## 4 Results and Discussion
### Kinetic Analysis  
Alcoholic fermentation is characterized by four distinct stages from the beginning to the end of the fermentations, and they correspond to the phases of the alcoholic fermentation processes. Sometimes, three distinct stages are observed as the absorption of one phase by its neighboring phase. The kinetic characteristics of each phase were calculated by plotting ln (\(H_{\infty}-H\)) against \(t\). Here, \(H_{\infty}\) represents the peak height of the sample collected at the end of fermentation, and \(h\) corresponds to the peak height of each sample collected at time point \(t\). Rate constants (\(k\)) were determined for each stage of the fermentation process. Representative plots for each strain at 18 \({}^{\circ}\)C are depicted in Figure 4, illustrating three distinct phases of alcoholic fermentation corresponding to the lag phase, log phase and stationary phase. These plots confirm that alcoholic fermentation can be modeled as a pseudo-first-order reaction. Consequently, the slopes mentioned above correspond to the lag, log and stationary phases. These slopes were validated by \(\tau^{2}\) values ranging between 0.94 and 1.00. By considering the slopes of the aforementioned lines and remembering Equation (6), the rate constants of ethanol production, \(k\), can be readily computed for the three phases observed during the alcoholic fermentations conducted with wild-type yeast strains as well as genetically modified strains at various temperatures. As the rate constants for ethanol production align with the phases of the alcoholic fermentation process, estimating the duration of each of these phases becomes straightforward. The results, presented in Table 1, represent mean values calculated after three replications for each system, along with their corresponding standard deviations. In Table 1, the reaction rate constants (\(k\)) for each phase (lag, log and stationary) at various temperatures, along with their respective standard deviations are illustrated. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Yeast Strain**} & \multirow{2}{*}{\(\mathbf{\theta}^{\circ}\)**C**} & \multicolumn{3}{c}{**(\(\mathbf{k\pm\sigma}\)) (10\({}^{3}\) h\({}^{-1}\))**} \\ \cline{3-5}  & & **Lag Phase** & **Log Phase** & **Stationary Phase** \\ \hline \multirow{3}{*}{W303} & 12 & 0.54 \(\pm\) 0.13 & 1.83 \(\pm\) 0.07 & 1.95 \(\pm\) 0.64 \\  & 18 & 2.19 \(\pm\) 0.49 & 7.02 \(\pm\) 0.48 & 5.25 \(\pm\) 0.09 \\  & 25 & 7.49 \(\pm\) 0.99 & 20.92 \(\pm\) 0.99 & 12.93 \(\pm\) 0.45 \\ \hline \multirow{3}{*}{W\_M4\_558} & 12 & 0.91 \(\pm\) 0.18 & 3.39 \(\pm\) 0.24 & 7.27 \(\pm\) 2.12 \\  & 18 & 2.59 \(\pm\) 0.08 & 10.34 \(\pm\) 0.77 & 9.52 \(\pm\) 0.48 \\  & 25 & 6.83 \(\pm\) 0.14 & 27.43 \(\pm\) 1.43 & 11.95 \(\pm\) 1.18 \\ \hlineFrom the results presented in Table 1, one can derive the following insights:  
* Throughout the fermentation process at 12 \({}^{\circ}\)C, the lag phase revealed an approximately 2-fold increase in the reaction rate constant for strain W_M4_558 and a more than 3-fold increment for W_M4_533, both in comparison to the wild-type strain. These disparities were found to be statistically significant (\(p<0.05\), one-way ANOVA). In the log phase, both genetically modified strains exhibited heightened reaction rate constants. Specifically, the Ser558 Ala modification resulted in a statistically significant 1.5-fold increase in k (\(p<0.05\), one-way ANOVA), while the Ser533 Ala modification proved notably more effective, yielding an almost 4-fold increase in the reaction rate constant (\(p=0.05\), one-way ANOVA). Moving to the stationary phase, both genetically modified strains demonstrated increased reaction rate constants compared to the wild type. W_M4_558 exhibited a 3.5-fold greater increase (\(p<0.05\), one-way ANOVA), and W_M4_533 showed a 2.5-fold increment (\(p<0.05\), one-way ANOVA). In summary, the Ser533 Ala substitution conferred the strain with efficient fermentation capabilities at low temperatures.