"Electrostatics of proteins in dielectric solvent continua. I. An accurate and efficient reaction field description."Sebastian Bauer, Gerald Mathias, and Paul Tavan
J. Chem. Phys. 140, 104102 (2014).
We present a reaction field (RF) method which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of an electrostatics calculation with polarizable molecular mechanics (MM) force fields. The method combines an approach originally suggested by Egwolf and Tavan (J. Chem. Phys. 118, 2039, 2003) with concepts generalizing the Born solution (Zeitschrift für Physik 1, 45, 1920) for a solvated ion. First, we derive an exact representation of the RF potential in terms of inducible atomic anti-polarization densities and of atomic shielding charge distributions, which immediately suggests the use of Gaussian approximations. The resulting approximate representation of the RF potential and energy takes the form of an electrostatics model, whose atomic sources are Gaussian shielding charge and anti-polarization densities. While the strengths of the shielding charge densities are directly given in terms of the static partial charges as defined, e.g. by standard MM force fields for the various atom types, the strengths of the anti-polarization densities are calculated by a self-consistency iteration. The effective atomic volumes of the Gaussian shaped atoms are calculated by a second self-consistency procedure serving to guarantee that the dielectric function ε(r) is close to one everywhere inside the protein. The Gaussian widths σi of the atoms i are parameters of the RF approximation. The remarkable accuracy of the method is demonstrated by comparison with Kirkwood’s analytical solution for a spherical protein (J. Chem. Phys. 2, 351, 1934) and with computationally expensive gridbased
numerical solutions for simple model systems in dielectric continua including a di-peptide (Ac-Ala-NHMe) as modeled by a standard MM force field. The latter example shows how weakly the RF conformational free energy landscape depends on the parameters σi. A summarizing discussion highlights the achievements of the new theory and of its approximate solution particularly by comparison with so-called generalized Born methods. A follow-up paper describes how the method enables Hamiltonian, efficient, and accurate MM molecular dynamics simulations of proteins in dielectric solvent continua.
BMO authors (in alphabetic order):
Long-range electrostatics in molecular dynamics simulations