(35) Sclove, Stanley L., and Sherman, Simon A. (1995). Cluster analysis of dihedral angles of amino acid residues in proteins. 1994 Proceedings of the Biopharmaceutical Section, 399-404. American Statistical Association, Alexandria, VA.
This research applies mixture-model cluster analysis to the problem of protein-structure determination. A protein is a directed sequence of amino acid residues. Each residue is one of twenty amino acids. The conformation (spatial structure) of an amino acid can be described by the three dihedral angles phi, psi and chi. The angles phi and psi determine the conformation of the main-chain; chi gives the orientation of the side-chain. Due to stereochemical restrictions there is much clustering of the points in angular space. The joint distribution of phi and psi is to some extent described in the literature, but the three variable distribution is of interest. It is known that the marginal distribution of chi is tri-modal, with modes at about -60, +60 and 180 degrees. This fact, and the nature of the two-variable distributions, enable us to propose a new classification of the conformational states of amino acids. This classification is obtained by fitting mixture models to data from the Brookhaven Protein Data Bank. The results obtained in this manner are used in a bottom-up procedure for building protein structure that is quite different from the usual top-down approach. The present paper focuses on statistical aspects; later papers will focus on biomolecular aspects.