Relative measure of geometrical entanglement to study folding-unfolding transitions. Application to analysis of molecular dynamics trajectories of proteinsin vacuo

In this work, we characterize and compare folding features in protein conformations. A three-dimensional fold is quantified by a geometrical measure of chain entanglement derived from the probability distribution of projected bond–bond crossings (or “overcrossings”) of the backbone. By comparing probability distributions, we can detect fold similarities among different proteins, as well as monitor the evolution of folding features during protein dynamics. As an illustration, we apply this approach to the analysis of molecular shape changes during the in vacuo unfolding (and subsequent relaxation) of lysozyme. The method provides insights for understanding distinct folding behaviors associated with pathways leading to nativelike or nonnative intermediates.