โ Scribed by Duan Chen; Zhan Chen; Changjun Chen; Weihua Geng; Guo-Wei Wei
No coin nor oath required. For personal study only.
The PoissonโBoltzmann equation (PBE) is an established model for the electrostatic analysis of biomolecules. The development of advanced computational techniques for the solution of the PBE has been an important topic in the past two decades. This article presents a matched interface and boundary (MIB)โbased PBE software package, the MIBPB solver, for electrostatic analysis. The MIBPB has a unique feature that it is the first interface techniqueโbased PBE solver that rigorously enforces the solution and flux continuity conditions at the dielectric interface between the biomolecule and the solvent. For protein molecular surfaces, which may possess troublesome geometrical singularities, the MIB scheme makes the MIBPB by far the only existing PBE solver that is able to deliver the secondโorder convergence, that is, the accuracy increases four times when the mesh size is halved. The MIBPB method is also equipped with a DirichletโtoโNeumann mapping technique that builds a Green's function approach to analytically resolve the singular charge distribution in biomolecules in order to obtain reliable solutions at meshes as coarse as 1 ร โ whereas it usually takes other traditional PB solvers 0.25 ร to reach similar level of reliability. This work further accelerates the rate of convergence of linear equation systems resulting from the MIBPB by using the Krylov subspace (KS) techniques. Condition numbers of the MIBPB matrices are significantly reduced by using appropriate KS solver and preconditioner combinations. Both linear and nonlinear PBE solvers in the MIBPB package are tested by proteinโsolvent solvation energy calculations and analysis of salt effects on proteinโprotein binding energies, respectively. ยฉ 2010 Wiley Periodicals, Inc. J Comput Chem, 2011
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