The Geometric and Electrostatic Properties of Binding Cavities and Their Usage in Protein-Ligand Docking

Abstract

A scoring function that quantifies the strength of protein-ligand interaction represents our best understanding of the physics of the interaction, and plays a fundamental role in the design of any protein-ligand docking algorithm. From the viewpoint of physics, the interaction is electrodynamic in nature but is commonly though artificially separated into electrostatic and van der Waals (VDW)interactions. A typical scoring function may include other empirical terms with no clear physical meaning. Since the interaction occurs in bulk solution, entropy also contributes importantly. Solvation energy accounts for, to a certain degree, the change in entropy. From the algorithmic viewpoint, the mathematical form of a scoring function determines how to conduct the search for best ligand poses that maximize the protein-ligand affinity as specified by the scoring function. Here we report a preliminary version of a novel protein-ligand docking algorithm that is built upon our unique transformation of electrostatic and VDW interactions. A smooth 2Dmanifold that is diffeomorphic to a patch in $S^2$ is constructed to capture the essence of the intermolecular VDW interaction. Electrostatic interaction in solution is represented by a correlation between the electrostatic potential and atom type that was observed by us after an analysis of a diverse set of known protein-ligand complex structures. Our algorithm differs greatly from other docking algorithms thank to the unique approach by which the geometric and electrostatic properties have been used to prune the search space. An implementation of the algorithm shows its accuracy and efficiency. The algorithm promises to be especially valuable for the docking of fragments, small compounds and for lead optimization, as well as for virtual screening.