Collaborative Research: Improved Boundary Element Methods for Electrostatics of Interacting Proteins in Solvent

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Protein molecules are basic components in all forms of life, and electrostatic effects play a key role in determining protein structure and function. However studying these effects experimentally is difficult, and there is great interest in using computer simulations to advance this area of biochemical research. This project will contribute by developing new mathematical algorithms to improve the accuracy and efficiency of these simulations. Potential biomedical applications include (1) protein-ligand binding, which is important for synthetic drug design, and (2) protein folding, which is important for understanding how misfolding causes disease. The investigators will collaborate with bioscientists, and the software developed in the project will be made available in open source format for use by the scientific community. The project results will be disseminated through conference and seminar presentations, and publications in scientific journals. The project will develop the national workforce in computational mathematics by training junior personnel at the postdoctoral, graduate student, and undergraduate student levels. Biochemical simulations of charged particle systems are often limited by the cost of computing long-range electrostatic interactions. To address this issue the PIs have developed a treecode-accelerated boundary integral (TABI) method to solve the Poisson-Boltzmann (PB) equation for the electrostatic potential of a solvated protein. In this project the PIs will extend the TABI solver to the challenging case of interacting proteins in solvent, focusing on subtle dielectric and ionic structural effects. The work entails advances in modeling, improvements in treecode and boundary element methods, and applications in molecular biochemistry including the following topics: (1) The TABI code will be extended to compute the binding energy of a solvated protein-protein complex. (2) The treecode will be adapted to accelerate computations of the total correlation function in the Reference Interaction Site Model (RISM) which provides a physically accurate description of the water structure near the solute/solvent interface. (3) Explicit ion simulations will be carried out to validate the PB and RISM simulations, and to investigate the effect of finite ion size on the interfacial charge structure. (4) The treecode will be improved by implementing a more effective multipole acceptance criterion, and parallel CPU and GPU implementations of the treecode will be developed. (5) A new method for computing electrostatic PB forces will be tested for application in molecular dynamics simulations of interacting proteins in solvent. (6) Efficient computation of pH-dependent effects in solvated proteins will be demonstrated using TABI.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.