A simple description of biological transmembrane potential from simple biophysical considerations: no equivalent circuits

Biological membranes mediate different physiological processes necessary for life. Ion movement around, into and out of cells, is arguably one of the most important of such processes, as it underlies electrical signaling and communication within and between cells. The difference between the electrical potentials inside and outside a biological membrane called transmembrane potential, or membrane potential for short, is one of the main biophysical variables affecting ionic movement. Most of the equations that describe the change in membrane potential are based on analogies with resistive-capacitative electrical circuits, with conductance and a capacitance proposed in classical studies as measures of the permeable and the impermeable properties of the membrane, respectively. However, the parts in ohmic circuits are not like the biological elements present in the spaces around and within biological membranes. This article presents a simple derivation for an equation describing local changes in the transmembrane potential that is not based on electrical circuit analogies. In doing so, concepts like the so-called membrane capacitance are explained and generalized. Importantly, the classical model for the membrane potential based on an equivalent RC-circuit is recovered as a particular case from the general derivation presented here. Modeling examples are presented to illustrate the use of the derivation and the effects of changing the way charges aggregate around the membrane as a function of the membrane potential.