Why aren't the small worlds of protein contact networks smaller

Abstract

Computer experiments are performed to investigate why protein contact networks (networks induced by spatial contacts between amino acid residues of a protein) do not have shorter average shortest path lengths in spite of their importance to protein folding. We find that shorter average inter-nodal distances is no guarantee of finding a global optimum more easily. Results from the experiments also led to observations which parallel an existing view that neither short-range nor long-range interactions dominate the protein folding process. Nonetheless, runs where there was a slight delay in the use of long-range interactions yielded the best search performance. We incorporate this finding into the optimization function by giving more weight to short-range links. This produced results showing that randomizing long-range links does not yield better search performance than protein contact networks au natural even though randomizing long-range links significantly reduces average path lengths and retains much of the clustering and positive degree-degree correlation inherent in protein contact networks. Hence there can be explanations, other than the excluded volume argument, beneath the topological limits of protein contact networks.