*2.2. Experimental Design*

The MAE conditions were optimized using a Box–Behnken experimental design (BBD), employing the Design Expert Software® Version 8.0.6 (Stat-Ease, MN, USA). The dependent variables for the two extraction methods are described in Table 1. From these conditions, 30 experimental runs were established and presented in a randomized pattern. The amount of total polyphenols determined by the Folin–Ciocalteu method, and the bixin (Bix) content were taken as independent variables [18].



The solvent pH at the concentrations determined by the BBD was adjusted with 0.1 M sodium hydroxide and acetic acid solutions. The microwave unit was operated at a frequency of 2450 MHz and power of 700 W (LG Ms-147xc, Seoul, South Korea), submitting the sample to 30-s cycles until reaching the desirable total time (Figure 1). In order to optimize the extraction conditions and investigate the effect of the independent variables the method of multiple regression of least squares was used. The coefficient of determination (r2) and the adjusted coefficient of determination (r2-adj model) were used as fitting parameters of the regression models. The experimental data were adjusted to the following polynomial equation:

Y = β0 + β1X1 + β2X2 + β3X3 + β4X4 + β11 X1X1 + β22 X2X2 + β33 X3X3 + β44 X4X4 + β12 X1X2 + β13 X1X3 + β14 X1X4 + β23 X2X3 + β24 X2X4 + β34 X3X4. (1)

where, Y represents the predicted response, β0, is the intercept of the model, β1, β2, β3, β4, β11, β22, β33, β44 and β12, β13, β14, β23, β24 and, β34 are linear and interaction coefficients, respectively, and X1, X2, X3, and, X4 are independent variables. The analysis of variance (ANOVA) was used to investigate the statistical significance of the independent variables from the models obtained (with a confidence level of 95%). The optimization of the extraction process was achieved by maximizing the extraction of polyphenol compounds and bixin having the same weight (weight of 1) and minimizing the solvent-to-seed ratio. The accuracy of the optimal conditions was determined with the desirability values of the dependent factors. The calculation of the relative and absolute errors was accomplished between the responses predicted by the model versus the ones obtained experimentally under optimal conditions.

**Figure 1.** Schematics for microwave-assisted extraction (MAE) from annatto seeds.

#### *2.3. Characterization of Optimal Annatto Seed Extracts*

The optimal extract obtained by the MAE was compared with the one obtained by leaching. The latter was obtained with ethanol using at optimum concentration, pH, and seeds-to-solvent ratio for the MAE, with a continuous agitation for 48 h. The results are presented as means and standard deviation (SD). The analysis was performed using the Statgraphics® Centurion XVI software (Madrid, Spain).

#### 2.3.1. Total Polyphenol Concentration

The total polyphenol concentration in the annatto seed extract was determined using the Folin–Ciocalteau method [19]. Briefly, 20 μL of sample were diluted in 1.58 μL of distilled water. Then, 100 μL of Folin–Ciocalteau reagen<sup>t</sup> and 300 μL of 20% sodium carbonate were added and mixed. The absorbance of the colored complex generated was read after 1 h of storage under darkness. The maximum absorbance was read at 725 nm in a UV/VIS spectrophotometer (UV-1700, Shimadzu®, Kyoto, Japan). The experiments were performed in triplicate and the results are expressed as mg of gallic acid (GA) per grams of seeds (mg GA/g seed).

#### 2.3.2. Quantification of Bixin

Here, 100 μL of sample were added to 2 mL of tetrahydrofuran and diluted to 10 mL with acetone to obtain an absorbance of less than 0.15 at 487 nm. The concentration of bixin in the sample was determined from a calibration curve built in a spectrophotometer (UV-1700, Shimadzu®, Kyoto Japan) using the following equation (Equation (2)) [20]:

$$\text{Bixin} \left( \% \right) = \frac{\text{A} \times 100 \times \text{V}}{A\_{1\text{cm}}^{1\text{\%}} \times 100} \tag{2}$$

where

*A*1%1cm = 3090 (1 g/100 mL)−<sup>1</sup> × 1 cm<sup>−</sup><sup>1</sup> (specific absorptivity coefficient of bixin in acetone) [20]; A = Absorbance value of the sample; and V=Dilutionvolume(mL)ofthesample.
