## 3 Bioprocess and Bioreactor Dynamic Model
### The Structured Hybrid Kinetic Model
The cell growth and dilution rates [related to the cell cycle, and the liquid residence time in a (semi-)continuous bioreactor] strongly influence the TRP system stability, as proved in silico by [PERSON] [35; 45]. The glycolytic oscillation occurrence mechanism is extensively discussed by [PERSON] et al. [43; 54]. The hybrid kinetic model ultimately adopted is that of [PERSON] [11], built-up and estimated by using the kinetic data of [PERSON] [72] (Figures 6, 8, 9 and 10). The necessary kinetic data were collected by [PERSON] [72] in a FBR, operated under the non-optimal conditions given in Table 1, using the modified T5 strain of _E. coli_. This complex structured kinetic model, presented in (Tables 2-4), is a deterministic one. Its core is the glycolysis model constructed by [PERSON] [54], validated using literature data. The rate constants of this core model were further used as a starting point in the final estimation step of the complete HSMDM of the FBR used here, and by [PERSON] [11] to simulate the TRP synthesis. As explained in Section 1, to offer more precise and detailed support for the engineering evaluations, the HSMDMs should also include the cell metabolic processes responsible for the synthesis of the target metabolite (herein referred to as TRP) in addition to the reactor macro-scale state variables. As a mandatory feature, the cell model should also include the core of the central carbon metabolism (CCM), such as the extended versions reviewed by [PERSON] et al. [52; 54]. This is because the enzymatic reactions in the CCM are interconnected, while the intermediates are starting points in the reaction chains producing all the cell metabolites, understood as the \"target\" metabolites of practical interest. In spite of concerted efforts to derive a sufficiently accurate/extended dynamic model of the CCM, a reduced model is usually preferred [52; 54; 55; 56; 57; 58; 59]. This is because, for the extended CCM kinetic models (e.g., 95 enzymatic reactions with 72 metabolites in the model of [PERSON] and [PERSON] [60], discussed by [PERSON] et al. [52; 54]), it is too difficult to make estimations from the few and often un-structured data, and they are too complex to be used in quick engineering evaluations. For these reasons, the reduced adequate CCM model, constructed by [PERSON] [11] was adopted in the present paper, being schematically presented in (Figure 2). It accounts for five reaction-pathway interconnected modules (briefly mentioned in Section 3.1, and in the caption of Figure 2), that is: (i) the phosphotransferase system (PTS, in a 'wild' strain; that is, the consecutive reactions from GLC(external) to F6P), or another GLC uptake system, like those based on the galactose permease/glucokinase (GalP/Glk) in this paper; (ii) glycolysis [54], (the consecutive reactions from GLC(external) to PYR); that is, the CCM model module [a]; (iii) the TRP synthesis (the grey area) [44]; that is, the CCM model module [c]; (iv) the synthesis of adenosin co-metabolites ATP, ADP, and AMP, as part of the ATP recovery system (the pink rectangle); that is, the CCM model module [b]; and (v) the lumped form of the TCA cycle. The connection of the TRP synthesis to glycolysis is realized through the PEP glycolytic node [11; 44; 45]. To conclude, the HSMDM includes only the key species of the following four linked reaction modules responsible for the TRP synthesis (Figure 2), using information from the literature as a starting point, with the rate constants taken from the literature [11; 45]. The first three modules concern the inner cell reactions, while the fourth concerns the biomass [X] growth dynamics in the FBR bulk, that is:  
Module [a]--glycolysis with a natural ('wild') GLC-uptake system (PTS), or with a modified GLC-uptake system (GalP/Glk in the modified _E. coli_ strain of this paper). Module [b]--ATP-recovery system. Module [c]--TRP-operon expression. Module [X]--biomass growth dynamics in the FBR bulk. The considered species' mass balance of HSMDM is given in (Tables 2-4).