Modelling of Escherichia coli Batch and Fed-Batch Processes in Semi-Defined Yeast Extract Media
Abstract
1. Introduction
2. Macro-Kinetic Model Formulation
3. Results
Extended Model Validation
4. Discussion
5. Conclusions
6. Materials and Methods
6.1. Strain, Media and Cultivation Conditions
6.2. Analytics
6.3. Parameter Estimation
6.4. Parameter Uncertainty Quantification
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Appendix A.1. Nomenclature
Abbreviation | Name | Unit | Bound [min, max] |
---|---|---|---|
A | Acetate | g L−1 | – |
C | Carbon content | – | – |
Dissolved oxygen tension in equilibrium with the gas phase | % air sat. L g−1 | – | |
S | Substrate | g L−1 | – |
Yeast Extract | g L−1 | – | |
Yeast Extract Fraction i, where i denotes a specific yeast extract fraction | g L−1 | – | |
X | Biomass | g L−1 | – |
Affinity constant, acetate consumption | g L−1 | ||
Inhibition constant, inhibition of oxidative substrate uptake by YE fraction B | g L−1 | ||
Inhibition constant, inhibition of oxidative substrate uptake by YE fraction B | g L−1 | ||
Inhibition constant, intracellular oxidative substrate uptake by YE fraction A | g L−1 | ||
Volumetric mass transfer coefficient | h−1 | – | |
Affinity constant, substrate consumption | g L−1 | ||
Affinity constant, consumption of YE fraction A | g L−1 | ||
Affinity constant, consumption of YE fraction B | g L−1 | ||
Affinity constant, uptake of substrate for oxidative metabolism | g L−1 | ||
Available specific maintenance coefficient | g g−1 h−1 | – | |
Maximum specific substrate uptake rate | g g−1 h−1 | ||
Maximum specific uptake rate for YE fraction A | g g−1 h−1 | ||
Maximum specific uptake rate for YE fraction B | g g−1 h−1 | ||
Specific acetate consumption rate | g g−1 h−1 | ||
Yield of acetate per gram of substrate | g g−1 | – | |
Oxygen used per gram of acetate metabolized | g g−1 | – | |
Yield of biomass per gram of substrate (glucose) | g g−1 | ||
Yield of biomass per gram of YE fraction A | g g−1 | ||
Yield of biomass per gram of YE fraction B | g g−1 | ||
Yield of biomass per gram of acetate | g g−1 | ||
Oxygen used per gram of substrate metabolized | g g−1 | – | |
Oxygen used per gram of YE metabolized | g g−1 | – | |
Dissolved oxygen probe response time | h | – |
Appendix A.2. Constants
Constant | Unit | Value | Comment |
---|---|---|---|
CA | g g−1 | 0.033 | stoichiometric constant |
CP | g g−1 | 0.044 | stoichiometric constant |
CS | g g−1 | 0.033 | stoichiometric constant |
CX | g g−1 | 0.041 | stoichiometric constant |
CYE | g g−1 | 0.036 | stoichiometric constant |
DOT* | % air sat. | 100 | dissolved oxygen concentration at saturation |
H | % air sat. | 14,000 | Henry law related constant |
Si | g L−1 | 600 | feed stock concentration |
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Batch | Batch and Fed Batch | ||||||||
---|---|---|---|---|---|---|---|---|---|
Model | Basic | One-YEF | Two-YEF | Three-YEF | Basic | One-YEF | Two-YEF | Three-YEF | |
RMSE | 3.64 | 2.44 | 2.40 | 2.40 | 1.95 | 1.10 | 0.68 | 0.75 | |
(3) | 1.02 ± 0.14 | 0.46 ± 0.01 | 0.55 ± 0.19 | 0.56 ± 0.23 | 1.62 ± 0.26 | 0.55 ± 0.05 | 0.62 ± 0.05 | 0.71 ± 0.27 | |
— | 1.99 | 1.71 | 1.48 | — | 1.80 | 1.63 | 1.60 | ||
— | — | 0.23 | 0.46 | — | — | 0.10 | 0.31 | ||
(1) | 0.04 | 0.04 | 0.04 | 0.04 | 0.04 | 0.04 | 0.04 | 0.04 | |
(4) | 0.70 ± 0.48 | 0.89 ± 0.47 | 0.37 ± 0.31 | 0.84 ± 0.45 | 0.42 ± 0.47 | 0.89 ± 0.40 | 0.55 ± 0.43 | 0.64 ± 0.45 | |
(3) | 0.83 ± 0.09 | 0.33 ± 0.04 | 0.42 ± 0.07 | 0.42 ± 0.06 | 0.42 ± 0.03 | 0.43 ± 0.02 | 0.43 ± 0.02 | 0.43 ± 0.04 | |
(3) | — | 0.41 ± 0.01 | 0.52 ± 0.03 | 0.50 ± 0.05 | — | 0.46 ± 0.01 | 0.56 ± 0.04 | 0.53 ± 0.11 | |
(4) | — | — | 0.14 ± 0.05 | 0.31 ± 0.14 | — | — | 0.12 ± 0.05 | 0.21 ± 0.14 | |
(1) | 0.27 | 0.28 | 0.30 | 0.42 | 0.37 | 0.50 | 0.42 | 0.42 | |
(1) | 1.07 | 1.07 | 1.07 | 1.07 | 1.07 | 1.07 | 1.07 | 1.07 | |
(1) | 1.07 | 1.07 | 1.07 | 1.07 | 1.07 | 1.07 | 1.07 | 1.07 | |
Parameter | (1) | 0.67 | 0.67 | 0.67 | 0.67 | 0.67 | 0.67 | 0.67 | 0.67 |
(2) | — | 1.16 | 1.16 | 1.16 | — | 1.16 | 1.16 | 1.16 | |
(1,3) | 0.05 ± 0.03 | 0.05 | 0.05 | 0.05 | 0.05 ± 0.03 | 0.05 | 0.05 | 0.05 | |
— | 0.07 | 0.77 | 0.05 | — | 2.99 | 0.23 | 0.05 | ||
— | — | 1.28 | 0.10 | — | — | 1.70 | 0.10 | ||
42.16 | 16.20 | 65.21 | 17.69 | 30.20 | 80.76 | 38.11 | 34.49 | ||
0.81 | 1.00 | 0.25 | 0.86 | 0.66 | 0.66 | 0.86 | 0.86 | ||
— | — | 25.88 | 49.18 | — | — | 49.27 | 49.34 | ||
0.28 | 0.05 | 2.33 | 0.08 | 2.64 | 0.05 | 0.05 | 0.008 | ||
— | 1.13 | 0.49 | 0.02 | — | 1.56 | 0.24 | 0.01 | ||
(4) | — | 1 | 0.61 ± 0.11 | 0.43 ± 0.16 | — | 1 | 0.27 ± 0.10 | 0.21 ± 0.14 | |
(4) | — | 1 | 1 | 0.71 ± 0.22 | — | 1 | 1 | 0.54 ± 0.27 |
Experiments | Scale [L] | OD600,init | Sinit [g L−1] | YEinit [g L−1] | YE Brand | Feed Regime | Feed Strategy | Si [g L−1] |
---|---|---|---|---|---|---|---|---|
Model evaluation | 3 | 0.0002 | 15 | 10 | Procelys® 1 | continuous | stepwise | 600 |
YE1 | 0.01 | 0.3 | 9 | 0, 5, 7.5, 10 | Procelys® | bolus | exponential | 400 |
YE2 | 0.01 | 0.5 | 12 | 10 | VWR 2 | — | — | — |
YE3 | 0.01 | 0.5 | 12 | 10 | Difco 3 | — | — | — |
YE4 | 0.01 | 0.5 | 12 | 10 | Bacto 3 | — | — | — |
YE5 | 0.01 | 0.5 | 12 | 10 | Roth 4 | — | — | — |
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Schröder-Kleeberg, F.; Zoellkau, M.; Glaser, M.; Bosch, C.; Brunner, M.; Cruz Bournazou, M.N.; Neubauer, P. Modelling of Escherichia coli Batch and Fed-Batch Processes in Semi-Defined Yeast Extract Media. Bioengineering 2025, 12, 1081. https://doi.org/10.3390/bioengineering12101081
Schröder-Kleeberg F, Zoellkau M, Glaser M, Bosch C, Brunner M, Cruz Bournazou MN, Neubauer P. Modelling of Escherichia coli Batch and Fed-Batch Processes in Semi-Defined Yeast Extract Media. Bioengineering. 2025; 12(10):1081. https://doi.org/10.3390/bioengineering12101081
Chicago/Turabian StyleSchröder-Kleeberg, Fabian, Markus Zoellkau, Markus Glaser, Christian Bosch, Markus Brunner, Mariano Nicolas Cruz Bournazou, and Peter Neubauer. 2025. "Modelling of Escherichia coli Batch and Fed-Batch Processes in Semi-Defined Yeast Extract Media" Bioengineering 12, no. 10: 1081. https://doi.org/10.3390/bioengineering12101081
APA StyleSchröder-Kleeberg, F., Zoellkau, M., Glaser, M., Bosch, C., Brunner, M., Cruz Bournazou, M. N., & Neubauer, P. (2025). Modelling of Escherichia coli Batch and Fed-Batch Processes in Semi-Defined Yeast Extract Media. Bioengineering, 12(10), 1081. https://doi.org/10.3390/bioengineering12101081