Development of models of active ion transport for whole-cell modelling: cardiac sodium-potassium pump as a case study
Alice
Boit
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML model runs in both OpenCell and COR.
Model Structure
ABSTRACT: This study presents a method for the reduction of biophysically-based kinetic models for the active transport of ions. A lumping scheme is presented which exploits the differences in timescales associated with fast and slow transitions between model states, while maintaining the thermodynamic properties of the model. The goal of this approach is to contribute to modelling of the effects of disturbances to metabolism, associated with ischaemic heart disease, on cardiac cell function. The approach is illustrated for the sodium-potassium pump in the myocyte. The lumping scheme is applied to produce a 4-state representation from the detailed 15-state model of Lauger and Apell, Eur. Biophys. J. 13 (1986) 309, for which the principles of free energy transduction are used to link the free energy released from ATP hydrolysis (deltaGATP) to the transition rates between states of the model. An iterative minimisation algorithm is implemented to determine the transition rate parameters based on the model fit to experimental data. Finally, the relationship between deltaGATP and pump cycling direction is investigated and compared with recent experimental findings.
The original paper reference is cited below:
Development of models of active ion transport for whole-cell modelling: cardiac sodium-potassium pump as a case study, N. P. Smith and E. J. Crampin, 2004, Progress in Biophysics and Molecular Biology
PubMed ID: 15142754
15-state State Diagram
The 15 states of the original model.
Smith-Crampin 4-state lumping scheme
The 4 states of the Smith-Crampin model.
active transport
cardiac myocyte
electrophysiology
cardiac
na/k pump
Calculation the energy released by ATP hydrolysis.
a.boit@auckland.ac.nz
Calculation of the Na contribution to dG_pump.
Calculation of the reverse transition rate called minus_alpha2 from the 3rd to the second state.
Calculation of the dimless_K_i parameter.
Calculation of the foward transition rate called alpha3 from the third to the fourth state.
This is the CellML description of N. P. Smith' and E. Crampin's 2004
mathematical model of the cardiac sodium-potassium pump.
Alice Boit
Calculation of the reverse transition rate called minus_alpha1 from the second to the first state.
Calculation of the dimless_K_e parameter.
Alice
Boit
Calculation of the diagram sum used in the denominator of the equation of cycle rate v_cyc.
Calculation of the clockwise cycle rate v_cyc.
Calculation the net free energy of the cycle.
Progress in Biophysics & Molecular Biology
2004
Calculation of the concentration of free inorganic phosphate cPi
related to the total measurable concentration given by cPi_sum.
The University of Auckland, Auckland Bioengineering Institute
Calculation of the foward transition rate called alpha1 from the first to the second lumped state.
The Na/K-pump is an energy-consuming transporter channel within the membrane.
It is indispensible for maintaining the electrochemical gradients of the involved ions
across the membrane which result in resting Vm. The pump splits up one ATP molecule as it undergoes a
conformational change transporting 3Na outwards and 2K inwards in each cycle.
Calculation of the dimless_MgATP parameter.
E
Crampin
J
N. P. Smith' and E. Crampin's 2004 mathematical model of the cardiac sodium-potassium pump.
Cardiac Myocyte
keyword
Calculation of the foward transition rate called alpha2 from the second to the third state.
Note that this transition rate is identical to k2 because state P7 (see paper) is not a lumped state.
Calculation of the dimless_Na_e parameter which is a
function of Vm because the equilibrium constant is
dependent on Vm (which occurs in the denominator's exponential). Note that the partition of the
voltage dependency in the exponential corresponds to the previous calculation of dimless_Na_i.
Calculation of the dimless_Na_i parameter which is a function of Vm because the equilibrium constant is
dependent on Vm (which occurs in the denominator's exponential).
Calculation of the K contribution to dG_pump.
Calculation of dG_pump.
Development of models of active ion transport for whole-cell modelling: cardiac sodium-potassium pump as a case study
85(2-3)
387
405
The University of Auckland
Auckland Bioengineering Institute
Calculation of the reverse transition rate called minus_alpha3 from the fourth to the 3rd state.
15142754
Calculation of the foward transition rate called alpha4 from the fourth to the first state.
2004-04-26T00:00:00+00:00
N
Smith
P
Calculation of the reverse transition rate called minus_alpha4 from the first to the fourth lumped state.