Motivation: The majority of the inter-residue distances in a protein structure are correlated given a fixed topology. Here, we investigate whether we are able to predict a structure's folding rate, which is known to depend on the complexity of its fold, while considering only a small, uncorrelated fraction of its contacts.
Results: We define an expression for the probabilistic information content associated to the relative position of a pair of amino acid residues in a protein structure. By means of fitting the protein chain to a self-avoiding random walk model, we derive a probability distribution for the distance between residues as a function of their separation along the sequence. We then show that the average information content for all residue pairs in a structure, considered as an estimate of its fold's complexity, is well correlated to the logarithm of its folding rate. Moreover, the same information content measure may be exploited to rank contacts and identify redundancies, allowing the prediction the structure's folding rate with similar accuracy while taking into account less than 5% of its contacts.
Availability and implementation: An implementation of the described model and the experimental data are available at http://github.com/luciano-censoni/sarw-lnkf.