# Online Monitoring of the Growth of Probiotic Bacteria and Metabolites in the Fermentation of a Teff Substrate Using Model-Based Calibration of 2D Fluorescence Spectra

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Starter Culture Preparation

#### 2.3. Enumeration of Viable Microbes and Fermentation Conditions

#### 2.4. Offline and Online Measurements

_{2}SO

_{4}solvent with a flow rate of 0.6 mL/min was used. The quantities of analytes were calculated using the chromatography software GalaxieTM, version number 1.10.0.5590 (Varian, Walnut Creek, CA, USA).

#### 2.5. Process Simulation and Optimization

#### 2.6. Process Simulation Models

_{t}is the biomass (cell counts of LPA6 and LCGG), µ is the microbial specific growth rate, X

_{o}is the inoculated biomass, t is the fermentation time, G

_{t}is the glucose concentration, G

_{o}is the initial glucose concentration, Y

_{GX}is the yield coefficient with respect to the conversion from glucose to biomass, L

_{t}is the lactic acid concentration, and Y

_{GL}indicates the yield coefficient with respect to the conversion from glucose to lactic acid.

#### 2.7. Classical Approach to the Optimization of Process Model Parameters

_{GX}), and the yield coefficient with respect to the conversion from glucose to lactic acid (Y

_{GL}). However, the concentration of the state variables, such as biomass, glucose, and lactic acid from simulation, might not reflect their actual concentrations. Since the process parameters are specific to a given bioprocess, the first step was to determine the process parameters. To find the optimum process model parameters (µ, Y

_{GX,}and Y

_{GL}) of the bioprocess under consideration, simulated process state variables were used to fit against the previously obtained offline data. The particle swarm optimization algorithm [14] was used to find the optimum process parameters, for which the simulated state variables fit to the corresponding offline data.

_{GX,}Y

_{GL}), if the sum of normalized fitness values is higher, it indicates that the simulated concentrations are significantly deviated from the actual measurements. A solution from particle swarm optimization is an optimum combination of process parameters (µ, Y

_{GX,}Y

_{GL}), for which the sum of the normalized fitness values is the minimum. The process model can estimate the state variables at any measurement point using the optimized process parameters with the initial conditions. More specifically, a classical approach for the optimization of process parameters is an optimized problem solved iteratively to find the optimum combination of process parameters, for which the simulated values are made equivalent to the offline values by using a least-square fitting approach. The quality functions are presented in Equations (6)–(9):

_{O}) and glucose (G

_{O}) with a random initial set of process parameters: specific growth rate (µ), yield coefficient with respect to the conversion from glucose to biomass (Y

_{GX}), and yield coefficient with respect to the conversion from glucose to lactic acid (Y

_{GL}). The constraints of the process parameters for the search space are defined based on initial investigations and set to a range of 0.2–0.9 [10

^{8}CFU/h] for µ and 2.0–4.0 (10

^{8}CFU/g) for Y

_{GX}and Y

_{GL}.

#### 2.8. Model-Based Calibration Approach for the Optimization of the Process Model and Chemometric Model Parameters

_{O}), glucose (G

_{O}), and lactic acid (L

_{O}) are assumed to be known; the constraint of the process parameter for the search space is defined based on initial investigations and set to a range of 0.2–0.9 (10

^{8}CFU/h) for µ, but for Y

_{GX}and Y

_{GL}, values were kept constant at 3.4 and 2.5 × 10

^{8}cfu/g, respectively. Initially, a random value for the microbial specific growth rate within the search space was proposed; the cultivations were simulated with the mathematical process model by using the proposed growth rate and the initial conditions. Different initial conditions could give different simulated values at a given point of measurement during the cultivation time; the intensity values of the fluorescence spectra were normalized with SNV and a partial least square regression model was applied.

#### 2.9. Validation of Model-Based Calibration

## 3. Results and Discussion

#### 3.1. Initial Conditions for the Cultivation and Optimization of the Process Parameters

#### 3.2. Validation of the Model-Based Calibration Approach

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Classical approach for the optimization of the process model parameters for the cultivation of Lactiplantibacillus plantarum A6 and Lacticaseibacillus rhamnosus GG; G

_{O}and X

_{O}are the initial concentrations of glucose and biomass, respectively; G

^{off}, L

^{off}, and X

^{off}are the offline data for glucose, lactic acid, and biomass, respectively; G

^{sim}, L

^{sim}, and X

^{sim}are the simulated data for glucose, lactic acid, and biomass, respectively; µ, microbial specific growth rate; Y

_{GX}, yield coefficient with respect to the conversion from glucose to biomass; and Y

_{GL}, yield coefficient with respect to the conversion from glucose to lactic acid. (

**A**) displays the offline data acquired during cultivation, (

**B**) shows the initial and optimized process model parameters, and (

**C**) illustrates the optimization process.

**Figure 2.**Model-based calibration process to find the optimized parameters in the cultivation of Lactiplantibacillus plantarum A6 and Lacticaseibacillus rhamnosus GG; G

_{O}and X

_{O}are the initial concentrations of glucose and biomass, respectively; G

^{off}, L

^{off}, and X

^{off}are the offline data for glucose, lactic acid, and biomass, respectively; G

^{sim}, L

^{sim}, and X

^{sim}are the simulated data for glucose, lactic acid, and biomass, respectively; µ, microbial specific growth rate; Y

_{GX}, yield coefficient with respect to the conversion from glucose to biomass; Y

_{GL}, yield coefficient with respect to the conversion from glucose to lactic acid; SNV is the standard normal variate; SE is the sum of the error; and PLSR is the partial least square regression. (

**A**) shows spectra data and initial values of biomass and glucose; section (

**B**) serves as input for the main optimization cycle carried out in section (

**C**) with the initial parameters for the theoretical process model and the corresponding search space costraints.

**Figure 3.**Validation of the chemometric model calibrated from 2D fluorescence spectra using a model-based calibration approach to predict biomass, glucose, and lactic acid, aligned with the actual offline measurements.

**Table 1.**Initial concentrations of glucose and biomass (initial levels of Lactiplantibacillus plantarum A6 and Lacticaseibacillus rhamnosus GG).

Cultivations | Initial Glucose (g/L) | * Initial Biomass (10^{8} CFU/mL) |
---|---|---|

Cultivation 1 | 1.21 | 0.02 |

Cultivation 2 | 1.21 | 0.002 |

Cultivation 3 | 0.76 | 0.02 |

**Table 2.**Optimized process parameters calculated with the classical and modal-based calibration approaches.

Approaches | µ (10^{8} CFU/h) | Y_{GX} (10^{8} CFU/g) | Y_{GL} (g/g) |
---|---|---|---|

Classical | 0.53 | 3.33 | 2.68 |

Model-based calibration | 0.54 | 3.40 * | 2.50 * |

_{GX}, yield coefficient with respect to the conversion from glucose to biomass; Y

_{GL}, yield coefficient with respect to the conversion from glucose to lactic acid.

**Table 3.**Validation of the simulated data with respect to the actual offline data. Simulated biomass, glucose, and lactic acid were used to train the chemometric model and to perform the partial least square regression model.

Approaches | Biomass RMSE | Glucose RMSE | Lactic Acid RMSE | |||
---|---|---|---|---|---|---|

$\left({10}^{8}\mathrm{CFU}\right)$ | (% range) | (g/L) | (% range) | (g/L) | (% range) | |

Classical | 0.33 | 6.3 | 0.13 | 10.5 | 0.15 | 7.9 |

MBC | 0.32 | 6.1 | 0.13 | 10.3 | 0.16 | 8.3 |

**Table 4.**Validation of the predicted biomass, glucose, and lactic acid concentrations with respect to the actual offline measurements. The prediction was performed by the chemometric model (partial least square regression) trained with the simulated concentrations of biomass, glucose, and lactic acid.

Approaches | Biomass RMSE | Glucose RMSE | Lactic Acid RMSE | |||
---|---|---|---|---|---|---|

$\left({10}^{8}\mathrm{CFU}\right)$ | (% range) | (g/L) | (% range) | (g/L) | (% range) | |

Classical | 0.36 | 6.9 | 0.13 | 10.5 | 0.16 | 8.6 |

MBC | 0.37 | 7.1 | 0.13 | 10.5 | 0.15 | 8.0 |

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**MDPI and ACS Style**

Alemneh, S.T.; Babor, M.; Zettel, V.; von Wrochem, A.; Hitzmann, B.
Online Monitoring of the Growth of Probiotic Bacteria and Metabolites in the Fermentation of a Teff Substrate Using Model-Based Calibration of 2D Fluorescence Spectra. *Microorganisms* **2023**, *11*, 1032.
https://doi.org/10.3390/microorganisms11041032

**AMA Style**

Alemneh ST, Babor M, Zettel V, von Wrochem A, Hitzmann B.
Online Monitoring of the Growth of Probiotic Bacteria and Metabolites in the Fermentation of a Teff Substrate Using Model-Based Calibration of 2D Fluorescence Spectra. *Microorganisms*. 2023; 11(4):1032.
https://doi.org/10.3390/microorganisms11041032

**Chicago/Turabian Style**

Alemneh, Sendeku Takele, Majharulislam Babor, Viktoria Zettel, Almut von Wrochem, and Bernd Hitzmann.
2023. "Online Monitoring of the Growth of Probiotic Bacteria and Metabolites in the Fermentation of a Teff Substrate Using Model-Based Calibration of 2D Fluorescence Spectra" *Microorganisms* 11, no. 4: 1032.
https://doi.org/10.3390/microorganisms11041032