Hierarchical Rigidity from Pair Distance Fluctuations

Often, experiments, observations or simulations generate large numbers of snapshots of the configurations of complex many-particle systems. It is important to find methods of extracting useful information from these ensembles of snapshots in order to document the motion as the system evolves. The most interesting information is contained in the correlated motions of individual constituents rather than in their absolute motion. We present a statistical method to identify hierarchies of correlated motions from a series of two or more snapshot configurations. This method is demonstrated in a number of systems, including freely-jointed polymer chains, hard plastic spheres, water, and proteins. These concepts are implemented as TIMME, the Tool for Identifying Mobility in Macromolecular Ensembles.