Identification of structurally important amino acids in proteins by graph-theoretic measures

Identifying key residues important for maintaining a protein structure is a non-trivial problem in Computational Biology. In this paper, we present results based on a graph model representing protein structures. This model considers the structure as residue-residue interactions in order to capture protein stability. We propose the application of approximate minimum vertex cover algorithms (MVC) as a novel approach for identifying the structurally important residues, which we shall refer to as key residues. We establish that MVC based algorithms captures the essence of protein structural stability by correlation analysis with ΔΔG, the change of protein free energies due to amino acid variations. We also benchmark our approach with popular approaches for analyzing large complex networks --- betweenness, and Eigenvector centrality. Our findings are such that they do not correlate well with ΔΔG. We give explanations from the free energy point of view, which shall benefit future development measures for protein structure stability.