AMS Weekly Seminar | Karthik Shekhar

Location: Gilman 50

When: May 1st at 1:30 p.m.

Title: Spatiotemporal ionic dynamics at the interfaces of biological membranes

Abstract: Electrical activity in biological systems arises from transmembrane ionic currents passing through sub-nanometer pores in ion channels and pumps. Although acting as localized“sources” and “sinks” on the cellular lipid membranes, these discrete currents trigger large-scale events such as neurotransmission and muscle contraction. The dominant approach for studying electrical signaling in biology relies on “equivalent circuit” models (e.g., Hodgkin and Huxley, 1952), which coarse-grain the microscopic and localized nature of ion channel currents. While these models phenomenologically capture many macroscopic observations, they leave the direct mechanistic link between microscopic ionic currents and the ensuing spatiotemporal phenomenalargely opaque.

In this talk, I will argue that bridging this gap requires a precise understanding of how these localized sources and sinks drive electrochemical reorganization at the cellular membrane interface. I will present a mathematical framework based on the Poisson–Nernst–Planck (PNP) equations, a nonlinear system of coupled PDEs. Using large-scale finite element simulations and analytical theory, I will show how nontrivial dynamical scaling behaviors emerge in the spatiotemporal evolution of charge during localized transmembrane currents (arXiv:2407.11947).I will then discuss ongoing efforts to extend this framework to spherical vesicles and cylindrical tubular membranes, highlighting how membrane geometry influences electrochemical reorganization. Finally, I will demonstrate that in all cases, a boundary layer theory yields analytical expressions that fully explain the numerical results and highlight the role of long-ranged electrostatic effects in ionic reorganization. These findings allow us to visualize the resulting dynamical regimes in space–time diagrams and to derive analytical expressions that can be applied to study emergent behavior in stochastic simulations of electrostatically coupled ion channels and pumps.

Bio: Karthik Shekhar is the John F. Heil Jr Assistant Professor in the Department of Chemical and Biomolecular Engineering at the UC Berkeley. His undergraduate (IIT Bombay) and graduate (MIT) degrees are in chemical engineering, while his research as a postdoc was at the intersection of single-cell genomics and neuroscience (Broad Institute). His research group at UC Berkeley focuses on problems in neuroscience and biophysics through a synthesis of theoretical,computational, and data-driven approaches. He has received fellowships from the McKnightFoundation, Hellman Foundation, and the Glaucoma Research Foundation. He is a recipient of the Donald E. Noyce Prize for university-wide excellence in undergraduate teaching.

Zoom link: https://wse.zoom.us/j/93287142219?pwd=z9fqWnRMzmzS0SGijRiie5yN3kHRSZ.1