Eigenvector Centrality Distribution for Characterization of Protein Allosteric Pathways

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.