{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T11:25:51Z","timestamp":1787225151730,"version":"build-2736575974"},"reference-count":33,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Math."],"published-print":{"date-parts":[[2023,2,28]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>Motivated by recent laboratory experiments, we study microbial populations with light-inducible genetic differentiation that generates a two-species microbial consortium relevant for bioproduction. First, we derive a hierarchy of models describing the evolution of the microbial populations, each with decreasing complexity. This sequential order reduction reveals the connections between several popular classes of models used in this context. Second, we demonstrate the analytical insight the order reduction provides by studying the optimal control of such a reduced-order system of nonlinear ordinary differential equations. Appealing to Pontryagin\u2019s maximum principle, we find different optimal control structures within different regions of the parameter space. Explicit solutions are obtained in a subset of parameter space, while, for the remainder of parameter space, closed-form solutions are obtained that depend on a scalar value that solves a particular transcendental equation. We show that a unique solution of the scalar equation exists and lies in a known compact interval, making its numerical approximation particularly easy. The analytical results are verified against direct numerical calculations.<\/jats:p>","DOI":"10.1137\/22m1476113","type":"journal-article","created":{"date-parts":[[2023,2,13]],"date-time":"2023-02-13T14:26:57Z","timestamp":1676298417000},"page":"144-171","source":"Crossref","is-referenced-by-count":1,"title":["Modeling and Optimal Control of a Two-Species Bioproducing Microbial Consortium"],"prefix":"10.1137","volume":"83","author":[{"given":"Davin","family":"Lunz","sequence":"first","affiliation":[{"name":"Inria Paris, 75012 Paris, France, and Institut Pasteur, 75015 Paris, France."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J.","family":"Fr\u00e9d\u00e9ric Bonnans","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Paris-Saclay, CNRS, CentraleSup\u00e9lec, Inria, Laboratory of Signals and Systems, 91190, Gif-sur-Yvette, France."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,2,13]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-021-26129-7"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2114438119"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1007\/s12532-018-0139-4"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1038\/s41564-020-0686-0"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.tibtech.2008.05.004"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1810858115"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1007\/BF02124750"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1126\/science.1237435"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.2003734117"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(76)90041-3"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1021\/j100540a008"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1016\/0378-4371(92)90283-V"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.tim.2021.04.001"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1016\/j.cell.2009.12.001"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1137\/0318002"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.ymben.2019.03.002"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.2307\/j.ctvcm4g0s"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1137\/20M1332293"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1009214"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2022.108866"},{"key":"ref21","unstructured":"D. Lunz , \nJ. F. Bonnans , and \nJ. Ruess , Optimal Control of Bioproduction in the Presence of Population Heterogeneity, preprint, https:\/\/hal.inria.fr\/hal-03445175."},{"key":"ref22","doi-asserted-by":"crossref","first-page":"1193","DOI":"10.1038\/s41467-020-15056-8","volume":"11","author":"Miano A.","year":"2020","journal-title":"Nat. Commun."},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1002480"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.1507291113"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1016\/j.copbio.2020.10.001"},{"key":"ref26","doi-asserted-by":"crossref","unstructured":"D. Salzano , \nD. Fiore , and \nM. di Bernardo , Controlling Reversible Cell Differentiation for Labor Division in Microbial Consortia, preprint, arXiv:2021.08.03.454926, 2021.","DOI":"10.1101\/2021.08.03.454926"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1038\/nchembio.218"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1038\/s41598-018-35927-x"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2014.09.005"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-004-0559-y"},{"key":"ref31","doi-asserted-by":"crossref","unstructured":"E. Weill , \nV. Andr\u00e9ani , \nC. Aditya , \nP. Martinon , \nJ. Ruess , \nG. Batt , and \nF. Bonnans , Optimal control of an artificial microbial differentiation system for protein bioproduction, in Proceedings of the 18th European Control Conference (ECC), IEEE, Washington, DC, 2019, pp. 2663\u20132668, https:\/\/doi.org\/10.23919\/ECC.2019.8795858.","DOI":"10.23919\/ECC.2019.8795858"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pcbi.1009381"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1038\/nbt.3095"}],"container-title":["SIAM Journal on Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/22M1476113","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T10:53:19Z","timestamp":1787223199000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/22M1476113"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,13]]},"references-count":33,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,2,28]]}},"alternative-id":["10.1137\/22M1476113"],"URL":"https:\/\/doi.org\/10.1137\/22m1476113","relation":{},"ISSN":["0036-1399","1095-712X"],"issn-type":[{"value":"0036-1399","type":"print"},{"value":"1095-712X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,13]]}}}