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 .
After revision:  Based on analysis of extensive molecular dynamics (MD) simulation trajectories of eleven proteins with different sizes and folds, we found that nonlinear backbone torsional pair correlations exist extensively in some proteins and are dominantly executed by loop residues .