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/complexes presents computational challenges, however, due to the difficulty of retaining atomic details in mode decomposition of large systems dynamics. Here, we present a novel approach to address this problem. Based on a Markovian description of communication/interaction stochastics, we map the full-atom GNM representation into a hierarchy of lower resolution networks, perform the analysis in the reduced space(s) and reconstruct the detailed models dynamics with minimal loss of data. The approach (hGNM) applied to chaperonin GroEL-GroES demonstrates that the shape and frequency dispersion of the dominant 25 modes of motion predicted by a full-residue (8015 nodes) GNM analysis are almost identically reproduced by reducing the complex into a network of 35 soft nodes.