An approach for determining and measuring network hierarchy applied to comparing the phosphorylome and the regulome

Many biological networks naturally form a hierarchy with a preponderance of downward information flow. In this study, we define a score to quantify the degree of hierarchy in a network and develop a simulated-annealing algorithm to maximize the hierarchical score globally over a network. We apply our algorithm to determine the hierarchical structure of the phosphorylome in detail and investigate the correlation between its hierarchy and kinase properties. We also compare it to the regulatory network, finding that the phosphorylome is more hierarchical than the regulome. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s13059-015-0624-2) contains supplementary material, which is available to authorized users.