BPS2026 – Electrical signal propagation on membranes: From single to multiple channels

Electrical signaling forms the basis of all nervous system function, enabling animals to sense their environment, coordinate movement, and make decisions. At the nanoscale, ion channels and pumps locally perturb their environments, which ultimately shapes the spatiotemporal properties of the electric signal at the cellular scale. Yet, electrophysiological data are still commonly interpreted using classical equivalent-circuit models, which represent the membrane system in terms of simple electrical components, such as capacitors and resistors. While useful, these models fail to capture critical features: the properties of individual ion channels and their collective interactions, the electrochemical transport of charges at the membrane interface, and more realistic descriptions of membrane behavior, including their mechanical responses and nonequilibrium dynamics. In this work, we develop a theoretical and computational framework—bridging continuum and statistical mechanics—that captures the detailed spatiotemporal dynamics of electrical signaling at neuronal membrane interfaces. We begin by analyzing how a single ion channel creates a propagating electrical signal along a planar membrane, which is long-ranged in both time and space. The speed of this signal is proportional to the membrane's thickness and the dielectric mismatch between the membrane and its surrounding electrolyte. Next, by treating the single-channel response as a kernel, we extend this framework to study the simultaneous activity of hundreds or thousands of voltage-gated channels. Because gating depends on the local membrane potential, channels influence one another by modifying the electric potential over a large area, establishing an effective communication between channels. This non-equilibrium coupling between channels gives rise to emergent collective dynamics that cannot be inferred from the behaviors of single channels alone.