A precise analytical method for calculating the electrostatic energy of macromolecules in aqueous solution

Abstract

A new method for calculating the total electrostatic free energy of a macromolecule in solution is presented. It is applicable to molecules of arbitrary shape and size, including membranes or macromolecular assemblies with substrate molecules and ions. The method is derived from integrating the energy density of the electrostatic field and is termed the field energy method. It is based on the dielectric model, in which the solute and the surrounding water are regarded as different continuous dielectrics. The field energy method yields both the interaction energy between all charge pairs and the self energy of single charges, effectively accounting for the interaction with water. First, the dielectric boundary and mirror charges are determined for all charges of the solute. The energy is then given as a simple function of the interatomic distances, and the standard atomic partial charges and volumes. The interaction and self energy are shown to result from three-body and pairwise interactions. Both energy terms explicitly involve apolar atoms, revealing that apolar groups are also subject to electrostatic forces. We applied the field energy method to a spherical model protein. Comparison with the Kirkwood solution shows that errors are within a small percentage. As a further test, the field energy method was used to calculate the electrostatic potential of the protein superoxide dismutase. We obtained good agreement with the result from a program that implements the numerical finite difference algorithm. The field energy method provides a basis for energy minimization and dynamics programs that account for the solvent and screening effect of water at little computational expense.