# Exploring Metalloprotease from _Dunaliella_ sp.: Production, Regulation, and Structural Insight
## 3 Results and Discussion
### Protein Production Optimization
The model's validity was confirmed by the non-significant lack of fit test, as shown in Table 3 (\(p\)-value = 0.704 > 0.05). The polynomial model demonstrates satisfactory accuracy and overall performance, as indicated by a coefficient of determination R\({}^{2}\) of 93.90%. The model's robustness was validated using the Fisher test, which showed that the regression model accounted for the variation in the factors being studied. This resulted in a test value of 13.19, exceeding the critical threshold for the Fisher test (Table 3). The statistical significance of the four variables, as well as their interactions, was determined through analysis of variance (ANOVA). Significant factors include the linear effects of both temperature (X\({}_{1}\)) and NaHCO\({}_{3}\) concentration (X\({}_{3}\)), the quadratic effects of temperature (X\({}_{1}^{2}\)) and light intensity (X\({}_{2}^{2}\)), and the interactions between temperature and luminosity (X\({}_{1}\times\) X\({}_{2}\)), temperature and NaHCO\({}_{3}\) concentration (X\({}_{1}\times\) X\({}_{3}\)), and luminosity and NaCl concentration (X\({}_{2}\times\) X\({}_{4}\)), all with \(p\)-values below 0.05. The assessment of protein accumulation revealed that the linear effects of temperature (X\({}_{1}\)), the quadratic effect of luminosity X\({}_{2}^{2}\), and the interactions between temperature and luminosity (X\({}_{1}\times\) X\({}_{2}\)), as well as luminosity and NaCl concentration (X\({}_{2}\times\) X\({}_{4}\)), had a positive impact on production. On the other hand, the significant linear effect of the NaHCO\({}_{3}\) concentration (X\({}_{3}\)), the quadratic effect of temperature (X\({}_{1}^{2}\)), and the interaction between temperature and NaHCO\({}_{3}\) concentration (X\({}_{1}\times\) X\({}_{3}\)) were found to have adverse effects, as detailed in Table 3.  
Response surface presentations were analyzed to investigate how the interactions among the variables influenced the protein content (%) of _Dunaliella salina_. Visual representation of these relationships was achieved through three-dimensional plots, where two parameters were varied while holding the others constant (Figure 2). By applying the mathematical model, it was determined that the apex of protein production accumulation, reaching 18.26%, was attained under optimized conditions. These conditions included a temperature of 28 \({}^{\circ}\)C, a luminosity of 400 \(\upmu\)mol photons/m\({}^{2}\)/s, a NaHCO\({}_{3}\) concentration \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Factor** & **Regression Coefficient** & \(p\)**-Value** \\ \hline Constant & 9.77392 & 0.000 \\ X\({}_{1}\) & 2.46564 & 0.000 \\ X\({}_{2}\) & 0.21114 & 0.472 \\ X\({}_{3}\) & \(-\)0.66642 & 0.037 \\ X\({}_{4}\) & 0.02123 & 0.942 \\ X\({}_{1}^{2}\) & \(-\)2.23708 & 0.000 \\ X\({}_{2}^{2}\) & 1.23719 & 0.013 \\ X\({}_{3}^{2}\) & \(-\)0.30482 & 0.488 \\ X\({}_{4}^{2}\) & 0.21379 & 0.625 \\ X\({}_{1}\times\) X\({}_{2}\) & 1.36795 & 0.017 \\ X\({}_{1}\times\) X\({}_{3}\) & \(-\)1.34743 & 0.018 \\ X\({}_{1}\times\) X\({}_{4}\) & \(-\)0.29625 & 0.558 \\ X\({}_{2}\times\) X\({}_{3}\) & \(-\)0.17104 & 0.734 \\ X\({}_{2}\times\) X\({}_{4}\) & 2.71626 & 0.000 \\ X\({}_{3}\times\) X\({}_{4}\) & \(-\)0.91497 & 0.088 \\ \hline \hline \multicolumn{3}{c}{Source of variation} & Degrees of freedom & Sum of square & Mean square & F-value & \(p\)-value \\ \hline Regression & 14 & 178.702 & 12.7645 & 13.19 & 0.000 \\ Residual & 12 & 11.616 & 0.9680 & \\ Lack of fit & 10 & 9.109 & 0.9109 & 0.73 & 0.704 \\ Pure Error & 2 & 2.508 & 1.2538 & \\ Total & 26 & 190.319 & & \\ \hline \hline \multicolumn{3}{c}{R\({}^{2}\) = 93.90\%} \\ \hline \end{tabular}
\end{table} 
Table 3: Protein biosynthesis by _Dunaliella_ sp. (%). Regression coefficients and ANOVA assessment. of 0.5 g/L, and a NaCl concentration of 135 g/L. This finding highlights the precise calibration of environmental variables necessary to maximize the yield of proteins by _Dunaliella_ sp.