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BIOMD0000000248 - Lai2007_O2_Transport_Metabolism

 

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Reference Publication
Publication ID: 17380394
Lai N, Camesasca M, Saidel GM, Dash RK, Cabrera ME.
Linking pulmonary oxygen uptake, muscle oxygen utilization and cellular metabolism during exercise.
Ann Biomed Eng 2007 Jun; 35(6): 956-969
Biomedical Engineering, Case Western Reserve University, Cleveland, OH 44106-6011, USA.  [more]
Model
Original Model: BIOMD0000000248.origin
Submitter: Nicola Lai
Submission ID: MODEL1004170000
Submission Date: 17 Apr 2010 20:06:55 UTC
Last Modification Date: 03 Jun 2014 14:58:51 UTC
Creation Date: 16 Oct 2009 20:26:03 UTC
Encoders:  Nicola Lai
   Justin Chiou
set #1
bqmodel:isDerivedFrom PubMed 10898733
PubMed 16636861
set #2
bqbiol:isVersionOf Gene Ontology cellular response to oxygen levels
Gene Ontology oxygen metabolic process
Gene Ontology oxygen transport
set #3
bqbiol:hasTaxon Taxonomy Homo sapiens
Notes

This file describes the SBML version of the mathematical model in the following journal article: Linking Pulmonary Oxygen Uptake, Muscle Oxygen Utilization and Cellular Metabolism during Exercise, Ann Biomed Eng. 2007 Jun;35(6):956-69. (Pubmed ID: 17380394). This mathematical model simulates oxygen transport and metabolism in skeletal muscle in response to a step change from a warm-up steady state to a higher work rate corresponding to exercise at different levels of intensity: moderate (M), heavy (H) and very heavy (VH). The model parameter values are listed in the tables of this article. The parameter values that are independent of the exercise level are reported in Table 2. The parameter values that depend on the exercise level are reported in Tables 1A, 3 and 4. The model simulations (Figures 2, 3, 4 and 5) were obtained for a representative subject with a set of parameter values different from those in Table 1A, 3 and 4. In the sbml model, these model parameters are used to simulate exercise at a very heavy (VH) intensity for the representative subject. Additionally, the parameter values needed to simulate exercise at moderate (M) and heavy (H) intensity are reported in the list of parameters of the file. The model simulates dynamics of (1) the concentrations of free (F) and total (T) oxygen concentration in blood (CFcap, CTcap) and tissue (CFtis, CTtis), Adenosine Triphosphate (ATP), Adenosine Diphosphate (ADP), Phosphocreatine (PCr) and Creatine (Cr); (2) the metabolic flux of oxidative phosphorylation, creatine kinase and ATPase; (3) the oxygen uptake in blood and oxygen transport rate from blood to tissue during exercise. The simulation also computes muscle oxygen saturation (StO2m) and relative muscle oxygen saturation (RStO2m) in order to compare simulated and experimental responses of human muscle oxygenation during exercise. The model was successfully tested with Roadrunner of the Systems Biology Workbench (SBW). The model simulations obtained with Roadrunner match those obtained with the mathematical model represented in Fortran and Matlab for relative and absolute tolerance smaller than 10-7.

To allow for simulations at varying levels of exercise, the parameter exercise_level was introduced. A value of 1 means medium, 2 heavy and 3 very heavy exercise. Setting this parameter assigns the parameters Vmax, KatpaseE, dQMm and tauQm with the relevant parameters. The warmup steady state is influenced by the parameter changes for this representative subject and the model has to be brought into steady state after each change of exercise level.

This model originates from BioModels Database: A Database of Annotated Published Models. It is copyright (c) 2005-2010 The BioModels Team.
For more information see the terms of use.
To cite BioModels Database, please use Le Nov��re N., Bornstein B., Broicher A., Courtot M., Donizelli M., Dharuri H., Li L., Sauro H., Schilstra M., Shapiro B., Snoep J.L., Hucka M. (2006) BioModels Database: A Free, Centralized Database of Curated, Published, Quantitative Kinetic Models of Biochemical and Cellular Systems Nucleic Acids Res., 34: D689-D691.

Model
Publication ID: 17380394 Submission Date: 17 Apr 2010 20:06:55 UTC Last Modification Date: 03 Jun 2014 14:58:51 UTC Creation Date: 16 Oct 2009 20:26:03 UTC
Mathematical expressions
Reactions
ATPase OxidativePhosphorylation ConvectionTransport DiffusionTransport
CreatineKinase      
Rules
Rate Rule (variable: CFcap) Rate Rule (variable: CFtis) Assignment Rule (variable: Katpase) Assignment Rule (variable: Qm)
Assignment Rule (variable: PSm) Assignment Rule (variable: StO2m) Assignment Rule (variable: RStO2m) Assignment Rule (variable: Vmax)
Assignment Rule (variable: KatpaseE) Assignment Rule (variable: dQMm) Assignment Rule (variable: tauQm) Assignment Rule (variable: ATPase_flux_mM)
Assignment Rule (variable: CK_flux_mM) Assignment Rule (variable: oxygen_phosphorilation_rate_mM)    
Physical entities
Compartments Species
Capillary CTcap CFcap  
Tissue ATP PCr ADP
Cr Pi CTtis
CFtis    
Global parameters
StO2m RStO2m Katpase KatpaseW
Kadp Kia Kiq Kib
Kp Kb Km VfCK
VrCK QRm QWm Qm
Qc PSR PSE PSm
nH Hct Wmc CmcMb
CrbcHb KMb KHb tE
CTart Vmax VmaxM VmaxH
VmaxVH KatpaseE KatpaseM KatpaseH
KatpaseVH dQMm dQMmM dQMmH
dQMmVH tauQm tauQmM tauQmH
tauQmVH StO2mW exercise_level ATPase_flux_mM
CK_flux_mM oxygen_phosphorilation_rate_mM    
Reactions (5)
 
 ATPase [ATP] ↔ [ADP];  
 
 OxidativePhosphorylation 6.0 × [ADP] + [CTtis] ↔ 6.0 × [ATP];   {Pi} , {CFtis}
 
 ConvectionTransport  ↔ [CTcap];  
 
 DiffusionTransport [CTcap] ↔ [CTtis];   {CFcap} , {CFtis}
 
 CreatineKinase [ADP] + [PCr] ↔ [ATP] + [Cr];  
 
Rules (14)
 
 Rate Rule (name: CFcap) d [ CFcap] / d t= (Qm*(CTart-CTcap)-PSm*(CFcap-CFtis))*1/Capillary/(1+4*Hct*CrbcHb*KHb*nH*CFcap^(nH-1)/(1+KHb*CFcap^nH)^2)
 
 Rate Rule (name: CFtis) d [ CFtis] / d t= (PSm*(CFcap-CFtis)/Tissue-Vmax*CFtis/(Km+CFtis)*ADP/(Kadp+ADP))/(1+Wmc*CmcMb*KMb/(1+KMb*CFtis)^2)
 
 Assignment Rule (name: Katpase) Katpase = piecewise(KatpaseW, time <= tE, KatpaseE)
 
 Assignment Rule (name: Qm) Qm = piecewise(QWm, time <= tE, QWm+dQMm*(1-exp((tE-time)/tauQm)))
 
 Assignment Rule (name: PSm) PSm = PSR+(PSE-PSR)*(1-exp((QRm-Qm)/Qc))
 
 Assignment Rule (name: StO2m) StO2m = 100*(Hct*CrbcHb*KHb*CFcap^nH/(1+KHb*CFcap^nH)*Capillary+Wmc*CmcMb*KMb*CFtis/(1+KMb*CFtis)*Tissue)/(CrbcHb*Hct*Capillary+CmcMb*Wmc*Tissue)
 
 Assignment Rule (name: RStO2m) RStO2m = StO2m/StO2mW-1
 
 Assignment Rule (name: Vmax) Vmax = piecewise(VmaxM, exercise_level == 1, piecewise(VmaxH, exercise_level == 2, VmaxVH))
 
 Assignment Rule (name: KatpaseE) KatpaseE = piecewise(KatpaseM, exercise_level == 1, piecewise(KatpaseH, exercise_level == 2, KatpaseVH))
 
 Assignment Rule (name: dQMm) dQMm = piecewise(dQMmM, exercise_level == 1, piecewise(dQMmH, exercise_level == 2, dQMmVH))
 
 Assignment Rule (name: tauQm) tauQm = piecewise(tauQmM, exercise_level == 1, piecewise(tauQmH, exercise_level == 2, tauQmVH))
 
 Assignment Rule (name: ATPase_flux_mM) ATPase_flux_mM = ATPase/Tissue
 
 Assignment Rule (name: CK_flux_mM) CK_flux_mM = 1*CreatineKinase/Tissue
 
 Assignment Rule (name: oxygen_phosph) oxygen_phosphorilation_rate_mM = OxidativePhosphorylation/Tissue*6
 
 Capillary Spatial dimensions: 3.0  Compartment size: 2.0979  (Units: litre)
 
 CTcap
Compartment: Capillary
Initial concentration: 5.281527
 
 CFcap
Compartment: Capillary
Initial concentration: 0.03969
 
 Tissue Spatial dimensions: 3.0  Compartment size: 27.8721  (Units: litre)
 
 ATP
Compartment: Tissue
Initial concentration: 8.198857
 
 PCr
Compartment: Tissue
Initial concentration: 40.98942
 
 ADP
Compartment: Tissue
Initial concentration: 0.001142
 
 Cr
Compartment: Tissue
Initial concentration: 1.01056
 
 Pi
Compartment: Tissue
Initial concentration: 0.5
 
 CTtis
Compartment: Tissue
Initial concentration: 0.4084824
 
 CFtis
Compartment: Tissue
Initial concentration: 0.0374
 
Global Parameters (50)
 
   StO2m
Value: NaN   (Units: dimensionless)
 
   RStO2m
Value: NaN   (Units: dimensionless)
 
   Katpase
Value: 0.3207601   (Units: perMin)
 
   KatpaseW
Value: 0.3207601   (Units: perMin)
Constant
 
   Kadp
Value: 0.058   (Units: mM)
Constant
 
   Kia
Value: 0.135   (Units: mM)
Constant
 
   Kiq
Value: 3.5   (Units: mM)
Constant
 
   Kib
Value: 3.9   (Units: mM)
Constant
 
   Kp
Value: 3.8   (Units: mM)
Constant
 
   Kb
Value: 1.11   (Units: mM)
Constant
 
   Km
Value: 7.0E-4   (Units: mM)
Constant
 
   VfCK
Value: 6000.0   (Units: mMperMin)
Constant
 
   VrCK
Value: 3008.65837589001   (Units: mMperMin)
Constant
 
   QRm
Value: 0.688   (Units: LperMin)
Constant
 
   QWm
Value: 3.118   (Units: LperMin)
Constant
 
   Qm
Value: 3.118   (Units: LperMin)
 
   Qc
Value: 8.0   (Units: LperMin)
Constant
 
   PSR
Value: 134.2828   (Units: LperMin)
Constant
 
   PSE
Value: 20000.0   (Units: LperMin)
Constant
 
   PSm
Value: 5338.8   (Units: LperMin)
 
   nH
Value: 2.7   (Units: dimensionless)
Constant
 
   Hct
Value: 0.45   (Units: dimensionless)
Constant
 
   Wmc
Value: 0.8064   (Units: dimensionless)
Constant
 
   CmcMb
Value: 0.5   (Units: mM)
Constant
 
   CrbcHb
Value: 5.18   (Units: mM)
Constant
 
   KMb
Value: 308.642   (Units: permM)
Constant
 
   KHb
Value: 7800.7   (Units: mM)
Constant
 
   tE
Value: 3.0   (Units: min)
Constant
 
   CTart
Value: 9.199981   (Units: mM)
Constant
 
   Vmax
Value: 23.11702   (Units: mMperMin)
 
   VmaxM
Value: 53.5150933   (Units: mMperMin)
Constant
 
   VmaxH
Value: 34.68714   (Units: mMperMin)
Constant
 
   VmaxVH
Value: 23.11702   (Units: mMperMin)
Constant
 
   KatpaseE
Value: 3.3423645   (Units: perMin)
 
   KatpaseM
Value: 1.71080439028658   (Units: perMin)
Constant
 
   KatpaseH
Value: 2.2581564   (Units: perMin)
Constant
 
   KatpaseVH
Value: 3.3423645   (Units: perMin)
Constant
 
   dQMm
Value: 12.74981   (Units: LperMin)
 
   dQMmM
Value: 7.9167374   (Units: LperMin)
Constant
 
   dQMmH
Value: 9.42198   (Units: LperMin)
Constant
 
   dQMmVH
Value: 12.74981   (Units: LperMin)
Constant
 
   tauQm
Value: 0.42   (Units: min)
 
   tauQmM
Value: 0.32   (Units: min)
Constant
 
   tauQmH
Value: 0.396   (Units: min)
Constant
 
   tauQmVH
Value: 0.42   (Units: min)
Constant
 
   StO2mW
Value: 81.17123516   (Units: dimensionless)
Constant
 
   exercise_level
Value: 3.0   (Units: dimensionless)
Constant
 
   ATPase_flux_mM
Value: NaN   (Units: mMperMin)
 
   CK_flux_mM
Value: NaN   (Units: mMperMin)
 
   oxygen_phosphorilation_rate_mM
Value: NaN   (Units: mMperMin)
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000248

Curator's comment: (updated: 19 Apr 2010 04:33:25 BST)

Reproduction of some of the results from the publication (figures 2 and 4) using Copasi 4.5.31.
Before running the time courses under medium and heavy exercise conditions (exercise_level=1,2), the initial conditions were equilibrated by integrating for 3 minutes and starting from the final values twice.

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