# Hybrid Modeling for On-Line Fermentation Optimization and Scale-Up: A Review

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Mechanistic Modeling

## 3. Data-Driven Modeling

Microorganism | Type of Model | Studied Parameter | Main Findings | Reference |
---|---|---|---|---|

Bacillus megaterium | PCA | Fault detection | On-line fault detection providing decision-making support | [39] |

Escherichia coli | Neural networks | $\mu $-stat feeding control | Increased cell growth and target protein production | [35] |

Reinforcement learning | Feed rate control | Product formation optimization in a simulated chemostat with co-cultures | [43] | |

Hybridoma cells | Maximum-likelihood PCA | Macroscopic reactions | Determine minimum number of reactions and parameters for process model | [40] |

Maximum-likelihood NMD | Prediction of relevant parameters | Identified model with good prediction results | [41] | |

Penicillium chrysogenum | Reinforcement learning | Feed rate control | Optimized yield and productivity of in silico penicillin production plant | [44] |

Reinforcement learning | Feed rate control | Overperformed other feed control strategies for a digital industrial penicillin plant | [45] | |

Saccharomyces cerevisiae | Neural networks | Temperature model predictive controller | More robust temperature control, compared to linear model predictive controller | [36] |

Neural networks | Monitoring of relevant parameters | Prediction results with on-line fluorescence spectroscopy and a process model were equivalent to those of the model where offline calibration data were used | [46] | |

Gaussian process regression | Manipulation of cycle time | Increased productivity from each batch to the following one | [38] | |

Streptomycetes sp. | PLS | API production | Identification of process variables responsible for variation in API production | [47] |

Not disclosed | PLS | Yield prediction | Similar performance to more complex genetic algorithm | [37] |

## 4. Hybrid Modeling

#### Applications in Fermentation Processes

## 5. Model Aided Scale-Up

#### 5.1. Use of CFD-Coupled Kinetic Models

#### 5.2. Use of Hybrid Modelling in Scale-Up

## 6. Conclusions

- Both mechanistic and data-driven models continue to be relevant strategies in the development of fermentation processes, both with different specific use cases. Data-driven models are particularly relevant for online process models and are frequently used in the development of soft-sensors. On the other hand, the interpretability and extrapolation capabilities of mechanistic models make them suitable for process optimization and understanding the impact of different parameters on the cell’s metabolic responses.
- Hybrid modeling is a rapidly evolving field and offers substantial benefits in the context of fermentation processes. It enables the exploitation of the strengths of both types of aforementioned models while combatting their weaknesses, ideally leading to a more agile development process.
- The level of mechanistic knowledge included in hybrid models must be carefully selected to avoid overparametrizing or biasing the model. If performed adequately, the result will be a more accurate and extrapolative model, with lower data requirements than a data-driven counterpart.
- Most use cases still focus on the prediction and monitoring of relevant process variables, but they present great potential for model predictive control applications. Furthermore, it appears to be an interesting tool for aiding in process upscaling due to good extrapolation capabilities across scales.
- The technology readiness level of hybrid modeling is still considered low. Some challenges, like the expansion of models as more data becomes available or the complexity in parameter estimation, need to be overcome for their successful implementation as relevant tools for industrial bioprocesses.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

ANN | artificial neural networks |

API | active pharmaceutical ingredient |

CFD | computational fluid dynamics |

CHO | Chinese hamster ovary |

CQA | critical quality attribute |

DOE | design of experiments |

NN | neural networks |

ODE | ordinary differential equation |

PCA | principal component analysis |

PFR | plug flow reactor |

PLS | partial least squares |

STR | stirred tank reactor |

## References

- Behera, S.S.; Ray, R.C.; Das, U.; Panda, S.K.; Saranraj, P. Microorganisms in Fermentation. In Essentials in Fermentation Technology; Berenjian, A., Ed.; Springer International Publishing: Cham, Switzerland, 2019; pp. 1–39. [Google Scholar] [CrossRef]
- González-Figueredo, C.; Flores-Estrella, R.A.; Rojas-Rejón, O.A. Fermentation: Metabolism, kinetic models, and bioprocessing. In Current Topics in Biochemical Engineering; IntechOpen: Rijeka, Croatia, 2018; Volume 1. [Google Scholar]
- Nadal-Rey, G.; McClure, D.D.; Kavanagh, J.M.; Cornelissen, S.; Fletcher, D.F.; Gernaey, K.V. Understanding gradients in industrial bioreactors. Biotechnol. Adv.
**2021**, 46, 107660. [Google Scholar] [CrossRef] [PubMed] - Pigou, M.; Morchain, J. Investigating the interactions between physical and biological heterogeneities in bioreactors using compartment, population balance and metabolic models. Chem. Eng. Sci.
**2015**, 126, 267–282. [Google Scholar] [CrossRef] - Gargalo, C.L.; de las Heras, S.C.; Jones, M.N.; Udugama, I.; Mansouri, S.S.; Krühne, U.; Gernaey, K.V. Towards the Development of Digital Twins for the Bio-manufacturing Industry. In Digital Twins: Tools and Concepts for Smart Biomanufacturing; Herwig, C., Pörtner, R., Möller, J., Eds.; Springer International Publishing: Cham, Switzerland, 2021; pp. 1–34. [Google Scholar] [CrossRef]
- Becker, T.; Enders, T.; Delgado, A. Dynamic neural networks as a tool for the online optimization of industrial fermentation. Bioprocess Biosyst. Eng.
**2002**, 24, 347–354. [Google Scholar] [CrossRef] - Lourenço, N.D.; Lopes, J.A.; Almeida, C.F.; Sarraguça, M.C.; Pinheiro, H.M. Bioreactor monitoring with spectroscopy and Chemometrics: A Review. Anal. Bioanal. Chem.
**2012**, 404, 1211–1237. [Google Scholar] [CrossRef] [PubMed] - Janoska, A.; Buijs, J.; van Gulik, W.M. Predicting the influence of combined oxygen and glucose gradients based on scale-down and modelling approaches for the scale-up of penicillin fermentations. Process Biochem.
**2023**, 124, 100–112. [Google Scholar] [CrossRef] - Mears, L.; Stocks, S.M.; Albaek, M.O.; Sin, G.; Gernaey, K.V. Mechanistic fermentation models for process design, monitoring, and Control. Trends Biotechnol.
**2017**, 35, 914–924. [Google Scholar] [CrossRef] [PubMed] - Gernaey, K.V.; Lantz, A.E.; Tufvesson, P.; Woodley, J.M.; Sin, G. Application of mechanistic models to fermentation and biocatalysis for next-generation processes. Trends Biotechnol.
**2010**, 28, 346–354. [Google Scholar] [CrossRef] [PubMed] - Tsopanoglou, A.; Jiménez del Val, I. Moving towards an era of hybrid modelling: Advantages and challenges of coupling mechanistic and data-driven models for upstream pharmaceutical bioprocesses. Curr. Opin. Chem. Eng.
**2021**, 32, 100691. [Google Scholar] [CrossRef] - von Stosch, M.; Oliveira, R.; Peres, J.; Feyo de Azevedo, S. Hybrid semi-parametric modeling in process systems engineering: Past, present and future. Comput. Chem. Eng.
**2014**, 60, 86–101. [Google Scholar] [CrossRef] - Narayanan, H.; Luna, M.; Sokolov, M.; Butté, A.; Morbidelli, M. Hybrid Models Based on Machine Learning and an Increasing Degree of Process Knowledge: Application to Cell Culture Processes. Ind. Eng. Chem. Res.
**2022**, 61, 8658–8672. [Google Scholar] [CrossRef] - Rogers, A.W.; Song, Z.; Ramon, F.V.; Jing, K.; Zhang, D. Investigating ‘greyness’ of hybrid model for bioprocess predictive modelling. Biochem. Eng. J.
**2023**, 190, 108761. [Google Scholar] [CrossRef] - Shah, P.; Sheriff, M.Z.; Bangi, M.S.F.; Kravaris, C.; Kwon, J.S.I.; Botre, C.; Hirota, J. Deep neural network-based hybrid modeling and experimental validation for an industry-scale fermentation process: Identification of time-varying dependencies among parameters. Chem. Eng. J.
**2022**, 441, 135643. [Google Scholar] [CrossRef] - Bangi, M.S.F.; Kao, K.; Kwon, J.S.I. Physics-informed neural networks for hybrid modeling of lab-scale batch fermentation for β-carotene production using Saccharomyces cerevisiae. Chem. Eng. Res. Des.
**2022**, 179, 415–423. [Google Scholar] [CrossRef] - Moser, A.; Appl, C.; Brüning, S.; Hass, V.C. Mechanistic Mathematical Models as a Basis for Digital Twins. In Digital Twins: Tools and Concepts for Smart Biomanufacturing; Springer: Berlin/Heidelberg, Germany, 2021. [Google Scholar] [CrossRef]
- Waldherr, S. Estimation methods for heterogeneous cell population models in systems biology. J. R. Soc. Interface
**2018**, 15, 20180530. [Google Scholar] [CrossRef] - Anane, E.; López C, D.C.; Neubauer, P.; Cruz Bournazou, M.N. Modelling overflow metabolism in Escherichia coli by acetate cycling. Biochem. Eng. J.
**2017**, 125, 23–30. [Google Scholar] [CrossRef] - Albaek, M.O.; Gernaey, K.V.; Hansen, M.S.; Stocks, S.M. Modeling enzyme production with Aspergillus oryzae in pilot scale vessels with different agitation, aeration, and agitator types. Biotechnol. Bioeng.
**2011**, 108, 1828–1840. [Google Scholar] [CrossRef] [PubMed] - Grisales Díaz, V.H.; Willis, M.J. Ethanol production using Zymomonas mobilis: Development of a kinetic model describing glucose and xylose co-fermentation. Biomass Bioenergy
**2019**, 123, 41–50. [Google Scholar] [CrossRef] - Du, Y.H.; Wang, M.Y.; Yang, L.H.; Tong, L.L.; Guo, D.S.; Ji, X.J. Optimization and Scale-Up of Fermentation Processes Driven by Models. Bioengineering
**2022**, 9, 473. [Google Scholar] [CrossRef] [PubMed] - Tang, W.; Deshmukh, A.T.; Haringa, C.; Wang, G.; van Gulik, W.; van Winden, W.; Reuss, M.; Heijnen, J.J.; Xia, J.; Chu, J.; et al. A 9-pool metabolic structured kinetic model describing days to seconds dynamics of growth and product formation by Penicillium chrysogenum. Biotechnol. Bioeng.
**2017**, 114, 1733–1743. [Google Scholar] [CrossRef] [PubMed] - Jahan, N.; Maeda, K.; Matsuoka, Y.; Sugimoto, Y.; Kurata, H. Development of an accurate kinetic model for the central carbon metabolism of Escherichia coli. Microb. Cell Factories
**2016**, 15, 112. [Google Scholar] [CrossRef] [PubMed] - Çelik, E.; Çalık, P.; Oliver, S.G. A structured kinetic model for recombinant protein production by Mut+ strain of Pichia pastoris. Chem. Eng. Sci.
**2009**, 64, 5028–5035. [Google Scholar] [CrossRef] - Haringa, C.; Tang, W.; Wang, G.; Deshmukh, A.T.; van Winden, W.A.; Chu, J.; van Gulik, W.M.; Heijnen, J.J.; Mudde, R.F.; Noorman, H.J. Computational fluid dynamics simulation of an industrial P. chrysogenum fermentation with a coupled 9-pool metabolic model: Towards rational scale-down and design optimization. Chem. Eng. Sci.
**2018**, 175, 12–24. [Google Scholar] [CrossRef] - Pan, S.; Chen, G.; Zeng, J.; Cao, X.; Zheng, X.; Zeng, W.; Liang, Z. Fibrinolytic enzyme production from low-cost substrates by marine Bacillus subtilis: Process optimization and kinetic modeling. Biochem. Eng. J.
**2019**, 141, 268–277. [Google Scholar] [CrossRef] - Xu, J.; Tang, P.; Yongky, A.; Drew, B.; Borys, M.C.; Liu, S.; Li, Z.J. Systematic development of temperature shift strategies for Chinese hamster ovary cells based on short duration cultures and kinetic modeling. mAbs
**2019**, 11, 191–204. [Google Scholar] [CrossRef] [PubMed] - Goldrick, S.; Ştefan, A.; Lovett, D.; Montague, G.; Lennox, B. The development of an industrial-scale fed-batch fermentation simulation. J. Biotechnol.
**2015**, 193, 70–82. [Google Scholar] [CrossRef] [PubMed] - Barrigon, J.M.; Valero, F.; Montesinos, J.L. A macrokinetic model-based comparative meta-analysis of recombinant protein production by Pichia pastoris under AOX1 promoter. Biotechnol. Bioeng.
**2015**, 112, 1132–1145. [Google Scholar] [CrossRef] [PubMed] - Germec, M.; Karhan, M.; Demirci, A.; Turhan, I. Kinetic modeling, sensitivity analysis, and techno-economic feasibility of ethanol fermentation from non-sterile carob extract-based media in Saccharomyces cerevisiae biofilm reactor under a repeated-batch fermentation process. Fuel
**2022**, 324, 124729. [Google Scholar] [CrossRef] - Mears, L.; Stocks, S.M.; Albaek, M.O.; Sin, G.; Gernaey, K.V. Application of a mechanistic model as a tool for on-line monitoring of pilot scale filamentous fungal fermentation processes—The importance of evaporation effects. Biotechnol. Bioeng.
**2017**, 114, 589–599. [Google Scholar] [CrossRef] [PubMed] - Alloghani, M.; Al-Jumeily, D.; Mustafina, J.; Hussain, A.; Aljaaf, A.J. A Systematic Review on Supervised and Unsupervised Machine Learning Algorithms for Data Science. In Supervised and Unsupervised Learning for Data Science; Springer: Berlin/Heidelberg, Germany, 2020. [Google Scholar] [CrossRef]
- Wiering, M.A.; Van Otterlo, M. Reinforcement learning. Adapt. Learn. Optim.
**2012**, 12, 739. [Google Scholar] - Tavasoli, T.; Arjmand, S.; Ranaei Siadat, S.O.; Shojaosadati, S.A.; Sahebghadam Lotfi, A. A robust feeding control strategy adjusted and optimized by a neural network for enhancing of alpha 1-antitrypsin production in Pichia pastoris. Biochem. Eng. J.
**2019**, 144, 18–27. [Google Scholar] [CrossRef] - Nagy, Z.K. Model based control of a yeast fermentation bioreactor using optimally designed artificial neural networks. Chem. Eng. J.
**2007**, 127, 95–109. [Google Scholar] [CrossRef] - Andersen, S.W.; Runger, G.C. Partitioned partial least squares regression with application to a batch fermentation process. J. Chemom.
**2011**, 25, 159–168. [Google Scholar] [CrossRef] - Barton, M.; Duran-Villalobos, C.A.; Lennox, B. Multivariate batch to batch optimisation of fermentation processes to improve productivity. J. Process. Control
**2021**, 108, 148–156. [Google Scholar] [CrossRef] - Nucci, E.R.; Cruz, A.J.; Giordano, R.C. Monitoring bioreactors using Principal Component Analysis: Production of penicillin G acylase as a case study. Bioprocess Biosyst. Eng.
**2009**, 33, 557–564. [Google Scholar] [CrossRef] [PubMed] - Dewasme, L.; Cote, F.; Filee, P.; Hantson, A.L.; Vande Wouwer, A. Dynamic modeling of hybridoma cell cultures using maximum likelihood principal component analysis. IFAC-PapersOnLine
**2017**, 50, 12143–12148. [Google Scholar] [CrossRef] - Pimentel, G.A.; Dewasme, L.; Wouwer, A.V. Data-driven Linear Predictor based on Maximum Likelihood Nonnegative Matrix Decomposition for Batch Cultures of Hybridoma Cells. IFAC-PapersOnLine
**2022**, 55, 903–908. [Google Scholar] [CrossRef] - Kaelbling, L.P.; Littman, M.L.; Moore, A.W. Reinforcement learning: A survey. J. Artif. Intell. Res.
**1996**, 4, 237–285. [Google Scholar] [CrossRef] - Treloar, N.J.; Fedorec, A.J.H.; Ingalls, B.; Barnes, C.P. Deep reinforcement learning for the control of microbial co-cultures in bioreactors. PLoS Comput. Biol.
**2020**, 16, e1007783. [Google Scholar] [CrossRef] [PubMed] - Kim, J.W.; Park, B.J.; Oh, T.H.; Lee, J.M. Model-based reinforcement learning and predictive control for two-stage optimal control of fed-batch bioreactor. Comput. Chem. Eng.
**2021**, 154, 107465. [Google Scholar] [CrossRef] - Oh, T.H.; Park, H.M.; Kim, J.W.; Lee, J.M. Integration of reinforcement learning and model predictive control to optimize semi-batch bioreactor. AIChE J.
**2022**, 68, e17658. [Google Scholar] [CrossRef] - Paquet-Durand, O.; Assawarajuwan, S.; Hitzmann, B. Artificial neural network for bioprocess monitoring based on fluorescence measurements: Training without offline measurements. Eng. Life Sci.
**2017**, 17, 874–880. [Google Scholar] [CrossRef] [PubMed] - Lopes, J.; Menezes, J.; Westerhuis, J.; Smilde, A. Multiblock PLS analysis of an industrial pharmaceutical process. Biotechnol. Bioeng.
**2002**, 80, 419–427. [Google Scholar] [CrossRef] [PubMed] - Schweidtmann, A.M.; Zhang, D.; von Stosch, M. A review and perspective on hybrid modeling methodologies. Digit. Chem. Eng.
**2024**, 10, 100136. [Google Scholar] [CrossRef] - von Stosch, M.; Hamelink, J.M.; Oliveira, R. Hybrid modeling as a QBD/PAT tool in process development: An industrial E. coli case study. Bioprocess Biosyst. Eng.
**2016**, 39, 773–784. [Google Scholar] [CrossRef] [PubMed] - Bayer, B.; Duerkop, M.; Striedner, G.; Sissolak, B. Model Transferability and Reduced Experimental Burden in Cell Culture Process Development Facilitated by Hybrid Modeling and Intensified Design of Experiments. Front. Bioeng. Biotechnol.
**2021**, 9, 740215. [Google Scholar] [CrossRef] [PubMed] - Brunner, V.; Siegl, M.; Geier, D.; Becker, T. Biomass soft sensor for a Pichia pastoris fed-batch process based on phase detection and hybrid modeling. Biotechnol. Bioeng.
**2020**, 117, 2749–2759. [Google Scholar] [CrossRef] [PubMed] - von Stosch, M.; Davy, S.; Francois, K.; Galvanauskas, V.; Hamelink, J.M.; Luebbert, A.; Mayer, M.; Oliveira, R.; O’Kennedy, R.; Rice, P.; et al. Hybrid modeling for quality by design and PAT-benefits and challenges of applications in biopharmaceutical industry. Biotechnol. J.
**2014**, 9, 719–726. [Google Scholar] [CrossRef] [PubMed] - von Stosch, M.; Oliveira, R.; Peres, J.; Feyo de Azevedo, S. A general hybrid semi-parametric process control framework. J. Process. Control.
**2012**, 22, 1171–1181. [Google Scholar] [CrossRef] - Psichogios, D.C.; Ungar, L.H. A hybrid neural network-first principles approach to process modeling. AIChE J.
**1992**, 38, 1499–1511. [Google Scholar] [CrossRef] - Cruz-Bournazou, M.N.; Narayanan, H.; Fagnani, A.; Butté, A. Hybrid Gaussian Process Models for continuous time series in bolus fed-batch cultures. IFAC-PapersOnLine
**2022**, 55, 204–209. [Google Scholar] [CrossRef] - Vega-Ramon, F.; Zhu, X.; Savage, T.R.; Petsagkourakis, P.; Jing, K.; Zhang, D. Kinetic and hybrid modeling for yeast astaxanthin production under uncertainty. Biotechnol. Bioeng.
**2021**, 118, 4854–4866. [Google Scholar] [CrossRef] [PubMed] - Read, J.; Bifet, A.; Pfahringer, B.; Holmes, G. Batch-Incremental versus Instance-Incremental Learning in Dynamic and Evolving Data. In Proceedings of the Advances in Intelligent Data Analysis XI, Helsinki, Finland, 25–27 October 2012; Springer: Berlin/Heidelberg, Germany, 2012; pp. 313–323. [Google Scholar]
- Rogers, A.W.; Cardenas, I.O.S.; Del Rio-Chanona, E.A.; Zhang, D. Investigating physics-informed neural networks for bioprocess hybrid model construction. Comput. Aided Chem. Eng.
**2023**, 52, 83–88. [Google Scholar] [CrossRef] - Rydal, T.; Frandsen, J.; Nadal-Rey, G.; Albæk, M.O.; Ramin, P. Bringing a scalable adaptive hybrid modeling framework closer to industrial use: Application on a multiscale fungal fermentation. Biotechnol. Bioeng.
**2024**, 121, 1609–1625. [Google Scholar] [CrossRef] [PubMed] - von Stosch, M.; Oliveria, R.; Peres, J.; de Azevedo, S.F. Hybrid modeling framework for process analytical technology: Application to Bordetella pertussis cultures. Biotechnol. Prog.
**2012**, 28, 284–291. [Google Scholar] [CrossRef] [PubMed] - Boareto, Á.J.M.; De Souza, M.B., Jr.; Valero, F.; Valdman, B. A hybrid neural model (HNM) for the on-line monitoring of lipase production by Candida rugosa. J. Chem. Technol. Biotechnol.
**2007**, 82, 319–327. [Google Scholar] [CrossRef] - Jenzsch, M.; Gnoth, S.; Kleinschmidt, M.; Simutis, R.; Lübbert, A. Improving the batch-to-batch reproducibility of microbial cultures during recombinant protein production by regulation of the total carbon dioxide production. J. Biotechnol.
**2007**, 128, 858–867. [Google Scholar] [CrossRef] [PubMed] - Dors, M.; Simutis, R.; Lübbert, A. Hybrid Process Modeling for Advanced Process State Estimation, Prediction, and Control Exemplified in a Production-Scale Mammalian Cell Culture. In Biosensor and Chemical Sensor Technology; American Chemical Society: Washington, DC, USA, 1996. [Google Scholar] [CrossRef]
- Pinto, J.; Mestre, M.; Ramos, J.; Costa, R.S.; Striedner, G.; Oliveira, R. A general deep hybrid model for bioreactor systems: Combining first principles with deep neural networks. Comput. Chem. Eng.
**2022**, 165, 107952. [Google Scholar] [CrossRef] - Cabaneros Lopez, P.; Udugama, I.A.; Thomsen, S.T.; Roslander, C.; Junicke, H.; Iglesias, M.M.; Gernaey, K.V. Transforming data to information: A parallel hybrid model for real-time state estimation in lignocellulosic ethanol fermentation. Biotechnol. Bioeng.
**2021**, 118, 579–591. [Google Scholar] [CrossRef] [PubMed] - Schmidt, F.R. Optimization and scale up of industrial fermentation processes. Appl. Microbiol. Biotechnol.
**2005**, 68, 425–435. [Google Scholar] [CrossRef] [PubMed] - Formenti, L.R.; Nørregaard, A.; Bolic, A.; Hernandez, D.Q.; Hagemann, T.; Heins, A.L.; Larsson, H.; Mears, L.; Mauricio-Iglesias, M.; Krühne, U.; et al. Challenges in industrial fermentation technology research. Biotechnol. J.
**2014**, 9, 727–738. [Google Scholar] [CrossRef] [PubMed] - Funke, M.; Buchenauer, A.; Schnakenberg, U.; Mokwa, W.; Diederichs, S.; Mertens, A.; Müller, C.; Kensy, F.; Büchs, J. Microfluidic biolector—microfluidic bioprocess control in microtiter plates. Biotechnol. Bioeng.
**2010**, 107, 497–505. [Google Scholar] [CrossRef] - Tajsoleiman, T.; Mears, L.; Krühne, U.; Gernaey, K.V.; Cornelissen, S. An industrial perspective on scale-down challenges using miniaturized bioreactors. Trends Biotechnol.
**2019**, 37, 697–706. [Google Scholar] [CrossRef] [PubMed] - Junne, S.; Klingner, A.; Kabisch, J.; Schweder, T.; Neubauer, P. A two-compartment bioreactor system made of commercial parts for bioprocess scale-down studies: Impact of oscillations on Bacillus subtilis fed-batch cultivations. Biotechnol. J.
**2011**, 6, 1009–1017. [Google Scholar] [CrossRef] [PubMed] - Wang, G.; Haringa, C.; Noorman, H.; Chu, J.; Zhuang, Y. Developing a Computational Framework To Advance Bioprocess Scale-Up. Trends Biotechnol.
**2020**, 38, 846–856. [Google Scholar] [CrossRef] [PubMed] - Siebler, F.; Lapin, A.; Hermann, M.; Takors, R. The impact of CO gradients on C. ljungdahlii in a 125 m
^{3}bubble column: Mass transfer, circulation time and lifeline analysis. Chem. Eng. Sci.**2019**, 207, 410–423. [Google Scholar] [CrossRef] - Haringa, C.; Tang, W.; Deshmukh, A.T.; Xia, J.; Reuss, M.; Heijnen, J.J.; Mudde, R.F.; Noorman, H.J. Euler-Lagrange computational fluid dynamics for (bio)reactor scale down: An analysis of organism lifelines. Eng. Life Sci.
**2016**, 16, 652–663. [Google Scholar] [CrossRef] [PubMed] - Kuschel, M.; Siebler, F.; Takors, R. Lagrangian Trajectories to Predict the Formation of Population Heterogeneity in Large-Scale Bioreactors. Bioengineering
**2017**, 4, 27. [Google Scholar] [CrossRef] [PubMed] - Lapin, A.; Müller, D.; Reuss, M. Dynamic behavior of microbial populations in stirred bioreactors simulated with Euler-Lagrange methods: Traveling along the lifelines of single cells. Ind. Eng. Chem. Res.
**2004**, 43, 4647–4656. [Google Scholar] [CrossRef] - Simon, L.L.; Fischer, U.; Hungerbühler, K. Modeling of a Three-Phase Industrial Batch Reactor Using a Hybrid First-Principles Neural-Network Model. Ind. Eng. Chem. Res.
**2006**, 45, 7336–7343. [Google Scholar] [CrossRef]

**Figure 3.**Schematic of the three ways to combine the two types of models. (

**a**) Parallel configuration. (

**b**,

**c**) Serial configurations.

Type of Model | Characteristics | Advantages | Disadvantages |
---|---|---|---|

Unstructured | Biomass as black-box | Description of the physical aspects of the process | Potential over-simplification of biomass-product dynamics |

Balanced growth approximation | |||

Mass balances and kinetic equations | |||

Structured | Biomass as a multi-component organism | Suitable to model complex systems (e.g., metabolic networks) | Extensive parameter identification (e.g metabolomics analysis) |

Cell growth calculated based on interaction of intracellular components | |||

Metabolic flux equations |

Microorganism | Type of Model | Studied Parameter | Main Findings | Reference |
---|---|---|---|---|

Aspergillus oryzae | Unstructured | Different agitation and aeration conditions | Prediction of several fermentation parameters, e.g., rheological behavior at different process conditions | [20] |

Bacillus subtilis | Unstructured | Oxygen supply | Optimize aeration rate for higher protein production, using low-cost substrates | [27] |

CHO cell | Unstructured | Temperature shift | Optimization of temperature profiles for optimal cell growth and productivity | [28] |

Escherichia coli | Unstructured | Overflow metabolism | Prediction of growth and acetate-induced dynamics | [19] |

Structured kinetic | Specific growth rate | Prediction of growth rate based on reaction kinetics for wild-type and genetic mutants | [24] | |

Penicillium chrysogenum | Pooled metabolic model | Dynamic feeding conditions | Prediction of metabolic response induced by feast-famine feeding cycles | [23] |

Structured kinetic | On- and off-line process measurements | Prediction of process measurements including e.g., off-gas analysis | [29] | |

Pichia pastoris | Unstructured | Protein production | Strategy to improve product formation based on growth kinetics | [30] |

Structured kinetic | Growth and recombinant protein production | Prediction of optimal feed strategy | [25] | |

Saccharomyces cerevisiae | Unstructured | Ethanol production | Prediction of ethanol production under non-sterile conditions in biofilm reactor | [31] |

Zymomonas mobilis | Unstructured | Glucose and xylose co-fermentation | Prediction of ethanol yield across a wide range of initial process conditions | [21] |

Not disclosed | Unstructured | On-line monitoring | On-line prediction of product concentration | [32] |

Type of Model | Advantages | Limitations |
---|---|---|

Mechanistic | Increased process understanding | Time-consuming development |

Process control and optimization | Extensive experimental work for validation | |

Model-based DOE | Intensive process knowledge required | |

Data-driven | Automatic model assembly | Poor extrapolation capabilities |

Real-time monitoring and fault detection | Requires representative and reliable data | |

Low computational burden | Limited for control and optimization |

**Table 5.**Model performance across hybridization levels [13].

Interpolation | Extrapolation | |||
---|---|---|---|---|

Degree of Hybridization | Optimal Run Number ^{1} | Best MSE ^{2} | Optimal Run Number | Best RMSE |

Data-driven | 50 | 0.039 | 50 | 0.32 |

Hybrid 1-rAcc ^{3} | 30 | 0.039 | 50 | 0.20 |

Hybrid 2-MB ^{4} | 30 | 0.030 | 50 | 0.10 |

Hybrid 3-rSp ^{5} | 30 | 0.025 | 30 | 0.05 |

Hybrid 4-rXv ^{6} | 50 | 0.025 | 50 | 0.05 |

Hybrid 5-kin ^{7} | 50 | 0.025 | 50 | 0.05 |

Mechanistic | 10 | 0.060 | 30 | 0.10 |

^{1}Number of training runs necessary to achieve the lowest MSE.

^{2}Lowest mean squared error.

^{3}Rate of accumulation.

^{4}Mass balance.

^{5}Specific rates.

^{6}Specific growth and death rates.

^{7}Kinetic terms.

Microorganism | Type of Model | Application | Studied Parameter | Main Findings | Reference |
---|---|---|---|---|---|

Aspergillus niger | Unstructured mechanistic model + LBGM | Prediction | Glucose, glycerol and biomass concentration | Soft-sensor for glucose concentration coupled with a kinetic model for glycerol and biomass prediction | [59] |

Bordetella pertussis | Unstructured mechanistic model + PLS | Monitoring | Biomass, glutamate, and lactate concentration | Real-time monitoring of the fermentation with improved prediction compared to the PLS model on its own | [60] |

Candida rugosa | Unstructured mechanistic model + NN | Monitoring | Lypolitic activity | Decreased prediction error of lipase activity with on-line implementation | [61] |

Cunninghamella echinulata | Unstructured mechanistic model + NN | Prediction | Kinetic parameter estimation | The data-driven model is directly built as the kinetic parameters are estimated | [58] |

Escherichia coli | Unstructured mechanistic model + NN | Optimization | Induction conditions | Significant reduction in required DOE to determine optimal parameters | [49] |

Unstructured mechanistic model + NN | Control | Feed rate | Improved batch-to-batch reproducibility by introducing a model-based feed rate control | [62] | |

Mammalian cell culture | Unstructured mechanistic model + NN | Control | Harvesting point | Real-time monitoring of the fermentation and model predictive feed control | [63] |

Unstructured mechanistic model + NN | Prediction | Degree of hybridization | Determination of the ideal level of mechanistic knowledge to be included for optimal performance | [13] | |

Pichia pastoris | Unstructured mechanistic model + NN | Prediction | Prediction of dynamic variables | Increased depth of the neural network led to a decrease in prediction errors | [64] |

Carbon balance + Multiple linear regression | Monitoring | Biomass concentration | Prediction of biomass concentration, based on online data of three different fermentation phases | [51] | |

Saccharomyces cerevisiae | Unstructured mechanistic model + Neural ODEs | Prediction | Unknown kinetic dynamics | Improved model accuracy from the incorporation of neural ODEs | [16] |

Unstructured mechanistic model + PLS | Monitoring | Substrate uptake and ethanol production | Real-time monitoring of the fermentation using advanced spectroscopy data | [65] | |

Xanthophyllomyces dendrorhous | Unstructured mechanistic model + Gaussian process model | Prediction | Kinetic parameter estimation in mixed-sugar conditions | Embedding of the Gaussian process model reduces model uncertainty and prediction error | [56] |

Non disclosed | Unstructured mechanistic model + NN | Prediction | Uncertain parameters, e.g., biomass, product and substrate | Superior performance versus the kinetic model | [15] |

Microorganism | Approach | Main Findings | Reference |
---|---|---|---|

Clostridium ljungdahlii | Unstructured kinetic model | Need to improve CO mass transfer and/or to engineer strains that cope with the conditions | [72] |

Escherichia coli | Metabolic model | Glucose gradients induce production/consumption of acetate in different parts of the reactor | [4] |

Penicillium chrysogenum | Dynamic gene regulation model | Statistical assessment of the substrate fluctuations experienced by organisms in industrial-scale fermentation | [73] |

Pooled metabolic model | Identified targets for metabolic and reactor optimization of large-scale fermentation | [26] | |

Pseudomonas putida | Cell cycle model | Insights into the intracellular mechanisms that determine growth phenotypes | [74] |

Saccharomyces cerevisiae | Unstructured kinetic model | The approach provides a simulation strategy for the design and operation of bioreactors, particularly when single cell behavior is relevant | [75] |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Albino, M.; Gargalo, C.L.; Nadal-Rey, G.; Albæk, M.O.; Krühne, U.; Gernaey, K.V.
Hybrid Modeling for On-Line Fermentation Optimization and Scale-Up: A Review. *Processes* **2024**, *12*, 1635.
https://doi.org/10.3390/pr12081635

**AMA Style**

Albino M, Gargalo CL, Nadal-Rey G, Albæk MO, Krühne U, Gernaey KV.
Hybrid Modeling for On-Line Fermentation Optimization and Scale-Up: A Review. *Processes*. 2024; 12(8):1635.
https://doi.org/10.3390/pr12081635

**Chicago/Turabian Style**

Albino, Mariana, Carina L. Gargalo, Gisela Nadal-Rey, Mads O. Albæk, Ulrich Krühne, and Krist V. Gernaey.
2024. "Hybrid Modeling for On-Line Fermentation Optimization and Scale-Up: A Review" *Processes* 12, no. 8: 1635.
https://doi.org/10.3390/pr12081635