Biological membranes separate two electrolyte compartments with different ionic compositions and, under physiological conditions, can develop transmembrane potentials when exposed to electric fields. The regulation of transmembrane potentials involves dynamic charging and discharging of the membrane capacitance, mediated by the diffuse charge reorganization at the membrane interface. A central question, therefore, is: what are the characteristic timescales governing this charging and discharging? We address this question using a minimal model of a biological membrane subjected to a step voltage via blocking electrodes. Through a perturbative analysis of the electrolyte transport equations, we show that the leading-order relaxation of the transmembrane potential occurs on a capacitive timescale, that is, a function of the screening length, the membrane-electrode separation, the ionic diffusivity, and the capacitance mismatch between the membrane and the screening layers. Due to the membrane's low permittivity and finite thickness, the capacitance mismatch is large, and the capacitive timescale is 1–2 orders of magnitude shorter than the traditional RC timescale for a bare electrolyte. Thus, the presence of the membrane substantially accelerates the charging/discharging process. Our estimate of the capacitive timescale agrees quantitatively with values estimated from the data reported in the classical experiments of Hodgkin, Huxley, and Katz. We also show that the capacitive timescale governs the leading-order charging dynamics during ion channel activity. A simple equivalent circuit model accurately captures the linear behavior, and the perturbation expansion remains applicable across the entire range of observed physiological transmembrane potentials. Beyond the linear regime, however, salt diffusion in the bulk electrolyte drives a secondary, nonlinear relaxation process of the transmembrane potential over a longer, diffusive timescale. Our results suggest that both the capacitive timescale and the diffusion-driven relaxation are essential for understanding transmembrane potential dynamics across biological systems.
Farhadi et al. (Sun,) studied this question.