{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T23:28:04Z","timestamp":1792106884819,"version":"4.4.0"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,1,2]],"date-time":"2024-01-02T00:00:00Z","timestamp":1704153600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,1,2]],"date-time":"2024-01-02T00:00:00Z","timestamp":1704153600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Open Seed Fund UC-UQ","award":["OSF2021 00193"],"award-info":[{"award-number":["OSF2021 00193"]}]},{"name":"Open Seed Fund UC-UQ","award":["OSF2021 00193"],"award-info":[{"award-number":["OSF2021 00193"]}]},{"name":"Basal ANID, National Center for Artificial Intelligence","award":["FB210017"],"award-info":[{"award-number":["FB210017"]}]},{"name":"Australian Research Council Future Fellowship","award":["FT210100260"],"award-info":[{"award-number":["FT210100260"]}]},{"DOI":"10.13039\/501100009708","name":"Novo Nordisk Foundation","doi-asserted-by":"crossref","award":["NNF20CC0035580, NNF14OC0009473"],"award-info":[{"award-number":["NNF20CC0035580, NNF14OC0009473"]}],"id":[{"id":"10.13039\/501100009708","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["BMC Bioinformatics"],"abstract":"<jats:title>Abstract<\/jats:title><jats:sec>\n                <jats:title>Background<\/jats:title>\n                <jats:p>Uniform random sampling of mass-balanced flux solutions offers an unbiased appraisal of the capabilities of metabolic networks. Unfortunately, it is impossible to avoid thermodynamically infeasible loops in flux samples when using convex samplers on large metabolic models. Current strategies for randomly sampling the non-convex loopless flux space display limited efficiency and lack theoretical guarantees.<\/jats:p>\n              <\/jats:sec><jats:sec>\n                <jats:title>Results<\/jats:title>\n                <jats:p>Here, we present LooplessFluxSampler, an efficient algorithm for exploring the loopless mass-balanced flux solution space of metabolic models, based on an Adaptive Directions Sampling on a Box (ADSB) algorithm. ADSB is rooted in the general Adaptive Direction Sampling (ADS) framework, specifically the Parallel ADS, for which theoretical convergence and irreducibility results are available for sampling from arbitrary distributions. By sampling directions that adapt to the target distribution, ADSB traverses more efficiently the sample space achieving faster mixing than other methods. Importantly, the presented algorithm is guaranteed to target the uniform distribution over convex regions, and it provably converges on the latter distribution over more general (non-convex) regions provided the sample can have full support.<\/jats:p>\n              <\/jats:sec><jats:sec>\n                <jats:title>Conclusions<\/jats:title>\n                <jats:p>LooplessFluxSampler enables scalable statistical inference of the loopless mass-balanced solution space of large metabolic models. Grounded in a theoretically sound framework, this toolbox provides not only efficient but also reliable results for exploring the properties of the almost surely non-convex loopless flux space. Finally, LooplessFluxSampler includes a Markov Chain diagnostics suite for assessing the quality of the final sample and the performance of the algorithm.<\/jats:p>\n              <\/jats:sec>","DOI":"10.1186\/s12859-023-05616-2","type":"journal-article","created":{"date-parts":[[2024,1,2]],"date-time":"2024-01-02T14:02:47Z","timestamp":1704204167000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["LooplessFluxSampler: an efficient toolbox for sampling the loopless flux solution space of metabolic models"],"prefix":"10.1186","volume":"25","author":[{"given":"Pedro A.","family":"Saa","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sebastian","family":"Zapararte","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christopher C.","family":"Drovandi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lars K.","family":"Nielsen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,1,2]]},"reference":[{"key":"5616_CR1","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1038\/s41540-019-0109-0","volume":"5","author":"HA Herrmann","year":"2019","unstructured":"Herrmann HA, Dyson BC, Vass L, Johnson GN, Schwartz J-M. Flux sampling is a powerful tool to study metabolism under changing environmental conditions. NPJ Syst Biol Appl. 2019;5:32.","journal-title":"NPJ Syst Biol Appl."},{"issue":"6","key":"5616_CR2","doi-asserted-by":"publisher","first-page":"1296","DOI":"10.1287\/opre.32.6.1296","volume":"32","author":"RL Smith","year":"1984","unstructured":"Smith RL. Efficient Monte Carlo procedures for generating points uniformly distributed over bounded regions. Oper Res. 1984;32(6):1296\u2013308.","journal-title":"Oper Res"},{"issue":"4","key":"5616_CR3","doi-asserted-by":"publisher","first-page":"0122670","DOI":"10.1371\/journal.pone.0122670","volume":"10","author":"D De Martino","year":"2015","unstructured":"De Martino D, Mori M, Parisi V. Uniform sampling of steady states in metabolic networks: heterogeneous scales and rounding. PLoS ONE. 2015;10(4):0122670.","journal-title":"PLoS ONE"},{"issue":"11","key":"5616_CR4","doi-asserted-by":"publisher","first-page":"1741","DOI":"10.1093\/bioinformatics\/btx052","volume":"33","author":"HS Haraldsd\u00f3ttir","year":"2017","unstructured":"Haraldsd\u00f3ttir HS, Cousins B, Thiele I, Fleming RM, Vempala S. Chrr: coordinate hit-and-run with rounding for uniform sampling of constraint-based models. Bioinformatics. 2017;33(11):1741\u20133.","journal-title":"Bioinformatics"},{"issue":"1","key":"5616_CR5","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1287\/opre.46.1.84","volume":"46","author":"DE Kaufman","year":"1998","unstructured":"Kaufman DE, Smith RL. Direction choice for accelerated convergence in hit-and-run sampling. Oper Res. 1998;46(1):84\u201395.","journal-title":"Oper Res"},{"issue":"7","key":"5616_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1371\/journal.pone.0235393","volume":"15","author":"S Fallahi","year":"2020","unstructured":"Fallahi S, Skaug HJ, Alendal G. A comparison of Monte Carlo sampling methods for metabolic network models. PLoS ONE. 2020;15(7):1\u201324. https:\/\/doi.org\/10.1371\/journal.pone.0235393.","journal-title":"PLoS ONE"},{"issue":"4","key":"5616_CR7","doi-asserted-by":"publisher","first-page":"2172","DOI":"10.1529\/biophysj.104.043000","volume":"87","author":"ND Price","year":"2004","unstructured":"Price ND, Schellenberger J, Palsson BO. Uniform sampling of steady-state flux spaces: means to design experiments and to interpret enzymopathies. Biophys J. 2004;87(4):2172\u201386. https:\/\/doi.org\/10.1529\/biophysj.104.043000.","journal-title":"Biophys J"},{"issue":"7","key":"5616_CR8","doi-asserted-by":"publisher","first-page":"e1000859","DOI":"10.1371\/journal.pcbi.1000859","volume":"6","author":"S Bordel","year":"2013","unstructured":"Bordel S, Agren R, Nielsen J. Sampling the solution space in genome-scale metabolic networks reveals transcriptional regulation in key enzymes. PLoS Comput Biol. 2013;6(7):e1000859.","journal-title":"PLoS Comput Biol"},{"key":"5616_CR9","doi-asserted-by":"publisher","first-page":"4","DOI":"10.3389\/fpls.2015.00004","volume":"6","author":"C Gomes de Oliveira Dal\u2019Molin","year":"2015","unstructured":"Gomes de Oliveira Dal\u2019Molin C, Quek L-E, Saa PA, Nielsen LK. A multi-tissue genome-scale metabolic modeling framework for the analysis of whole plant systems. Front Plant Sci. 2015;6:4. https:\/\/doi.org\/10.3389\/fpls.2015.00004.","journal-title":"Front Plant Sci"},{"key":"5616_CR10","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1016\/j.plantsci.2018.03.027","volume":"273","author":"C Gomes de Oliveira Dal\u2019Molin","year":"2018","unstructured":"Gomes de Oliveira Dal\u2019Molin C, Quek L-E, Saa PA, Palfreyman R, Nielsen LK. From reconstruction to c4 metabolic engineering: a case study for overproduction of polyhydroxybutyrate in bioenergy grasses. Plant Sci. 2018;273:50\u201360. https:\/\/doi.org\/10.1016\/j.plantsci.2018.03.027.","journal-title":"Plant Sci"},{"key":"5616_CR11","doi-asserted-by":"publisher","DOI":"10.1128\/msystems.00646-22","author":"B Hirmas","year":"2022","unstructured":"Hirmas B, Gasaly N, Orellana G, Vega-Sagard\u00eda M, Saa P, Gotteland M, Garrido D. Metabolic modeling and bidirectional culturing of two gut microbes reveal cross-feeding interactions and protective effects on intestinal cells. mSystems. 2022. https:\/\/doi.org\/10.1128\/msystems.00646-22.","journal-title":"mSystems"},{"issue":"6","key":"5616_CR12","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.95.062419","volume":"95","author":"D De Martino","year":"2017","unstructured":"De Martino D. Scales and multimodal flux distributions in stationary metabolic network models via thermodynamics. Phys Rev E. 2017;95(6): 062419.","journal-title":"Phys Rev E"},{"issue":"1","key":"5616_CR13","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/S0006-3495(02)75150-3","volume":"83","author":"DA Beard","year":"2002","unstructured":"Beard DA, Liang S-D, Qian H. Energy balance for analysis of complex metabolic networks. Biophys J. 2002;83(1):79\u201386.","journal-title":"Biophys J"},{"key":"5616_CR14","doi-asserted-by":"publisher","first-page":"140","DOI":"10.1186\/1752-0509-6-140","volume":"6","author":"E Noor","year":"2012","unstructured":"Noor E, Lewis N, Milo R. A proof for loop-law constraints in stoichiometric metabolic networks. BMC Syst Biol. 2012;6:140. https:\/\/doi.org\/10.1186\/1752-0509-6-140.","journal-title":"BMC Syst Biol."},{"issue":"5","key":"5616_CR15","doi-asserted-by":"publisher","first-page":"2879","DOI":"10.1016\/S0006-3495(02)75297-1","volume":"83","author":"N Price","year":"2002","unstructured":"Price N, Famili I, Beard D, Palsson B. Extreme pathways and Kirchhoff\u2019s second law. Biophys J. 2002;83(5):2879\u201382. https:\/\/doi.org\/10.1016\/S0006-3495(02)75297-1.","journal-title":"Biophys J."},{"issue":"5","key":"5616_CR16","doi-asserted-by":"publisher","first-page":"2879","DOI":"10.1016\/S0006-3495(02)75297-1","volume":"83","author":"ND Price","year":"2002","unstructured":"Price ND, Famili I, Beard DA, Palsson B. Extreme pathways and Kirchhoff\u2019s second law. Biophys J. 2002;83(5):2879\u201382. https:\/\/doi.org\/10.1016\/S0006-3495(02)75297-1.","journal-title":"Biophys J"},{"issue":"15","key":"5616_CR17","doi-asserted-by":"publisher","first-page":"2330","DOI":"10.1093\/bioinformatics\/btw132","volume":"32","author":"PA Saa","year":"2016","unstructured":"Saa PA, Nielsen LK. ll-achrb: a scalable algorithm for sampling the feasible solution space of metabolic networks. Bioinformatics. 2016;32(15):2330\u20137.","journal-title":"Bioinformatics"},{"issue":"1","key":"5616_CR18","first-page":"179","volume":"43","author":"WR Gilks","year":"1994","unstructured":"Gilks WR, Roberts GO, George EI. Adaptive direction sampling. J R Stat Soc Ser D (Stat). 1994;43(1):179\u201389.","journal-title":"J R Stat Soc Ser D (Stat)"},{"issue":"2","key":"5616_CR19","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1006\/jmva.1994.1028","volume":"49","author":"G Roberts","year":"1994","unstructured":"Roberts G, Gilks W. Convergence of adaptive direction sampling. J Multivar Anal. 1994;49(2):287\u201398.","journal-title":"J Multivar Anal"},{"issue":"3","key":"5616_CR20","doi-asserted-by":"publisher","first-page":"705","DOI":"10.1214\/aos\/1056562461","volume":"31","author":"RM Neal","year":"2003","unstructured":"Neal RM. Slice sampling. Ann Stat. 2003;31(3):705\u201367.","journal-title":"Ann Stat"},{"issue":"3","key":"5616_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/1921598.1921600","volume":"21","author":"S Kiatsupaibul","year":"2011","unstructured":"Kiatsupaibul S, Smith RL, Zabinsky ZB. An analysis of a variation of hit-and-run for uniform sampling from general regions. ACM Trans Model Comput Simul. 2011;21(3):1\u201311.","journal-title":"ACM Trans Model Comput Simul"},{"issue":"2","key":"5616_CR22","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1016\/j.compbiomed.2006.01.002","volume":"37","author":"R Nigam","year":"2007","unstructured":"Nigam R, Liang S. Algorithm for perturbing thermodynamically infeasible metabolic networks. Comput Biol Med. 2007;37(2):126\u201333. https:\/\/doi.org\/10.1016\/j.compbiomed.2006.01.002.","journal-title":"Comput Biol Med"},{"issue":"18","key":"5616_CR23","doi-asserted-by":"publisher","first-page":"2938","DOI":"10.1093\/bioinformatics\/btab194","volume":"37","author":"MG Gollub","year":"2021","unstructured":"Gollub MG, Kaltenbach H-M, Stelling J. Probabilistic thermodynamic analysis of metabolic networks. Bioinformatics. 2021;37(18):2938\u201345. https:\/\/doi.org\/10.1093\/bioinformatics\/btab194.","journal-title":"Bioinformatics."},{"issue":"2","key":"5616_CR24","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1287\/moor.18.2.255","volume":"18","author":"CJ B\u00e9lisle","year":"1993","unstructured":"B\u00e9lisle CJ, Romeijn HE, Smith RL. Hit-and-run algorithms for generating multivariate distributions. Math Oper Res. 1993;18(2):255\u201366.","journal-title":"Math Oper Res"},{"issue":"3","key":"5616_CR25","doi-asserted-by":"publisher","first-page":"639","DOI":"10.1038\/s41596-018-0098-2","volume":"14","author":"L Heirendt","year":"2019","unstructured":"Heirendt L, Arreckx S, Pfau T, Mendoza SN, Richelle A, Heinken A, Haraldsd\u00f3ttir HS, Wachowiak J, Keating SM, Vlasov V, et al. Creation and analysis of biochemical constraint-based models using the cobra toolbox v. 3.0. Nat Protoc. 2019;14(3):639\u2013702.","journal-title":"Nat Protoc"},{"issue":"24","key":"5616_CR26","doi-asserted-by":"publisher","first-page":"3807","DOI":"10.1093\/bioinformatics\/btw555","volume":"32","author":"PA Saa","year":"2016","unstructured":"Saa PA, Nielsen LK. Fast-snp: a fast matrix pre-processing algorithm for efficient loopless flux optimization of metabolic models. Bioinformatics. 2016;32(24):3807\u201314.","journal-title":"Bioinformatics"},{"issue":"1","key":"5616_CR27","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1128\/ecosalplus.10.2.1","volume":"4","author":"JD Orth","year":"2010","unstructured":"Orth JD, Fleming RMT, Palsson B. Reconstruction and use of microbial metabolic networks: the core Escherichia coli metabolic model as an educational guide. EcoSal Plus. 2010;4(1):10. https:\/\/doi.org\/10.1128\/ecosalplus.10.2.1.","journal-title":"EcoSal Plus."},{"issue":"2","key":"5616_CR28","doi-asserted-by":"publisher","first-page":"266","DOI":"10.1093\/bioinformatics\/bty550","volume":"35","author":"MP Gerstl","year":"2018","unstructured":"Gerstl MP, M\u00fcller S, Regensburger G, Zanghellini J. Flux tope analysis: studying the coordination of reaction directions in metabolic networks. Bioinformatics. 2018;35(2):266\u201373. https:\/\/doi.org\/10.1093\/bioinformatics\/bty550.","journal-title":"Bioinformatics."},{"issue":"3","key":"5616_CR29","doi-asserted-by":"publisher","first-page":"544","DOI":"10.1016\/j.bpj.2010.12.3707","volume":"100","author":"J Schellenberger","year":"2011","unstructured":"Schellenberger J, Lewis NE, Palsson B. Elimination of thermodynamically infeasible loops in steady-state metabolic models. Biophys J. 2011;100(3):544\u201353. https:\/\/doi.org\/10.1016\/j.bpj.2010.12.3707.","journal-title":"Biophys J"},{"issue":"13","key":"5616_CR30","doi-asserted-by":"publisher","first-page":"2159","DOI":"10.1093\/bioinformatics\/btv096","volume":"31","author":"AA Desouki","year":"2015","unstructured":"Desouki AA, Jarre F, Gelius-Dietrich G, Lercher MJ. CycleFreeFlux: efficient removal of thermodynamically infeasible loops from flux distributions. Bioinformatics. 2015;31(13):2159\u201365. https:\/\/doi.org\/10.1093\/bioinformatics\/btv096.","journal-title":"Bioinformatics."}],"container-title":["BMC Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s12859-023-05616-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s12859-023-05616-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s12859-023-05616-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,2]],"date-time":"2024-01-02T14:04:23Z","timestamp":1704204263000},"score":1,"resource":{"primary":{"URL":"https:\/\/bmcbioinformatics.biomedcentral.com\/articles\/10.1186\/s12859-023-05616-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,2]]},"references-count":30,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["5616"],"URL":"https:\/\/doi.org\/10.1186\/s12859-023-05616-2","relation":{},"ISSN":["1471-2105"],"issn-type":[{"value":"1471-2105","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,1,2]]},"assertion":[{"value":"20 April 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 December 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 January 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and consent to participate"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}},{"value":"The authors declare that they have no competing interests.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"3"}}