The Drosophila Protein Interaction Network May Be neither Power-Law nor Scale-Free

Abstract

Scale-free networks have become a topic of intense interest because of the potential to develop theories universally applicable to networks representing social interactions, internet connectivity, and biological processes. Scale-free topology is associated with power-law distributions of connectivity, in which most network components have only few connections while a very few components are extremely highly-connected. Here we investigate the power-law and scale-free properties of the network corresponding to protein-protein interactions in Drosophila melanogaster. We examine power-law behavior with a standard statistical technique designed to distinguish whether a power-law fit is adequate to describe the vertex degree distribution. We find that the degree distribution for the entire network, consisting of baits and preys, decays faster than power law. This fit may be confounded by artifacts of the screening procedure. The prey-only degree distribution is less likely to be confounded by the screening procedure, and is fit adequately by a power-law. When only the biologically relevant interactions are considered, however, the degree distribution again decays faster than power-law. Thus, power-law behavior may reflect interactions that are observed in vitro but not in vivo. We next describe an algorithm that may be able to extract the true distribution from the incomplete data. Finally, we investigate scale-free properties by characterizing organizational patterns over increasing spatial scales. We provide evidence for the existence of a length-scale that characterizes organization in the network. The existence of such a correlation length stands in contrast to scale-free networks, in which no length scale is special. These results suggest that the Drosophila protein interaction network may not be power-law and is not scale-free.