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Molecular dynamics simulations of biomolecules have been widely adopted inbiomedical studies. As classical point-charge models continue to be used inroutine biomolecular applications, there have been growing demands ondeveloping polarizable force fields for handling more complicated biomolecularprocesses. Here we focus on a recently proposed polarizable Gaussian Multipole(pGM) model for biomolecular simulations. A key benefit of pGM is its screeningof all short-range electrostatic interactions in a physically consistentmanner, which is critical for stable charge-fitting and is needed to reproducemolecular anisotropy. Another advantage of pGM is that each atom's multipolesare represented by a single Gaussian function or its derivatives, allowing formore efficient electrostatics than other Gaussian-based models. In this studywe present an efficient formulation for the pGM model defined with respect to alocal frame formed with a set of covalent basis vectors. The covalent basisvectors are chosen to be along each atom's covalent bonding directions. The newlocal frame allows molecular flexibility during molecular simulations andfacilitates an efficient formulation of analytical electrostatic forces withoutexplicit torque computation. Subsequent numerical tests show that analyticalatomic forces agree excellently with numerical finite-difference forces for thetested system. Finally, the new pGM electrostatics algorithm is interfaced withthe PME implementation in Amber for molecular simulations under the periodicboundary conditions. To validate the overall pGM/PME electrostatics, weconducted an NVE simulation for a small water box of 512 water molecules. Ourresults show that, to achieve energy conservation in the polarizable model, itis important to ensure enough accuracy on both PME and induction iteration.

Efficient Formulation of Polarizable Gaussian Multipole Electrostatics for Biomolecular Simulations