{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T02:00:48Z","timestamp":1784685648539,"version":"3.55.0"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,5,25]],"date-time":"2026-05-25T00:00:00Z","timestamp":1779667200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T00:00:00Z","timestamp":1784678400000},"content-version":"vor","delay-in-days":58,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["BMC Bioinformatics"],"DOI":"10.1186\/s12859-026-06485-1","type":"journal-article","created":{"date-parts":[[2026,5,25]],"date-time":"2026-05-25T05:33:53Z","timestamp":1779687233000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["MOFA: microbial optimization without forced altruism"],"prefix":"10.1186","volume":"27","author":[{"given":"Soraya","family":"Mirzaei","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mojtaba","family":"Tefagh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,5,25]]},"reference":[{"issue":"7244","key":"6485_CR1","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1038\/nature08058","volume":"459","author":"JA Fuhrman","year":"2009","unstructured":"Fuhrman JA. Microbial community structure and its functional implications. Nature. 2009;459(7244):193\u20139.","journal-title":"Nature"},{"issue":"4","key":"6485_CR2","doi-asserted-by":"publisher","first-page":"392","DOI":"10.1038\/nm.4517","volume":"24","author":"JA Gilbert","year":"2018","unstructured":"Gilbert JA, Blaser MJ, Caporaso JG, Jansson JK, Lynch SV, Knight R. Current understanding of the human microbiome. Nat Med. 2018;24(4):392\u2013400.","journal-title":"Nat Med"},{"issue":"7","key":"6485_CR3","doi-asserted-by":"publisher","first-page":"104676","DOI":"10.1016\/j.isci.2022.104513","volume":"25","author":"C Proffitt","year":"2022","unstructured":"Proffitt C, Bidkhori G, Lee S, Tebani A, Mardinoglu A, Uhlen M. Genome-scale metabolic modelling of the human gut microbiome reveals changes in the glyoxylate and dicarboxylate metabolism in metabolic disorders. iScience. 2022;25(7):104676.","journal-title":"iScience"},{"key":"6485_CR4","doi-asserted-by":"publisher","first-page":"226","DOI":"10.1016\/j.csbj.2020.12.003","volume":"19","author":"B Garc\u00eda-Jim\u00e9nez","year":"2021","unstructured":"Garc\u00eda-Jim\u00e9nez B, Torres-Bacete J, Nogales J. Metabolic modelling approaches for describing and engineering microbial communities. Comput Struct Biotechnol J. 2021;19:226\u201346.","journal-title":"Comput Struct Biotechnol J"},{"key":"6485_CR5","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1016\/j.copbio.2019.03.002","volume":"58","author":"A Eng","year":"2019","unstructured":"Eng A, Borenstein E. Microbial community design: methods, applications, and opportunities. Curr Opin Biotechnol. 2019;58:117\u201328.","journal-title":"Curr Opin Biotechnol"},{"issue":"9","key":"6485_CR6","doi-asserted-by":"publisher","first-page":"2121","DOI":"10.1021\/acssynbio.1c00140","volume":"10","author":"E Esvap","year":"2021","unstructured":"Esvap E, Ulgen KO. Advances in genome-scale metabolic modeling toward microbial community analysis of the human microbiome. ACS Synth Biol. 2021;10(9):2121\u201337.","journal-title":"ACS Synth Biol"},{"issue":"6","key":"6485_CR7","doi-asserted-by":"publisher","first-page":"1053","DOI":"10.1080\/1040841X.2024.2306465","volume":"50","author":"M Zulfiqar","year":"2024","unstructured":"Zulfiqar M, Singh V, Steinbeck C, Sorokina M. Review on computer-assisted biosynthetic capacities elucidation to assess metabolic interactions and communication within microbial communities. Crit Rev Microbiol. 2024;50(6):1053\u201392.","journal-title":"Crit Rev Microbiol"},{"issue":"3","key":"6485_CR8","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1038\/nbt.1614","volume":"28","author":"JD Orth","year":"2010","unstructured":"Orth JD, Thiele I, Palsson B\u00d8. What is flux balance analysis? Nat Biotechnol. 2010;28(3):245\u20138.","journal-title":"Nat Biotechnol"},{"issue":"124","key":"6485_CR9","doi-asserted-by":"publisher","first-page":"20160627","DOI":"10.1098\/rsif.2016.0627","volume":"13","author":"W Gottstein","year":"2016","unstructured":"Gottstein W, Olivier BG, Bruggeman FJ, Teusink B. Constraint-based stoichiometric modelling from single organisms to microbial communities. J R Soc Interface. 2016;13(124):20160627.","journal-title":"J R Soc Interface"},{"key":"6485_CR10","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/j.coisb.2021.04.001","volume":"26","author":"AV Colarusso","year":"2021","unstructured":"Colarusso AV, Goodchild-Michelman I, Rayle M, Zomorrodi AR. Computational modeling of metabolism in microbial communities on a genome-scale. Curr Opin Syst Biol. 2021;26:46\u201357.","journal-title":"Curr Opin Syst Biol"},{"issue":"8","key":"6485_CR11","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1011363","volume":"19","author":"WT Scott Jr","year":"2023","unstructured":"Scott WT Jr, Benito-Vaquerizo S, Zimmermann J, Baji\u0107 D, Heinken A, Suarez-Diez M, et al. A structured evaluation of genome-scale constraint-based modeling tools for microbial consortia. PLoS Comput Biol. 2023;19(8):e1011363.","journal-title":"PLoS Comput Biol"},{"issue":"1","key":"6485_CR12","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1038\/msb4100131","volume":"3","author":"S Stolyar","year":"2007","unstructured":"Stolyar S, Van Dien S, Hillesland KL, Pinel N, Lie TJ, Leigh JA, et al. Metabolic modeling of a mutualistic microbial community. Mol Syst Biol. 2007;3(1):92.","journal-title":"Mol Syst Biol"},{"issue":"2","key":"6485_CR13","doi-asserted-by":"publisher","first-page":"320","DOI":"10.1016\/j.cmet.2015.07.001","volume":"22","author":"S Shoaie","year":"2015","unstructured":"Shoaie S, Ghaffari P, Kovatcheva-Datchary P, Mardinoglu A, Sen P, Pujos-Guillot E, et al. Quantifying diet-induced metabolic changes of the human gut microbiome. Cell Metab. 2015;22(2):320\u201331.","journal-title":"Cell Metab"},{"issue":"13","key":"6485_CR14","doi-asserted-by":"publisher","first-page":"2332","DOI":"10.1093\/bioinformatics\/bty941","volume":"35","author":"F Baldini","year":"2019","unstructured":"Baldini F, Heinken A, Heirendt L, Magnusdottir S, Fleming RMT, Thiele I. The Microbiome Modeling Toolbox: from microbial interactions to personalized microbial communities. Bioinformatics. 2019;35(13):2332\u20134.","journal-title":"Bioinformatics"},{"key":"6485_CR15","doi-asserted-by":"crossref","unstructured":"Diener C, Gibbons SM, Resendis-Antonio O. MICOM: metagenome-scale modeling to infer metabolic interactions in the gut microbiota. mSystems. 2020;5(1):e10\u20131128.","DOI":"10.1128\/msystems.00606-19"},{"issue":"5","key":"6485_CR16","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1005539","volume":"13","author":"SHJ Chan","year":"2017","unstructured":"Chan SHJ, Simons MN, Maranas CD. SteadyCom: predicting microbial abundances while ensuring community stability. PLoS Comput Biol. 2017;13(5):e1005539.","journal-title":"PLoS Comput Biol"},{"issue":"2","key":"6485_CR17","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1006759","volume":"15","author":"S Koch","year":"2019","unstructured":"Koch S, Kohrs F, Lahmann P, Bissinger T, Wendschuh S, Benndorf D, et al. RedCom: a strategy for reduced metabolic modeling of complex microbial communities. PLoS Comput Biol. 2019;15(2):e1006759.","journal-title":"PLoS Comput Biol"},{"issue":"5","key":"6485_CR18","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pone.0064567","volume":"8","author":"RA Khandelwal","year":"2013","unstructured":"Khandelwal RA, Olivier BG, R\u00f6ling WFM, Teusink B, Bruggeman FJ. Community flux balance analysis for microbial consortia at balanced growth. PLoS ONE. 2013;8(5):e64567.","journal-title":"PLoS ONE"},{"key":"6485_CR19","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13068-016-0429-x","volume":"9","author":"S Koch","year":"2016","unstructured":"Koch S, Benndorf D, Fronk K, Reichl U, Klamt S. Predicting compositions of microbial communities from stoichiometric models with applications for the biogas process. Biotechnol Biofuels. 2016;9:1\u201316.","journal-title":"Biotechnol Biofuels"},{"issue":"3","key":"6485_CR20","doi-asserted-by":"publisher","first-page":"1331","DOI":"10.1016\/S0006-3495(02)73903-9","volume":"83","author":"R Mahadevan","year":"2002","unstructured":"Mahadevan R, Edwards JS, Doyle FJ. Dynamic flux balance analysis of diauxic growth in Escherichia coli. Biophys J. 2002;83(3):1331\u201340.","journal-title":"Biophys J"},{"key":"6485_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s12859-014-0409-8","volume":"15","author":"JA Gomez","year":"2014","unstructured":"Gomez JA, H\u00f6ffner K, Barton PI. DFBAlab: a fast and reliable MATLAB code for dynamic flux balance analysis. BMC Bioinform. 2014;15:1\u201310.","journal-title":"BMC Bioinform"},{"issue":"2","key":"6485_CR22","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1038\/ismej.2010.117","volume":"5","author":"K Zhuang","year":"2011","unstructured":"Zhuang K, Izallalen M, Mouser P, Richter H, Risso C, Mahadevan R, et al. Genome-scale dynamic modeling of the competition between Rhodoferax and Geobacter in anoxic subsurface environments. ISME J. 2011;5(2):305\u201316.","journal-title":"ISME J"},{"issue":"4","key":"6485_CR23","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1021\/sb4001307","volume":"3","author":"AR Zomorrodi","year":"2014","unstructured":"Zomorrodi AR, Islam MM, Maranas CD. d-OptCom: dynamic multi-level and multi-objective metabolic modeling of microbial communities. ACS Synth Biol. 2014;3(4):247\u201357.","journal-title":"ACS Synth Biol"},{"key":"6485_CR24","doi-asserted-by":"publisher","first-page":"574","DOI":"10.3389\/fbioe.2020.00574","volume":"8","author":"D Popp","year":"2020","unstructured":"Popp D, Centler F. $$\\mu $$BialSim: constraint-based dynamic simulation of complex microbiomes. Front Bioeng Biotechnol. 2020;8:574.","journal-title":"Front Bioeng Biotechnol"},{"issue":"4","key":"6485_CR25","doi-asserted-by":"publisher","first-page":"1104","DOI":"10.1016\/j.celrep.2014.03.070","volume":"7","author":"WR Harcombe","year":"2014","unstructured":"Harcombe WR, Riehl WJ, Dukovski I, Granger BR, Betts A, Lang AH, et al. Metabolic resource allocation in individual microbes determines ecosystem interactions and spatial dynamics. Cell Rep. 2014;7(4):1104\u201315.","journal-title":"Cell Rep"},{"issue":"5","key":"6485_CR26","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1005544","volume":"13","author":"E Bauer","year":"2017","unstructured":"Bauer E, Zimmermann J, Baldini F, Thiele I, Kaleta C. BacArena: individual-based metabolic modeling of heterogeneous microbes in complex communities. PLoS Comput Biol. 2017;13(5):e1005544.","journal-title":"PLoS Comput Biol"},{"issue":"5","key":"6485_CR27","doi-asserted-by":"publisher","first-page":"837","DOI":"10.1016\/j.jmb.2015.10.019","volume":"428","author":"AR Zomorrodi","year":"2016","unstructured":"Zomorrodi AR, Segr\u00e8 D. Synthetic ecology of microbes: mathematical models and applications. J Mol Biol. 2016;428(5):837\u201361.","journal-title":"J Mol Biol"},{"issue":"2","key":"6485_CR28","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1002363","volume":"8","author":"AR Zomorrodi","year":"2012","unstructured":"Zomorrodi AR, Maranas CD. OptCom: a multi-level optimization framework for the metabolic modeling and analysis of microbial communities. PLoS Comput Biol. 2012;8(2):e1002363.","journal-title":"PLoS Comput Biol"},{"issue":"24","key":"6485_CR29","doi-asserted-by":"publisher","first-page":"5649","DOI":"10.1093\/bioinformatics\/btaa1014","volume":"36","author":"J Cai","year":"2020","unstructured":"Cai J, Tan T, Chan SHJ. Predicting Nash equilibria for microbial metabolic interactions. Bioinformatics. 2020;36(24):5649\u201355.","journal-title":"Bioinformatics"},{"key":"6485_CR30","doi-asserted-by":"crossref","unstructured":"Colson B, Marcotte P, Savard G. Bilevel programming: a survey. 4OR. 2005;3:87\u2013107.","DOI":"10.1007\/s10288-005-0071-0"},{"issue":"1","key":"6485_CR31","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1038\/s41540-024-00373-1","volume":"10","author":"AK Raghu","year":"2024","unstructured":"Raghu AK, Palanikumar I, Raman K. Designing function-specific minimal microbiomes from large microbial communities. npj Syst Biol Appl. 2024;10(1):46.","journal-title":"npj Syst Biol Appl"},{"key":"6485_CR32","unstructured":"Osborne MJ, Rubinstein A. An introduction to game theory. Springer; 2004.(3rd ed.)."},{"issue":"5764","key":"6485_CR33","doi-asserted-by":"publisher","first-page":"1113","DOI":"10.1126\/science.1121357","volume":"311","author":"A Camilli","year":"2006","unstructured":"Camilli A, Bassler BL. Bacterial small-molecule signaling pathways. Science. 2006;311(5764):1113\u20136.","journal-title":"Science"},{"key":"6485_CR34","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1016\/j.bjm.2016.10.005","volume":"47","author":"RM Braga","year":"2016","unstructured":"Braga RM, Dourado MN, Ara\u00fajo WL. Microbial interactions: ecology in a molecular perspective. Braz J Microbiol. 2016;47:86\u201398.","journal-title":"Braz J Microbiol"},{"issue":"1","key":"6485_CR35","doi-asserted-by":"publisher","first-page":"23","DOI":"10.1038\/s41522-022-00291-2","volume":"8","author":"M de Celis","year":"2022","unstructured":"de Celis M, Duque J, Marquina D, Salvad\u00f3 H, Serrano S, Arregui L, et al. Niche differentiation drives microbial community assembly and succession in full-scale activated sludge bioreactors. NPJ Biofilms Microbiomes. 2022;8(1):23.","journal-title":"NPJ Biofilms Microbiomes"},{"issue":"1","key":"6485_CR36","doi-asserted-by":"publisher","first-page":"4","DOI":"10.1016\/j.copbio.2012.10.001","volume":"24","author":"I Thiele","year":"2013","unstructured":"Thiele I, Heinken A, Fleming RMT. A systems biology approach to studying the role of microbes in human health. Curr Opin Biotechnol. 2013;24(1):4\u201312.","journal-title":"Curr Opin Biotechnol"},{"issue":"3","key":"6485_CR37","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\u00d8. Elimination of thermodynamically infeasible loops in steady-state metabolic models. Biophys J. 2011;100(3):544\u201353.","journal-title":"Biophys J"},{"issue":"13","key":"6485_CR38","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.","journal-title":"Bioinformatics"},{"key":"6485_CR39","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511804441","volume-title":"Convex optimization","author":"S Boyd","year":"2004","unstructured":"Boyd S, Vandenberghe L. Convex optimization. Cambridge: Cambridge University Press; 2004."},{"issue":"6","key":"6485_CR40","doi-asserted-by":"publisher","first-page":"647","DOI":"10.1002\/bit.10803","volume":"84","author":"AP Burgard","year":"2003","unstructured":"Burgard AP, Pharkya P, Maranas CD. Optknock: a bilevel programming framework for identifying gene knockout strategies for microbial strain optimization. Biotechnol Bioeng. 2003;84(6):647\u201357.","journal-title":"Biotechnol Bioeng"},{"issue":"7","key":"6485_CR41","doi-asserted-by":"publisher","first-page":"563","DOI":"10.1016\/0098-1354(93)E0010-7","volume":"18","author":"R Raman","year":"1994","unstructured":"Raman R, Grossmann IE. Modelling and computational techniques for logic based integer programming. Comput Chem Eng. 1994;18(7):563\u201378.","journal-title":"Comput Chem Eng"},{"key":"6485_CR42","doi-asserted-by":"crossref","unstructured":"Maranas CD, Zomorrodi AR. Optimization methods in metabolic networks. John Wiley & Sons; 2016.","DOI":"10.1002\/9781119188902"},{"issue":"1","key":"6485_CR43","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/s10107-004-0559-y","volume":"106","author":"A W\u00e4chter","year":"2006","unstructured":"W\u00e4chter A, Biegler LT. On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math Program. 2006;106(1):25\u201357.","journal-title":"Math Program"},{"issue":"11","key":"6485_CR44","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1001002","volume":"6","author":"N Klitgord","year":"2010","unstructured":"Klitgord N, Segre D. Environments that induce synthetic microbial ecosystems. PLoS Comput Biol. 2010;6(11):e1001002.","journal-title":"PLoS Comput Biol"},{"issue":"3","key":"6485_CR45","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, 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"}],"container-title":["BMC Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s12859-026-06485-1","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s12859-026-06485-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s12859-026-06485-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T01:01:13Z","timestamp":1784682073000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1186\/s12859-026-06485-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,25]]},"references-count":45,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,12]]}},"alternative-id":["6485"],"URL":"https:\/\/doi.org\/10.1186\/s12859-026-06485-1","relation":{},"ISSN":["1471-2105"],"issn-type":[{"value":"1471-2105","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,25]]},"assertion":[{"value":"9 October 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 May 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 May 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Not applicable.","order":1,"name":"Ethics","label":"Ethics approval and consent to participate","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","label":"Consent for publication","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no conflict of interest.","order":3,"name":"Ethics","label":"Competing interests","group":{"name":"EthicsHeading","label":"Declarations"}}],"article-number":"155"}}