## 3 Results
On the second day of the reaction, the lactone concentration doubled (0.46 \(\pm\) 0.02 g/L), and the dissolved oxygen concentration in the medium was about 15-20%, which was more conducive to lactone synthesis. With regard to the first and second biotransformations, the concentrations of lactone were nearly 3 and 4 times lower, respectively. Cells multiplied slightly better than in bioreactor 3, but significantly weaker compared to bioreactors 1 and 2. Optical density (Figure 2d) was correlated to the biomass yield. OD increased from 5.19 \(\pm\) 0.32 on the first day of biotransformation to 9.60 \(\pm\) 0.91 on the second day, and the biomass yield increased from 5.80 \(\pm\) 0.85 g CDW/L to 9.60 \(\pm\) 0.95 g CDW/L. As in culture 3, extending the reaction time resulted in a decrease in the hydrophobic properties of the cells from 54.2 \(\pm\) 7.0% to 28.4 \(\pm\) 4.2%. Data are presented as the mean \(\pm\) standard deviation of three replicates. Comparing the kinetic parameters of all four cultures (Table 3), it can be noticed that the intensity of mixing and aeration of the medium were important in cell proliferation as well as in lactone biosynthesis [40; 41; 42]. In the first two cultures, in which a variable speed of agitation was used, taking into account the level of dissolved oxygen in the medium, better results of GDL biosynthesis were obtained. The best parameters for both conversion yield of GDL per biomass formed (Y\({}_{\text{L/X}}\)) or per carbon substrate (Y\({}_{\text{L/S}}\)) and for volumetric rate of GDL production (q\({}_{\text{Lv}}\)) or specific rate of GDL production (q\({}_{\text{L}}\)) were obtained in bioreactor 2. The yield of GDL synthesis in terms of carbon substrate in this culture was 0.043 g/g and was twice as high than in culture 1 and more than 10 times higher than in culture 3. Comparing the volumetric rate of GDL production (q\({}_{\text{Lv}}\)) g/L/h in individual cultures, it can be seen that between the most efficient and the least efficient biotransformation, the volumetric rate was 12.5 times lower. Similarly, in the case of the specific rate of GDL production efficiency, between the best culture ( bioreactor 2) and the worst (bioreactor 3), the specific rate of GDL production differed by 6.5-fold. Evaluation of Optimal Conditions for \(\gamma\)-Decalactone Biosynthesis in Bioreactor Culture Means of the Taguchi Statistical Design Method  
Performing four experiments in accordance with the assumptions of the Taguchi method of experimental design allowed for the selection of optimal parameters of GDL biosynthesis. The statistical analysis took into account the influence of three parameters, substrate acidity, mixing speed, and substrate concentration (castor oil), on the following initial values: maximum GDL concentration in the medium, dry biomass yield, and yeast cell viability. The results of the statistical analysis are visualized graphically in the form of mean Eta values, marginal means, informing about the input values for which it is forecast to obtain the most desirable value of the selected output parameter. Figure 3 shows the average Eta values obtained on the second day of the biotransformation reaction, on average after 45 h. The data in Figure 3a show that the most important factor influencing the increase in GDL concentration in the medium was the intensity of mixing. Variable mixing speed (200-500 rpm) allowed us to avoid complete oxygen depletion in the substrate, and ensuring adequate oxygenation of the substrate increases the efficiency of biotransformation of castor oil to GDL, because oxygen is a substrate of the \(\beta\)-oxidation pathway. The remaining factors ensuring the maximum concentration of lactone are presented in Table 4. The optimal parameters were revealed during the Taguchi design experiment. Taking into account the obtained cellular biomass yield (Figure 3b), the substrate concentration was the most important factor.