On the estimation of the molecular inaccessible volume and the molecular accessible surface of a ligand in protein–ligand systems

Abstract

In this paper, a novel approach is proposed based on the accurate computation of the inaccessible volume and the corresponding surface area which is defined by the locus of points where a ligand molecule can be placed so that it “touches” a protein molecule at a preset minimum interatomic distance without resulting in overlaps between the atoms of the protein and the atoms of the ligand. The proposed approach can be considered an extension of the widely used concept of the solvent accessible surface area (SASA). The SASA is defined as the surface where a solvent molecule can be in contact with the initial one without any overlaps. This excluded volume interaction is evaluated by treating atoms as hard core spheres, with the limitation of the solvent molecule being represented as a single sphere. In the proposed concepts of the molecular accessible surface (MASA) and the molecular inaccessible volume (MIV) we have practically removed this limitation and all atoms, both in the initial and the “inserted” molecules, are represented as hard spheres. In this paper we focus our examples on biological systems, especially on studying protein–ligand systems, since we expect that this will be one of the most promising fields of applications where the MASA and MIV extensions of the SASA will be of practical and immediate use. Therefore, the MASA and MIV are evaluated based on the surface generated by the ligand while it is being rolled over on all the atoms of the protein without penetrating them. Identification of the inaccessible volume of each candidate protein–ligand pair is also provided in the context of this study, along with the boundary surface where the ligand can be placed so as to be in “contact” with the protein. The proposed concepts of the MASA and MIV are expected to significantly enhance the ability to investigate specific protein–drug interactions by explicitly taking into account the polyatomic nature of a ligand. Several trials have been conducted using the analytical method of Dodd and Theodorou leading to accurate volume and surface area measurements of an arbitrary set of fused spheres in systems of various scales.