Bridging Offline Functional Model Carrying Aging-Specific Growth Rate Information and Recombinant Protein Expression: Entropic Extension of Akaike Information Criterion
Abstract
:1. Introduction
2. Materials and Methods
2.1. Cell Strains
2.2. Medium
2.3. Cultivation Conditions
2.4. Target Protein Analysis
3. Proposed Extension of Akaike Information Criterion
4. Combined Model Representing Hypothesis with Multiple Elements
5. System Identification and Parameter Estimation
5.1. Average Cell Age at the Induction
5.2. Model of Product Model Fitting
5.3. Pseudo-Global Offline Identification of Model Parameters
6. Model Selection Based on Experimental Model Calibration
- (a)
- There is significant doubt that belongs to the descriptor set;
- (b)
- Even if the specific growth rate surpasses the average cell age, the significance of either is still relatively similar. Therefore, there is a high chance that both of them combine in a single nonlinear relationship that is proportional to the maximum product formation rate.
7. Discussion and Conclusions
- (a)
- As regards rational, practical benefits, the proposed entropic measures can help with tuning the maximum count of the model parameters, thus helping devise standardized CDMO procedures for attaining higher product yields from biopharmaceutical efforts;
- (b)
- Secondly, both average age and biomass growth values at time of induction, or in other words, at the very start of product synthesis, are crucial. Therefore, the combined model employing Monod structures is the best recommendation for maximizing the total product yield.
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
References
- Goodwin, G. Predicting the Performance of Soft Sensors as a Route to Low Cost Automation. Annu. Rev. Control 2000, 24, 55–66. [Google Scholar] [CrossRef]
- Randek, J.; Mandenius, C.-F. On-Line Soft Sensing in Upstream Bioprocessing. Crit. Rev. Biotechnol. 2018, 38, 106–121. [Google Scholar] [CrossRef] [PubMed]
- Sagmeister, P.; Wechselberger, P.; Jazini, M.; Meitz, A.; Langemann, T.; Herwig, C. Soft Sensor Assisted Dynamic Bioprocess Control: Efficient Tools for Bioprocess Development. Chem. Eng. Sci. 2013, 96, 190–198. [Google Scholar] [CrossRef]
- Luttmann, R.; Bracewell, D.G.; Cornelissen, G.; Gernaey, K.V.; Glassey, J.; Hass, V.C.; Kaiser, C.; Preusse, C.; Striedner, G.; Mandenius, C.-F. Soft Sensors in Bioprocessing: A Status Report and Recommendations. Biotechnol. J. 2012, 7, 1040–1048. [Google Scholar] [CrossRef]
- Simutis, R.; Galvanauskas, V.; Levisauskas, D.; Repsyte, J.; Vaitkus, V. Comparative Study of Intelligent Soft-Sensors for Bioprocess State Estimation. J. Life Sci. Technol. 2013, 1, 163–167. [Google Scholar] [CrossRef]
- Zhang, H. Software Sensors and Their Applications in Bioprocess. In Computational Intelligence Techniques for Bioprocess Modelling, Supervision and Control; de Nicoletti, M.C., Jain, L.C., Eds.; Springer: Berlin/Heidelberg, Germany, 2009; Volume 218, pp. 25–56. [Google Scholar] [CrossRef]
- de Azevedo, S.F.; Dahm, B.; Oliveira, F.R. Hybrid modelling of biochemical processes: A comparison with the conventional approach. Comput. Chem. Eng. 1997, 21, S751–S756. [Google Scholar] [CrossRef]
- Wiechert, W.; Noack, S. Mechanistic pathway modeling for industrial biotechnology: Challenging but worthwhile. Curr. Opin. Biotechnol. 2011, 22, 604–610. [Google Scholar] [CrossRef] [PubMed]
- Kager, J.; Herwig, C.; Stelzer, I.V. State estimation for a penicillin fed-batch process combining particle filtering methods with online and time delayed offline measurements. Chem. Eng. Sci. 2018, 177, 234–244. [Google Scholar] [CrossRef]
- Gnoth, S.; Simutis, R.; Lübbert, A. Selective expression of the soluble product fraction in Escherichia coli cultures employed in recombinant protein production processes. Appl. Microbiol. Biotechnol. 2010, 87, 2047–2058. [Google Scholar] [CrossRef] [PubMed]
- Urniezius, R.; Survyla, A. Identification of Functional Bioprocess Model for Recombinant E. Coli Cultivation Process. Entropy 2019, 21, 1221. [Google Scholar] [CrossRef] [Green Version]
- Levisauskas, D.; Galvanauskas, V.; Henrich, S.; Wilhelm, K.; Volk, N.; Lübbert, A. Model-based optimization of viral capsid protein production in fed-batch culture of recombinant Escherichia coli. Bioprocess Biosyst. Eng. 2003, 25, 255–262. [Google Scholar] [CrossRef] [PubMed]
- San, K.-Y.; Stephanopoulos, G. Studies on on-line bioreactor identification. IV. Utilization of pH measurements for product estimation. Biotechnol. Bioeng. 1984, 26, 1209–1218. [Google Scholar] [CrossRef]
- Julier, S.J.; Uhlmann, J.K. Unscented Filtering and Nonlinear Estimation. Proc. IEEE 2004, 92, 401–422. [Google Scholar] [CrossRef] [Green Version]
- Giffin, A.; Urniezius, R. The Kalman Filter Revisited Using Maximum Relative Entropy. Entropy 2014, 16, 1047–1069. [Google Scholar] [CrossRef]
- de Assis, A.J.; Filho, R.M. Soft sensors development for on-line bioreactor state estimation. Comput. Chem. Eng. 2000, 24, 1099–1103. [Google Scholar] [CrossRef]
- Krämer, D.; King, R. On-line monitoring of substrates and biomass using near-infrared spectroscopy and model-based state estimation for enzyme production by S. cerevisiae. IFAC-PapersOnLine 2016, 49, 609–614. [Google Scholar] [CrossRef]
- Koch, C.; Posch, A.E.; Goicoechea, H.C.; Herwig, C.; Lendl, B. Multi-analyte quantification in bioprocesses by Fourier-transform-infrared spectroscopy by partial least squares regression and multivariate curve resolution. Anal. Chim. Acta 2014, 807, 103–110. [Google Scholar] [CrossRef] [PubMed]
- Sellick, C.A.; Hansen, R.; Jarvis, R.M.; Maqsood, A.R.; Stephens, G.M.; Dickson, A.J. Royston Goodacre Rapid monitoring of recombinant antibody production by mammalian cell cultures using fourier transform infrared spectroscopy and chemometrics. Biotechnol. Bioeng. 2010, 106, 432–442. [Google Scholar] [CrossRef] [PubMed]
- Montague, G.A.; Glassey, J.; Ignova, M.; Paul, G.C.; Kent, C.A.; Thomas, C.R.; Ward, A.C. Hybrid Modelling for On-Line Penicillin Fermentation Optimisation. IFAC Proc. 2002, 35, 395–400. [Google Scholar] [CrossRef] [Green Version]
- Bachinger, T.; Riese, U.; Eriksson, R.K.; Mandenius, C.F. Electronic nose for estimation of product concentration in mammalian cell cultivation. Bioprocess Eng. 2000, 23, 637–642. [Google Scholar] [CrossRef]
- Golabgir, A.; Herwig, C. Combining Mechanistic Modeling and Raman Spectroscopy for Real-Time Monitoring of Fed-Batch Penicillin Production. Chem. Ing. Tech. 2016, 88, 764–776. [Google Scholar] [CrossRef]
- Thibault, J.; van Breusegem, V.; Chéruy, A. On-line prediction of fermentation variables using neural networks: Prediction of Fermentation Variables. Biotechnol. Bioeng. 1990, 36, 1041–1048. [Google Scholar] [CrossRef]
- Simutis, R.; Lübbert, A. Hybrid Approach to State Estimation for Bioprocess Control. Bioengineering 2017, 4, 21. [Google Scholar] [CrossRef] [Green Version]
- Luedeking, R.; Piret, E.L. A kinetic study of the lactic acid fermentation. Batch process at controlled pH. Biotechnol. Bioeng. 1959, 1, 393–412. [Google Scholar] [CrossRef]
- Schaepe, S.; Kuprijanov, A.; Simutis, R.; Lübbert, A. Avoiding overfeeding in high cell density fed-batch cultures of E. coli during the production of heterologous proteins. J. Biotechnol. 2014, 192, 146–153. [Google Scholar] [CrossRef]
- Murari, A.; Peluso, E.; Cianfrani, F.; Gaudio, P.; Lungaroni, M. On the Use of Entropy to Improve Model Selection Criteria. Entropy 2019, 21, 394. [Google Scholar] [CrossRef] [Green Version]
- Urniezius, R.; Galvanauskas, V.; Survyla, A.; Simutis, R.; Levisauskas, D. From Physics to Bioengineering: Microbial Cultivation Process Design and Feeding Rate Control Based on Relative Entropy Using Nuisance Time. Entropy 2018, 20, 779. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Urniezius, R.; Survyla, A.; Paulauskas, D.; Bumelis, V.A.; Galvanauskas, V. Generic estimator of biomass concentration for Escherichia coli and Saccharomyces cerevisiae fed-batch cultures based on cumulative oxygen consumption rate. Microb. Cell Fact. 2019, 18, 190. [Google Scholar] [CrossRef] [Green Version]
- Garcia-Ochoa, F.; Gomez, E.; Santos, V.E.; Merchuk, J.C. Oxygen uptake rate in microbial processes: An overview. Biochem. Eng. J. 2010, 49, 289–307. [Google Scholar] [CrossRef]
- Sivashanmugam, A.; Murray, V.; Cui, C.; Zhang, Y.; Wang, J.; Li, Q. Practical protocols for production of very high yields of recombinant proteins using Escherichia coli. Protein Sci. 2009, 18, 936–948. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Çalik, P.; Yilgör, P.; Demir, A.S. Influence of controlled-pH and uncontrolled-pH operations on recombinant benzaldehyde lyase production by Escherichia coli. Enzym. Microb. Technol. 2006, 38, 617–627. [Google Scholar] [CrossRef]
- Kocabaş, P.; Çalık, P.; Özdamar, T.H. Fermentation characteristics of l-tryptophan production by thermoacidophilic Bacillus acidocaldarius in a defined medium. Enzym. Microb. Technol. 2006, 39, 1077–1088. [Google Scholar] [CrossRef]
- Bohlin, T. Practical Grey-Box Process Identification; Springer: London, UK, 2006. [Google Scholar] [CrossRef] [Green Version]
- Babaeipour, V.; Shojaosadati, S.A.; Maghsoudi, N. Maximizing Production of Human Interferon-γ in HCDC of Recombinant E. coli. Iran. J. Pharm. Res. 2013, 12, 563–572. [Google Scholar]
- Galvanauskas, V.; Volk, N.; Simutis, R.; Lübbert, A. Design of Recombinant Protein Production Processes. Chem. Eng. Commun. 2004, 191, 732–748. [Google Scholar] [CrossRef]
- Miao, F.; Kompala, D.S. Overexpression of cloned genes using recombinant Escherichia coli regulated by a T7 promoter: I. Batch cultures and kinetic modeling. Biotechnol. Bioeng. 1992, 40, 787–796. [Google Scholar] [CrossRef] [PubMed]
- Levisauskas, D.; Plaskute, V. Modeling and Optimization of Secondary Metabolites Production in Fed-Batch Biotechnological Processes Based on Physiologically Active Biomass Concept; Information Technology and Control: Kaunas, Lithuania, 1999; pp. 33–36. ISSN 1392-124X. [Google Scholar]
- Plaskute, V.; Levisauskas, D. Application of hybrid models for prediction and optimization of enzyme fermentation process. Comparative study. Syst. Sci. 2001, 27, 115–123. [Google Scholar]
- Zhao, F.; Heidrich, E.S.; Curtis, T.P.; Dolfing, J. The Effect of Anode Potential on Current Production from Complex Substrates in Bioelectrochemical Systems: A Case Study with Glucose. Appl. Microbiol. Biotechnol. 2020, 104, 5133–5143. [Google Scholar] [CrossRef] [Green Version]
- Monod, J. The Growth of Bacterial Cultures. Annu. Rev. Microbiol. 1949, 3, 371–394. [Google Scholar] [CrossRef] [Green Version]
- Bell, G.I.; Anderson, E.C. Cell Growth and Division. Biophys. J. 1967, 7, 329–351. [Google Scholar] [CrossRef] [Green Version]
- Swokowski, E.W. Calculus with Analytic Geometry, 2nd ed.; Prindle, Weber & Schmidt: Boston, MA, USA, 1979; ISBN 978-0-87150-268-1. [Google Scholar]
- Urniezius, R. Convex programming for semi-globally optimal resource allocation. In AIP Conference Proceedings; AIP Publishing: Beirut, Lebanon, 2016; p. 040002. [Google Scholar]
- Giffin, A.; Urniezius, R. Simultaneous State and Parameter Estimation Using Maximum Relative Entropy with Nonhomogenous Differential Equation Constraints. Entropy 2014, 16, 4974–4991. [Google Scholar] [CrossRef] [Green Version]
Model Type | Model Structure | Comment | Product | Reference | |
---|---|---|---|---|---|
Soluble | Insoluble | ||||
Conventional (based on balance equations) | Balance of production rate | Assessment of dilution and product concentration, hard to distinguish between estimation and prognostication | Penicillin V | - | [9] |
Balances of specific substrate uptake and growth rate | A hybrid model provides better results than a traditional one | Recombinant protein | - | [10] | |
Balances of biomass, specific growth rate, production rates | - | - | Recombinant protein | [11] | |
Balance of biomass, specific growth rate, and protein activity | Optimization for maximal protein using induction time and feed profiles | Recombinant protein | [12] | ||
Balance of biomass, pH, added ammonia | - | Ethanol | - | [13] | |
Spectroscopy data analysis with EKF | - | Ethanol | - | [17] | |
Empirical (data driven) | Spectroscopy data analysis with PLS | - | Penicillin V | [18] | |
Spectroscopy data analysis with PCA | - | - | Recombinant antibodies from mammalian cells | [19] | |
Off-gas analysis with ANN | Gas sensors suffer from signal drift which requires additional compensation | - | Recombinant human blood coagulation factor VIII | [21] | |
Hybrid | ANNs for product formation rate and specific growth rate | - | Recombinant protein | [10] | |
ANN for dissolved oxygen assessment | The assumption is valid only when the PID parameters for controlling the DO circuit are unchanged | Penicillin | [20] | ||
ANN with inputs of biomass, dilution rate, etc. | - | Ethanol | [23] | ||
Support vector regression for observations of oxygen undertake, carbon production, and base consumption rates | The presented model is for prediction, not for pseudo-global estimation | - | Recombinant protein | [24] |
Condition | Site 1 | Site 2 | Note |
---|---|---|---|
Bioreactor Volume | 15 L | 7 L | - |
Cultivation Type | Fed-batch | Fed-batch | - |
Temperature Setpoint | 30 °C | 37 °C | Both measured with a PT100 temperature sensor |
DO Setpoint | 30% | 20% | Both measured with an Ingold DO probe (Mettler Toledo) |
pH Setpoint | 7 | 6.8 | Both kept constant using a PID controller with the addition of NaOH |
Stirrer Setpoint Range | 100–1400 RPM | 800–1200 RPM | - |
Airflow | 0.3–15 L/min | 1.75–3.75 L/min | Pure oxygen flow was provided to bioreactors at a range from 0 to 7.5 L/min to increase the oxygen transfer rate |
Maximum average cell age at induction, hours | 3.105 | 2.985 | - |
Minimum average cell age at induction, hours | 1.14 | 1.237 | - |
Off-gas Tracking | Concentrations of O2 and CO2 | Concentration of O2 | Measured with a paramagnetic oxygen sensor (Maihak Oxor 610) during Site 1 cultivations and with BlueSens gas analyzer (BCpreFerm, BlueSens, Herten, Germany) during Site 2 cultivations. |
State Variables | Model Selection Arguments in This Study | Reference(s) | |
---|---|---|---|
1999, [38,39] | |||
2019, [11] | |||
2003, [12] | |||
, etc. | 2021/this study |
AIC | RSS | MAE | k | Model Selection Arguments | Reference(s) |
---|---|---|---|---|---|
−967.01 | 16.79 | 0.393 | 2 | 1999 [38,39] | |
−1005.6 | 14.83 | 0.424 | 3 | 2019 [11] | |
−977.17 | 16.07 | 0.442 | 4 | 2003 [12] | |
−1488.16 | 3.15 | 0.249 | 24 | Full overfit with Equation (18) |
Parameter and Its Value | State Variable or Argument | AIC | BIC | ||
---|---|---|---|---|---|
−591.28 | −587.49 | - | 10.5 | ||
−936.78 | −932.99 | 9.145 | 9.138 | ||
−905.04 | −901.25 | 9.273 | 9.267 |
Equation | RSS | MAE | k | ||||
---|---|---|---|---|---|---|---|
(29) | −0.13 | 0.0232 | −1.066 | 6.869 | 7.279 | 0.399 | 3 |
(30) | −0.0375 | 0.01148 | −1.244 | 6.979 | 8.723 | 0.432 | 3 |
(31) | −0.0337 | 0.0098 | −1.261 | 6.998 | 8.970 | 0.462 | 3 |
(32) | 0 | 0.00298 | −1.302 | 7.099 | 11.782 | 0.579 | 2 |
Equation | RSS | MAE | k | |||||
---|---|---|---|---|---|---|---|---|
(32) | 0.0159 | 0 | 0 | 0 | 5.976 | 18.524 | 0.639 | 1 |
(34) | 0 | 0.00138 | 0 | 0 | 6.047 | 20.412 | 0.497 | 1 |
(35) | 0 | 0 | 0.00321 | −1.298 | 6.054 | 11.857 | 0.577 | 2 |
(36) | 0.0453 | 0 | 0 | 0 | 6.109 | 16.475 | 0.603 | 2 |
(37) | 0 | 0.01176 | 0 | 0 | 6.114 | 16.785 | 0.393 | 2 |
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Urniezius, R.; Kemesis, B.; Simutis, R. Bridging Offline Functional Model Carrying Aging-Specific Growth Rate Information and Recombinant Protein Expression: Entropic Extension of Akaike Information Criterion. Entropy 2021, 23, 1057. https://doi.org/10.3390/e23081057
Urniezius R, Kemesis B, Simutis R. Bridging Offline Functional Model Carrying Aging-Specific Growth Rate Information and Recombinant Protein Expression: Entropic Extension of Akaike Information Criterion. Entropy. 2021; 23(8):1057. https://doi.org/10.3390/e23081057
Chicago/Turabian StyleUrniezius, Renaldas, Benas Kemesis, and Rimvydas Simutis. 2021. "Bridging Offline Functional Model Carrying Aging-Specific Growth Rate Information and Recombinant Protein Expression: Entropic Extension of Akaike Information Criterion" Entropy 23, no. 8: 1057. https://doi.org/10.3390/e23081057