Electrical Signal Propagation Along Biological Membranes
Joshua Fernandes, University of California, Berkeley
Authors: Joshua B. Fernandes, Hyeongjoo Row, Karthik Shekhar, Kranthi K. Mandadapu
Abstract: Selective transport of ions across lipid membranes is the physical basis for electrical signaling in biological cells. Commonly used frameworks, such as equivalent circuits, neglect the diffuse dynamics of ions and the spatial locality of ion transporters. We study a model system of a single, selective ion transporter in a biological membrane using the Poisson-Nernst-Planck framework to understand dynamics along the membrane (in-plane) and away from the membrane (out-of-plane). Asymptotic solutions of the linearized equations are found in certain limits, as well as numerical solutions of the exact nonlinear equations via large scale finite element simulations. We find that long-ranged electrostatic forces arise from the separation of charge across the lipid membrane, resulting in three distinct regimes along the membrane. These regimes exhibit distinct scaling of the transmembrane electrical potential: (i) a constant potential near-field region, (ii) a monopole-like intermediate region, and (iii) a dipole-like far-field region. Under the action of constant pumping, the monopolar region expands along the membrane with a constant velocity that increases with the membrane thickness and dielectric ratio between water and the membrane. This results in a propagation speed of approximately ~50 m/s along unmyelinated lipid membranes, faster than is attainable by any diffusive process. This work shows that ionic transport across a lipid membrane induces long-ranged electric fields in electrolyte solutions, which may have a role in biological signaling.