Properties of Amino Acid Contact Networks of Delaunay Tessellated Protein Structures

The authors have subjected several sets of real and simplified model protein structures to Delaunay tessellation. The system of contacts defined by residues joined with simplex edges in the tessellation can be thought of as a graph or network. Properties like the graph distances between residues and clustering coefficients can be computed to investigate the nature of such contact networks. Using metric multi-dimensional scaling, the effective dimensionality d of the space in which such networks live can also be computed from a matrix of all inter-residue graph distances. We find that protein contact networks are not strictly small world networks, as has previously been asserted, and the variation of d with simplex edge length cutoff gives a set of natural distance scales for proteins. These two results are related—d determines how the characteristic path length of the contact graph scales with the number of residues N.