## 3 Results and Discussion
### Optimization of the Enzymatic Hydrolysis Process
\begin{table}
\begin{tabular}{c c c c c} \hline \multicolumn{4}{c}{**Coded Variables**} & \multicolumn{2}{c}{**Response**} \\ \hline \(\mathbf{X_{1}}\) & \(\mathbf{X_{2}}\) & \(\mathbf{X_{3}}\) & \(\mathbf{Y_{1}}\)**: DPPH (RSA%)** & \(\mathbf{Y_{2}}\)**: ABTS (RSA%)** \\ \hline
0 & 0 & 0 & 58.12 & 38.40 \\ \(-1\) & 1 & 0 & 77.08 & 35.86 \\
0 & 0 & 0 & 54.28 & 37.18 \\
0 & \(-1\) & 1 & 59.87 & 28.07 \\
1 & 1 & 0 & 71.75 & 42.54 \\
0 & \(-1\) & \(-1\) & 55.67 & 20.49 \\
0 & 0 & 0 & 58.12 & 37.18 \\ \(-1\) & 0 & 1 & 54.94 & 42.10 \\
0 & 0 & 0 & 54.28 & 38.40 \\ \(-1\) & 0 & \(-1\) & 54.56 & 34.87 \\
0 & 0 & 0 & 56.10 & 37.18 \\
0 & 0 & 0 & 56.10 & 38.40 \\
0 & 1 & \(-1\) & 70.05 & 37.60 \\
0 & 1 & 1 & 71.04 & 39.46 \\
0 & 0 & 0 & 53.10 & 38.40 \\
1 & 0 & \(-1\) & 58.04 & 37.77 \\ \(-1\) & \(-1\) & 0 & 49.48 & 29.26 \\
0 & 0 & 0 & 56.10 & 37.18 \\
1 & \(-1\) & 0 & 51.43 & 28.97 \\
1 & 0 & 1 & 58.76 & 39.44 \\ \hline \end{tabular}
\end{table} 
Table 3: Effect of independent variables \(X_{1}\) (papain concentration), \(X_{2}\) (temperature), and \(X_{3}\) (hydrolysis time) on responses: DPPH radical scavenging activity (\(Y_{1}\)) and ABTS radical scavenging activity (\(Y_{2}\)) of obtained LPH. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Source** & **Sum of Squares** & **df** & **Mean Square** & **F-Value** & **\(p\)-Value** & \\ \hline Model & 579.67 & 9 & 64.41 & 5.30 & 0.0060 & significant \\ A-Papain & 40.70 & 1 & 40.70 & 3.35 & 0.0445 & \\ concentration & 0.1964 & 1 & 0.1964 & 0.0162 & 0.9012 & \\ C-hydrolysis time & 2.18 & 1 & 2.18 & 0.1794 & 0.6801 & \\ AB & 62.20 & 1 & 62.20 & 5.12 & 0.0450 & \\ AC & 0.4970 & 1 & 0.4970 & 0.0409 & 0.8435 & \\ BC & 309.64 & 1 & 309.64 & 25.47 & 0.0004 & \\ A\({}^{2}\) & 17.31 & 1 & 17.31 & 1.42 & 0.2579 & \\ B\({}^{2}\) & 151.65 & 1 & 151.65 & 12.47 & 0.0047 & \\ C\({}^{2}\) & 1.28 & 1 & 1.28 & 0.1051 & 0.7519 & \\ \hline \end{tabular}
\end{table} 
Table 5: ANOVA for Quadratic model for Response 1: DPPH. In Figure 2, a series of model graphs is presented. The perturbation plot (Figure 2a) shows the influence of the input factors on the corresponding response. In this case, on the DPPH, the most significant influence is factor A (papain concentration), followed by factor B (temperature). The factor C line is almost parallel to the \(x\)-axis and therefore has no significant influence. The response surface plots (Figure 2b-d) visualize the variation of the values of two independent variables within the experimental domain while holding the other one constant. Figure 2b reveals that the maximum value of DPPH can be achieved by keeping the temperature and papain concentration at 40 \({}^{\circ}\)C and 2.0%, respectively, while the hydrolysis time is chosen to be a minimum of 60 min. It appears that Factor C has the opposite effect on DPPH. Also shown with flags are the actual and model-predicted values at two experimental points, demonstrating the minimum prediction error. Figure 2c shows that the maximum value of DPPH can be achieved with a minimum hydrolysis time, papain concentration in the range of 1-2.5%, and maximum temperature. Figure 2: Perturbation and response surface plots: DPPH. (**a**) perturbation; (**b**) contour surface plot of DPPH against of papain concentration and temperature; (**c**) contour surface plot of DPPH against of papain concentration and hydrolysis time; (**d**) Contour surface plot of DPPH against of hydrolysis time and temperature. Figure 2d reveals two regions with maximum DPPH values. Getting into one (bottom right) requires a hydrolysis time of over 90 min, a temperature of 20 \({}^{\circ}\)C degrees or less (which is outside the considered range), and a maximum papain concentration. To get into the other area (located on the opposite diagonal), a minimum time for hydrolysis (60 min), a temperature above 35 \({}^{\circ}\)C, and a minimum concentration of papain are required. Two-factor interaction terms have been obtained to describe the dependence of ABTS on the input variables (Table 7).