{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T11:55:16Z","timestamp":1778154916470,"version":"3.51.4"},"reference-count":55,"publisher":"Oxford University Press (OUP)","issue":"7","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Motivation: Flux variability analysis (FVA) is an important tool to further analyse the results obtained by flux balance analysis (FBA) on genome-scale metabolic networks. For many constraint-based models, FVA identifies unboundedness of the optimal flux space. This reveals that optimal flux solutions with net flux through internal biochemical loops are feasible, which violates the second law of thermodynamics. Such unbounded fluxes may be eliminated by extending FVA with thermodynamic constraints.<\/jats:p>\n               <jats:p>Results: We present a new algorithm for efficient flux variability (and flux balance) analysis with thermodynamic constraints, suitable for analysing genome-scale metabolic networks. We first show that FBA with thermodynamic constraints is NP-hard. Then we derive a theoretical tractability result, which can be applied to metabolic networks in practice. We use this result to develop a new constraint programming algorithm Fast-tFVA for fast FVA with thermodynamic constraints (tFVA). Computational comparisons with previous methods demonstrate the efficiency of the new method. For tFVA, a speed-up of factor 30\u2013300 is achieved. In an analysis of genome-scale metabolic networks in the BioModels database, we found that in 485 of 716 networks, additional irreversible or fixed reactions could be detected.<\/jats:p>\n               <jats:p>Availability and implementation: \u00a0Fast-tFVA is written in C++ and published under GPL. It uses the open source software SCIP and libSBML. There also exists a Matlab interface for easy integration into Matlab. Fast-tFVA is available from page.mi.fu-berlin.de\/arnem\/fast-tfva.html.<\/jats:p>\n               <jats:p>Contact: \u00a0arne.mueller@fu-berlin.de; Alexander.Bockmayr@fu-berlin.de<\/jats:p>\n               <jats:p>Supplementary information: \u00a0Supplementary data are available at Bioinformatics online.<\/jats:p>","DOI":"10.1093\/bioinformatics\/btt059","type":"journal-article","created":{"date-parts":[[2013,2,7]],"date-time":"2013-02-07T06:27:54Z","timestamp":1360218474000},"page":"903-909","source":"Crossref","is-referenced-by-count":43,"title":["Fast thermodynamically constrained flux variability analysis"],"prefix":"10.1093","volume":"29","author":[{"given":"Arne C.","family":"M\u00fcller","sequence":"first","affiliation":[{"name":"1 Department of Mathematics and Computer Science, Freie Universit\u00e4t Berlin, 14195 Berlin, 2International Max Planck Research School for Computational Biology and Scientific Computing (IMPRS-CBSC), Max Planck Institute for Molecular Genetics, 14195 Berlin, 3Berlin Mathematical School (BMS), 10623 Berlin and 4DFG-Research Center Matheon, 10623 Berlin, Germany"},{"name":"1 Department of Mathematics and Computer Science, Freie Universit\u00e4t Berlin, 14195 Berlin, 2International Max Planck Research School for Computational Biology and Scientific Computing (IMPRS-CBSC), Max Planck Institute for Molecular Genetics, 14195 Berlin, 3Berlin Mathematical School (BMS), 10623 Berlin and 4DFG-Research Center Matheon, 10623 Berlin, Germany"},{"name":"1 Department of Mathematics and Computer Science, Freie Universit\u00e4t Berlin, 14195 Berlin, 2International Max Planck Research School for Computational Biology and Scientific Computing (IMPRS-CBSC), Max Planck Institute for Molecular Genetics, 14195 Berlin, 3Berlin Mathematical School (BMS), 10623 Berlin and 4DFG-Research Center Matheon, 10623 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander","family":"Bockmayr","sequence":"additional","affiliation":[{"name":"1 Department of Mathematics and Computer Science, Freie Universit\u00e4t Berlin, 14195 Berlin, 2International Max Planck Research School for Computational Biology and Scientific Computing (IMPRS-CBSC), Max Planck Institute for Molecular Genetics, 14195 Berlin, 3Berlin Mathematical School (BMS), 10623 Berlin and 4DFG-Research Center Matheon, 10623 Berlin, Germany"},{"name":"1 Department of Mathematics and Computer Science, Freie Universit\u00e4t Berlin, 14195 Berlin, 2International Max Planck Research School for Computational Biology and Scientific Computing (IMPRS-CBSC), Max Planck Institute for Molecular Genetics, 14195 Berlin, 3Berlin Mathematical School (BMS), 10623 Berlin and 4DFG-Research Center Matheon, 10623 Berlin, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2013,2,6]]},"reference":[{"key":"2023020303304647300_btt059-B1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s12532-008-0001-1","article-title":"SCIP: Solving constraint integer programs","volume":"1","author":"Achterberg","year":"2009","journal-title":"Math. 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