## 4 Results and Discussion
### Kinetic Analysis
Furthermore, while the Ser558 Ala substitution did not manifest increased fermentative ability during the log phase, it exhibited enhanced capability during the stationary phase, particularly in the presence of elevated ethanol levels in the medium, suggesting a potential ethanol-resistant phenotype at low temperatures. Figure 4: Kinetic analysis of alcoholic fermentation. Representative plots depicting ln(\(H_{\infty}-H\)) against time for fermentation at 18 \({}^{\circ}\)C elucidate three discernible phases of fermentation: lag, log and stationary. The slope of each line corresponds to the reaction rate constant (\(k\)). * In the context of fermentation at 18 \({}^{\circ}\)C, there is an increment in the \(k\) value during the Lag phase for both genetically modified yeasts when compared to wild-type yeasts; however, these differences do not attain statistical significance at \(p<0.05\), one-way ANOVA. Conversely, during the subsequent log and stationary phases, the observed enhancements in the \(k\) constant values are statistically significant (\(p<0.05\), one-way ANOVA). This observation may be ascribed to the assumption that genetic modification does not manifest a discernible impact on the rate of yeast adaptation to the fermentation environment at 18 \({}^{\circ}\)C--a condition intrinsically stressful for the yeasts. After that, the fermentation efficiency of the genetically modified yeasts appears to be significantly augmented owing to the specific genetic modifications implemented, as contrasted with the wild-type strains. * Similar observations to those at 18 \({}^{\circ}\)C are drawn for fermentations at 25 \({}^{\circ}\)C regarding the behavior of the yeasts across the three phases of alcoholic fermentation. This further strengthens the conclusion that at elevated temperatures, genetic modifications impact the fermentation capacity by reducing fermentation time, while not affecting the duration of the yeasts' adaptation to the fermentation medium. * These observations align with the observed duration of alcoholic fermentation. As noted, the most significant impact of genetic modification was evident during fermentation at 12 \({}^{\circ}\)C, while the effects at 18 \({}^{\circ}\)C and 25 \({}^{\circ}\)C were not statistically significant. * The findings presented in Table 1 exhibit a consistency in magnitude with previous research endeavors. In a study conducted by Ozilgen et al. [51], the rate constant for the lag phase was calculated to range between 0.024 h\({}^{-1}\) (for fast fermentation) and 0.006 h\({}^{-1}\) (for slow fermentation), while the rate constant for the stationary phase varied between 0.039 h\({}^{-1}\) (for fast fermentation) and 0.042 h\({}^{-1}\) (for slow fermentation). Additionally, Giovanelli et al. [52] reported a specific growth rate of _S. cerevisiae_ amounting to 0.13 h\({}^{-1}\) under aerobic conditions and 0.07 h\({}^{-1}\) under anaerobic conditions. Utilizing the Arrhenius equation, the activation energies (\(E_{\alpha}\)) for various stages of alcoholic fermentation were determined:  
\[\ln(k)=\ln(A)-\frac{E_{\alpha}}{R}\frac{1}{T} \tag{7}\]  
Here, \(k\) represents the reaction rate constants of the alcoholic fermentation phases, \(A\) is the pre-exponential factor, \(E_{\alpha}\) is the activation energy, \(R\) is the gas constant, and \(T\) is the temperature. Activation energies for each stage of the fermentation process were calculated from the slopes of the graphical representations using the determined values of rate constants for each stage of alcoholic fermentation. The results are illustrated in Table 2.  
It appears that the results presented in Table 2 align with previously drawn conclusions. Specifically, the activation energy during the lag phase for the wild-type yeast strain is nearly double that of the activation energies observed for the W_M4_533 genetically modified strain. Additionally, the activation energy for the wild-type strain during the lag phase is approximately half as large as the activation energy for the W_M4_558 modified strain.