Residue-Level Allostery Propagates Through the Effective Coarse-Grained Hessian

Abstract

<jats:title>Abstract</jats:title><jats:p>The long-ranged coupling between residues that gives rise to allostery in a protein is built up from short-ranged physical interactions. Computational tools used to predict this coupling and its functional relevance have relied on the application of graph theoretical metrics to residue-level correlations measured from all-atom molecular dynamics (aaMD) simulations. The short-ranged interactions that yield these long-ranged residue-level correlations are quantified by the effective coarse-grained Hessian. Here we compute an effective harmonic coarse-grained Hessian from aaMD simulations of a benchmark allosteric protein, IGPS, and demonstrate the improved locality of this graph Laplacian over two other connectivity matrices. Additionally, two centrality metrics are developed that indicate the direct and indirect importance of each residue at producing the covariance between the effector binding pocket and the active site. The residue importance indicated by these two metrics is corroborated by previous mutagenesis experiments and leads to unique functional insights; in contrast to previous computational analyses, our results suggest that fP76-hK181 is the most important contact for conveying direct allosteric paths across the HisF-HisH interface. The connectivity around fD98 is found to be important at affecting allostery through indirect means.</jats:p>

Molecular Paradigms for Biological Mechanosensing

“…The covariance matrix of residue displacements is proportional to the inverse of the Hessian of an elastic network model, representing Gaussian fluctuations about the free energy minimum of the protein structure. 15 Previous studies have exploited this connection to determine the importance of particular intermediate residues in propagating changes from one side of the protein to another during chemical allostery 15−17 (Figure 4). Mechanical allostery could play an important role in biological signaling processes.…”

“…Example of chemical allostery. The 100 shortest allosteric pathways from the residues at the end of the Q arrows to the residues indicated by the Q′ arrows for the protein IGPS, adapted from ref 15.In IGPS, binding a ligand near the highlighted residues in the orange/left domain accelerates catalysis of a chemical reaction in the white/right domain at the highlighted region by ∼5000 fold 15.…”

Rational design of allosteric modulators: Challenges and successes

“…In graph theory, proteins are represented by an atomistic graph network model, where nodes are atoms and weighted edges are the covalent and noncovalent bonds, 123 or by a coarse‐grained network model, which is the most usual case, where nodes are residue Cα atoms, or residue center of mass, connected with edges based on a distance cutoff maintained in the MD trajectory at a certain percent (e.g., 75% of the MD trajectory) 108,124 or based on other inter‐residue properties 125,126 . The edge weights are usually based on the covariance matrix of the displacement of Cα atoms, or from mutual information analysis from MD simulations, and the allosteric hot spots and communities are identified using centrality measures, for example, betweenness centrality, eigenvector centrality, and other metrics 124,127–132 . The allosteric pathway is then detected using the Dijkstra algorithm, 133 or the Bellman–Ford algorithm, 134 which finds the shortest path between two nodes in a graph.…”

“…125,126 The edge weights are usually based on the covariance matrix of the displacement of Cα atoms, or from mutual information analysis from MD simulations, and the allosteric hot spots and communities are identified using centrality measures, for example, betweenness centrality, eigenvector centrality, and other metrics. 124,[127][128][129][130][131][132] The allosteric pathway is then detected using the Dijkstra algorithm, 133 or the Bellman-Ford algorithm, 134 which finds the shortest path between two nodes in a graph. A plethora of tools integrating graph theory and network models for detecting protein dynamics and allosteric communications pathways have been recently reviewed in Ref.…”

Coevolution-based prediction of key allosteric residues for protein function regulation

“…Unfortunately, identifying key allo-residues remains challenging. Currently available computational methods mainly focused on the prediction of allosteric sites 15,16 , allosteric pathways 17,18 and key residues in allosteric pathways 19 . Kalescky et al developed the rigid residue scan method to identify key residues for protein allostery, in which multiple molecular dynamics (MD) simulations need to be performed for unbound and bound proteins.…”