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Comparative analyses of cellular interaction networks enable understanding of the cell's modular organization through identification of functional modules and complexes. These techniques often rely on topological features such as connectedness and density, based on the premise that functionally related proteins are likely to interact densely and that these interactions follow similar evolutionary trajectories. Significant recent work has focused on efficient algorithms for identification of such functional modules and their conservation. In spite of algorithmic advances, development of a comprehensive infrastructure for interaction databases is in relative infancy compared to corresponding sequence analysis tools. One critical, and as yet unresolved aspect of this infrastructure is a measure of the statistical significance of a match, or a dense subcomponent. In the absence of analytical measures, conventional methods rely on computationally expensive simulations based on ad-hoc models for quantifying significance. In this paper, we present techniques for analytically quantifying statistical significance of dense components in reference model graphs. We consider two reference models--a G(n, p) model in which each pair of nodes in a graph 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 observed in interaction networks. Experiments performed on a rich collection of protein interaction (PPI) networks show that the proposed model provides a reliable means of evaluating statistical significance of dense patterns in these networks. We also adapt existing state-of-the-art network clustering algorithms by using our statistical significance measure as an optimization criterion. Comparison of the resulting module identification algorithm, SIDES, with existing methods shows that SIDES outperforms existing algorithms in terms of sensitivity and specificity of identified clusters with respect to available GO annotations.

Molecular interaction data plays an important role in understanding biological processes at a modular level by providing a framework for understanding cellular organization, functional hierarchy, and evolutionary conservation. As the quality and quantity of network and interaction data increases rapidly, the problem of effectively analyzing this data becomes significant. Graph theoretic formalisms, commonly used for these analysis tasks, often lead to computationally hard problems due to their relation to subgraph isomorphism. This paper presents an innovative new algorithm, MULE, for detecting frequently occurring patterns and modules in biological networks. Using an innovative graph simplification technique based on ortholog contraction, which is ideally suited to biological networks, our algorithm renders these problems computationally tractable and scalable to large numbers of networks. We show, experimentally, that our algorithm can extract frequently occurring patterns in metabolic pathways and protein interaction networks from the KEGG, DIP, and BIND databases within seconds. When compared to existing approaches, our graph simplification technique can be viewed either as a pruning heuristic, or a closely related, but computationally simpler task. When used as a pruning heuristic, we show that our technique reduces effective graph sizes significantly, accelerating existing techniques by several orders of magnitude! Indeed, for most of the test cases, existing techniques could not even be applied without our pruning step. When used as a stand-alone analysis technique, MULE is shown to convey significant biological insights at near-interactive rates. The software, sample input graphs, and detailed results for comprehensive analysis of nine eukaryotic PPI networks are available at www.cs.purdue.edu/homes/koyuturk/mule.

With an ever-increasing amount of available data on protein-protein interaction (PPI) networks and research revealing that these networks evolve at a modular level, discovery of conserved patterns in these networks becomes an important problem. Although available data on protein-protein interactions is currently limited, recently developed algorithms have been shown to convey novel biological insights through employment of elegant mathematical models. The main challenge in aligning PPI networks is to define a graph theoretical measure of similarity between graph structures that captures underlying biological phenomena accurately. In this respect, modeling of conservation and divergence of interactions, as well as the interpretation of resulting alignments, are important design parameters. In this paper, we develop a framework for comprehensive alignment of PPI networks, which is inspired by duplication/divergence models that focus on understanding the evolution of protein interactions. We propose a mathematical model that extends the concepts of match, mismatch, and gap in sequence alignment to that of match, mismatch, and duplication in network alignment and evaluates similarity between graph structures through a scoring function that accounts for evolutionary events. By relying on evolutionary models, the proposed framework facilitates interpretation of resulting alignments in terms of not only conservation but also divergence of modularity in PPI networks. Furthermore, as in the case of sequence alignment, our model allows flexibility in adjusting parameters to quantify underlying evolutionary relationships. Based on the proposed model, we formulate PPI network alignment as an optimization problem and present fast algorithms to solve this problem. Detailed experimental results from an implementation of the proposed framework show that our algorithm is able to discover conserved interaction patterns very effectively, in terms of both accuracies and computational cost.

Motivation: With rapidly increasing amount of network and interaction data in molecular biology, the problem of effectively analyzing this data is an important one. Graph theoretic formalisms, commonly used for these analysis tasks, often lead to computationally hard problems due to their relation with subgraph isomorphism., Results: This paper presents an innovative new algorithm for detecting frequently occurring patterns and modules in biological networks. Using an innovative graph simplification technique, which is ideally suited to biological networks, our algorithm renders these problems computationally tractable. Indeed, we show experimentally that our algorithm can extract frequently occurring patterns in metabolic pathways extracted from the KEGG database within seconds. The proposed model and algorithm are applicable to a variety of biological networks either directly or with minor modifications., Availability: Implementation of the proposed algorithms in the C programming language is available as open source at http://www.cs.purdue.edu/homes/koyuturk/pathway/