Analysis of graph centrality measures for identifying Ankyrin repeats

Internal repetition within proteins is a commonly observed phenomenon as these provide multiple binding sites for protein-protein interactions by forming integrated multi-repeat assemblies in three-dimension. However, at the sequence level the similarity between internal copies of the repeats is generally low, and identification at the structural level is desired. In recent studies it has been shown that graph representation of protein structures is capable of capturing the 3-dimensional fold of the protein very well, thus providing a computationally efficient approach for protein structure analysis. Here we exploit this feature of protein structure graphs and carry out a comparative analysis of eight graph centrality measures for the identification of tandem structural repeats. We observe that principal eigen spectra of the adjacency matrix and Katz status index are able to capture the repetitive pattern of the structural units. The spectral analysis being computationally efficient, in this paper we present the analysis of the principal eigen spectra of the adjacency matrix of proteins containing Ankyrin (ANK) repeats, the most commonly occurring structural motifs in proteins.