pKA in proteins solving the Poisson–Boltzmann equation with finite elements

Knowledge on pK_A values is an eminent factor to understand the function of proteins in living systems. We present a novel approach demonstrating that the finite element (FE) method of solving the linearized Poisson–Boltzmann equation (lPBE) can successfully be used to compute pK_A values in proteins with high accuracy as a possible replacement to finite difference (FD) method. For this purpose, we implemented the software molecular Finite Element Solver (mFES) in the framework of the Karlsberg+ program to compute pK_A values. This work focuses on a comparison between pK_A computations obtained with the well‐established FD method and with the new developed FE method mFES, solving the lPBE using protein crystal structures without conformational changes. Accurate and coarse model systems are set up with mFES using a similar number of unknowns compared with the FD method. Our FE method delivers results for computations of pK_A values and interaction energies of titratable groups, which are comparable in accuracy. We introduce different thermodynamic cycles to evaluate pK_A values and we show for the FE method how different parameters influence the accuracy of computed pK_A values. © 2015 Wiley Periodicals, Inc.