Markov Methods for Hierarchical Coarse-Graining of Large Protein Dynamics

Coarse-graining of protein structures for the normal mode studies

The coarse-grained structural model such as Gaussian network has played a vital role in the normal mode studies for understanding protein dynamics related to biological functions. However, for the large proteins, the Gaussian network model is computationally unfavorable for diagonalization of Hessian (stiffness) matrix for the normal mode studies. In this article, we provide the coarse-graining method, referred to as "dynamic model condensation," which enables the further coarse-graining of protein structures consisting of small number of residues. It is shown that the coarser-grained structures reconstructed by dynamic model condensation exhibit the dynamic characteristics, such as low-frequency normal modes, qualitatively comparable to original structures. This sheds light on that dynamic model condensation and may enable one to study the large protein dynamics for gaining insight into biological functions of proteins.

Markov propagation of allosteric effects in biomolecular systems: application to GroEL-GroES

We introduce a novel approach for elucidating the potential pathways of allosteric communication in biomolecular systems. The methodology, based on Markov propagation of 'information' across the structure, permits us to partition the network of interactions into soft clusters distinguished by their coherent stochastics. Probabilistic participation of residues in these clusters defines the communication patterns inherent to the network architecture. Application to bacterial chaperonin complex GroEL-GroES, an allostery-driven structure, identifies residues engaged in intra- and inter-subunit communication, including those acting as hubs and messengers. A number of residues are distinguished by their high potentials to transmit allosteric signals, including Pro33 and Thr90 at the nucleotide-binding site and Glu461 and Arg197 mediating inter- and intra-ring communication, respectively. We propose two most likely pathways of signal transmission, between nucleotide- and GroES-binding sites across the cis and trans rings, which involve several conserved residues. A striking observation is the opposite direction of information flow within cis and trans rings, consistent with negative inter-ring cooperativity. Comparison with collective modes deduced from normal mode analysis reveals the propensity of global hinge regions to act as messengers in the transmission of allosteric signals.