A generalization of the Goldman equation, including the effect of electrogenic pumps

Abstract

An equation similar to the Goldman equation is derived for the steady-state diffusion of univalent ions across a membrane with arbitrary potential profile and in the presence of electrogenic pumps. The presence of electrogenic pumps adds a term proportional to the net pump flux to both numerator and denominator in the Goldman equation. For arbitrary potential profiles the permeabilities of the positive ions are all divided by one potential-dependent factor and the permeabilities of the negative ions are divided by another such factor. Both factors are determined by the potential function and tend to vary inversely. If the symmetric part of the potential function is zero, both factors are equal to 1.0. Hence in the general form of the Goldman equation the relative contributions of the positive and negative ions are weighted by factors that are easily calculated if the potential function is known.