Brent A. Gregersen

High-order discretization schemes for biochemical applications of boundary element solvation and variational electrostatic projection methods

A series of high-order surface element discretization schemes for variational boundary element methods are introduced. The surface elements are chosen in accord with angular quadrature rules for integration of spherical harmonics. Surface element interactions are modeled by Coulomb integrals between spherical Gaussian functions with exponents chosen to reproduce the exact variational energy and Gausss law for a point charge in a spherical cavity. The present work allows high-order surface element expansions to be made for variational methods such as the conductorlike screening model for solvation and the variational electrostatic projection method for generalized solvent boundary potentials in molecular simulations.

A charge‐scaling implementation of the variational electrostatic projection method

Two new charge‐scaling methods for efficient modeling of the solvated macromolecular environment in hybrid QM/MM calculations of biological reactions are presented. The methods are extensions of the variational electrostatic projection (VEP) method, and allows a subset of atomic charges in the external environment to be adjusted to mimic, in the active dynamical region, the electrostatic potential and field due to the large surrounding macromolecule and solvent. The method has the advantages that it offers improved accuracy, does not require the use of a three‐dimensional grid or auxiliary set of fitting points, and requires only minor molecular simulation code modifications. The VEP−cs and VEP‐RVM+cs methods are able to attain very high accuracy (relative force errors of 10−7 or better with appropriate choice of control parameters), and take advantage of a recently introduced set of high‐order discretization schemes and Gaussian exponents for boundary element solvation and VEP methods. The methods developed here serve as potentially powerful tools in the arsenal of computational techniques used in multiscale computational modeling problems.