**3. Results and Discussion**

Microbial growth is influenced by the culture medium constituents and the physico-chemical factors in particular, temperature, pH, and substrate concentration. Indeed, in the present study, the temperature, the initial pH and the concentration of the carbon source (total sugars extracted from dates) were supposed to optimize the biomass production of *S. cerevisiae* using the central composite experimental design. The biomass concentration over 16 h of fermentation varied with the change in temperature, initial pH and sugar concentration (Table 5).


**Table 5.** The central composite design for biomass production.

\* Each experiment was carried out twice and the average value is used here.

Using the results obtained in diverse experiments, the correlation gives the influence of temperature (*X1*), initial pH (*X2*) and total sugar concentration (*X3*) on the response. This correlation is obtained by Minitab 16 software and expressed by the following second order polynomial (Equation (7)):

$$Y\_i = 40.074 - 0.568X\_1 - 0.090X\_2 + 1.373X\_3 - 5.999X\_1^2 - 4.248X\_2^2 - 5.893X\_3^2 - 0.070X\_1X\_2 + 2.772X\_1X\_3 - 1.925X\_2X\_3 \tag{7}$$

Table 6 shows the coefficient regression corresponding with *t* and *p*-values for all the linear, quadratic and interaction effects of parameters tested. A positive sign in the *t*-value indicates a synergistic effect, while a negative sign represents an antagonistic effect of the parameters on the biomass concentration [29].


**Table 6.** Estimated regression coefficients of t and *p*-values of the model. ‐

 − − − − − − −

‐

‐

*R* <sup>2</sup> = 91.1%, *R* 2 (adj) = 83.16%, S = 3.41104, PRESS = 884.951. β − −

The examination of Table 6 shows that all coefficient regression of the quadratic terms are statistically significant *p* ≤ 0.05 and negatively affect the biomass production (Figure 2). In contrast all coefficient regression of linear and interaction terms were statistically not significant *p* > 0.005, except the interaction term *X1X3*, which is significant *p* = 0.044 and has a synergistic effect on the response (Figure 2). ≤

**Figure 2.** Variable effect signification on a biomass production.

The analysis of variance (ANOVA) of the coefficient regression for the cell growth production (Table 7) demonstrates that the model is significant due to the *F*-value of 11.43 and the low probability *p* value (*p* = 0.000). Generally, the *F*-value with a low probability *p*-value indicates a high significance of the regression model [30].

Moreover, the coefficient of determination (*R* 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.

significance of the regression model [30].

not explained by the model.


**Table 7.** Analysis of variance (ANOVA). C 1 25.78 25.78 25.779 2.22 0.167 

**2017**, *6*, 64 9 of 17

**Table 7.** Analysis of variance (ANOVA).

**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

  

The analysis of variance (ANOVA) of the coefficient regression for the cell growth production (Table 7) demonstrates that the model is significant due to the *F*‐value of 11.43 and the low probability *p* value (*p* = 0.000). Generally, the *F*‐value with a low probability *p*‐value indicates a high

 

DF: degrees of freedom; Seq SS: sequential sum of squares; Adj SS: adjusted, sum of squares; AdjMS: adjusted, mean of squares F: Fischer's variance ratio; P: probability value. [31]. On the other hand, the obtained *R*<sup>2</sup> 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 

**Figure 3.** The fit between the model and experimental data of cell growth. **Figure 3.** The fit between the model and experimental data of cell growth.

According to the literature, the study proposed by Boudjemaet al. [22] was carried out using a

design of experiment to describe the batch fermentation of bioethanol and biomass production on sweet cheese whey by *Saccharomyces cerevisiae* DIV13‐Z087C0VS. The results showed a good According to the literature, the study proposed by Boudjemaet al. [22] was carried out using a design of experiment to describe the batch fermentation of bioethanol and biomass production on sweet cheese whey by *Saccharomyces cerevisiae* DIV13-Z087C0VS. The results showed a good agreement with experimental data (a low probability *p* value ≤ 0.000 and a good correlation coefficient (*R* <sup>2</sup> = 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* <sup>2</sup> = 0.9421).

The optimization of the response *Y<sup>i</sup>* (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).

≤

**Figure 4.** Surface plot for the effect of different parameters on biomass production.

**Figure 5.** Isoresponse contour plot for the effect of the studied variables on biomass production.

These figures show that there is an optimum, located at the center of the field of study. In addition, the use of the minitab optimizer will give exact values of the optimum operating conditions of the process (Figure 6).

− −

‐

**Figure 6.** Coded values of optimal conditions on biomass production.

− − Figure 6 shows the maximum biomass production by *S. cerevisiae* (40.162 g/L) corresponding to coded values of temperature (−0.0170), pH (−0.0510) and sugar concentration (0.1189).These values are equivalent to real values of 32.9 ◦C, 5.35 and 70.93 g/L, respectively. Jiménez Islas et al. [27] obtained the highest cell concentration of *S. cerevisiae* ATCC 9763 (7.9 g/L) after 26 h when the strain grew at 30 ◦C and pH 5.5.

The validation of the baker's yeast biomass concentration and total reducing sugar consumption, over time, at optimized conditions, are presented in Figure 7. In the beginning, the biomass concentration increased with a decrease in the sugar level, reaching the maximum (40 g/L) at 16 h of fermentation, which confirms the biomass obtained by the CCD predictions (40.1620) (Figure 6). After this period, the diminution of a biomass concentration was observed, which could be explained by the sugar consumption, which ran out after18 h of fermentation.

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

The same results were obtained by Nancib et al. [33], where the production of biomass from baker's yeast *S. cerevisiae* on a medium containing date byproducts was 40 g/L. Khan et al. [34] used six different strains of *S*. *cerevisiae* in fermentation medium containing date extract (with 60% sugars),

t ‐

*μ* <sup>−</sup>

−

μ

‐

*μ* ‐

in addition to 2 g/L ammonium sulfate and 50 mg/L biotin. Their results showed that the theoretical yields were about 42.8%. In addition, Al Obaidi et al. [35] studied two substrates i.e, date syrup and molasses for the propagation of baker's yeast strain *S. cerevisiae* on a pilot plant scale. The results showed that higher productivity of baker's yeast was observed when date extract was used. Other results were obtained in several studies using an alternative substrate of fermentation. In fact, the optimal biomass production (6.3 g/L) was depicted at 24 h using *Saccharomyces cerevisiae* DIV13-Z087C0VS on a medium containing sweet cheese as a sole carbon source [22]. On the other hand, the production of baker's yeast from apple pomace gives a yield of 0.48 g/g [36]. Therefore, it was concluded from these studies that the medium containing the date extract as a sole carbon source is an excellent fermentation medium for baker's yeast production.

The results of the kinetic parameters of *S. cerevisiae* growth with the different kinetic models based on the curve fitting method are presented in Table 8.


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

The curve fitting of cell growth using the Monod model (1/µ versus 1/S) is presented in Figure 8. Based on the results obtained in Table 8 for this model the *µmax* 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* <sup>2</sup> 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. ‐

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

*μ* − Figure 9 illustrates the linear curve fitting (µ versus X) to examine the reliability of cell kinetic performance via the Verhulst model. The analysis of the results obtained showed that the experimental data of the cell growth and substrate consumption in batch system have an excellent fitness with this model (*R* <sup>2</sup> = 0.981). The maximum specific growth rate (*µmax*) and the maximum concentration of biomass (*Xm*), were 0.376 h−<sup>1</sup> 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.

−

‐

μ

μ

‐

‐

μ

−

*μ*

**Figure 9.** A plot fitting the experimental data using the Verhulst kinetic model.

μ − μ ‐ The kinetic behavior fitness of *S. cerevisiae* with the Tessier kinetic model is illustrated in Figure 10. The coefficient of correlation *R* 2 equal to 0.979 and the estimation parameters (µmax 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* <sup>2</sup> and µmax values, the model is not suitable with the experimental data due to the illogical value of the half-saturation constant (negative Ks).

**Figure 10.** A plot fitting the experimental data using the Tessier kinetic model.

The comparison between the three kinetic models tested in this study showed that the Verhulst kinetic model with *R* <sup>2</sup> = 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.*

A profile of biomass and total reducing sugar concentration during fermentation time is compared to the values predicted by the equations model obtained in Figure 11.

∆ ▲

□ ■

− ‐

‐

‐

‐

‐

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

At the beginning of the fermentation, values of biomass between predicted and experimental data were approximately the same. However, after 10 h and until the end of the fermentation, the difference was remarkable. In fact, the values relative to biomass were inferior compared to the values predicted by the Verhulst model. The correlation coefficient is 0.992. As for total reducing sugar concentration, the values obtained by the Leudeking Piret model were lower than those predicted in the first 7 h only. After this period, total reducing sugar values were almost identical. The correlation coefficient is 0.984. In addition, the parameter values of *p* and *q* were optimized using the experimental data for substrate based on the square minimized between observed and predicted data. Excel software illustrated the values of *<sup>p</sup>* = 2.1235 and *<sup>q</sup>* <sup>=</sup> <sup>−</sup>0.0256 h−<sup>1</sup> . 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* <sup>2</sup> = 0.91) for cell growth and (*R* <sup>2</sup> = 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* <sup>2</sup> = 0.984). The coefficient equation were also calculated (*p* and *q*) their values were 1.41 (g/g) and 0.0007 (1/h) respectively.
