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Here, we defined modules as sets of reversible reactions isolated from the rest of metabolism by irreversible reactions except for the exchange of currency metabolites. Our approach identifies topologically independent modules under specific conditions associated with different metabolic functions. As case studies, the\n                    <jats:italic>E<\/jats:italic>\n                    .\n                    <jats:italic>coli i<\/jats:italic>\n                    JO1366 and Human Recon 2.2 genome-scale metabolic models were split in 103 and 321 modules respectively, displaying significant correlation patterns in expression data. Finally, we addressed a fundamental question about the metabolic flexibility conferred by reversible reactions: \u201cOf all Directed Topologies (DTs) defined by fixing directions to all reversible reactions, how many are capable of carrying flux through all reactions?\u201d. Enumeration of the DTs for\n                    <jats:italic>i<\/jats:italic>\n                    JO1366 model was performed using an efficient depth-first search algorithm, rejecting infeasible DTs based on mass-imbalanced and loopy flux patterns. We found the direction of 79% of reversible reactions must be defined before all directions in the network can be fixed, granting a high degree of flexibility.\n                  <\/jats:p>","DOI":"10.1371\/journal.pcbi.1010203","type":"journal-article","created":{"date-parts":[[2022,6,27]],"date-time":"2022-06-27T13:38:06Z","timestamp":1656337086000},"page":"e1010203","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":8,"title":["The topology of genome-scale metabolic reconstructions unravels independent modules and high network flexibility"],"prefix":"10.1371","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2729-5278","authenticated-orcid":true,"given":"Ver\u00f3nica S.","family":"Mart\u00ednez","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1659-9041","authenticated-orcid":true,"given":"Pedro A.","family":"Saa","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2169-0552","authenticated-orcid":true,"given":"Jason","family":"Jooste","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3501-8924","authenticated-orcid":true,"given":"Kanupriya","family":"Tiwari","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9313-8740","authenticated-orcid":true,"given":"Lake-Ee","family":"Quek","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8191-3511","authenticated-orcid":true,"given":"Lars K.","family":"Nielsen","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2022,6,27]]},"reference":[{"issue":"2","key":"pcbi.1010203.ref001","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1038\/nrmicro1949","article-title":"Reconstruction of biochemical networks in microorganisms","volume":"7","author":"AM Feist","year":"2009","journal-title":"Nat Rev Microbiol"},{"issue":"1","key":"pcbi.1010203.ref002","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1038\/nprot.2009.203","article-title":"A protocol for generating a high-quality genome-scale metabolic reconstruction.","volume":"5","author":"I Thiele","year":"2010","journal-title":"Nat Protoc."},{"issue":"2","key":"pcbi.1010203.ref003","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1104\/pp.109.148817","article-title":"AraGEM, a genome-scale reconstruction of the primary metabolic network in Arabidopsis","volume":"152","author":"CG de Oliveira Dal\u2019Molin","year":"2010","journal-title":"Plant Physiol"},{"key":"pcbi.1010203.ref004","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1038\/msb.2011.65","article-title":"A comprehensive genome-scale reconstruction of Escherichia coli metabolism\u20142011","volume":"7","author":"JD Orth","year":"2011","journal-title":"Mol Syst Biol"},{"issue":"4","key":"pcbi.1010203.ref005","first-page":"215","article-title":"Revising the Representation of Fatty Acid, Glycerolipid, and Glycerophospholipid Metabolism in the Consensus Model of Yeast Metabolism","volume":"9","author":"HW Aung","year":"2013","journal-title":"Ind Biotechnol (New Rochelle N Y)."},{"issue":"5","key":"pcbi.1010203.ref006","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1016\/j.cels.2016.10.020","article-title":"A consensus genome-scale reconstruction of Chinese hamster ovary cell metabolism","volume":"3","author":"H Hefzi","year":"2016","journal-title":"Cell systems"},{"issue":"7","key":"pcbi.1010203.ref007","doi-asserted-by":"crossref","DOI":"10.1007\/s11306-016-1051-4","article-title":"Recon 2.2: from reconstruction to model of human metabolism","volume":"12","author":"N Swainston","year":"2016","journal-title":"Metabolomics"},{"issue":"1","key":"pcbi.1010203.ref008","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1186\/s13059-019-1730-3","article-title":"Current status and applications of genome-scale metabolic models","volume":"20","author":"C Gu","year":"2019","journal-title":"Genome Biol"},{"issue":"4","key":"pcbi.1010203.ref009","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1016\/j.ymben.2012.04.006","article-title":"Expanding the chemical palate of cells by combining systems biology and metabolic engineering","volume":"14","author":"KA Curran","year":"2012","journal-title":"Metabolic Engineering"},{"issue":"6","key":"pcbi.1010203.ref010","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1038\/nbt1401","article-title":"The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli","volume":"26","author":"AM Feist","year":"2008","journal-title":"Nature Biotechnology"},{"issue":"24","key":"pcbi.1010203.ref011","doi-asserted-by":"crossref","first-page":"3900","DOI":"10.1016\/j.febslet.2009.09.031","article-title":"Metabolic systems biology","volume":"583","author":"B. 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