Simulation of the voltage dependence of the Na, K pump applied to cardiac cells

Abstract

We use simulation to study the dependence of the Na, K pump on membrane potential. Two consecutive mechanisms for the Na, K pump, based on a reduced Post-Albers scheme, are examined: one with six steps called GV3 and one with seven steps called MGV3. In GV3, a single voltage-dependent step combines both Na+ translocation and Na+ release into the extracellular medium. In MGV3, these two processes are allocated to two separate consecutive steps, but only the Na+ translocation step is voltage-dependent. Using the optimization software SCoPfit, numerical values of rate coefficients, symmetry factor (beta), and pump site density were found by fitting the models to published experimental data so that both GV3 and MGV3 could quantitatively reproduce steady-state current-voltage relationships for both forward and backward running of the pump, as well as [Na+]in and [K+]out activation curves. Using the rate coefficient values found by SCoPfit, we simulated a voltage-clamp experiment with both models running under their Na(+)-Na+ exchange mode, and we computed the transient currents generated following voltage steps in both depolarizing and hyperpolarizing directions from a basic potential of -40 mV. The voltage dependence of the rate constant (1/tau) of decay of the transient currents could qualitatively be reproduced when beta = 0.884 for GV3, and 0.932 for MGV3. The quantitative discrepancy between published experimental data and the theoretical curve generated by GV3 at potentials more negative than -20 mV was considerably reduced by using model MGV3. This finding alone suggests that a more detailed mechanism containing a single voltage-dependent step may reproduce all major steady-state and transient characteristics of the Na, K pump without the need of a second voltage sensitive step. However, the quantitative discrepancy between published experimental data and the theoretical curve generated by MGV3 at potentials more negative than -60 mV may be fully removed if either beta itself is voltage-dependent, or if a second voltage-dependent step is included in the model.