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

TL;DR

This paper introduces a novel measure called maximum intrachain contact entanglement to better predict protein folding rates, showing it complements existing methods and improves prediction accuracy.

Contribution

The study proposes a new entanglement-based descriptor for protein structures that enhances the prediction of folding kinetics beyond traditional contact order measures.

Findings

The new entanglement index correlates well with folding rates.

It provides additional predictive power when combined with existing methods.

The measure is computationally feasible using discretized line integrals.

Abstract

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.