## 5 Optimization Results and Discussion
The FBR optimal NLP operation with a variable feeding reported a similar dilution of the reactor content (2.7 L final volume), compared to the constant feeding in the best Pareto-optimal alternative (2.64 L final volume), as revealed by (Table 5, Figure 9b). Also, the high biomass growth is similar in both cases. On the other hand, as expected, a higher TRP productivity requires a higher substrate consumption, as is the case when using the modified _E. coli_ T5 strain presented by [PERSON] [72] (3.15 moles GLC), compared to the wild type of [PERSON] et al. [55] (0.06 moles GLC). As revealed by Table 5, the GLC consumption is influenced by the FBR operating mode, even if the same cell strain is used. Not surprisingly, the optimally operated FBR requires less substrate consumption. Thus, the same low GLC consumption was reported by the constant Pareto-optimal feeding policy (2.14 moles), and by the variable NLP-optimal feeding (4.53 moles), compared to the NLP-optimal but constant feeding (10.99 moles). 5. The comparative analysis of the glycolytic species dynamics in (Figure 6) reveals close trajectories (even quasi-identical for the F6P and FDP species), with any accumulation tendency, for both non-optimal (curve 1), or optimal (curves 2-4) FBR operation. By contrast, the intermediate PEP and the ATP species tend to be formed in higher amounts, but then they are quickly consumed in the subsequent TRP synthesis, or in the glycolysis reactions, ultimately tending to reach their QSS. Such an intensive GLC import during the optimal FBR variable feeding operation (curve 2), and the GLC successive transformation over the glycolysis pathway, and _Trp_-operon expression is reflected by a higher ATP consumption compared to the non-optimal or sub-optimal FBR operation. The PYR metabolite is consumed in the TCA cycle, and the excess is excreted in the bulk phase (fairly predicted by our kinetic model, matching the experimental data). The better GLC use for an optimal FBR operation is also proven  
Figure 5: The Pareto-optimal operating mode of the FBR in terms of the required initial biomass, for various amount of maximum TRP produced. The blue curve is the “rough” Pareto-optimal front. The black curve illustrates the approximated Pareto-optimal front by using the cubic spline procedure of Matlab(tm) (function “CSAPS”), with a smoothing constant \(10^{-20}\). The marked points correspond to those of the Pareto-optimal curve of Figure 3.  
by the more produced and consumed secondary metabolite PYR (curve 2), and by a smaller QSS concentration of the PEP intermediate, quickly transformed in the final product TRP. 6. The comparative analysis of the _Trp_-operon expression species dynamics in (Figure 7) reveals very close trajectories, except for the excreted TRP, for both the non-optimal (curves 1), or optimal (curves 2-4) FBR operation. Such a result can be explained by the operon expression mechanism, involving a tight control via its inhibition terms presented in (Table 4). 7. The comparative plots of the GLC concentration dynamics in the FBR bulk phase are presented in (Figure 8). They indicate similar decreasing trajectories for all the investigated FBR operating alternatives. However, in the optimal operation cases (curves 2-4), the GLC decline in the bulk phase is more pronounced compared to the non-optimal operating case (curves 1). The higher GLC consumption in these last optimal operating cases can be explained by the higher TRP productivity. The  
Figure 6: Model-based simulated trajectories () for the glycolytic key species (PYR, F6P, FDP, ATP, PEP) in the modified _E. coli_ T5 strain for the FBR operated in several alternative forms, as follows: (1, blue) Curves simulated with the HSMDM (this paper, and Maria [11]) compared to the experimental data (\(\bullet\), blue) of [PERSON] [72] under the nominal, non-optimal operation of the FBR of (Table 1), which involves a constant feed [GLC], and constant feed flow rate \(\mathrm{F_{L}}\).