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