## 2 Materials and Methods
### Response Surface Methodology: Box-Behnken Design  
An RSM with a Box-Behnken design was performed to determine the influence of three independent parameters in the hydro-ethanolic extracts: liquid-solid ratio (mL-g\({}^{-1}\)) (LSR), time of extraction (min), and ethanol percentage, as established below (Table 1).  
A second assay was designed to assess the influence of the extraction temperature (\({}^{\circ}\)C), pH, and ethanol percentage (\(v\)/\(v\)) (Table 2). In this case, the LSR and extraction time were defined according to results obtained from the first optimization assay (time of extraction of 60 min and LSR of 40 mL-g\({}^{-1}\)).  
Extracts of _Gratelopia turuturu_ were obtained by mixing 5.0 g of the seaweed biomass with the assigned volume of the assigned solvent, for the assigned time under constant magnetic stirring and thermostatized. After the extraction procedure, each extract was centrifuged (10,000\(\times\)\(g\) for 5 min) and the supernatant filtered at low pressure (Whatmann n\({}^{\circ}\)1) and stored at 4 \({}^{\circ}\)C until further processing (maximum 24 h). The extracts were then evaporated under reduced pressure at 40 \({}^{\circ}\)C and desiccated under a vacuum concentrator at room temperature (Vacufuge, Eppendorf, Germany). Dry extracts were weighed and yield was calculated (g extract-g\({}^{-1}\) biomass).  
Each extract was then resuspended for further assaying their UV-absorbance and antioxidant activities. Water extracts were resuspended in water at 25 mg-mL\({}^{-1}\); 25% (\(v\)/\(v\)) ethanol extracts were  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Coded Variables**} & \multicolumn{3}{c}{**Actual Variable Values**} \\ \cline{2-6}
**Run** & \(\mathbf{(X_{1})}\) & \(\mathbf{(X_{2})}\) & \(\mathbf{(X_{3})}\) & \% EtOH (\(v\)/\(v\)) (\(X_{1}\)) & LSR (mL-g\({}^{-1}\)) (\(X_{2}\)) & Time (Minutes) (\(X_{3}\)) \\ \hline
2 & 1 & 0 & \(-1\) & 50 & 25 & 20 \\
3 & \(-1\) & 0 & 1 & 0 & 25 & 100 \\
4 & 1 & 0 & 1 & 50 & 25 & 100 \\
5 & \(-1\) & \(-1\) & 0 & 0 & 10 & 60 \\
6 & \(-1\) & 1 & 0 & 0 & 40 & 60 \\
7 & 1 & \(-1\) & 0 & 50 & 10 & 60 \\
8 & 1 & 1 & 0 & 50 & 40 & 60 \\
9 & 0 & \(-1\) & \(-1\) & 25 & 10 & 20 \\
10 & 0 & \(-1\) & 1 & 25 & 10 & 100 \\
11 & 0 & 1 & \(-1\) & 25 & 40 & 20 \\
12 & 0 & 1 & 1 & 25 & 40 & 100 \\
13 & 0 & 0 & 0 & 25 & 25 & 60 \\
14 & 0 & 0 & 0 & 25 & 25 & 60 \\
15 & 0 & 0 & 0 & 25 & 25 & 60 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Independent variables tested during the first optimization of the extraction process using a Box–Behnken design: ethanol percentage (\(X_{1}\)), liquid-solid ratio (LSR) (\(X_{2}\)), and extraction time (\(X_{3}\)).  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Coded Variables**} & \multicolumn{3}{c}{**Actual Variable Values**} \\ \cline{2-6}
**Run** & \(\mathbf{(X_{1})}\) & \(\mathbf{(X_{2})}\) & \(\mathbf{(X_{3})}\) & \% EtOH (\(v\)/\(v\)) (\(X_{1}\)) & Temperature (\({}^{\circ}\)C) (\(X_{2}\)) & pH (\(X_{3}\)) \\ \hline
1 & 0 & \(-1\) & \(-1\) & 25 & 25 & 4 \\
2 & 0 & \(-1\) & 1 & 25 & 25 & 10 \\
3 & 0 & 1 & \(-1\) & 25 & 95 & 4 \\
4 & 0 & 1 & 1 & 25 & 95 & 10 \\
5 & \(-1\) & 0 & \(-1\) & 0 & 60 & 4 \\
6 & 1 & 0 & \(-1\) & 50 & 60 & 4 \\
7 & \(-1\) & 0 & 1 & 0 & 60 & 10 \\
8 & 1 & 0 & 1 & 50 & 60 & 10 \\
9 & \(-1\) & \(-1\) & 0 & 0 & 25 & 7 \\
10 & \(-1\) & 1 & 0 & 0 & 95 & 7 \\
11 & 1 & \(-1\) & 0 & 50 & 25 & 7 \\
12 & 1 & 1 & 0 & 50 & 95 & 7 \\
13 & 0 & 0 & 0 & 25 & 60 & 7 \\
14 & 0 & 0 & 0 & 25 & 60 & 7 \\
15 & 0 & 0 & 0 & 25 & 60 & 7 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Independent variables tested during the second optimization of the extraction process using a Box–Behnken design: ethanol percentage (\(X_{1}\)), extraction temperature (\(X_{2}\)), and pH (\(X_{3}\)).  
resuspended in 25% (_v/v_) DMSO in water at 50 mg\(\cdot\)mL\({}^{-1}\); 50% (_v/v_) ethanol extracts were resuspended in 50% (_v/v_) DMSO in water at 100 mg\(\cdot\)mL\({}^{-1}\).