Ion Transport and Dynamics of Electrical Double Layers Around Cellular Membranes
Joshua Fernandes, University of California, Berkeley
The lipid membranes of all cells contain transmembrane proteins that function as selective passages for ionic species. The transport and partitioning of ionic species across membranes is of particular importance in neurons, which transmit signals by transient, spatially propagating changes in the membrane electric potential. We investigate the short-time dynamics of a model system consisting of a rigid membrane separating two electrolyte solutions following an instantaneous transmembrane flux of an ionic species. Concentration dynamics are modeled using the Nernst-Planck equation, and the electric potential is quasi-statically evolved using the Poisson equation. When the flux is uniform over the membrane area, the solution only varies in the direction perpendicular to the membrane and permits a perturbation solution where the imposed flux is the small parameter. We numerically solve the general case of variable flux over the membrane area by a finite element spatial discretization with an implicit time stepper.
We model the ionic flux either as a uniform planar source or a point source on the membrane, where the former case permits the perturbation solution. For the planar source case, we find that charge density decays exponentially with distance from the membrane, in good agreement with the first-order perturbation solution. For the point source case, we observe spreading both axially (away from the membrane) and radially (along the membrane surface). The radial spreading of charge density is primarily driven by the development of a dipole-like electric field caused by the ionic flux. This induces development of a double layer along the radial direction of the membrane that decays as a power law in distance, unlike the Gaussian distribution that would be observed for an uncharged species. Future directions will involve understanding the long-time dynamics of the point source system and gaining a theoretical understanding of the radial spreading phenomenon.
Abstract Author(s): Joshua B. Fernandes, Hyeongjoo Row, Karthik Shekhar, Kranthi K. Mandadapu