Kinetic Analysis of Gluconacetobacter diazotrophicus Cultivated on a Bench Scale: Modeling the Effect of pH and Design of a Sucrose-Based Medium
Abstract
:1. Introduction
2. Materials and Methods
2.1. Microorganism
2.2. Inoculum Preparation
2.3. Cultivation Conditions for Culture Medium Design
2.4. Screening of Medium Components
2.5. One-Factor Design
2.6. Submerged Cultivation on a Bench Scale
2.7. Analytical Methods
3. Model Development
3.1. Model Formulation
3.2. Preliminary Modeling and Fitting
3.3. First Modeling Approach
3.4. Second Modeling Approach
3.5. Statement of the Fitting Procedure
- The parameters of biomass and µ models are estimated on biomass measurements by minimization of SSE (18); in the µ model (6), the [H+] values are obtained by interpolation of the experimental [H+] data, and the signal is computed as well, whereas the pH definition is [42];
- The parameters of hydrogen models (17a) and (17b) are estimated on measurements of pH and biomass concentration via least squares, using Equation (19), with the values of computed in the previous step;
- The parameters of the biomass model (1) and specific growth rate model (6) are estimated on biomass measurements by minimization of the SSE (18); in the specific growth rate model (6), the [H+] values are obtained by using the hydrogen models (17a) and (17b) fitted in the previous step, instead of using interpolation.
4. Results and Discussion
4.1. Cultivation of Gluconacetobacter Diazotrophicus on a Laboratory Scale
4.2. Key Components of the Culture Medium
4.3. Definition of Carbon Source Concentration
4.4. Bench-Scale Submerged Cultivation
4.5. Fitting of the Kinetic Model
4.5.1. Fitting of First Approach Models
4.5.2. Fitting of Second Approach Models
4.6. Comparison of Model Fitting via First and Second Approaches
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Overview of Scientific Literature on Modeling Approaches for the Relationship between Hydrogen Ions, Acids, Bases, and Buffer
- The Wiener models [24].
Appendix B. Equation of pH for the Case of External Addition of Acids/Bases/Buffer Compounds
Appendix C. Fitting of Substrate Concentration
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N. | Component | Amount for 1 L | Concentration (g/L) |
---|---|---|---|
1 | White sugar | 100 g | 100 |
2 | K2HPO4 (10% solution) | 2 mL | 0.02 |
3 | KH2PO4 (10% solution) | 6 mL | 0.06 |
4 | MgSO4·7H2O (10% solution) | 2 mL | 0.02 |
5 | CaCl2·2H2O (1% solution) | 2 mL | 0.002 |
6 | Na2MoO4·2H2O (0,1% solution) | 2 mL | 0.0002 |
7 | FeCl3·6H2O (1% solution) | 1 mL | 0.001 |
8 | (NH4)2SO4 | 1 g | 1 |
Coded Factor | Factor | Experimental Range (g/L) | |
---|---|---|---|
Low Level (−1) | High Level (+1) | ||
Z1 | Sucrose | 70 | 130 |
Z2 | K2HPO4 | 0.005 | 0.035 |
Z3 | KH2PO4 | 0.045 | 0.075 |
Z4 | MgSO4·7H2O | 0.005 | 0.035 |
Z5 | CaCl2·2H2O | 0.0005 | 0.0035 |
Z6 | Na2MoO4·2H2O | 0.00005 | 0.00035 |
Z7 | FeCl3·6H2O | 0.0001 | 0.0019 |
Z8 | (NH4)2SO4 | 0.1 | 1.9 |
Z9–Z11 | Dummy factors | - | - |
N. | Coded Factors | Biomass (g/L) 1 | Standard Deviation | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Z1 | Z2 | Z3 | Z4 | Z5 | Z6 | Z7 | Z8 | Z9 | Z10 | Z11 | |||
1 | +1 | −1 | +1 | +1 | +1 | +1 | +1 | −1 | −1 | −1 | −1 | 0.83 | 0.20 |
2 | +1 | +1 | −1 | +1 | −1 | +1 | −1 | +1 | −1 | +1 | −1 | 1.08 | 0.32 |
3 | −1 | +1 | +1 | −1 | −1 | +1 | +1 | +1 | −1 | −1 | +1 | 1.10 | 0.23 |
4 | −1 | +1 | +1 | +1 | +1 | −1 | −1 | −1 | −1 | +1 | +1 | 1.17 | 0.11 |
5 | −1 | −1 | +1 | −1 | +1 | +1 | −1 | +1 | +1 | +1 | −1 | 1.10 | 0.04 |
6 | −1 | −1 | −1 | +1 | −1 | +1 | +1 | −1 | +1 | +1 | +1 | 1.42 | 0.63 |
7 | +1 | −1 | +1 | +1 | −1 | −1 | −1 | +1 | +1 | −1 | +1 | 1.11 | 0.20 |
8 | −1 | +1 | −1 | +1 | +1 | −1 | +1 | +1 | +1 | −1 | −1 | 1.28 | 0.19 |
9 | −1 | −1 | −1 | −1 | −1 | −1 | −1 | −1 | −1 | −1 | −1 | 1.32 | 0.22 |
10 | +1 | +1 | −1 | −1 | +1 | +1 | −1 | −1 | +1 | −1 | +1 | 1.35 | 0.43 |
11 | +1 | +1 | +1 | −1 | −1 | −1 | +1 | −1 | +1 | +1 | −1 | 1.15 | 0.17 |
12 | +1 | −1 | −1 | −1 | +1 | −1 | +1 | +1 | −1 | +1 | +1 | 1.19 | 0.24 |
Source | Chi-Squared | Degrees of Freedom | t-Value | Mean Squared Deviation | p-Value |
---|---|---|---|---|---|
Z1 | 1.370723 | 1 | 2.032245 | 7.097078 | 0.2416877 |
Z2 | 0.272593 | 1 | 2.032245 | 7.212022 | 0.6015979 |
Z3 | 2.604274 | 1 | 2.032245 | 6.965699 | 0.1065760 |
Z4 | 1.261836 | 1 | 2.032245 | 7.108559 | 0.2613038 |
Z5 | 0.002253 | 1 | 2.032245 | 7.240039 | 0.9621434 |
Z6 | 1.766220 | 1 | 2.032245 | 7.055222 | 0.1838505 |
Z7 | 0.361454 | 1 | 2.032245 | 7.202788 | 0.5476996 |
Z8 | 0.012265 | 1 | 2.032245 | 7.239003 | 0.9118151 |
Contrast | Difference | +/− Limits | Lower Limit | Higher Limit |
---|---|---|---|---|
15–30 | −0.22601 | 0.132147 | −0.358157 | −0.093863 |
15–60 | −0.14268 | 0.132147 | −0.274827 | −0.010533 |
30–75 | 0.32433 | 0.132147 | 0.192183 | 0.456477 |
30–90 | 0.13634 | 0.132147 | 0.004193 | 0.268487 |
30–105 | 0.31333 | 0.132147 | 0.181183 | 0.445477 |
30–120 | 0.35267 | 0.132147 | 0.220523 | 0.484817 |
30–135 | 0.29701 | 0.132147 | 0.164863 | 0.429157 |
30–150 | 0.187 | 0.132147 | 0.054853 | 0.319147 |
45–75 | 0.20699 | 0.132147 | 0.074843 | 0.339137 |
45–105 | 0.19599 | 0.132147 | 0.063843 | 0.328137 |
45–120 | 0.23533 | 0.132147 | 0.103183 | 0.367477 |
45–135 | 0.17967 | 0.132147 | 0.047523 | 0.311817 |
60–75 | 0.241 | 0.132147 | 0.108853 | 0.373147 |
60–105 | 0.23 | 0.132147 | 0.097853 | 0.362147 |
60–120 | 0.26934 | 0.132147 | 0.137193 | 0.401487 |
60–135 | 0.21368 | 0.132147 | 0.081533 | 0.345827 |
75–90 | −0.18799 | 0.132147 | −0.320137 | −0.055843 |
75–150 | −0.13733 | 0.132147 | −0.269477 | −0.005183 |
90–105 | 0.17699 | 0.132147 | 0.044843 | 0.309137 |
90–120 | 0.21633 | 0.132147 | 0.084183 | 0.348477 |
90–135 | 0.16067 | 0.132147 | 0.028523 | 0.292817 |
120–150 | −0.16567 | 0.132147 | −0.297817 | −0.033523 |
Modeling Approach and Model | Parameter and R2 | Value |
---|---|---|
First modeling approach; biomass model (1) and µ model (20) | µmax | 0.0093 ± 0.0017 h−1 |
Xmax | 0.3578 ± 0.0503 g/L | |
R2 (for biomass concentration over time) | 0.9364 | |
Second modeling approach; hydrogen model (21) | θ1 | 0.0665 ± 0.0093 |
θ2 | 158.5 ± 9.1 | |
R2 (for H+ concentration as a function of biomass concentration) | 0.9841 | |
Second modeling approach; hydrogen model (22) | θ | 29,449,609 ± 1,652,515 |
R2 (for H+ concentration as a function of the integral of biomass concentration) | 0.9811 | |
Second modeling approach; biomass model (1) and µ model (23), with [H+] provided by the hydrogen model (21) | µmax | 0.0076 ± 0.0012 h−1 |
Hmax | 0.00184 ± 0.00032 mol/L (corresponds to pHmin = 2.735) | |
R2 (for biomass concentration over time) | 0.9364 | |
Second modeling approach; biomass model (1) and µ model (23), with [H+] provided by the hydrogen model (22) | µmax | 0.0078 ± 0.0010 h−1 |
Hmax | 0.00181 ± 0.00027 mol/L | |
R2 (for biomass concentration over time) | 0.9357 |
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Restrepo, G.M.; Rincón, A.; Sánchez, Ó.J. Kinetic Analysis of Gluconacetobacter diazotrophicus Cultivated on a Bench Scale: Modeling the Effect of pH and Design of a Sucrose-Based Medium. Fermentation 2023, 9, 705. https://doi.org/10.3390/fermentation9080705
Restrepo GM, Rincón A, Sánchez ÓJ. Kinetic Analysis of Gluconacetobacter diazotrophicus Cultivated on a Bench Scale: Modeling the Effect of pH and Design of a Sucrose-Based Medium. Fermentation. 2023; 9(8):705. https://doi.org/10.3390/fermentation9080705
Chicago/Turabian StyleRestrepo, Gloria M., Alejandro Rincón, and Óscar J. Sánchez. 2023. "Kinetic Analysis of Gluconacetobacter diazotrophicus Cultivated on a Bench Scale: Modeling the Effect of pH and Design of a Sucrose-Based Medium" Fermentation 9, no. 8: 705. https://doi.org/10.3390/fermentation9080705