# Exploring Metalloprotease from _Dunaliella_ sp.: Production, Regulation, and Structural Insight
## 3 Results and Discussion
### Specific Proteolytic Activity Optimization  
A Box-Behnken design was performed to identify the optimal levels of the four selected variables. Details of the experimental design matrix and the corresponding output response (specific proteolytic activity in our case) can be found in Table 4. The specific proteolytic activity (U/mg of proteins) results were fitted to a second-order polynomial function (Equation (4)), which encompasses only the significant effects of the various factors. Specific proteolytic activity (U/mg of proteins) = 5.4636 + 0.8304 \(\times\) X\({}_{1}\) - 0.6898 \(\times\) X\({}_{2}\)  
+1.2445 \(\times\) X\({}_{3}\) + 0.4226 \(\times\) X\({}_{1}^{2}\) + 0.8218 \(\times\) X\({}_{2}^{2}\) - 0.8443 \(\times\) X\({}_{4}^{2}\) - 0.6606 \(\times\) X\({}_{1}\) \(\times\) X\({}_{2}\) + 1.5993 \(\times\) X\({}_{1}\) \(\times\) X\({}_{3}\)  
- 0.9399 \(\times\) X\({}_{2}\) \(\times\) X\({}_{4}\)  
where the variables X\({}_{1}\), X\({}_{2}\), X\({}_{3}\), and X\({}_{4}\) correspond to the temperature, luminosity, NaHCO\({}_{3}\) concentration, and NaCl concentration, respectively. The coefficient of determination (R\({}^{2}\))was 97.52%, and the adjusted determination coefficient was 94.63%, highlighting the high accuracy and reliability of the proposed model. The statistical assessment of Equation (4) was studied through ANOVA using Minitab software. Table 4 shows that the lack of fit was non-significant, indicating a high-quality fit of the determined model across the entire experimental range. The obtained \(p\)-values for the linear effects of temperature (X\({}_{1}\)), luminosity (X\({}_{2}\)), and NaHCO\({}_{3}\) concentration (X\({}_{3}\)),  
Figure 3: (**A**) Protein production and (**B**) specific proteolytic activity under standard conditions (red color) and optimized conditions (blue color). the quadratic effects of temperature (\(X_{1}^{2}\)), luminosity (\(X_{2}^{2}\)) and NaCl concentration (\(X_{4}^{2}\)), and the interactions between temperature and luminosity (X\({}_{1}\)\(\times\) X\({}_{2}\)), temperature and NaHCO\({}_{3}\) concentration (X\({}_{1}\)\(\times\) X\({}_{3}\)), temperature and NaCl concentration (X\({}_{1}\)\(\times\) X\({}_{4}\)), and luminosity and NaCl concentration (X\({}_{2}\)\(\times\) X\({}_{4}\)) collectively indicate strong dependencies of the experimental data on the factors under investigation. To illustrate the correlations between specific proteolytic activity (U/mg of proteins) and the experimental levels of each variable, three-dimensional response surface plots were generated (Figure 2). The assessment of these surface plots revealed substantial interactions between each pair of variables, consistent with the ANOVA findings detailed in this investigation (Table 4). The optimization of culture conditions for _Dunaliella_ sp. revealed a peak in specific proteolytic activity reaching 12.7094 U/mg of proteins, achieved with a desirability of 100%. This optimal activity was attained when the temperature, light intensity, NaHCO\({}_{3}\) concentration, and NaCl concentration were precisely set to 28 \({}^{\circ}\)C, 100 umol photons/m\({}^{2}\)/s, 1.5 g/L, and 45.54 g/L, respectively. Under these optimized conditions, the measured average specific proteolytic activity was 12.54 \(\pm\) 0.86 U/mg of proteins, closely matching the predicted value. This represents an enhancement from the standard conditions, where the proteolytic activity was 7.36 \(\pm\) 0.74 U/mg of proteins at 23 \({}^{\circ}\)C, 100 umol photons/m\({}^{2}\)/s, and using F/2 medium (Figure 3B). The optimization led to a 1.7-fold increase compared to the standard conditions. Comparing enzyme activities across different studies poses challenges due to the considerable diversity in producer organisms and experimental conditions reported data in the literature. Typically, cysteine proteases of plant origin have shown protease activities ranging from 10 to 33 U/mL [104; 105].