Efficient Numerical Algorithms for Analysis and Design of Biomolecules

Jaydeep Bardhan, Massachusetts Institute of Technology

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I will present highlights of our recent research on numerical methods for analyzing and optimizing the electrostatic interactions between biomolecules. These interactions, which play important roles in determining binding affinity and specificity, are challenging to model computationally because electrostatic forces are long-range and because almost all reactions occur surrounded by mobile water molecules and possibly ions. Models based on continuum electrostatic theory have been extensively validated and have been widely adopted. However, existing numerical methods have not been able to achieve high accuracy without excessive use of computational resources. Our research has focused on the development of an efficient and accurate boundary-element method (BEM) approach to the biomolecule electrostatics problem. We discretize the molecular boundaries exactly using curved boundary elements, use specialized numerical integration methods to evaluate singular and near-singular integrals, and solve the BEM linear systems using preconditioned Krylov iterative methods and the FFTSVD fast BEM algorithm to evaluate the needed dense matrix-vector products. Our work represents significant progress towards a regime of unprecedented accuracy. In addition, we have developed a novel method for calculating a biomolecule’s charge distribution that optimizes the electrostatic component of the free energy of binding to a target molecule. This method tightly couples optimization and BEM simulation to significantly reduce the computational expense usually associated with these optimizations.

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