## Materials and Methods
### Mathematical Methods
#### 2.6.1 Polynomial Models and Fitting Methods
Introducing these additional constraints in the MATLAB script reduced the number of feasible combinations to 310 (see tab \"Pass 1\" in Excel file \"Results.xlsx\" in Supplementary Materials). Subsequently, in line with the previous argument A1, the MATLAB script was used with those combinations maximizing the difference between \(E_{\Pi 1}\) levels (\(-2\)) and (\(+2\)), which further reduced the number of combinations to 31 (see tab \"Pass 2\" in Excel file \"Results.xlsx\" in Supplementary Materials). Finally, selecting the combinations resulting in the greatest differences between \(E_{\Pi 2}\) levels (\(-2\)) and (\(+2\)) reduced the number of choices to 4 (see Table 4). On the other hand, too low an \(E_{\Pi 2}\) value would slow down the process exceedingly at the loading stage. This fact allows the combinations involving the lowest \(E_{\Pi 2}\) value at level (\(-2\)) (viz., 1, 3 and 4 in Table 4) to be discarded, thus leaving a single one which fulfils all constraints imposed (viz., combination 2 in Table 4). Tables 5-7 show the set of experiments corresponding to such a combination as established according to the \(2^{6-2}\) experimental design previously described by using an identical range for both working temperatures (\(T_{1}\) and \(T_{2}\)): 26-34 \({}^{\circ}\)C.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Variable** & **Level** & **Combination 1** & **Combination 2** & **Combination 3** & **Combination 4** \\ \hline \multirow{6}{*}{\(V_{u1}\) (L)} & \(-2\) & 3.50 & 3.50 & 3.50 & 4.00 \\  & \(+2\) & 6.50 & 6.50 & 6.50 & 7.00 \\  & \(-1\) & 4.25 & 4.25 & 4.25 & 4.75 \\  & \(+1\) & 5.75 & 5.75 & 5.75 & 6.25 \\  & \(0\) & 5.00 & 5.00 & 5.00 & 5.50 \\  
performed in random order. Therefore, depending on the differences in the operating conditions between consecutive experiments, either a lower or a greater number of cycles may be required for the system to become stable again as a result. By way of example, Figure 3 shows the results in terms of ethanol, acidity, volume, and total and viable cells in the first reactor in Experiment 1. Each result was the mean of 5 replicate cycles with its standard deviation (see Table 8). Similarly, Figure 4 shows the ethanol, acidity, and volume results for the second reactor as the means for 5 replicated runs and their standard deviations. The previous results were used to obtain the values of Table 9. The procedure used to calculate the values of non-measurable variables (e.g., mean rate of acetic acid formation, total acetic acid production and mean volume) is described in file \"S1.doc\" in Supplementary Materials. Figure S1.1 in such file shows the typical time course of ethanol concentration, acidity and volume in the first bioreactor and Figures S1.2-S1.3 show the time course of such variables in the second bioreactor when a fast loading or pre-depletion step exists, respectively. Also, the results obtained in the 18 experiments of Tables 5 and 6 are compiled in file \"S2.docx\" in Supplementary Materials (Figures S2.1 to S2.36 and Tables S2.2 to S2.19). On the other hand, Tables 10 and 11 show the experimental values of the key variables intended to be modelled using polynomial models relating them to the operational variables. led to identical conclusions for all target variables. Accordingly, the experimental \(\left(r_{A}\right)_{global}\) data in Table 10 were fitted to a second-order polynomial by Forward Stepwise Regression, as described in Section 2.6.1, using the software SigmaStat 2.0 [49]. Although 27 terms (viz., the 6 individual operational variables and their 21 possible interactions) were initially considered, the maximum possible number was that of the experiments performed: 18. Each fitted polynomial was checked for significant differences in the regressions between each step and the previous one by the effect of the addition or removal of terms. ANOVA revealed the presence of significant differences at a 95% confidence level in all cases and, therefore, the results are worth no additional detailed description here.