A Boundary‐Integral Approach for the Poisson–Boltzmann Equation with Polarizable Force Fields

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Implicit-solvent models are widely used to study the electrostatics in dissolved biomolecules, which are parameterized using force fields. Standard force fields treat the charge distribution with point charges; however, other force fields have emerged which offer a more realistic description by considering polarizability. In this work, we present the implementation of the polarizable and multipolar force field atomic multipole optimized energetics for biomolecular applications (AMOEBA), in the boundary integral Poisson-Boltzmann solver PyGBe. Previous work from other researchers coupled AMOEBA with the finite-difference solver APBS, and found difficulties to effectively transfer the multipolar charge description to the mesh. A boundary integral formulation treats the charge distribution analytically, overlooking such limitations. This becomes particularly important in simulations that need high accuracy, for example, when the quantity of interest is the difference between solvation energies obtained from separate calculations, like happens for binding energy. We present verification and validation results of our software, compare it with the implementation on APBS, and assess the efficiency of AMOEBA and classical point-charge force fields in a Poisson-Boltzmann solver. We found that a boundary integral approach performs similarly to a volumetric method on CPU. Also, we present a GPU implementation of our solver. Moreover, with a boundary element method, the mesh density to correctly resolve the electrostatic potential is the same for standard point-charge and multipolar force fields. Finally, we saw that for binding energy calculations, a boundary integral approach presents more consistent results than a finite difference approximation for multipolar force fields. © 2019 Wiley Periodicals, Inc.