{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T21:05:18Z","timestamp":1757624718219,"version":"3.44.0"},"publisher-location":"Cham","reference-count":29,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783032014351"},{"type":"electronic","value":"9783032014368"}],"license":[{"start":{"date-parts":[[2025,8,19]],"date-time":"2025-08-19T00:00:00Z","timestamp":1755561600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,8,19]],"date-time":"2025-08-19T00:00:00Z","timestamp":1755561600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>Microorganisms growing together within a community can either cooperate by exchanging nutrients or compete for the same nutrients. The resulting complex network of interactions leads to the emergence of various community functions. However, metabolic interactions are difficult to identify experimentally, and current computational predictions assume a community objective. Here, we propose a community objective-free computational method using a constraint-based metabolic model for predicting the minimal exchanges of nutrients between species coexisting in a chemostat at steady state. For a toy model, we showed that the species can be involved in different metabolic strategies, depending on the scarcity of resources and on their biomasses, and that alternate steady states exist. We then extended our method to larger-scale metabolic models and predicted the minimal interactions in a community of two amino acid auxotrophic <jats:italic>E. coli<\/jats:italic> strains. Overall, our approach proves promising for better identifying community interactions, for example, in the gut microbiome.<\/jats:p>","DOI":"10.1007\/978-3-032-01436-8_19","type":"book-chapter","created":{"date-parts":[[2025,8,18]],"date-time":"2025-08-18T03:25:26Z","timestamp":1755487526000},"page":"356-369","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Minimal Metabolic Exchanges for\u00a0Microbial Communities in\u00a0a Chemostat at\u00a0Steady State"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-4104-4167","authenticated-orcid":false,"given":"Alix","family":"Moawad","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1145-891X","authenticated-orcid":false,"given":"J\u00f6rg","family":"Stelling","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,8,19]]},"reference":[{"issue":"2","key":"19_CR1","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1016\/s0025-5564(99)00006-1","volume":"158","author":"M Ballyk","year":"1999","unstructured":"Ballyk, M., Smith, H.: A model of microbial growth in a plug flow reactor with wall attachment. Math. Biosci. 158(2), 95\u2013126 (1999). https:\/\/doi.org\/10.1016\/s0025-5564(99)00006-1","journal-title":"Math. Biosci."},{"issue":"1","key":"19_CR2","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1016\/j.jbiotec.2011.10.001","volume":"157","author":"HC Bernstein","year":"2012","unstructured":"Bernstein, H.C., Paulson, S.D., Carlson, R.P.: Synthetic escherichia coli consortia engineered for syntrophy demonstrate enhanced biomass productivity. J. Biotechnol. 157(1), 159\u2013166 (2012). https:\/\/doi.org\/10.1016\/j.jbiotec.2011.10.001","journal-title":"J. Biotechnol."},{"issue":"2","key":"19_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/nmicrobiol.2016.215","volume":"2","author":"S Brugiroux","year":"2016","unstructured":"Brugiroux, S., et al.: Genome-guided design of a defined mouse microbiota that confers colonization resistance against salmonella enterica serovar typhimurium. Nat. Microbiol. 2(2), 1\u201312 (2016)","journal-title":"Nat. Microbiol."},{"issue":"24","key":"19_CR4","doi-asserted-by":"publisher","first-page":"5649","DOI":"10.1093\/bioinformatics\/btaa1014","volume":"36","author":"J Cai","year":"2021","unstructured":"Cai, J., Tan, T., Chan, S.H.J.: Predicting nash equilibria for microbial metabolic interactions. Bioinformatics 36(24), 5649\u20135655 (2021). https:\/\/doi.org\/10.1093\/bioinformatics\/btaa1014","journal-title":"Bioinformatics"},{"issue":"83","key":"19_CR5","first-page":"1","volume":"17","author":"S Diamond","year":"2016","unstructured":"Diamond, S., Boyd, S.: Cvxpy: a python-embedded modeling language for convex optimization. J. Mach. Learn. Res. 17(83), 1\u20135 (2016)","journal-title":"J. Mach. Learn. Res."},{"issue":"5","key":"19_CR6","doi-asserted-by":"publisher","first-page":"1213","DOI":"10.2307\/1936839","volume":"61","author":"D Dykhuizen","year":"1980","unstructured":"Dykhuizen, D., Davies, M.: An experimental model: Bacterial specialists and generalists competing in chemostats. Ecology 61(5), 1213\u20131227 (1980)","journal-title":"Ecology"},{"key":"19_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/1752-0509-7-74","volume":"7","author":"A Ebrahim","year":"2013","unstructured":"Ebrahim, A., Lerman, J.A., Palsson, B.O., Hyduke, D.R.: Cobrapy: constraints-based reconstruction and analysis for python. BMC Syst. Biol. 7, 1\u20136 (2013)","journal-title":"BMC Syst. Biol."},{"key":"19_CR8","doi-asserted-by":"crossref","unstructured":"Flint, H.J.: Why gut microbes matter. Springer (2020)","DOI":"10.1007\/978-3-030-43246-1"},{"issue":"19","key":"19_CR9","doi-asserted-by":"publisher","first-page":"R1176","DOI":"10.1016\/j.cub.2020.08.007","volume":"30","author":"M Gralka","year":"2020","unstructured":"Gralka, M., Szabo, R., Stocker, R., Cordero, O.X.: Trophic interactions and the drivers of microbial community assembly. Curr. Biol. 30(19), R1176\u2013R1188 (2020)","journal-title":"Curr. Biol."},{"issue":"4","key":"19_CR10","doi-asserted-by":"publisher","first-page":"1104","DOI":"10.1016\/j.celrep.2014.03.070","volume":"7","author":"WR Harcombe","year":"2014","unstructured":"Harcombe, W.R., et al.: Metabolic resource allocation in individual microbes determines ecosystem interactions and spatial dynamics. Cell Rep. 7(4), 1104\u20131115 (2014)","journal-title":"Cell Rep."},{"issue":"8","key":"19_CR11","doi-asserted-by":"publisher","first-page":"3138","DOI":"10.1002\/bit.27837","volume":"118","author":"EE Kelly","year":"2021","unstructured":"Kelly, E.E., Fischer, A.M., Collins, C.H.: Drawing up a collaborative contract: Amino acid cross-feeding between interspecies bacterial pairs. Biotechnol. Bioeng. 118(8), 3138\u20133149 (2021). https:\/\/doi.org\/10.1002\/bit.27837","journal-title":"Biotechnol. Bioeng."},{"issue":"2","key":"19_CR12","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1111\/2041-210X.12873","volume":"9","author":"H Kettle","year":"2018","unstructured":"Kettle, H., Holtrop, G., Louis, P., Flint, H.J.: micropop: modelling microbial populations and communities in r. Methods Ecol. Evol. 9(2), 399\u2013409 (2018)","journal-title":"Methods Ecol. Evol."},{"issue":"D1","key":"19_CR13","doi-asserted-by":"publisher","first-page":"D515","DOI":"10.1093\/nar\/gkv1049","volume":"44","author":"ZA King","year":"2016","unstructured":"King, Z.A., et al.: Bigg models: a platform for integrating, standardizing and sharing genome-scale models. Nucleic Acids Res. 44(D1), D515\u2013D522 (2016)","journal-title":"Nucleic Acids Res."},{"issue":"11","key":"19_CR14","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1001002","volume":"6","author":"N Klitgord","year":"2010","unstructured":"Klitgord, N., Segr\u00e8, D.: Environments that induce synthetic microbial ecosystems. PLoS Comput. Biol. 6(11), e1001002 (2010)","journal-title":"PLoS Comput. Biol."},{"issue":"8","key":"19_CR15","doi-asserted-by":"publisher","first-page":"1253","DOI":"10.1038\/s41564-019-0491-9","volume":"4","author":"M Kumar","year":"2019","unstructured":"Kumar, M., Ji, B., Zengler, K., Nielsen, J.: Modelling approaches for studying the microbiome. Nat. Microbiol. 4(8), 1253\u20131267 (2019)","journal-title":"Nat. Microbiol."},{"issue":"2\u20137","key":"19_CR16","doi-asserted-by":"publisher","first-page":"711","DOI":"10.1016\/s0098-1354(00)00323-9","volume":"24","author":"S Lee","year":"2000","unstructured":"Lee, S., Phalakornkule, C., Domach, M.M., Grossmann, I.E.: Recursive milp model for finding all the alternate optima in lp models for metabolic networks. Comput. Chem. Eng. 24(2\u20137), 711\u2013716 (2000). https:\/\/doi.org\/10.1016\/s0098-1354(00)00323-9","journal-title":"Comput. Chem. Eng."},{"issue":"3","key":"19_CR17","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, J.S., Doyle, F.J.: Dynamic flux balance analysis of diauxic growth in escherichia coli. Biophys. J . 83(3), 1331\u20131340 (2002)","journal-title":"Biophys. J ."},{"issue":"6","key":"19_CR18","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1016\/j.tibs.2023.02.001","volume":"48","author":"B Moiz","year":"2023","unstructured":"Moiz, B., Sriram, G., Clyne, A.M.: Interpreting metabolic complexity via isotope-assisted metabolic flux analysis. Trends Biochem. Sci. 48(6), 553\u2013567 (2023). https:\/\/doi.org\/10.1016\/j.tibs.2023.02.001","journal-title":"Trends Biochem. Sci."},{"issue":"3","key":"19_CR19","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1038\/nbt.1614","volume":"28","author":"JD Orth","year":"2010","unstructured":"Orth, J.D., Thiele, I., Palsson, B.\u00d8.: What is flux balance analysis? Nat. Biotechnol. 28(3), 245\u2013248 (2010)","journal-title":"Nat. Biotechnol."},{"issue":"32","key":"19_CR20","doi-asserted-by":"publisher","first-page":"15979","DOI":"10.1073\/pnas.1906172116","volume":"116","author":"P Piccardi","year":"2019","unstructured":"Piccardi, P., Vessman, B., Mitri, S.: Toxicity drives facilitation between 4 bacterial species. Proc. Natl. Acad. Sci. 116(32), 15979\u201315984 (2019)","journal-title":"Proc. Natl. Acad. Sci."},{"key":"19_CR21","doi-asserted-by":"publisher","DOI":"10.1109\/ccdc.2017.7978647","author":"X Shen","year":"2017","unstructured":"Shen, X., Diamond, S., Udell, M., Gu, Y., Boyd, S.: Disciplined multi-convex programming (2017). https:\/\/doi.org\/10.1109\/ccdc.2017.7978647","journal-title":"Disciplined multi-convex programming"},{"issue":"2","key":"19_CR22","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., et al.: Quantifying diet-induced metabolic changes of the human gut microbiome. Cell Metab. 22(2), 320\u2013331 (2015)","journal-title":"Cell Metab."},{"issue":"12","key":"19_CR23","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1003388","volume":"9","author":"RR Stein","year":"2013","unstructured":"Stein, R.R., et al.: Ecological modeling from time-series inference: insight into dynamics and stability of intestinal microbiota. PLoS Comput. Biol. 9(12), e1003388 (2013)","journal-title":"PLoS Comput. Biol."},{"issue":"5","key":"19_CR24","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1109\/jproc.2022.3158396","volume":"110","author":"A Theorell","year":"2022","unstructured":"Theorell, A., Stelling, J.: Metabolic networks, microbial consortia, and analogies to smart grids. Proc. IEEE 110(5), 541\u2013556 (2022). https:\/\/doi.org\/10.1109\/jproc.2022.3158396","journal-title":"Proc. IEEE"},{"issue":"Suppl 1","key":"19_CR25","doi-asserted-by":"publisher","first-page":"262","DOI":"10.1186\/s12859-023-05325-w","volume":"24","author":"A Theorell","year":"2023","unstructured":"Theorell, A., Stelling, J.: Assumptions on decision making and environment can yield multiple steady states in microbial community models. BMC Bioinform. 24(Suppl 1), 262 (2023)","journal-title":"BMC Bioinform."},{"issue":"1","key":"19_CR26","doi-asserted-by":"publisher","first-page":"4780","DOI":"10.1038\/s41467-023-40372-0","volume":"14","author":"AS Weiss","year":"2023","unstructured":"Weiss, A.S., Niedermeier, L.S., von Strempel, A., Burrichter, A.G., Ring, D., Meng, C., Kleigrewe, K., Lincetto, C., H\u00fcbner, J., Stecher, B.: Nutritional and host environments determine community ecology and keystone species in a synthetic gut bacterial community. Nat. Commun. 14(1), 4780 (2023)","journal-title":"Nat. Commun."},{"issue":"11","key":"19_CR27","doi-asserted-by":"publisher","first-page":"2557","DOI":"10.1038\/ismej.2016.45","volume":"10","author":"S Widder","year":"2016","unstructured":"Widder, S., et al.: Challenges in microbial ecology: building predictive understanding of community function and dynamics. ISME J. 10(11), 2557\u20132568 (2016)","journal-title":"ISME J."},{"issue":"1","key":"19_CR28","doi-asserted-by":"publisher","first-page":"407","DOI":"10.1038\/msb.2010.66","volume":"6","author":"EH Wintermute","year":"2010","unstructured":"Wintermute, E.H., Silver, P.A.: Emergent cooperation in microbial metabolism. Mol. Syst. Biol. 6(1), 407 (2010)","journal-title":"Mol. Syst. Biol."},{"issue":"2","key":"19_CR29","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1002363","volume":"8","author":"AR Zomorrodi","year":"2012","unstructured":"Zomorrodi, A.R., Maranas, C.D.: Optcom: a multi-level optimization framework for the metabolic modeling and analysis of microbial communities. PLoS Comput. Biol. 8(2), e1002363 (2012)","journal-title":"PLoS Comput. Biol."}],"container-title":["Lecture Notes in Computer Science","Computational Methods in Systems Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-01436-8_19","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,9]],"date-time":"2025-09-09T15:14:40Z","timestamp":1757430880000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-01436-8_19"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,19]]},"ISBN":["9783032014351","9783032014368"],"references-count":29,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-01436-8_19","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2025,8,19]]},"assertion":[{"value":"19 August 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"The authors have no competing interests to declare that\u00a0are relevant to the content of this article.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Disclosure of Interests"}},{"value":"CMSB","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Computational Methods in Systems Biology","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Lyon","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"France","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"10 September 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"12 September 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"23","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"cmsb2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/cmsb2025.sciencesconf.org\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}