  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 non-covalently 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 include the details of side chain
connectivity, (b) The contribution to node clustering as a function of bound
ligand, explaining the global effect of local changes in phenomena such as
allostery and (c) The 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 and HIV protease, and discuss the
biological implications. We then briefly describe how concepts from percolation
theory further augment our analyses. In our concluding perspective for future
developments, we suggest a further unifying approach to protein structure
analyses and a judicious choice of questions to employ our methods for larger,
more complex networks, such as metabolic and disease networks.
