Graph Centrality Analysis of Structural Ankyrin Repeats

Abstract

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. Centrality measures are generally used to identify the relative importance of a node in the network. Here we demonstrate a novel application of centrality analysis: to identify tandemly repeated structural motifs in 3-d protein structures. This is done by analyzing the profile of various centrality measures in the repeat region. The comparative analysis of five centrality measures based on local connectivity, shortest paths, principal eigen spectra and feedback centrality is presented on proteins containing contiguous ankyrin structural motifs to identify which centrality measure best captures the repetitive pattern of ankyrin. We observe that principal eigen spectra of the adjacency matrix and Katz status index, both exhibit a distinct profile for the ankyrin motif capturing its characteristic anti-parallel helix-turn-helix fold. No such conserved pattern was observed in the repeat regions of equivalent random networks, suggesting that the conserved pattern arises from the 3d fold of the structural motif.