Prof Dr Gheorghe Maria Juniper Publishers-PDF Free Download

Prof Dr Gheorghe Maria Juniper Publishers

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Prof. Dr. Gheorghe Maria I Deterministic Modelling Approach of Metabolic Processes in Living Cells - A Still Powerful Tool for Representing the Metabolic Processes Dynamics. Contents Acknowledgment I Abstract 01 Keywords 01 Abbreviations 01 Introduction 02 The structural hierarchy 02 The functional hierarchy 02 The time hierarchy 02 An emergent border field: Systems Biology 03 (Bio)chemical ...



Deterministic Modelling Approach of Metabolic Processes in
Living Cells A Still Powerful Tool for Representing the Metabolic
Processes Dynamics
Prof Dr Gheorghe Maria
Department of Chemical Biochemical Engineering University Politehnica of
Bucharest UPB
Published By
Juniper publishers Inc
United States
Date June 14 2017
Deterministic Modelling Approach of Metabolic Processes in Living Cells A Still
Powerful Tool for Representing the Metabolic Processes Dynamics
Acknowledgement
Author is grateful to Prof Dr Stefan Szedlacsek from the Department of Enzymology of the Institute of Biochemistry of the
Romanian Academy Bucharest for the very constructive suggestions and discussions I am also grateful to the late Prof Wolf
Dieter Deckwer from GBF Gesellschaft f r Biotechnologische Forschung mbH Biochemical Engineering Division Braunschweig
Germany for funding my summer research stay on 2006 Many thanks are also addressed to Prof Jibin Sun from the Tianjin
Institute of Industrial Biotechnology China for funding my summer research stay on 2010 in Tianjin Many thanks are also
addressed to Prof An Ping Zeng from TU Hamburg Institute of Bioprocess and Biosystems Engineering Germany for hosting
my summer DAAD fellow on 2009 Finally I want to address many thanks to my PhD students Diana Ene Ionela Lu a Mara Cri an
and Andreea coban all being co authors of some of my works in the bioengineering area
Prof Dr Gheorghe Maria
Deterministic Modelling Approach of Metabolic Processes in Living Cells A Still
Powerful Tool for Representing the Metabolic Processes Dynamics
Acknowledgment I
Abstract 01
Keywords 01
Abbreviations 01
Introduction 02
The structural hierarchy 02
The functional hierarchy 02
The time hierarchy 02
An emergent border field Systems Biology 03
Bio chemical engineering deterministic approach rules advantages and limitations 06
Mathematical modeling in molecular biology using Bio Chemical Engineering tools 08
Modular modelling of genetic regulatory circuits 10
Some examples of modular deterministic dynamic models 13
A whole cell model to simulate mercuric ion reduction by E coli under stationary or
perturbed conditions 14
In silico design of a genetic modified E coli cell to concomitantly maximize the production
of biomass and succinate 14
In silico study of glycolytic oscillations occurrence in E coli cell by using a reduced modular
deterministic model 15
Conclusions 17
Deterministic Modelling Approach of Metabolic Processes in Living Cells A Still
Powerful Tool for Representing the Metabolic Processes Dynamics
List of Figures
Figure 1 The hierarchical organization of living cells 02
Figure 2 KEGG 34 result the central carbon metabolic fluxes metabolic pathway map
of Mycobacterium smegmatis MC2155 after 2 03
Figure 3 On 2000 the human genome has been deciphered 04
Figure 4 Quoted from the obituary of R Heinrich 3 05
Figure 5 Systems Biology publications and EU programs after 2000 05
Figure 6 Boolean topological representation of GRC 50 07
Figure 7 An electronic circuit like representation of a GRC A human cancer cell pathway
from http www bio itworld com archive 111202 virtual html 07
Figure 8 The variable cell volume whole cell VVWC dynamic modelling framework and
its basic hypotheses 1 8 10
Figure 9 The cover of the ebook of Maria 1 https juniperpublishers com ebook info php 10
Figure 10 Simplified representations of a regulatory module GERM for a generic gene G
expression up left down right with perfectly coupled enzyme regulator P expression
Down right is a GERM of G P 1 type Such GERM models are further used to construct
various GRC models Notations In inducer AA aminoacids horizontal arrows indicate
reactions vertical arrows indicate catalytic actions G gene encoding protein P
M mRNA R R transcriptional factors repressors MetG DNA precursor metabolites
The enzyme protein P interacts with the inducer In for controlling the transcription
rate by means of feedback positive or negative regulatory loops 1 11
Figure 11 Various types of GERM regulatory modules for protein synthesis 1 Horizontal
arrows indicate reactions vertical arrows indicate catalytic actions absence of a substrate or
product indicates an assumed concentration invariance of these species 12
Figure 12 The whole cell model of Maria 68 70 in the VVWC approach used to simulate the
reduction of Hg 2 ions from environment to volatile Hg 0 in E coli bacteria The simplified
reaction path includes Two modules for mediated transport of Hg 2 into cytosol catalysed
by the enzyme PT and its reduction catalysed by the enzyme PA Five regulatory modules
of mer operon expression including successive synthesis of the enzyme PR the transcriptional
activator of other protein synthesis lumped PT permease PA reductase and of the control
protein PD One module for the lumped proteome P and genome G replication of G P 1 type
The regulatory system is placed in a growing cell by mimicking the homeostasis and cell
response to stationary and dynamic perturbations in the environmental Hg2 The reductant
NADPH and RSH are considered in excess into the cell Figure adapted from 68 70 14
Figure 13 In silico design of a genetic modified E coli cell to concomitantly maximize the
production of biomass and succinate the Pareto optimal front method beloe right In the
parentheses are the deleted gene numbers from the genome see the corresponding reaction
in the left scheme The used structured reduced model is those of Edwards and Palsson 72
See the computing details in 71 15
Figure 14 In silico study of glycolytic oscillations occurrence in E coli cell by using the mTRM
model of Maria 21 right obtained by reducing the Chassagnole et al 73 16
Figure 15 Chemical node inducing glycolytic oscillations 21 denotes the feedback
positive or negative regulatory loops Glc glucose F6P fructose 6 phosphate
FDP fructose 1 6 biphosphate V1 V3 reaction rates belonging to the glycolysis reduced
model left of Maria 21 17
Figure 16 Oscillation occurrence in chemical systems Franck 74 denotes the feedback
positive or negative regulatory loops X is a generic species denoting the engine node 17
Deterministic Modelling Approach of Metabolic Processes in Living Cells A Still
Powerful Tool for Representing the Metabolic Processes Dynamics
Systems Biology 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 Inst Systems Biology Seattle is one of the modern tools which uses advanced mathematical simulation models
for in silico design of micro organisms that possess specific and desired functions and characteristics The present work
makes a short review of the bio chemical engineering principles and deterministic modelling rules used by the Systems
Biology for modelling cellular metabolic processes This involves application of the classical modelling techniques mass
balance thermodynamic principles algorithmic rules and nonlinear system control theory 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
Keywords Systems biology Cell metabolism modelling Deterministic modelling Gene expression modelling
Genetic regulatory circuits
Abbreviations GRC Genetic Regulatory Circuits TF s Transcription Factors VVWC Whole Cell Variable Volume
CGE Gene Circuit Engineering GERM Gene Expression Regulatory Modules CVWC Constant Volume Whole Cell ODE
Ordinary Differential Equations QSS Quasi Steady state G Generic Gene P Generic Protein M mRNA CCM Central
Carbon Metabolism GMO Genetic Modified Organisms P I Performance Indices
Deterministic Modelling Approach of Metabolic Processes in Living Cells A Still
Powerful Tool for Representing the Metabolic Processes Dynamics
Introduction micro elements all the cell components should be associated
with specific functions into the cell following a
Living cells are evolutionary auto catalytic self adjustable
structures able to convert raw materials from environment The functional hierarchy
into additional copies of themselves Living cells are organized According to the species structure e g sources of energy
self replicating evolvable and responsive biological systems ATP ADP AMP reaction intermediates TF s 10 Provided
to environmental stimuli The structural and functional cell examples of biological systems that have evolved in a modular
organization including components and reactions is extremely fashion and in different contexts perform the same basic
complex involving O 103 4 components O 103 4 transcription functions Each module grouping several cell components and
factors TF s activators inhibitors and at least one order reactions generates an identifiable function e g regulation of
of magnitude higher number of bio chemical reactions all a certain reaction of enzymes activity gene expression etc
ensuring a fast adaptation of the cell to the changing environment More complex functions such as regulatory networks synthesis
1 3 Relationships between structure function and regulation networks or metabolic cycles can be built up using the building
in complex cellular networks are better understood at a low blocks rules of the Synthetic Biology 11 This is why the
component level rather than at the highest level 4 modular GRC dynamic models of an adequate mathematical
Cell regulatory and adaptive properties are based on representation seem to be the most comprehensive mean for a
homeostatic mechanisms which maintain quasi constant key rational design of the regulatory GRC with desired behavior 12
species concentrations and output levels by adjusting the By chance such a building blocks cell structure is computationally
synthesis rates by switching between alternative substrates very tractable when developing cell reduced dynamic models by
or development pathways Cell regulatory mechanisms include defining and characterizing various metabolic sub processes
allosteric enzymatic interactions and feedbacks in gene such as regulatory functions of the gene expression regulatory
transcription networks metabolic pathways signal transduction modules GERM and of genetic regulatory circuits GRC
and other species interactions 5 In particular protein synthesis enzymatic reaction kinetics energy balance functions for
homeostatic regulation includes a multi cascade control of the ATP ADP AMP renewable system electron donor systems
gene expression with negative feedback loops and allosteric of the NADH NADPH FADH FADH2 renewable components
adjustment of the enzymatic activity 1 6 8 hydrophobic effects or functions related to the metabolism
regulation regulatory components reactions of the metabolic
Cells have a hierarchic organization structural functional
cycles gene transcription and translation genome replication
and temporal Figure 1
gene expression regulation protein synthesis storage of the
genetic information etc functions for cell cycle regulation
nucleotide replication and partitioning cell division In the case
of modelling GRC s by chance the number of interacting GERM s
is limited one gene interacting with no more than 23 25 13
The Time Hierarchy
The wide separation of time constants of the metabolic
reactions in the cell systems is called time hierarchy Thus the
reactions are separated in slow and fast according to their time
constant in fact only fast and slow reactions are of interest while
the very slow processes are neglected or treated as parameters
such as the external nutrient or metabolite evolution Aggregate
pools combining fast reactions are usually used in building up
cell dynamic models in a way that intermediates are produced in a
minimum quantity and consumed only by irreversible reactions
Figure 1 The hierarchical organization of living cells
All cell processes obey a certain succession of events while
The structural hierarchy stationary or dynamic perturbations are treated by maintaining
the cell components homeostasis steady state levels and by
Includes all cell components from simple molecules
minimizing the recovering or transition times after perturbations
nutrients saccharides fatty acids aminoacids simple
metabolites then macromolecules or complex molecules lipids A central part of such cell models concerns self regulation of
proteins nucleotides peptidoglycans coenzymes fragments the metabolic processes via GRC s Consequently one particular
of proteins nucleosides nucleic acids intermediates and application of such dynamic deterministic cell models is the study
continuing with well organized nano structures membranes of GRC s in order to predict ways by which biological systems
ribosomes genome operons energy harnessing apparatus respond to signals or environmental perturbations The emergent
replisome partitioning apparatus Z ring etc 9 To ensure field of such efforts is the so called gene circuit engineering GCE
self replication of such a complex structure through enzymatic and a large number of examples have been reported with in silico
metabolic reactions using nutrients Nut metabolites Met and re creation of GRC s conferring new properties functions to the
substrates glucose fructose N source dissolved oxygen and mutant cells i e desired motifs in response to external stimuli
Deterministic Modelling Approach of Metabolic Processes in Living Cells A Still
Powerful Tool for Representing the Metabolic Processes Dynamics
1 14 Simulation of gene expression and of GRC makes possible 1 8 such structured deterministic kinetic models have been
in silico design of organisms that possess specific and desired proved to be extremely useful for in silico design of novel
functions By inserting new GRC s into organisms one may create GRC s conferring new properties functions to the mutant cells
a large variety of mini functions tasks or desired motifs in that is desired motifs in response to the external stimuli 1
response to external stimuli
With the aid of recombinant DNA technology it has become
possible to introduce specific changes in the cellular genome
This enables the directed improvement of certain properties
of microorganisms such as the productivity which is referred
to as Metabolic Engineering 15 17 This is potentially a
great improvement compared to earlier random mutagenesis
techniques but requires that the targets for modification are
known The complexity of pathway interaction and allosteric
regulation limits the success of intuition based approaches
which often only take an isolated part of the complete system
into account Mathematical models are required to evaluate the
effects of changed enzyme levels or properties on the system as a
whole using metabolic control analysis or a dynamic sensitivity Figure 2 KEGG 34 result the central carbon metabolic
analysis 18 In this context GRC dynamic models are powerful fluxes metabolic pathway map of Mycobacterium
tools in developing re design strategies of modifying genome smegmatis MC2155 after 2
and gene expression seeking for new properties of the mutant
The scope of this paper is to review some novel concepts and
cells in response to external stimuli 1 Examples of such GRC
bio chemical engineering rules applied to modular modelling
modulated functions include
of gene expression regulatory modules GERM GRC s and other
o Toggle switch i e mutual repression control in two gene metabolic processes on a deterministic basis by using continuous
expression modules and creation of decision making branch variable dynamic models under the novel whole cell variable
points between on off states according to the presence of certain volume VVWC modelling framework 1
An Emergent Border Field Systems Biology
o Hysteretic GRC behaviour that is a bio device able to behave
Efforts to understand and to develop mathematical models
in a history dependent fashion in accordance to the presence of a
on a mechanistic deterministic basis of the cell metabolic
certain inducer in the environment
processes started many decades ago but with modest results
o GRC oscillator producing regular fluctuations in network Studies on this subject were amplified after the famous question
elements and reporter proteins and making the GRC to evolve formulated by the distinguished physicist Erwin Schroedinger in
among two or several quasi steady states his famous lecture at Trinity College Dublin on 1943 What is
life and after the famous cryptanalyst Alan Turing published
o Specific treatment of external signals by controlled
on 1952 his paper The chemical basis of morphogenesis in
expression such as amplitude filters noise filters or signal
Philosophical Transactions of the Royal Society of London Series
stimuli amplifiers
B No 641 Vol 237 proving the bio chemical reaction basis
o GRC signalling circuits and cell cell communicators acting of metabolic processes Notable progresses in the structured
as programmable memory units modelling of GRC and in the study of their regulatory properties
have been reported after publication of the book of General
The development of dynamic models on a deterministic
System Theory by Ludwig von Bertalanffy on 1968
basis to adequately simulate in detail the cell metabolism self
regulation cell growth and replication for such an astronomical Amazing but the first pioneers in dynamic modelling of
cell metabolism complexity is practical impossible due to lack of biological systems were not the bio chemical engineers which
structured information and computational limitations A review are better trained to translate from the language of molecular
of some trials is presented by Styczynski Stephanopoulos 19 biology to that of mechanistic bio chemistry by preserving the
structural hierarchy and component functions The first dynamic
In spite of such tremendous modelling difficulties
models of some cell processes have been reported by the
development of reduced dynamic models to adequately
electronists on 1952 22 23 Later such electronic circuits like
reproduce such complex synthesis related to the central carbon
models have been extensively used to understand intermediate
metabolism Figure 2 18 21 but also to the genetic regulatory
levels of regulation but they failed to reproduce in detail
system 20 tightly controlling the metabolic processes reported
molecular interactions with slow and continuous responses
significant progresses over the last decades in spite of the
to perturbations and eventually they have been abandoned
lack of structured experimental kinetic information In spite
However the electronists underlined the main characteristics of
of being rather based on sparse information from various
the cell systems which must be included in any simulation model
sources and unconventional identification lumping algorithms
Deterministic Modelling Approach of Metabolic Processes in Living Cells A Still
Powerful Tool for Representing the Metabolic Processes Dynamics
o The dynamic character of species interactions and design of new biotechnological processes new devices based
processes on cell cell communicators biosensors etc By assembling
functional parts of an existing cell such as promoters ribosome
o The feedback character of processes ensuring their
binding sites coding sequences and terminators protein
o Optimal regulation with domains or by designing new GRC s on a modular basis it is
possible to reconstitute an existing cell or to produce novel
o Consuming minimum of resources nutrients substrates
biological entities with new properties
and cell energy but ensuring maximum reaction rates
Encouraging results have been reported for the design of
All these cell metabolic characteristics will be accounted in
artificial gene networks for reprogramming signalling pathways
all the subsequent cell in silico simulators based on extended
for refactoring of small genomes or for re design of metabolic
mathematical models All these metabolic process characteristics
fluxes with using switching genes 1 By assembling functional
are also in the agreement of the Darwin theory Living organisms
parts of an existing cell such as promoters ribosome binding
have evolved to maximize their chances for survival It explains
sites coding sequences and terminators protein domains or by
structures behaviours of living organisms
designing new gene regulatory networks on a modular basis it is
possible to reconstitute an existing cell the so called integrative
understanding or to produce novel biological entities with
modified characteristics 11
To help the efforts of the Synthetic Biology to in silico
design genetic modified micro organisms GMO with desired
characteristics the emergent border field of the Systems Biology
has been very quickly developed based on using mathematical
tools and numerical calculus as well as bio chemical engineering
concepts and tools 1 together with the control theory of the
nonlinear systems to characterize the kinetics and self regulation
of the cell metabolic processes
In the Synthetic Biology the genetic components may be
considered as building blocks because they may be extracted
replicated altered and spliced into the new biological organisms
The Synthetic Biology is in direct connection with the Systems
Figure 3 On 2000 the human genome has been deciphered
Biology focus on the cell organization the former being one of the
The modelling efforts have intensified a lot after 2000 when main tools for the in silico design of GMO s In such a topics the
the human genome has been deciphered Figure 3 being proved metabolism characterization by means of lumped but adequate
that the difficult task to model and design complex biological cell models plays a central role as underlined by the following
circuits with a building blocks strategy can be accomplished by definition Systems Biology is the science of discovering
properly defining the cell basic components functions and modelling understanding and ultimately engineering at the
structural organisation Because many cell regulatory systems are molecular level the dynamic relationships between the biological
organized as modules 24 it is natural to model GRC s using a molecules that define living organisms Leroy Hood president
modular approach 1 Further analyses including engineered Institute for Systems Biology Seattle USA cited by Banga 2008
GRC s can lead to predict design desirable cell characteristics Beside the Institute for Systems Biology in Seattle a large number
that is 25 a tight control of gene expression i e low expression of research groups appeared worldwide based on the increased
in the absence of inducers and accelerated expression in the computing power of the new generations of computers 28 32
presence of specific external signals a quick dynamic response
Various definitions of Systems Biology exist in the dedicated
and high sensitivity to specific inducers GRC robustness i e a low
literature 3
sensitivity vs undesired inducers external noise Through the
combination of induced motifs in modified cells one may create o The science of discovering modelling understanding
potent applications in industrial environmental and medical and ultimately engineering at the molecular level the dynamic
fields e g biosensors gene therapy Valuable implementation relationships between the biological molecules that define living
tools of the design GRC in real cells have been reported over the organisms Leroy Hood Inst Systems Biology Seattle
last years 11
o System Biology is a comprehensive quantitative analysis
The emergent field of Synthetic Biology 26 interpreted of the manner in which all the components of a biological system
as the engineering driven building of increasingly complex interact functionally over time Alan Aderem Director Inst
biological entities 11 aims at applying engineering principles Systems Biology Seattle
of systems design to biology with the idea to produce predictable
o Perhaps surprisingly a concise definition of Systems
and robust systems with novel functions in a broad area of
Biology that most of us can agree upon has yet to emerge Ruedi
applications 11 27 such as therapy of diseases gene therapy
Aebersold Inst Systems Biology Seattle
Deterministic Modelling Approach of Metabolic Processes in Living Cells A Still
Powerful Tool for Representing the Metabolic Processes Dynamics
o The real advance in the application of systems theory to increases with two orders of magnitude from 2000 to 2007 and
biology will come about only when the biologists start asking it is still exponentially increasing most of them being founded by
questions which are based on the system theoretic concepts programs of the European Science Foundation Figure 5
rather than using these concepts to represent in still another
way the phenomena which are already explained in terms of
biophysical or biochemical principles Then we will have a
field of Systems Biology Mike Mesarovic in System Theory and
Biology 1968
o The discipline of systems biology aims at understanding
Figure 4 Quoted from the obituary of R Heinrich 3
the dynamic interaction between components of a living system
or between living systems http www erasysbio net Here it is to mention the huge contributions of Reinhart
Heinrich 1946 2006 in the field of modelling the regulation
o Systems biology is an approach by which biological
of cellular systems 28 So that at his obituary on 2006 M W
questions are addressed through integrating experiments with
Kirschner Nature 444 700 said Figure 4 If Systems Biology
computational modelling simulation and theory in iterative
has heroes one of them is Reinhart Heinrich
cycles http www erasysbio net
o Modelling is not the final goal but is a tool to increase
understanding of the system to develop more directed
experiments and finally allow predictions http www
erasysbio net
In the post genomic era a large number of Systems Biology
projects have been developed leading to simulate parts of cell
metabolism such as 8 EcoCyc 33 database KEGG 34
database Whole Cell models cell organization and dynamics
a E Cell compartments compounds genes reactions 35
b V Cell model geometry applications biological
interface 36
c M Cell stochastic simulator of some cell sub systems Figure 5 Systems Biology publications and EU programs
37 after 2000
d A Cell electrical circuit models 38 Tremendous applications of systems biology have been
reported over the next decades in the area of 41
e Silicon Cell computer replica of cell processes to be
linked 39 Designing mutant cloned cells
Cell biology
with desired motifs
f Specific programming languages SBML JWS 40 etc
Genetics biology or genetics Food science
g Single cell growth e g Escherichia coli Haemophilus
Biotechnology Bioengineering Immunology
influenzae Mycoplasma genitalium yeast
Biomedical engineering Molecular biology
h Model metabolic oscillations red blood cell synthesis
Biochemistry Biodiversity
glycolysis TCA cycle oxidative phosphorylation key species
Agricultural biology and Ecology Bioinformatics
oscillations etc
Biophysics
i Metabolic control of protein synthesis regulation
GERM GRC So that 50 years after the first reported models of living cells
22 23 the optimistic researchers advanced very ambitious
j Modelling the cell cycle targets such as Modeling the heart from genes to cells to the
k Modelling the drug release and cell drug interactions whole organ 42
l Modelling cellular communications neuronal As in all scientific controversies the are also skeptic opinions
transmission such as 3
m Analysis of logical essence of life life minimal In spite of a full mapping of the human genome which yielded
requirements a code of three billion letters we are still far from a satisfactory
answer to the question formulated by the distinguished physicist
Among the milestone works in Systems Biology it is to
Erwin Schroedinger in his famous lecture at Trinity College Dublin
mention the contributions of some of their pioneers Heinrich
in 1943 What is life However two important observations
Schuster 28 Torres Voit 29 Bowden 30 Brazhnik 31
were made by the world renowned physiologist Denis Noble in
etc The number of published papers in the Systems Biology area
his book The music of life 2006
Deterministic Modelling Approach of Metabolic Processes in Living Cells A Still
Powerful Tool for Representing the Metabolic Processes Dynamics
a We must move away from our obsession with genes alone extreme pathway analysis ExPA constrained based modelling
We must look not at one level but at the interaction of processes of metabolic network CBM
at various levels from the realm of Systems Biology
MCA methods are able to efficiently characterize the metabolic
b The reductionist approach of molecular biology has proved network robustness and functionality linked with the cell
itself immensely powerful But DNA isn t life phenotype and gene regulation MCA allows a rapid evaluation of
the system response to perturbations especially of the enzymatic
i These Systems Biology tools they really work
activity possibilities of control and self regulation for the
ii http www systemsbiology org Systems Biology in whole path or some subunits Functional subunits are metabolic
Depth Some pessimists charge that systems biology is nothing subsystems called modules such as amino acid or protein
more than a fashion fad that will pass once the hype dies synthesis protein degradation mitochondria metabolic path
down Others maintain that systems biology is in essence a etc 6 Because the living cells are self evolutive systems new
repackaging of established concepts and methodologies under reactions recruited by cells together with enzyme adaptations
a new description can lead to an increase in the cell biological organisation and
to optimal performance indices When constructing methods
iii And a third camp endorses the idea of systems biology
to optimize evolutive metabolic systems MCA concepts and
as an enticing and powerful new discipline but thinks that it s
appropriate performance criteria have been used leading to
premature to be considered
maximize reaction rates and steady state fluxes minimize
Bio Chemical Engineering Deterministic Approach metabolic intermediate concentrations minimize transient
Rules Advantages and Limitations times optimise the reaction stoichiometry network topology
maximize thermodynamic efficiency All these objectives
A review of mathematical model types used to describe
are subjected to various mass balance thermodynamic and
metabolic processes is presented in 8 19 32 Each model
biological constraints 28 However by not accounting for
type presents advantages but also limitations To model such
the system dynamics and grounding the analysis on the linear
a complex metabolic regulatory mechanisms at a molecular
system theory topological methods presents inherent limitations
level two main approaches have been developed over decades
see for instance some violations of stoichiometric constraints
structure oriented analysis and dynamic kinetic models 4
discussed by Atauri et al 45 or the use of modified control
Each theory presents strengths and shortcomings in providing
coefficients 46
an integrated predictive description of the cellular regulatory
network Classical approach to develop deterministic dynamic models
is based on a hypothetical reaction mechanism kinetic equations
Structure oriented analyses or topological models ignore
and known stoichiometry This route meets difficulties when
some mechanistic details and the process kinetics and use
the analysis is expanded to large scale metabolic networks
the only network topology to quantitatively characterize to
because the necessary mechanistic details and standard
what extent the metabolic reactions determines the fluxes and
kinetic data to derive the rate constants are difficult to be
metabolic concentrations 28 The so called metabolic control
obtained However advances in genomics transcriptomics
analysis MCA is focus on using various types of sensitivity
proteomics and metabolomics lead to a continuous expansion of
coefficients the so called response coefficients which
bioinformatic databases while advanced numerical techniques
are quantitative measures of how much a perturbation an
non conventional estimation procedures and massive software
influential variable affects the cell system states e g reaction
platforms reported progresses in formulating such reliable
rates metabolic fluxes stationary reaction rates species
cell models Valuable structured dynamic models based on cell
concentrations around the steady state QSS The systemic
biochemical mechanisms have been developed for simulating
response of fluxes or concentrations to perturbation parameters
various sub systems see chap An emergent border field
i e the control coefficients or of reaction rates to perturbations
Systems Biology
i e the elasticity coefficients have to fulfil the summation
theorems which reflect the network structural properties and To model in detail the cell process complexity is a challenging
the connectivity theorems related to the properties of single and difficult task The large number of inner cell species complex
enzymes vs the system behaviour regulatory chains cell signalling motility organelle transport
gene transcription morphogenesis and cellular differentiation
Originally MCA has been introduced by Kacser Burns 8
cannot easily be accommodated into existing computer
Heinrich Rapoport 8 to quantify the rate limitation in complex
frameworks Inherently any model represents a simplification
enzymatic systems MCA have been followed by a large number
of the real phenomenon while relevant model parameters are
of improvements mainly dealing with the control analysis of the
estimated based on the how close the model behaviour is to the
stationary states by pointing out the role of particular reactions
real cell behaviour A large number of software packages have
and cell components in determining certain metabolic behaviour
been elaborated allowing the kinetic performance of enzyme
Successive extensions of such definitions allow 8 to study any
pathways to be represented and evaluated quantitatively
limit set for non steady time dependent conditions 43 44
8 47 Oriented and unified programming languages have been
the flux balance analysis and optimization FBA elementary
developed see SBML JWS see chap An emergent border field
mode analysis EMA dynamic flux balance analysis DFBA
Systems Biology to include the bio system organization and
Deterministic Modelling Approach of Metabolic Processes in Living Cells A Still
Powerful Tool for Representing the Metabolic Processes Dynamics
complexity in integrated platforms for cellular system simulation until more detailed data on process dynamics become available
E Cell V Cell M Cell A Cell see chap An emergent border field Electronic circuits structures see an example in Figure 7
Systems Biology Such integrated simulation platforms tend to have been extensively used to understand intermediate levels
use a large variety of biological databanks including enzymes of regulation but they cannot reproduce in detail molecular
proteins and genes characteristics together with metabolic interactions with slow and continuous responses to perturbations
reactions CRGM database 48 NIH database 49
From the mathematical point of view various structured
mechanism based dynamic models have been proposed to
simulate the metabolic processes and their regulation accounting
for continuous discrete and or stochastic variables in a
modular construction circuit like network or compartmented
simulation platforms 5 8 50 Such models can include
i Boolean discrete variables such a topological structure
is displayed in the Figure 6 50 due to the very large number
of states O 103 104 and O 103 of TFs involved in the gene
expression such GRC models are organized in clusters modules
of a multi layer organization
Figure 7 An electronic circuit like representation of a
GRC A human cancer cell pathway from http www bio
itworld com archive 111202 virtual html
Metabolic processes at a low molecular level are generally
better clarified Based on that conventional dynamic models
based on ordinary differential ODE species mass balance with
a mechanistic deterministic description of reactions tacking
place among individual species proteins mRNA intermediates
etc have been proved to be a convenient route to analyse
continuous metabolic regulatory processes and perturbations
When systems are too large or poorly understood coarser and
more phenomenological kinetic models may be postulated e g
protein complexes metabolite channelling etc In dynamic
deterministic models usually only essential reactions are
retained the model complexity depending on the measurable
variables and available information To reduce the structure
of such a model an important problem to be considered is the
distinction between the qualitative and quantitative process
knowledge stability and instability of involved species the
dominant fast and slow modes of process dynamics reaction
time constants macroscopic and microscopic observable
Figure 6 Boolean topological representation of GRC 50
elements of the state vector Such kinetic models can be useful
ii Continuous variable models among other advantages to analyse the regulatory cell functions both for stationary
such models can perfectly represent the cell response to and dynamic perturbations to model cell cycles and oscillatory
continuous perturbations and their structure and size can metabolic paths 21 and to reflect the species interconnectivity
be easily adapted based on the available omics information or perturbation effects on cell growth 1 55 Mixtures of ordinary
8 28 32 50 51 differential equation ODE kinetic models with discrete states
i e continuous logical models and of continuous ODE kinetics
iii Stochastic variable models 52 54
with stochastic terms can lead to promising mixed models able to
iv Mixed variable models 50 simulate both deterministic and non deterministic cell processes
In the Boolean approach variables can take only discrete 50 Representation of metabolic process kinetics is made
values Even if less realistic such an approach is computationally usually by using rate expressions of extended Michaelis Menten
tractable involving networks of genes that are either on or off or Hill type 20 21 55
e g a gene is either fully expressed or not expressed at all Figure Stochastic models replace the average solution of continuous
6 according to simple Boolean relationships in a finite space variable ODE kinetics e g species concentrations by a detailed
Such a coarse representation is used to obtain a first model for random based simulator accounting for the exact number of
a complex biosystem including a large number of components molecules present in the system Because the small number of
Deterministic Modelling Approach of Metabolic Processes in Living Cells A Still
Powerful Tool for Representing the Metabolic Processes Dynamics
molecules for a certain species is more sensitive to stochasticity of model functions in respect to model states that is species
of a metabolic process than the species present in larger amounts concentrations the in cell metabolic models has been proved to
simulation via continuous models sometimes can lack of enough be insufficient 55 61
accuracy for random process representation as cell signalling
The work with reduced kinetic models of cell syntheses and
gene mutation etc Monte Carlo simulators are used to predict
GRC s even if computationally very convenient presents some
individual species molecular interactions while rate equations
inherent disadvantages that is multiple reduced model structures
are replaced by individual reaction probabilities and the model
might exist difficult to be discriminated a loss of information is
output is stochastic in nature Even if the required computational
reported on certain species on some reaction steps and a loss in
effort is extremely high stochastic representation is useful
system flexibility given by the no of intermediates and species
to simulate the cell system dynamics by accounting for a large
interactions a loss in the model prediction capabilities a lack
number of species of which spatial location is important 52 54
of physical meaning of some model parameters constants thus
By applying various modelling routes successful structured limiting its robustness and portability alteration of some cell
models have been elaborated to simulate various regulatory GRC holistic properties stability multiplicity sensitivity
mechanisms 8 52 56 59 In fact as mentioned by Crampin
Mathematical Modeling in Molecular Biology Using
Schnell 5 a precondition for a reliable modelling is the correct
identification of both topological and kinetic properties As few Bio Chemical Engineering Tools
kinetic data are present in a standard form non conventional Even if complicated and often over parameterized the
estimation methods have been developed by accounting for continuous variable dynamic deterministic ODE models of
various types of information even incomplete and global cell GRC s present a significant number of advantages being able
regulatory properties 5 61 to reproduce in detail the molecular interactions the cell slow
or fast continuous response to exo endo geneous continuous
Development of deterministic dynamic models to adequately
perturbations 8 19 Besides the use of ODE kinetic models
reproduce such complex synthesis related to the central carbon
presents the advantage of being computationally tractable
metabolism 20 21 but also the genetic regulatory system
flexible easily expandable and suitable to be characterized using
tightly controlling such metabolic processes reported significant
the tools of the nonlinear system theory 3 28 accounting for the
progresses over the last decades in spite of the lack of structured
regulatory system properties that is dynamics feedback feed
experimental kinetic information being rather based on
forward and optimality And most important such ODE kinetic
sparse information from various sources and unconventional
modelling approach allows using the strong tools of the classical
identification lumping algorithms 1 8 61
bio chemical engineering modelling that is 62
Reduction in the model structure via lumping of species and
i Molecular species conservation law stoichiometry
reactions is necessary due to 1
analysis species differential mass balance set
a The high complexity of cell metabolic processes vs
ii Atomic species conservation law atomic species mass
available data
b Large number of species reactions transport parameters
iii Thermodynamic analysis of reactions that is quantitative
and interaction s
assignment of reaction directionality 63
c low data observability reproducibility
iv Set equilibrium reactions Gibbs free energy balance
d Metabolic process variability analysis set cyclic reactions find species at quasi steady state
e Interpretable representation of cell complexity improved evaluation of steady state flux distributions that
provide important information for metabolic engineering 64
f Requirement to get quick simulations of cell behavior allowing application of ODE model species and or reaction
under various environmental conditions lumping rules 61
g Computational tractability and easier application of The ODE deterministic models have been developed in two
algorithmic rules from bio chemical engineering and numerical alternatives
o The default Constant Volume Whole Cell CVWC classical
However a trade off between model complexity and adequacy continuous variable ODE dynamic models which do not explicitly
must be maintained 62 to use such models for the in silico consider the cell volume exponential increase during the cell
design GMO by in silico re programming the cell metabolism or growth
by optimal cell cloning 69 70 Application of systematic math
lumping rules to metabolic processes must account for physical When the continuous variable CVWC dynamic models are
significance of lumps species interactions and must preserve used to model the cell enzymatic processes the default modelling
the systemic holistic properties of the metabolic pathway The frame work eq 1 is that of a constant volume and implicitly
only separation of components and reactions based on the time of a constant osmotic pressure eventually accounting for the
constant scale as in the modal analysis of the Jacobian of the ODE cell growing rate as a pseudo decay rate of key species often
model the ODE model Jacobian being defined as the derivatives lumped with the degrading rate in a so called diluting rate
Deterministic Modelling Approach of Metabolic Processes in Living Cells A Still
Powerful Tool for Representing the Metabolic Processes Dynamics
The CVWC formulation results from the species concentration additional constraint must be also considered to preserve the
definition of Cj nj V leading to the default kinetic model system isotonicity constancy of the osmotic pressure p under
isothermal conditions This constraint should be considered
together with the ODE model 2 3 that is the Pfeiffers law of
sij ri n V k t h j C k t
V t dt i 1 diluted solutions 66 adopted and promoted by Maria 1 8
d n j V dC j nr R T ns
k t h j C k t 1
sij ri n V V t n t 4
dt dt p j 1 j
Where Cj cell species j concentration V system cell Which by derivation and division with V leads to 1
volume nj species j number of moles rj j th reaction rate
s i j stoichiometric coefficient of the species j individual 1 dV RT ns 1 dn j 5
or lumped in the reaction i t time j 1 ns number of V dt p j V dt
cell species individual or lumped k rate constant vector I
In the above relationships T absolute temperature and R
1 nr number of reactions The above formulation assumes
universal gas constant V cell cytosol volume As revealed by
a homogeneous volume with no inner gradients or species
the Pfeffer s law eqn 4 in diluted solutions 66 and by the
diffusion resistance The used reaction rate expressions for the
eq 5 the volume dynamics is directly linked to the molecular
metabolic reactions are usually those of extended Michaelis
species dynamics under isotonic and isothermal conditions
Menten or Hill type Being very over parameterized and strongly
nonlinear parameter estimation of such models in the presence Consequently the cell dilution D results as a sum of reacting
of multiple constraints translates into a mixed integer nonlinear rates of all cell species individual or lumped The RT p
progeamming problem MINLP difficult to be solved because the term can be easily deducted in an isotonic cell system from the
searching domain is not convex 3 fulfilment of the following invariance relationship derived from
Such a CVWC dynamic model might be satisfactory for
modelling many cell subsystems but not for an accurate RT ns RT V t 1 1
t n j t ns constant
modelling of cell GRC and holistic cell properties under perturbed p j 1 p ns ns 6
n j t Cj C jo
j 1 j 1 j 1
conditions or the division of cells by distorting very much or
even misrepresenting the prediction results as exemplified by As another observation from 5 it results that the cell
1 dilution is a complex function D C k being characteristic to each
cell and its environmental conditions
o As an alternative Maria 1 8 promoted over the last 15
years the holistic variable volume whole cell VVWC modelling Relationships 5 6 are important constraints imposed to the
framework by explicitly including in the model constraint VVWC cell model 2 3 eventually leading to different simulation
equations accounting for the cell volume growth and by results compared to the CVWC cell kinetic models that neglect the
preserving the same cell osmotic pressure while the continuous cell volume growth and isotonic effects see an example in 1
ODE model was re written either in terms of species moles or of
On the contrary application of the default classical CVWC ODE
species concentrations as following 1
kinetic models of eqn 1 type with neglecting the isotonicity
dCj 1 d nj 1 d nj constraints presents a large number of inconveniences related to
ignoring lots of cell properties discussed in detail in 1 that is
dt V dt V dt
a The influence of the cell ballast in smoothing the
j 1 no of species
homeostasis perturbations
b The secondary perturbations transmitted via cell
D d In V dt 2 volume following a primary perturbation
Because c The more realistic evaluation of GERM regulatory
performance indices P I s
dCj d nj 1 d nj d ln V 1 d n j
C j DC j h j C k t 3
dt dt V V dt dt V dt d The more realistic evaluation of the recovering
transient times after perturbations
Where V cell volume in fact cytosol volume nj species j
number of moles rj j th reaction rate D cell content dilution e Loss of the intrinsic model stability
rate i e cell volume logarithmic growing rate species inside the
f Loss of the self regulatory properties after a dynamic
cell are considered individually or lumped t time The 2 3
perturbation etc
mass balance formulation is that given by Aris 65 for the bio
chemical reacting systems of variable volume
In the VVWC formulation of the cell dynamic model an
Deterministic Modelling Approach of Metabolic Processes in Living Cells A Still
Powerful Tool for Representing the Metabolic Processes Dynamics
analyse the regulatory cell functions and the treatment of both
stationary and dynamic perturbations the cell cycles oscillatory
metabolic paths and lot of cell biosyntheses related to the central
carbon metabolism 1 by reflecting the species interconnectivity
or perturbation effects on cell growth
Modular Modelling of Genetic Regulatory Circuits
One of the very successfully application of VVWC
deterministic models with continuous variables is those of
simulating the regulatory properties of the individual gene
expression regulatory modules GERM and of the genetic
regulatory circuits GRC comprising a certain number of linked
GERM s no more than 23 25 13 A review of the systematic
and comprehensive approaches in modelling the dynamics of the
GRC s based on VVWC deterministic models and bio chemical
engineering concepts and principles was presented by Maria in
his work Figure 9 1
Figure 9 The cover of the ebook of Maria 1 https
juniperpublishers com ebook info php
Why the GRC are important to be understood and simulate
their properties That is because the cell core metabolism is
ensured by the optimized GERM s and GRC s that maintain the
optimized protein enzymes synthesis and thus a balanced
cell metabolism and an equilibrated cell growth despite the
continuous perturbations in the environment by also ensuring the
Figure 8 The variable cell volume whole cell VVWC cell evolution and competitiveness eventually by gene mutations
dynamic modelling framework and its basic hypotheses 1 8 3 It is here to mention only some of the GRC functions
The basic equations and hypotheses of a VVWC model are a Cell metabolism regulation via hierarchically organized
presented in Figure 8 Even if all cell regulation mechanisms GRC key proteins being the regulatory nodes
are not fully understood metabolic regulation at a low level
b Sustain cell homeostasis and a balanced cell growth
is generally better clarified Based on that conventional
under variable environmental conditions nutrients substrates
deterministic dynamic models based on ODE kinetics using
continuous variables approached in this paper based on a c Preserve the holistic and local GRC regulatory
mechanistic description of cell reactions taking place among properties
individual species including proteins mRNA DNA transcription
i Ensure Self regulation of cell Self replication
factors TF s intermediates etc proved to be a convenient route
to analyse continuous metabolic regulatory processes and ii Ensure fast cell response to environmental
perturbations When systems are too large or poorly understood perturbations
coarser and more phenomenological kinetic models may be iii Ensure fast metabolic reactions with low level of
postulated e g protein complexes metabolite channelling intermediates
etc In dynamic models only essential reactions are retained
species and reactions often being included as lumps the model iv Ensure optimized metabolic fluxes stationary reaction
complexity depending on measurable variables and available rates
information Such reduced VVWC kinetic models can be useful to


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