Real spherical harmonic expansion coefficients as 3D shape descriptors for protein binding pocket and ligand comparisons

Motivation: An increasing number of protein structures are being determined for which no biochemical characterization is available. The analysis of protein structure and function assignment is becoming an unexpected challenge and a major bottleneck towards the goal of well-annotated genomes. As shape plays a crucial role in biomolecular recognition and function, the examination and development of shape description and comparison techniques is likely to be of prime importance for understanding protein structure-function relationships. Results: A novel technique is presented for the comparison of protein binding pockets. The method uses the coefficients of a real spherical harmonics expansion to describe the shape of a protein's binding pocket. Shape similarity is computed as the L-2 distance in coefficient space. Such comparisons in several thousands per second can be carried out on a standard linux PC. Other properties such as the electrostatic potential fit seamlessly into the same framework. The method can also be used directly for describing the shape of proteins and other molecules.