An accelerated nonlocal Poisson‐Boltzmann equation solver for electrostatics of biomolecule

Abstract The nonlocal modified Poisson‐Boltzmann equation (NMPBE) is one important variant of a commonly used dielectric continuum model, the Poisson‐Boltzmann equation (PBE), for computing electrostatics of biomolecules. In this paper, an accelerated NMPBE solver is constructed by finite element and finite difference hybrid techniques. It is then programmed as a software package for computing electrostatic solvation and binding free energies for a protein in a symmetric 1:1 ionic solvent. Numerical results validate the new solver and its numerical stability. They also demonstrate that the new solver has much better performance than the corresponding finite element solver in terms of computer CPU time. Furthermore, they show that the binding free energies produced by NMPBE can match chemical experiment data better than those by PBE.