## 3 Results and Discussion
### Optimization of the Enzymatic Hydrolysis Process
Figure 4b reveals that the maximum ABTS value can be achieved when both temperature and bromelain concentration are maintained above 30 \({}^{\circ}\)C and 3.0%, respectively, while the hydrolysis time is minimized to 60 min. In Figure 4c, two distinct zones for achieving maximum ABTS values are identified. The first zone requires a maximum bromelain concentration above 2.5% combined with minimal hydrolysis time, while the second zone achieves maximum ABTS activity with maximum hydrolysis time but minimal bromelain concentration. Both scenarios assume maximum temperature. Figure 4d demonstrates that the optimal ABTS radical scavenging activity can be obtained by simultaneously maximizing both bromelain concentration and temperature while keeping the hydrolysis time to a minimum. These findings provide valuable insights into the critical factors and their interactions that drive ABTS activity, offering a clear  
Figure 3: ABTS radical scavenging activity model diagnostics: (**a**) normality plot; (**b**) residuals vs. predicted; (**c**) predicted vs. actual. pathway for optimizing conditions to achieve the highest antioxidant potential in the enzymatic hydrolysis process. The response surface plots underscore the importance of precise control over temperature and bromelain concentration while suggesting that hydrolysis time plays a secondary role under these optimal conditions. An optimization process was conducted to simultaneously achieve maximum values for both DPPH and ABTS radical scavenging activities. The constraints applied during this optimization are outlined in Table 9. The optimization yielded 100 potential solutions, of which only the top 10 are presented in Table 10 for clarity and brevity. Analysis of these results identified the optimal conditions for enzymatic hydrolysis as follows: a bromelain concentration of 3.0%, a temperature of 40 \({}^{\circ}\)C, and a hydrolysis time of 60 min. These conditions were found to produce the highest levels of DPPH and ABTS radical activity. These findings are consistent with previous studies, such as the research by [PERSON] et al. (2018), which also found that bromelain is one of the most effective enzymes for enhancing the antioxidant activity of hemp proteins. Figure 4: ABTS perturbation and response surface plots: (**a**) perturbation plot; (**b**) contour surface plot: bromelain concentration vs. temperature; (**c**) contour surface plot: bromelain concentration vs. hydrolysis time; (**d**) contour surface plot: temperature vs. hydrolysis time. The data from the analysis of the radical-scavenging activity of LHPH after enzymatic hydrolysis of HSC under the established optimal conditions are presented in Table 11. The results are expressed as mg TE/g lyophilize and compared to those of aqueous extracts from the raw material without enzyme treatment (mg TE/g hemp cake). A significant increase in antioxidant activity was observed--11 times higher by the ABTS method and 19 times higher by the DPPH method. When comparing these results with studies on other plant proteins, such as soy [43] and pea proteins [44], it is observed that hemp proteins demonstrate similar or even higher antioxidant activity under comparable hydrolysis conditions. For example, in [43] it was found that the antioxidant activity of soybean hydrolysates prepared with alcalase or protamex peaked at relatively higher temperatures and hydrolysis times, but remained below the levels recorded in the present study for hemp proteins hydrolysates. The analysis of the significance of the results shows that the combination of high bromelain concentration and moderate temperature is crucial for achieving optimal outcomes. Interestingly, increasing the hydrolysis time beyond 60 min does not significantly increase antioxidant activity, suggesting that certain hydrolysis parameters play a more significant role than others.