This paper presents a novel method for solving the Poisson-Boltzmann (PB) equation based on a rigorous treatment of geometric singularities of the dielectric interface and a Green’s function formulation of charge singularities. Geometric singularities, such as cusps and self-intersecting surfaces, in the dielectric interfaces are bottleneck in developing highly accurate PB solvers. Based on an advanced mathematical technique, the matched interface and boundary (MIB) method, we have recently developed a PB solver by rigorously enforcing the flux continuity conditions at the solvent-molecule interface where geometric singularities may occur. The resulting PB solver, denoted as MIBPB-II, is able to deliver second order accuracy for the molecular surfaces of proteins. However, when the mesh size approaches half of the van der Waals radius, the MIBPB-II cannot maintain its accuracy because the grid points that carry the interface information overlap with those that carry distributed singular charges. In the present Green’s function formalism, the charge singularities are transformed into interface flux jump conditions, which are treated on an equal footing as the geometric singularities in our MIB framework. The resulting method, denoted as MIBPB-III, is able to provide highly accurate electrostatic potentials at a mesh as coarse as for proteins. Consequently, at a given level of accuracy, the MIBPB-III is about three times faster than the APBS, a recent multigrid PB solver. The MIBPB-III has been extensively validated by using analytically solvable problems, molecular surfaces of polyatomic systems, and 24 proteins. It provides reliable benchmark numerical solutions for the PB equation.
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21 September 2007
Research Article|
September 18 2007
Treatment of charge singularities in implicit solvent models
Weihua Geng;
Weihua Geng
Department of Mathematics,
Michigan State University
, East Lansing, Michigan 48824, USA
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Sining Yu;
Sining Yu
Department of Mathematics,
Michigan State University
, East Lansing, Michigan 48824, USA
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Guowei Wei
Guowei Wei
a)
Department of Mathematics,
Michigan State University
, East Lansing, Michigan 48824, USA
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a)
Author to whom correspondence should be addressed. Also at the Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824. Electronic mail: wei@math.msu.edu
J. Chem. Phys. 127, 114106 (2007)
Article history
Received:
May 29 2007
Accepted:
July 10 2007
Citation
Weihua Geng, Sining Yu, Guowei Wei; Treatment of charge singularities in implicit solvent models. J. Chem. Phys. 21 September 2007; 127 (11): 114106. https://doi.org/10.1063/1.2768064
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