# 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)
 \tag{6}\]  
Furthermore, the mathematical model corresponding to the inhibitory effect of the formulated sourdoughs against _Aspergillus flavus_ strain was expressed by the Equation (7):  
\[ \begin{array}{l}I,\%=-143.200+0.143A+10.900B-2.640C+0.930D+6.830E+1.628F-0. 592B^{2}-0.572C^{2}+\\ 0.013D^{2}-0.106E^{2}-0.004F^{2}-0.004 AB+0.004 AC+0.001 AE-1.131 BC+0.009 BD+0.028 BE- \\ 0.044 BF+0.700 CD+0.186 CE-0.030 CF-0.034 DE-0.026 DF-0.023 EF\end{array}  \tag{7}\]  
A significant interaction effect on the antifungal activity of the formulated sourdoughs against _Aspergillus flavus_ strain was perceived between the factors' fermentation time and temperature. It can be concluded, from the surface (Figure 2a) and contour (Figure 2b) plots, that a fermentation temperature higher than 44 \({}^{\circ}\)C would minimize the antifungal effects of the gluten-free fermented products against _Aspergillus flavus_ strain, which is obviously related to the effect of the temperature on the LAB's activity and growth-rates. Regarding the inhibitory effect of the formulated sourdoughs against _Penicillium_ spp. and _Bacillus_ spp. indicator strains, the inhibition effects induced by varying the factors \(B\) and \(C\) (Table 2) in their 2-way interaction were shown in Figures 3 and 4. For the antifungal activity against _Penicillium_ spp. indicator strain the calculated regression Equation (8) was:  
\[ \begin{array}{l}I,\%=-193.200+0.200A+20.250B+16.750C+0.520D+6.400E+1.517F-1.2 61B^{2}-0.612C^{2}-\\ 0.010D^{2}-0.089E^{2}-0.005F^{2}-0.005 AC+0.001 AD+0.001 AE-3.979 BC-0.029 BD+0.069 BE-\\ 0.020 BF+0.416 CD+0.073 CE-0.020 CF-0.002 DE-0.010 DF-0.021 EF\end{array}  \tag{8}\]  
Consequently, a full inhibition against _Penicillium_ spp. indicator strain was determined by the sourdoughs inoculated with a co-culture containing above 5% (\(v/w\)) of \(L\). _paracasei_ ssp. _paracasei_ MIUG BL 21 strain and up to 0.20% (\(v/w\)) of \(L\). _parabuchneri_ MIUG BL 24 strain. Similarly, the total inhibition is likely to be reached when a maximum of 1.10% (\(v/w\)), of \(L\). _paracasei_ ssp. _paracasei_ MIUG BL 21 strain together with no more than 6.68% (\(v/w\)) of \(L\). _parabuchneri_ MIUG BL 24 strain inoculum was employed in the biotechnological process of the sourdoughs's SSF fermentation (Figure 3a,b). Figure 2: Surface (**a**) and contour (**b**) plots for the two-way interactions between the significant fermentation variables \(E\) and \(F\) on the antifungal activity (inhibition ratio, %) against _Aspergillus flavus_. The mean of the factors \(A\) to \(F\) is given in Table 2.  
Furthermore, _Bacillus_ spp. strain growth was totally inhibited by two formulated gluten-free sourdough samples: (i) the sample fermented by the co-culture containing at least 3.76% (\(v/w\)) of \(L\). _parabuchneri_ MIUG BL 24 strain and maximum 2.35% (\(v/w\)) of \(L\). _paracasei_ ssp. _paracasei_ MIUG BL 21 strain, or (ii) the sourdough sample fermented with a minimum volume of 4.39% (\(v/w\)) of \(L\). _paracasei_ ssp. _paracasei_ MIUG BL 21 strain combined with maximum 2.21% (\(v/w\)) of \(L\). _parabuchneri_ MIUG BL 24 strain (Figure 4a,b). Resorting to the obtained experimental data, the following Equation (9) was attained for the antibacterial activity of the sourdoughs against _Bacillus_ spp. strain as follows:  
\[ \begin{array}{c}I,\%=-202.000+0.163A+16.400B+22.600C-3.290D+7.550E+2.061F-0.8 00B^{2}-1.390C^{2}-\\ 0.108D^{2}-0.096E^{2}-0.006F^{2}+0.027 AB+0.001 AD+0.001 AE-5.720 BC-0.315 BD-0.203 BE+\\ 0.032 BF+0.585 CD-0.064 CE+0.070 CF+0.069 DE+0.014 DF-0.031 EF//\end{array}  \tag{9}\]  
It can be concluded that each selected starter culture has a different fermentation behavior when composed of a co-culture of these LAB strains (Figure 4). Additionally, the inoculum size possesses a strong influence on the fermented product's composition and properties.