Empirical and accurate method for the three-dimensional electrostatic potential (EM-ESP) of biomolecules

The electrostatic potential (ESP) is an important property of interactions within and between macromolecules, including those of importance in the life sciences. Semiempirical quantum chemical methods and classical Coulomb calculations fail to provide even qualitative ESP for many of these biomolecules. A new empirical ESP calculation method, namely, EM-ESP, is developed in this study, in which the traditional approach of point atomic charges and the classical Coulomb equation is discarded. In its place, the EM-ESP generates a three-dimensional electrostatic potential V(EM)(r) in molecular space that is the sum of contributions from all component atoms. The contribution of an atom k is formulated as a Gaussian function g(r(k);alpha(k),beta(k)) = alpha(k)/r(k)(betak) with two parameters (alpha(k) and beta(k)). The benchmark for the parameter optimization is the ESP obtained by using higher-level quantum chemical approaches (e.g., CCSD/TZVP). A set of atom-based parameters is optimized in a training set of common organic molecules. Calculated examples demonstrate that the EM-ESP approach is a vast improvement over the Coulombic approach in producing the molecular ESP contours that are comparable to the results obtained with higher-level quantum chemical methods. The atom-based parameters are shown to be transferrable between one part of closely related aromatic molecules. The atom-based ESP formulization and parametrization strategy can be extended to biological macromolecules, such as proteins, DNA, and RNA molecules. Since ESP is frequently used to rationalize and predict intermolecular interactions, we expect that the EM-ESP method will have important applications for studies of protein-ligand and protein-protein interactions in numerous areas of chemistry, molecular biology, and other life sciences.