Nonlinear backbone torsional pair correlations in proteins

Protein allostery requires dynamical structural correlations. Physical origin of which, however, remain elusive despite intensive studies during last two and half decades. Based on analysis of molecular dynamics (MD) simulation trajectories for ten proteins with different sizes and folds, we found that nonlinear backbone torsional pair (BTP) correlations, which are mainly spatially long-ranged and are dominantly executed by loop residues, exist extensively in most analyzed proteins. Examination of torsional motion for correlated BTPs suggested that such nonlinear correlations are mainly associated aharmonic torsional state transitions and in some cases strongly anisotropic local torsional motion of participating torsions, and occur on widely different and relatively longer time scales. In contrast, correlations between backbone torsions in stable α helices and β strands are mainly linear and spatially short-ranged, and are more likely to associate with harmonic local torsional motion. Further analysis revealed that the direct cause of nonlinear contributions are heterogeneous linear correlations. These findings implicate a general search strategy for novel allosteric modulation sites of protein activities.