[Paper Review] Eigenvector Centrality Distribution for Characterization of Protein Allosteric Pathways

Christian F. A. Negre, Uriel N. Morzan+7 more|arXiv (Cornell University)|Jun 7, 2017

Protein Structure and Dynamics1 references3 citations

TL;DR

This paper introduces an eigenvector centrality (EC) metric based on mutual information to identify key residues and long-range correlation pathways in allosteric proteins, using imidazol glycerol phosphate synthase (IGPS) as a test case. The method successfully maps allosteric communication routes, identifies functionally critical residues at the HisH-HisF interface, and is validated by NMR relaxation dispersion data, offering a robust, cost-effective strategy for probing allosteric mechanisms at atomic resolution.

ABSTRACT

Determining the principal energy pathways for allosteric communication in biomolecules, that occur as a result of thermal motion, remains challenging due to the intrinsic complexity of the systems involved. Graph theory provides an approach for making sense of such complexity, where allosteric proteins can be represented as networks of amino acids. In this work, we establish the eigenvector centrality metric in terms of the mutual information, as a mean of elucidating the allosteric mechanism that regulates the enzymatic activity of proteins. Moreover, we propose a strategy to characterize the range of the physical interactions that underlie the allosteric process. In particular, the well known enzyme, imidazol glycerol phosphate synthase (IGPS), is utilized to test the proposed methodology. The eigenvector centrality measurement successfully describes the allosteric pathways of IGPS, and allows to pinpoint key amino acids in terms of their relevance in the momentum transfer process. The resulting insight can be utilized for refining the control of IGPS activity, widening the scope for its engineering. Furthermore, we propose a new centrality metric quantifying the relevance of the surroundings of each residue. In addition, the proposed technique is validated against experimental solution NMR measurements yielding fully consistent results. Overall, the methodologies proposed in the present work constitute a powerful and cost effective strategy to gain insight on the allosteric mechanism of proteins.

Motivation & Objective

• To develop a network-based method that identifies principal energy pathways for allosteric communication in proteins, overcoming limitations of traditional correlation-based approaches.
• To characterize the range of physical interactions underlying allosteric signaling by distinguishing local from non-local (long-range) correlations.
• To validate the proposed centrality metric against experimental NMR relaxation dispersion data to confirm its predictive power.
• To provide a mechanistic interpretation of site-directed mutagenesis results by quantifying the environmental relevance of each residue’s centrality.
• To offer a computationally efficient alternative to principal component analysis for identifying dominant collective modes in protein dynamics.

Proposed method

• The method models proteins as networks where amino acid residues are nodes and physical interactions (e.g., dynamical correlations) are weighted edges, represented by an adjacency matrix A.
• Eigenvector centrality (EC) is computed using the dominant eigenvector of the adjacency matrix, quantifying the relative importance of each residue in momentum transfer across the network.
• The EC metric is redefined using generalized mutual information to capture non-linear, non-collinear correlations, overcoming the limitations of Pearson correlation coefficients.
• A new metric, 'environmental relevance centrality,' is introduced to assess the functional importance of a residue’s surrounding neighborhood.
• The analysis is performed at multiple correlation length scales (λ = 5, 10, 20 Å) to distinguish short-range and long-range contributions to allosteric pathways.
• The method is applied to the IGPS protein in both apo and PRFAR-bound states to compare centrality distributions and identify effector-induced changes in network dynamics.

Experimental results

Research questions

• RQ1 How can eigenvector centrality based on mutual information improve the identification of key residues in allosteric pathways compared to traditional correlation-based methods?
• RQ2 What is the contribution of long-range (non-local) correlations to allosteric communication in IGPS, and how does it differ from short-range dynamics?
• RQ3 How do changes in effector binding (PRFAR) alter the centrality distribution and identify functionally critical residues in the allosteric network?
• RQ4 To what extent do the predicted centrality patterns align with experimental NMR relaxation dispersion data on millisecond motions?
• RQ5 Can the proposed environmental relevance metric help interpret site-directed mutagenesis results by identifying functionally critical residue neighborhoods?

Key findings

• The eigenvector centrality analysis successfully identifies key residues at the HisH-HisF interface as central to allosteric communication, consistent with prior community network analysis and experimental data.
• The long-range centrality distribution (λ = 20 Å) shows a nearly uniform distribution, indicating that the characteristic correlation distances in the breathing motion are within 5–20 Å.
• The largest increase in long-range centrality upon PRFAR binding occurs on the sideL of the HisF subunit, correlating with a previously reported interdomain breathing motion that increases in frequency nearly fourfold.
• NMR relaxation dispersion experiments confirm that millisecond-timescale motions induced by PRFAR binding are primarily localized on sideL, supporting the EC prediction of enhanced long-range dynamics there.
• The sideL/sideR asymmetry in centrality distributions is inverted between short- and long-range scales, indicating distinct dynamical regimes for local and non-local interactions.
• The environmental relevance metric provides a plausible explanation for site-directed mutagenesis results, linking functional importance to the centrality of a residue’s surrounding network.