Quadratic Shape Descriptors. 1. Rapid Superposition of Dissimilar Molecules Using Geometrically Invariant Surface Descriptors

In this paper, we present a novel approach to shape-based molecular similarity searching. The method that we introduce is able to superimpose dissimilar molecules by using geometrically invariant molecular surface descriptors. The shape descriptors are calculated by least-squares fitting of a quadratic function to small sections of the molecular surface of a ligand. Invariant geometric properties of the approximated surface patch are then extracted from the fitted quadratic function. The extracted properties are used to quantify the shape and to obtain a canonical orientation for this section of surface. The superimposition algorithm uses these geometric invariants to recognize similar regions of surface shape existing on two molecules and to bring these regions (and consequently the molecules) into registration. Because these geometric descriptors are based upon local surface shape, the superimposing algorithm is insensitive to the connectivity and the relative sizes of the molecules being matched. The capabilities of our algorithm are demonstrated by superimposing dissimilar ligands known to inhibit the same enzyme system. In all cases examined the algorithm generates superpositions that are in agreement with crystallographic results. The algorithm is also applied to align the two different proteins on the basis of the shape of their active sites.