Multi-Body Interactions within the Graph of Protein Structure

We construct a graphical representation of protein structure based on the 3D C-alpha carbon point set, using the Delaunay tessellation to define interacting quadruples of amino acid residues. The tessellation is filtered by two criteria: interaction distance less than 9.5 angstroms and circumsphere radius less than 8.0 angstroms using dataset of 608 protein structures of low mutual sequence identity and a likelihood ratio test, we show that 3-body and 4-body interactions are indeed significant. We identify particular significant three-body interactions by first reducing the dataset to interacting triples, and classifying amino acid residues in a reduced alphabet. Although cystein was previously shown to be a dominant source of 3-body interactions, we now identify additional significant 3-body interactions of charged, hydrophobic and small residues.