An important goal in biology is to uncover the fundamental design principles that provide the common underlying structure and function in all cells and microorganisms [6][7][8][9][10][11][12][13] . For example, it is increasingly appreciated that the robustness of various cellular processes is rooted in the dynamic interactions among its many constituents [14][15][16] , such as proteins, DNA, RNA, and small molecules.Recent scientific developments improve our ability to identify the design principles that integrate these interactions into a complex system. Large-scale sequencing projects have not only provided complete sequence information for a number of genomes, but also allowed the development of integrated pathway-genome databases [17][18][19] that provide organism-specific connectivity maps of metabolic-and,

A set of linear pathways often does not capture the full range of behaviors of a metabolic network. The concept of 'elementary flux modes' provides a mathematical tool to define and comprehensively describe all metabolic routes that are both stoichiometrically and thermodynamically feasible for a group of enzymes. We have used this concept to analyze the interplay between the pentose phosphate pathway (PPP) and glycolysis. The set of elementary modes for this system involves conventional glycolysis, a futile cycle, all the modes of PPP function described in biochemistry textbooks, and additional modes that are a priori equally entitled to pathway status. Applications include maximizing product yield in amino acid and antibiotic synthesis, reconstruction and consistency checks of metabolism from genome data, analysis of enzyme deficiencies, and drug target identification in metabolic networks.

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Motivation: With the exponential growth of expression and protein–protein interaction (PPI) data, the frontier of research in systems biology shifts more and more to the integrated analysis of these large datasets. Of particular interest is the identification of functional modules in PPI networks, sharing common cellular function beyond the scope of classical pathways, by means of detecting differentially expressed regions in PPI networks. This requires on the one hand an adequate scoring of the nodes in the network to be identified and on the other hand the availability of an effective algorithm to find the maximally scoring network regions. Various heuristic approaches have been proposed in the literature.Results: Here we present the first exact solution for this problem, which is based on integer-linear programming and its connection to the well-known prize-collecting Steiner tree problem from Operations Research. Despite the NP-hardness of the underlying combinatorial problem, our method typically computes provably optimal subnetworks in large PPI networks in a few minutes. An essential ingredient of our approach is a scoring function defined on network nodes. We propose a new additive score with two desirable properties: (i) it is scalable by a statistically interpretable parameter and (ii) it allows a smooth integration of data from various sources.We apply our method to a well-established lymphoma microarray dataset in combination with associated survival data and the large interaction network of HPRD to identify functional modules by computing optimal-scoring subnetworks. In particular, we find a functional interaction module associated with proliferation over-expressed in the aggressive ABC subtype as well as modules derived from non-malignant by-stander cells.Availability: Our software is available freely for non-commercial purposes at http://www.planet-lisa.net.Contact: tobias.mueller@biozentrum.uni-wuerzburg.de