Electrostatic Interactions Between Biomolecules: A PDE-Constrained Approach

Jaydeep Bardhan, Wilkinson Fellow, Argonne National Laboratory

Electrostatic interactions between biomolecules represent an interesting and highly relevant area for numerical simulation and optimization. Continuum-theory-based mathematical models for these interactions, such as the linearized Poisson-Boltzmann equation, have proven to be surprisingly useful tools for biomolecular analysis and design. However, although numerical methods for solving these electrostatic models have been studied for decades, the physical approximations on which the models rest, as well as the combinatorial nature of molecular design, continue to present new challenges for computational research. As one example, the electrostatic interactions between two biomolecules can, under certain assumptions, be optimized for tight binding, and the resulting optimal solutions can be used to guide design processes towards chemical modifications likely to improve binding. Traditional approaches, which rely on “black-box” PDE solvers and optimization software, are computationally expensive. However, by breaking the black-box abstraction and solving the optimization and simulation problems simultaneously, the cost can be dramatically reduced. This talk will present a PDE-constrained approach to electrostatic optimization of biomolecules, highlighting a few details where the interplay between physical modeling and numerical implementation clearly illustrates the spirit of computational science.

Abstract Author(s): Jaydeep P. Bardhan, Michael D. Altman, Bruce Tidor, and Jacob K. White