Collaborative Research: Implicit Solvent Modeling and Fast Algorithm Development for Simulating Solutes with Atomic Polarizable Multipoles

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This collaborative research project aims to improve the implicit solvent modeling for studying electrostatic interaction between solutes, such as proteins, DNA, and RNA, and their surrounding solvent environment. The research will improve on current approaches and will formulate a new polarizable multipole implicit solvent model with improved and enhanced modeling accuracy. Furthermore, efficient and accurate numerical algorithms will be developed to meet computational challenges of the new model. This research will provide biophysicists a new tool for analyzing electrostatic interactions of solvated biomolecules in the form of models and algorithms implemented in a freely available software package. In addition, this project will offer interdisciplinary research and training opportunities for undergraduate and graduate students in biological modeling, computation, and mathematical analysis.The project will address limitations in the existing implicit solvent models for studying electrostatic interaction between solutes. These include the facts that the solute charge sources are often modeled as point charges located at atomic centers, and this rough approximation to the quantum mechanical charge density is known to be a major source of the modeling errors. Moreover, polarization, an important physical phenomenon account for the redistribution of the electron density in the presence of an external electric field is missing in this point charge model. The project will develop a novel nonlinear Poisson-Boltzmann (PB) model associated with an atomic polarizable multipole (PM) force field to describe the self-consistent polarization process and study electrostatic interactions among permanent multipoles, induced dipoles, and reaction-field potential. The coupling of PM source with the nonlinear PB (NPB) equation, as opposed to the linearized PB, is challenging in many aspects involving modeling and numerical difficulties such as charge singularities, geometric complexity, interface jumps, nonlinearity, polarization, as well as high computational cost. To overcome such difficulties, a set of efficient, accurate, and seamlessly coupled numerical methods will be developed to resolve numerical challenges associated with the PM-NPB model. In particular, multipole charge singularities are regularized using Green’s function based decomposition; self-consistent polarization, which involves repeatedly solving an NPB equation across the molecular interface, is efficiently realized by a linearized iterative algorithm coupled with a fast 3D Augmented Matched Interface and Boundary (AMIB) method. Finally, model benchmarking and biological applications will be carried out to ensure that the research results provide a robust tool for simulating electrostatic interactions.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.