# Statistical Approach to Potentially Enhance the Postbiotication of Gluten-Free Sourdough
## 2 Materials and Methods
### Optimization of Sourdoughs Fermentation Parameters
#### 2.3.2 Response Surface Methodology (RSM)  
The factors that determined the significant predicable postbiotic effects on each of the studied responses were selected after PBD analysis. Moreover, it is important to highlight the significant interaction effects between the most important factors listed in Table 2.  
The interaction effects were identified by a Central Composite Design (CCD) by RSM. With those 6 independent variables (\(A\) to \(F\)) and the corresponding levels previously described (Table 2), a two-level factorial design, half-fractional, CCD with 53 runs was employed, following the second order polynomial Equation (4):  
\[Y=\beta_{0}+\sum_{i=1}^{k}\beta_{i}X_{i}+\sum_{i=1}^{k}\beta_{ii}X_{i}^{2}+\sum _{i=1}^{k}\beta_{ij}X_{i}X_{j} \tag{4}\]  
where \(Y\) represents the response--i.e., TTA expressed as mL NaOH 0.1N, and antifungal and antibacterial activities, expressed as inhibition ratios; \(\beta_{0}\) is the constant of the model; \(\beta_{i}\), \(\beta_{ii}\), and \(\beta_{ij}\) are the coefficients for the linear, quadratic and interaction effects; \(X_{i}\) and \(X_{j}\) are independent variables, and k is the number of the studied factors [64]. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Modification of the Independent** & **Minimum Value,** & **Maximum Value,** \\
**Variables/Factors** & \(-\)**1** & **+1** \\ \hline \hline \(A\), Dough Yield (DY) & 250.00 & 700.00 \\ \(B\), Inoculum of \(L\). _paracasei_ ssp. _paracasei_ & 0.00 & 4.00 \\ MIUG BL 21 (\% \(\
icefrac{{v}}{{w}}\)) & 0.00 & 4.00 \\ \(C\), Inoculum of \(L\). _brevis_ MIUG BL 38 (\% \(\
icefrac{{v}}{{w}}\)) & 0.00 & 4.00 \\ \(D\), Inoculum of \(L\). _parabuchneri_ MIUG BL 24 & 0.00 & 4.00 \\ (\(\%\)\(\
icefrac{{v}}{{w}}\)) & 0.00 & 4.00 \\ \(E\), Inoculum of _Leu. mesenteroides_ ssp. & 0.00 & 4.00 \\ _mesenteroides_ MIUG BL 40 (\(\%\)\(\
icefrac{{v}}{{w}}\)) & 0.00 & 10.00 \\ \(F\), Okara (\(\%\)\(\
icefrac{{v}}{{w}}\)) & 0.00 & 10.00 \\ \(G\), Fermentation temperature (\({}^{\circ}\)C) & 25.00 & 45.00 \\ \(H\), Fermentation time (h) & 24.00 & 96.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Plackett–Burman Design (PBD) independent variables (or factors). \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Independent Variable/Factors** & **Minimum Value,** & **Central Value,** & **Maximum Value,** & \multicolumn{2}{c}{**Axial Points**} \\  & \(-\)**1** & **0** & **+1** & \(-\)**\(\alpha\)** & **+\(\alpha\)** \\ \hline \(A\), Dough Yield (DY) & 250.00 & 475.00 & 700.00 & \(-\)60.14 & 1010.14 \\ \(B\), Inoculum of \(L\). _paracasei_ ssp. & 0.00 & 2.00 & 4.00 & \(-\)2.75 & 6.75 \\ \(\sigma\)_paracasei_ MIUG BL 21 (\(\%\)\(\
icefrac{{v}}{{w}}\)) & & & & & \\ \(C\), Inoculum of \(L\). _parabuchneri_ MIUG & 0.00 & 2.00 & 4.00 & \(-\)2.75 & 6.75 \\ BL 24 (\(\%\)\(\
icefrac{{v}}{{w}}\)) & & & & & \\ \(D\), Okara (\(\%\), \(\
icefrac{{v}}{{w}}\)) & & & & & \\ \(E\), Fermentation temperature (\({}^{\circ}\)C) & 25.00 & 35.00 & 45.00 & 11.21 & 58.78 \\ \(F\), Fermentation time (h) & 24.00 & 60.00 & 96.00 & \(-\)25.62 & 145.62 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Response Surface Methodology (RSM) factors. The Composition of Organic Acids, Flavonoids and Polyphenolic Compounds in Sourdougls by RP-HPLC-DAD  
Organic acids, flavonoids and polyphenolic compounds were separated and partially identified by Reversed Phase (RP) High-Performance Liquid Chromatography system coupled with a Diode Array Detector (DAD). The organic acids in the unfermented (control) and the optimized fermented sourdough obtained by RSM were separated and partially identified using an HPLC system (Perkin Elmer, Flexar, Waltham, MA, USA) equipped with a solvent degasser, column oven, binary pump system and a DAD detector (Perkin Elmer, Flexar, Waltham, MA, USA).