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

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 ( β), 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/ τ) of decay of the transient currents could qualitatively be reproduced when β = 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 β itself is voltage-dependent, or if a second voltage-dependent step is included in the model.