Statistical Analysis of Global Connectivity and Activity Distributions in Cellular Networks

TL;DR

This study investigates the distribution patterns of molecular interaction networks and activity profiles in yeast and E. coli, revealing heavy-tailed distributions that do not conform strictly to power-law models, challenging existing assumptions.

Contribution

It provides a comprehensive statistical analysis showing that biological networks are heavy-tailed but do not generally follow power-law distributions, questioning previous models of network formation.

Findings

Networks exhibit heavy-tailed distributions.

Most networks do not fit power-law models statistically.

Alternative distributions explain the data equally well.

Abstract

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 E. 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.