Only a Subset of Normal Modes is Sufficient to Identify Linear Correlations in Proteins

Identification of correlated residues in proteins is very important for many areas of protein research such as drug design, protein domain classification, signal transmission, allostery and mutational studies. Pairwise residue correlations in proteins can be obtained from experimental and theoretical ensembles. Since it is difficult to obtain proteins in various conformational states experimentally, theoretical methods such as all-atom molecular dynamics simulations and normal-mode analysis are commonly used methods to obtain protein ensembles and, therefore, pairwise residue correlations. The extent of agreement for the correlations obtained with all-atom molecular dynamics and elastic network model based normal-mode analysis is an important issue to investigate due to orders of magnitude computational advantage in terms of wall time for normal-mode based calculation. We performed multiple microsecond long equilibrium classical molecular dynamics simulations for six proteins. We calculated normalized dynamical cross-correlations and linear mutual information as pairwise residue correlations from the trajectories of these simulations. Then, we calculated the same pairwise residue correlations with two elastic network model based normal-mode analysis methods and compared our results with the former. The results show that elastic network model based normal-mode analysis can provide a fast and accurate estimation of linear correlations within proteins. Finally, we observed that only a subset of modes is sufficient to obtain linear correlations in proteins. This conclusion has crucial implications for understanding correlations within very large protein assemblies such as viral capsids.