 530.0; q_tilde_4a = 0.004; k_tilde_4bm = 3.6 
Fibrin = k_tilde_6*Fibrinogen  k_tilde_6*Fibrinogen  k_tilde_6 = 1500.0 
Xa_ATIII = k_tilde_1b*Xa+k_tilde_3a*k_tilde_3b/q_tilde_3a*Va_Xa  k_tilde_1b*Xa+k_tilde_3a*k_tilde_3b/q_tilde_3a*Va_Xa  k_tilde_3a = 150.0; q_tilde_3a = 1.0; k_tilde_3b = 0.038; k_tilde_1b = 0.19 
IIa = (k_tilde_4a*Xa_L*II/(V+1+II)+k_tilde_4a*k_tilde_4b*Va_Xa_L*II/(q_tilde_4a*(II+k_tilde_4bm)))IIa  (k_tilde_4a*Xa_L*II/(V+1+II)+k_tilde_4a*k_tilde_4b*Va_Xa_L*II/(q_tilde_4a*(II+k_tilde_4bm)))IIa  k_tilde_4b = 530.0; k_tilde_4a = 0.12; q_tilde_4a = 0.004; k_tilde_4bm = 3.6 
Curator's comment:
(added: 26 Mar 2020, 14:50:26, updated: 26 Mar 2020, 14:50:26)
(added: 26 Mar 2020, 14:50:26, updated: 26 Mar 2020, 14:50:26)
All the figures within the Figure 4 has been successfully reproduced except of a slight shift in the Yaxis