{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,22]],"date-time":"2025-02-22T00:45:16Z","timestamp":1740185116268,"version":"3.37.3"},"reference-count":29,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2018,7,2]],"date-time":"2018-07-02T00:00:00Z","timestamp":1530489600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Austrian BMWD"},{"DOI":"10.13039\/501100004956","name":"BMVIT","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004956","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007945","name":"SFG","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100007945","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100011035","name":"Standortagentur Tirol","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100011035","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100015053","name":"Government of Lower Austria","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100015053","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Business Agency Vienna"},{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["P28406","P27229"],"award-info":[{"award-number":["P28406","P27229"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,1,15]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:sec>\n                  <jats:title>Motivation<\/jats:title>\n                  <jats:p>Elementary flux mode (EFM) analysis allows an unbiased description of metabolic networks in terms of minimal pathways (involving a minimal set of reactions). To date, the enumeration of EFMs is impracticable in genome-scale metabolic models. In a complementary approach, we introduce the concept of a flux tope (FT), involving a maximal set of reactions (with fixed directions), which allows one to study the coordination of reaction directions in metabolic networks and opens a new way for EFM enumeration.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Results<\/jats:title>\n                  <jats:p>A FT is a (nontrivial) subset of the flux cone specified by fixing the directions of all reversible reactions. In a consistent metabolic network (without unused reactions), every FT contains a \u2018maximal pathway\u2019, carrying flux in all reactions. This decomposition of the flux cone into FTs allows the enumeration of EFMs (of individual FTs) without increasing the problem dimension by reaction splitting. To develop a mathematical framework for FT analysis, we build on the concepts of sign vectors and hyperplane arrangements. Thereby, we observe that FT analysis can be applied also to flux optimization problems involving additional (inhomogeneous) linear constraints. For the enumeration of FTs, we adapt the reverse search algorithm and provide an efficient implementation. We demonstrate that (biomass-optimal) FTs can be enumerated in genome-scale metabolic models of B.cuenoti and E.coli, and we use FTs to enumerate EFMs in models of M.genitalium and B.cuenoti.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Availability and implementation<\/jats:title>\n                  <jats:p>The source code is freely available at https:\/\/github.com\/mpgerstl\/FTA.<\/jats:p>\n               <\/jats:sec>\n               <jats:sec>\n                  <jats:title>Supplementary information<\/jats:title>\n                  <jats:p>Supplementary data are available at Bioinformatics online.<\/jats:p>\n               <\/jats:sec>","DOI":"10.1093\/bioinformatics\/bty550","type":"journal-article","created":{"date-parts":[[2018,6,29]],"date-time":"2018-06-29T12:11:58Z","timestamp":1530274318000},"page":"266-273","source":"Crossref","is-referenced-by-count":13,"title":["Flux tope analysis: studying the coordination of reaction directions in metabolic networks"],"prefix":"10.1093","volume":"35","author":[{"given":"Matthias P","family":"Gerstl","sequence":"first","affiliation":[{"name":"Department of Biotechnology, University of Natural Resources and Life Sciences, Vienna, Austria, EU"},{"name":"Austrian Centre of Industrial Biotechnology, Vienna, Austria, EU"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stefan","family":"M\u00fcller","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics, University of Vienna, Vienna, Austria, EU"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Georg","family":"Regensburger","sequence":"additional","affiliation":[{"name":"Institute for Algebra, Johannes Kepler University Linz, Linz, Austria, EU"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1964-2455","authenticated-orcid":false,"given":"J\u00fcrgen","family":"Zanghellini","sequence":"additional","affiliation":[{"name":"Department of Biotechnology, University of Natural Resources and Life Sciences, Vienna, Austria, EU"},{"name":"Austrian Centre of Industrial Biotechnology, Vienna, Austria, EU"},{"name":"Austrian Biotech University of Applied Sciences, Tulln, Austria, EU"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2018,7,2]]},"reference":[{"key":"2023013107225918700_bty550-B1","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.biosystems.2008.06.015","article-title":"Modes and cuts in metabolic networks: complexity and algorithms","volume":"95","author":"Acu\u00f1a","year":"2009","journal-title":"Biosystems"},{"key":"2023013107225918700_bty550-B2","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/0166-218X(95)00026-N","article-title":"Reverse search for enumeration","volume":"65","author":"Avis","year":"1996","journal-title":"Discrete Appl. 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