The short-cut network within protein residue networks

A protein residue network (PRN) is a network of interacting amino acids within a protein. We describe characteristics of a sparser, highly central and more volatile sub-network of a PRN called the short-cut network (SCN), as a protein folds under molecular dynamics (MD) simulation with the goal of understanding how proteins form navigable small-world networks within themselves. The edges of an SCN are found via a local greedy search on a PRN. SCNs grow in size and transitivity strength as a protein folds, and SCNs from “successful” MD trajectories are better formed in these terms. Findings from an investigation on how to model the formation of SCNs using dynamic graph theory, and suggestions to move forward are presented. A SCN is enriched with short-range contacts and its formation correlates positively with secondary structure formation. Thus our approach to modeling PRN formation, in essence protein folding from a graph theoretic view point, is more in tune with the notion of increasing order to a random graph than the other way around, and this increase in order coincides with improved navigability of PRNs.