Motion Tree Delineates Hierarchical Structure of Protein Dynamics Observed in Molecular Dynamics Simulation

Molecular dynamics (MD) simulations of proteins provide important information to understand their functional mechanisms, which are, however, likely to be hidden behind their complicated motions with a wide range of spatial and temporal scales. A straightforward and intuitive analysis of protein dynamics observed in MD simulation trajectories is therefore of growing significance with the large increase in both the simulation time and system size. In this study, we propose a novel description of protein motions based on the hierarchical clustering of fluctuations in the inter-atomic distances calculated from an MD trajectory, which constructs a single tree diagram, named a "Motion Tree", to determine a set of rigid-domain pairs hierarchically along with associated inter-domain fluctuations. The method was first applied to the MD trajectory of substrate-free adenylate kinase to clarify the usefulness of the Motion Tree, which illustrated a clear-cut dynamics picture of the inter-domain motions involving the ATP/AMP lid and the core domain together with the associated amplitudes and correlations. The comparison of two Motion Trees calculated from MD simulations of ligand-free and -bound glutamine binding proteins clarified changes in inherent dynamics upon ligand binding appeared in both large domains and a small loop that stabilized ligand molecule. Another application to a huge protein, a multidrug ATP binding cassette (ABC) transporter, captured significant increases of fluctuations upon binding a drug molecule observed in both large scale inter-subunit motions and a motion localized at a transmembrane helix, which may be a trigger to the subsequent structural change from inward-open to outward-open states to transport the drug molecule. These applications demonstrated the capabilities of Motion Trees to provide an at-a-glance view of various sizes of functional motions inherent in the complicated MD trajectory.