Catabolite repression in Escherichia coli – a comparison of
modelling approaches
Andreas Kremling, Sophia Kremling and Katja Bettenbrock
Systems Biology Group, Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany
Research in systems biology requires experimental
effort as well as theoretical attempts to elucidate the
general principles of cellular dynamics and control
and to help to improve molecular processes for engi-
neering purposes or drug design. This interdisciplinary
approach provides a promising method for advances
in biotechnology and molecular medicine. In systems
biology, quantitative experimental data and mathe-
matical models are combined in an attempt to obtain
information on the dynamics and regulatory structures
of the systems. However, depending on the degree of
biological knowledge and the amount of quantitative
data, the models developed so far differ in their degree
of granularity, starting with a simple on ⁄ off binary
description of the state variables of the system and
ending with fully mechanistic models. Carbohydrate
uptake via the phosphoenolpyruvate-dependent phos-
photransferase system (PTS) in Escherichia coli is one
of the best studied biochemical networks from theo-
retical and experimental points of view, and has
Keywords
Escherichia coli; model verification; modular
modelling; phosphotransferase system; time
hierarchies
Correspondence
A. Kremling, Systems Biology Group, Max
Planck Institute for Dynamics of Complex

component in the network, must be solved numerically); PTS, phosphotransferase system (uptake and sensory system in many bacteria,
consists of several proteins); rFBA, regulatory FBA (takes into account the transcriptional regulatory network to describe the presence or
absence of the enzyme of the network as a function of the environmental conditions).
594 FEBS Journal 276 (2009) 594–602 ª 2008 The Authors Journal compilation ª 2008 FEBS
become more and more important during recent years.
A comprehensive review of the experimental and theo-
retical work is provided in [1].
The PTS represents a group translocation system
that catalyses the uptake and concomitant phosphory-
lation of glucose and a number of other carbohydrates
(Fig. 1). It consists of two common cytoplasmic pro-
teins, enzyme I (EI) and histidine-containing protein
(HPr), as well as an array of carbohydrate-specific
enzyme II (EII) complexes. EII is typically composed
of EIIA, B and C domains, with the EIIA and B do-
mains being part of the phosphorylation chain and the
EIIC domain representing the membrane domain. As
all components of the PTS, depending on their phos-
phorylation status, can interact with various key regu-
lator proteins, the output of the PTS is represented by
the degree of phosphorylation of the proteins. In par-
ticular, the glucose-specific EIIA
Crr
(throughout the
text, we use the abbreviation EIIA for EIIA
Crr
)
domain is an important regulatory protein: unphos-
phorylated EIIA inhibits the uptake of other non-PTS
carbohydrates by a process called inducer exclusion,

equation (o.d.e.) model of the slow time scales is called
dynamic flux balance analysis (dFBA), and was
applied for diauxic growth of E. coli on glucose and
acetate [8]. The model predicts very well the time
course of the external metabolites and the growth of
biomass. In Santillan and Mackey [9], a detailed model
of the lac operon was provided and analysed with
respect to the bistable behaviour and influence of
external glucose. Moreover, the model takes into
account delays inherent to transcription and transla-
tion. A qualitative approach to catabolite repression
was suggested by Ropers et al. [10]. The model
describes the transition from exponential growth to the
stationary growth phase, and vice versa. Sevilla et al.
[11] extended the model of Kremling et al. [12] to
describe l-carnithine biosynthesis with E. coli as host
strain. Using the same modular model set-up, a clear
relationship between external cAMP and l-carnithine
biosynthesis was predicted with the model and finally
verified with experimental data. Recently, Covert et al.
[13] combined a regulatory FBA (rFBA) model of
catabolite repression with the o.d.e. model of Kremling
et al. [14] to predict intracellular fluxes of central
metabolism and gene expression of the lactose and
glucose transport systems.
In this study, we compare two models describing
catabolite repression in E. coli by discussing some
relevant issues of modelling in systems biology, model
validation, dynamics and control. Nishio et al. [15]
described the glucose PTS, the main glucose uptake

A. Kremling et al. Modelling catabolite repression in E. coli
FEBS Journal 276 (2009) 594–602 ª 2008 The Authors Journal compilation ª 2008 FEBS 595
and experimental data were provided and compared
with the theoretical results. The structure of the model
of Bettenbrock and coworkers [14,16–19] is similar and
describes the dynamic behaviour of growth of E. coli
in different environmental conditions and with differ-
ent strain variants. These models were chosen because
they describe catabolite repression in a very com-
prehensive manner, taking into account signal trans-
duction, gene expression and metabolism.
Model description
Both models are set up in a modular way. The mod-
ules defined in Nishio et al. [15] are represented by a
special graphical notation [20]. The following modules
are defined. Plant: includes the four PTS proteins;
feedback sensor: includes the activation of CyaA by
phosphorylated EIIA; computer: describes catabolite
repression protein (Crp) and Cya gene expression and
cAMP synthesis; accelerator actuator: comprises the
control and synthesis of the PTS mRNA; brake actua-
tor: describes the control and synthesis of the PtsG
repressor Mlc. Protein synthesis is described by taking
into account transcription (mRNAs of the respective
proteins are dynamic state variables) and translation.
Transcriptional control includes the interaction of the
regulator proteins Mlc and Crp with the respective
binding sites.
The model is validated by a qualitative comparison
with experimental data. With the model at hand,

together a set of enzyme catalyzed reactions that ful-
fills a specific task like the break down of substrates,
the generation of energy in form of ATP, or the syn-
thesis of amino acids. Based on this more fuzzy defini-
tion, the idea of a modular representation of cellular
processes is very popular [21]. One advantage of the
method of modular modeling is that the granularity of
the submodels can easily be adjusted to the objective
of the model and to the level of biological knowledge
that is incorporated in the model.
Phosphoenolpyruvate
⁄
pyruvate ratio is the most
important input into the PTS module
A modular concept was used by Nishio et al. [15] to
define the units that describe the genetic organization
of the PTS: the genes and enzymes ⁄ proteins involved
are separated into four units. The contribution focuses
on the extracellular glucose concentration as input into
the defined units; changes in this concentration will
lead to different degrees of phosphorylation of the
PTS proteins EI, HPr, EIIA and EIICB. Although
Nishio et al. [15] performed some simulation studies
Table 1. Overview of functional units, process description and
number of state variables for both models (·, considered in the
model; –, not considered in the model).
Nishio
et al. [15]
Bettenbrock
et al. [18]

of phosphorylation of PTS proteins to changes only in
the extracellular glucose concentration (Fig. 1).
It has been argued by our group and others [22,23]
that the phosphoenolpyruvate ⁄ pyruvate ratio is a very
important factor for the determination of the degree of
phosphorylation of EIIA as the PTS reaction network
works in a reversible manner. Therefore, in our repre-
sentation, the phosphoenolpyruvate and pyruvate con-
centrations are seen as important inputs into the PTS.
In [16], we suggested that the PTS should be defined
as a functional unit and as part of a signal transduc-
tion unit that processes information from the cellular
exterior (concentration of substrates) and also from
inside the cell, mainly the flux through glycolysis,
which is reflected by the ratio of the concentrations of
phosphoenolpyruvate and pyruvate and the concentra-
tions of PTS enzymes. In recent publications
[14,19,22], the system was analysed for a large number
of substrates using a mathematical model, and it was
shown that, in the case of non-PTS carbohydrates
(carbohydrates that are not phosphorylated during
uptake, such as lactose or arabinose), a simple rela-
tionship between the degree of phosphorylation of
EIIA (EIIAP) and the ratio of the concentrations of
phosphoenolpyruvate and pyruvate (PEP ⁄ Prv) could
be established:
EIIAP ¼ EIIA
0
PEP=Prv
PEP=Prv þ K

comparable with those on glucose [23]. This may be
the reason why the glucose 6-phosphate transporter
does not require the activation of transcription factor
Crp (Crp is known to be active in the case of a hunger
situation).
The structure of the model of Bettenbrock et al. [18],
namely the connection between the glycolytic flux and
the PTS, made it possible to analyse and to understand
the above-mentioned results on how the cell can adjust
precisely to the degree of activation of the transcription
factor Crp as a function of the growth rate. In addi-
tion, it allows the analysis of cellular processes in the
case of mutations in the glucose uptake system or the
PTS. Setting the concentration of phosphoenolpyruvate
and pyruvate to constant values independent of the
glycolytic flux, as in Nishio et al. [15], means that this
crucial and very important point is disregarded when
trying to understand and model glucose uptake via the
PTS.
Dilution caused by cellular growth
It is well accepted that mass balance equations are a
sound basis for describing the temporal changes of
model components. A problem may occur when not
the masses per se but the concentration (mass of a
compound based on a certain volume, or mass of a
compound based on the entire biomass as usual in bio-
engineering) is the focus of the model, as in the two
contributions discussed here. This requires that the
balance equation be converted because, in cellular sys-
tems, the reference value, the biomass, is also subject

are
the reaction rates. As the growth rate changes for the
different experimental set-ups and depends on time t,
the influence of the dilution term can be very promi-
nent. During examination of the general form of the
A. Kremling et al. Modelling catabolite repression in E. coli
FEBS Journal 276 (2009) 594–602 ª 2008 The Authors Journal compilation ª 2008 FEBS 597
equations used by Nishio et al. [15], dilution was not
considered.
Dynamics of the environmental state variables
In biotechnology, increased production rates of desired
products are obtained by designing the feed rate and
feed concentration of the major substrates of a biore-
actor system. This also requires that the components
of the liquid phase are described with mass balances.
In the model of Nishio et al. [15], the only variable
that describes the environment is the glucose concen-
tration. This concentration must be fixed before a sim-
ulation starts. In contrast, the model of Bettenbrock
et al. [18] considers the liquid phase as an additional
module that is connected to the biophase. In the liquid
phase, o.d.e.’s to describe the dynamics of the biomass
and various medium compounds are implemented.
This allows the simulation of different strategies, such
as batch, fed-batch, ‘disturbed’ batch (that is, growth
on one carbohydrate and pulsing a second carbo-
hydrate in the second phase of the experiment) and
continuous culture. By taking into consideration the
dynamics of the environmental state variables, there
is high flexibility to design new experiments and to

Glc
concentrations, and total cAMP concen-
trations, under various growth conditions. The entire
database consisted of 18 experiments performed with
nine different strains (wild-type and mutant strains).
The model describes the expression of 17 key enzymes,
38 enzymatic reactions and the dynamic behaviour of
more than 50 metabolites. Based on the experiments
and with the help of the ProMoT ⁄ Diva environment
[24] with highly sophisticated methods for sensitivity
analysis, parameter analysis and parameter estimation,
50 parameters (34%) could be estimated.
In particular, the analysis of mutant strains offers
the possibility to check whether the control structures
are reproduced well. In addition, pulse experiments,
‘disturbed’ batch experiments and continuous cultures
allow the determination and analysis of the dynamics
in different time windows. The analysis of the mutant
strains clearly showed that a large experimental effort
is necessary for the rational design of bacterial strains
based on mathematical models.
Nishio et al. [15] provided simulation data of their
model and discussed the agreement with literature
experimental data from a qualitative point of view
only, e.g. they saw that, for high glucose concentra-
tions, the model shows low cAMP concentrations (see
fig. 4 in Nishio et al. [15]); this observation is in
agreement with experimental data. However, systems
biology aims to describe cellular processes quantita-
tively in terms of mathematical models, which also

model improvement would mean the creation of a
model (via parameter estimation and ⁄ or improvement
of model structure) which is able to reproduce both
the experiments used for validation and new experi-
ments which cannot be explained by the old model.
This example shows that model validation and a
critical evaluation of modelling, and also of experimen-
tal results, are of particular importance. This includes
the careful selection of biological experiments and
experimental conditions. For the evaluation of model
predictions, only reliable and reproducible data should
be used that cover a broad range of different condi-
tions, allowing for an extensive analysis of the strains
at hand.
Dynamics and time hierarchies
To show an application of their model, Nishio et al.
[15] simulated an experiment in which the external glu-
cose was reduced from saturating to limiting concen-
trations. As the model comprises metabolic processes,
protein–protein and protein–DNA interactions as well
as protein synthesis, it is expected that the dynamics
can be seen on fast time scales and on slower time
scales. In addition to the difficulties of realizing such
an experiment in the wet laboratory (to guarantee that,
in a reactor system, the glucose concentration is con-
stant at 0.2 nm over a period of time of several hours,
a highly sophisticated control scheme is required that
is able to measure the concentration on-line and to
adjust a glucose feed in such a way that the glucose
consumed by the cells is replaced by the feed), these

from exponential growth to carbohydrate-limited
499.5 500 500.5 501 501.5 502
0
0.5
1
1.5
2
2.5
3
3.5
4
Time (min)
PEP (solid), pyruvate (µmol·gDW
–1
)
480 500 520 540 560 580 600
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
Time (min)
Time (min)
EIIAP

in the experiments, the PTS enzyme concentrations
may differ from steady-state values. With artificial ptsI
gene amplification, however, the models show qualita-
tively different results. With the model of Nishio et al.
[15], a tenfold increase in ptsI gene concentration leads
to extremely high uptake rates and high degrees of
phosphorylation (inverted open triangle in Fig. 3),
whereas, in the model of Bettenbrock et al. [18], only
slightly increased carbohydrate fluxes are detected that
do not lead to significant EIIA phosphorylation (open
triangle in Fig. 3). This is based on the fact that the
reaction rates of glycolysis are much slower than the
PTS reaction rates, leading to a limited glycolytic flux.
Not until – in a simulation study – we destroy the
robustness of the model by modification of the glyco-
lytic enzyme concentrations and by increasing the PTS
enzyme concentrations the model shows uptake rates
and EIIA phosphorylation degrees comparable with
those of the model of Nishio et al. [15] (filled triangle
in Fig. 3).
Nishio et al. [15] reported that cAMP values do not
increase with ptsI gene amplification. The model of
Bettenbrock et al. [18] explains this result: ptsI gene
amplification does not lead to significant EIIA phos-
phorylation, hence explaining the lack of CyaA activa-
tion. This again shows that it is crucial for modelling
to cover all significant reactions. If this is not con-
sidered, model predictions may be quantitatively
incorrect.
Conclusions

Experimental
data
c
Wild-type 1.0 1.0 1.0 1.0
PtsI overexpression 10.8 3.87 1.2 1.2
Mlc mutant 1.0 1.21 1.0 1.1
Mlc mutant with
PtsI overexpression
11.1 5.7 1.2 1.7
PtsG overexpression 0.81 1.25 1.0 ND
Comparison of
a
primary model (values from table 1 in [15]) and
b
modified model (values from table 3 in [15]) with predictions of
the model of [18], and comparison with the experimental results of
[15].
c
Data are scaled for the wild-type: that is, the values obtained
for the wild-type are set to unity and the measurements for the
mutant strains are taken as values relative to the wild-type value.
10
−6
10
−4
10
−2
10
0
0

Modelling catabolite repression in E. coli A. Kremling et al.
600 FEBS Journal 276 (2009) 594–602 ª 2008 The Authors Journal compilation ª 2008 FEBS
has been used to explain the relationship between the
glycolytic flux, the ratio of phosphoenolpyruvate and
pyruvate, and the degree of phosphorylation of the
sensor protein EIIA of the PTS. Disregarding this very
crucial input of glycolysis on the PTS leads to a model
with only low predictive power.
The use of mathematical models for experimental
design is an important aim in a systems biology
approach. One can only succeed if comprehensive
models are used that allow for a holistic analysis of
cellular behaviour. Reduced or simplified models are
good tools to elucidate design principles from a quali-
tative point of view. Unfortunately, most of these
models fail to describe a holistic cell behaviour under
different environmental conditions. The use of detailed
models is strictly coupled with the need for careful and
extensive model validation, because the majority of
kinetic parameters need to be estimated from experi-
mental data. The reports by Nishio et al. [15] and
Bettenbrock et al. [18] are good examples which show
that experimental data can be reproduced with a cer-
tain quality. However, because of its greater complex-
ity and completeness, the model of Bettenbrock et al.
[18] is able to predict experiments in environmental
conditions that are different from those used for model
validation.
Acknowledgements
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