# Optimization of Baker’s Yeast Production on Date Extract Using Response Surface Methodology (RSM)

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{2}= 0.945 and 0.979, respectively. An excellent adequacy was noted in the case of the Verhulst model (R

^{2}= 0.981). The values of kinetic parameters (Ks, X

_{m}, μ

_{m}, p and q) calculated by the Excel software, confirmed that Monod and Verhulst were suitable models, in contrast, the Tessier model was inappropriately fitted with the experimental data due to the illogical value of Ks (−9.434). The profiles prediction of the biomass production with the Verhulst model, and that of the substrate consumption using Leudeking Piret model over time, demonstrated a good agreement between the simulation models and the experimental data.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Origin and Reactivation of theYeast S. cerevisiae

#### 2.2. Preparation of Dates Extract

#### 2.3. Preparation of Culture Medium Based on the Dates Extract and Inoculums

#### 2.4. Statistical Design of Experiments

#### 2.4.1. Factor Selection and Organization of Experiments

#### 2.4.2. Effect Estimation

_{0}, is the natural value at the center point and Δx, is the step change value (the half of the interval (−1 +1)). The mathematical model describing the relation between dependent and independent variables for this process has the quadratic form for the experimental design used:

_{i}= β

_{0}+ β

_{1}X

_{1}+ β

_{2}X

_{2}+ β

_{3}X

_{3}+ β

_{11}X

_{1}² + β

_{22}X

_{2}² + β

_{33}X

_{3}² + β

_{12}X

_{1}X

_{2}+ β

_{13}X

_{1}X

_{3}+ β

_{23}X

_{2}X

_{3}

_{i}, is the predicted response (in our case, the Biomass production (g/L); β

_{0}, is offset term; β

_{1}, β

_{2}, β

_{3}are the linear effects (showing the predicted response); β

_{11}, β

_{22}, β

_{33}are the squared effects β

_{12}, β

_{13}, β

_{23}are the interaction terms and X

_{1}, X

_{2}, X

_{3}are the independent variables. The calculation of the effect of each variable and the establishment of a correlation between the response Y

_{i}and the variables X, were performed using a Minitab 16 software (Minitab, Inc., State College, PA, USA).

#### 2.4.3. Statistical Analysis

**Student test (t); Fisher test (F); and p-value. In our study, the statistical significance test level was set at 5% (probability (p) < 0.05).**

^{2}#### 2.5.Validation of Biomass Production in Optimum Medium

#### 2.6. Analytical Techniques

#### 2.6.1. Determination of Total Reducing Sugars

#### 2.6.2. Determination of Biomass Concentration

#### 2.7. Modeling

_{max}, Ks and X

_{m}), were determined using the curve fitting method of each model. The fitness evaluation of experimental data on cell growth by models was performed using Excel software (Microsoft, Redmond, WA, USA).

#### Profile Prediction of Biomass and Substrate Concentration

_{X/S}and q is a maintenance coefficient.

_{0}; t = 0) give the following Equation:

## 3. Results and Discussion

_{1}), initial pH (X

_{2}) and total sugar concentration (X

_{3}) on the response. This correlation is obtained by Minitab 16 software and expressed by the following second order polynomial (Equation (7)):

_{i}= 40.074 −0.568X

_{1}− 0.090X

_{2}+ 1.373X

_{3}− 5.999X

_{1}² − 4.248X

_{2}² − 5.893X

_{3}² − 0.070X

_{1}X

_{2}+ 2.772X

_{1}X

_{3}− 1.925X

_{2}X

_{3}

_{1}X

_{3}, which is significant p = 0.044 and has a synergistic effect on the response (Figure 2).

^{2}) measures the fit between the model and experimental data. Figure 3 was also determined to evaluate the regression model. In this study, the obtained value of R

^{2}is 0.911 approximate to 1, which justifies an excellent consistency of the model [31]. On the other hand, the obtained R

^{2}implies that 91.1% of the sample variation in the cell growth is attributed to the independent variables. This value indicates also that only 8.86% of the variation is not explained by the model.

^{2}= 0.914%), which confirms a high significance of the regression model. In addition, the study carried out by Bennamoun et al. [32] showed that the optimization of the medium components, which enhance the polygalacturonase activity of the strain Aureobasidium pullulans, was achieved with the aid of the same method used in the present study (response surface methodology). The obtained results showed a significance of the method used in comparison with the experimental data; a very low p value (0.001) and a high coefficient of determination (R

^{2}= 0.9421).

_{i}(Biomass production) and the prediction of the optimum levels of temperature, initial pH and sugars concentration of fermentation were obtained. This optimization resulted in surface plots (Figure 4) and an isoresponse contour plot (Figure 5).

_{max}and Ks were evaluated as 0.496 h

^{-1}and 0.228 g/L, respectively. These values indicate a rapid cell growth due to the high value of the specific growth rate and an elevated affinity between substrate consumption and cell growth thanks to the small half-saturation constant. In this case, R

^{2}was also fitted on 0.945. According to the results obtained, the Monod kinetic model is an appropriate model to make the kinetic performance of this strain.

^{2}= 0.981). The maximum specific growth rate (μ

_{max}) and the maximum concentration of biomass (X

_{m}), were 0.376 h

^{−1}and 15.04 g/L respectively (Table 8). Higher values of these parameters indicated a rapid growth of the biomass which confirms the goodness of fit of the Verhulst model.

^{2}equal to 0.979 and the estimation parameters (µ

_{max}and Ks) shown in Table 8 were 0.408 and −9.434 respectively. The examination of the cell growth fitting curve with the Tessier kinetic model showed that, even though they were appropriate R

^{2}and µ

_{max}values, the model is not suitable with the experimental data due to the illogical value of the half-saturation constant (negative Ks).

^{2}= 0.981 was the best and most appropriate model to explain S. cerevisiae growth and substrate utilization. Approximate results were obtained by Ardestani and Shafiei [37], who proved that the Verhulst kinetic model with R

^{2}equal to 0.97 was the most appropriate to describe the biomass growth rate of S. cerevisiae. In contrast, Ardestani and Kasebkar [38], applied an unstructured kinetic model of Aspergillus niger growth and substrate uptake in a submerged batch culture and have confirmed that Monod and Verhulst kinetic models were not in an acceptable range to fit a growth of Aspergillus niger.

^{−1}. On the basis of these results, good correlation coefficients showed that the proposed Verhulst model and the Luedeking Piret model were adequate to explain the development of biomass production process on date extract. According to the literature, the study proposed by Kara Ali et al. [39] was carried out using the logistic empirical kinetic model and Leudeking Piret model to describe batch fermentation of P. caribbica on inulin. The results showed a good agreement with the experimental data (R

^{2}= 0.91) for cell growth and (R

^{2}= 0.95) for substrate consumption. In addition, the values of p and q were 14.735 and −0.077 1/h, respectively, thus, the model equations were found to represent an appropriate kinetic model for successfully describing yeast cell growth in batch fermentation. Another kinetic study proposed by Zajšek and Goršek [40] which used the unstructured models of batch kefir fermentation kinetics for ethanol production by mixed natural microflora confirmed that the growth of kefir grains could be expressed by a logistic function model, and it can be employed for the development and optimization of bio-based ethanol production processes. Furthermore, the study of Pazouki et al. [41] which illustrated the kinetic models of cell growth, substrate utilization and bio-decolorization of distillery waste water by Aspergillus fumigatus UB260. This study confirmed that the Logistic equation for the growth and the Leudeking Piret kinetic model for substrate utilization were able to fit the experimental data (R

^{2}= 0.984). The coefficient equation were also calculated (p and q) their values were 1.41 (g/g) and 0.0007 (1/h) respectively.

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 7.**The biomass production (■), and total reducing sugar consumption (▲) over time at optimized conditions.

**Figure 8.**The Lineweaver Burk linear plot fitting the experimental data using the Monod kinetic model.

**Figure 11.**The comparison between predicted (□), experimental data (■) for biomass production of baker’s yeast; and predicted (∆), experimental data (▲), for total reducing sugar consumption.

Variables | Coded Levels | ||||

−α | −1 | 0 | +1 | +α | |

Real Values | |||||

X_{1} = Temperature (°C) | 27 | 29 | 33 | 37 | 39 |

X_{2} = Initial pH | 2.4 | 3.6 | 5.5 | 7.3 | 8.6 |

X_{3} = concentration of sugars (g/L) | 1 | 44.1 | 107.5 | 170.9 | 214 |

_{f}, where N

_{f}is a number of experiments).

**Table 2.**The central composite experimental design (CCD) matrix for different variables (coded levels).

Experiments | Coded Levels | ||
---|---|---|---|

X_{1} | X_{2} | X_{3} | |

01 | −1 | −1 | −1 |

02 | +1 | −1 | −1 |

03 | −1 | +1 | −1 |

04 | +1 | +1 | −1 |

05 | −1 | −1 | +1 |

06 | +1 | −1 | +1 |

07 | −1 | +1 | +1 |

08 | +1 | +1 | +1 |

09 | −1.68 | 0 | 0 |

10 | +1.68 | 0 | 0 |

11 | 0 | −1.68 | 0 |

12 | 0 | +1.68 | 0 |

13 | 0 | 0 | −1.68 |

14 | 0 | 0 | +1.68 |

15 | 0 | 0 | 0 |

16 | 0 | 0 | 0 |

17 | 0 | 0 | 0 |

18 | 0 | 0 | 0 |

19 | 0 | 0 | 0 |

20 | 0 | 0 | 0 |

^{3}; two axial points on the axis of each design variable at a distance of α = 1.682 from the design center and 5 points at the domain center. The actual experimental values corresponding to the coded levels used for the creation of the experiment matrix are presented below (Table 3).

Experiments | Actual Values | ||
---|---|---|---|

Temperature (°C) | Initial pH | Sugars Concentration (g/L) | |

01 | 29 | 3.6 | 44.1 |

02 | 37 | 3.6 | 44.1 |

03 | 29 | 7.3 | 44.1 |

04 | 37 | 7.3 | 44.1 |

05 | 29 | 3.6 | 170.9 |

06 | 37 | 3.6 | 170.9 |

07 | 29 | 7.3 | 170.9 |

08 | 37 | 7.3 | 170.9 |

09 | 27 | 5.5 | 107.5 |

10 | 39 | 5.5 | 107.5 |

11 | 33 | 2.4 | 107.5 |

12 | 33 | 8.6 | 107.5 |

13 | 33 | 5.5 | 1 |

14 | 33 | 5.5 | 214 |

15 | 33 | 5.5 | 107.5 |

16 | 33 | 5.5 | 107.5 |

17 | 33 | 5.5 | 107.5 |

18 | 33 | 5.5 | 107.5 |

19 | 33 | 5.5 | 107.5 |

20 | 33 | 5.5 | 107.5 |

Kinetic Models | Equations | Linearized Form | Description | Symbols |
---|---|---|---|---|

Monod | $\mu ={\mu}_{max}\frac{S}{S+{K}_{S}}$ | $\frac{1}{\mathsf{\mu}}=\frac{{K}_{S}}{{\mu}_{max}}\frac{1}{S}+\frac{1}{{\mu}_{max}}$ | Monod kinetic model is a substrate concentration dependent. | $\mu $: is the specific growth rate (h^{−1}).${\mu}_{max}$: is the maximum specific growth rate (h ^{−1}).${K}_{S}$: is the half-saturation constant (g/L). S: is the concentration in limiting substrate (g/L). $X$: is the biomass concentration (g/L). ${X}_{m}$: is the Maximum biomass concentration (g/L). |

Verhulst | $\mu ={\mu}_{max}(1-\frac{X}{{X}_{m}})$ | $\mu ={\mu}_{max}-\frac{{\mu}_{max}}{{X}_{m}}X$ | Verhulst kinetic model is an unstructured model depends on biomass concentration. | |

Tessier | $\mu ={\mu}_{max}\left(1-{\mathrm{e}}^{-KsS}\right)$ | $\mathrm{ln}\mu =\frac{1}{{K}_{s}}S+\mathrm{ln}{\mu}_{max}$ | Tessier is an unstructured model for a substrate concentration dependent. |

Experiments | Coded Levels | Real Values | (Y_{i}): Biomass (g/L) | |||||
---|---|---|---|---|---|---|---|---|

X_{1} | X_{2} | X_{3} | Temperature (°C) | Initial pH | Concentration of Sugar (g/L) | Observed Mean Values * | Predicted Values | |

01 | −1 | −1 | −1 | 29 | 3.6 | 44.1 | 24.07 | 23.99 |

02 | +1 | −1 | −1 | 37 | 3.6 | 44.1 | 15.99 | 17.45 |

03 | −1 | +1 | −1 | 29 | 7.3 | 44.1 | 25.70 | 27.80 |

04 | +1 | +1 | −1 | 37 | 7.3 | 44.1 | 15.79 | 20.98 |

05 | −1 | −1 | +1 | 29 | 3.6 | 170.9 | 28.40 | 25.05 |

06 | +1 | −1 | +1 | 37 | 3.6 | 170.9 | 29.86 | 29.59 |

07 | −1 | +1 | +1 | 29 | 7.3 | 170.9 | 20.78 | 21.16 |

08 | +1 | +1 | +1 | 37 | 7.3 | 170.9 | 23.51 | 25.42 |

09 | −1.68 | 0 | 0 | 27 | 5.5 | 107.5 | 22.61 | 24.06 |

10 | +1.68 | 0 | 0 | 39 | 5.5 | 107.5 | 26.20 | 22.15 |

11 | 0 | −1.68 | 0 | 33 | 2.4 | 107.5 | 26.00 | 28.21 |

12 | 0 | +1.68 | 0 | 33 | 8.6 | 107.5 | 32.72 | 27.90 |

13 | 0 | 0 | −1.68 | 33 | 5.5 | 1 | 25.37 | 21.09 |

14 | 0 | 0 | +1.68 | 33 | 5.5 | 214 | 24.04 | 25.71 |

15 | 0 | 0 | 0 | 33 | 5.5 | 107.5 | 40.00 | 40.07 |

16 | 0 | 0 | 0 | 33 | 5.5 | 107.5 | 40.00 | 40.07 |

17 | 0 | 0 | 0 | 33 | 5.5 | 107.5 | 40.00 | 40.07 |

18 | 0 | 0 | 0 | 33 | 5.5 | 107.5 | 40.00 | 40.07 |

19 | 0 | 0 | 0 | 33 | 5.5 | 107.5 | 40.00 | 40.07 |

20 | 0 | 0 | 0 | 33 | 5.5 | 107.5 | 40.00 | 40.07 |

Terms | Coefficients | Square Error | t-Value | p |
---|---|---|---|---|

β_{0} | 40.0744 | 1.3912 | 28.806 | 0.000 |

β_{1} | −0.5684 | 0.9230 | −0.616 | 0.552 |

β_{2} | −0.0907 | 0.9230 | −0.098 | 0.924 |

β_{3} | 1.3739 | 0.9230 | 1.488 | 0.167 |

β_{11} | −6.0000 | 0.8985 | −6.677 | 0.000 |

β_{22} | −4.2481 | 0.8985 | −4.728 | 0.001 |

β_{33} | −5.8939 | 0.8985 | −6.559 | 0.000 |

β_{12} | −0.0700 | 1.2060 | −0.058 | 0.955 |

β_{13} | 2.7725 | 1.2060 | 2.299 | 0.044 |

β_{23} | −1.9250 | 1.2060 | −1.596 | 0.142 |

^{2}= 91.1%, R

^{2}(adj) = 83.16%, S = 3.41104, PRESS = 884.951.

Source | DF | Seq SS | Adj SS | Adj MS | F | p |
---|---|---|---|---|---|---|

Regression | 9 | 1196.65 | 1196.65 | 132.961 | 11.43 | 0.000 |

Linear | 3 | 30.30 | 30.30 | 10.101 | 0.87 | 0.489 |

A | 1 | 4.41 | 4.41 | 4.412 | 0.38 | 0.552 |

B | 1 | 0.11 | 0.11 | 0.112 | 0.01 | 0.924 |

C | 1 | 25.78 | 25.78 | 25.779 | 2.22 | 0.167 |

Square | 3 | 1075.17 | 1075.17 | 358.390 | 30.80 | 0.000 |

A*A | 1 | 379.27 | 518.80 | 518.799 | 44.59 | 0.000 |

B*B | 1 | 195.28 | 260.07 | 260.071 | 22.35 | 0.001 |

C*C | 1 | 500.62 | 500.62 | 500.618 | 43.03 | 0.000 |

Interaction | 3 | 91.18 | 91.18 | 30.393 | 2.61 | 0.109 |

A*B | 1 | 0.04 | 0.04 | 0.039 | 0.00 | 0.955 |

A*C | 1 | 61.49 | 61.49 | 61.494 | 5.29 | 0.044 |

B*C | 1 | 29.64 | 29.64 | 29.645 | 2.55 | 0.142 |

Residual Error | 10 | 116.35 | 116.35 | 11.635 |

**Table 8.**Kinetic parameters of S. cerevisiae growth and substrate utilization using unstructured models.

Kinetic Models | Parameters Estimation | |||
---|---|---|---|---|

R^{2} | Ks (g/L) | μ_{max} (h^{−1}) | X_{m} | |

Monod | 0.945 | 0.228 | 0.496 | - |

Verhulst | 0.981 | - | 0.376 | 15.04 |

Tessier | 0.979 | −9.434 | 0.408 |

© 2017 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kara Ali, M.; Outili, N.; Ait Kaki, A.; Cherfia, R.; Benhassine, S.; Benaissa, A.; Kacem Chaouche, N.
Optimization of Baker’s Yeast Production on Date Extract Using Response Surface Methodology (RSM). *Foods* **2017**, *6*, 64.
https://doi.org/10.3390/foods6080064

**AMA Style**

Kara Ali M, Outili N, Ait Kaki A, Cherfia R, Benhassine S, Benaissa A, Kacem Chaouche N.
Optimization of Baker’s Yeast Production on Date Extract Using Response Surface Methodology (RSM). *Foods*. 2017; 6(8):64.
https://doi.org/10.3390/foods6080064

**Chicago/Turabian Style**

Kara Ali, Mounira, Nawel Outili, Asma Ait Kaki, Radia Cherfia, Sara Benhassine, Akila Benaissa, and Noreddine Kacem Chaouche.
2017. "Optimization of Baker’s Yeast Production on Date Extract Using Response Surface Methodology (RSM)" *Foods* 6, no. 8: 64.
https://doi.org/10.3390/foods6080064