CAM Colloquium: Sanjay Dharmavaram (Bucknell University) - A hybrid discrete-continuum model for protein-membrane interaction

Description

Abstract: Cell membranes are made of rod-like fat molecules that form a protective shell-like enclosure around its organelles and genome. In most cells, the surface of the membrane is embedded with a variety of proteins that help orchestrate biochemical reactions vital for life. The organization of proteins on the membrane is therefore crucial for a cell’s proper functioning. This raises the following fundamental questions concerning protein-membrane interaction: (1) How do protein molecules organize themselves on the membrane surface? (2) How does this organization affect the membrane’s shape? To address these questions, I will present a hybrid discrete-continuum model for such systems. Here, the membrane is modeled as a fluid shell and the embedded proteins, as mutually interacting point particles. While conceptually straightforward, computing equilibrium states by numerically discretizing this model poses significant challenges. These stem from the fact that the location of particles and the shape of the surface are inextricably coupled. Particles need to be constrained to lie on the surface of the shell whose shape is itself determined by the organization of the particles. Existing numerical methods often employ expensive constraints to anchor particles to the shell's surface or artificially restrict their movement thereby producing spurious equilibria. In this talk, I will present a new "Lagrangian"-Galerkin discretization scheme as an efficient and reliable alternative. Bio: Dr. Dharmavaram is an Assistant Professor in the Department of Mathematics at Bucknell University. He received his Ph.D. at Cornell University in Theoretical and Applied Mechanics and held a postdoctoral position at the University of California Los Angeles. His research interests lie at the interface of nonlinear partial differential equations, soft matter physics, and computational science.