### An Integral Formulation and Fast Solver for Biomolecule Electrostatic Analysis

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Jaydeep Bardhan, Massachusetts Institute of Technology
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We are working to enable the rapid solution of electrostatic problems that arise in rational drug design, and we introduce here a fast boundary element method solver that we have developed as one component of this project. Electrostatic interactions between biomolecules have significant effects on the molecules’ binding affinity and specificity. The slow decay of electrostatic fields and the presence of many solvent molecules around the biomolecules pose difficult challenges for modeling molecular electrostatics. Using an implicit solvent representation allows interactions to be computed approximately using continuum models, and we present a boundary integral formulation of the continuum problem. Discretization of the integral equations produces a dense linear system that is too large for direct solution; instead, we solve the system using preconditioned Krylov subspace iterative methods. We have developed a new fast algorithm to perform the dense matrix-vector multiplications required to compute the Krylov vectors. The algorithm, multipole-accelerated SVD (MASVD), is a multilevel scheme that approximates long-range interactions using a compressed multipole representation. We are currently working to combine the MASVD algorithm with a new technique for optimizing the electrostatic affinity between two molecules.

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