Accurate p$K_a$ Computation Using Matched Interface and Boundary (MIB) Method Based Poisson-Boltzmann Solver (Communications in Computational Physics, 2018)
The p$K_a$ values are important quantities characterizing the ability of proteinactive sites to give up protons. p$K_a$ can be measured using NMR by tracing chemical-shiftsof some special atoms, which is however expensive and time-consuming. Alternatively, p$K_a$ can be calculated numerically by electrostatic free energy changes subjectto the protonation and deprotonation of titration sites. To this end, the Poisson-Boltzmann(PB) model is an effective approach for the electrostatics. However, numericallysolving PB equation is challenging due to the jump conditions across thedielectric interfaces, irregular geometry of the molecular surface, and charge singularities.Our recently developed matched interface and boundary (MIB) method treatsthese challenges rigorously, resulting in a solid second order MIBPB solver. Since theMIBPB solver uses Green's function based regularization of charge singularities by decomposingthe solution into a singular component and a regularized component, itis particularly efficient in treating the accuracy-sensitive, numerous, and complicatedcharge distributions from the p$K_a$ calculation. Our numerical results demonstrate thataccurate free energies and p$K_a$ values are achieved at coarse grid rapidly. In addition,the resulting software, which pipelines the entire p$K_a$ calculation procedure, isavailable to all potential users from the greater bioscience community.
Keywords: pKa; acid dissociation constant; Poisson-Boltzmann; finite difference; charge singularity.