Functional similarities of reaction sets in metabolic pathways
Proceedings of the First ACM International Conference on Bioinformatics and Computational Biology
Parallel extreme ray and pathway computation
PPAM'09 Proceedings of the 8th international conference on Parallel processing and applied mathematics: Part II
Structures and hyperstructures in metabolic networks
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Minimum ratio cover of matrix columns by extreme rays of its induced cone
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
An integrated computational environment for elementary modes analysis of biochemical networks
International Journal of Data Mining and Bioinformatics
Decomposing Biochemical Networks Into Elementary Flux Modes Using Graph Traversal
Proceedings of the International Conference on Bioinformatics, Computational Biology and Biomedical Informatics
Heterogeneous combinatorial candidate generation
Euro-Par'13 Proceedings of the 19th international conference on Parallel Processing
An evolutionary approach for searching metabolic pathways
Computers in Biology and Medicine
Solving the maximum edge biclique packing problem on unbalanced bipartite graphs
Discrete Applied Mathematics
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Motivation: Elementary flux modes (EFMs)—non-decomposable minimal pathways—are commonly accepted tools for metabolic network analysis under steady state conditions. Valid states of the network are linear superpositions of elementary modes shaping a polyhedral cone (the flux cone), which is a well-studied convex set in computational geometry. Computing EFMs is thus basically equivalent to extreme ray enumeration of polyhedral cones. This is a combinatorial problem with poorly scaling algorithms, preventing the large-scale analysis of metabolic networks so far. Results: Here, we introduce new algorithmic concepts that enable large-scale computation of EFMs. Distinguishing extreme rays from normal (composite) vectors is one critical aspect of the algorithm. We present a new recursive enumeration strategy with bit pattern trees for adjacent rays—the ancestors of extreme rays—that is roughly one order of magnitude faster than previous methods. Additionally, we introduce a rank updating method that is particularly well suited for parallel computation and a residue arithmetic method for matrix rank computations, which circumvents potential numerical instability problems. Multi-core architectures of modern CPUs can be exploited for further performance improvements. The methods are applied to a central metabolism network of Escherichia coli, resulting in ≈26 Mio. EFMs. Within the top 2% modes considering biomass production, most of the gain in flux variability is achieved. In addition, we compute ≈5 Mio. EFMs for the production of non-essential amino acids for a genome-scale metabolic network of Helicobacter pylori. Only large-scale EFM analysis reveals the 85% of modes that generate several amino acids simultaneously. Availability: An implementation in Java, with integration into MATLAB and support of various input formats, including SBML, is available at http://www.csb.ethz.ch in the tools section; sources are available from the authors upon request. Contact: joerg.stelling@inf.ethz.ch Supplementary information:Supplementary data are available at Bioinformatics online.