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