Development of models of active ion transport for whole-cell modelling: cardiac sodium–potassium pump as a case study

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 Läuger 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 (Δ G ATP) 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 Δ G ATP and pump cycling direction is investigated and compared with recent experimental findings.