Volume 13, Issue 1
An Adaptive, Finite Difference Solver for the Nonlinear Poisson-Boltzmann Equation with Applications to Biomolecular Computations

Mohammad Mirzadeh, Maxime Theillard, Asdís Helgadóttir, David Boy & Frédéric Gibou

Commun. Comput. Phys., 13 (2013), pp. 150-173.

Published online: 2013-01

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  • Abstract

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 surfacesis explained; this allows to accuratelyrepresentthe 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. 

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@Article{CiCP-13-150, author = {Mohammad Mirzadeh, Maxime Theillard, Asdís Helgadóttir, David Boy and Frédéric Gibou}, title = {An Adaptive, Finite Difference Solver for the Nonlinear Poisson-Boltzmann Equation with Applications to Biomolecular Computations}, journal = {Communications in Computational Physics}, year = {2013}, volume = {13}, number = {1}, pages = {150--173}, abstract = {

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 surfacesis explained; this allows to accuratelyrepresentthe 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. 

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.290711.181011s}, url = {http://global-sci.org/intro/article_detail/cicp/7216.html} }
TY - JOUR T1 - An Adaptive, Finite Difference Solver for the Nonlinear Poisson-Boltzmann Equation with Applications to Biomolecular Computations AU - Mohammad Mirzadeh, Maxime Theillard, Asdís Helgadóttir, David Boy & Frédéric Gibou JO - Communications in Computational Physics VL - 1 SP - 150 EP - 173 PY - 2013 DA - 2013/01 SN - 13 DO - http://dor.org/10.4208/cicp.290711.181011s UR - https://global-sci.org/intro/cicp/7216.html KW - AB -

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 surfacesis explained; this allows to accuratelyrepresentthe 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. 

Mohammad Mirzadeh, Maxime Theillard, Asdís Helgadóttir, David Boy & Frédéric Gibou. (1970). An Adaptive, Finite Difference Solver for the Nonlinear Poisson-Boltzmann Equation with Applications to Biomolecular Computations. Communications in Computational Physics. 13 (1). 150-173. doi:10.4208/cicp.290711.181011s
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