Assessing Significance of Connectivity and Conservation in Protein Interaction Networks

Computational and comparative analysis of protein-protein interaction (PPI) networks enable understanding of the modular organization of the cell through identification of functional modules and protein complexes. These analysis techniques generally rely on topological features such as connectedness, based on the premise that functionally related proteins are likely to interact densely and that these interactions follow similar evolutionary trajectories. Significant recent work in our lab, and in other labs has focused on efficient algorithms for identification of modules and their conservation. Application of these methods to a variety of networks has yielded novel biological insights. In spite of algorithmic advances, development of a comprehensive infrastructure for interaction databases is in relative infancy compared to corresponding sequence analysis tools such as BLAST and CLUSTAL. One critical component of this infrastructure is a measure of the statistical significance of a match or a dense subcomponent. Corresponding sequence-based measures such as E-values are key components of sequence matching tools. In the absence of an analytical measure, conventional methods rely on computer simulations based on ad-hoc models for quantifying significance. This paper presents the first such effort, to the best of our knowledge, aimed at analytically quantifying statistical significance of dense components and matches in reference model graphs. We consider two reference graph models – a G(n,p) model in which each pair of nodes has an identical likelihood, p, of sharing an edge, and a two-level G(n,p) model, which accounts for high-degree hub nodes generally occurring in PPI networks. We argue that by choosing conservatively the value of p, the G(n,p) model will dominate that of the power-law graph that is often used to model PPI networks. We also propose a method for evaluating statistical significance based on the results derived from this analysis, and demonstrate the use of these measures for assessing significant structures in PPI networks. Experiments performed on a rich collection of PPI networks show that the proposed model provides a reliable means of evaluating statistical significance of dense patterns in these networks.