Statistical Analysis of Global Connectivity and Activity Distributions in Cellular Networks

Various molecular interaction networks have been claimed to follow power-law decay for their global connectivity distribution. It has been proposed that there may be underlying generative models that explain this heavy-tailed behavior by self-reinforcement processes such as classical or hierarchical scale-free network models. Here, we analyze a comprehensive data set of protein-protein and transcriptional regulatory interaction networks in yeast, an Escherichia coli metabolic network, and gene activity profiles for different metabolic states in both organisms. We show that in all cases the networks have a heavy-tailed distribution, but most of them present significant differences from a power-law model according to a stringent statistical test. Those few data sets that have a statistically significant fit with a power-law model follow other distributions equally well. Thus, while our analysis supports that both global connectivity interaction networks and activity distributions are heavy-tailed, they are not generally described by any specific distribution model, leaving space for further inferences on generative models. Supplementary Material is available online at www.liebertonline.com.