## 5 Optimization Results and Discussion
(2, black) The optimal operation of the FBR (this paper), with a time-step-wise optimally varied feed [GLC], and feed flow rate, with the control variable limits of Equation (12). (3, red) The optimal operation of the FBR (this paper), with a constant but optimal feed [GLC], and feed flow rate (FL), with the control variable limits of Equation (11). (4, green) The optimal operation of the FBR (this paper), with a constant but Pareto-optimal feed [GLC], and feed flow rate (FL; see Figures 3–5), with the control variable limits of Equation (12). * It proves that the medium-size, bi-level (hybrid) HSMDM [11 cell metabolites, plus 4 bulk species, in a construction including four interconnected reaction modules, which are: [a] glycolysis, [b] ATP-recovery system, [c] TRP-operon expression, and the biomass [X] growth] adopted in this paper is able to adequately and concomitantly represent the dynamics for both macroscopic state variables of the FBR, and for the cell key species of the CCM related to the TRP synthesis. This hybrid structured model, linking the macro-state variables to the nano cell-scale variables, validated by [PERSON] [11] using the recorded data from the lab-scale FBR over a sufficient batch time (63 h), offers enough credentials for providing predictions of an increased accuracy. * By coupling the structured reduced modular kinetic model of CCM with those for the TRP synthesis (_trp_-operon expression module) in the _E. coli_ modified cells, this paper performs an in silico analysis, for the first time in the dedicated literature, regarding (i) the way by which the two processes interfere through the PEP glycolysis shared node, (ii) the consequences on the TRP-synthesis yield, and (iii) the way by which the cellular (nano-scale) bioprocess model, directly coupled with the bioreactor macroscopic dynamic model allows for determining the bioreactor's best operating mode, leading to the TRP biosynthesis maximization. * Compared to the HSMDMs from the literature, the applied (hybrid) HSMDM of this paper, even in a reduced form, is able to simulate the influence of the glycolysis process intensity on the target metabolite (TRP) production, and on the raw material consumption, for the \"wild\" strain [11; 44; 98] compared to the modified T5 _E. coli_ strain [11; 32]. * The HSMDMs allow for an easy evaluation of cellular metabolic fluxes. Such an analysis (not detailed here) quickly opens up the possibility of re-designing some cell fluxes via an in silico re-programming of the cell metabolism for designing GMO with industrial/medical applications [11; 32; 35; 41; 43; 52]. * The HSMDM allows for an easy evaluation of TRP-synthesis performance in a FBR depending on the reactor operation mode, but also on characteristics of the _E. coli_ strain used {directly linked to the GLC import system, and to the ATP recovery system efficiency}, both determined by the cell phenotype, which is T5 strain in this paper [11; 32; 43; 44]. * Although the production of TRP by engineered _E. coli_ has been extensively studied, \"the need of multiple precursors for its synthesis and the complex regulations of the biosynthetic pathways make the achievement of a high product yield still very challenging\" [11]. This difficult engineering problem was solved here by the concomitant use of a model-based (in silico) approach, completed with a biological improvement by using the modified T5 _E. coli_ cell culture. Such a concomitant approach is seldom used in the literature. * The derived optimal operating policy of the FBR is given in time intervals (the so-called \"time-arcs\") of equal length, of a reduced number, to be easily implemented. The control variables present optimal but constant levels over each time-arc (different between time-arcs) during the FBR operation. * The used biomass culture here refers to a modified _E. coli_ T5 strain. The characteristics of this strain were reflected in the rate constants estimated by [PERSON] [11]. This T5 strain was produced by [PERSON] [72] and [PERSON] et al.