An algorithm for modularity analysis of directed and weighted

An algorithm for modularity analysis of directed and weighted biological networks based on edge-betweenness centrality Jeongah Yoon, Anselm Blumer 1 and Kyongbum Lee C3 Department of Chemical and Biological Engineering and 1 Computer Science, Tufts University, Medford, MA 02155, USA Received on May 17, 2006; revised on August 14, 2006; accepted on October 12, 2006 Advance Access publication October 23, 2006 Associate Editor: Alvis Brazma ABSTRACT Motivation: Modularity analysis is a powerful tool for studying the design of biological networks, offering potential clues for relating the biochemicalfunction(s)ofanetworkwiththe‘wiring’ofitscomponents. Relativelylittleworkhas beendone to examine whetherthe modularity of a network depends on the physiological perturbations that influence its biochemical state. Here, we

present a novel modularity analysis algorithm based on edge-betweenness centrality, which facilitates the use of directional information and measurable biochemical data. Contact: kyongbum.lee@tufts.edu Supplementary information: Supplementary data are available at Bioinformatics online. 1 INTRODUCTION A common feature of large, complex biological networks is that they are organized into smaller sub-networks consisting of directly interacting, or ‘connected,’ molecular components. Recent studies have suggested that these sub-networks correspond to biologically meaningful, functional units or ‘modules’ (Hartwell et al., 1999). In this light, one approach to understanding the design of biological networks is to examine their modularity e.g. comparative analyses of structurally similar modules across different species may identify mutually shared functions, associate a modular structure with a new function, and provide insight into the evolution of various network structures (Sharan and Ideker, 2006). One issue that remains to be addressed is whether particular structures are inherent to a network or dependent on its functional state. This issue can be addressed by incorporating experimental and derived measures that correlate the functional state of a biological network with the extents of inter- actions, or ‘connection strengths’, between the many molecular components (Patil and Nielsen, 2005). In recent years, analytical technologies have emerged enabling parallel measurements on the most common types of biochemical processes. For example, the DNA micro-array technology is now widely used to compre- hensively profile the transcriptional activity of a gene network (di Bernardo et al., 2005). Recent reports have also described the use of isotopomer modeling and metabolomic technologies for high-throughput analyses of metabolic reaction fluxes in intact cells (Fischer and Sauer, 2005). In this application note, we describe an algorithm for data-driven modularity analysis, with the principal aim of disseminating the source code. A novel feature of this analysis is that it incorporates functional information on the interactions between the network’s components. Our core algorithm extends the edge-betweenness analysis algorithm (Newman and Girvan, 2004) to partition directed graphs with non-uniform edge costs. Additional components of our algorithm consist of well-known techniques for graph (Freeman, 1979) and vector space calculations. Our algorithm is general with respect to the type of connections between network components, and should be applicable to a variety of biological networks, such as transcriptional regulatory and protein–protein interaction networks. The inputs of the algorithm are an adjacency matrix describing the ‘static’ connectivity of the network components and a weight matrix describing the extents of interactions between these components....

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