Concepts and Tools to Model GRCs, and Some Essential CCM Pathways in Living Cells 1. Generalities
Gheorghe Maria1,2,*
1Department of Chemical and Biochemical Engineering, Politehnica University of Bucharest, Polizu Str. 1-7, Bucharest 011061, Romania
2Romanian Academy, Chemical Sciences section., Calea Victoriei 125, Bucharest 010071, Romania
Submission:November 06, 2023; Published:December 20, 2023
*Corresponding author:Gheorghe Maria, Dept of Chemical and Biochemical Engineering, Politehnica University of Bucharest, Polizu Str. 1-7, Bucharest 011061, Romania, email: gmaria99m@hotmail.com; https://en.wikipedia.org/wiki/Gheorghe_Maria
How to cite this article:Gheorghe M. Application Of (Bio)Chemical Engineering Concepts and Tools to Model GRCs, and Some Essential CCM Pathways in Living Cells 1. Generalities. Curr Trends Biomedical Eng & Biosci. 2023; 22(1): 556080. DOI:10.19080/CTBEB.2023.22.556080
Summary
Biologically catalyzed reactions (with enzymes, or living cell cultures) can successfully replace complex chemical syntheses, being more selective, by using milder reaction conditions, and generating less waste. As proved by the recent literature, the developed in-silico (math-model-based) numerical analysis of such biochemical/biological systems turned out to be a beneficial tool to (i) off-line determine optimal operating policies of complex multi-enzymatic or biological reactors with a higher precision and predictability, or (ii) to design GMO (genetically modified micro-organisms) of desired characteristics for various uses. This work presents a holistic ‘closed loop’ approach that facilitate the control of the in vitro through the in silico development of dynamic models for living cell systems, 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 about the tremendous complexity of cell metabolic processes, stored in large bio-omics databanks (including genomic, proteomic, metabolomic, fluxomic cell data for various micro-organisms), but also about the bioreactors’ operation necessitates the advancement of a systematic methodology to organise and utilise these data.
Keywords:Biochemical engineering concepts applied in bioinformatics; Deterministic modular structured cell kinetic model (MSDKM); Hybrid structured modular dynamic (kinetic) models (HSMDM);Whole cell variable cell volume (WCVV) modelling framework; Whole cell constant cell volume (WCCV) modelling framework; Individual gene expression regulatory module (GERM); Genetic regulatory circuits (GRC), or networks (GRN); Chemical and biochemical engineering principles (CBE), Rules of the control theory of nonlinear systems (NSCT).
Abbreviations:ADP: Adenosin-diphosphate; AMP: Adenosin-monophosphate; ATP: Adenosin-triphosphate; BCE- (Bio)chemical engineering; CBE: chemical and biochemical engineering; BR: Batch reactor; CABEQ Jl: Chemical and biochemical engineering journal; CCM- Central carbon metabolism; CIT: Citrate; CSTR: Continuous stirred tank reactor; FBA: Flux balance analysis; FBR: Fed-batch bioreactor; G: The active Gene (DNA); GRC, GRN: Genetic regulatory circuits; GERM: Individual Gene expression regulatory module; GMO: Genetically modified micro-organisms; GP: The inactive complex of G with the transcription factor P (its encoding protein in the reduced model here); GRC, GRN: Genetic regulatory circuits (GRC), or networks; GS- Genetic switch; HSMDM: Hybrid structured modular dynamic (kinetic) models; L: Species at which regulatory element acts; M: mRNA; MCA: Metabolic control analysis; Met (MetG, MetP): Metabolites (lumped DNA and protein precursor metabolites, respectively); MINLP- Mixed-integer nonlinear programming; MSDKM: Deterministic modular structured cell kinetic model; MFA: Metabolic flux analysis; NLP: (non)linear programming problem [48]; nM: Nano-moles/L, nano-molar (i.e. 10-9 mol/L concentration); NG: Negligible; NSCT - the control theory of nonlinear systems; Nut (NutG, NutP): Nutrient (external nutrients imported to produce metabolites involved in the G and P synthesis respectively); ODE: Ordinary differential equations set; P: Protein; PTS: Phosphotransferase GLC import system; PPP: Pentose-phosphate pathway; SCR: Semi-continuous bioreactor; SNP: Single nucleotide polymorphisms; SUCC: Succinate; Re(x): Real part of ”x” variable; TF: Transcription factor; TCA: Citric acid cycle (or tricarboxylic acid cycle); TPFB: Three-phase fluidized bioreactor; TRP: Tryptophan; QSS: Quasi steady-state; WC: Whole cell; WCCV: Whole cell of constant volume hypothesis; WCVV: Whole cell of variable volume hypothesis; [.]: Concentration.
Introduction
This work is aiming to prove the feasibility and the advantages of using the classical and novel concepts and numerical tools of the chemical and biochemical engineering (CBE) to develop MSDKM of the extended cell-scale CCM-based (central carbon metabolism), and of genetic regulatory circuits (GRC) / networks (GRN). These extended kinetic models will be further linked to those of the bioreactor dynamic models (including macro-scale state variables), thus resulting hybrid structured modular dynamic (kinetic) models (HSMDM) proved to successfully solve more accurately difficult bioengineering problems.
In such HSMDM, the cell-scale model part (including nano-level state variables) is linked to the biological reactor macro-scale state variables for improving the both model prediction quality and its validity range. By contrast, the current (classical/default) approach in biochemical engineering and bioengineering practice for solving design, optimization and control problems based on the math models of industrial biological reactors is to use unstructured Monod (for cell culture reactor) or Michaelis-Menten (if only enzymatic reactions are retained) global kinetic models by ignoring detailed representations of metabolic cellular processes. The applied engineering rules to develop MSDKM and HSMDM dynamic math models presented in the 1-st and 2-nd parts of this work are similar to those used in the CBE, and in the control theory of nonlinear systems (NSCT).
This 1-st part of the paper presents some general concepts of CBE, of the NSCT, and of Bioinformatics used to derive MSDKM and HSMDM models, with continuous variables and based on cellular metabolic reaction mechanisms. Such extended structured cell math (kinetic) models consider, with a degree of detail suitable to the each approached case study, the cellular key-metabolic reactions and the cell key-species dynamics. These structured models can satisfactorily represent the key steps of the CCM at a cell scale, by also can include GRC-s responsible for the CCM syntheses regulation, besides reaction modules responsible for the synthesis of cellular metabolites of interest for the industrial biosynthesis. Special attention is paid to the conceptual and numerical rules used to construct various individual GERM-s kinetic models, but also various GRC-s (e.g. toggle-switch, amplitude filters, modified operons, etc.) modular kinetic models from linking individual GERM-s.
The 2-nd part of the paper will briefly reviews the ’whole-cell of variable-volume’ (WCVV) modelling framework introduced and promoted by the author in previous works. Also, this 2-nd part points-out the features of the deterministic WCVV models, and its advantages when simulating GERM-s, and GRC-s dynamics in living cells, by contrast to the classical (default) WCCV (whole-cell constant-volume modelling framework); P.I.-s of GERM-s; rules to link GERM-s when modelling GRC-s, and other related theoretical aspects necessary to construct MSDKM and HSMDM models.
The 3&4 parts of the paper proves, by means of several demonstrative relevant examples the superiority of using MSDKM and HSMDM dynamic math models when solving various bioengineering problems (i) to in-silico off-line optimize the operating policy of various types of bioreactors, and (ii) to in-silico design/check some GMO-s of industrial use able to improve the performances of several bioprocess/bioreactors.
By contrast, by considering only the macroscopic key-variables of the process (biomass, substrate, and product concentrations), the unstructured (apparent, global) math models do not adequately reflect the metabolic changes of the bioreactor biomass, being inadequate to accurately predict the cellular response to the medium disturbances through the self-regulated cellular metabolism. These classical global/ unstructured dynamic models may be satisfactory for an approximate modeling of the biological process, but not for modeling of cellular metabolic processes, and they can not make any correlation between the bioreactor operation and the continuous adaptation of the biomass metabolism to the variable conditions of the bioreactor. Even worst, as proved by the author in previous papers, such global models may lead to biased and distorted conclusions about the GERM’s performances, thus making difficult the modular constructions of GRC-s by linking individual GERM-s.
In the last decades, there has been a tendency to replace the complex processes of fine chemical synthesis, highly energy-consuming and generating large amounts of toxic waste, with biosynthesis processes (using isolated and purified enzymes, or cell cultures as bio-catalysts). The motivation is given by the multiple advantages offered by enzymatic processes (Figure 1): 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 significant number of enzymatic or biological industrial processes have been reported [1-4] in order to obtain chemical products/derivatives in the fine organic synthesis industry, in the pharmaceutical industry, in the food industry or in the detergent industry, by using various bioreactors with cell or enzyme cultures [1,4]. Among these new processes are the production of derivatives of monosaccharides, organic acids, alcohols, amino acids, etc., using mono- or multi-enzymatic reactors, or bioreactors with cell cultures used in the production of yeast, food additives, recombinant proteins (enzymes, vaccines), biopolymers [1,2,5]. 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 [6-8].
The current approach in biochemical engineering and bioengineering practice for solving design, optimization and control problems based on the math models of industrial biological reactors is to use unstructured Monod (for cell culture reactor) or Michaelis-Menten (if only enzymatic reactions are retained) by ignoring detailed representations of metabolic cellular processes. The engineering rules applied are similar to those used in the chemical and biochemical engineering (CBE), and in the control theory of nonlinear systems (NSCT). However, by considering only the macroscopic key-variables of the process (biomass, substrate, and product concentrations), these unstructured (apparent) math models do not adequately reflect the metabolic changes of the bioreactor biomass, being inadequate to accurately predict the cellular response to the medium disturbances through the self-regulated cellular metabolism. These global dynamic models may be satisfactory for an approximate modeling of the biological process, but not for modeling of cellular metabolic processes, and they casn not make any correlation between bioreactor operation and the continuous adaptation of biomass metabolism to the variable conditions of the bioreactor.
![Click here to view Large Figure 1](images/CTBEB.MS.ID.556080.G001.png)
The current trend to more accurately solve such engineering problems is to use deterministic modular structured cell kinetic models (MSDKM), with continuous variables, and based on cellular metabolic reaction mechanisms, that consider, with a degree of detail suitable to the each approached case study, the cellular metabolic reactions and the cell key-species dynamics. These structured models can satisfactorily represent the key steps of the central carbon metabolism (CCM) at a cell scale, by also including reaction modules responsible for the synthesis of cellular metabolites of interest for the industrial biosynthesis. As proved ny Maria [11-14,32], and Yang et al. [175], the modular structured kinetic models can reproduce the dynamics of complex metabolic syntheses inside living cells. This is why, the modular GRC and CCM dynamic models, of an adequate mathematical representation, seem to be the most comprehensive mean for a rational design of the regulatory GRC with desired behaviour [110]. 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, by means of complex "genetic regulatory circuits" (GRC-s), which include chains of individual „gene expression regulatory modules" (GERM-s).
In this context, this work shortly review the essential CBE principles and rules used to elaborate MSDKM, but also the so-called ’’Hybrid structured modular dynamic (kinetic) models” (HSMDM) [9,10] that combine the characteristics of the cellular metabolic process involving species participating to the essential reaction modules of CCM at a nano-scopic level, with the macro-scopic processes involving the state variables of the industrial bioreactor. In this way, more accurate predictions are obtained both for the dynamics of the biological process at the cellular level, and for the dynamics of the operating parameters of the analyzed industrial bioreactor. The immediate applications of these MSDKM and HSMDM refer to (i) the more precise determination of the optimal operating policy of an industrial bioreactor, and (ii) facilitates, by means of an in-silico numerical analysis, determination of GMO-s with a cell metabolism of desired characteristics.
In this first part of this work, the general concepts to construct MSDKM models with continuous variables are presented by using CBE and NSCT principles/concepts and rules. Special attention is paid to the conceptual and numerical rules used to build-up modular CCM kinetic models, in direct connection to various individual GERM-s kinetic models, but also to various GRC-s (e.g. toggle-switch, amplitude filters, operons expression, etc.) modular kinetic models by linking a couple of GERM-s. To do such a complex modelling work in a consistent way, this part also briefly reviews the novel „Whole cell variable cell volume” (WCVV) modelling framework introduced and promoted by [11-18], as an essential modelling instrument to develop more realistic and precise MSDKM-s and HSMDM-s. Besides presenting the WCVV deterministic model hypotheses, this paper points-out its advantages when simulating GERM-s, and GRC-s dynamics in living cells, in a holistic approach, by contrast to the classical (default) WCCV (whole-cell constant-volume modelling framework). The WCVV discussion is extended by briefly reviewing the P.I.-s of GERM-s; and the rules to link GERM-s when modelling/build-up GRC-s.
However, industrial bioprocesses still have a limited spread due to the high costs of enzyme/biomass isolation and stabilization on a suitable support, as well as its high sensitivity in relation to the operating conditions, the rather low reproducibility of the biological process due to biomass changes from one cell cycle to another, and of the difficult controllability of the bioreactor. However, many of these drawbacks can be overcome by an efficient immobilization of the biomass on suitable supports, by using suitable GMO-s with superior catalytic activity, and/or by optimizing the working conditions and the operation mode of the selected biological reactor, by using an advanced off-line in-silico analysis of the engineering part of bioprocess development based on effective math models and numerical algorithms. This last alternative is briefly reviewed in the 2-nd part of the paper.
As proved in the literature, the in-silico (math/kinetic model-based) numerical analysis of biochemical or biological processes by using MSDKM or HSMDM models are proved to be not only an essential but also an extremely beneficial tool for engineering evaluations aiming (i) to determine with a higher accuracy the optimal operating policies of complex multi-enzymatic reactors, [5,19-23], or of bioreactors including the biomass adaptation to the variable bioreactor environment over hundreds of cell cycles [2,9,24-26], or even (ii) to easier and quickly simulate and analyse the performances/ characteristics of various GMO-s alternatives, by using the “metabolic flux analysis” (MFA), [26-30], together with the gene-knock-out technique) [9,10,14,30-32].
Biochemical Reactor Case
To solve engineering problems for this case, the trend is to use complex multi-enzymatic systems which successfully replace complex chemical syntheses, by using milder reaction conditions, and generating less waste. Progresses in enzymes immobilization, and genetic engineering lead to prolonging the biocatalyst life and efficiency [169-171].
Even if the multi-enzymatic systems are advantageous, the engineering part used to optimize such a complex process is not an easy task because it must account for the interacting enzymatic reactions, enzymes deactivation kinetics (if significant), multiple and often opposed optimization objectives, technological constraints, and uncertainties coming from multiple sources (model / constraints inaccuracies, disturbances in the control variables), and a highly nonlinear process dynamics [2,19,20,22-24,33-35]. All these parametric/model/data uncertainties require updating (with a certain frequency) the enzymatic process model, the optimal operating policies of the reactor being determined by using rather deterministic (model-based) optimization rules [36]. Multi-objective criteria, including economic benefits, operating and materials costs, product quality, etc., are used to off-line, or to on-line derive feasible optimal operating/control policies for various bioreactor types [34] by using specific numerical algorithms [20,22,23,25,32,35,37-39].
Biological reactor case
In thw last decades, the trend is to use biological processes conducted in complex biological reactors to successfully replace complex chemical syntheses, by using milder reaction conditions, and generating less waste. Progresses in biomass immobilization, and genetic engineering lead to prolonging the biocatalyst life and efficiency [172].
To solve engineering problems for this case, development of extended cell-scale CCM / GRC-s structured MSDKM or HSMDM kinetic models on a deterministic basis to adequately simulate in detail the cell metabolism self-regulation, cell growth, and its replication for such an astronomical cell metabolism complexity is practically impossible due to the lack of structured and comprehensive experimental information, and computational limitations. A review of some trials are reviewed by [40,11,12,14,32]. That is because the cell metabolism is highly sophisticated, involving O(103-4) components, O(103-4) transcription factors (TF-s), activators, inhibitors, and at least one order of magnitude higher number of (bio)chemical reactions, all ensuring a fast adaptation of the cell metabolism to the changing environment through complex genetic regulatory circuits (GRC-s), that includes individual or chains of „gene expression regulatory modules of reactions” (GERM-s), genetic switches (GS), operon expression, etc. [11,12,14,32]. The cell is highly responsive to the environmental stimuli and highly evolvable by self-changing its genome/proteome and metabolism, that is the stoichiometry and the reaction rates (fluxes) of the enzymatic reactions to get an optimized and balanced growth by using minimum resources (nutrients/substrates).
In spite of such tremendous modelling difficulties, the development of structured reduced deterministic (rather than stochastic) MSDKM or HSMDM models on a deterministic basis reported significant progresses over the last decades [10,11,12,14,32,31,41-43]. Such reduced cell models are able to adequately reproduce the dynamics of some CCM complex metabolic syntheses [10,31,32,40,44,45,46,47], but also the dynamics of some GRC-s [9,11,12,14,32,] tightly controlling the metabolic processes. Even if they are rather based on sparse information from various sources, unconventional statistical identification, and lumping algorithms [11,12,14,32,15,16,48,49], such structured reduced deterministic kinetic models have been proved to be extremely useful for in-silico (a) analyse and characterize the cell CCM, (b) for designing novel GRC-s conferring new properties/functions to the mutant cells, or (c) for engineering bioreactor evaluations [10,24,11,12,14,32, 50] (see the part 2 of this paper).
The current (default) approach to solve the model-based design, optimization and control problems of industrial biological reactors is the use of unstructured models of Monod type (for cell culture reactors)[3] or of Michaelis-Menten type (if only enzymatic reactions are retained)[21,22,23,35,51,52] that ignores detailed representations of cell processes. The applied engineering rules are similar to those used by the CBE and inspired from the NSCT [25,34,53,54-60].
However, by accounting for only key process variables (biomass, substrate and product concentrations), these global (unstructured) dynamic models do not properly reflect the metabolic changes, being unsuitable to accurately predict the cell response to environmental perturbations by means of (self-)regulated cell metabolism [9,61,11,12,14,32].
The alternative is to use structured kinetic models, by accounting for cell metabolic reactions and component dynamics. Such deterministic models lead to a considerable improvement in the predictive power, with the expense of incorporating a larger number of species mass balances including parameters (rate constants) difficult to be estimated from often incomplete data (by using complex NLP, MINLP, and statistical procedures [48,168,32,49,15,16]), and, consequently, difficult to be used for industrial scale purposes [9,10,15,16,32,62,].
As a result, an impressive large number of valuable structured deterministic kinetic models (based on a mechanistic description of the metabolic enzymatic reactions tacking place among individual or lumped species of the cell) have been proposed in the literature to simulate the cell CCM dynamics, with including tenths-to-hundreds of key species. Here, it is worth mentioning the E. coli model of [63] used by [31,44,64,65,66,67,68] for various purposes, or the S. cerevisiae glycolysis model of [69], or the JWS platform of [70], or the MPS platform of [71] to simulate cell metabolism (dynamics and/or stationary fluxes), to mention only few of them. Simulation platforms, such as E-cell of [72,73], or V-cell of [74], accounting for thousands of species and reactions, display extended capabilities to predict the dynamics of the cell metabolism under various conditions, based on EcoCyc, KEGG, Prodoric, Brenda and other bio–omics databanks (review of [14]). A worthwhile CCM-based dynamic or stationary models were reported by Maria [10,31,44] based on a lumped reaction pathway schematically represented in (Figure 2).
Some of structured deterministic CCM kinetic models have been reviewed by [11,12,14,32]. Deterministic MSDKM kinetic models using continuous variables has been developed by Maria [44] for the glycolysis, and by [64,65,75,76,77,78] for the CCM in bacteria of industrial interest. Such MSDKM models can adequately reproduce the cell response to continuous perturbations. The MSDKM cell model structure and size is adapted based on the available bio–omics databanks, and experimental information. Even if such extended structured models are currently used only for research purposes, being difficult to be identified, it is a question of time until they will be adapted in the form of HSMDM–s for industrial / engineering purposes. As proved by this work, and by several examples given in the part 2 of this paper, already significant progresses have been reported in this respect.
The Parts 1 and 2 of this work presents a holistic ‘closed loop’ approach for the development of models of biological systems [79]. 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 organise and utilise these data. The resulted HSMDM–s were proved to successfully solving more accurately difficult bioengineering problems. In such HSMDM-s, the cell-scale model part (that is the nano-level state variables) is linked to the biological reactor macro-scale state variables for improving the both model prediction quality and its validity range. The case studies presented and discussed in the parts 3&4 of this work prove this engineering aspect.
In fact, the use of HSMDM hybrid models realizes a valuable combination of the process modelling-scales, by linking unstructured with structured process characteristics to generate more precise predictions (see the examples given by [9,10,24]). Basically, the HSMDM 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 cell syntheses of practical interest (usually resulting in excretable valuable metabolites).
![Click here to view Large Figure 2](images/CTBEB.MS.ID.556080.G002.png)
In fact, such a HSMDM (hybrid structured cell dynamic model) must include only the pathway responsible for the target metabolite synthesis, linked to the essential parts of the CCM, that is the lumped modules of the cell core. These CCM core modules include, among others, the glycolysis, the glucose (GLC) uptake system [i.e. the phosphotransferase (PTS), or an equivalent system], the “adenosine triphosphate” (ATP)-recovery system (i.e. the ATP-use-recovery cycle), TCA (tricarboxylic acid, or citric acid cycle), PPP (Pentose-phosphate pathway). Of course, additional CCM reaction pathways modules must be added to the structured cell model (in a detailed or reduced/lumped form) if their presence is absolutely necessary to derive consistent CCM simulations. See for instance the discussion of [10,24,31,32,44,46,61,80].
A special interest was given to the accurate modelling of the glycolysis dynamics and its self-regulation [44,61,81-83] as long as this core-module of the CCM includes intermediates which are starting nodes for the internal production of lot of cell metabolites (e.g. succinate (SUCC), citrate (CIT), amino-acids like cysteine, lysine, phenyl-alanine, tryptophan (TRP), etc., see Figure 3) [2,31,47,83]. This need to have good quality structured cell models to simulate the dynamics of the bacteria CCM (and its regulation via cell GRC-s/GRN-s) became a subject of very high interest over the last decades, allowing an in-silico design of GMO-s with desirable characteristics of various applications in the biosynthesis industry, civil engineering, medicine, and other fields [11,12,14,32].
![Click here to view Large Figure 3](images/CTBEB.MS.ID.556080.G003.png)
MSDKM and HSMDM models advantages
Even if such complex / extended dynamic model requires more experimental and computational efforts to be built-up, as proved by the approached case studies in the parts 3&4 of this work, the resulted deterministic modular structured cell kinetic model (MSDKM) of the key-parts of cell CCM and GRC-s (of interest), as well as the hybrid (bi-level, that is the cell-species state variables, linked to the macro-level bioreactor state variables) dynamic models (HSMDM) present a large number of advantages compared to 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 metabolic processes. Thus, among the multiple advantages of HSMDM models are to be mentioned the following most relevant ones:
(i).- A higher prediction detailing degree. Thus,
(i-a). For the case study referring to the HSMDM used to design and simulate the GRC responsible for mercury (mer) operon expression in the wild or GMO design E. coli cell (see the part 4 of this work), a higher prediction detailing degree is reported, that is predicted dynamics of [26(cell species) + 3(bulk species)] vs. only [3 (bulk species)] by a classical macroscopic SCR- TPFB unstructured (global) dynamic model, while covering a wider range of input [Hg2+] loads, with also using cloned E. coli cells with various amounts of mer-plasmids [Gmer]. Here SCR denotes a semi-continuous bioreactor, that is a CSTR (continuous stirred tank reactor) of variable feeding, of TPFB (three-phase fluidized bioreactor) constructive type [9,173].
(i-b). For the case study referring to the HSMDM used to simulate the dynamics of the species at cell-level, and bulk-phase level in a fed-batch bioreactor (FBR), but also to maximize the tryptophan (TRP) production (see the part 3 of this work), a higher prediction detailing degree is reported, by characterizing the dynamics of [11(cell species) + 4(bulk species)] vs. only [3 (bulk species)] by a classical macroscopic FBR global model, while covering a wider range of control variables, and allowing the design/check of various GMO E. coli cells strains.
(ii).- Prediction of the inner cell key-species reaction rates (different from the apparent rates of the substrates and excreted products observed in the bioreactor). See the above case study (i-a) of [9,84,85], and the case study (i-b) of [10,24].
(iii).- The structured [cell-and-bioreactor] hybrid model predictions can cover a wider range of input/control variables of the bioreactor. Thus, for the above case study (i-a), the HSMDM of Maria and Luta [9] realizes a higher prediction detailing degree, that is simulated dynamics of [26(cell species) + 3(bulk species)] vs. the dynamics of only [3 (bulk) state variable] predicted by a classical macroscopic SCR- TPFB model. Such a an advanced HSMDM predictions can cover a wider range of input [Hg2+] loads (0–100 mg/L), and can be used to design cloned E. coli cells with various amounts of mer-plasmids [Gmer] in a wider feasible range of (3–140 nM).
(iv).- The HSMDM model can predict the bacteria metabolism adaptation to environmental changes over dozens of cell cycles, and the effect of cloning wild E. coli cells to obtain (GMO) with modified characteristics/properties/behaviour under stationary or perturbed bioreactor operating conditions. See the case study (i-a) for details (Part-4).
(v).- The extended HSMDM can offer predictions of a higher accuracy when they are used to in-silico (model-based) engineering developments (bioreactor design, or its off-line optimization) compared to unstructured/global models (see the parts 3&4 of this work, for several bioreactor cases). For instance, (i-b) the HSMDM could better predict the optimal time stepwise feeding policy of a fed-batch reactor (FBR) to increase the tryptophan (TRP) production (Part 3) [10,24]. In the above case study (i-a), the extended HSMDM allows optimizing the operating policy of a SCR-TPFB regarding the biomass concentration, the inlet feed flow-rate, the inlet [Hg2+], the immobilized biomass support size, and the [Gmer] concentration in the used cloned E. coli cells [Maria and Luta, 2013; Maria et al., 2013].
(vi).- A similar procedure of using hybrid dynamic models can be applied to optimize the multi-enzymatic systems, by linking several interacting complex enzymatic reactions to the reactor state-variables. For instance, in a bi-enzymatic reactor case, [21,22,23,35,86] used a HSMDM to derive optimal operating policies of a batch reactor (BR), a series of BR-s of equal size but of different (adjustable) initial load (SeqBR), or of a FBR by accounting for multiple competing optimization objectives.
(vii).- Complex HSMDM-s can also be used for bioinformatics studies, by evaluating the influence of the bioreactor operating conditions (that is the control macro-variables) on the dynamics of cell nano-scale key-intermediates and fluxes involved in the synthesis of the metabolite of interest. For instance, in the above case study (i-b) , the HSMDM including the reaction modules of glycolysis, ATP-recovery system, TRP-operon expression, and biomass [X] production allows a quick evaluation of the E.coli cell metabolic fluxes (related to the metabolic engineering topics of [27] ), thus directing the design of GMO cells with desirable properties (‘motifs’) [10,24].
(viii).- Extended HSMDM can successfully be used to obtain lumped dynamic models of the bioreactor useful for rapid engineering calculations, by employing specific model reduction rules and additional kinetic data valid in the local operating domains (in the control variable space). Specific kinetic model consistent reduction rules are given by [48,49,87] for nonlinear models, or [88,89] for linear models cases. As a result of such an approach, the bioprocess complexity may be described by a succession of local reduced models enfolded on the real process. The locally reduced models include only the key metabolic pathways to obtain the relevant process state predictions (of interest).
(ix).- As a corollary to the issue (vii), The structured HSMDM [cell-and-bioreactor] models are also useful for understanding the cellular bioprocess in direct connection to the bioreactor operating mode. For instance, in the above case study (i-b), such an extended cell model can in-silico determine the conditions of occurrence of oscillations for the cell glycolysis [44,47,80,81,83], or oscillations in the TRP-operon expression [47,61,], or those leading to a balanced cell growth (quasi-steady-state QSS, conditions, i.e. the cell homeostasis) [80]. As another example, in the above case study (i-a), the extended HSMDM can predict the mer-enzymes expression levels and the cytosolic mercury reduction rate depending on the mer-plasmids level [Gmer] in the cloned E. coli cells.
(x).- Some other case studies supporting the use of complex HSMDM are mentioned in the parts 3&4 of this work for various purposes. For instance,(a) to in-silico design GMO E. coli strains for maximizing the production of both succinate (SUCC) and of biomass in a batch reactor (BR) by using the gene-knockout and the Pareto front techniques [31]; (b) to off-line optimize the operating policy of a FBR to maximize the monoclonal antibodies (mAbs) production [2,90], etc.
Application of CBE and NSCT concepts/principles and rules to construct HSMDM dynamic models
Basically, by reviewing the rules to construct MSDKM and HSMDM models, and their applications, this work is aiming to prove the feasibility and the advantages of using the classical and novel concepts and numerical tools of the chemical and biochemical engineering (CBE), and of the control theory of nonlinear systems (NSCT) to develop extended cell dynamic math models with including the key-reaction modules of the cell CCM, and of GRC-s involved in the regulation of the metabolites’ syntheses of practical interest.
While the 1-st part of this work is aiming at reviewing the general CBE concepts used for such an approach, the 2-nd part of the work will briefly reviews the ’whole-cell of variable-volume’ (WCVV) modelling framework introduced and promoted by the author in previous works, inspired by the CBE applied rules in the case of nonlinear reacting systems of variable volume. Also, this 2-nd part reviews and points-out the features of the deterministic WCVV models, and its advantages when simulating GERM-s, and GRC-s dynamics in living cells, by contrast to the classical (default) WCCV (whole-cell constant-volume modelling framework). The same review includes a short description of the regulatory performance indices (P.I.-s) of GERM-s (inspired from the NSCT), and also rules to link GERM-s when modelling GRC-s, as well as other related theoretical aspects necessary to construct MSDKM and HSMDM models. Special attention is paid to the conceptual and numerical rules used to construct various individual GERM-s kinetic models, but also various GRC-s (e.g. toggle-switch, amplitude filters, operon expression, etc.).
To apply the CBE and NSCT principles and rules, as documented by [11,12,14,32], to overcome the cell process dynamics complexity, the metabolic pathway representation with continuous and/or stochastic individual or lumped reactions/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 utilisation scope.
![Click here to view Large Figure 4](images/CTBEB.MS.ID.556080.G004.png)
The main advantages of deterministic / continuous variable kinetic models are coming from the use of experience, concepts, math representation, rules, and algorithms of the CBE (Figure 4 and Figure 5) [11,12,14,32, 46,48,13]. The reaction rate expressions in the deterministic models of continuous variables are the usual ones of CBE that is of (extended) Michaelis-Menten, or Hill type (see Figure 6). Based on these CBE principles and rules, a large number of CCM kinetic models have been reported in the literature, such as those of [26,44,64,65,91]. A short discussion is given by [10,44]. Such a CCM-based kinetic model (Figure 2) was used by [10,24] to optimize an experimental pilot-scale FBR. In fact, the glycolysis together with the phosphotransferase (PTS)-system, or an equivalent one for GLC(glucose)-uptake, and with the pentose-phosphate pathway (PPP), and with the tricarboxylic acid cycle (TCA), all these are part of the so-called “central carbon metabolism” (CCM)(Figure 2 and Figure 3) [31].
Even if complicated and, often over-parameterized, the continuous variable dynamic deterministic ODE models (eq. 1A-B, eq. 3A-B, eq. 4A-B, eq.5-6, eq. 8 from Part-2) 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 [40,43]. 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 [92], 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 (BCE) modelling concepts summarized in (Figure 4 and Figure 5). The most important ones are the followings [11,12,14,32, 46,13,82]:
C1. Fulfillment of the molecular, and elementary species (atoms types) conservation law (species differential mass balance set) [12,14,32].
C2. Fulfillment of the atomic species conservation law ( atomic species mass balance).
C3. The thermodynamic analysis of reactions (that is quantitative assignment of reaction directionality) [93]
C4. Set equilibrium reactions by using Gibbs free energy balance analysis; set cyclic reactions; find species at quasi-steady-state to replace its differential mass balance with an algebraic equation [94]
C5. Extended HSMDM–s allow improved evaluation of steady-state flux distributions (i.e. stationary metabolic reaction rates) that provide important information for metabolic engineering [94,14,32].
C6. Allow application of ODE model species and/or reaction lumping rules [48,49].
![Click here to view Large Figure 5](images/CTBEB.MS.ID.556080.G005.png)
When developing deterministic models for the CCM, or for other cell metabolic processes of a micro-organism, to be further used for GMO design, an important aspect is to also include math (kinetic) models of individual GERM-s characterizing the gene expression control of the enzymes production. Also, by linking the interfering GERM modules, complex GRC regulatory chains can thus be obtained [11,12,14,32,95]. Such GRC-s refers to genetic switches (Figure 7), or operon expression (Figure 8), genetic amplifiers, etc. [11,12,14,32, 43,96,97,98,99].
![Click here to view Large Figure 6](images/CTBEB.MS.ID.556080.G006.png)
Development of ODE dynamic models to adequately reproduce such complex synthesis related to the CCM [26,64,91], but also to the GRC-s tightly controlling such metabolic processes reported significant progresses over the last decades in spite of the lack of structured experimental kinetic information, being rather based on sparse information from various sources and unconventional identification / lumping algorithms [11,12,14,32, 43,48,49,100]. However, such structured models are extremely useful for in-silico design of novel GRC-s conferring new properties/functions to the mutant cells, in response to external stimuli. This emergent field belongs to the Synthetic Biology (see below) [31,101-112]. This topics belongs to the so-called ’computational systems biology’, or simply ’bioinformatics’. In fact, the two emergent research/applicative fields are closely inter-connected, as depicted in (Figure 9), and strongly related to the CBE, NSCT, and Systems Biology principles and rules.
Systems Biology
Systems Biology is defined as “the science of discovering, modelling, understanding and ultimately engineering at the molecular level the dynamic relationships between the biological molecules that define living organisms” (Leroy Hood, Head Inst. Systems Biology, Seattle, USA). Systems Biology is one of the modern tools, which uses advanced mathematical simulation models for in-silico design of GMOs that possess specific and desired functions and characteristics. The works of [11,12,14,32, 43,48] presented short reviews about Systems Biology , by including a short history, their modern concepts, and their principles, and math/numerical-experimental tools and modelling rules, derived from those of the CBE and NSCT to construct deterministic models used by the Systems Biology to numerically simulate the dynamics of cellular metabolic processes. This involves application of the classical CBE modelling techniques (mass balance, thermodynamic principles, see the above (C1-C6) principles), and algorithmic rules, and also the NSCT principles/rules (see in the part 2 of this work, the definitions of the P.I.-s used to characterize the individual GERM–s and GRC–s self-regulatory efficiency inside the cell), and of the bioinformatics rules, briefly presented in (Figure 4, and Figure 5), and in the above (C1-C6) principles. The main principles, concepts, and rules of the CBE are also shortly reviewed by [113-117]. The metabolic pathway representation with continuous and/or stochastic variables remains the most adequate and preferred representation of the cell processes, the adaptable-size and structure of the lumped model depending on available information and the utilisation scope [11,12,14,32, 43,48,49].
![Click here to view Large Figure 7](images/CTBEB.MS.ID.556080.G007.png)
The in-silico re-design of the cell metabolism is an up-to-date subject in Synthetic Biology. But in this effort, Synthetic Biology is closely assisted by the Systems Biology focus on the cell organization, the former being one of the main tools in the in-silico design of genetically modified micro-organisms (GMO) with desired characteristics, and with applications in medicine, such as therapy of diseases (gene therapy), production of new devices based on cell-cell communicators, biosensors, production of vaccines, etc. The Systems Biology also aims at understanding the dynamic interaction between components of a living system or between living systems. (http://www.erasysbio.net/). To realize these ambitious objectives, Systems Biology uses a wide range of tools, but mainly complex mathematical simulation models and numerical rules imported from the CBE, NSCT , and Bioinformatics linked to the bio–omics databanks (see below).
When developing extended structured HSMDM models, besides CBE, NSCT, and Systems Biology principles and rules (Figure 4, Figure 5, Figure 9), the Bioinformatics concepts and rules play an essential role because they make the connection with t he bio-omics databanks [see the below databanks and cell simulation platforms (a-e) ], from which the most important information refers to the genome map and its correspondence to the proteome map for a certain micro-organism.
The main objective of the ’computational systems biology’ is to model the kinetics of entire living cells at the molecular level on a mechanistic base. Given the enormous complexity and unknown aspects of such systems, formulating reliable models with predictive ability remains only a dream. However, advances in genomics, transcriptomics, proteomics, metabolomics, and in the computing power provide hope that this objective might be realized within next couple of decades. Bioinformatic databases and software platforms are being constructed for modeling entire cells with massive amounts of data [72,73,103,118]. For example:
![Click here to view Large Figure 8](images/CTBEB.MS.ID.556080.G008.png)
![Click here to view Large Figure 9](images/CTBEB.MS.ID.556080.G009.png)
![Click here to view Large Figure 10](images/CTBEB.MS.ID.556080.G0010.png)
a) E-Cell software allows simulating reaction pathways within compartment-based cells using the continuous-differential modeling approach [72,73,119,120] (Figure 11-left). The computing platform objects are the followings: [compartments, compounds, genes, reactions)]. The E-cell cell simulation platform [72,73] has been used in conjunction with the EcoCyc [121], and KEGG [122,123] databases to simulate the dynamics of 127 genes/protein found in genitalium.
b) V-Cell [124,125]. The computing platform objects are the followings: [model and geometry attached to each application, and the biological interface (real images taken with the Electron Microscope)].
c) CellML, JWS (Silicon-cell) [70,126-129] is a cell modelling and simulation framework (Figure 11-right) with compartments and membranes, each of which may include species, reactions and membrane fluxes.
d) M-Cell simulation platform of [130] (Figure 12-left) allows simulating high-level complex cell sub-systems, such as beural communication networks, together with proteins and enzymes involved in exo-/endo-cytosis, synaptic transmission, transport and signal reception. The M-Cell simulator includes simulation of Brownian random walk, and Monte Carlo stochastic algorithms for modeling small numbers of diffusing ligands interacting with individual 3D binding sites in spatially complex environments.
The e) A-Cell platform [131,132] (Figure 12-right; Figure 13) uses (‚electrical circuit‘ like models) to simulate biochemical reaction schemes, neurons connections, and pathways. For other bio-modelling software packages the reader is referred to the reviews of [118,131,132,133].
![Click here to view Large Figure 11](images/CTBEB.MS.ID.556080.G0011.png)
![Click here to view Large Figure 12](images/CTBEB.MS.ID.556080.G0012.png)
![Click here to view Large Figure 13](images/CTBEB.MS.ID.556080.G0013.png)
![Click here to view Large Figure 14](images/CTBEB.MS.ID.556080.G0014.png)
To easier realize the numerical simulations of such complex cell math models, specific programming languages (SBML, [118,133]), or on-line simulation platforms (JWS, [70,126]) have been developed. By using such modern computing tools, simulation of various biological systems was possible, such as [11,12,14,32, 13,43,46,134]:
• Single cell growth (e.g. Escherichia coli, Haemophilus influenzae, Mycoplasma genitalium, yeast, etc.
• Model metabolic oscillations (red-blood-cell synthesis, glycolysis, TCA (tricarboxylic acid cycle) cycle, oxidative phosphorylation, key species oscillations, etc.) [44,61,47,80,81,83,104,135]. Conditions for oscillations occurrence for various cell processes are given by [44,47,61,81,175].
• Metabolic control of protein synthesis regulation (GERM-s, GRC-s) [11,12,14,32, 43,134, 136-140].
• Modelling the central carbon metabolism (CCM) [45,64,91]. Dynamic models of some CCM-core modules and applications are given by [10,26,31,44,61] (Figure 2, Figure 3, Figure 11-left).
• FBA (flux balance analysis of the cell metabolism) used to design of GMO-s [95] (Figure 14). Metabolic fluxes (v(j)) are defined as the enzymatic reaction rates at the quasi-stationary-cell-conditions (QSS), that is at the cell balanced growth (homeostasis). Determination of metabolic fluxes (by using the metabolic engineering tools [27], or the dynamic HSMDM models) allowed to in-silico derive GMO-s of desired characteristics by using the so-called “gene knock-out” technique [174]. By removing a certain enzyme (and its attached encoding gene), the catalyzed reaction is also removed from the CCM. Similarly, the target reaction (flux) can be amplified / diminished by increasing / decreasing the corresponding enzyme (biocatalyst) concentration, and, correspondingly by increasing / decreasing the encoding gene plasmid concentration in the analyzed micro-organism genome. In other words, FBA, and of the metabolic engineering are the essential preliminary steps in design GMO-s. [237].
• Modelling the cell cycle [141,142].
• Modelling the drug release and cell-drug interactions [143,144].
• Modelling cellular communications, neuronal transmission
• Analysis of ‘logical essence’ of life (life minimal requirements)
At the same time, the exponential-like increase of the experimental biological information lead to development of valuable bio-omics databanks, such as those described by [11,12,14,32]:
-.- KEGG [122,123];
-.- JWS [70,126];
-.- EcoCyc [121];
-.- Roche [145], etc.
However, it is only over the last decades when Systems Biology reported notable successes due to a considerable increase in computing power of the modern computers. It is to mention here, for instance, the cell simulator platforms, and online model repository JWS of [70,126], or those developed by Rocha et al. [42], or by Tomita et al. [72,73], together with continuous expansion of the above referred bio-omics databases JWS, KEGG, EcoCyc, Roche, etc., and reported advances in the numerical algorithms used by bioinformatics, CBE, and NSCT [11,12,14,32].
Due to such favourable premises, related to the expansion of bio-omics databanks, and cell metabolism (CCM, GRC-s) dynamic models, novel works have been reported over the last decades. Among the milestone works in Systems Biology it is to mention the contributions in modelling / design of GRC-s, GERM-s, FBA, MCA of [11,12,14,32, 92,146-149]. The number of published papers in the Systems Biology area increases with two orders of magnitude from 2000 to 2007, and it is still exponentially increasing, most of them was being founded by programs of the European Science Foundation.
As stated by [150,151], tremendous applications of Systems Biology have been reported over the next decades in the below areas (see also [11,12,14,32]) (Table 1):
![Click here to view Large Table 1](images/CTBEB.MS.ID.556080.T001.png)
Bioinformatics
According to [152], the bioinformatics is an inter-disciplinary field that develops methods and software tools for understanding and interpret the biological data, in particular when the data sets are large and complex. As an interdisciplinary field of science, the bioinformatics combines several classic/modern disciplines, such as: biology, chemistry, physics, computer science, information engineering, mathematics, and statistics to analyze and interpret the biological data. Bioinformatics has been used rather for in-silico analyses of biological queries using a large number of computational and statistical techniques, aiming to design novel GMO-s of practical (industrial) use [41,153-162]. The most important rule of the Bioinformatics refers to the rapid, and computer-assisted genome sequentiation [152]. Some of the common rules used by the bioinformatics are given in (Figure 10) [152].
![Click here to view Large Figure 15](images/CTBEB.MS.ID.556080.G0015.png)
Thus, Bioinformatics includes biological studies that use computer programming as part of their methodology/rules, as well as specific analysis ‘pipelines’ that are repeatedly used, particularly in the field of genomics. Common uses of bioinformatics include identification of candidates genes and “single nucleotide polymorphisms” (SNP-s). Often, such identification is made with the aim to better understand the genetic basis of disease, unique adaptations, desirable properties (esp. in agricultural species), or differences between populations. In a less formal way, bioinformatics also tries to understand the organizational principles within nucleic acid and protein sequences, called proteomics [152].
And, “in a context of increasing calls for biology to be predictive, modelling and optimization tools of Bioinformatics (most of them imported from CBE, and NSCT ) are the only approaches biology has for making satisfactory predictions” [163]. Due to the computing facilities offered by the algorithmic rules developed by the (bio)chemical engineering and nonlinear systems biology rules (Figure 4, Figure 5, Figure 6, Figure 15), the developed cell math models use a vectorial-matriceal approach (Figure 16), with a continuous model upgrading based on dynamic experimental data recorded in a chemostat (i.e. a continuously operated bioreactor), operated under steady-state, or in a dynamic regime following an input perturbation in the substrate/enzymes/biomass concentration in the solution fed in the bioreactor [64,95].
![Click here to view Large Figure 16](images/CTBEB.MS.ID.556080.G0016.png)
Given these developments, as well as the seemingly inexorable advances in computing power, it is tempting to believe that reliable whole-cell models (WC) with predictive power will be forthcoming once complete sets of ’bio-omic’ information become available. However, a better theoretical understanding of cellular life, viewed holistically, may be required before we can understand how life emerges out of complex networks of molecular-level interactions between cellular components. This study represents a foyer into whole-cell kinetic modelling, in an attempt to understand holistic aspects of cell-system from a quantitative computational perspective.
Related to the WC math modelling aspect, a concerned section in the Part-2 of this work is aiming at examining some fundamental properties of living cells relevant to WC holistic math-modelling. Thus, a methodology to build-up regulatory kinetic schemes in a ’whole cell variable cell volume’ (WCVV) modelling framework, but also under stationary/perturbed environmental conditions was proposed, developed, and promoted by Maria [11,12,14,32, 17,18,43,99,100] for a generic protein/gene (P/G) pair synthesis process, its GERM regulatory module, but also for cell GRC-s, and for the whole CCM dynamic model construction. The model elements of novelty consist in accounting variable cell-volume, and constant osmotic pressure conditions. Thus, most of the drawbacks of classical (default) continuous-concentration simulators (developed for a constant volume system, WCCV) are removed. Exemplification is made for several relatively simple GRC-s from literature [11,12,14,32, 43,99,100]. The chosen examples analyse the impact of the proposed WCVV modelling approach on the MSDKM model prediction better quality, such as: (a) a more realistic prediction of regulatory scheme sensitivity to both stationary and dynamic perturbed conditions; (b) better pointed-out the cell species interconnectivity (direct, or indirect through the cell volume to which all species contributes); (c) the effect of the so-called “cell-ballast” on the cell-behaviour vs. various type of perturbations; (d) a more realistic way to design interconnected GERM-s and rules to link them in GRC-s in a common volume growing environment. Other analysis aspects, not developed in this paper, but exemplified in the Part 2 and 3&4 of this work, can be easily approached under the presented WCVV modelling hypotheses (Part 2), such as the cell system state multiplicity, and characterization of their oscillatory phenomena.
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