## 3 Bioprocess and Bioreactor Dynamic Model
### The Structured Hybrid Kinetic Model
The dynamic model is hybrid (bi-level) because it connects the macro-state variable of the FBR (biomass X, GLC, TRP, PYR) with the considered cell nano-level variables (GLC, F6P, FDP, PEP, PYR, ATP, in Tables 2 and 3) for the glycolysis, and (TRP, OR, OT, MRNA) for the TRP-operon expression (in Table 4). A detailed description of these modules is given by [PERSON] [11]. species belonging to the three inter-connected modules {[a], [b], and [X]} can be simulated concomitantly, according to the reduced reaction pathway of (Figure 2). In fact, the glycolysis is the core module of the CCM. In the adopted HSMDM, the glycolysis module [a] (presented in Figure 2), is the reduced model of that constructed by [PERSON] [54]. An adequate modelling of the glycolysis dynamics is important, because the intermediates provide entry/exit points to/from glycolysis. For example, PEP is the starting point for the synthesis of essential amino-acids (**AA**), such as tryptophan, cysteine, arginine, serine, etc. [44; 55; 84; 86]. Due to the tremendous importance of the glycolysis in simulating the cell CCM, intense efforts have been made both in its experimental study, and in modeling the dynamics of this process specifically in bacteria. The large number of glycolysis reduced or extended kinetic models proposed in the literature [45; 54; 87] present a complexity ranging from 18-30 species, included in 48-52 reactions, with a total of 24-300 or more rate constants [54]. Most of these models are however too complex to be easily identified from (often) few available kinetic data, and too complex to be further used for engineering calculations. Beside, with few exceptions [45; 54], most of them can not satisfactorily reproduce the glycolytic oscillations occurrence on a mechanistic basis [43; 45]. The adopted glycolysis kinetic model constructed by [PERSON] [45; 54], even in a reduced form, by accounting only for nine key species in 6 lumped reactions, including 17 easily identifiable rate constants belonging to V1-V6 metabolic fluxes (Figure 2, and Tables 2 and 3), has been experimentally validated. Additionally, this glycolysis model was proven to adequately reproduce the cell glycolysis under steady-state, oscillatory, or transient conditions depending on several factors, which are as follows [43; 44; 45]: (i) the defined glucose concentration level/dynamics in the bioreactor, (ii) the total A(MDT)P cell energy resources, and (iii) the cell phenotype characteristics related to the activity of enzymes involved in the ATP utilization and recovery system (denoted here as module [b]). When including the glycolysis model in the HSMDM, the GLC import system (V1) corresponds to the basic PTS system for the 'wild' strain [54; 55], or presents a form modified by [PERSON] [11] to match the T5 _E. coli_ strain kinetic data of [PERSON] [72]. According to the experimental data, the produced TRP (see module [c] below) is excreted (Figure 2) through a process described by [PERSON] [72]. The PYR key-metaboltic concentration in the cell is regulated through complex mechanisms [88; 89], with the excess being excreted, as experimentally proven by [PERSON] [72]. As revealed by the reactions figured in the pink square of (Figure 2), the efficiency and the dynamics of the ATP recovery system {that is module [b] of the present model} is essential for the reaction rates of the whole CCM, as long as ATP plays a catalytic-chemical energy provider role. As underlined by [PERSON] et al. [43; 44; 45], among the involved parameters, an essential factor is the \(k\delta\) reaction rate (determined by the _ATP-ase_ characteristics in Figure 2) and included in the glycolysis model of (Tables 2 and 3). The involved enzymes characteristics are directly related to the cell phenotype (that is cell genomics) controlling the [AMDTP] total energy resources level. To not complicate the simulations, the [AMDTP] level was kept unchanged in the present analysis at an average value given in (Table 1), as suggested by [PERSON] et al. [55].