On the Contribution of Linear Correlations to Quasi-harmonic Conformational Entropy in Proteins

We study the contribution of linear, pairwise atom-positional correlations (covariances) to absolute and relative conformational entropy as calculated by quasi-harmonic analysis of molecular dynamics (MD) trajectories (SQH and ΔSQH). By analyzing a total of 25 micros of MD simulations of ubiquitin and six of its binding partners in bound and unbound states, and 2.4 micros of simulations of eight different proteins in phosphorylated and unphosphorylated states, we show that ΔSQH represents a remarkably constant fraction of a quasi-harmonic entropy change obtained if one ignores the contribution of covariance terms and uses mass-weighted atom-positional variances only (ΔSVAR). In other words, the relative contribution of linear correlations to conformational entropy change for different proteins and in different biomolecular processes appears to be largely constant. Based on this, we establish an empirical relationship between relative quasi-harmonic conformational entropy and changes in crystallographic B-factors induced by different processes, and we use it to estimate conformational-entropic contribution to the free energy of binding for a large set of protein complexes based on their X-ray structures. Our results suggest a simple way for relating other types of dynamical observables with conformational entropy in the absence of information on correlated motions, such as in the case of NMR order parameters.