Collaborative Research: Laplacian-Centered Poisson Solvers and Multilevel Summation Algorithms

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Solvent interactions play a critical role in determining the structure andfunction of biomolecular systems. However, accurate modeling is a challengingtask 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 applicationof an implicit solvent model which replaces the explicit atoms and ions with adielectric continuum. One of the more accurate implicit solvent models isdescribed by a generalized Poisson equation or Poisson-Boltzmann equation withpoint charge source terms. Although the generalized Poisson approach isconsidered in very many cases to be sufficiently accurate, most current methodsfor approximating its solution have been deemed prohibitively expensive forvery large systems and for applications requiring rapid repetitive evaluation.This project centers on the creation and analysis of algorithms of unsurpassedeffectiveness for approximating the solution to the generalized Poissonequation (GPE) and its extensions. The approach involves solving for an"effective charge distribution" given by the Laplacian of the solutionto the GPE. The corresponding electrostatic potential can be recovered usinga fast N-body solver. Broader impact of this project will be realized throughthe incorporation of novel algorithms in simulation software. Better methodsand software in the hands of scientists will enable biomolecular simulation ofmuch larger systems with improved accuracy which will result in contributionsto society. In addition, this project provides an opportunity for a graduatestudent to engage in research that spans computer science, physical science,and mathematics.