A general relation between membrane potential, ion activities, and pump fluxes for symmetric cells in a steady state

Abstract

For steady states of cells that have uniform cell membranes, there must be zero net fluxes of each ion. This provides a set of conditions more restrictive than the condition of zero net current flow that is used to derive the Goldman equation. We show that this leads to a set of general relations between the membrane potential, ion activities, ion permeabilities, and pump fluxes and that the Goldman equation is but one of this set. Further, we demonstrate that the transmembrane potential is uniquely defined by the intracellular and extracellular activities, the permeability coefficients, and the ratio of the net mediated (nondiffusional) fluxes of any two ions of the same valence in a steady state, regardless of the behavior of other ions and without assumptions with respect to the electrical potential profile across the membrane. In the course of this, we also give an exact and general derivation of the Mullins-Noda relation.