Markov methods for hierarchical coarse-graining of large protein dynamics

Elastic network models (ENMs) and, in particular, the Gaussian Network Model (GNM) have been widely used in recent years to gain insights into the machinery of proteins. The extension of ENMs to supramolecular assemblies presents computational challenges, because of the difficulty in retaining atomic details in mode decomposition of large protein dynamics. Here, we present a novel approach to address this problem. We rely on the premise that, all the residues of the protein machinery (network) must communicate with each other and operate in a coordinated manner to perform their function successfully. To gain insight into the mechanism of information transfer between residues, we study a Markov model of network communication. Using the Markov chain perspective, we map the full-atom network representation into a hierarchy of ENMs of decreasing resolution, perform analysis of dominant communication (or dynamic) patterns in reduced space(s) and reconstruct the detailed models with minimal loss of information. The communication properties at different levels of the hierarchy are intrinsically defined by the network topology. This new representation has several features, including: soft clustering of the protein structure into stochastically coherent regions thus providing a useful assessment of elements serving as hubs and/or transmitters in propagating information/interaction; automatic computation of the contact matrices for ENMs at each level of the hierarchy to facilitate computation of both Gaussian and anisotropic fluctuation dynamics. We illustrate the utility of the hierarchical decomposition in providing an insightful description of the supramolecular machinery by applying the methodology to the chaperonin GroEL-GroES.