The resting potential of nerve cells and the Na,K-pump

TL;DR

This paper provides a coherent, causally-based explanation of the nerve cell resting potential, emphasizing active ion transport, membrane permeabilities, and intracellular concentrations, resulting in a simple formula and new insights into potential limits.

Contribution

It introduces a causal approach to the resting potential, deriving a simple formula and revealing bounds and small differences not shown in traditional models.

Findings

Derived a simple formula for resting potential based on active transport and permeabilities.

Identified an upper bound for the magnitude of the resting potential.

Showed the difference between resting and diffusion potential is small after pump poisoning.

Abstract

In this pedagogical paper a coherent explanation of the resting potential of nerve cells is given in terms of its determining factors. These are the currents of active transport of the ions to which the membrane is permeable, their membrane permeabilities and their concentrations in the extracellular fluid. They play the role of the independent variables in the problem and simultaneously also determine the concentrations of the permeating ions inside the cell. The resting state is assumed to be a stationary state, and the resting potential is understood to be the membrane potential in this state. The explanation presented here differs from the conventional one found in textbooks with respect to the handling of the intracellular concentrations of the permeant ions. In the conventional description the causal relations between these and the independent variables are not taken into account, and the intracellular concentrations are treated like additional independent variables. The "causal" theory presented here leads to a simple formula for the resting potential in terms of the currents of active transport (pumping by the Na,K-pump and carrier transport) and the membrane permeabilities for sodium and potassium ions. In addition it leads to two results not obtained in the conventional treatment: An upper bound exists for the magnitude of the resting potential, and the difference between the resting potential and the diffusion potential, which can be measured after poisoning of the ion pumps, is small.