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The folding of a protein towards its native state is a rather complicatedprocess. However there are empirical evidences that the folding time correlateswith the contact order, a simple measure of the spatial organisation of thenative state of the protein. Contact order is related to the average length ofthe main chain loops formed by amino acids which are in contact. Here we arguethat folding kinetics can be influenced also by the entanglement that loops mayundergo within the overall three dimensional protein structure. In order toexplore such possibility, we introduce a novel descriptor, which we call"maximum intrachain contact entanglement". Specifically, we measure the maximumGaussian entanglement between any looped portion of a protein and any othernon-overlapping subchain of the same protein, which is easily computed bydiscretized line integrals on the coordinates of the $C_{\alpha}$ atoms. Byanalyzing experimental data sets of two-state and multistate folders, we showthat also the new index is a good predictor of the folding rate. Moreover,being only partially correlated with previous methods, it can be integratedwith them to yield more accurate predictions.

Exploring the correlation between the folding rates of proteins and the entanglement of their native states