Compositional Preferences in Quadruplets of Nearest Neighbor Residues in Protein Structures: Statistical Geometry Analysis

Three-dimensional structure and amino acid sequence of proteins are related by an unknown set of rules that is often referred to as the folding code. This code is believed to be significantly influenced by nonlocal interactions between the residues. A quantitative description of nonlocal contacts requires the identification of neighboring residues. We applied statistical geometry approach to analyze the patterns of spatial proximity of residues in known protein structures. Structures from a dataset of well resolved nonhomologous proteins with a single point representation of residues by Cα atoms were tessellated using Delaunay algorithm. The Delaunay tessellation generates an aggregate of space-filling irregular tetrahedra, or Delaunay simplices. The vertices of each simplex objectively define four nearest neighbor Cα atoms and therefore four nearest neighbor residues. Compositional analysis of Delaunay simplices reveals highly nonrandom clustering of amino acid residues in protein structures. Relative abundance or deficiency of residue quadruplets with certain compositions reflects propensities of different types of amino acids to be associated or disassociated in folded proteins. The likelihood of occurrence of four residues in one simplex displays strong nonrandom signal also in the case of a reduced amino acid alphabet. We used several different three-letter alphabets based on the residue chemical and structural properties and on the complementarity of the corresponding codons. In all cases the clustering of residues correlates with their properties or genetic origin. The results of this analysis are being implemented in algorithms for protein structure classification and prediction.