{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T18:22:37Z","timestamp":1772821357651,"version":"3.50.1"},"reference-count":45,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,9,6]],"date-time":"2023-09-06T00:00:00Z","timestamp":1693958400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004504","name":"Research Council of Lithuania (LMTLT)","doi-asserted-by":"publisher","award":["01.2.2-LMT-K-718-03-0039"],"award-info":[{"award-number":["01.2.2-LMT-K-718-03-0039"]}],"id":[{"id":"10.13039\/501100004504","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Accurate estimations of the concentrations of soluble compounds are crucial for optimizing bioprocesses involving Escherichia coli (E. coli). This study proposes a hybrid model structure that leverages off-gas analysis data and physiological parameters, including the average biomass age and specific growth rate, to estimate soluble compounds such as acetate and glutamate in fed-batch cultivations We used a hybrid recurrent neural network to establish the relationships between these parameters. To enhance the precision of the estimates, the model incorporates ensemble averaging and information gain. Ensemble averaging combines varying model inputs, leading to more robust representations of the underlying dynamics in E. coli bioprocesses. Our hybrid model estimates acetates with 1% and 8% system precision using data from the first site and the second site at GSK plc, respectively. Using the data from the second site, the precision of the approach for other solutes was as fallows: isoleucine \u22128%, lactate and glutamate \u22129%, and a 13% error for glutamine., These results, demonstrate its practical potential.<\/jats:p>","DOI":"10.3390\/e25091302","type":"journal-article","created":{"date-parts":[[2023,9,6]],"date-time":"2023-09-06T10:07:37Z","timestamp":1693994857000},"page":"1302","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["An Approach for the Estimation of Concentrations of Soluble Compounds in E. coli Bioprocesses"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6205-8908","authenticated-orcid":false,"given":"Deividas","family":"Masaitis","sequence":"first","affiliation":[{"name":"Department of Automation, Kaunas University of Technology, LT-51367 Kaunas, Lithuania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8095-890X","authenticated-orcid":false,"given":"Renaldas","family":"Urniezius","sequence":"additional","affiliation":[{"name":"Department of Automation, Kaunas University of Technology, LT-51367 Kaunas, Lithuania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rimvydas","family":"Simutis","sequence":"additional","affiliation":[{"name":"Department of Automation, Kaunas University of Technology, LT-51367 Kaunas, Lithuania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vygandas","family":"Vaitkus","sequence":"additional","affiliation":[{"name":"Department of Automation, Kaunas University of Technology, LT-51367 Kaunas, Lithuania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mindaugas","family":"Matukaitis","sequence":"additional","affiliation":[{"name":"Department of Automation, Kaunas University of Technology, LT-51367 Kaunas, Lithuania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Benas","family":"Kemesis","sequence":"additional","affiliation":[{"name":"Department of Automation, Kaunas University of Technology, LT-51367 Kaunas, Lithuania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5472-2776","authenticated-orcid":false,"given":"Vytautas","family":"Galvanauskas","sequence":"additional","affiliation":[{"name":"Department of Automation, Kaunas University of Technology, LT-51367 Kaunas, Lithuania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Benas","family":"Sinkevicius","sequence":"additional","affiliation":[{"name":"Department of Automation, Kaunas University of Technology, LT-51367 Kaunas, Lithuania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"29","DOI":"10.4137\/MBI.S10878","article-title":"Role of Escherichia coli in Biofuel Production","volume":"9","author":"Koppolu","year":"2016","journal-title":"Microbiol. Insights"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"953","DOI":"10.4014\/jmb.1412.12079","article-title":"Production of Biopharmaceuticals in E. coli: Current Scenario and Future Perspectives","volume":"25","author":"Baeshen","year":"2015","journal-title":"J. Microbiol. Biotechnol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1007\/s00253-010-2970-z","article-title":"Metabolic engineering of Escherichia coli for biotechnological production of high-value organic acids and alcohols","volume":"89","author":"Yu","year":"2011","journal-title":"Appl. Microbiol. Biotechnol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1080\/07388551.2017.1312271","article-title":"On-line soft sensing in upstream bioprocessing","volume":"38","author":"Randek","year":"2018","journal-title":"Crit. Rev. Biotechnol."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Rathore, A.S., Mishra, S., Nikita, S., and Priyanka, P. (2021). Bioprocess Control: Current Progress and Future Perspectives. Life, 11.","DOI":"10.3390\/life11060557"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3724","DOI":"10.1128\/aem.60.10.3724-3731.1994","article-title":"Stoichiometric flux balance models quantitatively predict growth and metabolic by-product secretion in wild-type Escherichia coli W3110","volume":"60","author":"Varma","year":"1994","journal-title":"Appl. Environ. Microbiol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.bej.2017.05.013","article-title":"Modelling overflow metabolism in Escherichia coli by acetate cycling","volume":"125","author":"Anane","year":"2017","journal-title":"Biochem. Eng. J."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1023\/A:1008887514011","article-title":"Model based calculation of substrate\/inducer feed-rate profiles in fed-batch processes for recombinant protein production","volume":"13","author":"Levisauskas","year":"1999","journal-title":"Biotechnol. Tech."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"709","DOI":"10.1016\/S0967-0661(01)00020-X","article-title":"Probing control of fed-batch cultivations: Analysis and tuning","volume":"9","author":"Hagander","year":"2001","journal-title":"Control. Eng. Pract."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1046","DOI":"10.3182\/20100901-3-IT-2016.00224","article-title":"Nonlinear model predictive control of fed-batch cultures of E. coli: Performance and robustness analysis","volume":"43","author":"Santos","year":"2010","journal-title":"IFAC Proc. Vol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1002\/bit.10645","article-title":"Metabolic load of recombinant protein production: Inhibition of cellular capacities for glucose uptake and respiration after induction of a heterologous gene in Escherichia coli","volume":"83","author":"Neubauer","year":"2003","journal-title":"Biotechnol. Bioeng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1007\/11529798_8","article-title":"Bioprocess State Estimation: Some Classical and Less Classical Approaches","volume":"Volume 322","author":"Meurer","year":"2005","journal-title":"Control and Observer Design for Nonlinear Finite and Infinite Dimensional Systems"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"516","DOI":"10.1002\/jctb.5798","article-title":"Modelling concentration gradients in fed-batch cultivations of E. coli\u2014Towards the flexible design of scale-down experiments: Modelling concentration gradients in fed-batch","volume":"94","author":"Anane","year":"2019","journal-title":"J. Chem. Technol. Biotechnol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"108345","DOI":"10.1016\/j.bej.2022.108345","article-title":"Event driven modeling for the accurate identification of metabolic switches in fed-batch culture of S. cerevisiae","volume":"180","author":"Jouned","year":"2022","journal-title":"Biochem. Eng. J."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1081","DOI":"10.1016\/j.ifacol.2015.09.112","article-title":"An Observer-based Robust Control Strategy for Overflow Metabolism Cultures in Fed-Batch Bioreactors","volume":"48","author":"Pimentel","year":"2015","journal-title":"IFAC-PapersOnLine"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"e00640","DOI":"10.1016\/j.btre.2021.e00640","article-title":"Generic and specific recurrent neural network models: Applications for large and small scale biopharmaceutical upstream processes","volume":"31","author":"Smiatek","year":"2021","journal-title":"Biotechnol. Rep."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2494","DOI":"10.1002\/bit.28405","article-title":"Data-driven prediction models for forecasting multistep ahead profiles of mammalian cell culture toward bioprocess digital twins","volume":"120","author":"Park","year":"2023","journal-title":"Biotechnol. Bioeng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"564","DOI":"10.1007\/s002530051433","article-title":"Glucose overflow metabolism and mixed-acid fermentation in aerobic large-scale fed-batch processes with Escherichia coli","volume":"51","author":"Xu","year":"1999","journal-title":"Appl. Microbiol. Biotechnol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1002\/bit.1054","article-title":"Avoiding acetate accumulation in Escherichia coli cultures using feedback control of glucose feeding: Avoiding Acetate Accumulation in E. coli Cultures","volume":"73","author":"Hagander","year":"2001","journal-title":"Biotechnol. Bioeng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.jbiotec.2010.02.023","article-title":"Evaluation of software sensors for on-line estimation of culture conditions in an Escherichia coli cultivation expressing a recombinant protein","volume":"147","author":"Warth","year":"2010","journal-title":"J. Biotechnol."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.jprocont.2012.09.004","article-title":"Experimental validation of an Extended Kalman Filter estimating acetate concentration in E. coli cultures","volume":"23","author":"Dewasme","year":"2013","journal-title":"J. Process Control"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/j.jprocont.2021.06.006","article-title":"A robust hybrid observer for monitoring high-cell density cultures exhibiting overflow metabolism","volume":"104","author":"Saa","year":"2021","journal-title":"J. Process Control"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"S369","DOI":"10.1016\/S0098-1354(09)80044-6","article-title":"Comparison of feed-forward and recurrent neural networks for bioprocess state estimation","volume":"16","author":"Karim","year":"1992","journal-title":"Comput. Chem. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1002\/bit.10226","article-title":"Monitoring of complex industrial bioprocesses for metabolite concentrations using modern spectroscopies and machine learning: Application to gibberellic acid production","volume":"78","author":"McGovern","year":"2002","journal-title":"Biotechnol. Bioeng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"143","DOI":"10.3182\/20060705-3-FR-2907.00026","article-title":"Monitoring and Control of a Bioprocess for Malaria Vaccine Production","volume":"39","author":"Hulhoven","year":"2006","journal-title":"IFAC Proc. Vol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1007\/s00449-004-0385-x","article-title":"Hybrid process models for process optimisation, monitoring and control","volume":"26","author":"Galvanauskas","year":"2004","journal-title":"Bioprocess Biosyst. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"578","DOI":"10.1002\/btpr.143","article-title":"Data reconciliation of concentration estimates from mid-infrared and dielectric spectral measurements for improved on-line monitoring of bioprocesses","volume":"25","author":"Dabros","year":"2009","journal-title":"Biotechnol. Prog."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Matukaitis, M., Masaitis, D., Urnie\u017eius, R., Zlatkus, L., and Vaitkus, V. (2022). Non-Invasive Estimation of Acetates Using Off-Gas Information for Fed-Batch E. coli Bioprocess. Eng. Proc., 19.","DOI":"10.3390\/ECP2022-12668"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1186\/s12934-019-1241-7","article-title":"Generic estimator of biomass concentration for Escherichia coli and Saccharomyces cerevisiae fed-batch cultures based on cumulative oxygen consumption rate","volume":"18","author":"Urniezius","year":"2019","journal-title":"Microb. Cell Fact."},{"key":"ref_30","unstructured":"NineSigma (2023, July 25). GSK Bio-Manufacturing Omics Data Chalange. Available online: https:\/\/ninesights.ninesigma.com\/apps\/IMT\/UploadedFiles\/00\/f_bd7b6e1b8526318cc5b6427d022807e4\/2._Challenge_and_Data_Summary_-_GSK_BioManufacturing_Omics_D.pdf?v=1624239394."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Maanan, S., Dumitrescu, B., and Giurc\u0103neanu, C.D. (2018). Maximum Entropy Expectation-Maximization Algorithm for Fitting Latent-Variable Graphical Models to Multivariate Time Series. Entropy, 20.","DOI":"10.3390\/e20010076"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"124121","DOI":"10.1016\/j.talanta.2022.124121","article-title":"Viable cell estimation of mammalian cells using off-gas-based oxygen uptake rate and aging-specific functional","volume":"254","author":"Survyla","year":"2023","journal-title":"Talanta"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Urniezius, R., Galvanauskas, V., Survyla, A., Simutis, R., and Levisauskas, D. (2018). From Physics to Bioengineering: Microbial Cultivation Process Design and Feeding Rate Control Based on Relative Entropy Using Nuisance Time. Entropy, 20.","DOI":"10.3390\/e20100779"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"15565","DOI":"10.3182\/20080706-5-KR-1001.02632","article-title":"Implementation of a Specific Rate Controller in a Fed-Batch E. coli Fermentation","volume":"41","author":"Rocha","year":"2008","journal-title":"IFAC Proc. Vol."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s00449-007-0163-7","article-title":"Control of cultivation processes for recombinant protein production: A review","volume":"31","author":"Gnoth","year":"2008","journal-title":"Bioprocess Biosyst. Eng."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Galvanauskas, V., Simutis, R., Levi\u0161auskas, D., and Urnie\u017eius, R. (2019). Practical Solutions for Specific Growth Rate Control Systems in Industrial Bioreactors. Processes, 7.","DOI":"10.3390\/pr7100693"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Urniezius, R., Kemesis, B., and Simutis, R. (2021). Bridging Offline Functional Model Carrying Aging-Specific Growth Rate Information and Recombinant Protein Expression: Entropic Extension of Akaike Information Criterion. Entropy, 23.","DOI":"10.3390\/e23081057"},{"key":"ref_38","first-page":"265","article-title":"Modeling the Specific Glucose Consumption Rate for the Recombinant E. coli Bioprocesses Based on Aging-Specific Growth Rate","volume":"93","author":"Arnas","year":"2022","journal-title":"Chem. Eng. Trans."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1016\/j.ijforecast.2020.06.008","article-title":"Recurrent Neural Networks for Time Series Forecasting: Current status and future directions","volume":"37","author":"Hewamalage","year":"2021","journal-title":"Int. J. Forecast."},{"key":"ref_40","unstructured":"Petneh\u00e1zi, G. (2019). Recurrent Neural Networks for Time Series Forecasting. arXiv."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1671","DOI":"10.1016\/j.sigpro.2011.03.015","article-title":"Variable selection in linear regression: Several approaches based on normalized maximum likelihood","volume":"91","author":"Razavi","year":"2011","journal-title":"Signal Process."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1007\/s12155-013-9375-7","article-title":"Comparative Assessment of the Artificial Neural Network and Response Surface Modelling Efficiencies for Biohydrogen Production on Sugar Cane Molasses","volume":"7","author":"Whiteman","year":"2014","journal-title":"BioEnergy Res."},{"key":"ref_43","unstructured":"Shannon, C.E. (2009). A Mathematical Theory of Communication, IEEE."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Ribeiro, M.T., Singh, S., and Guestrin, C. (2016). \u2018Why Should I Trust You?\u2019: Explaining the Predictions of Any Classifier. arXiv.","DOI":"10.1145\/2939672.2939778"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1002\/bit.27980","article-title":"A transfer learning approach for predictive modeling of bioprocesses using small data","volume":"119","author":"Rogers","year":"2022","journal-title":"Biotechnol. Bioeng."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/9\/1302\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:46:01Z","timestamp":1760129161000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/9\/1302"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,6]]},"references-count":45,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2023,9]]}},"alternative-id":["e25091302"],"URL":"https:\/\/doi.org\/10.3390\/e25091302","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,9,6]]}}}