Before revision:  Based on analysis of extensive molecular dynamics (MD) simulation trajectories of eleven proteins with different sizes and folds, we found that significant spatially long-range backbone torsional pair correlations exist extensively in some proteins and are dominantly executed by loop residues . Further examinations suggest that such correlations are inherently non-linear and are associated with aharmonic torsional state transitions . Correspondingly, they occur on widely different and relatively longer time scales.
After revision:  Based on analysis of extensive molecular dynamics (MD) simulation trajectories of eleven proteins with different sizes and folds, we found that significant spatially long-range backbone torsional pair correlations exist extensively in some proteins and are dominantly executed by loop residues , exist extensively in most analyzed proteins. Examination of torsional motion for correlated BTPs suggested that aharmonic torsional state transitions . Correspondingly, they occur on widely different and relatively longer time scales.