Hybrid Computational Models and Robust Numerical Methods for Electrostatic Interactions in Biomolecules

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This project develops hybrid computational models and robust numerical methods for electrostatic interactions in biomolecular systems. The computational models are constructed at different levels. They include variational mean-field models with atomistic details, particularly ionic size effects, and Monte Carlo simulation models for treating individual ions. These models are coupled with an advanced, variational approach to the solvation of biomolecules. A robust numerical method for solving the related elliptic interface problem and calculating the dielectric boundary force is designed and analyzed. Special interface algebraic multigrid methods and the GPU (Graphics Processing Unit) implementation are developed to accelerate the related large-scale computations. Numerical analysis focuses on the accuracy of the proposed schemes, particularly that of the boundary force approximation.Biomolecules such as proteins and DNA are assemblies of atoms of which a significant portion are charged. Charged biomolecules polarize the solvent (water or salted water) and produce ions that are mobile charged particles in the solution. The electrostatic or charge-charge interaction gives rise to strong forces that determine the structure, dynamics, and function of underlying biological systems. For instance, the electrostatic interaction affects how a drug molecule binds to a target molecule, which in turn determines how effective the drug is in the process of curing a disease. Through the development of modern mathematical theories and computational tools, this project aims at understanding the fundamental principles of biological systems at the molecular level and advancing the research of computational mathematics. The success of this project can potentially help reduce the high cost often needed for experiments and speed up the process of drug discovery. In addition, this highly interdisciplinary research brings opportunities for students at different levels to receive training at the interface of computational mathematics and molecular biological science. Such training is critical to keeping our strength in scientific research in an competitive international environment.