Background Many structural centrality measures were proposed to predict putative disease genes on biological networks. Closeness is one of the best-known structural centrality measures, and its effectiveness for disease gene prediction on undirected biological networks has been frequently reported. However, it is not clear whether closeness is effective for disease gene prediction on directed biological networks such as signaling networks. Results In this paper, we first show that closeness does not significantly outperform other well-known centrality measures such as Degree, Betweenness, and PageRank for disease gene prediction on a human signaling network. In addition, we observed that prediction accuracy by the closeness measure was worse than that by a reachability measure, but closeness could efficiently predict disease genes among a set of genes with the same reachability value. Based on this observation, we devised a novel structural measure, hierarchical closeness, by combining reachability and closeness such that all genes are first ranked by the degree of reachability and then the tied genes are further ranked by closeness. We discovered that hierarchical closeness outperforms other structural centrality measures in disease gene prediction. We also found that the set of highly ranked genes in terms of hierarchical closeness is clearly different from that of hub genes with high connectivity. More interestingly, these findings were consistently reproduced in a random Boolean network model. Finally, we found that genes with relatively high hierarchical closeness are significantly likely to encode proteins in the extracellular matrix and receptor proteins in a human signaling network, supporting the fact that half of all modern medicinal drugs target receptor-encoding genes. Conclusion Taken together, hierarchical closeness proposed in this study is a novel structural measure to efficiently predict putative disease genes in a directed signaling network. 
Hierarchical closeness efficiently predicts disease genes in a directed signaling network