## Application of (Bio-) Chemical Engineering Concepts and Rules in Bioinformatics. Review of a CCM-Based Modular and Hybrid Kinetic Model Used to Simulate and Optimize a Bioreactor with Genetically Modified Cells

### Gheorghe Maria^{1}^{3}^{*}, Cristina Maria^{2}and Laura Renea^{1}

^{1}1Department of Chemical and Biochemical Engineering, Politehnica University of Bucharest, Romania

^{2}2National Institute for Research and Development in Environmental Protection, Bucharest, Romania

^{3}Romanian Academy, Chemical Sciences Section, Romania

**Submission:** February 07, 2022; **Published:**February 21, 2022

***Corresponding author:**Gheorghe Maria, Department of Chemical and Biochemical Engineering, Politehnica University of Bucharest, Polizu Str. 1-7, 011061, Bucharest, Romania

**How to cite this article:**Gheorghe Maria. Application of (Bio-) Chemical Engineering Concepts and Rules in Bioinformatics. Review of a CCM-Based
Modular and Hybrid Kinetic Model Used to Simulate and Optimize a Bioreactor with Genetically Modified Cells. Curr Trends Biomedical Eng & Biosci. 2022; 20(3): 556039. DOI:10.19080/CTBEB.2022.20.556039

**Abstract**

This work briefly reviews the main concepts and principles used to solve difficult biochemical engineering, or bioengineering problems, by using extended structured cell kinetic models (including nano-scale state variables) linked in hybrid models to the biological reactor dynamic models (including macro-scale state variables). Exemplification is made for the case of the numerical methodology used by [Maria, 2021] to derive a structured hybrid modular kinetic model able to simulate the dynamics of a Fed-batch bioreactor (FBR), at both cell and bulk-phase species levels. The approached FBR includes a genetically modified E. coli culture used for the tryptophan (TRP) production. Eventually this complex hybrid dynamic model was used by [Maria and Renea, 2021] to derived the FBR optimal operating policy leading to the TRP production maximization.

**Keywords: **Biochemical engineering concepts; Principles and rules; Fed-batch bioreactor; Hybrid structured kinetic models; Tryptophan production

**Introduction**

As proved in the literature, the *in-silico* (math/kinetic model-based) numerical analysis of biochemical or biological processes are proved to be not only an essential but also an extremely beneficial tool for engineering evaluations aiming to determine the optimal operating policies of complex multi-enzymatic reactors [1-5], or bioreactors [6,7].

As reported over the last years, the use of structured cell models (based on the Central Carbon Metabolism - CCM) in the engineering evaluations “(to solve model-based design, optimization and control problems of industrial biological reactors) instead of the classical (default) *unstructured* models of Monod type (for cell culture bioreactors), or of Michaelis-Menten type (if only enzymatic reactions are retained) that ignores detailed representations of cell processes, presents a large number of advantages [8]. Thus, by accounting for only key process variables (biomass, substrate and product concentrations), these unstructured models do not properly reflect the metabolic changes, being unsuitable to accurately predict the cell response to environmental perturbations by means of (self-) regulation of the cell metabolism [9,10]. The alternative use of *structured* models (based on the cell reaction pathways), by accounting for cell metabolic reactions and component dynamics, leading to a considerable improvement in the predictive power, with the expense of incorporating a larger number of species mass balances with parameters difficult to be estimated from often incomplete data and, consequently, difficult to be used for industrial scale purposes. An alternative compromise is to use *hybrid* models that combine unstructured with structured process characteristics to generate more precise predictions [8]. Basically, hybrid models use a two-level hierarchy: the bioreactor macroscopic state variables linked with the nano-scale variables describing the cell metabolic processes of interest. Even if such a complex/extended
model requires more experimental and computational efforts to
be built-up, the resulted *hybrid* (bi-level) dynamic model presents
a several advantages, as followings:

i. The extended model allows further *in-silico* (modelbased)
engineering developments (bioreactor design, and its offline
optimization) of a higher accuracy compared to unstructured
models. For instance, the model could better predict the optimal
time stepwise feeding policy of a Fed-batch reactor (FBR) to
increase the Tryptophan (TRP) production (this paper example)
[7,8].

ii. It can be used for bioinformatics purposes, by evaluating the influence of the bioreactor operating conditions (control macro-variables) on the dynamics of cell nano-scale keyintermediates and fluxes involved in the metabolite synthesis of interest (that is those belonging to glycolysis, ATP-recovery system, and TRP-operon expression in the present case), thus directing the design of genetically modified cells with desirable ‘motifs’ [8].

iii. It can be used to obtain lumped dynamic models for rapid
engineering calculations, by employing specific model reduction
rules and kinetic data valid in the *local* operating domains. See
general models [11,12], or linear models [13,14]. Because of such
an approach, the bioprocess complexity may be described by a
succession of local reduced models *enfolded* on the real process.
The local / reduced models include only some metabolic pathways
to obtain relevant (of interest) process state predictions.

iv. The structured cell models are also useful for understanding the cellular bioprocess in direct connection to the bioreactor-operating mode. For instance, in such a way can be determined, by means of numerical techniques, conditions of occurrence of oscillations for the glycolysis [15], or oscillations in the TRP-operon expression [9,16], or those leading to a balanced cell growth (quasi-steady-state QSS, i.e. homeostasis) [17].

v. As proved in the present case study, such hybrid bilevel
models allow more robust extrapolations of the bioprocess
behaviour in the case of TRP production optimization in a FBR [7].
Some other case studies with using *hybrid* models to describe the
dynamics of bioreactors and cell bioprocesses are given by: Maria
and Luta to optimize the mercury uptake by modified *E. coli* cells
in a FBR [10]; Maria et al. to optimize the succinate production by
*E. coli* in a batch mode [18]; reviews of Maria [6]; Dorka on FBR
optimization for the monoclonal antibodies (mAbs) production,
etc. [6,19].

Generally, modelling the dynamics (and regulation) of the
bacteria CCM is a subject of very high interest, allowing *in silico*
design of modified cells with desirable characteristics of various
applications in the biosynthesis industry, civil engineering,
and other fields [20,21]. The interest for such a subject is even
higher as long as most of the glycolysis intermediates are starting nodes for the internal production of lot of cell metabolites (e.g.,
amino-acids, succinate, citrate, etc. [16,18]). As documented
by Maria, to overcome the cell process dynamics complexity,
the metabolic pathway representation with continuous and/or
stochastic variables remains the most adequate and preferred
representation of cell processes, the adaptable-size and structure
of the lumped model (species and/or reactions) depending on
available information and the utilization scope [20,21].

As underlined by Maria, the main advantages of *deterministic*/
*continuous* *variable* kinetic models are coming from the use of
experience, concepts, math representation, rules, and algorithms
of the biochemical reaction engineering [20-22]. The reaction
rate expressions in the deterministic models are the usual ones of
biochemical reaction engineering that is of Michaelis-Menten or
Hill type (see fig. 47 of Maria [21]). A large number of CCM kinetic
models have been reported in the literature, such as those of
[23-25]. A short discussion is given by Maria [8,26]. Such a CCMbased
kinetic model (Figure 1) was used by to optimize a FBR
[7,8]. In fact, the glycolysis together with the phosphotransferase
**(PTS)**-system, or an equivalent one for GLC-uptake, and with the
pentose-phosphate pathway **(PPP)**, and the tricarboxylic acid
cycle **(TCA)**, all these are part of the so-called central carbon
metabolism **(CCM)** (Figure 1)[18].

The parameters (rate constants) of deterministic dynamic
models are estimated using the common (bio)chemical
engineering rules of (Figures 2 & 3) [11,20,21], by using either
dynamic (kinetic) data obtained in a chemostat under transient
regime (e.g. pulse-like perturbations in the bioreactor influent
[25], or using steady-state data (metabolites concentrations)
obtained at homeostasis (i.e. balanced cell growth [20,27]),
by solving the math model stationary algebraic set dCj/dt = 0
(where “j” indexes the cell species taken individually or lumped;
C= species concentrations; t = time). Parameter estimate must
fulfill physico-chemical meaning constraints related to metabolic
reaction stoichiometry. Besides, the rate constants must be
limited by the diffusional processes, and in agreement with
the thermodynamic equilibrium steps. Additionally, due to the
optimized metabolic cell process, when modelling individual
Gene Expression Regulation **(GERM)**, or Genetic Regulation
Circuits **(GRC)** in living cells, under a whole-cell approach
[20,27,28], cell models must fulfil some optimality constraints,
that is: reaction rates must be maximal, but with rate constants
limited by the diffusional processes; the total enzyme (proteine)
content of the cell is limited by the isotonicity condition; also the
total cell energy (ATP) and reducing agent (NADH) resources are
limited; the reaction intermediate levels must be minimum; the
cell model at homeostasis must be stable, that is will reach the
steady-state after termination of a perturbation [29]; the keyspecies
concentrations must be constant at homeostasis. Most of
the mentioned aspects are discussed and exemplified by Maria
[20,21,27,28,30].

Even if complicated and, often over-parameterized, the
continuous variable dynamic deterministic **ODE** (ordinary
differential equations) models of the **CCM** metabolic pathways,
or of **GRC**-s present a significant number of advantages, being
able to reproduce in detail molecular interactions, the cell slow
or fast continuous response to exo/ando-geneous continuous
perturbations [31,32]. Besides, the use of **ODE** kinetic models
presents the advantage of being computationally tractable,
flexible, easily expandable, and suitable to be characterized using
the tools of the nonlinear system theory [29], by accounting for
the regulatory system properties, that is: dynamics, feedback
/ feedforward, and optimality. And, most important, such ODE
kinetic modelling approach allows using the strong tools of
the classical (bio-)chemical engineering modelling concepts
summarized in (Figures 2 & 3). The most important ones are the
followings [20,21,27,28]:

i. Molecular species conservation law (stoichiometry analysis; species differential mass balance set).

ii. atomic species conservation law ( atomic species mass balance).

iii. thermodynamic analysis of reactions (that is quantitative assignment of reaction directionality) [33].

iv. set equilibrium reactions; Gibbs free energy balance
analysis; set cyclic reactions; find species at quasi-steady-state;
improved evaluation of steady-state flux distributions that provide
important information for metabolic engineering [34], allowing application of **ODE** model species and/or reaction lumping rules
[11].

A discussion of the (bio-) chemical engineering concepts, principles, and tools is given by [35,36].

This paper is aiming to review the numerical methodology
used by Maria and by Maria and Renea to derive a structured
hybrid model able to simulate the dynamics of a **FBR** including
a genetically modified *E. coli* culture used for the TRP production
[7,8]. Eventually this complex modular structured and hybrid
dynamic model was used to derive the optimal FBR operating
policy leading to the TRP production maximization [7].

**Short Review of a Case Study**

**The structured hybrid model**

To exemplify a methodology to develop a structured CCMbased kinetic model linked to a classical macro-level dynamic model of a FBR, the case study of Maria was approached here [8].

The approached case study refers to the tryptophan (**TRP**)
synthesis in modified *E. coli* cells (i.e. T5 strain of Chen et al.
[37]). The required experimental data were collected from a labscale
FBR by Chen [38]. The developed *structured* kinetic model
includes several inter-connected reaction pathway (*modules*) able
to simulate the dynamics of glycolysis, TRP-operon expression,
ATP-recovery system, all belonging to the **CCM**. Experiments were
carried out by using an *E. coli* strain (T5) modified to replace
the PTS-system with a more efficient one to uptake the glucose (GLC) from the environment. By linking the FBR macroscopic
state variables with the nano-scale variables describing the cell
metabolic processes of interest, the resulted *hybrid* dynamic
model presents a large number of advantages. Thus, the model
allows further *in-silico* (model-based) more accurate engineering
developments of practical interest for the biosynthesis industry
related to TRP production maximization in a FBR using optimal
feeding policies to be determined in a separate numerical
analysis. Beside, such a hybrid structured model can be used
for bioinformatics purposes, by evaluating the influence of the
FBR operating conditions on the dynamics of key-intermediates
involved in the cell (TRP) synthesis, thus directing the design of
modified cells with desirable ‘motifs’ of practical interest

The metabolic flux analysis of Chen [38]; Chen [39]; Chen
& Zeng [40] suggests that replacement of the *wild* PTS glucose
uptake system with the galactose permease/glucokinase (galp/ glk) uptake system can theoretically double the TRP yield from
glucose [38-40]. Finally, a promising strain T5 was obtained
and fed-batch fermentations showed an increase of TRP specific
production rate by 52.93% (25.3mg/gDW biomass /h) [37].
The cell flux analysis of Chen [39], and Chen [38] indicated the
doubling of fluxes responsive with the TRP synthesis [7,38,39].

Basically, the structured CCM-based kinetic model of Maria includes four linked modules, that is (Figure 4-Left) [8]:

**Module [X]:** The biomass growth kinetic model (in the
FBR bulk-phase). The rate constants of [X] module have been
estimated by evaluating every time the biomass model with using
the experimentally recorded species dynamic trajectories (i.e. X,
and GLC here) instead of the required simulated data coming from
the (missing at this stage) kinetic modules of (FBR-dynamics, and
glycolysis).

**Module [a]:** Glycolysis kinetic model (cell level). Starting from
the extended reaction pathway of (Figure 1), and from the CCM
model of Chassagnole et al. and of Maria et al. and by applying
chemical engineering lumping techniques [18,25], Maria proposed
a valuable reduced dynamic model of glycolysis (denoted by **MGM**) 26], by accounting only for 9 key-species in 7 lumped reactions,
with including 17 easily identifiable rate constants belonging to
V1-V6 metabolic fluxes (Figure 4-Left). The **MGM** rate constants
have been identified by Maria with using the kinetic experimental
kinetic data of Chassagnole et al. and Visser et al. obtained from FBR including a “wild” *E.coli* culture [25,26,41]. When using the
modified *E.coli* in the FBR, Maria adjusted the **MGM** rate constants
by using the GLC, (excreted) PYR, X experimental kinetic curves
recorded over the FBR batch [8].

The **MGM** model has been proved to adequately reproduce
the cell glycolysis under steady state, oscillatory, or transient
conditions according to: i) the defined glucose concentration
level/dynamics in the bioreactor, ii) the total **A(MDT)P** cell
energy resources; iii) the cell phenotype characteristics (related
to the activity of enzymes involved in the **ATP** utilization and
recovery system) [9,15,16]. Here **A(MDT)P** denotes the lump
of the following species: ATP = Adenosin-triphosphate; ADP =
Adenosin-diphosphate; AMP = Adenosin-monophosphate. This is
why, the FBR and the MGM glycolysis dynamic models are to be
considered together when simulating the dynamics of the [GLC]
in the FBR bulk-phase [8], and of the cell metabolites of interest
{F6P(fructose-6-phosphate), FDP(fructose-1,6-biphosphate),
PEP(phosphoenolpyruvate), PYR(Pyruvate), ATP} into the cell.
The adopted rate expressions for the glycolysis main metabolic
fluxes V1-V6 are those of the basic MGM model.

**Module [b]:** ATP recovery system (cell level, the pink rectangle
in Figure 4). The adopted model for ATP-ADP-AMP dynamics (V6,
and equilibrium relationships) in (Figure 4 - the pink square)
imported from Maria was proved to fairly represent the dynamics
and the thermodynamics of such an important internal module
[9,26]. Rate constants were identified concomitantly with those of
module [a], in the same way. As an observation, the two modules
[a-b] are inter-connected by sharing the ATP species, while the
module [a], and [X] are inter-connected by sharing {X, and GLC}
species. Thus, the dynamics of species belonging to the three
inter-connected modules {[a], [b], and [X]} can be simulated
concomitantly, according to the reduced reaction pathway of
(Figure 4).

**Module [c]:** TRP-synthesis (cell level, Figure 4). The kinetic
models from the literature trying to reproduce the TRP-operon
expression self-regulation are too extended for our purposes
[42,43]. This is why, in the present analysis, simulations of the TRP
synthesis were performed by using the reduced kinetic model of
Maria et al. [9,16,17], and of Bhartiya et al. [44]. The rate constants
estimation rule is repeated by also considering the module [c] of
TRP-synthesis. First, one simulates the dynamics of this module
individually, by using the rate constants and the reaction rate
expressions from literature, as an initial guess. Because, the TRPmodule
[c] includes the species (PEP) shared with the glycolysis
module [a], simulations have been used the (PEP) time-trajectory
transferred from the concomitant simulations of the (now
available) three inter-connected modules {[a], [b], and [X]}. The
necessary TRP time-trajectory was taken the experimental one (if
necessary, interpolated with the cubic splines “INTERP1” facility
of Matlab^{™} package). Because the adopted TRP-inhibition model
of Bhartiya et al. [44] does not fit properly the experimental data of Chen [38], another inhibition model has been proved to
satisfactorily represent the experimental TRP data.

All the above described four kinetic model modules are integrated in the FBR dynamic model. To not complicate the numerical simulations, the FBR model adopted by Maria is a classical one [8], developed with the following main hypotheses: i) the operation is isothermal, iso-pH, and iso-DO; ii) it is selfunderstood that nutrients (that is, compounds playing roles of sources of carbon, nitrogen, and phosphorus) are added initially and during the FBR operation, in recommended quantities, and of an optimal C/N/P ratio [38], together with an excess of aeration for ensuring an optimally biomass maintenance, and any growth limitation due to such factors; iii) the volume of the perfectly mixed liquid phase (with no concentration gradients) increases according to the liquid feed flow-rate.

**The use of the hybrid model to evaluate the modified
E.coli strain efficiency**

By using the structured hybrid model, Maria was able to
simulate the (non-optimal) FBR performances when employing
a “wild” *E.coli* culture, or a modified T5 strain [8]. The results
indicated the superiority of the modified T5 *E. coli* strain in
maximizing the TRP productivity under similar operating
conditions, that is: i) a 100x higher flux (at the initial FBR
conditions) of the imported **GLC** into the cell, leading to ca. 50%
higher **TRP**-productivity of the **FBR** even if its operation is not the
optimal one.

**The use of the hybrid model to derive the optimal FBR
operating policy**

structured cell metabolic processes to the dynamics of macroscopic variables of the bioreactor, are more and more used in engineering evaluations to derive more precise predictions of the process dynamics under variable operating conditions. Depending on the cell model complexity, such a math tool can be used to evaluate the metabolic fluxes in relation to the bioreactor operating conditions, thus suggesting ways to genetically modify the microorganism purposes. Even if development of such an extended dynamic model requires more experimental and computational efforts, its use is advantageous [7].

The approached probative example refers to the four
modules model described above successfully used to simulate the
dynamics of some key-species from several pathways of the CCM
of a modified *E. coli* cells, linked to the macroscopic state variables
of a FBR used for the tryptophan (TRP) production. The used *E.
coli* strain was modified to replace the PTS system for glucose
(GLC) uptake with a more efficient one. In this chapter, one review
the way by which Maria and Renea used this complex hybrid
model to solve a difficult engineering problem [7], that is off-line
determination of the optimal feeding policy of a FBR (Figure 4 [Right-down]). The difficulty of the optimization problem comes
from several sources, that is: (i) the highly nonlinear hybrid model
of the process-reactor; (ii) highly nonlinear constraints defining a
non-convex domain; (iii) possible existence of multiple solutions
of the optimization problem.

To solve this problem, (i) the batch time (48h. here) is divided
in N_{div} “time-arcs” of equal lengths, and (ii) the control variables
are kept constant only over every “time-arc” at optimal values for
each time-arc determined from solving an optimization problem
(i.e., maximization of the TRP production in this case). The time
intervals of equal lengths Δt = t_{f} /N_{div} are obtained by dividing the
batch time t_{f} into N_{div} parts t_{j-1} ≤ t ≤ t_{j}, where t_{j} = jΔt are switching
points (where the reactor input is continuous and differentiable).
For the present case study, a value of N_{div} = 10 was adopted. A finer
division of the batch time (that is for larger N_{div}) is not desirable
because the necessary computational effort grows significantly
(due to a considerable increase in the number of searching
variables), thus hindering the quick (real-time) implementation
of the derived FBR operating policy. Additionally, multiple optimal
operating policies can exist for the resulting over-parameterized
constrained optimization problem of a high nonlinearity, thus
increasing the difficulty in quickly locating a feasible globally
optimal solution of the FBR optimization problem. Additionally,
as N_{div} increases, the derived operating policy is more difficult
to implement, since the optimal feeding policy requires a larger
number of stocks with feeding substrate solutions of different
concentrations, separately prepared to be fed for every time-arc
of the FBR operation (an overly expensive alternative) [7].

The chosen control variables are the followings:

a) The GLC substrate concentration in the feeding solution
for every N_{div} time-arc.

b) The liquid feed flow rate for every N_{div} time-arc.

c) In total, there are N_{div} × 2 = 10 unknowns to be
determined.

The objective function (Ω) used to solve the optimization problem must ensure maximization of the TRP production, that is:

variables to be determined. By applying a very effective solver
(that is the MMA algorithm of Maria [45]), the optimal time
stepwise continuously feeding policy of the FBR was obtained
(Figure 4 [Right-up]). As proved, this optimal FBR is able to
increase the TRP production with 75% from which 50% is due to
the used modified *E. coli* instead of the „wild” one, while 25% is
coming from the time variable optimal feeding of the FBR.

**Conclusion**

The extended bi-level (hybrid) kinetic model reviewed in this paper was proven to adequately represent the dynamics of an experimentally studied FBR under a nominal (uniform feeding) operating policy, for both macroscopic state variables and for the cell key species of the CCM reaction modules related to the TRP production in the FBR, i.e. [a] glycolysis, [b] ATP recovery system, [c] TRP operon expression, and biomass [X] growth. The hybrid structured model, linking the macro state variables to the nano cell-scale variables, was validated using the recorded data from the lab-scale FBR over a long batch time (63h).

The paper exemplifies how the use of a moderate-size CCMbased
hybrid kinetic model, of modular construction, including
the inter-connected complex metabolic pathways of interest, is
a continuously challenging subject when developing structured
cell simulators for various engineering applications, such as (a)
metabolic flux analysis under variable operating conditions;
(b) target metabolite synthesis optimization by optimizing
the bioreactor operation, and/or by modifying the cell strain;
(c) *in silico* reprogramming of the cell metabolism to design
GMOs (Genetically Modified Organisms); (d) a quick analysis
of the cell metabolism, leading to an evaluation of substrate
utilization, oscillation occurrence, and reactor Quasi-Steady-
State (QSS) operating conditions, or structured interpretations
of the metabolic changes in modified cells or in direct connection
to the bioreactor operation mode; (e) bioreactor/bioprocess
optimization (the present study); (f) to derive simple lumped
models, locally valid (in the operating parameters domain); (g)
to allow more robust extrapolations of the bioprocess behavior;
(h) to determine operating conditions leading to minimization of
the substrate consumption over the batch time, by keeping a high
TRP-yield [7].

The use of the main concepts, principles, and rules of the (bio) chemical engineering were proved to be beneficial when developing extended structured cell kinetic models used to solve difficult biochemical engineering, or bioengineering problems [46].

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