{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T22:51:51Z","timestamp":1778712711378,"version":"3.51.4"},"reference-count":64,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,14]],"date-time":"2023-03-14T00:00:00Z","timestamp":1678752000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Yolocuauhtli Salazar by the TecNM project 14166.22-P: Modelizado de la producci\u00f3n y vida de anaquel de microorganismos en productos fermentados","award":["252465"],"award-info":[{"award-number":["252465"]}]},{"name":"Yolocuauhtli Salazar by the TecNM project 14166.22-P: Modelizado de la producci\u00f3n y vida de anaquel de microorganismos en productos fermentados","award":["10197-21-P"],"award-info":[{"award-number":["10197-21-P"]}]},{"name":"Paul A. Valle by the TecNM project: Gemelos digitales para el an\u00e1lisis y control de sistemas biol\u00f3gicos","award":["252465"],"award-info":[{"award-number":["252465"]}]},{"name":"Paul A. Valle by the TecNM project: Gemelos digitales para el an\u00e1lisis y control de sistemas biol\u00f3gicos","award":["10197-21-P"],"award-info":[{"award-number":["10197-21-P"]}]},{"name":"Nicol\u00e1s O. Soto-Cruz and Jes\u00fas B. P\u00e1ez-Lerma by the CONACyT project Ciencia B\u00e1sica","award":["252465"],"award-info":[{"award-number":["252465"]}]},{"name":"Nicol\u00e1s O. Soto-Cruz and Jes\u00fas B. P\u00e1ez-Lerma by the CONACyT project Ciencia B\u00e1sica","award":["10197-21-P"],"award-info":[{"award-number":["10197-21-P"]}]},{"name":"TecNM project","award":["252465"],"award-info":[{"award-number":["252465"]}]},{"name":"TecNM project","award":["10197-21-P"],"award-info":[{"award-number":["10197-21-P"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper presents results concerning mechanistic modeling to describe the dynamics and interactions between biomass growth, glucose consumption and ethanol production in batch culture fermentation by Kluyveromyces marxianus (K. marxianus). The mathematical model was formulated based on the biological assumptions underlying each variable and is given by a set of three coupled nonlinear first-order Ordinary Differential Equations. The model has ten parameters, and their values were fitted from the experimental data of 17 K. marxianus strains by means of a computational algorithm design in Matlab. The latter allowed us to determine that seven of these parameters share the same value among all the strains, while three parameters concerning biomass maximum growth rate, and ethanol production due to biomass and glucose had specific values for each strain. These values are presented with their corresponding standard error and 95% confidence interval. The goodness of fit of our system was evaluated both qualitatively by in silico experimentation and quantitative by means of the coefficient of determination and the Akaike Information Criterion. Results regarding the fitting capabilities were compared with the classic model given by the logistic, Pirt, and Luedeking\u2013Piret Equations. Further, nonlinear theories were applied to investigate local and global dynamics of the system, the Localization of Compact Invariant Sets Method was applied to determine the so-called localizing domain, i.e., lower and upper bounds for each variable; whilst Lyapunov\u2019s stability theories allowed to establish sufficient conditions to ensure asymptotic stability in the nonnegative octant, i.e., R+,03. Finally, the predictive ability of our mechanistic model was explored through several numerical simulations with expected results according to microbiology literature on batch fermentation.<\/jats:p>","DOI":"10.3390\/e25030497","type":"journal-article","created":{"date-parts":[[2023,3,14]],"date-time":"2023-03-14T03:04:46Z","timestamp":1678763086000},"page":"497","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Mechanistic Modelling of Biomass Growth, Glucose Consumption and Ethanol Production by Kluyveromyces marxianus in Batch Fermentation"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5563-2692","authenticated-orcid":false,"given":"Yolocuauhtli","family":"Salazar","sequence":"first","affiliation":[{"name":"Postgraduate Program in Engineering, Tecnol\u00f3gico Nacional de M\u00e9xico\/IT Durango, Blvd. Felipe Pescador 1830 Ote., Durango 34080, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6567-1065","authenticated-orcid":false,"given":"Paul A.","family":"Valle","sequence":"additional","affiliation":[{"name":"Postgraduate Program in Engineering Sciences, BioMath Research Group, Tecnol\u00f3gico Nacional de M\u00e9xico\/IT Tijuana, Blvd. Alberto Lim\u00f3n Padilla s\/n, Tijuana 22454, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4781-5138","authenticated-orcid":false,"given":"Emmanuel","family":"Rodr\u00edguez","sequence":"additional","affiliation":[{"name":"Postgraduate Program in Engineering Sciences, BioMath Research Group, Tecnol\u00f3gico Nacional de M\u00e9xico\/IT Tijuana, Blvd. Alberto Lim\u00f3n Padilla s\/n, Tijuana 22454, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5821-9943","authenticated-orcid":false,"given":"Nicol\u00e1s O.","family":"Soto-Cruz","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00edas Qu\u00edmica y Bioqu\u00edmica, Tecnol\u00f3gico Nacional de M\u00e9xico\/IT Durango, Blvd. Felipe Pescador 1830 Ote., Durango 34080, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4579-6431","authenticated-orcid":false,"given":"Jes\u00fas B.","family":"P\u00e1ez-Lerma","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00edas Qu\u00edmica y Bioqu\u00edmica, Tecnol\u00f3gico Nacional de M\u00e9xico\/IT Durango, Blvd. Felipe Pescador 1830 Ote., Durango 34080, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7288-6371","authenticated-orcid":false,"given":"Francisco J.","family":"Reyes-S\u00e1nchez","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00edas Qu\u00edmica y Bioqu\u00edmica, Tecnol\u00f3gico Nacional de M\u00e9xico\/IT Durango, Blvd. Felipe Pescador 1830 Ote., Durango 34080, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,14]]},"reference":[{"key":"ref_1","unstructured":"Zamora, F. 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