Understanding Protein Electrostatics using Boundary-Integral Equations
The electrostatic interactions between biological molecules play important roles determining their structure and function, but are challenging to model because they depend on the collective response of thousands of surrounding water molecules. Continuum electrostatic theory -- e.g., the Poisson equation -- offers a successful and simple theory for biomolecule science and engineering, and boundary-integral equation formulations of the problem offer several theoretical and computational advantages. In this talk, I will highlight some recent modeling advances derived from the boundary-integral perspective, which have important applications in biophysics and whose mathematical foundations may be useful in other domains as well. First, one may derive a fast electrostatic model that resembles Generalized Born theory, but is based on a rigorous operator approximation for rapid, accurate estimation of a Green's function. In addition, we have been exploring a boundary-integral approach to nonlocal continuum theory as a means to model the influence of water structure, an important piece of molecular physics left out of the standard continuum theory.