Solvent interactions play a critical role in determining the structure and function of biomolecular systems. However, accurate modeling is a challenging task due to long-range correlations and vast numbers of solvent atoms and ions. For very large systems, one method for reducing this expense is the application of an implicit solvent model which replaces the explicit atoms and ions with a dielectric continuum. One of the more accurate implicit solvent models is described by a generalized Poisson equation or Poisson-Boltzmann equation with point charge source terms. Although the generalized Poisson approach is considered in very many cases to be sufficiently accurate, most current methods for approximating its solution have been deemed prohibitively expensive for very large systems and for applications requiring rapid repetitive evaluation.

This project centers on the creation and analysis of algorithms of unsurpassed effectiveness for approximating the solution to the generalized Poisson equation (GPE) and its extensions. The approach involves solving for an "effective charge distribution" given by the Laplacian of the solution to the GPE. The corresponding electrostatic potential can be recovered using a fast N-body solver. Broader impact of this project will be realized through the incorporation of novel algorithms in simulation software. Better methods and software in the hands of scientists will enable biomolecular simulation of much larger systems with improved accuracy which will result in contributions to society. In addition, this project provides an opportunity for a graduate student to engage in research that spans computer science, physical science, and mathematics.

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University of Illinois Urbana-Champaign
United States
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