## 2 Materials and Methods
### Total Soluble Phenols (TSP)  
TSP content was determined in a 96-well microplate applying a modified version of the Montreau method [26], as recommended [27]. The mixture reaction comprises corn extract (12 \(\upmu\)L), Folin-Ciocalteu reagent at 2N (12 \(\upmu\)L), sodium bicarbonate solution at 7.5% _w/v_ (116 \(\upmu\)L), and distilled water (164 \(\upmu\)L). The mixture was homogenized in darkness (15 min), and the absorbance (750 nm) was recorded in a microplate reader (ACCURIS Instruments, SmartReader MR-9600, Nankin, China). Gallic acid was used as a standard (R\({}^{2}\) = 0.998), and the results are given as milligrams of gallic acid equivalents per gram of dry sample.  
Figure 1: Visual appearance of corn kernel (**a**) and corn kernel powder (**b**) of native Mexican pigmented corn.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Predictors 1**} & \multicolumn{3}{c}{**Response Variables**} & \multicolumn{3}{c}{**Relative**} & \multicolumn{3}{c}{**Response Variables**} \\ \cline{2-10}
**Run** & \(\mathbf{X_{T}}\) & \(\mathbf{X_{pc}}\) & \(\mathbf{X_{up}}\) & **Experimental** & **Predicted** & **Error (\%)** & **Yield (\%)** & **Experimental** & **Predicted** & **Error (\%)** & **Yield (\%)** \\  & (min) & (s) & (F5) & **TSP 1** & **TSP 3** & & & & & \\ \hline
1 & 2 & 3 & 90 & 27.72 \(\pm\) 0.52  & 28.50 & -2.73 & 5.54 & 16.59 \(\pm\) 0.43  & 17.64 & -5.95 & 3.31 \\
2 & 6 & 3 & 90 & 28.28 \(\pm\) 0.68  & 29.09 & -2.78 & 5.65 & 18.34 \(\pm\) 0.75  & 17.71 & 3.55 & 3.66 \\
3 & 4 & 2 & 90 & 29.97 \(\pm\) 0.56  & 31.20 & -3.94 & 5.99 & 22.48 \(\pm\) 0.37  & 20.95 & -7.30 & 4.49 \\
4 & 6 & 2 & 100 & 29.86 \(\pm\) 0.39  & 29.66 & 2.75 & 5.97 & 22.99 \(\pm\) 0.33  & 24.14 & -4.76 & 4.59 \\
5 & 6 & 1 & 90 & 29.91 \(\pm\) 0.39  & 30.71 & -2.60 & 5.98 & 24.57 \(\pm\) 0.45  & 23.94 & 2.63 & 4.91 \\
6 & 4 & 2 & 90 & 30.12 \(\pm\) 0.56  & 31.20 & -3.30 & 6.54 & 20.35 \(\pm\) 0.55  & 20.95 & -2.86 & 4.07 \\
7 & 2 & 2 & 100 & 32.04 \(\pm\) 0.59  & 31.27 & 2.46 & 6.40 & 23.51 \(\pm\) 0.33  & 23.32 & 0.81 & 4.70 \\
8 & 4 & 3 & 80 & 31.20 \(\pm\) 0.52  & 31.99 & -2.46 & 6.24 & 26.66 \(\pm\) 0.33  & 27.49 & -3.23 & 5.52 \\
9 & 4 & 1 & 80 & 27.35 \(\pm\) 0.19  & 28.13 & -2.77 & 5.47 & 25.76 \(\pm\) 0.57  & 28.66 & -3.37 & 5.15 \\
10 & 6 & 2 & 80 & 34.75 \(\pm\) 0.68  & 33.95 & 2.35 & 6.95 & 27.28 \(\pm\) 0.37  & 27.94 & -2.36 & 5.45 \\
11 & 4 & 1 & 100 & 34.87 \(\pm\) 0.68  & 35.67 & -2.24 & 6.67 & 27.65 \(\pm\) 0.79  & 26.58 & 1.76 & 5.41 \\
12 & 2 & 2 & 80 & 33.43 \(\pm\) 1.09  & 32.66 & 2.35 & 6.68 & 26.61 \(\pm\) 0.18  & 24.71 & 7.68 & 5.32 \\
13 & 4 & 3 & 100 & 34.69 \(\pm\) 0.52  & 35.47 & -2.19 & 6.93 & 23.86 \(\pm\) 0.11  & 23.38 & 2.05 & 4.77 \\
14 & 4 & 2 & 90 & 30.07 \(\pm\) 0.59  & 31.20 & -3.63 & 6.81 & 20.87 \(\pm\) 0.33  & 20.95 & -0.38 & 4.17 \\
15 & 2 & 1 & 90 & 31.45 \(\pm\) 0.98  & 32.22 & -2.38 & 6.29 & 19.33 \(\pm\) 0.70  & 20.38 & -5.15 & 3.86 \\ \hline \end{tabular}
\end{table}
Table 1: Experimental runs and experimental and predicted values of the total soluble phenol and total flavonoid contents, error rate, and yield after ultrasound-assisted extraction from native Mexican pigmented corn kernel powder.