{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,30]],"date-time":"2026-05-30T02:58:47Z","timestamp":1780109927930,"version":"3.54.0"},"reference-count":33,"publisher":"Oxford University Press (OUP)","issue":"10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2006,5,15]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Motivation: Flux estimation using isotopomer information of metabolites is currently the most reliable method to obtain quantitative estimates of the activity of metabolic pathways. However, the development of isotopomer measurement techniques for intermediate metabolites is a demanding task. Careful planning of isotopomer measurements is thus needed to maximize the available flux information while minimizing the experimental effort.<\/jats:p>\n               <jats:p>Results: In this paper we study the question of finding the smallest subset of metabolites to measure that ensure the same level of isotopomer information as the measurement of every metabolite in the metabolic network. We study the computational complexity of this optimization problem in the case of the so-called positional enrichment data, give methods for obtaining exact and fast approximate solutions, and evaluate empirically the efficacy of the proposed methods by analyzing a metabolic network that models the central carbon metabolism of Saccharomyces cerevisiae.<\/jats:p>\n               <jats:p>Contact: \u00a0ajrantan@cs.helsinki.fi<\/jats:p>","DOI":"10.1093\/bioinformatics\/btl069","type":"journal-article","created":{"date-parts":[[2006,2,28]],"date-time":"2006-02-28T01:13:38Z","timestamp":1141089218000},"page":"1198-1206","source":"Crossref","is-referenced-by-count":22,"title":["Planning optimal measurements of isotopomer distributions for estimation of metabolic fluxes"],"prefix":"10.1093","volume":"22","author":[{"given":"Ari","family":"Rantanen","sequence":"first","affiliation":[{"name":"Department of Computer Science 1 \u00a0 1 \u00a0 \u00a0 P.O. Box 68 (Gustaf H\u00e4llstr\u00f6min katu 2b) \u00a0 \u00a0 Finland"},{"name":"00014 University of Helsinki 1 \u00a0 1 \u00a0 \u00a0 P.O. Box 68 (Gustaf H\u00e4llstr\u00f6min katu 2b) \u00a0 \u00a0 Finland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Taneli","family":"Mielik\u00e4inen","sequence":"additional","affiliation":[{"name":"Department of Computer Science 1 \u00a0 1 \u00a0 \u00a0 P.O. Box 68 (Gustaf H\u00e4llstr\u00f6min katu 2b) \u00a0 \u00a0 Finland"},{"name":"00014 University of Helsinki 1 \u00a0 1 \u00a0 \u00a0 P.O. Box 68 (Gustaf H\u00e4llstr\u00f6min katu 2b) \u00a0 \u00a0 Finland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Juho","family":"Rousu","sequence":"additional","affiliation":[{"name":"Department of Computer Science 1 \u00a0 1 \u00a0 \u00a0 P.O. Box 68 (Gustaf H\u00e4llstr\u00f6min katu 2b) \u00a0 \u00a0 Finland"},{"name":"00014 University of Helsinki 1 \u00a0 1 \u00a0 \u00a0 P.O. Box 68 (Gustaf H\u00e4llstr\u00f6min katu 2b) \u00a0 \u00a0 Finland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hannu","family":"Maaheimo","sequence":"additional","affiliation":[{"name":"NMR Laboratory, VTT Technical Research Centre of Finland 2 \u00a0 2 \u00a0 \u00a0 P.O. Box 65, 00014 Helsinki, Finland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Esko","family":"Ukkonen","sequence":"additional","affiliation":[{"name":"Department of Computer Science 1 \u00a0 1 \u00a0 \u00a0 P.O. Box 68 (Gustaf H\u00e4llstr\u00f6min katu 2b) \u00a0 \u00a0 Finland"},{"name":"00014 University of Helsinki 1 \u00a0 1 \u00a0 \u00a0 P.O. Box 68 (Gustaf H\u00e4llstr\u00f6min katu 2b) \u00a0 \u00a0 Finland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2006,2,27]]},"reference":[{"key":"2023012408205569800_b1","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/S0168-1656(03)00169-X","article-title":"An improved method for statistical analysis of metabolic flux analysis using isotopomer mapping matrices with analytical expressions","volume":"105","author":"Ara\u00fazo-Bravo","year":"2003","journal-title":"J. Biotechnol."},{"key":"2023012408205569800_b2","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-58412-1","volume-title":"Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties","author":"Ausiello","year":"1999"},{"key":"2023012408205569800_b3","doi-asserted-by":"crossref","first-page":"1085","DOI":"10.1099\/mic.0.26845-0","article-title":"UCA cycle activity in Saccharomyces cerevisiae is a function of the environmentally determined specific growth and glucose uptake rates","volume":"150","author":"Blank","year":"2004","journal-title":"Microbiology"},{"key":"2023012408205569800_b4","first-page":"435","article-title":"Use of metabolic pathway flux information in targeted cancer drug design","volume":"1","author":"Boros","year":"2004","journal-title":"Drug Discov. Today: Therap. Strat."},{"key":"2023012408205569800_b5","doi-asserted-by":"crossref","first-page":"E8","DOI":"10.1006\/mben.1999.0117","article-title":"Isotopomer Analysis Using GC-MS","volume":"1","author":"Christensen","year":"1999","journal-title":"Metab. Eng."},{"key":"2023012408205569800_b6","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1016\/j.ab.2003.10.036","article-title":"High-throughput metabolic flux analysis based on gas chromatography-mass spectrometry derived 13C constraints","volume":"325","author":"Fisher","year":"2004","journal-title":"Anal. Biochem."},{"key":"2023012408205569800_b7","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1046\/j.1432-1327.1998.2520360.x","article-title":"Effect of reversible reactions on isotope label redistribution\u2014analysis of the pentose phosphate pathway","volume":"252","author":"Follstad","year":"1998","journal-title":"Eur. J. Biochem."},{"key":"2023012408205569800_b8","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1016\/j.compchemeng.2004.08.027","article-title":"Closing the loop between feasible flux scenario identification for construct evaluation and resolution of realized fluxes via nmr","volume":"29","author":"Ghosh","year":"2005","journal-title":"Comput. chem. Eng."},{"key":"2023012408205569800_b9","doi-asserted-by":"crossref","first-page":"1441","DOI":"10.1128\/JB.183.4.1441-1451.2001","article-title":"Network identification and flux quantification in the central metabolism of Saccharomyces cerevisiae under different conditions of glucose repression","volume":"183","author":"Gombert","year":"2001","journal-title":"J. Bacteriol."},{"key":"2023012408205569800_b10","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/S0025-5564(02)00222-5","article-title":"Metabolic isotopomer labeling systems. Part II: structural identifibiality analysis","volume":"183","author":"Isermann","year":"2003","journal-title":"Math. Biosci."},{"key":"2023012408205569800_b11","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1006\/mben.2001.0185","article-title":"Flux estimation using isotopic tracers: common ground for metabolic physiology and metabolic engineering","volume":"3","author":"Kelleher","year":"2001","journal-title":"Metab. Eng."},{"key":"2023012408205569800_b12","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1023\/A:1020394300385","article-title":"Calculating as many fluxes as possible in underdetermined metabolic networks","volume":"29","author":"Klamt","year":"2002","journal-title":"Mol. Biol. Rep."},{"key":"2023012408205569800_b13","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1145\/357062.357071","article-title":"A fast algorithm for finding dominators in a flowgraph","volume":"1","author":"Lengauer","year":"1979","journal-title":"ACM Trans. Program. Lang. Syst."},{"key":"2023012408205569800_b14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/3-540-45586-8_1","article-title":"General mixed integer programming: computational issues for branch-and-cut algorithms","volume-title":"Computational Combinatorial Optimization: Optimal and Provably Near-Optimal Solutions, Lecture Notes in Computer Science","author":"Martin","year":"2001"},{"key":"2023012408205569800_b15","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1002\/(SICI)1097-0290(19960120)49:2<111::AID-BIT1>3.0.CO;2-T","article-title":"Determination of the fluxes in the central metabolism of Corynebacterium glutamicum by nuclear magnetic resonance spectroscopy combined with metabolite balancing","volume":"49","author":"Marx","year":"1996","journal-title":"Biotechnol. Bioeng."},{"key":"2023012408205569800_b16","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1002\/(SICI)1097-0290(1999)66:2<86::AID-BIT2>3.0.CO;2-A","article-title":"Bidirectional reaction steps in metabolic networks IV: optimal design of isotopomer labeling systems","volume":"66","author":"M\u00f6llney","year":"1999","journal-title":"Biotechnol. Bioeng."},{"key":"2023012408205569800_b17","doi-asserted-by":"crossref","first-page":"7031","DOI":"10.1128\/JB.185.24.7031-7035.2003","article-title":"It is all about metabolic fluxes","volume":"185","author":"Nielsen","year":"2003","journal-title":"J. Bacteriol."},{"key":"2023012408205569800_b18","first-page":"242","article-title":"Flow analysis of metabolite fragments for flux estimation","author":"Rantanen","year":"2005"},{"key":"2023012408205569800_b19","first-page":"88","article-title":"A method for estimating metabolic fluxes from incomplete isotopomer information","author":"Rousu","year":"2003"},{"key":"2023012408205569800_b20","doi-asserted-by":"crossref","first-page":"831","DOI":"10.1002\/(SICI)1097-0290(19970920)55:6<831::AID-BIT2>3.0.CO;2-H","article-title":"Modeling isotopomer distributions in biochemical networks using isotopomer mapping matrices","volume":"55","author":"Schmidt","year":"1997","journal-title":"Biotechnol. Bioeng."},{"key":"2023012408205569800_b21","doi-asserted-by":"crossref","first-page":"166","DOI":"10.1006\/mben.1999.0114","article-title":"Quantification of intracellular metabolic fluxes from fractional enrichment and 13C\u201313C coupling constraints on the isotopomer distribution in labeled biomass components","volume":"1","author":"Schmidt","year":"1999","journal-title":"Metab. Eng."},{"key":"2023012408205569800_b22","doi-asserted-by":"crossref","first-page":"3387","DOI":"10.1093\/bioinformatics\/bth412","article-title":"An optimized algorithm for flux estimation from isotopomer distribution in glucose metabolites","volume":"20","author":"Selivanov","year":"2004","journal-title":"Bioinformatics"},{"key":"2023012408205569800_b23","doi-asserted-by":"crossref","first-page":"8235","DOI":"10.1073\/pnas.96.14.8235","article-title":"Determination of the rate of the glutamate\/glutamine cycle in the human brain by in vivo13C NMR","volume":"96","author":"Shen","year":"1999","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"2023012408205569800_b24","doi-asserted-by":"crossref","first-page":"2462","DOI":"10.1111\/j.1432-1033.2004.04176.x","article-title":"Amino acid biosynthesis and metabolic flux profiling of Pichia pastoris","volume":"271","author":"Sola","year":"2004","journal-title":"Eur. J. Biochem."},{"key":"2023012408205569800_b25","volume-title":"Metabolic Engineering: Principles and Methodologies","author":"Stephanopoulos","year":"1998"},{"key":"2023012408205569800_b26","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1006\/mben.1999.0116","article-title":"Bioreaction network topology and metabolic flux ratio analysis by biosynthetic fractional 13C labeling and two-dimensional NMR spectrometry","volume":"1","author":"Szyperski","year":"1999","journal-title":"Metab. Eng."},{"key":"2023012408205569800_b27","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1111\/j.1432-1033.1995.tb20829.x","article-title":"Biosynthetically directed fractional 13C-labelling of proteinogenic amino acids. An efficient analytical tool to investigate intermediary metabolism","volume":"232","author":"Szyperski","year":"1995","journal-title":"Eur. J. Biochem."},{"key":"2023012408205569800_b28","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1017\/S0033583598003412","article-title":"13C-NMR, MS and metabolic flux balancing in biotechnology research","volume":"31","author":"Szyperski","year":"1998","journal-title":"Q. Rev. Biophys."},{"key":"2023012408205569800_b29","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1002\/bit.1142","article-title":"A priori analysis of metabolic flux identifiability from 13C-labeling data","volume":"74","author":"van Winden","year":"2001","journal-title":"Biotechnol. Bioeng."},{"key":"2023012408205569800_b30","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1016\/j.femsyr.2004.10.007","article-title":"Metabolic-flux analysis of Saccharomyces cerevisiae CEN.PK113-7D based on mass isotopomer measurements of 13C-labeled primary metabolites","volume":"5","author":"van Winden","year":"2005","journal-title":"FEMS Yeast Res."},{"key":"2023012408205569800_b31","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1006\/mben.2001.0188","article-title":"A Universal Framework for 13C metabolic flux analysis","volume":"3","author":"Wiechert","year":"2001","journal-title":"Metab. Eng."},{"key":"2023012408205569800_b32","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1002\/(SICI)1097-0290(19970705)55:1<118::AID-BIT13>3.0.CO;2-I","article-title":"Bidirectional reaction steps in metabolic networks: II. flux estimation and statistical analysis","volume":"55","author":"Wiechert","year":"1997","journal-title":"Biotechnol. Bioeng."},{"key":"2023012408205569800_b33","doi-asserted-by":"crossref","first-page":"739","DOI":"10.1002\/(SICI)1097-0290(19990320)62:6<739::AID-BIT13>3.0.CO;2-E","article-title":"Mass spectrometry for metabolic flux analysis","volume":"62","author":"Wittmann","year":"1999","journal-title":"Biotechnol. Bioeng."}],"container-title":["Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/22\/10\/1198\/48839040\/bioinformatics_22_10_1198.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article-pdf\/22\/10\/1198\/48839040\/bioinformatics_22_10_1198.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,24]],"date-time":"2023-01-24T08:23:45Z","timestamp":1674548625000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/bioinformatics\/article\/22\/10\/1198\/237100"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,2,27]]},"references-count":33,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2006,5,15]]}},"URL":"https:\/\/doi.org\/10.1093\/bioinformatics\/btl069","relation":{},"ISSN":["1367-4811","1367-4803"],"issn-type":[{"value":"1367-4811","type":"electronic"},{"value":"1367-4803","type":"print"}],"subject":[],"published-other":{"date-parts":[[2006,5,15]]},"published":{"date-parts":[[2006,2,27]]}}}