## 3 Results and Discussion  
### Physical Properties of Bread and Optimization of the Bread Formulation through Experimental Design  
Textural parameters and specific volume values obtained for the different bread prepared according to the experimental design are shown in Table S1. It is observed that the conditions of experiment 2 (80% maize flour, 20% buckwheat flour, 0% xanthan gum, 100% psyllium husk, and 120% hydration) obtained the highest specific volume value. These conditions presented the lowest hardness value, although they did not show significant differences with the conditions of experiment 13. The conditions of experiment 7 (80% maize flour, 20% buckwheat flour, 50% xanthan gum, 50% psyllium husk, and 95% hydration) provided the highest springiness values. The regression model analysis was applied to analyze the experimental data regarding the specific volume and textural parameters (in Table S1) and to evaluate the relationship between the responses (specific volume, springiness, and hardness) and the independent variables, which are represented by the following second-order polynomial equations:  
\[ \begin{split}\text{Y}_{1}\text{ (specific volume)}=1.62+6.58\text{X}_{1}-0.02\text{X}_{2}+4.75\text{X}_{3}+0.12 \text{X}_{1}^{2}-2.2\text{X}_{1}\text{X}_{2}-0.13\text{X}_{1}\text{X}_{3}-2.67 \text{X}_{1}^{2}-0.02\text{X}_{2}^{2}+\\ 8.33\text{X}_{2}\text{X}_{3}-0.14\text{X}_{3}^{2}\end{split}  \tag{2}\]  
\[ \begin{split}\text{Y}_{2}\text{ (springiness)}=0.8+0.03\text{X}_{1}+0.02\text{X}_{2}+0.0 6\text{X}_{3}-0.06\text{X}_{1}^{2}+0.02\text{X}_{1}\text{X}_{2}-0.04\text{X}_{ 1}\text{X}_{3}-0.06\text{X}_{2}^{2}+0.07\text{X}_{2}\text{X}_{3}\\ -0.009\text{X}_{3}^{2}\end{split}  \tag{3}\]  
\[\text{Y}_{3}\text{ (hardness)}=1980-852\text{X}_{1}-422\text{X}_{2}-1353 \text{X}_{3}+1911\text{X}_{1}^{2}+1261\text{X}_{1}\text{X}_{2}+296\text{X}_{1 }\text{X}_{3}+138\text{X}_{2}^{2}-254\text{X}_{2}\text{X}_{3}+2310\text{X}_{ 3}^{2}\end{split} \tag{4}\]  
Regarding \(\text{Y}_{1}\) (specific volume) and \(\text{Y}_{2}\) (springiness) models, the most significant coefficients (\(p<0.05\)) were hydration and maize proportion. On the other hand, hydration, maize proportion, and xanthan proportion were the most significant (\(p<0.05\)) for \(\text{Y}_{3}\) (hardness). These adjusted models explained 70%, 73%, and 97% of the variability of \(\text{Y}_{1}\), \(\text{Y}_{2}\), and \(\text{Y}_{3}\), respectively. Figure 2 presents the results of fitting the experimental data to the model of Equation (2) for \(\text{Y}_{1}\), Equation (3) for \(\text{Y}_{2}\), and Equation (4) for \(\text{Y}_{3}\). The three-dimensional response surface graphs outlined the combined effect of the independent variables (proportion of maize and buckwheat as gluten-free flours, proportion of xanthan, and hydration percentage) on the dependent variables studied. The plots are constructed as a function of two variables while keeping the third variable constant (at the central value). Figure 2a shows that springiness values were higher at higher hydration and higher xanthan proportions, with similar results found for specific volumes (Figure 2b). However, hardness decreased as the hydration percentage increased, and it can be observed that there was no significant change as the xanthan percentage increased (Figure 2c). The interactions of maize flour and hydration at 50% xanthan are shown in Figure 2d-f. Springiness increased with low to intermediate maize proportion values and with high hydration levels (Figure 2d). Specific volume increased as maize proportion increased and also with high to intermediate hydration values (Figure 2e). Hardness decreased with both maize proportion and hydration intermediate values (Figure 2f). Regarding the effect of maize and xanthan percentage, springiness increased with intermediate values (Figure 2g), specific volume increased with a high maize proportion and high and low values for xanthan (Figure 2h).