Catalytic and binding sites prediction in globular proteins through discrete Markov chains and network centrality measures

In this work we use a discrete Markov chain approach combined with network centrality measures to identify and predict the location of active sites in globular proteins. To accomplish this, we use a three-dimensional network of protein Ca atoms as nodes connected through weighted edges which represent the varying interaction degree between protein's atoms. We compute the mean first passage time matrix H = {H-ji} for this Markov chain and evaluate the averaged number of steps < H-j > to reach single node nj in order to identify such residues that, on the average, are at the least distant from every other node. We also carry out a graph theory analysis to evaluate closeness centrality C-c, betweenness centrality C-b and eigenvector centrality C-e measures which provide relevant information about the connectivity structure and topology of the C-alpha protein networks. Finally we also performed an analysis of equivalent random and regular networks of the same size N in terms of the average path length L and the average clustering coefficient < C > comparing these with the corresponding values for Ca protein networks. Our results show that the mean-first passage time matrix H and its related quantity < H-j > together with C-c, C-b and C-e can not only predict with relative high accuracy the location of active sites in globular proteins but also exhibit a high feasibility to use them to predict the existence of new regions in protein's structure to identify new potential binding or catalytic activity or, in some cases, the presence of new allosteric pathways.