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Multi‐multigrid solution of modified Poisson–Boltzmann equation for arbitrarily shaped molecules
Author(s) -
Tomac Sebastian,
Gräslund Astrid
Publication year - 1998
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/(sici)1096-987x(199806)19:8<893::aid-jcc8>3.0.co;2-k
Subject(s) - poisson–boltzmann equation , multigrid method , boltzmann equation , discretization , poisson's equation , statistical physics , partial differential equation , discontinuity (linguistics) , mathematics , physics , mathematical analysis , ion , thermodynamics , quantum mechanics
A new multi‐multigrid method is presented for solving the modified Poisson–Boltzmann equation based on the Kirkwood Hierarchy of equations, with Loeb's closure, on a three‐dimensional grid. The results are compared with standard Poisson–Boltzmann calculations, which are known to underestimate the local concentration of counterions near charged parts of molecules, mainly due to neglect of fluctuations in the ionic concentrations. In the present study, the Kirkwood hierarchy of equations is discretized with the finite volume method and solved using multigrid techniques. The new possibility for solution of the three‐dimensional modified Poisson–Boltzmann equation, for the first time within a model including a dielectric discontinuity, and within reasonable computational time, enables the calculation of higher valence ion distributions around arbitrarily shaped biological macromolecules. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 893–901, 1998