{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T12:12:50Z","timestamp":1778587970893,"version":"3.51.4"},"reference-count":39,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,6]],"date-time":"2020-02-06T00:00:00Z","timestamp":1580947200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100014440","name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","doi-asserted-by":"publisher","award":["MTM2017-84446-C2-1-R"],"award-info":[{"award-number":["MTM2017-84446-C2-1-R"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014440","name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","doi-asserted-by":"publisher","award":["PRX18\/00112"],"award-info":[{"award-number":["PRX18\/00112"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The dynamics of cellular aggregates is driven by the interplay of mechanochemical processes and cellular activity. Although deterministic models may capture mechanical features, local chemical fluctuations trigger random cell responses, which determine the overall evolution. Incorporating stochastic cellular behavior in macroscopic models of biological media is a challenging task. Herein, we propose hybrid models for bacterial biofilm growth, which couple a two phase solid\/fluid mixture description of mechanical and chemical fields with a dynamic energy budget-based cellular automata treatment of bacterial activity. Thin film and plate approximations for the relevant interfaces allow us to obtain numerical solutions exhibiting behaviors observed in experiments, such as accelerated spread due to water intake from the environment, wrinkle formation, undulated contour development, and the appearance of inhomogeneous distributions of differentiated bacteria performing varied tasks.<\/jats:p>","DOI":"10.3390\/e22020188","type":"journal-article","created":{"date-parts":[[2020,2,7]],"date-time":"2020-02-07T03:13:27Z","timestamp":1581045207000},"page":"188","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Incorporating Cellular Stochasticity in Solid\u2013Fluid Mixture Biofilm Models"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8623-6521","authenticated-orcid":false,"given":"Ana","family":"Carpio","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada, Universidad Complutense, 28040 Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8389-0907","authenticated-orcid":false,"given":"Elena","family":"Cebri\u00e1n","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas y Computaci\u00f3n, Universidad de Burgos, 09001 Burgos, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1038\/nrmicro2415","article-title":"The biofilm matrix","volume":"8","author":"Flemming","year":"2010","journal-title":"Nat. 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