Accurate and efficient description of protein vibrational dynamics: comparing molecular dynamics and Gaussian models

Current all-atom potential based molecular dynamics (MD) allows the identification of a protein's functional motions on a wide-range of timescales, up to few tens of nanoseconds. However, functional, large-scale motions of proteins may occur on a timescale currently not accessible by all-atom potential based MD. To avoid the massive computational effort required by this approach, several simplified schemes have been introduced. One of the most satisfactory is the Gaussian network approach based on the energy expansion in terms of the deviation of the protein backbone from its native configuration. Here, we consider an extension of this model that captures in a more realistic way the distribution of native interactions due to the introduction of effective side-chain centroids. Since their location is entirely determined by the protein backbone, the model is amenable to the same exact and computationally efficient treatment as previous simpler models. The ability of the model to describe the correlated motion of protein residues in thermodynamic equilibrium is established through a series of successful comparisons with an extensive (14 ns) MD simulation based on the AMBER potential of HIV-1 protease in complex with a peptide substrate. Thus, the model presented here emerges as a powerful tool to provide preliminary, fast yet accurate characterizations of protein near-native motion.