## 2 Modified _E. coli_ Strain and Experimental FBR
### The Experimental bioreactor and Data Acquisition  
To estimate the rate constants of the extended HSMDM (bi-level) for the studied TRP synthesis using the modified _E. coli_ T5 strain, [PERSON] [11] used the experimental kinetic data of [PERSON] [72], obtained in a lab-scale FBR (see the Acknowledgements). The completely automated 10 L capacity FBR in (Table 1) includes a large number of facilities (the automatic addition of nutrients, antibiotics, and pH-control compounds to ensure the optimal growth of the biomass; a reduced scheme is given in Figure 1), all described in detail by [PERSON] [72]. By using this FBR, [PERSON] [72] conducted a 'nominal' operation to obtain the kinetic data necessary to derive a kinetic model of the bioprocess. This non-optimal operation meant an addition of a constant feed flow rate and GLC solution during the whole batch time of 63 h.  
Samples have been taken from the FBR during the batch with a certain frequency (every 2 to 5 h), by determining the concentration dynamics of four key species from the bulk-phase of interest (GLC, TRP, PYR, biomass-X), with each species time-trajectory including 17 quasi-uniformly distributed recorded points. These data are represented as blue points, corresponding to recorded PYR in (Figure 6), recorded [GLC] in (Figure 8), the recorded [X] in (Figure 9c,d), and the recorded [TRP] in (Figure 10).  
Concerning the analytical techniques used to derive such measurements, the reader can refer to the work of [PERSON] [72].  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **The FBR Initial Conditions** & \\ \hline
**Parameter** & **Nominal (Initial) Value** & **Remarks** \\ \hline Biomass initial concentration (\(c_{x,0}\)) & \begin{tabular}{c} 0.16 (gDW/L) \\ Experimental data of [PERSON] [72] \\ (Figure 9c,d) \\ \end{tabular} & courtesy of [PERSON] [72] \\ \hline Batch time (\(t_{f}\)) & 3780 min (63 h) & [PERSON] [72] \\ \hline Cell content dilution rate (\(\mu\)), & \begin{tabular}{c} Estimated [55] \\ (1/min) \\ \end{tabular} & \begin{tabular}{c} 0.015 L/h \\ (nominal SP, constant) \\ \end{tabular} & \begin{tabular}{c} maintained quasi-constant and \\ non-optimal by [PERSON] [72] \\ \end{tabular} \\ \cline{2-3} Feed flow rate (\(F_{L}\)) & \begin{tabular}{c} optimally varied in this paper, but not \\ exceeding an imposed 7 L liquid volume \\ at the batch end. \\ \end{tabular} \\ \hline Bioreactor dilution rate (\(D\)) & \begin{tabular}{c} \(D=F_{L}/\mathcal{V}_{L}\) \\ \end{tabular} & \begin{tabular}{c} Usually adjusted to be close to \(\mu\), to avoid \\ the biomass washout [55; 76] \\ \end{tabular} \\ \hline Bioreactor liquid initial volume (\(V_{L,0}\)) & 0.5 L & Maximum 10 L \\ \hline Glucose feeding solution & \begin{tabular}{c} 3330.5 mM \\ (nominal SP, constant) \\ \end{tabular} & \
\begin{tabular}{c} maintained constant and non-optimal by \\ [PERSON] [72] \\ \end{tabular} \\ \cline{2-3} concentration \(c_{glc}^{\textit{f}ead}\) & 1-5 M &
\begin{tabular}{c} optimized variable, or constant policy in \\ this paper within imposed limits \\ \end{tabular} \\ \hline
**Parameter** & **Nominal (Initial) Value** & **Remarks** \\ \hline Glucose solution properties & \
\begin{tabular}{c} Solubility in water 5 M (25 \({}^{\circ}\)C), 7 M \\ (30 \({}^{\circ}\)C), 10.2 M (40 \({}^{\circ}\)C) \\ \end{tabular} & [PERSON] [77] \\ \cline{2-3} Glucose solution properties & 1000 cps (4.5 M, 30 \({}^{\circ}\)C), & Laos and Harak [78] \\ \end{tabular} \\ \cline{2-3}  & compared to & [Wikipedia—molasse viscosity \\ 1094 cps (molasses, 38 \({}^{\circ}\)C) &
\begin{tabular}{c} [Wikipedia—molasse viscosity \\ centi-poise (cps), 2024] \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 1: The nominal operating conditions of the FBR (a constant feed flow rate of a GLC solution of constant concentration) used by [PERSON] [72] (Fig. 1) to collect kinetic data for the TRP synthesis by using a suspended culture of genetically modified _E. coli_ cells (T5 strain). SP = set point.