Application of (bio) chemical engineering concepts and tools to model genetic regulatory circuits, and some essential central carbon metabolism pathways in living cells. Part 4. Applications in the design of some Genetically Modi ﬁ ed Micro-Organisms (GMOs)

In the ﬁ rst part of this work, the general Chemical and Biochemical Engineering (CBE) concepts and rules are brie ﬂ y reviewed, together with the rules of the control theory of Nonlinear Systems (NSCT), all in


Abbreviations and notations
consuming and generating large amounts of toxic waste, with biosynthesis processes (using isolated and purifi ed enzymes, or cell cultures as bio-catalysts).The motivation is given by the multiple advantages offered by enzymatic processes [3]: i) very high selectivity; ii) very high conversion; iii) does not generate toxic by-products; iv) very mild reaction conditions, easy to achieve without high costs (low temperatures of 20-60°C, normal pressure, pH within controllable limits).Thus, in recent years, a signifi cant number of enzymatic or biological industrial processes have been reported [5][6][7][8] to obtain chemical products/derivatives in the fi ne organic synthesis industry, the pharmaceutical industry, the food industry, or the detergent industry, by using various bioreactors with cell or enzyme cultures [5,8].Among these new processes is the production of derivatives of monosaccharides, organic acids, alcohols, amino acids, etc., using mono-or multienzymatic reactors, or bioreactors with cell cultures used in the production of yeast, food additives, recombinant proteins (enzymes, vaccines), biopolymers [5,6,9].The development of a sustainable biological process must consider several aspects related to the characteristics of the biocatalyst, the integration of the process and the minimization of costs, satisfying economic, environmental / safety, and social objectives [10][11][12].
When scale-up a new biological process (of known kinetics) several biochemical engineering problems must be solved, consisting of: i) Choosing the type of biological reactor most suitable for the studied bioprocess [6,13,14]; ii) Choosing the optimal mode of operation of the selected bioreactor (discontinuous BR; semi-continuous (fedbatch) FBR with a variable feeding; discontinuous with intermittent addition of biomass/substrate BRP; or continuous stirred tank reactor CSTR, with continuous feeding and evacuation of the liquid-phase (chemostat), etc. [6]); iii) Choosing how to use the biocatalyst (biomass in a free state or immobilized on a suitable solid/gel support to increase its stability [13,14,16]).As discussed in the literature, the biocatalyst contributes the most to the production cost [3,16].

The importance of optimal operation of biological reactors
In the case of biological reactors (with free, or immobilized biomass), the trend in the biosynthesis industry is to use complex systems, with more effi cient genetically modifi ed micro-organisms (GMO), and employ sophisticated but effi cient immobilization systems, which prevent premature inactivation of the biomass due to mechanical and chemical stress from the bioreactor environment.Thus, modern biological processes, together with the multi-enzymatic ones, prove to be very effective in the biosynthesis of numerous chemical compounds, thus competing in terms of effi ciency with organic chemical synthesis, proceeding with high selectivity and specifi city, by reducing consumption of energy and generating less environmental pollution [3].This characteristic of industrial biosynthesis is exploited for various economic purposes (industry, medicine, environment, agriculture, fuel production) [17,18].In this context, the insilico derivation of an optimal operating policy of the industrial bioreactors becomes a challenging engineering problem.
As reviewed in the literature [1][2][3][4][19][20][21][22], and shortly in the Part-1 of this work, the in-silico (math/kinetic model-based) numerical analysis of biochemical or biological processes, by using the CBE concepts / numerical rules is proved to be not only an essential but also an extremely benefi cial tool for engineering evaluations aiming to determine the optimal operating policies of complex multi-enzymatic reactors [9,[23][24][25][26], or bioreactors [3,4,6,19,27,28].Among these numerical tools, is the deterministic modular structured cell kinetic models (MSDKM -with continuous variables, based on cellular metabolic reaction mechanisms).and the hybrid structured modular dynamic models (HSMDM) (with continuous variables, linking the cell-nano-scale MSDKM state variables to the macro-scale state variables of the bioreactor dynamic model) are the essential ones., proved by the exponential-like increase in the reported applications in the last decades.
In Part-2 of this work, special attention is paid to the authors' contributions related to the dynamics simulation of the Gene Expression Regulatory Modules (GERM) and of Genetic Regulation Circuits/Networks (GRC/GRN) in living cells, by introducing and promoting the concepts of a novel dynamic modelling framework of the cell processes, that is the so-called "WHOLE-CELL VARIABLE CELL VOLUME" (WCVV) for isotonic/homeostatic cell systems.The advantages of using the more realistic WCVV math modelling approach to simulate the cell metabolic processes have been proved and shortly reviewed when building-up dynamic modular models of CCMbased syntheses, and GRC-s inside living cells.
The MSDKM models can also be used to evaluate the cell metabolic fl uxes, thus assisting the in-silico design of GMOs.This area belongs to the border fi eld of Synthetic Biology defi ned as "putting engineering into biology" [29].By inserting new genes (plasmids) or knock-out some of them, modifi ed CCM / GRC-s can be obtained inside a target micro-organism, thus creating a large variety of mini-functions / tasks (desired 'motifs') to the mutant (GMO) cells in response to external stimuli [3,4,.Besides, the use of extended HSMDM models presents multiple advantages, such as (i) a higher degree of accuracy and the prediction detailing for the bioreactor dynamic parameters (at a macro-and nano-scale level); (ii) the prediction of the biomass metabolism adaptation over tens cell cycles to the changing conditions from the bioreactor; (iii) prediction of the CCM key-species dynamics, by also including the metabolites of interest for the industrial biosynthesis (Part 2, [4,5]); (iv) prediction of the CCM stationary reaction rates (i.e.metabolic fl uxes) allow to in-silico design GMO of desired characteristics.
As proved by Maria [1][2][3][4]51], and Yang, et al. [52], the modular structured kinetic models can reproduce the dynamics of complex metabolic syntheses inside living cells.This is why, the metabolic pathway representation of GRC and CCM in dynamic models, with continuous and/or stochastic variables seems to be the most comprehensive mean for a rational design of the regulatory GRC with desired behaviour [53].The same MSDKM can satisfactorily simulate, on a deterministic basis, the self-regulation of cell metabolism for its rapid adaptation to the changing bioreactor reaction environment, using complex GRC-s, which include chains of individual GERMs.
As exemplifi ed in Parts 3 and 4 of this work, the MSDKM and HSMDM models (developed under the novel WCVV math modelling framework) can simulate the dynamics of the bioreactor simultaneously with those of the cellular metabolic processes occurring in the bioreactor biomass.This work is aiming at proving, by using a relevant case study, the feasibility, and advantage of using the relatively novel HSMDM concept by coupling the GRC-based cell structured deterministic nano-scale models with the macroscale state-variables of the analyzed bioreactor.The resulted hybrid dynamic model was successfully used for engineering evaluations and to design a GMO E. coli.
For more case studies on using MSDKM and HSMDM models, under the WCVV modelling framework, the reader is asked to consult the following works [3,4,[55][56][57][58]: 1) In-silico design of a genetic switch in E. coli with the role of a biosensor [3,4,[54][55][56][57][58]; 2) An HSMDM math model able to simulate the dynamics of the mercury-operon expression in E. coli cells, and its self-regulation over dozens of cell cycles, simultaneously with the dynamics of the macro-level state variables of a semi-continuous reactor (SCR) of a Three-Phase Fluidized Bioreactor Type (TPFB).The same extended model was used for the in-silico designing of cloned E. coli cells (with variable mer-plasmid concentrations) aiming at maximizing the biomass capacity of mercury uptake from wastewaters [59][60][61][62].This case study is also approached here.
3) An HSMDM math model able to simulate the dynamics of key-species of the CCM of E. coli cell coupled with the simulation of the macro-scale state variables of a Batch Reactor (BR).The HSMDM model was used for the insilico design of a GMO E. coli with a maximized capacity of both biomass and succinate (SUCC) production.The used numerical techniques were those of the gene knock-out, and of the Pareto-front for multi-objective problems [30].
4) The use of an HSMDM math model for the in-silico design of a GMO E. coli with a modifi ed glycolytic oscillator [31][32][33][34][35][36][37][63][64][65][66][67][68][69][70][71][72][73].The HSMDM model can be further extended, becoming the core of a modular dynamic model used to simulate the CCM and regulation of various metabolite syntheses, with application to in silico reprogramming of the cell metabolism to design GMO of various applications [3,4,32,74].One example is the in-silico off-line optimization of the operating conditions of a fed-batch bioreactor (FBR) with GMO E. coli to maximize the production of tryptophan (TRP).Thus, compared to a simple batch bioreactor (BR) using a wild E. coli cell culture, the TRP production was increased by 73% (50% due to the in-silico design of a novel GMO E. coli strain, and 23% due to the model-based off-line optimization of the variable feeding of the FBR).[3,4,27,31,34,71,75].
Complex MSDKM structured models including CCM and GRC modules are able to predict conditions for oscillations occurrence for various cell processes [1-4,31-34,37,51, 52,63,64,].As studied by Yang et al. [52], "all biochemical reactions in organisms can not occur simultaneously due to constraints of thermodynamic feasibility and resource availability, just as all trains in a country cannot run simultaneously.Therefore, oscillations provide overall planning and coordination for the inner workings of the cellular system.This seems to be contrary to the theoretical basis of genomescale metabolic models (GEMs), which are based on the steady-state hypothesis and fl ux balance analysis [76], but just as computers will not operate in the same way as the human brain, this difference can be understood and accepted, so that non-equilibrium theory and the steady-state hypothesis have been and will continue to coexist and guide our reasoning."[52] (see also Part 3 of this work).
6) An MSDKM math model able to simulate the dynamics of key-species of the CCM of E. coli cells involved in the synthesis of Phenyl-alanine (PHA).The HSMDM model was used to in-silico re-confi gure the metabolic pathway for Phenyl-alanine synthesis in E. coli [54] to maximize its production.That implies modifying the structure and activity of the involved enzymes, and modifi cation of the existing regulatory loops.Searching variables of the formulated mixed-integer nonlinear programming (MINLP) multi-objective optimization problem are the followings: the regulatory loops (that is integer variables, taking a "0" value when the loop has to be deleted, or the value "1" when it has to be retained); the enzyme expression levels (that is continuous variables), and all these in the presence of the stoichiometric and thermodynamic constraints.To solve this complex optimization problem, two contrary objectives are formulated: maximization of the PHA selectivity, with minimization of cell metabolites' concentration deviations from their homeostatic levels (to avoid an unbalanced cell growth).The elegant solution to the problem is the so-called Pareto-optimal front, which is the locus of the best trade-off between the two adverse objectives.Choosing two problem-solution alternatives from this Pareto-curve [3,54] is to observe the large differences between the two pathways into the cell, fully achievable by using genetic engineering techniques to produce desirable GMOs.
7) A HSMDM model to simulate the dynamics of the key species and the FBR state variables used for monoclonal antibodies (mAbs) production.This extended dynamic model was used for the in-silico off -line derivation of the multi-objective optimal control policies to maximize the mAbs production in an industrial FBR [6].

The case study purpose -an overview
This section 2 exemplifi es the use of a complex HSMDM to solve an engineering problem at an industrial pilot scale, that is the use of a complex cell WCVV structured kinetic model of the mer-operon GRC expression (Figure 1) in an HSMDM model to optimize a pilot-scale semi-continuous (SCR) TPFB bioreactor (Figure 2) used for mercury uptake from wastewaters by immobilized E. coli cells cloned with mer-plasmids.The developed HSMDM dynamic model links the cell-scale model part (including the dynamics of the nano-scale keystate variables/species) to the biological reactor macro-scale key-state variables for improving the both model prediction quality and its validity range.Eventually, the HSMDM model was used to in-silico design a GMO (i.e. an E. coli cloned with mer-plasmids in a degree to be determined) for improving its capacity for mercury uptake from wastewaters (Figure 3). to uptake the mercury ions from wastewaters and in eliminating these ions as mercury vapours entrained by the continuously sparged air into the bioreactor [3,4,7,[59][60][61][62]87].
This HSMDM dynamic model is a worthy example of applying WCVV models, and the GERMs properties (P.I.-s) described in Part 2 of this work, to adequately represent a complex modular GRC-s for the mer-operon expression in E. coli cells.
The structured GRC-WCVV model was proposed by Maria [59][60][61] to reproduce the dynamics of the mer-operon expression in Gram-negative bacteria, such as E. coli, and Pseudomonas sp., for the uptake of mercury ions from wastewaters under various environmental conditions.The complex structured dynamic modular model was constructed and validated by using the Philippidis et al. [88][89][90] experimental data, and the Barkay et al. [91] information on the mer-operon expression characteristics.
As evidenced by this application, the current trend in bioengineering is to use multi-layer (hybrid) HSMDM models [3,4,92] to extend the detailing degree of the developed bioreactor dynamic models, by also including the dynamics of the concerned cell key-species metabolism.Exemplifi cation is made in this section by coupling an unstructured dynamic model of a TPFB, used for mercury uptake from wastewaters by immobilized E. coli cells, with a cell simulator of the GRC controlling the mercuric ion reduction in the bacteria cytosol.

Mercury ion reduction in bacteria cells -the apparent kinetics
"Bacteria resistance to mercury is one of the most studied metallic-ion uptake and release processes (see the review of Barkay et al. [91]) due to its immediate large-scale application for mercury removal from industrial wastewaters [93][94].
The bacteria response to the presence of toxic mercuric ions in the environment        (r P rate, see Table 1).To highlight the slowest process step, separate experiments have been conducted with cultures of intact cells or 'permeabilized' cells (with a more permeable cell membrane to metallic ionic species).The results clearly showed that membranar permeation is the rate-controlling step, being one order of magnitude slower than the cytosolic mercuric ion reduction.Identifi cation of rate constants of the two main reactions for cloned E. coli cells with an increasing copy number of mer-plasmids, in the range of [Gmer] = 3-140 nM, compared to those identifi ed for [Gmer] = 1-2 nM (for wild-types of E. coli) reveals the following aspects (Table 1): (i) The rate constants are strongly dependent on the merplasmid (genes) level in the cloned cells of E. coli, the real reaction mechanism inside the cell being more complex  (iv) When an immobilized biomass alternative is used,   8).By including these reduced global models in the TPFB bioreactor model (Table 7), the r app mercury reduction apparent reaction rate results.

The TPFB bioreactor reduced model (with global kinetics) and its nominal operating conditions
To exemplify the construction of an un-structured dynamic model for the approached mercury removal process, the TPFB bioreactor of Deckwer et al. [93] Besides, the dynamic model must include the ranked infl uential factors on the mercury uptake effi ciency in the approached TPFB bioreactor for further operating decisions.
The used lab-scale TPFB bioreactor (Figure 2, and Figure 3,  Initially, to study this bioprocess, Deckwer et al. [93] used E. coli bacteria immobilized on alginate beads (Table 6 (alginate)), but further tests have been extended by using immobilized biomass on porous pumice granules of 0.9 mm to 4 mm diameter (Table 2 (pumice)).The pumice carrier checked in the present paper is particularly attractive, the carrier exhibiting a high BET area and porosity, and a large pore size (even higher than 10 μm), thus allowing a good diffusion of the substrate (mercuric ions) to the cells from inside the support.The operating conditions are tightly controlled, that is the liquid fl ow rate, the aeration rate (pO 2 ), pH, and the temperature required by an equilibrated bacteria growth [Table 2(pumice), and Table 6 (alginate)].The suffi cient supplied oxygen guarantees a good cell metabolism and a high content of cytosolic NADPH necessary for mercury reduction.Besides, the continuously bubbling air plays also the role of volatile metallic mercury carrier, by removing it from the liquid system.Eventually, the mercury vapours from the air leaving the system are condensed and recovered [93].A background pollution of ca. 100 nM is considered in the input water (that is ca.0.02 mg/L, which is smaller than the metabolic regulation threshold of 0.05 mg/L), thus maintaining active the meroperon into the E. coli cell.The biomass content of the support is variable (ca.0.6-3 gX/L, according to [93,96], but a quasiconstant level of ca. 1 gX/L can be maintained by employing a purge/renewal system for the solid particles.At an industrial scale, when treating polluted waters, the outlet gas (air) from the bioreactor, containing the volatile metallic mercury, is passed through an adsorption device, or a de-sublimation system allowing the recovery of metallic mercury [97].
For such global kinetics, the apparent mercury reduction rate (r app ) necessary in the bioreactor model (Table 7) is evaluated following the (Table 8) rule.The apparent rate 0 Hg cyt was evaluated by solving on every integration time-increment the quasi-steady-state equality of mass fl uxes at the solid-liquid (S-L) external interface (on the liquid side), by also including the external diffusion coeffi cient K S a S [100].This rule also includes the diffusional resistance of the substrate (mercury ions) / product (dissolved metallic mercury) transport through the support pores.
If the apparent (Michaelis-Menten) mercury uptake kinetics of Philippidis et al. [88][89][90] (Table 1) are introduced in the TPFB bioreactor model, then a better unstructured global model is obtained (Table 3).By also including the [Gmer]-dependent rate constants, it results in the apparent mercury reduction rate (r app ) by the immobilized bacteria of concentration c X in (Table 1) in the spherical solid carrier [of fraction  s in Table 2 (pumice)] for different levels of [Gmer] plasmids.The mercury mass balance in the liquid and gas phases is presented in (Table 7).This reduced (unstructured) TPFB reactor dynamic model (Table 7, and Table 8) includes terms referring to the mass balance in the bulk (liquid, L) phase, the gas phase (G), the interphase L-G transport (r trans ) of the volatile mercury, and the overall/apparent bioprocess of mercury reduction inside the solid particles (r app ).In such a way, the apparent mercury reduction rate also includes the diffusional resistance of the substrate (mercury ions) / product (dissolved metallic mercury) transport through the pumice support pores.
A hybrid reduced/unstructured dynamic model of the TPFB can by constructed by linking the macro0scale state-variables of the TPFB (Table 7), with the Michaelis-Menten kinetics of Philippidis et al. [88][89][90] (Table 1).This apparent model (Figure  (e) the reaction rate is ca. 10 4 nM/min, being similar to the TF (repressor monomer) Dimerization (with a rate constant of ca. 10 2 nM -1 min -1 [38]).(f) the reaction rate is ca. 10 4 nM/min, similar to the TF binding to the gene operator (with a rate constant of ca. 10 2 nM/min [38]).(g) the reaction rate is ca. 10 1 -10 2 nM/min, being similar to the mRNA (genes) synthesis reactions (with a rate constant of ca. 10 -4 1/nM/min [114]).

Monoculture cell:
Cell cycle time [116] t Biomass concentration in the bioreactor c X = 1 g/L (ca.0.6-3 g/L; [93,96] ) Cell density in the culture medium p cell = 10 6 mg/(L cell) [118] Species Footnotes: (a) Inner cell concentrations are evaluated with the formula [1,4]: j c c j = (copy numbers of species j per cell) / (N A V cyt ) , where N A = 6.022  10 23 is the Avogadro number, V cyt = average volume of the cell.
6) can only give a rough idea of the bioreactor dynamics, but it is unable to describe the biomass adaptation to environmental changes, that is variations in both inlet feed fl ow-rate and inlet mercury load in the infl uent.To offer a prediction to such engineering requirements, a structured kinetic model of the mercury uptake in the E. coli bacteria at a cellular level is necessary.The next chapter describes the complex HSMDM structured model proposed by Maria [59][60][61], by considering the macro-level TPFB model linked to the cell biological process included by using the WCVV modelling approach (Part 2 of this work) to simulate the dynamics of the cell mer-operon expression self-regulation in the wild, or modifi ed E. coli under various environmental (bioreactor operating) conditions.
The resulting unstructured TPFB global dynamic model of (Table 7), while keeping the apparent M-M kinetics of (Table 8) only for the mercury cytosolic reduction step, allows a rough simulation of the transient operating conditions of the TPFB bioreactor.This apparent model of (Figure 6, plus Table 8), even if suitable for quick/rough engineering evaluations, is unable to describe the biomass adaptation to environmental changes, that is variations in the both inlet feed fl ow rate and inlet mercury load in the infl uent, or the effect of cloning E. coli cells on the bioreactor effi ciency.

Extended HSMDM model of the TPFB bioreactor
To avoid the above-mentioned limitations of the unstructured / reduced dynamic model of the TPFB bioreactor, an extended and complex HSMDM structured model was elaborated by also including the effect of cloning E. coli with various concentrations of mer-plasmids [Gmer], by also including the Michaelis-Menten [Gmer]-dependent kinetics of Philippidis et al. [88][89][90] in the cytosolic mercury reduction step (Table 4).
To offer a prediction to such engineering requirements, an extended HSMDM structured kinetic model of the mercury uptake in the E. coli bacteria at a cellular level is necessary (of WCVV type, see Part-2 of this work).And, of course, this cellstate-variables (nano-scale) part of the HSMDM should be linked to the TPFB bioreactor state-variables (macro-scale), because they are interrelated.This section describes the WCVV-type structured cell model proposed by Maria [59][60][61] to simulate the dynamics of the meroperon expression induction by the presence of environmental mercury, and the expression self-regulation in the "wild", or in-silico design GMO E. coli under various environmental (bioreactor operating) conditions.This HSMDM structured and modular cell kinetic model has been developed by Maria [59][60][61].Roughly, the part of the extended HSMDM structured model referring to the mer-operon expression WCVV model includes a GRC of 7 GERMs (Figure 1) linked by following the rules described in this section, and by accounting for the few experimental information of Philippidis et al. [88][89][90], and of Barkay et al. [91].The derived GRC model can simulate the dynamics of the mer-operon expression, and the process self-control at a molecular level under isothermal and isotonic conditions.4), completed with the [Gmer]dependent apparent Michaelis-Menten kinetics of (Table 1) for the mercury reduction reaction in the cell cytosol.All the cell parameters included in the HSMDM model correspond to the E. coli characteristics (Table 5), and (Figure 12).

The macro-scale state variables
More specifi cally, the mercury differential mass balance, in the TPFB model of (Table 3) includes the following terms: (i) The apparent mercury reduction rate, evaluated at the solid interface; (ii) The substrate (that is S = transport in the particle, expressed by the effectiveness factor () evaluated using the Thiele modulus for a Michaelis-Menten type reaction [101], the effective diffusivity (DS,ef) accounting for the molecular diffusion (DS,L), the particle porosity ( p ) and the tortuosity ( ) (other resistances being neglected [102]); (iii) The apparent rate r j, app was evaluated by solving on every integration time-increment the quasi-steadystate equality of mass fl uxes at the solid-liquid (S-L) external interface (on the liquid side), by also including the external diffusion coeffi cient k S a S [100].This rule also includes the diffusional resistance of the substrate (mercury ions) / product (dissolved metallic mercury) transport through the support pores.
(iv) The liquid-to-gas transport rate r trans of the metallic mercury ( 0 0 Hg to Hg L G ), evaluated from the quasisteady-state equality of mass fl uxes at bubbles G-L interface, by accounting for the mass transfer coeffi cients k L a L (on the liquid fi lm side; experimental value adopted), and k G a G (on the gas fi lm side; evaluated from the Sharma's relationship given by Trambouze et al. [99] ).

The cell-scale state variables
This paragraph describes the WCVV structured cell model proposed by Maria [59][60][61] to simulate the dynamics of the mer-operon-induced expression, and its self-regulation under various environmental conditions.This model was constructed and validated by using the experimental data of Philippidis et al. [88][89][90], and the experimental information of Barkay et al.The proposed E. coli cell model by Maria [59][60][61] includes the GRC responsible for the control of the mer-operon expression and the whole process of mercury ions removal.
The proposed GRC includes 4 lumped genes (denoted by GR, GT, GA, GD in (Figure 1, Figure 2, Figure 3, and Figure 4) of individual expression levels induced and adjusted according to the level of mercury and other metabolites into the cytosol.
As it follows from these fi gures, the mer-operon expression process is induced by the presence of a small concentration of mercury ions in the environment, leading to the appearance in the cytosol as Hg(SR) 2 compounds.The whole process is tightly cross-and self-regulated to hinder the import of large (ii) A GERM to control the expression of the PR protein that induces and controls the whole mer-operon expression in the presence of cytosolic 2 Hg cyt  (even if they are present in traces, that is low nM concentrations, (Table 5) and Figure 12).This GERM acts as an amplifi er of the mer-expression leading to a quick (over ca.(iv) A GERM controlling the protein PD synthesis.This protein has a complex role, by maintaining a certain level of GR expression even when the mercury is absent in the cytosol [91].It also hinders the over-expression of GR and GT when too large concentrations of mercury (vi) Thus, the whole mer-operon expression consists of a controlled expression in cascade (Figure 11) of all 4 mer-genes {GR, GT, GA, GD in (Figure 1, Figure 2)}.
In total, the cell GRC dynamic model describing the meroperon expression includes only 26 individual or lumped cellular species involved in 33 reactions (Figure 1, Figure 11, and Table 4).The structured cell WCVV model is presented in the (Table 4).The cell model is coupled with the SCR -TPFB dynamic model (Table 3) through the r j , app link to the individual reactions ,( , ) r j Cj S occurring inside the cell.The WCVV cell model includes not only the reactions and the dynamics of the mer-GRC, but also the enzymatic reactions directly responsible for the environmental mercury All reactions in the cell model of (Table 4) are considered elementary, except some of them for which extended experimental information exists, that is [59][60][61]:  f) The WCVV model equations for the mercury uptake in E.
coli, together with the general hypotheses of the WCVV model are presented in (Table 4).The cell is considered an open system, of uniform content and negligible inner gradients.To not increase the number of parameters, the structured model includes GERM of the simplest form [G(PP)1] (see Part-2 of this work) for all mer-genes, by using dimeric TF-s (of Protein: Protein type) to increase the GERM regulatory effi ciency, as experimentally proved by [1,2,3,38,55,58].The resulting HSMDM model includes 26 individual or lumped cellular species and 33 reactions.All reactions are considered elementary, except some of them for which extended experimental information exists, that is the Michaelis-Menten rate expression for mercury permeation into the cell, and its reduction in cytosol.A Hill-type induction of the GR expression is adopted to rapidly amplify the mer-operon expression when mercuric ions are present in signifi cant amounts inside the cell.Dimerization reactions of TF-s are considered to be much more rapid than the enzyme synthesis, while equal concentrations of active (G(i)) and inactive (G(i): TFTF) forms of the generic gene G(i) are considered at homeostasis to maximize the GERM effi ciency [1,2,3,4,55].The homeostatic characteristics of E. coli cells (belonging to a uniform culture) from the reactor, and the adopted species concentrations are presented in (Table 5).

HSMDM structured model advantages
As extensively discussed in Part 2 of this work, and proved in this section, such a cell WCVV structured model presents a large number of advantages, being able to: 1) Simulate the cell metabolism adaptation when the environmental mercury level changes.Such a reconfi guration of the levels of mer-genes and merproteins is presented in (Figure 13 [Gmer] = 140 nM.Simulations of Maria [59][60][61][62] revealed that as the mer-plasmids level increases, the mercury uptake capacity also increases.However, an upper limit exists (around 140 nM) over which the cell resources will be exhausted, putting its metabolism in danger.
3) The simulated state-variables plotted in (Figure 14), for using the unstructured global model (Table 7 and  extended HSMDM model, reveal a higher quality (vs.-experimental data), and more detailed/refi ned predictions for a larger number of state-variables.4) By coupling the structured MSDKM cell model of (Table 4) with the three-phase (TPFB) continuous bioreactor model of Table 3 (with immobilized E. coli cells on pumice beads; see also the bioreactor model in Figure 6), Maria et al. [59][60][61][62] have been able to determine the optimal operating policies of the bioreactor in relationship to the culture of cloned E. coli cells.Similar studies are reported by [7,[59][60][61][62]88].

Quick comparison between the structured HSMDM and the unstructured/global dynamic model of the TPFB reactor:
The superiority of the structured extended HSMDM model (Table 3 and Table 4) against the unstructured reduced model (Table 7 and Table 8) was used to simulate the TPFB dynamics over a wide range of time.
Thus, when simulating the TPFB reactor performance (of nominal conditions given in Table 2, for the biomass immobilized on pumice support) by employing a classical unstructured reactor model, the biomass adaptation to variable input loads is not accounted for, that is the maximum rates v m,t , v m, P, and the Michaelis inhibition constants K mt , K m P and K i P of (Table 1) are kept constant (eventually depending only on the Gmer plasmid level).In fact, v m,t and v m, P rate constants depend on the cell enzyme levels of PA (reductase) and PT (permease) (Figure 1), which vary during the bacteria adaptation in the bioreactor under stationary or transient conditions.
To solve this problem by also offering a more detailed and robust prediction on the system dynamics/cell metabolism evolution, more detailed (structured) dynamic models are necessary for the TPFB bioreactor, linked to the structured kinetic model of mer-GRC in E. coli cell.Thus, it results in the   7, Table 8), while curves indexed by "2" denote the predictions of the structured HSMDM bioreactor model (including the cell model of Table 4).2. Notation "E" denotes the experimental curves of Philippidis et al. [88][89][90].Adapted from [59][60][61].
the HSMDM model of (Table 3 and Table 4)., due to its structure, only the HSMDM model can simulate the E. coli cell response to dynamic or stationary perturbations from the environment (i.e. the TPFB bulk-phase).And also the infl uence of [Gmer] plasmids on the bioreactor performances.
For instance, (Figure 13) displays the E. coli cell adaptation after a 'step'-like perturbation in the environmental [  7 and Table 8).A more detailed comparison between the structured HSMDM model, and the unstructured/global one, for this case study is made by Maria [3,4].

The link between the macro-, and cell-scale state variables when solving the HSMDM model
The link between the two parts of the macro-sate-variables and the cell-state-variables of the HSMDM is made by the [ 2+ Hg L,env ] controlling the [ 2+ Hg L,cyt ], which, in turn, will control the whole mer-operon dynamics and the mercury reduction process through the cascade expression of the key-proteins {PR, PT, PA, PD} (see Table 4).In turn, the cell The link between the bioreactor macro-state variables and the cell nano-scale-state variables can be better pointed out when describing the HSMDM DAE model solution, that is its integration over a large time domain.
Due to its high complexity, the solving rule of the HSMDM model involves successive integration steps with an adopted time-interval equal to the cell cycle (ca.The procedure is repeated a large number of times, over hundreds of cell cycles.For instance, (Figure 13 7 and Table 8).

Some simulations with the HSMDM extended dynamic model
The resulting hybrid dynamic HSMDM model of (Table 3), including the WCVV kinetic model of the GRC responsible for the mer-operon expression of (Table 4) allows simulating with more accuracy the dynamics of the TPFB bioreactor at both macro-and (call) nano-scale level.By also including in (Table 4) the Michaelis-Menten kinetics of Philippidis et al. [88][89][90], the above-described extended HSMDM model can also be used to study the parametric sensitivity of the studied TPFB.Thus, the dynamics of the TPFB (with the characteristics of (  [93], with the reduced kinetic model of (Table 8).
model, and to increase their confi dence and physical meaning, a three-step procedure was employed based on the available experimental data and additional information from literature, as followings.a) Mass transport parameters of the TPFB reactor, that is interfacial partial transfer coeffi cients (k S a S, k L a L, k G p G ), effective diffusivity (D ef ) and particle effectiveness factor ( ) have been estimated by using the experimental data of Deckwer et al. [93], and based on common correlations from the chemical engineering literature (Table 3) evaluated for the specifi ed reactor operating conditions of (  Table 8::Tested apparent kinetic models ( r app ) for mercury ion reduction by using immobilized Ps. putida cells on alginate, after [93,101].Notation:  4), while the Michaelis-Menten rate constants of mercury membranar transport (r max , t ,K mt ) and its reduction rates' constants (r max ,P, K mP , K iP ) have been kept at the fi tted values of Philippidis et al. [88][89][90] (Table 1).The reference concentration CHg2cy,ref was    4) are in good agreement with the reported data from the literature, as remarked in the same (Table 4).The fi tted rate constants multiplied by the reactant lead to reaction rates of the same order of magnitude as those reported in the literature for similar genetic processes, such as the TF (repressor monomer) dimerization, the TF binding to gene operator, or the mRNA (genes) synthesis reactions (Table 4) [59][60][61].This observation sustains the physical meaning of model parameters, thus increasing the HSMDM model robustness.

Conclusions
Meritorious structured deterministic CCM kinetic models have been reviewed by Maria [2].Deterministic kinetic models using continuous variables have been developed by Maria [3] for the glycolysis, and by [77,[104][105][106][107] for the CCM in bacteria The superiority of structured HSMDM models is proved by several case studies approached by the author and briefl y mentioned in the Introduction section of this paper.For details, the reader is asked to consult the above-indicated references.
However, to avoid the intensive experimental and computational efforts necessary to develop an extended structured HSMDM model, unstructured dynamic models of bioprocesses continue to be used for various engineering purposes.Even if of low precision, the unstructured/global models for the bioreactors and the conducted bioprocesses continue to be largely used in the engineering practice, for a quick design, optimization, or control of the industrial bioprocesses.For instance, for the case study mentioned in this paper, a method was presented to optimize the operating policy of a SCR bioreactor by using the reduced unstructured hybrid model.Maria [4,62,92].
a G : G-L-specifi c interfacial area; a L : L-G -interfacial area (identical to a G ); a S : L-S-specifi c interfacial area; A j : Atomic (molecular) mass of species j; a,b: Rate constants in the Hill-type kinetic expression; C j : Species j concentration; D j : Diffusivity of species j in a certain phase; D: Cell content dilution rate (i.e.cell-volume logarithmic growing rate); d b : Bubble average diameter; d p : Particle diameter; d r : Reactor diameter; F: Feed fl ow rate; FL: Liquid feed fl ow-rate; g: Gravitational acceleration; [ 2 Hg L  ]: Concentration of the mercury ions in the liquid (bulk) phase of the bioreactor; K m : Michaelis-Menten constants; K G : G-L mass transfer coeffi cient (on the gas side); K H : Henry constant; K L : L-G mass transfer coeffi cient (on the liquid side); K S : L-S mass transfer coeffi cient (on the liquid side); k: Rate constants; n H : Hill-coeffi cient; n PD ,n PR : Partial orders of reaction; n j : number of moles of species j; n s: number of species in the cell; N A : Avogadro number; p: overall pressure; Pj: Partial pressure of species j;number (liquid); R g : universal gas constant; r j : species j Translation of the CBE and NSCT concepts/rules (see Part 1-2 of this work) in Systems Biology, Computational biology, and Bioinformatics is leading to obtaining extended structured cellular kinetic models MSDKM including nano-scale state variables adequately representing the dynamics of the cell keyreaction-modules.If the MSDKM model is further linked to those of the bioreactor macro-scale dynamic model, the result is the HSMDM dynamic model that can satisfactorily simulate, for instance, the self-regulation of the cell metabolism and its adaptation to the changing bioreactor environment, utilizing Citation: Maria G (2024) Application of (bio) chemical engineering concepts and tools to model genetic regulatory circuits, and some essential central carbon metabolism pathways in living cells.Part 4. Applications in the design of some Genetically Modified Micro-Organisms (GMOs).Ann Syst Biol 7(1): 001-034.DOI: https://dx.doi.org/10.17352/asb.000021complex GRC-s, which include chains of individual GERMs.The HSMDM kinetic models are related to solving various diffi cult bioengineering problems, such as (i) in-silico offline optimization of the operating policy of various types of bioreactors, and (ii) in-silico design/checking some GMOs of industrial use, able to improve the performances of several bioprocess/bioreactors.
The {cell + TPFB} HSMDM dynamic model of the E. coli cloned bacterium can simulate the self-control of the GRC responsible for the mer-operon expression, and predict a) The infl uence of the TPFB bioreactor control variables [such as the feed fl ow-rate (FL), the mercury ions concentration [ 2 Hg L  ] in in the feeding liquid], and the biomass concentration in the bioreactor [X]; b) The infl uence of various bioreactor running parameters [such as the size of the solid porous particles (dp) of pumice on which the biomass was immobilized; the concentration [Gmer] of the mer-plasmids used in the cloned E. coli cells) on the bioreactor's performance The obtained results reported: a) A signifi cant improvement in the model prediction quality (ca.3%-12% in state variables, and up to 40% in reduction rate vs. experimental information); b) A signifi cant improvement in the detailing degree [i.e.simulation of 26+3 (cell + bulk) state-variable dynamics (nano-and macro-levels) by the HSMDM model vs.only 3 (bulk, macro-level) state-variable dynamics by the overall unstructured Monod / Michaelis-Menten kinetic model].The major advantages of the hybrid HSMDM model come from the possibility of predicting the bacteria metabolism adaptation to environmental changes over a large number of cell generations (cell cycles), and also the effect of cloning cells with certain plasmids to modify its behaviour under stationary or perturbed conditions.This section exemplifi es the possibility of coupling an unstructured TPFB dynamic model including macro-scale state variables [93] used to simulate the dynamics of the mercury uptake by immobilized E. coli cells on pumice milli-meter size support, with a structured E. coli cell model of Maria [59-62].The advantage of using such a hybrid (bi-level) modelling approach is related to the improvement of the prediction accuracy of the reactor performance/state variable dynamics, and of the prediction of the bacteria metabolism adaptation to environmental 'step'-like changes in the environmental mercury content [ 2 Hg L  ]env through the modelled cell GRC related to the mer-operon expression, and by mimicking the whole-cell growth under balanced conditions.If successful, such an approach can support the idea of I. Improving the bioreactor performances, by employing an off-line in-silico (model-based) multi-objective optimization procedure to determine the optimal operating policy of the bioreactor [59-62]; II.Improving the quality of process monitoring (control), by using an optimal operating policy determined with a reduced unstructured dynamic model obtained by lumping the extended HSMDM model [9,59,87]; III.In-silico design cloned E. coli with an increased content of mer-plasmids.Such a facility is offered only by the complex HSMDM dynamic model of increased predictive

Figure 1 :
Figure 1: Time-dependent mercury transfer between the E. coli cell and the three-phase fl uidized bed bioreactor (TPFB), according to the proposed hybrid dynamic model HSMDM of Maria [59-62].Enzyme concentrations in E. coli determine the apparent reaction rates in the bioreactor model (especially PT lumped permease, and PA lumped reductase), while the reactor state-variables (e.g.[Hg 2+ ] L , nutrients) determine the cell metabolism and mer-operon expression adaptation.E. coli cell model notations: The simplifi ed GRC pathway of the mer-operon expression for the mercury ion uptake in E. coli cells includes 7 gene expression lumped regulatory modules (GERMs), by which 4 of type [G(PP)1] (see the Part-1 of this work) that is: 2 modules for mediated transport of [Hg 2+ ]env into the cytosol (catalysed by PT) and its reduction (catalysed by PA); 5 regulatory modules of mer operon expression including successive synthesis of the corresponding proteins, that is: PR [ the transcriptional activator of other protein syntheses; its synthesis being triggered by the import of the mercury ions immediately linked as Hg(SR)2 into the cell]; the lumped PT permease; the lumped PA reductase, and of the control protein PD.One additional GERM regulatory module of the simplest type [G(P)1] (see Part 1 of this work) deals with the lumped proteome P and genome G replication into the cell (by thus mimicking the cell "ballast").The mer-operon GRC is placed in a growing cell, by mimicking the homeostasis, and cell response to stationary and dynamic perturbations in the environmental [Hg 2+ ]env.The reductant NADPH and RSH are considered in excess of the cell.Notations: P = lumped proteome; G = lumped genome; NutG, NutP = lumped nutrients used for gene and protein synthesis, respectively; P• = proteins; G• = genes; RSH = low molecular mass cytosolic thiol redox buffer (such as glutathione).Perpendicular arrows on the reaction path indicate the catalytic activation, repressing, or inhibition actions.The absence of a substrate or product indicates an assumed concentration invariance of these species;  / Θ positive or negative feedback regulatory loops.

2
Hg env  is surprising.Instead of building carbon-and energy-intensive disposal 'devices' into the cell (like chelate-compounds) to 'neutralize' the cytosolic mercury 2 Hg cyt  and thus maintain a tolerable level, a simpler and more effi cient defending system is used.The metallic ions 2 Hg cyt  are catalytically reduced to the volatile metal 0 Hg cyt ,

Figure 3 :
Figure 3: The present case study -In-silico design of a cloned E. coli with a maximized capacity of mercury uptake from wastewaters [9,59-62,88].[Down-right] Prof. G. Maria and late Prof. W. Deckwer at the 2nd Croatian-German Conference on Enzyme Reaction Engineering, 21-24 Sept. 2005, Dubrovnik (Croatia), sharing opinions about the bioprocess of mercury removal from wastewaters by using cultures of cloned E. coli cells.
power.In general, such in-silico investigations to design GMOs are supported by the tremendous improvement in the computing power over the last decades, and by the continuous expansion of the available information from cellular bio-omics databanks (see Parts 1-2 of this work), despite steady efforts necessary to elaborate such detailed HSMDM cellular numerical simulators.Citation: Maria G (2024) Application of (bio) chemical engineering concepts and tools to model genetic regulatory circuits, and some essential central carbon metabolism pathways in living cells.Part 4. Applications in the design of some Genetically Modified Micro-Organisms (GMOs).Ann Syst Biol 7(1): 001-034.DOI: https://dx.doi.org/10.17352/asb.000021

Figure 6 :
Figure 6: The macroscopic model of the three-phase fl uidized-bed bioreactor (TPFB) with suspended immobilized E. coli on pumice beads.The Michaelis-Menten mercury reduction model rate constants depend on the mer-plasmid level [59-62].

Figure 7 :
Figure 7: Three-phase fl uidized bed (TPFB) reactor parametric sensitivity related to the variations in the inlet [ 2 Hg L  ]in, leading to variations of the following operating

Figure 9 :
Figure 9: Three-phase fl uidized bed (TPFB) reactor parametric sensitivity related to biomass concentration C X variations, leading to variations of: outlet [ 2 Hg L  ](top-left);
up-right) includes a resistant E. coli cell culture.The bioreactor is completely automated being able to maintain its control parameters of [

Figure 12 :
Figure 12: The main characteristics of the E. coli (K-12 strain) used in the present case study.Data from EcoCyc [103].
The extended HSMDM structured bioreactor bi-level model includes two inter-connected parts: (a) The macro-level statevariables of the TPFB bioreactor (Table3), that is the phase; (b) The cell nano-level state-variables, that is the mass balance of the cell key-species included in the WCVV-GRC model of (Table

[ 90 ]
on the mer-operon characteristics.The WCVV cell model was built up by accounting for the GERMs library, their P.I.-s, and the linking rules presented in Part 2 of this work.Citation: Maria G (2024) Application of (bio) chemical engineering concepts and tools to model genetic regulatory circuits, and some essential central carbon metabolism pathways in living cells.Part 4. Applications in the design of some Genetically Modified Micro-Organisms (GMOs).Ann Syst Biol 7(1): 001-034.DOI: https://dx.doi.org/10.17352/asb.000021 amounts of mercury into the cell, which eventually might lead to the blockage of cell resources (RSH, NADPH, other metabolites, and proteins), thus compromising the whole cell metabolism.The GRC model includes four GERMs of simple but effective [G(PP)1] type (see the discussion of Part-2 of this work) as follows (see Figure 11, and Table 4): (i) A GERM to regulate the Hg 2+ transport across the cellular membrane, mediated by three proteins (PmerP, PmerT, and PmerC) from the periplasmatic space, considered as a lumped permease PT in the model.Phillippidis et al. [88-90] found this transport step to be energy-dependent and the rate-determining step for the whole mercury uptake process.Once the mercuric ion complex arrives in the cytosol, thiol redox buffers (such as glutathione of millimolar concentrations) form a dithiol derivative Hg(SR) 2 .Instantly, the GT lumped gene expression is induced by the regulatory protein PR, and easily 'smoothed' by the large 'ballast' effect of the proteome lump P. (see rule 6 of chapter.2.3.6 of Part-2 of this work).

,
30 s) cell response by starting the mer-enzymes production.First, the expression of the GR gene leads to obtaining the encoded PR protein.The process magnitude is also controlled by the protein PD, present in small amounts in the cell.(iii) A GERM to control the expression of PA enzyme responsible for the Hg(SR) 2 (that is 2 Hg cyt  ) reduction to metallic mercury ( 0 Hg cyt ) into the cytosol.The metallic mercury is relatively non-toxic for the cell, being easily removable through membranar diffusion into the bioreactor bulk liquid phase ( being entrained and continuously removed by the sparged air as mercury vapours ( o Hg G ), to be later recovered.The GA gene expression is induced and controlled by the PT protein, whose expression is controlled by the PR level, which in turn is controlled by the cytosolic mercury and PD levels.

2
Hg cyt  are present in the environment.(v)A GERM controlling the replication of the lumped cell proteome (P) and genome (G) (of concentrations 10 7 nM, and 4500 nM, respectively, to mimic the effect of "cell ballast", see Part-2 of this work) in the immobilized E. coli cells.These data are based on the Ecocyc[103] databank (Table5, and (Figure12), thus mimicking the cell 'ballast' effect on the cell genes expression, and on all considered reactions.The need to include the cell content lump (the so-called 'cell ballast') in the WCVV model is legitimate by the possibility offered by such a structured cell model to reproduce the smoothing effect of perturbations leading to more realistic transient times (compared to a cell with a 'sparing' content), the synchronized response to certain inducers, and the 'secondary perturbation' effect transmitted via the cell volume to which all cell components contribute (see the discussion in the Part-2 of this work).

0
Hg cyt in the E. coli cells cloned with a defi ned [Gmer] concentration of mer-plasmids.
a) A Michaelis-Menten rate expression for the mercuric ion permeation through the membrane into the cell; b) A Michaelis-Menten rate expression for the mercuric ion reduction in the cytosol; c) A Hill-type quick induction of the GR expression that Citation: Maria G (2024) Application of (bio) chemical engineering concepts and tools to model genetic regulatory circuits, and some essential central carbon metabolism pathways in living cells.Part 4. Applications in the design of some Genetically Modified Micro-Organisms (GMOs).Ann Syst Biol 7(1): 001-034.DOI: https://dx.doi.org/10.17352/asb.000021can rapidly initiate the production of permease PT (through the control protein PR) when mercuric ions are present in large amounts.d) Dimmerization reactions of TF-s are considered to be much more rapid than the enzyme synthesis, while equal concentrations of active gene (G) and inactive (GPP) forms of the generic gene G are considered at homeostasis to maximize the GERM effi ciency (see Part-2 of this work) (Figure 1, and Figure 11).

e)
The lumped proteome P, present in a large amount, is included in all gene expression rates, thus leading to a more realistic evaluation of the GERM regulatory effi ciency indices P.I.-s (see Part-2 of this work)[1,2,3,4,57,58].

g)
Figure 6).Simple correlations are used to include this essential aspect in the model.

2 )
) as a step response after a ‚step'-like perturbation in the mercury level from [ 2 Hg env  ]s = 0.1 μM to 10 μM (ca. 2 mg/L), in a cloned E. coli cell with mer-plasmids of [Gmer]= 140nM, compared to a cell cloned with only [Gmer]= 3 nM.The transient state toward the cell's new homeostasis of the "adapted" mer-gene/protein levels stretches over 15-20 cell cycles (of ca.0.5 h each) as long as the environment stationary step perturbation is maintained.An E. coli cell with a higher content of mer-plasmids reacts much strongly to the environmental perturbations, by quickly starting to produce the enzymes responsible for the mercury removal.Because the Hg 2+ reduction rate constants are dependent on the mer-plasmid level in the cell, the WCVV GRC model can predict the maximum level of mer-plasmids that can be added to the cell genome for improving its mercury uptaking capacity without exhausting the internal cell resources, thus putting in danger the cell survival.Consequently, it follows that this cell MSDKM model allows the in-silico design of modifi ed E. coli cloned with a suitable amount of mer-plasmids to improve its effi ciency in cleaning wastewater by improving the mercury uptaking capacity.As an example, (Figure 14 presented the cell key-species stationary levels, and the mercury concentration in the TPFB bioreactor bulkphase for two GMOs: An E. coli cloned with [Gmer] = 67 nM, and another culture of E. coli cells cloned with

Figure 13 :
Figure 13: Typical evolution of relevant species concentrations predicted by the E. coli cell model, after a "step" perturbation in the TPFB bioreactor inlet from [ 2 Hg env  ]s = 0.1 to 10 μM (ca. 2 mg/L), for the case of cell cloned with [Gmer]= 3 nM (___), or with [Gmer]= 140 nM (• • • • • ).The arrow indicates the quick and vigorous response of the two key mer-enzymes: PT = the mercury ions permease, and PA = the mercury ions reductase.
here-described hybrid structured HSMDM model.The two linked differential models are solved together simultaneously, by applying a mutual exchange of input/output parameters {[ 2 Hg env  )], [ 0 Hg env ], PT, PA} on every small time increment throughout the solution (integration) of the HSMDM model, as graphically represented in (Figure 1).As described in the below paragraph dedicated to solving Citation: Maria G (2024) Application of (bio) chemical engineering concepts and tools to model genetic regulatory circuits, and some essential central carbon metabolism pathways in living cells.Part 4. Applications in the design of some Genetically Modified Micro-Organisms (GMOs).Ann Syst Biol 7(1): 001-034.DOI: https://dx.doi.org/10.17352/asb.000021

Figure 14 :
Figure 14: [Left].Dynamics of metallic mercury concentrations in the liquid and gas phases, and in the bioreactor outlet after a "step" perturbation in the reactor inlet from [ 2 Hg L  ] = 0.1 μM to 100 μM (ca.20 mg/L), for immobilized cells on pumice granules under nominal conditions of Table 2. Comparison is made for the cases of cells cloned with [Gmer]= 67 nM ( ___ ), or with [Gmer]= 140 nM (• • • • •).The curves indexed by "1" denote predictions of the unstructured (apparent) reactor model (Table7, Table8), while curves indexed by "2" denote the predictions of the structured HSMDM bioreactor model (including the cell model of Table4).[Right].Dynamics of relevant mer-species concentrations (that is genes GA, GT, GD, GR, and their encoded proteins PA, PT, PD, PR) inside the cell, and the mercury [Right].Dynamics of relevant mer-species concentrations (that is genes GA, GT, GD, GR, and their encoded proteins PA, PT, PD, PR) inside the cell, and the mercury reduction rate following the same "step" perturbation in the reactor inlet from [ 2 Hg L  ] = 0.1 μM to 100 μM (ca.20 mg/L), for immobilized E. coli cells on pumice granules under nominal conditions of Table that is in the bioreactor bulk-phase) from the background level of 0.1 μM to 10 μM (ca. 2 mg/L), for the case of cell cloned with [Gmer]= 3 nM (full line), or with [Gmer]= 140 nM (dash line) mer-plasmids.The transient state toward the cell's new homeostasis usually lies over 15-20 cell cycles as long as the environmental stationary perturbation is maintained.The simulated species dynamic trajectories plotted in (Figure 13) reveal a vigorous response of the cell mer-species (especially of PT, and PA) to the perturbation in the environmental [ .e. liquid bulk-phase).Such cell responses to environmental perturbations are impossible to reproduce by the simple unstructured reduced model (Table bioprocess induced and intensifi ed by the [ 2+ Hg L,env ] level, controls the TPFB bioreactor output [ 30 min), enough to obtain the steady-state of the TPFB reactor on every time-Citation: Maria G (2024) Application of (bio) chemical engineering concepts and tools to model genetic regulatory circuits, and some essential central carbon metabolism pathways in living cells.Part 4. Applications in the design of some Genetically Modified Micro-Organisms (GMOs).Ann Syst Biol 7(1): 001-034.DOI: https://dx.doi.org/10.17352/asb.000021
coli cells cloned with mer-plasmids in the amount of [Gmer] = 3 nM (A), [Gmer] = 78 nM (B), and [Gmer] = 140 nM (C).Plots (D) display the predicted cytosolic concentration of mer-reductase [PmerA] = [PA] for [Gmer] = 3 nM, and [Gmer] = 140 nM.interval, as follows: (i) The rule starts with solving the extended hybrid HSMDM E. coli cell model by using the known initial condition (the cell variables' initial state, or those from the end of the previous integration cycle), and by considering the current concentration of [ 2 Hg env  ] in the bioreactor liquid phase (the nutrients are considered in excess and of constant levels).Thus, the cell species dynamics over one cell cycle are obtained from solving the WCVV cellular model.(ii) Then, the TPFB reactor model is solved over the current time-interval by using the known initial conditions (i.e. the reactor state variables from the end of the previous time-interval), and by considering the enzymes PT and PA concentrations resulting from the E. coli model solution.The [PT] and [PA] are necessary for setting the maximum reaction rates model.The biomass level on the support is taken constant in the simulated case study, but an additional mass balance can be easily added to the reactor model if a kinetic model about biomass (X) growth is available.
) displays the E. coli cell adaptation after a 'step'-like perturbation in the environmental [ 2 Hg env  ]s (that is in the bioreactor bulk-phase) from the background level of 0.1 μM to 10 μM (ca. 2 mg/L), for the case of cell cloned with [Gmer]= 3 nM (full line), or with [Gmer]= 140 nM (dash line) mer-plasmids.The transient state toward the cell's new homeostasis usually lies over 15-20 cell cycles as long as the environmental stationary perturbation is maintained.The simulated species dynamic trajectories plotted in (Figure 13) reveal a vigorous response of the cell mer-species (especially of PT, and PA) to the perturbation in the environmental [ 2 Hg env  ]s (i.e.liquid bulk-phase).Such cell responses to the environmental (dynamic or stationary) perturbations are impossible to reproduce by the simple unstructured reduced model (Table b) Cell model parameters are estimated by using the Philippidis et al. [88-90] kinetic data obtained from separate batch experiments with "wild" (not-cloned) E. coli cells.By using the defi ned cell nominal characteristics of (Table 5) (some key notations are: t C = cell cycle time; Vcyt,O = born cell volume; C X = biomass concentration in the bioreactor; P = cell lumped proteome; G = cell lumped genome; NutG, NutP = lumped nutrients for G and P synthesis, respectively; [Gmer] = mer-plasmid levels into the cloned cell.The stationary levels of the essential cell mer-proteins (PA, PR, PD) are taken from the literature data.The involved TFs (PRPR, PTPT, Citation: Maria G (2024) Application of (bio) chemical engineering concepts and tools to model genetic regulatory circuits, and some essential central carbon metabolism pathways in living cells.Part 4. Applications in the design of some Genetically Modified Micro-Organisms (GMOs).Ann Syst Biol 7(1): 001-034.DOI: https://dx.doi.org/10.17352/asb.000021

2 c
Hg e = 2 c Hg L = environmental Hg 2+ concentration; 2 c Hg s = Hg 2+ concentration at the solid surface.These r app reaction rates are part of the TPFB bioreactor model (Table 7).PAPA, PDPD) intermediate concentrations resulted by maximizing the GERMs regulatory effi ciency P.I.-s (see Part-2 of this work) [1,2,3,4,21,22].The resulting rate constants of (Table 4) have been estimated for the most severe experimental conditions of [ 2 Hg env  ]s = 120 μM, and [Gmer] = 140 nM.The used fi rst guess of Hill-induction rate constants (nPD = 1, nPR = -0.5, nH = 2, a = 3) have been adopted at values recommended in the literature, by similarity with the Hill-induction of gene expression in genetic switches (see the remarks included in Table adopted at the average cytosolic level of mercuric ions detected by Philippidis et al. [88-90].When applying the model estimation rule, the GERM regulatory indices have been kept at their optimized levels, which corresponds to: (i) Equal concentrations of catalytically active/inactive forms [G(j)]s = [G(j)TFn]s adopted at steady-state to ensure GERM maximum regulatory effi ciency vs. perturbations (i.e.smallest sensitivities Citation: Maria G (2024) Application of (bio) chemical engineering concepts and tools to model genetic regulatory circuits, and some essential central carbon metabolism pathways in living cells.Part 4. Applications in the design of some Genetically Modified Micro-Organisms (GMOs).Ann Syst Biol 7(1): 001-034.DOI: https://dx.doi.org/10.17352/asb.000021 of the homeostatic levels vs. external perturbations [1-4], and (Part-2 of this work); (ii) adjustable optimum [TF]s level (ca. 4 nM here; unstructured reduced model of the TPFB bioreactor is due to the rough bioprocess representation by the M-M model, and due to the inclusion of the mass transport resistance between the three phases in contact.The extended HSMDM model adequacy in terms of standard error 'Std' / average observed value 'Obs' ratio is evaluated for every cloned cell culture, leading to Std/ Obs of 22.3%, 16.7%, 20.4%, 19.9%, 18.8% for [Gmer] levels of 3, 67, 78, 124, and 140 nM respectively, that is acceptable values when compared to the maximum experimental error (ca.25-33% in Figure 15).The predicted structured vs. unstructured model outputs, in terms of outlet concentration of mercury ( , c Hg out ) are also in fair agreement (curves not displayed here), that is Std/Obs values of 3.0%, 4.7%, 3.7%, and 12% for [Gmer] levels of 67, 78, 124, and 140 nM respectively.The model's poor adequacy for the [Gmer] = 3 nM data set and low [ 2 Hg L  ] in the environment (input) might be explained by the use of a less adapted E. coli cell than probably those studied by Phillipidis et al. [88-90], refl ected by a smaller [PA] initial level of 600 nM (see the PA-curve in Figure 15-D).Once a higher level of Gmer-plasmids is introduced into the cell, then, when higher 2 Hg L  stimulus levels are present in the environment, the cytosolic PA level is tripling.The extended HSMDM structured model cellular rate constants (see the above point (b), and Table

As a fi nal
observation, by extending the detailing degree of the bioreactor dynamic model at a cellular level, the resulting structured HSMDM model not only preserves but also extends the adequacy of the unstructured model, adding the possibility to predict the cell species/fl uxes dynamics over dozens of cell cycles.By offering details on the cell metabolism adaptation, the 'intrinsic' reduction rate, and the possibility to in-silico predict the modifi ed (cloned) cell response to various stimuli, such an HSMDM model presented in this paper is superior compared to the unstructured (apparent) bioreactor dynamic models.Eventually, the extended HSMDM models are worth the supplementary experimental and computational effort to derive/identify them.
of industrial interest.Such models can adequately reproduce the cell response to continuous perturbations, the cell model structure and size being adapted based on the available -Citation: Maria G (2024) Application of (bio) chemical engineering concepts and tools to model genetic regulatory circuits, and some essential central carbon metabolism pathways in living cells.Part 4. Applications in the design of some Genetically Modified Micro-Organisms (GMOs).Ann Syst Biol 7(1): 001-034.DOI: https://dx.doi.org/10.17352/asb.000021omics information.Even if such extended structured models are currently used only for research purposes, being diffi cult to identify, it is a question of time until they will be adapted for industrial / engineering purposes in the form of reduced HSMDM models.In other words, this work presents a holistic "closed loop" approach that facilitates the control of the in vitro through the in silico development of dynamic models for living cell (biological) systems[108], by deriving deterministic modular, structured cell kinetic models (MSDKM), with continuous variables, and based on cellular metabolic reaction mechanisms.The ever-increasing availability of experimental (qualitative and quantitative) information, at the cell metabolism level, but also about the bioreactors' operation necessitates the advancement of a systematic methodology to organize and utilize these data.The resulting HSMDM was proved to successfully solve diffi cult bioengineering problems.In such HSMDM models, the cell-scale model part (including nanolevel state variables) is linked to the biological reactor macroscale state variables for improving the both model prediction quality and its validity range.The case study presented and discussed here proves this engineering aspect.An alternative compromise is to use hybrid models that combine unstructured with structured process characteristics to generate more precise predictions (see the review of Maria[74]).Hybrid models use a two-level hierarchy: the bioreactor macroscopic state variables linked with the nano-scale variables describing the cell key metabolic processes, and those of practical interest.As proved by the case study presented in this paper, and by some additional ones mentioned in the Introduction section of this work, the use of MSDKM and HSMDM models (developed under the novel WCVV modelling framework) to simulate the dynamics of the bioreactor and, implicitly, the dynamics of the key cellular metabolic processes (CCM-based, related GRC-s, and target metabolites syntheses) occurring in the bioreactor biomass, presents multiple advantages, such as: (i) a higher degree of accuracy and the prediction detailing for the bioreactor dynamic parameters (at both macro-and nano-scale level); (ii) the prediction of the biomass metabolism adaptation over tens of cell cycles to the variation of the operating conditions in the bioreactor; (iii) prediction of the CCM key-species dynamics, by also including the metabolites of interest for the industrial biosynthesis; (iv) prediction of the CCM stationary reaction rates (i.e.metabolic fl uxes) allow to in-silico design GMO of desired characteristics.

Table 2
(pumice), and Table 6 (alginate)] at their optimal set-point, by ensuring a constant pH, temperature, a constant inlet feed fl ow-rate, and inlet mercury concentration [ 2 Hg L  ] in, a constant sparkling air inlet feed fl ow-rate, and a constant concentration of nutrients used as C/N/P source for the biomass optimal growth.

Table 8 )
comparatively with using the structured Citation: Maria G (2024) Application of (bio) chemical engineering concepts and tools to model genetic regulatory circuits, and some essential central carbon metabolism pathways in living cells.Part 4. Applications in the design of some Genetically Modified Micro-Organisms (GMOs).Ann Syst Biol 7(1): 001-034.DOI: https://dx.doi.org/10.17352/asb.000021

Table 2 (
pumice)) have been simulated under the nominal operating conditions of Table2, but every time-varying one operating parameter, that is: Citation: Maria G (2024) Application of (bio) chemical engineering concepts and tools to model genetic regulatory circuits, and some essential central carbon metabolism pathways in living cells.Part 4. Applications in the design of some Genetically Modified Micro-Organisms (GMOs).Ann Syst Biol 7(1): 001-034.DOI: https://dx.doi.org/10.17352/asb.000021

Table 7 :
:The reduced mathematical model of the TPFB bioreactor of Deckwer et al.

Table 5 )
involved in the gene expressions to get the minimum recovering times after a dynamic perturbation in the key species [1,2,21,22,51,58], (see Part-2 of this work).Other adjustable parameters, such as the cell concentration in biomass (C cell ), are tuned to fi t the experimental cellular mercury reduction rate of Philippidis et al. [88-90].

Table 1 ,
Table 7, and Table8) with using the Philippidis The extended HSMDM model predictions are in satisfactory agreement with the experimental data.Thus, the model predictions for rHg in (Figure15, A-C) (curves '2') roughly fall within the confi dence band [‚Eup', ‚Elow'] of the experimental curves (‚E') of Philippidis et al. [88-90] for three different cloned cell cases (confi dence curves being plotted by taking constant the reported maximum relative error of ca.19%).The unstructured model (chap.2.3, Table 1, Table 7), and [88][89][90]9][90]Michaelis-Menten parameters and the mass transfer terms, to fi t with those of the structured (cell + reactor) extended HSMDM model of (Table3, and Table4).The Hill parameter b=2a 4 was adjusted by using the following approximate linear dependence on the inlet mercury load:

Table 8 )
predictions (that is curves '1') reported apparent rHg of low adequacy, that is too low values.Such a result for the