Treatment of charge singularities in implicit solvent models

Weihua Geng, Sining Yu, Guowei Wei
2007 Journal of Chemical Physics  
This paper presents a novel method for solving the Poisson-Boltzmann ͑PB͒ 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 ͑MIB͒ method, we have recently
more » ... loped 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 1.2 Å 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. ,38 and CHARMM. 39 It was argued by Baker that finite difference based PB solvers, particularly in conjunction with multigrid linear algebraic solvers, can offer the best combination of speed, accuracy, and efficiency, making them the most popular approaches in structural biology. 4 Implicit solvent models require a solvent-molecule interface to separate the solvent domain from the biomolecular domain. The molecular surface 40,41 is commonly used in the PBE for this purpose. The dielectric constants of the solvent domain and molecular domain are usually chosen as 80 and 1 ͑or 2͒, respectively, leading to discontinuous coefficients in the PBE. Moreover, molecular surfaces admit geometric singularities, 40,42-44 such as cusps and self-intersecting surfaces. Explicit interface treatment of geometric singularities a͒
doi:10.1063/1.2768064 pmid:17887827 fatcat:usfqb4xo75celnf52rzl7ycszu