Tài liệu Báo cáo khoa học: Catabolite repression in Escherichia coli – a comparison of modelling approaches docx

The focus is thereby on modular modelling with the relevant input in the central modules, the impact of quantitative model validation, the identification of control struc-tures and the co

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

Technical Systems, Sandtorstr 1, 39106

Magdeburg, Germany

Fax: +49 0391 6110 526

Tel: +49 0391 6110 466

E-mail: kremling@mpi-magdeburg.mpg.de

(Received 26 September 2008, revised 14

November 2008, accepted 19 November

2008)

doi:10.1111/j.1742-4658.2008.06810.x

The phosphotransferase system in Escherichia coli is a transport and sen-sory system and, in this function, is one of the key players of catabolite repression Mathematical modelling of signal transduction and gene expres-sion of the enzymes involved in the transport of carbohydrates is a promis-ing approach in biotechnology, as it offers the possibility to achieve higher production rates of desired components In this article, the relevance of methods and approaches concerning mathematical modelling in systems biology is discussed by assessing and comparing two comprehensive mathe-matical models that describe catabolite repression The focus is thereby on modular modelling with the relevant input in the central modules, the impact of quantitative model validation, the identification of control struc-tures and the comparison of model predictions with respect to the available experimental data

Abbreviations

cAMP, cyclic AMP (signalling molecule); Crp, catabolite repression protein (transcription factor); CyaA, adenylate cyclase (protein,

synthesizes cAMP); dFBA, dynamic FBA (takes into account the slow dynamics of extracellular components); EI, enzyme I (protein, component of the PTS); EIIA, enzyme IIA (protein, component of the PTS, ‘output’ of the system as it activates the synthesis of cAMP); EIIBC (PtsG), enzyme IIBC (main membrane standing transport protein for glucose uptake); FBA, flux balance analysis (tool to determine the flux distribution in cellular networks, requires steady-state conditions); HPr, histidine-containing protein (component of the PTS); LacZ, protein of the lactose degradation pathway (b-galactodidase); Mlc, repressor protein (inhibits the synthesis of EIIBC if glucose is not present

in the medium); o.d.e., ordinary differential equation (basic structure of a mathematical model, it describes the temporal changes of a 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).

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 EIIACrr (throughout the

text, we use the abbreviation EIIA for EIIACrr)

domain is an important regulatory protein:

unphos-phorylated EIIA inhibits the uptake of other non-PTS

carbohydrates by a process called inducer exclusion,

whereas phosphorylated EIIA activates adenylate

cyclase (CyaA) and leads to an increase in the

intra-cellular cyclic AMP (cAMP) level [1]

Mathematical models of catabolite

repression in E coli

The (isolated) reactions of the PTS have been

sub-jected to various kinetic studies These models have

focused on the kinetics of phosphotransfer between the

components [2] or have taken into account diffusion

between the membrane and cytosol [3], but have

neglected metabolism and gene expression

Mathematical models of carbohydrate uptake and

metabolism in E coli are represented very well in the

literature Wong et al [4] have provided a

compre-hensive model of glucose and lactose uptake, including catabolite repression and inducer inclusion The model describes diauxic growth qualitatively well, but was not calibrated with time course experimental data Growth on mixed substrates, such as sucrose and glyc-erol, has been analysed in [5] and [6] A detailed model

of glycolysis has been provided by Chassagnole et al [7] The kinetic parameters of the model were fitted with time course data of a glucose pulse, and describe the dynamics during the first 40 s after the pulse As a result of the short time scale, gene expression was not included Consideration of longer time scales in cellu-lar networks allows the simplification of the set of equations by assuming a steady state of the intra-cellular metabolites An approach that combines flux balance analysis (FBA) with an ordinary differential 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 system of E coli The authors argued that an improved and higher uptake rate of glucose would have some benefits in biotechnological applications, as the uptake of the main carbohydrate is the key for the production of secondary metabolites or foreign pro-teins For this purpose, a rational design based on a mathematical description of the system was presented

P~HPr P~EIICB

P~EI

EI

Pyk HPr

EIICB

Non−PTS systems

P~EIIA

pyruvate

Chemotaxis Mlc

PtsG repressor

Glycolysis

Adenylate cyclase

Glc6P

Glucose

(extracellular)

Fig 1 Glucose uptake by the PTS The phosphoryl group of

phosphoenolpyruvate is transferred to the incoming glucose The

degrees of phosphorylation of the various PTS proteins represent

starting points for a number of signal transduction pathways.

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,

Nishio et al [15] performed an experimental design to

increase glucose uptake They reported that an Mlc

mutant with amplified ptsI gene results in an increased

glucose uptake by a factor of 11.08, which is the

high-est value that could be achieved based on the model

The model of Bettenbrock et al [18] describes the

uptake of five carbohydrates (glucose, lactose, glycerol,

galactose, sucrose) The model is structured in such a

way that pathways well known from biochemical text

books are represented as modules The pathways for

the individual carbohydrates, including the description

of protein synthesis, are connected to the glycolysis

module The PTS reactions, the synthesis of cAMP

and the activation of Crp by cAMP are described in a

module that represents the signal flow on the modulon

level Although the model has a large number of

unknown or uncertain parameters, nearly 34% of the

kinetic constants could be estimated from a

compre-hensive set of experiments

Both models are based on balance equations of the

involved components, that is, processes that increase

or decrease the components are summed This results

in a set of first-order o.d.e as mathematical

represen-tation Table 1 summarizes the specific attributes for the two models It follows a systematic comparison of both models with respect to the model structure, model validation and model prediction

Model structure – reasonable application of modular modelling

In microbiology, the term pathway is used to lump 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]

Gene expression Includes mRNA

dynamics

Only protein synthesis Multiple binding sites a Yes Partial

Model verification Qualitative Quantitative

a Multiple binding sites, that is, the number of binding sites for every transcription factor; this number varies for every gene For example, Nishio et al [15] take into account that the mlc gene possesses two binding sites for Crp and two for Mlc.

with different concentrations of intracellular

phospho-enolpyruvate and pyruvate, the concentrations were

always held constant during these experiments, and no

account was taken of changes in the

phosphoenol-pyruvate and phosphoenol-pyruvate concentrations as a result of

altered glycolytic fluxes Neglecting this important

input into the PTS restricts the changes in the degree

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 informatransduc-tion 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:

EIIAP¼ EIIA0 PEP=Prv

PEP=Prvþ KPTS

ð1Þ

where KPTS is the overall equilibrium constant of the

first three PTS reactions and EIIA0is the total

concen-tration of EIIA With the experimental data available

from Bettenbrock et al [23] for different experimental

conditions, the relationship between the degree of

phosphorylation of EIIA and the specific growth rate

could thus be described with good accuracy In the

case of PTS sugars, Eqn (1) represents an upper bound

for the degree of phosphorylation of EIIA that can be

reached if the PTS enzyme concentrations are

suffi-ciently high In the case of uptake of a PTS sugar,

EIIA will be less phosphorylated because, during the

PTS uptake reaction, phosphoryl groups are

trans-ferred from EIIA to glucose

The consideration of external glucose only as input

could lead to the conclusion that, in the absence of

glucose or during growth on other carbohydrates, the degree of phosphorylation of EIIA is always high, leading to the activation of the transcription factor Crp However, this contradicts experimental observa-tions which show that growth on carbon sources such

as glucose 6-phosphate or lactose results in rather low degrees of phosphorylation of EIIA [22,23] Moreover, growth on glucose 6-phosphate leads to growth rates 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

to change This results in a dilution term d, which is the product of a specific growth rate and the concen-tration of the compound that has to be taken into account So, the general form of an o.d.e will read:

_

ci¼Xn j¼1

cjirj d ¼Xn

j¼1

cjirj lðtÞci ð2Þ

where cji are the stoichiometric coefficients and rj 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

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

complement strategies that focus only on genetic

modi-fications of the system

Large efforts to validate quantitative

models

Mathematical models are valuable tools for the

anal-ysis of inherently complex biological systems To date,

there are no holistic models that represent complete

cells This means that only subsystems of cells can be

analysed, which can lead to severe problems in the

suitability of a model This is especially true for a

rational design if the effects of a modification are not

limited to the subsystem represented in the model or

not described in a quantitative manner to guarantee

high model accuracy Quantitative model validation is

therefore a prerequisite for meaningful model analysis

and experimental design

To simulate the dynamics of cellular systems, it is

desirable to determine kinetic parameters from

experi-mental data As, in most cases, a direct measurement

is not possible, the parameters are estimated during a

parameter identification procedure This comprises the

check of identifiability and the estimation of the

parameters With the model of Bettenbrock et al [18],

kinetic parameters for a detailed dynamic model of

carbohydrate uptake were estimated Model

predic-tions were verified by measuring the time courses of

several extra- and intracellular components, such as glycolytic intermediates (in a pulse experiment), EIIA phosphorylation level, both b-galactosidase and EIICBGlc 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 requires that measurements are available and are of good quality In the contribution by Nishio et al [15], the standard deviations for biomass production of the mutant strains are extremely high, indicating that the perturbations introduced lead to severe growth prob-lems of the strains This is especially true for the strain predicted to have the highest glucose uptake rate, the mlc mutant with increased copy number of ptsI This strain seems to have serious growth problems [final attenuance (D) = 0.11; for the wild-type strain, final

D= 0.81]; therefore, such a strain would be absolutely unsuitable for use as a production strain

As can be seen in Nishio et al [15], there are sub-stantial differences between model prediction and experiment Realizing that their model did not describe their experimental results, Nishio et al [15] eliminated the biologically well accepted activation of CyaA by phosphorylated EIIA in their model, and called this an ‘improved model’ One could argue that, indeed, the activation of CyaA is not necessary

in the case of glucose excess as, in this case, the

degree of phosphorylation of EIIA is low and

there-fore the intracellular cAMP level is also low

How-ever, this inaccurate description of the signalling

pathway, starting from PTS and ending with the

tran-scription factor Crp, will limit the predictive power of

the model for situations different from glucose excess

In contrast, from a systems biological point of view,

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 time scales cannot be presented in an adequate manner

in only one plot (see fig 3 in [15]) Figure 2 shows the simulation results with the model of Bettenbrock et al [18] in the same conditions As can be seen, the state variables show dynamics in different time windows

Comparing model predictions

A critical issue is the prediction of the behaviour of mutant strains and subsequent experimental examina-tion We simulated the experiments shown in table 1 in Nishio et al [15] with the model of Bettenbrock et al [18] The results are summarized in Table 2 As can be seen, the predictions with our model are much closer

to the experimental results The values measured for the strain with ptsI overexpression could be repro-duced with our model very well For the mlc mutant, both models give similar results and the measured values indicate that the mutation has almost no influ-ence on the specific glucose uptake For a strain with ptsG overexpression, Van der Vlag et al [25] measured

an increase in glucose uptake, whereas with the pri-mary model of Nishio et al [15] a decrease was simu-lated and with the model of Bettenbrock et al [18] a slight increase was observed

Degree of phosphorylation of EIIA shows high sensitivity with respect to glycolytic reaction parameters

To further demonstrate the relationship between the carbohydrate flux into the cell and the degree of phos-phorylation of EIIA, Fig 3 shows the experimental results of continuous cultures during the transition 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)

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

0 0.5

1

1.5

2

2.5

–1 )

Fig 2 Dynamics of state variables after glucose depletion, calculated using the model of Bettenbrock et al [18] The value of glucose was set from 0.2 M to 2 n M at time 500 min, as in Nishio et al [15] Left: fast dynamics of phosphoenolpyruvate and pyruvate; middle: dynamics

of EIIAP; right: slow dynamics of intracellular cAMP Note the different time scales of the response curves.

growth, as published in Kremling et al [14] These

experimental results have not been used for model

vali-dation for the detailed model Plotting the simulation

results with the model of Nishio et al [15] (values

taken from fig 4 in [15] and scaled to the overall EIIA concentration), together with the results of the model

of Bettenbrock et al [18], into the same plot demon-strates that both models are able to reproduce the data with good accuracy, although it should be noted that,

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

The bacterial PTS is an interesting but complex signal transduction and transport system that has been sub-jected to research in systems biology for a long time period If the aim of modelling is to make predictions and to explain experimental results, attention must be paid to the mathematical correctness of the model, the inclusion of relevant biological knowledge and quanti-tative (and mostly iterative) validation of the model The model of Nishio et al [15] fails to meet these requirements, and hence is unable to predict new exper-iments with high accuracy Predictions with the model

of Bettenbrock et al [18], which has been validated quantitatively with great effort, could meet the experi-mental results of Nishio et al [15], demonstrating that the model is able to predict experimental data that were not used for model validation A simplified model [14]

Table 2 Comparison of the predictions of the specific glucose

uptake by the model of [15] with the model of [18], and with the

experimental results of [15].

Strain

Nishio

et al.

[15]a

Nishio

et al.

[15]b Bettenbrock

et al [18]

Experimental datac

PtsI overexpression 10.8 3.87 1.2 1.2

Mlc mutant with

PtsI overexpression

PtsG overexpression 0.81 1.25 1.0 ND

Comparison of aprimary 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].cData 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.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Log (carbohydrates (g·L –1 ))

Fig 3 Comparison of simulation and experimental results The

residual carbohydrate concentrations and corresponding degrees of

phosphorylation of EIIA are shown for different dilution rates.

Experimental data (circles) are taken from [23]; theoretical

predic-tions from the model of Nishio et al [15] (full line with squares);

theoretical predictions from the model of Bettenbrock et al [18]

(broken line with diamonds); theoretical prediction from the model

of Nishio et al [15] with excess carbohydrate and tenfold

overpro-duced PtsI concentration (inverted open triangle); theoretical

predic-tion from the model of Bettenbrock et al [18] with excess

carbohydrate and tenfold overproduced PtsI concentration (white

triangle); theoretical prediction from the model of Bettenbrock et al.

[18] with excess carbohydrate, increased PtsI, PtsH and PtsG

con-centrations and altered values of glycolytic reaction parameters

(filled triangle).

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

Files to simulate the Bettenbrock model with

MAT-LAB are available and can be downloaded [26] The

files allow the reproduction of the data shown in the

paper AK and KB are funded by the FORSYS

initia-tive from the German Federal Ministry of Education

and Research (BMBF)

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