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 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). 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, 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 HPrEIICB Non−PTS systems P~EIIA EIIA PEP 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. 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, 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] Crp modulon ·· PTS reactions ·· Glucose transport ·· Other carbohydrates – · Glycolytic reactions – · Environment Constant Dynamic Gene expression Includes mRNA dynamics Only protein synthesis Multiple binding sites a Yes Partial Number dynamic states 19 29 Number algebraic states 44 41 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. Modelling catabolite repression in E. coli A. Kremling et al. 596 FEBS Journal 276 (2009) 594–602 ª 2008 The Authors Journal compilation ª 2008 FEBS 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 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 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 PTS ð1Þ where K PTS is the overall equilibrium constant of the first three PTS reactions and EIIA 0 is 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: _ c i ¼ X n j¼1 c ji r j À d ¼ X n j¼1 c ji r j À lðtÞc i ð2Þ where c ji are the stoichiometric coefficients and r j 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 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 EIICB 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 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 Modelling catabolite repression in E. coli A. Kremling et al. 598 FEBS Journal 276 (2009) 594–602 ª 2008 The Authors Journal compilation ª 2008 FEBS 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) 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 (µmol·gDW –1 ) 500 600 700 800 900 1000 0 0.5 1 1.5 2 2.5 cAMP (µmol·gDW –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 nM 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. 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 599 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 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 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Log (carbohydrates (g·L –1 )) Degree of phosphorylation EIIA (−) 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). 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 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). References 1 Deutscher J, Francke C & Postma PW (2006) How phosphotransferase system-related protein phosphoryla- tion regulates carbohydrate metabolism in bacteria. Microbiol Mol Biol Rev 70, 939–1031. 2 Rohwer JM, Meadow ND, Roseman S, Westerhoff HV & Postma PW (2000) Understanding glucose transport by the bacterial phosphoenolpyruvate:glucose phospho- transferase system on the basis of kinetic measurements in vitro. J Biol Chem 275, 34909–34921. 3 Francke C, Westerhoff HV, Blom JG & Peletier MA (2002) Flux control of the bacterial phosphoenolpyr- uvate:glucose phosphotransferase system and the effect of diffusion. Mol Biol Rep 29, 21–26. 4 Wong P, Gladney S & Keasling JD (1997) Mathemati- cal model of the lac operon: inducer exclusion, catabo- lite repression, and diauxic growth on glucose and lactose. Biotechnol Prog 13, 132–143. 5 ang JW, Gilles ED, Lengeler JW & Jahreis K (2001) Modeling of inducer exclusion and catabolite repression based on a PTS-dependent sucrose and non-PTS-depen- dent glycerol transport system in Escherichia coli K-12 and its experimental verification. J Biotechnol 92, 133– 158. 6 Sauter T & Gilles ED (2004) Modeling and experimen- tal validation of the signal transduction via the Escherichia coli sucrose phosphotransferase system. J Biotechnol 110, 181–199. 7 Chassagnole C, Noisommit-Rizzi N, Schmid JW, Mauch K & Reuss M (2002) Dynamic modeling of the central carbon metabolism of Escherichia coli. Biotech- nol Bioeng 79, 53–73. 8 Mahadevan R, Edwards JS & Doyle FJ (2002) Dynamic flux balance analysis of diauxic growth in Escherichia coli. Biophys J 83, 1331–1340. 9 Santillan M & Mackey MC (2004) Influence of catabo- lite repression and inducer exclusion on the bistable behavior of the lac operon. Biophys J 86, 1282–1292. 10 Ropers D, deJong H, Page M, Schneider D & Geisel- mann J (2006) Qualitative simulation of the carbon starvation response in Escherichia coli. BioSystems 84, 124–152. 11 Sevilla A, Canovas M, Keller D, Reimers S & Iborra JL (2007) Impairing and monitoring glucose catabolite repression in l-carnithine biosynthesis. Biotechnol Prog 23, 1286–1296. 12 Kremling A, Bettenbrock K, Laube B, Jahreis K, Leng- eler JW & Gilles ED (2001) The organization of meta- bolic reaction networks: III. Application for diauxic growth on glucose and lactose. Metab Eng 3, 362–379. 13 Covert IMW, Xiao N, Chen TJ & Karr JR (2008) Inte- grating metabolic, transcriptional regulatory and signal transduction models in Escherichia coli. Bioinformatics 24, 2044–2050. 14 Kremling A, Bettenbrock K & Gilles ED (2007) Analy- sis of global control of Escherichia coli carbohydrate uptake. BMC Syst Biol 1, 42. 15 Nishio Y, Usada Y, Matsui K & Kurata H (2008) Computer-aided rational design of the phosphotransfer- ase system for enhanced glucose uptake in Escherichia coli. Mol Sys Biol 4, 160. 16 Kremling A, Jahreis K, Lengeler JW & Gilles ED (2000) The organization of metabolic reaction networks: a signal-oriented approach to cellular models. Metab Eng 2, 190–200. 17 Kremling A & Gilles ED (2001) The organization of met- abolic reaction networks: II. Signal processing in hierar- chical structured functional units. Metab Eng 3, 138–150. 18 Bettenbrock K, Fischer S, Kremling A, Jahreis K, Sauter T & Gilles ED (2006) A quantitative approach 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 601 to catabolite repression in Escherichia coli. J Biol Chem 281, 2578–2584. 19 Kremling A, Bettenbrock K & Gilles ED (2008) A feed- forward loop guarantees robust behavior in Escherichia coli carbohydrate uptake. Bioinformatics 24, 704–710. 20 Kurata H, Masaki K, Sumida Y & Iwasaki R (2005) Cadlive dynamic simulator: direct link of biochemical networks to dynamic models. Genome Res 15, 590–600. 21 Hartwell LH, Hopfield JJ, Leibler S & Murray AW (1999) From molecular to modular cell biology. Nature 402 (Suppl.), C47–C52. 22 Hogema M, Arents JC, Bader R, Eijkemanns K, Yosh- ida H, Takahashi H, Aiba H & Postma PW (1998) Inducer exclusion in Escherichia coli by non-PTS sub- strates: the role of the PEP to pyruvate ratio in deter- mining the phosphorylation state of enzyme IIA Glc . Mol Microbiol 30, 487–498. 23 Bettenbrock K, Sauter T, Jahreis K, Kremling A, Leng- eler JW & Gilles ED (2007) Analysis of the correlation between growth rate, EIIA Crr (EIIA Glc ) phosphoryla- tion levels and intracellular cAMP levels in Escherichia coli K-12. J Bacteriol 189, 6891–6900. 24 Ginkel M, Kremling A, Nutsch T, Rehner R & Gilles ED (2003) Modular modeling of cellular systems with ProMoT ⁄ Diva. Bioinformatics 19, 1169–1176. 25 Van der Vlag J, Hof R, Van Dam K & Postma PW (1995) Control of glucose metabolism by the enzymes of the glucose phosphotransferase system in Salmonella typhimurium. Eur J Biochem 230, 170–182. 26 Kremling A (2008) Comparison of Two Mathematical Models for Carbohydrate Uptake of E. coli – Files to Simulate the Bettenbrock Model. Available at: http:// www.mpi-magdeburg.mpg.de/people/kre/ecoli_model/ nishio.htm. Modelling catabolite repression in E. coli A. Kremling et al. 602 FEBS Journal 276 (2009) 594–602 ª 2008 The Authors Journal compilation ª 2008 FEBS . Catabolite repression in Escherichia coli – a comparison of modelling approaches Andreas Kremling, Sophia Kremling and Katja Bettenbrock Systems. activates adenylate cyclase (CyaA) and leads to an increase in the intra- cellular cyclic AMP (cAMP) level [1]. Mathematical models of catabolite repression