Boundary Element Methods for Biomolecule Electrostatics

Jaydeep Bardhan, Massachusetts Institute of Technology

We are working to enable the rapid solution of electrostatic problems that arise in rational drug design. Electrostatic interactions between biomolecules have significant effects on the molecules’ binding affinity and specificity, which makes them an important factor in drug design. However, the slow decay of electrostatic fields and the presence of many solvent molecules around the biomolecules pose difficult computational challenges. Continuum-theory approximations simplify the problem but still require efficient numerical solution; we use boundary element methods (BEMs) to solve these continuum electrostatics problems because BEMs have a number of advantages relative to other methods. Here, we present a set of numerical techniques tailored for boundary element simulations of biomolecule electrostatics problems. Recently, we have been developing techniques for discretizing molecular surfaces using curved panels and for integrating singular functions on these curved panels. Such curved panel solutions achieve excellent accuracy much more quickly than BEM simulations based on discretizing molecular surfaces using planar triangles. Also, we have most recently demonstrated that a method known as qualocation can allow a simple integral formulation to achieve competitive accuracy relative to more complicated formulations.

Abstract Author(s): J. P. Bardhan, M. D. Altman, B. Tidor, J. K. White