The energy barrier model in membrane biophysics: Ion flow, current-voltage relations, and Donnan osmosis.

Abstract

Theoretical analysis of an energy barrier model for the electrical properties of a biological membrane yields new results. Discontinuities at the membrane-solution interfaces are crucial and receive careful attention, as does the polarization charge density due to electroneutral but polarized ion distributions. The topics explored include the equilibrium and time-dependent Nernst potential, the resting potential, the capacitance-resistance equation for membrane voltage, and large electrical effects on osmosis (bulk volume flow). The generalization of Nernst-Hartley salt diffusion to the diffusion of mixed salts as a necessary tool is accomplished. The electric field inside the membrane is especially strong at the membrane-solution interfaces. The analysis of the resting potential differs from the Goldman-Hodgkin-Katz formulation but predicts realistic numerical values for animal cells and also captures the effect of switching sodium and potassium ion permeabilities. An analysis of the physical basis of bulk water flow in the presence of impermeant and permeant ions, that is, Donnan osmosis, reveals large ion charge effects that have not previously been considered. The equation derived here for Donnan osmotic flow helps to explain why the action of the sodium pump is essential for the prevention of excessive osmotic stress on cellular membranes.