Generalized correlation for biomolecular dynamics

Correlated motions in biomolecules are often essential for their function, e.g., allosteric signal transduction or mechanical/thermodynamic energy transport. Because correlated motions in biomolecules remain difficult to access experimentally, molecular dynamics (MD) simulations are particular useful for their analysis. The established method to quantify correlations from MD simulations via calculation of the covariance matrix, however, is restricted to linear correlations and therefore misses part of the correlations in the atomic fluctuations. Herein, we propose a general statistical mechanics approach to detect and quantify any correlated motion from MD trajectories. This generalized correlation measure is contrasted with correlations obtained from covariance matrices for the B1 domain of protein G and T4 lysozyme. The new method successfully quantifies correlations and provides a valuable global overview over the functionally relevant collective motions of lysozyme. In particular, correlated motions of helix 1 together with the two main lobes of lysozyme are detected, which are not seen by the conventional covariance matrix. Overall, the established method misses more than 50% of the correlation. This failure is attributed to both, an interfering and unnecessary dependence on mutual orientations of the atomic fluctuations and, to a lesser extent, attributed to nonlinear correlations. Our generalized correlation measure overcomes these problems and, moreover, allows for an improved understanding of the conformational dynamics by separating linear and nonlinear contributions of the correlation.