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 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.

Surveying the Side-Chain Network Approach to Protein Structure and Dynamics: The SARS-CoV-2 Spike Protein as an Illustrative Case

“…Further, it lends itself for quantitative comparison of networks by providing a score and allows us to identify the regions of the network which are dissimilar. A brief review of these aspects has been presented earlier (Gadiyaram et al, 2019).…”

“…Network theory-based analyses of protein structure (Bagler and Sinha, 2005;Atilgan et al, 2012) and dynamics have provided unprecedented insights into the global structural connectivity of proteins and its complexes in the context of allostery and other biological processes (Atilgan et al, 2012;Di Paola et al, 2013;Bhattacharyya et al, 2016;Gadiyaram et al, 2019;Krieger et al, 2020;Verkhivker et al, 2020). When combined with information on conformational variations, as obtained from molecular dynamics, network approaches have elucidated several examples of protein structure-function relationships (Doruker et al, 2000;Sethi et al, 2009;Bhattacharyya et al, 2013;Papaleo, 2015;Tse and Verkhivker, 2015;Doshi et al, 2016).…”

Small Conformational Changes Underlie Evolution of Resistance to NNRTI in HIV Reverse Transcriptase

“…Since the insightful study on the big role of small changes in protein structures (53), the use of alternative approaches, such as protein contact network representation and their analysis has slowly grown in importance (54,55). In this work on HIV-1 reverse transcriptase protein, we have used the combined approach of static network analysis and molecular dynamics simulations to demonstrate the effect of small local contact changes arising due to drug binding and single mutations on global changes in the communication pattern and dynamics of the protein.…”

6'ya 6 Tahta Üzeri̇nde at Kaplama Problemi̇ni̇ Çözmek İçi̇n Deneti̇msi̇z Maki̇ne Öğrenme Algori̇tmasi

“…Every knight and their place on the board is explicitly shown in Figure 3. The graph analyses provide important information to extract information from data presented in the form of networks such as computational networks [28][29][30], social networks [31][32][33][34], biological networks [35][36][37], word networks [38][39][40], infection networks [41,42]. One of the many analysis methods is clustering which divides the whole network into smaller relational clusters of the nodes.…”