Full correlation analysis of conformational protein dynamics

Correlated motions in biomolecules are often essential for their function, for example, allosteric signal transduction or mechanical/thermodynamic energy transport. Principal component analysis (PCA) is a widely used method to extract functionally relevant collective motions from a molecular dynamics (MD) trajectory. Being based on the covariance matrix, however, PCA detects only linear correlations. Here we present a new method, full correlation analysis (FCA), which is based on mutual information and thus quantifies all correlations, including nonlinear and higher order correlations. For comparison, we applied both, PCA and FCA, to approximately 100 ns MD trajectories of T4 lysozyme and the hexapeptide neurotensin. For both systems, FCA yielded better resolved conformational substates and aligned its modes more often with actual transition pathways. This improved resolution is shown to be due to a strongly increased anharmonicity of FCA modes as compared to the respective PCA modes. The high anharmonicity further suggests that the motions extracted by FCA are functionally more relevant than those captured by PCA. In summary, FCA should provide improved collective degrees of freedom for dimension-reduced descriptions of macromolecular dynamics.