Collaborative Research: Advances in Nonlocal Dielectric Modeling and Free Energy Calculation for Protein in Ionic Solvent

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The nonlocal dielectric approach can significantly enhance the classic Poisson dielectric model by considering the polarization correlations among water molecules. However, current studies on the approach are mostly restricted to the water solvent, due to modeling and algorithmic complications that arise in the case of ionic solvents. The current ionic models that do exist fail to incorporate crucial nonlocal dielectric effects. Recent developments also indicate that entropic changes due to protein-ligand association are critical to understanding binding affinity. The computation of entropy, however, remains a very difficult task. Motivated by these challenges, this project aims to develop new nonlocal continuum electrostatic models and new numerical quadratures for the direct calculation of entropy and free energy for protein in ionic solvent. The new nonlocal models will be constructed from a novel combination of the nonlocal dielectric approach with the fundamental measure theory of hard-sphere mixture fluids under the constrained functional optimization protocol. They are expected to significantly improve the accuracy of electrostatic potential calculations in comparison to the classic Poisson-Boltzmann equation, since they reflect both ionic size effects and polarization correlations among water molecules. The new numerical quadratures will be developed by using a special prismatic element interpolation constructed from a prismatic mesh of a bounded state region near a potential energy minimum point. The computing complexity will be further reduced through using a new nonlocal model for computing involved electrostatic potential. Lastly, new fast numerical algorithms and program packages will be developed for solving the new dielectric models and for implementing the new numerical quadratures. Calculation of electrostatic potential energy, entropy, and free energy for protein in ionic solvent is a fundamental task in biomolecular simulations. The new nonlocal dielectric models, numerical quadratures for computing entropy and free energy, and the accompanying efficient numerical algorithms and program packages produced from this project will be a considerable contribution to the fields of mathematical biology, computational biochemistry, computational mathematics, and computer science. They will play important roles in ion channel studies, rational drug design, and other bioengineering applications, and will improve our quantitative understanding of critical physiological processes, cellular energetics, and affinity in protein-ligand binding, and of health and disease in general. The findings from this project are expected to have a significant impact on the development of mathematics, computer science, biochemistry, and bioengineering. Because there has been substantial interest recently in algorithms for solving high-dimensional problems, any advances made in this project will have broad potential impact in a variety of areas that are related to high-dimensional integrals with integrands that decay exponentially.