From Quantum Chemistry to Networks in Biology: A Graph Spectral Approach to Protein Structure Analyses
Abstract
In this perspective article, we present a multidisciplinary approach for characterizing protein structure networks. We first place our approach in its historical context and describe the manner in which it synthesizes concepts from quantum chemistry, biology of polymer conformations, matrix mathematics, and percolation theory. We then explicitly provide the method for constructing the protein structure network in terms of noncovalently interacting amino acid side chains and show how a mine of information can be obtained from the graph spectra of these networks. Employing suitable mathematical approaches, such as the use of a weighted, Laplacian matrix to generate the spectra, enables us to develop rigorous methods for network comparison and to identify crucial nodes responsible for the network integrity through a perturbation approach. Our scoring methods have several applications in structural biology that are elusive to conventional methods of analyses. Here, we discuss the instances of (a) protein structure comparison that includes the details of side chain connectivity, (b) contribution to node clustering as a function of bound ligand, explaining the global effect of local changes in phenomena such as allostery, and (c) identification of crucial amino acids for structural integrity, derived purely from the spectra of the graph. We demonstrate how our method enables us to obtain valuable information on key proteins involved in cellular functions and diseases such as GPCR…
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