## 3 Bioprocess and Bioreactor Dynamic Model  
### The Structured Hybrid Kinetic Model  
In this paper, an HSMDM has been adopted from the literature [11; 35; 44]. Such dynamic models were proven to successfully solve difficult bioengineering problems more accurately and with a higher degree of detail. In such a complex model, the cell-scale part (including nano-level state variables) is linked to the biological reactor macro-scale state variables. Thus, both the model prediction quality and its validity range are improved [35; 41; 42]. This structured modular HSMDM has been chosen for several reasons: (a) It includes modules characterizing the dynamics of the cell pathways (that is, the glycolysis, ATP-recovery system, TRP-operon expression), and of the biomass growth, involved in the TRP-synthesis. (b) This HSMDM was experimentally identified, and checked the extensive experiments conducted by several authors, for the glycolysis [11; 54; 55; 71] and for the TRP synthesis [11; 47; 72]. The rate constants of this model have been estimated by [PERSON] [11] using the experimental data of [PERSON] [72]. (c) The relevant plots of (Figures 6, 8, 9 and 10) prove the very good performance of this hybrid model. Even if such a complex/extended dynamic model requires more experimental and computational efforts to be built-up and identified from structured kinetic data, the resulting hybrid (bi-level) dynamic model presents major and remarkable advantages, well pointed out by the case studies presented by [PERSON] [35]. Among these, we mention only the increased degree of detail of the predictions of such an HSMDM model, and the more robust extrapolations of the bioprocess behaviour [35; 41]. With these compelling reasons in mind, an HSMDM from the literature was adopted in the present engineering analysis. A significant number of simplified kinetic models with lumped terms (species and/or reactions) have been proposed in the literature regarding TRP-synthesis complex regulation process (in a review by [PERSON] et al. [44]). Unlike other models, the adopted HSMDM is able to predict, under certain operating conditions, the oscillation occurrence of the glycolysis, and of the TRP synthesis (not the case here) [43; 44; 45; 79; 80; 81]. Oscillations in the TRP synthesis are produced due to the concomitant activation and high-order repression of the TRP-operon expression, together with a nonlinear demand for the end product, \begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**The FBR Initial Conditions**} \\ \hline Initial glucose concentration in the bioreactor \(c_{glc}^{ext}\) at (\(t=0\)). & 194.53 mM & Experimental data of [PERSON] [72] (Figure 8) \\ \cline{2-3}  & & To be optimized for a FBR & Optimized in this paper within imposed limits \\ \hline Temperature/pH & 37 \({}^{\circ}\)C/6.8 & [PERSON] [72] \\ \hline Bioreactor capacity [max(\(V_{L}\))], & 10 L, automatic control of pH, & \\ and facilities & DO, temperature & \\ \hline Biomass density (\(\rho_{x}\)) & 565.5 gDW-(L cytosol)\({}^{-1}\) & [PERSON] et al. [55] \\ \hline Initial concentrations for the glycolytic cell species (in mM) & \(c_{F0P}(t\,=\,0)=0.6003\) & \\  & \(c_{F0P}(t\,=\,0)=0.2729\) & \\ Initial concentrations for the glycolytic cell species (in mM) & \(c_{ATP}(t\,=\,0)=2.6729\) & measured by \\  & \(c_{PYR}(t\,=\,0)=2.6706\) & [PERSON] et al. [55] \\  & \(c_{ATP}(t\,=\,0)=4.27\) & \\  & [AMDTP]total = 5.82 & \\ \hline Initial concentrations for the & \(c_{QR}(t=0)=0.01\) & \\ Initial concentrations for the & \(c_{OT}(t=0)=3.32\) (nM) (quasi-constant) & measured by \\ TRP-synthesis operon species (in mM) & \(c_{MRNA}(t=0)=0.01\) & [PERSON] et al. [79] \\  & \(c_{E}(t=0)=928\) (nM) & \\ \cline{2-3}  & \(c_{TRP}(t=0)=0.164\) & this paper; data from [PERSON] [72] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._facilitating the cyclic nature of its expressions.