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 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 spatially more long-ranged and are mainly executed by loop residues, exist extensively in most analyzed proteins. Examination of torsional motion for correlated BTPs suggested that aharmonic torsional state transitions are essential for such non-linear correlations, which correspondingly occur on widely different and relatively longer time scales. In contrast, BTP correlations between backbone torsions in stable $\alpha$ helices and $\beta$ strands are mainly linear and spatially more short-ranged, and are more likely to associate with intra-well torsional dynamics. Further analysis revealed that the direct cause of non-linear contributions are heterogeneous, and in extreme cases canceling, linear correlations associated with different torsional states of participating torsions. Therefore, torsional state transitions of participating torsions for a correlated BTP are only necessary but not sufficient condition for significant non-linear contributions. These findings implicate a general search strategy for novel allosteric modulation of protein activities. Meanwhile, it was suggested that ensemble averaged correlation calculation and static contact network analysis, while insightful, are not sufficient to elucidate mechanisms underlying allosteric signal transmission in general, dynamical and time scale resolved analysis are essential. 
Shiyang Long and Pu Tian
q-bio.BM