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An Adaptive, Finite Difference Solver for the Nonlinear Poisson-Boltzmann Equation with Applications to Biomolecular Computations

Published online by Cambridge University Press:  03 June 2015

Mohammad Mirzadeh*
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
Maxime Theillard*
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
Asdís Helgadöttir*
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
David Boy*
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
Frédéric Gibou*
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA Department of Computer Science, University of California, Santa Barbara, CA 93106, USA
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We present a solver for the Poisson-Boltzmann equation and demonstrate its applicability for biomolecular electrostatics computation. The solver uses a level set framework to represent sharp, complex interfaces in a simple and robust manner. It also uses non-graded, adaptive octree grids which, in comparison to uniform grids, drastically decrease memory usage and runtime without sacrificing accuracy. The basic solver was introduced in earlier works [16,27], and here is extended to address biomolecular systems. First, a novel approach of calculating the solvent excluded and the solvent accessible surfaces is explained; this allows to accurately represent the location of the molecule’s surface. Next, a hybrid finite difference/finite volume approach is presented for discretizing the nonlinear Poisson-Boltzmann equation and enforcing the jump boundary conditions at the interface. Since the interface is implicitly represented by a level set function, imposing the jump boundary conditions is straightforward and efficient.

Research Article
Copyright © Global Science Press Limited 2013

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