A Thermodynamic Model of the Cardiac Sarcoplasmic/Endoplasmic Ca(2+) (SERCA) Pump
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML model has been unit checked and is known to run in both OpenCell and COR. This particular version of the CellML model describes the three-state cooperative SERCA model and recreates figure 13. In order to recreate this figure we have had to add an additional equation to the model to define the rate of change in Casr. Please also note there are typographical errors in the original paper and [H+] should be raised to the power of n (n=2) for T_Hi and T_Hsr. Also in figure 12 the concentrations of ADP should be 8uM and 20uM rather than 20uM and 40uM.
Model Structure
ABSTRACT: We present a biophysically based kinetic model of the cardiac SERCA pump that consolidates a range of experimental data into a consistent and thermodynamically constrained framework. The SERCA model consists of a number of sub-states with partial reactions that are sensitive to Ca(2+) and pH, and to the metabolites MgATP, MgADP, and Pi. Optimization of model parameters to fit experimental data favors a fully cooperative Ca(2+)-binding mechanism and predicts a Ca(2+)/H(+) counter-transport stoichiometry of 2. Moreover, the order of binding of the partial reactions, particularly the binding of MgATP, proves to be a strong determinant of the ability of the model to fit the data. A thermodynamic investigation of the model indicates that the binding of MgATP has a large inhibitory effect on the maximal reverse rate of the pump. The model is suitable for integrating into whole-cell models of cardiac electrophysiology and Ca(2+) dynamics to simulate the effects on the cell of compromised metabolism arising in ischemia and hypoxia.
The complete original paper reference is cited below:
A Thermodynamic Model of the Cardiac Sarcoplasmic/Endoplasmic Ca(2+) (SERCA) Pump, Kenneth Tran, Nicolas P. Smith, Denis S. Loiselle, and Edmund J. Crampin, 2009,
Biophysical Journal
, 96 (5) 2029-2042.
PubMed ID: 19254563
Schematic of the simplified three-state model. Application of the rapid equilibrium assumption to the ion-binding partial reactions (states within the two dotted boxes in Fig. 1) results in a simplified three-state model. The apparent rate constants (alphai + or -, i = 1, 2, 3) replace the forward and backward rate constants and are a function of ion concentrations and dissociation constants.
$\mathrm{T\_Cai}=\frac{\mathrm{Ca\_i}}{\mathrm{kdcai}}\mathrm{T\_Casr}=\frac{\mathrm{Ca\_sr}}{\mathrm{kdcasr}}\mathrm{T\_H1}=\frac{\mathrm{H\_i}}{\mathrm{kdh1}}\mathrm{T\_Hi}=\frac{\mathrm{H\_i}^{n}}{\mathrm{kdhi}}\mathrm{T\_Hsr}=\frac{\mathrm{H\_i}^{n}}{\mathrm{kdhsr}}\mathrm{T\_H}=\frac{\mathrm{H\_i}}{\mathrm{kdh}}\mathrm{a\_p1}=\mathrm{k\_p1}\mathrm{ATP}\mathrm{a\_p2}=\frac{\mathrm{k\_p2}\mathrm{T\_Cai}^{2}}{\mathrm{T\_Cai}^{2}+\mathrm{T\_Cai}^{2}\mathrm{T\_Hi}+\mathrm{T\_Hi}(1+\mathrm{T\_H1})}\mathrm{a\_p3}=\frac{\mathrm{k\_p3}\mathrm{T\_Hsr}}{\mathrm{T\_Casr}^{2}\mathrm{T\_H}+\mathrm{T\_H}+\mathrm{T\_Hsr}(1+\mathrm{T\_H})}\mathrm{a\_m1}=\frac{\mathrm{k\_m1}\mathrm{T\_Hi}}{\mathrm{T\_Cai}^{2}+\mathrm{T\_Cai}^{2}\mathrm{T\_Hi}+\mathrm{T\_Hi}(1+\mathrm{T\_H1})}\mathrm{a\_m2}=\frac{\mathrm{k\_m2}\mathrm{ADP}\mathrm{T\_Casr}^{2}\mathrm{T\_H}}{\mathrm{T\_Casr}^{2}\mathrm{T\_H}+\mathrm{T\_H}+\mathrm{T\_Hsr}(1+\mathrm{T\_H})}\mathrm{a\_m3}=\mathrm{k\_m3}\mathrm{P\_i}\mathrm{s1}=\mathrm{a\_p2}\mathrm{a\_p3}+\mathrm{a\_m1}\mathrm{a\_p3}+\mathrm{a\_m1}\mathrm{a\_m2}\mathrm{s2}=\mathrm{a\_p1}\mathrm{a\_p3}+\mathrm{a\_m2}\mathrm{a\_p1}+\mathrm{a\_m2}\mathrm{a\_m3}\mathrm{s3}=\mathrm{a\_p1}\mathrm{a\_p2}+\mathrm{a\_m3}\mathrm{a\_m1}+\mathrm{a\_m3}\mathrm{a\_p2}\mathrm{v\_cycle}=\frac{\mathrm{a\_p1}\mathrm{a\_p2}\mathrm{a\_p3}-\mathrm{a\_m1}\mathrm{a\_m2}\mathrm{a\_m3}}{\mathrm{s1}+\mathrm{s2}+\mathrm{s3}}\frac{d \mathrm{Ca\_sr}}{d \mathrm{time}}=1.0$
Simulation time domain
A Thermodynamic Model of the Cardiac Sarcoplasmic/Endoplasmic Ca(2+) (SERCA) Pump: the three-state SERCA model
Catherine Lloyd
This CellML model has been unit checked and is known to run in both PCEnv and COR. This particular version of the CellML model describes the three-state cooperative SERCA model and recreates figure 13. In order to recreate this figure we have had to add an additional equation to the model to define the rate of change in Casr.
The University of Auckland
Auckland Bioengineering Institute
Simulation time domain
Concentration of adenosine triphosphate in the cytosol
Concentration of calcium in the sarcoplasmic reticulum
Concentration of calcium in the cytosol
A Thermodynamic Model of the Cardiac Sarcoplasmic/Endoplasmic Ca(2+) (SERCA) Pump
Biophysical Journal
2009-03-00 00:00
keyword
electrophysiology
cardiac
SERCA
calcium dynamics
Brian Carlson
Model of the cardiac SERCA pump
Concentration of phosphate in the cytosol
Concentration of adenosine diphosphate in the cytosol
Concentration of hydrogen in the cytosol