# Statistical Approach to Potentially Enhance the Postbiotication of Gluten-Free Sourdough
## 3 Results and Discussion
### Sourdough Fermentation Process Optimization
#### 3.1.1 Selection of the Most Important Fermentation Parameters by Plackett-Burman Design (PBD)
In fact, in this work it was essential to identify the most important fermentation factors, and their most favorable amounts and combinations in order to maximize the sourdough's overall antimicrobial properties and its content of the studied compounds with potential bioactive and/or technological functionalities, viz. organic acids, flavonoids and polyphenolic compounds [3; 72; 73]. \begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & \multicolumn{1}{c}{**Factors**} & \multicolumn{1}{c}{**Respons**} & \multicolumn{1}{c}{**Respons**} & \multicolumn{1}{c}{**Antifungal Activity**} & \multicolumn{1}{c}{**Antifungal Activity**} & \multicolumn{1}{c}{**Antifungal Activity**} & \multicolumn{1}{c}{**Antifungal Activity**} & \multicolumn{1}{c}{**Antifungal Activity**} & \multicolumn{1}{c}{**Antifungal Activity**} \\
**Run** & **A** & **B** & \(C\) & \(D\) & \(E\) & **F** & **0.1N**  
Regarding the TTA, the impact of each independent variable on its value can be determined by the mathematical model expressed in Equation (5) and obtained via RSM:  
\[ \begin{split} TTA=-46.500+0.051A+1.270B-1.690C-0.050D+2.338E+0.305F-0. 032B^{2}-0.143C^{2}-\\ 0.002D^{2}-0.031E^{2}-0.001E^{2}+0.001 AB+0.001 AC+0.002 AE-0.170 BC-0.040 BD-0.021 BE+\\ 0.014 BF+0.059 CD+0.074 CE+0.019 CF-0.001 DE-0.004 EF\end{split}  \tag{5}\]  
The significant interaction effects on TTA (\(p<0.05\)) were identified, on the one hand, between variables \(C\) and \(E\) (\(L\). _parabuchneri_ MIUG BL 24 strain's inoculum (\(\%\)\(v/w\)), and the fermentation temperature, \({}^{\circ}\)C), as it is shown in Table S6 for the ANOVA results. The TTA values increased along with the increment of the inoculum volume of \(L\). _parabuchneri_ MIUG BL 24 strain. The maximum TTA values could be reached when the inoculum volumes above 6.74 (\(\%\)\(v/w\)) of \(L\). _parabuchneri_ MIUG BL 24 strain were used simultaneously with temperatures ranging between 35.90 and 47.92 \({}^{\circ}\)C (Figure 1a,b). On the other hand, a significant interaction effect was identified between variables \(E\) and \(F\) (fermentation temperature, \({}^{\circ}\)C and fermentation time, h, respectively) for the TTA. A prolonged fermentation time determined a high level of TTA, whereas a minimized response was observed at a fermentation temperature below 21 \({}^{\circ}\)C or above 45 \({}^{\circ}\)C (Figure 1c,d). As displayed in Table S6 the regression coefficient (R\({}^{2}\)) for the mathematical model of TTA was 88%, showing that the model fits very well with the experimental values and is in agreement with the P-value obtained for the lack of fit (\(p>0.05\)). (2) Inhibitory Effects  
Regarding the microbial growth inhibition studies, the _Aspergillus niger_ strain's growth was significantly influenced (\(p<0.05\)) only by the linear effect of the sourdough's fermentat  
Figure 1: Surface (left) and contour (right) plots for the two-way interactions between the significant fermentation factors on the total titralable acidity (TTA, mL NaOH 0.1N). Surface (**a**) and contour (**b**) plots for the interaction between the factors \(C\) and \(E\), and (**c**) surface and (**d**) contour plots for the interaction between the factors \(E\) and \(F\). The mean of the factors \(A\) to \(F\) is given in Table 2.  
tion variables \(B\), \(C\) and \(E\) (Table 2) by their quadratic effects \(A^{2}\), \(E^{2}\), \(F^{2}\), respectively. Table S6 highlighted the good fit of the above-mentioned model to the experimental results, proven by the P-value for the lack of fit (0.25) and, concurrently, by the regression coefficient higher than 70% (R\({}^{2}\) = 0.72). The regression Equation (6) obtained for the inhibition against _Aspergillus niger_ strain by RSM was as follows:  
\[ \begin{array}{l}I,\%=-174.000+0.127A+20.300B+5.200C+1.350D+5.710E+2.333F-1.012 B^{2}+0.137C^{2}-\\ 0.105D^{2}-0.106E^{2}-0.008F^{2}-0.006 AB+0.012 AC-0.007 AD+0.004 AE-0.590 BC+0.140 BD-\\ 0.242 BE-0.006 BF+0.475 CD-0.097 CE-0.062 CF+0.079 DE-0.020 DF-0.019 EF\end{array}