Fast empirical pKa prediction by Ewald summation

Abstract

pK(a) calculations for macromolecules are normally performed by solving the Poisson-Boltzmann equation, accounting for the different dielectric constants of solvent and solute, as well as the ionic strength. Despite the large number of successful applications, there are some situations where the current algorithms are not suitable: (1) large scale, high-throughput analysis which requires calculations to be completed within a fraction of a second, e.g. when permanently monitoring pK(a) shifts during a molecular dynamics simulation; (2) prediction of pK(a)s in periodic boundaries, e.g. when reconstructing entire protein crystal unit cells from PDB files, including the correct protonation patterns at experimental pH. Such in silico crystals are needed by 'self-parameterizing' molecular dynamics force fields like YASARA YAMBER, that optimize their parameters while energy-minimizing high-resolution protein crystals. To address both problems, we define an empirical equation that expresses the pK(a) as a function of electrostatic potential, hydrogen bonds and accessible surface area. The electrostatic potential is evaluated by Ewald summation, which captures periodic crystal environments and the uncertainty in atom positions using Gaussian charge densities. The empirical proportionality constants are derived from 217 experimentally determined pK(a)s, and despite its simplicity, this pK(a) calculation method reaches a high overall jack-knifed accuracy, and is fast enough to be used during a molecular dynamics simulation. A reliable null-model to judge pK(a) prediction accuracies is also presented.