The effect of backbone on the small-world properties of protein contact maps

In the last years, small-world behavior has been extensively described for proteins, when they are represented by the undirected graph defined by the inter-residue protein contacts. By adopting this representation it was possible to compute the average clustering coefficient (C) and characteristic path length (L) of protein structures, and their values were found to be similar to those of graphs characterized by small-world topology. In this comment, we analyze a large set of non-redundant protein structures (1753) and show that by randomly mimicking the protein collapse, the covalent structure of the protein chain significantly contributes to the small-world behavior of the inter-residue contact graphs. When protein graphs are generated, imposing constraints similar to those induced by the backbone connectivity, their characteristic path lengths and clustering coefficients are indistinguishable from those computed using the real contact maps showing that L and C values cannot be used for 'protein fingerprinting'. Moreover we verified that these results are independent of the selected protein representations, residue composition and protein secondary structures.