Local search on protein residue networks

Self-avoiding random walks were performed on protein residue networks. Compared with protein residue networks with randomized links, the probability of a walk being successful is lower and the length of successful walks shorter in (non-randomized) protein residue networks. Fewer successful walks and shorter successful walks point to higher communication specificity between protein residues, a conceivably favourable attribute for proteins to have. The use of random walks instead of shortest paths also produced lower node centrality, lower edge betweeness and lower edge load for (non-randomized) protein residue networks than in their respective randomized counterparts. The implications of these properties for protein residue networks are discussed in terms of communication congestion and network vulnerability. The randomized protein residue networks have lower network clustering than the (nonrandomized) protein residue networks. Hence, our findings also shed light on a hitherto neglected aspect: the importance of high network clustering in protein residue networks. High clustering increases navigability of a network for local search and the combination of a local search process on a highly clustered small-world network topology such as protein residue networks reduces communication congestion and network vulnerability.