Protein-ligand recognition using spherical harmonic molecular surfaces: towards a fast and efficient filter for large virtual throughput screening

Molecular surfaces are important because surface-shape complementarity is often a necessary condition in protein-ligand interactions and docking studies. We have previously described a fast and efficient method to obtain triangulated surface-meshes by topologically mapping ellipsoids on molecular surfaces. In this paper, we present an extension of our work to spherical harmonic surfaces in order to approximate molecular surfaces of both ligands and receptor-cavities and to easily check the surface-shape complementarity. The method consists of (1) finding lobes and holes on both ligand and cavity surfaces using contour maps of radius functions with spherical harmonic expansions, (2) superposing the surfaces around a given binding site by minimizing the distance between their respective expansion coefficients. This docking procedure capabilities was demonstrated by application to 35 protein-ligand complexes of known crystal structures. The method can also be easily and efficiently used as a filter to detect in a large conformational sampling the possible conformations presenting good complementarity with the receptor site, and being, therefore, good candidates for further more elaborate docking studies. This "virtual screening" was demonstrated on the platelet thrombin receptor.