Data-Efficient Hybrid Parameter Scaling for Accurate Microbial Bioreactor Scale-Up

Data-Efficient Hybrid Parameter Scaling for Accurate Microbial Bioreactor Scale-Up | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Data-Efficient Hybrid Parameter Scaling for Accurate Microbial Bioreactor Scale-Up Otabek Atabaev, Moulay Rachid Babaa This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8245520/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 13 You are reading this latest preprint version Abstract Accurately predicting microbial fermentation performance at industrial scale is challenging due to hydrodynamic and oxygen-transfer limitations, which disrupt geometric similarity and cause nonlinear changes in growth kinetics. In this study, sigmoidal growth curves from 10 L, 100 L, 4 m³, and 100 m³ lipase-production bioreactors were extracted from published data and fitted using Logistic, Gompertz, and Baranyi-Robertson (BR) models. Kinetic parameters (C max , k or µ, t mid or λ) obtained from small-scale bioreactors (10 L and 100 L) were used to construct two minimal two-point relations: power-law and logarithmic. As these relations showed systematic overshoot and undershoot during extrapolation, a hybrid convex-weighting scheme was developed and calibrated at the 4 m³ pilot scale. When applied to the 100 m³ industrial dataset, the hybrid method significantly improved prediction accuracy compared to either scaling law alone, reducing RMSE by more than 60%. The Baranyi–Robertson model combined with hybrid scaling achieved the highest overall accuracy (RMSE = 2.651). Requiring only three experimental scales, this approach is computationally efficient, mechanistically interpretable, and suitable for industrial contexts where extensive pilot campaigns or computational fluid dynamics simulations are not feasible. The hybrid scaling framework thus offers a practical and data-efficient solution for reliable bioreactor scale-up. Bioprocess scale-up microbial kinetics hybrid scaling sigmoidal models industrial fermentation Full Text Additional Declarations Competing interest reported. The work described in this manuscript is covered by a patent application currently under review by [Intellectual Property Agency of the Republic of Uzbekistan, Ref: DT 202509951]. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 28 Jan, 2026 Reviews received at journal 24 Jan, 2026 Reviews received at journal 22 Jan, 2026 Reviews received at journal 16 Dec, 2025 Reviewers agreed at journal 08 Dec, 2025 Reviewers agreed at journal 07 Dec, 2025 Reviewers agreed at journal 06 Dec, 2025 Reviewers agreed at journal 06 Dec, 2025 Reviewers agreed at journal 04 Dec, 2025 Reviewers invited by journal 04 Dec, 2025 Editor assigned by journal 01 Dec, 2025 Submission checks completed at journal 01 Dec, 2025 First submitted to journal 30 Nov, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8245520","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":553860500,"identity":"e80cf44c-12b8-4ddb-8a4f-d766a4cf562a","order_by":0,"name":"Otabek Atabaev","email":"","orcid":"","institution":"New Uzbekistan University","correspondingAuthor":false,"prefix":"","firstName":"Otabek","middleName":"","lastName":"Atabaev","suffix":""},{"id":553860501,"identity":"be5eb8d6-fbb6-4775-aee0-96c47b88fe8a","order_by":1,"name":"Moulay Rachid 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In this study, sigmoidal growth curves from 10 L, 100 L, 4 m\u0026sup3;, and 100 m\u0026sup3; lipase-production bioreactors were extracted from published data and fitted using Logistic, Gompertz, and Baranyi-Robertson (BR) models. Kinetic parameters (C\u003csub\u003emax\u003c/sub\u003e, k or \u0026micro;, t\u003csub\u003emid\u003c/sub\u003e or λ) obtained from small-scale bioreactors (10 L and 100 L) were used to construct two minimal two-point relations: power-law and logarithmic. As these relations showed systematic overshoot and undershoot during extrapolation, a hybrid convex-weighting scheme was developed and calibrated at the 4 m\u0026sup3; pilot scale. When applied to the 100 m\u0026sup3; industrial dataset, the hybrid method significantly improved prediction accuracy compared to either scaling law alone, reducing RMSE by more than 60%. The Baranyi\u0026ndash;Robertson model combined with hybrid scaling achieved the highest overall accuracy (RMSE\u0026thinsp;=\u0026thinsp;2.651).\u003c/p\u003e\u003cp\u003eRequiring only three experimental scales, this approach is computationally efficient, mechanistically interpretable, and suitable for industrial contexts where extensive pilot campaigns or computational fluid dynamics simulations are not feasible. 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