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

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.

arXiv comment8 figures. v2: new title

References in corpus (6)

• How knots influence properties of proteins
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• Threading Dynamics of Ring Polymers in a Gel
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Cited by in corpus (6)

• Sequence and structural patterns detected in entangled proteins reveal the importance of co-translational folding
• Knot polynomials of open and closed curves
• Vassiliev measures of complexity for open and closed curves in 3-space
• Folding Rate Optimization Promotes Frustrated Interactions in Entangled Protein Structures
• Time- and ensemble-average statistical mechanics of the Gaussian Network Model
• Link Node: A Method to Characterize the Chain Topology of Intrinsically Disordered Proteins