The relationship between pump and leak: Part 1. Application of the Butler-Volmer equation

Abstract

The Na,K-ATPase transports three Na + ions outward and two K + ions inward. Calculations show that movement of very few uncompensated Na + ions completely charges the membrane and that after 9 seconds of operation of the pump on the red blood cell membrane the third Na + ion transported outward must be accompanied by an anion or exchange for a cation. It is concluded that Na + efflux measured over periods of minutes or hours is always compensated by simultaneous movement of other charge. Since passive fluxes of Na + and K + have rather high activation energies, the Butler-Volmer equation is used to describe this charge exchange. It is suggested that the passive permeability coefficient calculated from influx of Na + in the steady state overestimates the true value by a factor of r, the Na +/K + coupling ratio of the Na,K-ATPase. There is a single mixed potential across the plasma membrane in the steady state set equally by the passive fluxes and by the pump. It is found that a physiological steady state with steep cation gradients can only be achieved if the number of Na + and K + leakage channels on a membrane is of the same order of magnitude as the number of pumps, and if the passive permeability of Na + decreases and that of K + increases with increasing membrane potential. It is suggested as a possible mechanism of matching numbers of pumps and numbers of leakage channels that the Na,K-ATPase itself might function as both pump and leak.