Modeling the dynamic features of the electrogenic Na,K pump of cardiac cells

The purpose of this paper is to examine the dynamic features of the electrogenic Na,K pump of cardiac cells, based on a comparative analysis of a mechanistic model and an ad hoc mathematical description of the Na,K pump. Both representations are incorporated into a modified version of the Beeler-Reuter model for the ventricular membrane, and the resulting action potential models are studied under conditions of repetitive stimulation at steady rates between 0 and 3 Hz. The two Na,K pump representations have nearly identical steady-state characteristics of sensitivity to internal Na+ concentration, external K+ concentration, and membrane potential. Rapid voltage-dependent transient pump currents are present in the mechanistic model, while they are absent in the ad hoc mathematical description we used. The stimulation results show that a sizable peak of pump current caused by the action potential upstroke in the mechanistic model affects phase 1 repolarization, and that this effect is relatively independent of the stimulation rate. The pump current generated by our ad hoc mathematical description is constant during the action potential and does not affect directly the repolarization time course. While the two Na,K pump models show similar pumping efficiency at low stimulation rates, the mechanistic pump is more efficient at high rates of activity. In essence, the distinctive features of the mechanistic model are due to an energy barrier expressing the voltage dependence of the translocation step of the mechanism, and to the redistribution of the intermediates of the biochemical reactions during activity. In comparison, the ad hoc mathematical description exhibits a fixed dependence of the pump current on voltage and ionic concentrations.