{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T01:03:43Z","timestamp":1773277423530,"version":"3.50.1"},"reference-count":53,"publisher":"Oxford University Press (OUP)","issue":"16","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2011,8,15]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Motivation: Elementary flux mode (EFM) is a fundamental concept as well as a useful tool in metabolic pathway analysis. One important role of EFMs is that every flux distribution can be decomposed into a set of EFMs and a number of methods to study flux distributions originated from it. Yet finding such decompositions requires the complete set of EFMs, which is intractable in genome-scale metabolic networks due to combinatorial explosion.<\/jats:p><jats:p>Results: In this article, we proposed an algorithm to decompose flux distributions into EFMs in genome-scale networks. It is an iterative scheme of a mixed integer linear program. Unlike previous optimization models to find pathways, any feasible solutions can become EFMs in our algorithm. This advantage enables the algorithm to approximate the EFM of largest contribution to an objective reaction in a flux distribution. Our algorithm is able to find EFMs of flux distributions with complex structures, closer to the realistic case in which a cell is subject to various constraints. A case of Escherichia coli growth in the Lysogeny broth (LB) medium containing various carbon sources was studied. Essential metabolites and their syntheses were located. Information on the contribution of each carbon source not obvious from the apparent flux distribution was also revealed. Our work further confirms the utility of finding EFMs by optimization models in genome-scale metabolic networks.<\/jats:p><jats:p>Contact: \u00a0joshua.chan@connect.polyu.hk<\/jats:p><jats:p>Supplementary information: \u00a0Supplementary data are available at Bioinformatics online.<\/jats:p>","DOI":"10.1093\/bioinformatics\/btr367","type":"journal-article","created":{"date-parts":[[2011,6,18]],"date-time":"2011-06-18T04:15:07Z","timestamp":1308370507000},"page":"2256-2262","source":"Crossref","is-referenced-by-count":27,"title":["Decomposing flux distributions into elementary flux modes in genome-scale metabolic networks"],"prefix":"10.1093","volume":"27","author":[{"given":"Siu Hung Joshua","family":"Chan","sequence":"first","affiliation":[{"name":"Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong"}]},{"given":"Ping","family":"Ji","sequence":"additional","affiliation":[{"name":"Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong"}]}],"member":"286","published-online":{"date-parts":[[2011,6,17]]},"reference":[{"key":"2023012511513062400_B1","doi-asserted-by":"crossref","first-page":"839","DOI":"10.1038\/nature02289","article-title":"Global organization of metabolic fluxes in the bacterium Escherichia coli","volume":"427","author":"Almaas","year":"2004","journal-title":"Nature"},{"key":"2023012511513062400_B2","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1007\/s00253-006-0317-6","article-title":"Growth of Escherichia coli MG1655 on LB medium: monitoring utilization of sugars, alcohols, and organic acids with transcriptional microarrays","volume":"71","author":"Baev","year":"2006","journal-title":"Appl. Microbiol. Biotechnol."},{"key":"2023012511513062400_B3","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1007\/s00253-005-0310-5","article-title":"Growth of Escherichia coli MG1655 on LB medium: monitoring utilization of amino acids, peptides, and nucleotides with transcriptional microarrays","volume":"71","author":"Baev","year":"2006","journal-title":"Appl. Microbiol. Biotechnol."},{"key":"2023012511513062400_B4","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1038\/nprot.2007.99","article-title":"Quantitative prediction of cellular metabolism with constraint-based models: The COBRA Toolbox","volume":"2","author":"Becker","year":"2007","journal-title":"Nat. Protocols"},{"key":"2023012511513062400_B5","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1093\/bioinformatics\/btl554","article-title":"Recovering metabolic pathways via optimization","volume":"23","author":"Beasley","year":"2007","journal-title":"Bioinformatics"},{"key":"2023012511513062400_B6","doi-asserted-by":"crossref","first-page":"1258","DOI":"10.1093\/bioinformatics\/btm082","article-title":"Metabolic systems cost-benefit analysis for interpreting network structure and regulation","volume":"23","author":"Carlson","year":"2007","journal-title":"Bioinformatics"},{"key":"2023012511513062400_B7","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1093\/bioinformatics\/btn589","article-title":"Decomposition of complex microbial behaviors into resource-based stress responses","volume":"25","author":"Carlson","year":"2009","journal-title":"Bioinformatics"},{"key":"2023012511513062400_B8","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1006\/jtbi.2001.2405","article-title":"Regulation of gene expression in flux balance models of metabolism","volume":"213","author":"Covert","year":"2001","journal-title":"J. Theor. Biol."},{"key":"2023012511513062400_B9","doi-asserted-by":"crossref","first-page":"3158","DOI":"10.1093\/bioinformatics\/btp564","article-title":"Computing the shortest elementary flux modes in genome-scale metabolic networks","volume":"25","author":"de Figueiredo","year":"2009","journal-title":"Bioinformatics"},{"key":"2023012511513062400_B10","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1093\/bioinformatics\/btn621","article-title":"Can sugars be produced from fatty acids? A test case for pathway analysis tools","volume":"25","author":"de Figueiredo","year":"2009","journal-title":"Bioinformatics"},{"key":"2023012511513062400_B11","doi-asserted-by":"crossref","first-page":"1777","DOI":"10.1073\/pnas.0610772104","article-title":"Global reconstruction of the human metabolic network based on genomic and bibliomic data","volume":"104","author":"Duarte","year":"2007","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"2023012511513062400_B12","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1111\/j.1574-6976.2008.00146.x","article-title":"Genome-scale models of bacterial metabolism: reconstruction and applications","volume":"33","author":"Durot","year":"2009","journal-title":"FEMS Microbiol. Rev."},{"key":"2023012511513062400_B13","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1038\/msb4100155","article-title":"A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information","volume":"3","author":"Feist","year":"2007","journal-title":"Mol. Syst. Biol."},{"key":"2023012511513062400_B14","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1186\/1471-2105-5-175","article-title":"Computation of elementary modes: a unifying framework and the new binary approach","volume":"5","author":"Gagneur","year":"2004","journal-title":"BMC Bioinformatics"},{"key":"2023012511513062400_B15","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1093\/bioinformatics\/btg395","article-title":"Minimal cut sets in biochemical reaction networks","volume":"20","author":"Klamt","year":"2004","journal-title":"Bioinformatics"},{"key":"2023012511513062400_B16","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1023\/A:1020390132244","article-title":"Combinatorial complexity of pathway analysis in metabolic networks","volume":"29","author":"Klamt","year":"2002","journal-title":"Mol. Biol. Rep."},{"key":"2023012511513062400_B17","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1093\/bioinformatics\/19.2.261","article-title":"FluxAnalyzer: exploring structure, pathways, and flux distributions in metabolic networks on interactive flux maps","volume":"19","author":"Klamt","year":"2003","journal-title":"Bioinformatics"},{"key":"2023012511513062400_B18","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1049\/ip-syb:20050035","article-title":"Algorithmic approaches for computing elementary modes in large biochemical reaction networks","volume":"152","author":"Klamt","year":"2005","journal-title":"IEE Proc. Syst. Biol."},{"key":"2023012511513062400_B19","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1186\/1471-2105-7-56","article-title":"A methodology for the structural and functional analysis of signaling and regulatory networks","volume":"7","author":"Klamt","year":"2006","journal-title":"BMC Bioinformatics"},{"key":"2023012511513062400_B20","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1186\/1752-0509-1-2","article-title":"Structural and functional analysis of cellular networks with CellNetAnalyzer","volume":"1","author":"Klamt","year":"2007","journal-title":"BMC Syst. Biol."},{"key":"2023012511513062400_B21","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1186\/1752-0509-1-31","article-title":"Integration of enzyme activities into metabolic flux distributions by elementary mode analysis","volume":"1","author":"Kurata","year":"2007","journal-title":"BMC Syst. Biol."},{"key":"2023012511513062400_B22","doi-asserted-by":"crossref","first-page":"753904","DOI":"10.1155\/2010\/753904","article-title":"Which metabolic pathways generate and characterize the flux space? A comparison among elementary modes, extreme pathways and minimal generators","volume":"2010","author":"Llaneras","year":"2010","journal-title":"J. Biomed. Biotechnol."},{"key":"2023012511513062400_B23","doi-asserted-by":"crossref","first-page":"1535","DOI":"10.1002\/bit.21339","article-title":"Identification of flux regulation coefficients from elementary flux modes: a systems biology tool for analysis of metabolic networks","volume":"97","author":"Nookaew","year":"2007","journal-title":"Biotechnol. Bioeng."},{"key":"2023012511513062400_B24","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1093\/bioinformatics\/15.3.251","article-title":"METATOOL: for studying metabolic networks","volume":"15","author":"Pfeiffer","year":"1999","journal-title":"Bioinformatics"},{"key":"2023012511513062400_B25","doi-asserted-by":"crossref","first-page":"2723","DOI":"10.1093\/bioinformatics\/btp441","article-title":"An optimization model for metabolic pathways","volume":"25","author":"Planes","year":"2009","journal-title":"Bioinformatics"},{"key":"2023012511513062400_B26","doi-asserted-by":"crossref","first-page":"886","DOI":"10.1038\/nrmicro1023","article-title":"Genome-scale models of microbial cells: evaluating the consequences of constraints","volume":"2","author":"Price","year":"2004","journal-title":"Nat. Rev. Microbiol."},{"key":"2023012511513062400_B27","doi-asserted-by":"crossref","first-page":"534","DOI":"10.1093\/bioinformatics\/btq681","article-title":"Exploring metabolic pathways in genome-scale networks via generating flux modes","volume":"27","author":"Rezola","year":"2010","journal-title":"Bioinformatics"},{"key":"2023012511513062400_B28","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1038\/msb4100162","article-title":"Systematic evaluation of objective functions for predicting intracellular fluxes in Escherichia coli","volume":"3","author":"Schuetz","year":"2007","journal-title":"Mol. Syst. Biol."},{"key":"2023012511513062400_B29","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1142\/S0218339094000131","article-title":"On elementary flux modes in biochemical reaction systems at steady state","volume":"2","author":"Schuster","year":"1994","journal-title":"J. Biol. Syst."},{"key":"2023012511513062400_B30","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1142\/9789812819826_0012","article-title":"Elementary modes of functioning in biochemical networks","volume-title":"Computation in Cellular and Molecular Biological Systems","author":"Schuster","year":"1996"},{"key":"2023012511513062400_B31","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/S0167-7799(98)01290-6","article-title":"Detection of elementary flux modes in biochemical networks: a promising tool for pathway analysis and metabolic engineering","volume":"17","author":"Schuster","year":"1999","journal-title":"Trends Biotechnol."},{"key":"2023012511513062400_B32","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/s002850200143","article-title":"Reaction routes in biochemical reaction systems: algebraic properties, validated calculation procedure and example from nucleotide metabolism","volume":"45","author":"Schuster","year":"2002","journal-title":"J. Math. Biol."},{"issue":"Suppl. 2","key":"2023012511513062400_B33","doi-asserted-by":"crossref","first-page":"ii204","DOI":"10.1093\/bioinformatics\/bti1132","article-title":"A quadratic programming approach for decomposing steady-state metabolic flux distributions onto elementary modes","volume":"21","author":"Schwartz","year":"2005","journal-title":"Bioinformatics"},{"key":"2023012511513062400_B34","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1186\/1471-2105-7-186","article-title":"Quantitative elementary mode analysis of metabolic pathways: the example of yeast glycolysis","volume":"7","author":"Schwartz","year":"2006","journal-title":"BMC Bioinformatics"},{"key":"2023012511513062400_B35","doi-asserted-by":"crossref","first-page":"554","DOI":"10.1002\/bit.22062","article-title":"Reduction of a set of elementary modes using yield analysis","volume":"102","author":"Song","year":"2009","journal-title":"Biotechnol. Bioeng."},{"key":"2023012511513062400_B36","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1038\/nature01166","article-title":"Metabolic network structure determines key aspects of functionality and regulation","volume":"420","author":"Stelling","year":"2002","journal-title":"Nature"},{"key":"2023012511513062400_B37","doi-asserted-by":"crossref","first-page":"1378","DOI":"10.1093\/bioinformatics\/btm065","article-title":"From structure to dynamics of metabolic pathways: application to the plant mitochondrial TCA cycle","volume":"23","author":"Steuer","year":"2007","journal-title":"Bioinformatics"},{"key":"2023012511513062400_B38","first-page":"333","article-title":"Accelerating the computation of elementary modes using pattern trees","volume-title":"WABI, Vol. 4175 of Lecture Notes in Computer Science","author":"Terzer","year":"2006"},{"key":"2023012511513062400_B39","doi-asserted-by":"crossref","first-page":"2229","DOI":"10.1093\/bioinformatics\/btn401","article-title":"Large-scale computation of elementary flux modes with bit pattern trees","volume":"24","author":"Terzer","year":"2008","journal-title":"Bioinformatics"},{"key":"2023012511513062400_B40","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1002\/wsbm.37","article-title":"Genome-scale metabolic network","volume":"1","author":"Terzer","year":"2009","journal-title":"Wiley Interdis. Rev. Syst. Biol. Med."},{"key":"2023012511513062400_B41","doi-asserted-by":"crossref","first-page":"6696","DOI":"10.1128\/AEM.00670-09","article-title":"Metabolic engineering of Escherichia coli for efficient conversion of glycerol to ethanol","volume":"75","author":"Trinh","year":"2009","journal-title":"Appl. Environ. Microbiol."},{"key":"2023012511513062400_B42","doi-asserted-by":"crossref","first-page":"3634","DOI":"10.1128\/AEM.02708-07","article-title":"Minimal Escherichia coli cell for the most efficient production of ethanol from hexoses and pentoses","volume":"74","author":"Trinh","year":"2008","journal-title":"Appl. Environ. Microbiol."},{"key":"2023012511513062400_B43","doi-asserted-by":"crossref","first-page":"813","DOI":"10.1007\/s00253-008-1770-1","article-title":"Elementary mode analysis: a useful metabolic pathway analysis tool for characterizing cellular metabolism","volume":"81","author":"Trinh","year":"2009","journal-title":"Appl. Microbiol. Biotechnol."},{"key":"2023012511513062400_B44","doi-asserted-by":"crossref","first-page":"1203","DOI":"10.1093\/bioinformatics\/bti127","article-title":"An improved algorithm for stoichiometric network analysis: theory and applications","volume":"21","author":"Urbanczik","year":"2005","journal-title":"Bioinformatics"},{"key":"2023012511513062400_B45","doi-asserted-by":"crossref","first-page":"1930","DOI":"10.1093\/bioinformatics\/btl267","article-title":"Metatool 5.0: fast and flexible elementary modes analysis","volume":"22","author":"von Kamp","year":"2006","journal-title":"Bioinformatics"},{"key":"2023012511513062400_B46","doi-asserted-by":"crossref","first-page":"2425","DOI":"10.1021\/jp034523f","article-title":"Nullspace approach to determine the elementary modes of chemical reaction systems","volume":"108","author":"Wagner","year":"2004","journal-title":"J. Phys. Chem. B"},{"key":"2023012511513062400_B47","doi-asserted-by":"crossref","first-page":"1049","DOI":"10.1093\/bioinformatics\/btm074","article-title":"Metabolic network properties help assign weights to elementary modes to understand physiological flux distributions","volume":"23","author":"Wang","year":"2007","journal-title":"Bioinformatics"},{"key":"2023012511513062400_B48","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/S0022-5193(03)00168-1","article-title":"Reconstructing metabolic flux vectors from extreme pathways: defining the\u03b1-spectrum","volume":"224","author":"Wiback","year":"2003","journal-title":"J. Theor. Biol."},{"key":"2023012511513062400_B49","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1186\/1471-2105-8-363","article-title":"Estimation of the number of extreme pathways for metabolic networks","volume":"8","author":"Yeung","year":"2007","journal-title":"BMC Bioinformatics"},{"key":"2023012511513062400_B50","doi-asserted-by":"crossref","first-page":"2433","DOI":"10.1093\/bioinformatics\/btm374","article-title":"Modular decomposition of metabolic reaction networks based on flux analysis and pathway projection","volume":"23","author":"Yoon","year":"2007","journal-title":"Bioinformatics"},{"key":"2023012511513062400_B51","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.copbio.2010.08.009","article-title":"13C metabolic flux analysis in complex systems","volume":"22","author":"Zamboni","year":"2010","journal-title":"Curr. Opin. Biotechnol."},{"key":"2023012511513062400_B52","doi-asserted-by":"crossref","first-page":"1702","DOI":"10.1093\/bioinformatics\/btp298","article-title":"Genetic modification of flux for flux prediction of mutants","volume":"25","author":"Zhao","year":"2009","journal-title":"Bioinformatics"},{"key":"2023012511513062400_B53","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.jbiosc.2008.09.011","article-title":"Maximum entropy decomposition of flux distribution at steady state to elementary modes","volume":"107","author":"Zhao","year":"2009","journal-title":"J. Biosci. Bioeng."}],"container-title":["Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/27\/16\/2256\/48862417\/bioinformatics_27_16_2256.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/27\/16\/2256\/48862417\/bioinformatics_27_16_2256.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,7]],"date-time":"2024-04-07T18:57:51Z","timestamp":1712516271000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article\/27\/16\/2256\/254324"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,6,17]]},"references-count":53,"journal-issue":{"issue":"16","published-print":{"date-parts":[[2011,8,15]]}},"URL":"https:\/\/doi.org\/10.1093\/bioinformatics\/btr367","relation":{},"ISSN":["1367-4811","1367-4803"],"issn-type":[{"value":"1367-4811","type":"electronic"},{"value":"1367-4803","type":"print"}],"subject":[],"published-other":{"date-parts":[[2011,8,15]]},"published":{"date-parts":[[2011,6,17]]}}}