The organization of metabolic reaction networks. III. Application for diauxic growth on glucose and lactose

Functional expansion of the natural inorganic phosphorus starvation response system in Escherichia coli

Phosphorus, an indispensable nutrient, plays an essential role in cell composition, metabolism, and signal transduction. When inorganic phosphorus (Pi) is scarce, the Pi starvation response in E. coli is activated to increase phosphorus acquisition and drive the cells into a non-growing state to reduce phosphorus consumption. In the six decades of research history, the initiation, output, and shutdown processes of the Pi starvation response have been extensively studied. Simultaneously, Pi starvation has been used in biosensor development, recombinant protein production, and natural product biosynthesis. In this review, we focus on the output process and the applications of the Pi starvation response that have not been summarized before. Meanwhile, based on the current status of mechanistic studies and applications, we propose practical strategies to develop the natural Pi starvation response into a multifunctional and standardized regulatory system in four aspects, including response threshold, temporal expression, intensity range, and bifunctional regulation, which will contribute to its broader application in more fields such as industrial production, medical analysis, and environmental protection.

Production of soluble regulatory hydrogenase from Ralstonia eutropha in Escherichia coli using a fed-batch-based autoinduction system

BACKGROUND

Autoinduction systems can regulate protein production in Escherichia coli without the need to monitor cell growth or add inducer at the proper time following culture growth. Compared to classical IPTG induction, autoinduction provides a simple and fast way to obtain high protein yields. In the present study, we report on the optimization process for the enhanced heterologous production of the Ralstonia eutropha regulatory hydrogenase (RH) in E. coli using autoinduction. These autoinduction methods were combined with the EnPresso B fed-batch like growth system, which applies slow in situ enzymatic glucose release from a polymer to control cell growth and protein synthesis rate.

RESULTS

We were able to produce 125 mg L-1 RH corresponding to a productivity averaged over the whole process time of 3 mg (L h)-1 in shake flasks using classic single-shot IPTG induction. IPTG autoinduction resulted in a comparable volumetric RH yield of 112 mg L-1 and due to the shorter overall process time in a 1.6-fold higher productivity of 5 mg (L h)-1. In contrast, lactose autoinduction increased the volumetric yield more than 2.5-fold and the space time yield fourfold reaching 280 mg L-1 and 11.5 mg (L h)-1, respectively. Furthermore, repeated addition of booster increased RH production to 370 mg L-1, which to our knowledge is the highest RH concentration produced in E. coli to date.

CONCLUSIONS

The findings of this study confirm the general feasibility of the developed fed-batch based autoinduction system and provide an alternative to conventional induction systems for efficient recombinant protein production. We believe that the fed-batch based autoinduction system developed herein will favor the heterologous production of larger quantities of difficult-to-express complex enzymes to enable economical production of these kinds of proteins.

Emergence of diauxie as an optimal growth strategy under resource allocation constraints in cellular metabolism

Diauxie, or the sequential consumption of carbohydrates in bacteria such as Escherichia coli, has been hypothesized to be an evolutionary strategy which allows the organism to maximize its instantaneous specific growth-giving the bacterium a competitive advantage. Currently, the computational techniques used in industrial biotechnology fall short of explaining the intracellular dynamics underlying diauxic behavior. In particular, the understanding of the proteome dynamics in diauxie can be improved. We developed a robust iterative dynamic method based on expression- and thermodynamically enabled flux models to simulate the kinetic evolution of carbohydrate consumption and cellular growth. With minimal modeling assumptions, we couple kinetic uptakes, gene expression, and metabolic networks, at the genome scale, to produce dynamic simulations of cell cultures. The method successfully predicts the preferential uptake of glucose over lactose in E. coli cultures grown on a mixture of carbohydrates, a manifestation of diauxie. The simulated cellular states also show the reprogramming in the content of the proteome in response to fluctuations in the availability of carbon sources, and it captures the associated time lag during the diauxie phenotype. Our models suggest that the diauxic behavior of cells is the result of the evolutionary objective of maximization of the specific growth of the cell. We propose that genetic regulatory networks, such as the lac operon in E. coli, are the biological implementation of a robust control system to ensure optimal growth.

Computer-Aided Rational Design of Efficient NADPH Production System by Escherichia coli pgi Mutant Using a Mixture of Glucose and Xylose

Lignocellulosic biomass can be hydrolyzed into two major sugars of glucose and xylose, and thus the strategy for the efficient consumption of both sugars is highly desirable. NADPH is the essential molecule for the production of industrially important value-added chemicals, and thus its availability is quite important. Escherichia coli mutant lacking the pgi gene encoding phosphoglucose isomerase (Pgi) has been preferentially used to overproduce the NADPH. However, there exists a disadvantage that the cell growth rate becomes low for the mutant grown on glucose. This limits the efficient NADPH production, and therefore, it is quite important to investigate how addition of different carbon source such as xylose (other than glucose) effectively improves the NADPH production. In this study, we have developed a kinetic model to propose an efficient NADPH production system using E. coli pgi-knockout mutant with a mixture of glucose and xylose. The proposed system adds xylose to glucose medium to recover the suppressed growth of the pgi mutant, and determines the xylose content to maximize the NADPH productivity. Finally, we have designed a mevalonate (MVA) production system by implementing ArcA overexpression into the pgi-knockout mutant using a mixture of glucose and xylose. In addition to NADPH overproduction, the accumulation of acetyl-CoA (AcCoA) is necessary for the efficient MVA production. In the present study, therefore, we considered to overexpress ArcA, where ArcA overexpression suppresses the TCA cycle, causing the overflow of AcCoA, a precursor of MVA. We predicted the xylose content that maximizes the MVA production. This approach demonstrates the possibility of a great progress in the computer-aided rational design of the microbial cell factories for useful metabolite production.

The Effects of Lactose Induction on a Plasmid-Free E. coli T7 Expression System

Recombinant production of pharmaceutical proteins like antigen binding fragments (Fabs) in the commonly-used production host Escherichia coli presents several challenges. The predominantly-used plasmid-based expression systems exhibit the drawback of either excessive plasmid amplification or plasmid loss over prolonged cultivations. To improve production, efforts are made to establish plasmid-free expression, ensuring more stable process conditions. Another strategy to stabilize production processes is lactose induction, leading to increased soluble product formation and cell fitness, as shown in several studies performed with plasmid-based expression systems. Within this study we wanted to investigate lactose induction for a strain with a genome-integrated gene of interest for the first time. We found unusually high specific lactose uptake rates, which we could attribute to the low levels of lac-repressor protein that is usually encoded not only on the genome but additionally on pET plasmids. We further show that these unusually high lactose uptake rates are toxic to the cells, leading to increased cell leakiness and lysis. Finally, we demonstrate that in contrast to plasmid-based T7 expression systems, IPTG induction is beneficial for genome-integrated T7 expression systems concerning cell fitness and productivity.

Impact of Glycerol as Carbon Source onto Specific Sugar and Inducer Uptake Rates and Inclusion Body Productivity in E. coli BL21(DE3)

The Gram-negative bacterium E. coli is the host of choice for a multitude of used recombinant proteins. Generally, cultivation is easy, media are cheap, and a high product titer can be obtained. However, harsh induction procedures using isopropyl β-d-1 thiogalactopyranoside as inducer are often referred to cause stress reactions, leading to a phenomenon known as "metabolic" or "product burden". These high expressions of recombinant proteins mainly result in decreased growth rates and cell lysis at elevated induction times. Therefore, approaches tend to use "soft" or "tunable" induction with lactose and reduce the stress level of the production host. The usage of glucose as energy source in combination with lactose as induction reagent causes catabolite repression effects on lactose uptake kinetics and as a consequence reduced product titer. Glycerol-as an alternative carbon source-is already known to have positive impact on product formation when coupled with glucose and lactose in auto-induction systems, and has been referred to show no signs of repression when cultivated with lactose concomitantly. In recent research activities, the impact of different products on the lactose uptake using glucose as carbon source was highlighted, and a mechanistic model for glucose-lactose induction systems showed correlations between specific substrate uptake rate for glucose or glycerol (qs,C) and the maximum specific lactose uptake rate (qs,lac,max). In this study, we investigated the mechanistic of glycerol uptake when using the inducer lactose. We were able to show that a product-producing strain has significantly higher inducer uptake rates when being compared to a non-producer strain. Additionally, it was shown that glycerol has beneficial effects on viability of cells and on productivity of the recombinant protein compared to glucose.

Modeling and simulation of the redox regulation of the metabolism in Escherichia coli at different oxygen concentrations

BACKGROUND

Microbial production of biofuels and biochemicals from renewable feedstocks has received considerable recent attention from environmental protection and energy production perspectives. Many biofuels and biochemicals are produced by fermentation under oxygen-limited conditions following initiation of aerobic cultivation to enhance the cell growth rate. Thus, it is of significant interest to investigate the effect of dissolved oxygen concentration on redox regulation in Escherichia coli, a particularly popular cellular factory due to its high growth rate and well-characterized physiology. For this, the systems biology approach such as modeling is powerful for the analysis of the metabolism and for the design of microbial cellular factories.

RESULTS

Here, we developed a kinetic model that describes the dynamics of fermentation by taking into account transcription factors such as ArcA/B and Fnr, respiratory chain reactions and fermentative pathways, and catabolite regulation. The hallmark of the kinetic model is its ability to predict the dynamics of metabolism at different dissolved oxygen levels and facilitate the rational design of cultivation methods. The kinetic model was verified based on the experimental data for a wild-type E. coli strain. The model reasonably predicted the metabolic characteristics and molecular mechanisms of fnr and arcA gene-knockout mutants. Moreover, an aerobic-microaerobic dual-phase cultivation method for lactate production in a pfl-knockout mutant exhibited promising yield and productivity.

CONCLUSIONS

It is quite important to understand metabolic regulation mechanisms from both scientific and engineering points of view. In particular, redox regulation in response to oxygen limitation is critically important in the practical production of biofuel and biochemical compounds. The developed model can thus be used as a platform for designing microbial factories to produce a variety of biofuels and biochemicals.

Bistability and Nonmonotonic Induction of the lac Operon in the Natural Lactose Uptake System

The Escherichia coli lac operon is regulated by a positive feedback loop whose potential to generate an all-or-none response in single cells has been a paradigm for bistable gene expression. However, so far bistable lac induction has only been observed using gratuitous inducers, raising the question about the biological relevance of bistable lac induction in the natural setting with lactose as the inducer. In fact, the existing experimental evidence points to a graded rather than an all-or-none response in the natural lactose uptake system. In contrast, predictions based on computational models of the lactose uptake pathway remain controversial. Although some argue in favor of bistability, others argue against it. Here, we reinvestigate lac operon expression in single cells using a combined experimental/modeling approach. To this end, we parameterize a well-supported mathematical model using transient measurements of LacZ activity upon induction with different amounts of lactose. The resulting model predicts a monostable induction curve for the wild-type system, but indicates that overexpression of the LacI repressor would drive the system into the bistable regime. Both predictions were confirmed experimentally supporting the view that the wild-type lac induction circuit generates a graded response rather than bistability. More interestingly, we find that the lac induction curve exhibits a pronounced maximum at intermediate lactose concentrations. Supported by our data, a model-based analysis suggests that the nonmonotonic response results from saturation of the LacI repressor at low inducer concentrations and dilution of Lac enzymes due to an increased growth rate beyond the saturation point. We speculate that the observed maximum in the lac expression level helps to save cellular resources by limiting Lac enzyme expression at high inducer concentrations.

MbT-Tool: An open-access tool based on Thermodynamic Electron Equivalents Model to obtain microbial-metabolic reactions to be used in biotechnological process

Modelling cellular metabolism is a strategic factor in investigating microbial behaviour and interactions, especially for bio-technological processes. A key factor for modelling microbial activity is the calculation of nutrient amounts and products generated as a result of the microbial metabolism. Representing metabolic pathways through balanced reactions is a complex and time-consuming task for biologists, ecologists, modellers and engineers. A new computational tool to represent microbial pathways through microbial metabolic reactions (MMRs) using the approach of the Thermodynamic Electron Equivalents Model has been designed and implemented in the open-access framework NetLogo. This computational tool, called MbT-Tool (Metabolism based on Thermodynamics) can write MMRs for different microbial functional groups, such as aerobic heterotrophs, nitrifiers, denitrifiers, methanogens, sulphate reducers, sulphide oxidizers and fermenters. The MbT-Tool's code contains eighteen organic and twenty inorganic reduction-half-reactions, four N-sources (NH4 (+), NO3 (-), NO2 (-), N2) to biomass synthesis and twenty-four microbial empirical formulas, one of which can be determined by the user (CnHaObNc). MbT-Tool is an open-source program capable of writing MMRs based on thermodynamic concepts, which are applicable in a wide range of academic research interested in designing, optimizing and modelling microbial activity without any extensive chemical, microbiological and programing experience.

PTS 50: Past, Present and Future, or Diauxie Revisited

<b><i>Past:</i></b> The title ‘PTS 50 or The PTS after 50 years' relies on the first description in 1964 of the phosphoenolpyruvate-dependent carbohydrate:phosphotransferase system (PTS) by Kundig, Gosh and Roseman [Proc Natl Acad Sci USA 1964;52:1067-1074]. The system comprised proteins named Enzyme I, HPr and Enzymes II, as part of a novel PTS for carbohydrates in Gram-negative and Gram-positive bacteria, whose ‘biological significance remained unclear'. In contrast, studies which would eventually lead to the discovery of the central role of the PTS in bacterial metabolism had been published since before 1942. They are primarily linked to names like Epps and Gale, J. Monod, Cohn and Horibata, and B. Magasanik, and to phenomena like ‘glucose effects', ‘diauxie', ‘catabolite repression' and carbohydrate transport. <b><i>Present:</i></b> The pioneering work from Roseman's group initiated a flood of publications. The extraordinary progress from 1964 to this day in the qualitative and in vitro description of the genes and enzymes of the PTS, and of its multiple roles in global cellular control through ‘inducer exclusion', gene induction and ‘catabolite repression', in cellular growth, in cell differentiation and in chemotaxis, as well as the differences of its functions between Gram-positive and Gram-negative bacteria, was one theme of the meeting and will not be treated in detail here. <b><i>Future:</i></b> At the 1988 Paris meeting entitled ‘The PTS after 25 years', Saul Roseman predicted that ‘we must describe these interactions [of the PTS components] in a quantitative way [under] in vivo conditions'. I will present some results obtained by our group during recent years on the old phenomenon of diauxie by means of very fast and quantitative tests, measured in vivo, and obtained from cultures of isogenic mutant strains growing under chemostat conditions. The results begin to hint at the problems relating to future PTS research, but also to the ‘true science' of Roseman.

An integrative top-down and bottom-up qualitative model construction framework for exploration of biochemical systems

Computational modelling of biochemical systems based on top-down and bottom-up approaches has been well studied over the last decade. In this research, after illustrating how to generate atomic components by a set of given reactants and two user pre-defined component patterns, we propose an integrative top-down and bottom-up modelling approach for stepwise qualitative exploration of interactions among reactants in biochemical systems. Evolution strategy is applied to the top-down modelling approach to compose models, and simulated annealing is employed in the bottom-up modelling approach to explore potential interactions based on models constructed from the top-down modelling process. Both the top-down and bottom-up approaches support stepwise modular addition or subtraction for the model evolution. Experimental results indicate that our modelling approach is feasible to learn the relationships among biochemical reactants qualitatively. In addition, hidden reactants of the target biochemical system can be obtained by generating complex reactants in corresponding composed models. Moreover, qualitatively learned models with inferred reactants and alternative topologies can be used for further web-lab experimental investigations by biologists of interest, which may result in a better understanding of the system.

Understanding carbon catabolite repression in Escherichia coli using quantitative models

Carbon catabolite repression (CCR) controls the order in which different carbon sources are metabolized. Although this system is one of the paradigms of the regulation of gene expression in bacteria, the underlying mechanisms remain controversial. CCR involves the coordination of different subsystems of the cell that are responsible for the uptake of carbon sources, their breakdown for the production of energy and precursors, and the conversion of the latter to biomass. The complexity of this integrated system, with regulatory mechanisms cutting across metabolism, gene expression, and signaling, and that are subject to global physical and physiological constraints, has motivated important modeling efforts over the past four decades, especially in the enterobacterium Escherichia coli. Different hypotheses concerning the dynamic functioning of the system have been explored by a variety of modeling approaches. We review these studies and summarize their contributions to the quantitative understanding of CCR, focusing on diauxic growth in E. coli. Moreover, we propose a highly simplified representation of diauxic growth that makes it possible to bring out the salient features of the models proposed in the literature and confront and compare the explanations they provide.

Glycolysis is governed by growth regime and simple enzyme regulation in adherent MDCK cells

Due to its vital importance in the supply of cellular pathways with energy and precursors, glycolysis has been studied for several decades regarding its capacity and regulation. For a systems-level understanding of the Madin-Darby canine kidney (MDCK) cell metabolism, we couple a segregated cell growth model published earlier with a structured model of glycolysis, which is based on relatively simple kinetics for enzymatic reactions of glycolysis, to explain the pathway dynamics under various cultivation conditions. The structured model takes into account in vitro enzyme activities, and links glycolysis with pentose phosphate pathway and glycogenesis. Using a single parameterization, metabolite pool dynamics during cell cultivation, glucose limitation and glucose pulse experiments can be consistently reproduced by considering the cultivation history of the cells. Growth phase-dependent glucose uptake together with cell-specific volume changes generate high intracellular metabolite pools and flux rates to satisfy the cellular demand during growth. Under glucose limitation, the coordinated control of glycolytic enzymes re-adjusts the glycolytic flux to prevent the depletion of glycolytic intermediates. Finally, the model's predictive power supports the design of more efficient bioprocesses.

Glycolysis generates biomass precursors and energy from sugars and is therefore a key element in the metabolism of mammalian cells. Changes in its activity greatly affect cellular function which is often recognized as metabolic disease but also as opportunity for the design of efficient bioprocesses. Metabolic research discovered that continuously growing mammalian cells often exhibit a high glycolytic activity but also delivered seemingly endless facets in the pathway operation. The latter call for a systems-level understanding regarding capacity and regulation for a broad range of cultivation conditions. In this work, we couple a cell growth model to a simple kinetic description of glycolysis to consistently explain intracellular metabolite pool dynamics of the Madin-Darby canine kidney cell line over a variety of experiments and time scales while considering the growth status and cultivation history of the cells. We argue that the many different dynamics in glycolysis result from an interplay between a growth-dependent sugar uptake together with simple intrinsic enzyme regulation.

Single-cell dynamics reveals sustained growth during diauxic shifts

Stochasticity in gene regulation has been characterized extensively, but how it affects cellular growth and fitness is less clear. We study the growth of E. coli cells as they shift from glucose to lactose metabolism, which is characterized by an obligatory growth arrest in bulk experiments that is termed the lag phase. Here, we follow the growth dynamics of individual cells at minute-resolution using a single-cell assay in a microfluidic device during this shift, while also monitoring lac expression. Mirroring the bulk results, the majority of cells displays a growth arrest upon glucose exhaustion, and resume when triggered by stochastic lac expression events. However, a significant fraction of cells maintains a high rate of elongation and displays no detectable growth lag during the shift. This ability to suppress the growth lag should provide important selective advantages when nutrients are scarce. Trajectories of individual cells display a highly non-linear relation between lac expression and growth, with only a fraction of fully induced levels being sufficient for achieving near maximal growth. A stochastic molecular model together with measured dependencies between nutrient concentration, lac expression level, and growth accurately reproduces the observed switching distributions. The results show that a growth arrest is not obligatory in the classic diauxic shift, and underscore that regulatory stochasticity ought to be considered in terms of its impact on growth and survival.

Bioprocess systems engineering: transferring traditional process engineering principles to industrial biotechnology

The complexity of the regulatory network and the interactions that occur in the intracellular environment of microorganisms highlight the importance in developing tractable mechanistic models of cellular functions and systematic approaches for modelling biological systems. To this end, the existing process systems engineering approaches can serve as a vehicle for understanding, integrating and designing biological systems and processes. Here, we review the application of a holistic approach for the development of mathematical models of biological systems, from the initial conception of the model to its final application in model-based control and optimisation. We also discuss the use of mechanistic models that account for gene regulation, in an attempt to advance the empirical expressions traditionally used to describe micro-organism growth kinetics, and we highlight current and future challenges in mathematical biology. The modelling research framework discussed herein could prove beneficial for the design of optimal bioprocesses, employing rational and feasible approaches towards the efficient production of chemicals and pharmaceuticals.

The phosphoenolpyruvate-dependent glucose-phosphotransferase system from Escherichia coli K-12 as the center of a network regulating carbohydrate flux in the cell

The phosphoenolpyruvate-(PEP)-dependent-carbohydrate:phosphotransferase systems (PTSs) of enteric bacteria constitute a complex transport and sensory system. Such a PTS usually consists of two cytoplasmic energy-coupling proteins, Enzyme I (EI) and HPr, and one of more than 20 different carbohydrate-specific membrane proteins named Enzyme II (EII), which catalyze the uptake and concomitant phosphorylation of numerous carbohydrates. The most prominent representative is the glucose-PTS, which uses a PTS-typical phosphorylation cascade to transport and phosphorylate glucose. All components of the glucose-PTS interact with a large number of non-PTS proteins to regulate the carbohydrate flux in the bacterial cell. Several aspects of the glucose-PTS have been intensively investigated in various research projects of many groups. In this article we will review our recent findings on a Glc-PTS-dependent metalloprotease, on the interaction of EIICB(Glc) with the regulatory peptide SgrT, on the structure of the membrane spanning C-domain of the glucose transporter and on the modeling approaches of ptsG regulation, respectively, and discuss them in context of general PTS research.

Elementary network reconstruction: a framework for the analysis of regulatory networks in biological systems

Complexity of regulatory networks arises from the high degree of interaction between network components such as DNA, RNA, proteins, and metabolites. We have developed a modeling tool, elementary network reconstruction (ENR), to characterize these networks. ENR is a knowledge-driven, steady state, deterministic, quantitative modeling approach based on linear perturbation theory. In ENR we demonstrate a novel means of expressing control mechanisms by way of dimensionless steady state gains relating input and output variables, which are purely in terms of species abundances (extensive variables). As a result of systematic enumeration of network species in nxn matrix, the two properties of linear perturbation are manifested in graphical representations: transitive property is evident in a special L-shape structure, and additive property is evident in multiple L-shape structures arriving at the same matrix cell. Upon imposing mechanistic (lowest-level) gains, network self-assembly through transitive and additive properties results in elucidation of inherent topology and explicit cataloging of higher level gains, which in turn can be used to predict perturbation results. Application of ENR to the regulatory network behind carbon catabolite repression in Escherichia coli is presented. Through incorporation of known molecular mechanisms governing transient and permanent repressions, the ENR model correctly predicts several key features of this regulatory network, including a 50% downshift in intracellular cAMP level upon exposure to glucose. Since functional genomics studies are mainly concerned with redistribution of species abundances in perturbed systems, ENR could be exploited in the system-level analysis of biological systems.

Regelung – Schlüssel zum Verständnis biologischer Systeme (Control – Key to Better Understanding Biological Systems)

Zellen verfügen über sehr leistungsfähige und hierarchisch strukturierte Regulationen, um ihren Stoffwechsel zu kontrollieren und den Umgebungsbedingungen anzupassen. Erst diese Regulationen bringen Ordnung in ein potentielles Chaos von tausenden individueller Reaktionen, die in einer Zelle ablaufen. Will man die Wirkungsweise dieser Regulationen und ihre wechselseitigen Beeinflussungen verstehen, so ist eine molekularbiologisch orientierte mathematische Modellierung zellulärer Funktionseinheiten nicht nur hilfreich sondern geboten. Dabei erweist sich ein Modellierungskonzept als sehr nützlich, das auf einer Verschaltung elementarer Modellbausteine basiert, die elementaren molekularbiologischen Zellbausteinen zugeordnet sind. Die dadurch erreichte biologische Transparenz erleichtert die interdisziplinäre Kooperation zwischen Biologie und Systemwissenschaften, der im Hinblick auf eine Aufklärung der Regulationsvorgänge eine entscheidende Bedeutung zukommt. An zwei typischen zellulären Funktionseinheiten, nämlich der Kataboliten-Repression in Escherichia coli und dem Zellzyklus in Saccharomyces cerevisiae wird die überragende Bedeutung, die der Regelung in zellulären biologischen Systemen zukommt, verdeutlicht. Dabei zeigt sich, dass die Regulationen im allgemeinen hierarchisch strukturiert sind und dadurch eine hohe Effizienz aufweisen. Es liegt nahe, aus den Erkenntnissen Anregungen für die Strukturierung von Regelungen für komplexe technische Prozesse zu ziehen.

On the accessibility of adaptive phenotypes of a bacterial metabolic network

The mechanisms by which adaptive phenotypes spread within an evolving population after their emergence are understood fairly well. Much less is known about the factors that influence the evolutionary accessibility of such phenotypes, a pre-requisite for their emergence in a population. Here, we investigate the influence of environmental quality on the accessibility of adaptive phenotypes of Escherichia coli's central metabolic network. We used an established flux-balance model of metabolism as the basis for a genotype-phenotype map (GPM). We quantified the effects of seven qualitatively different environments (corresponding to both carbohydrate and gluconeogenic metabolic substrates) on the structure of this GPM. We found that the GPM has a more rugged structure in qualitatively poorer environments, suggesting that adaptive phenotypes could be intrinsically less accessible in such environments. Nevertheless, on average ∼74% of the genotype can be altered by neutral drift, in the environment where the GPM is most rugged; this could allow evolving populations to circumvent such ruggedness. Furthermore, we found that the normalized mutual information (NMI) of genotype differences relative to phenotype differences, which measures the GPM's capacity to transmit information about phenotype differences, is positively correlated with (simulation-based) estimates of the accessibility of adaptive phenotypes in different environments. These results are consistent with the predictions of a simple analytic theory that makes explicit the relationship between the NMI and the speed of adaptation. The results suggest an intuitive information-theoretic principle for evolutionary adaptation; adaptation could be faster in environments where the GPM has a greater capacity to transmit information about phenotype differences. More generally, our results provide insight into fundamental environment-specific differences in the accessibility of adaptive phenotypes, and they suggest opportunities for research at the interface between information theory and evolutionary biology.

Adaptation involves the discovery by mutation and spread through populations of traits (or “phenotypes”) that have high fitness under prevailing environmental conditions. While the spread of adaptive phenotypes through populations is mediated by natural selection, the likelihood of their discovery by mutation depends primarily on the relationship between genetic information and phenotypes (the genotype-phenotype mapping, or GPM). Elucidating the factors that influence the structure of the GPM is therefore critical to understanding the adaptation process. We investigated the influence of environmental quality on GPM structure for a well-studied model of Escherichia coli's metabolism. Our results suggest that the GPM is more rugged in qualitatively poorer environments and, therefore, the discovery of adaptive phenotypes may be intrinsically less likely in such environments. Nevertheless, we found that the GPM contains large neutral networks in all studied environments, suggesting that populations adapting to these environments could circumvent the frequent “hill descents” that would otherwise be required by a rugged GPM. Moreover, we demonstrated that adaptation proceeds faster in environments for which the GPM transmits information about phenotype differences more efficiently, providing a connection between information theory and evolutionary theory. These results have implications for understanding constraints on adaptation in nature.

Gene regulation in continuous cultures: a unified theory for bacteria and yeasts

During batch growth on mixtures of two growth-limiting substrates, microbes consume the substrates either sequentially (diauxie) or simultaneously. The ubiquity of these growth patterns suggests that they may be driven by a universal mechanism common to all microbial species. Recently, we showed that a minimal model accounting only for enzyme induction and dilution, the two processes that occur in all microbes, explains the phenotypes observed in batch cultures of various wild-type and mutant/recombinant cells (Narang and Pilyugin in J. Theor. Biol. 244:326-348, 2007). Here, we examine the extension of the minimal model to continuous cultures. We show that: (1) Several enzymatic trends, attributed entirely to cross-regulatory mechanisms, such as catabolite repression and inducer exclusion, can be quantitatively explained by enzyme dilution. (2) The bifurcation diagram of the minimal model for continuous cultures, which classifies the substrate consumption pattern at any given dilution rate and feed concentrations, provides a precise explanation for the empirically observed correlations between the growth patterns in batch and continuous cultures. (3) Numerical simulations of the model are in excellent agreement with the data. The model captures the variation of the steady state substrate concentrations, cell densities, and enzyme levels during the single- and mixed-substrate growth of bacteria and yeasts at various dilution rates and feed concentrations. This variation is well approximated by simple analytical expressions that furnish deep physical insights. (4) Since the minimal model describes the behavior of the cells in the absence of cross-regulatory mechanisms, it provides a rigorous framework for quantifying the effect of these mechanisms. We illustrate this by analyzing several data sets from the literature.

Ins and outs of glucose transport systems in eubacteria

Glucose is the classical carbon source that is used to investigate the transport, metabolism, and regulation of nutrients in bacteria. Many physiological phenomena like nutrient limitation, stress responses, production of antibiotics, and differentiation are inextricably linked to nutrition. Over the years glucose transport systems have been characterized at the molecular level in more than 20 bacterial species. This review aims to provide an overview of glucose uptake systems found in the eubacterial kingdom. In addition, it will highlight the diverse and sophisticated regulatory features of glucose transport systems.

Effect of weight-added regulatory networks on constraint-based metabolic models of Escherichia coli

Though the traditional flux balance analysis (FBA) has successfully predicted intracellular fluxes using stoichiometry, linear programming, and metabolic pathways, it has not automatically reflected any potential genetic effects in response to the environmental changes in the metabolic pathways. Recently, attempts have been made to impose regulatory constraints described as a binary system, such as if-then rules using Boolean logic, on the traditional FBA. Yet this binary system has limited the representation of complex interactions between transcriptional factors and target genes. In addition, it is difficult to intuitively or visually recognize changes to the interactions among stimuli, sensors/regulatory proteins, and target genes due to the properties of the if-then rule systems. Thus, in the current work, in order to improve upon the previous approaches, we have (1) determined weight values after deducing from the inequality signs of the relative strengths of interactions between sensors/regulators and target genes based on the experimental data of gene expression, (2) divided expression level into eight levels, and (3) constructed and incorporated weight-added regulatory networks using the defined symbols within the FBA. Finally, a model system with the central metabolic pathway of Escherichia coli was examined under the aerobic batch culture with glucose and acetate reutilization and the aerobic and anaerobic batch culture with glucose only to demonstrate our suggested approach.

Correlation between growth rates, EIIACrr phosphorylation, and intracellular cyclic AMP levels in Escherichia coli K-12

In Escherichia coli K-12, components of the phosphoenolpyruvate-dependent phosphotransferase systems (PTSs) represent a signal transduction system involved in the global control of carbon catabolism through inducer exclusion mediated by phosphoenolpyruvate-dependent protein kinase enzyme IIA(Crr) (EIIA(Crr)) (= EIIA(Glc)) and catabolite repression mediated by the global regulator cyclic AMP (cAMP)-cAMP receptor protein (CRP). We measured in a systematic way the relation between cellular growth rates and the key parameters of catabolite repression, i.e., the phosphorylated EIIA(Crr) (EIIA(Crr) approximately P) level and the cAMP level, using in vitro and in vivo assays. Different growth rates were obtained by using either various carbon sources or by growing the cells with limited concentrations of glucose, sucrose, and mannitol in continuous bioreactor experiments. The ratio of EIIA(Crr) to EIIA(Crr) approximately P and the intracellular cAMP concentrations, deduced from the activity of a cAMP-CRP-dependent promoter, correlated well with specific growth rates between 0.3 h(-1) and 0.7 h(-1), corresponding to generation times of about 138 and 60 min, respectively. Below and above this range, these parameters were increasingly uncoupled from the growth rate, which perhaps indicates an increasing role executed by other global control systems, in particular the stringent-relaxed response system.

Analysis of global control of Escherichia coli carbohydrate uptake

Background

Global control influences the regulation of many individual subsystems by superimposed regulator proteins. A prominent example is the control of carbohydrate uptake systems by the transcription factor Crp in Escherichia coli. A detailed understanding of the coordination of the control of individual transporters offers possibilities to explore the potential of microorganisms e.g. in biotechnology.

Results

An o.d.e. based mathematical model is presented that maps a physiological parameter – the specific growth rate – to the sensor of the signal transduction unit, here a component of the bacterial phosphotransferase system (PTS), namely EIIA^Crr. The model describes the relation between the growth rate and the degree of phosphorylation of EIIA ^crr for a number of carbohydrates by a distinctive response curve, that differentiates between PTS transported carbohydrates and non-PTS carbohydrates. With only a small number of kinetic parameters, the model is able to describe a broad range of experimental steady-state and dynamical conditions.

Conclusion

The steady-state characteristic presented shows a relationship between the growth rate and the output of the sensor system PTS. The glycolytic flux that is measured by this sensor is a good indicator to represent the nutritional status of the cell.

Introduction to systems biology

The developments in the molecular biosciences have made possible a shift to combined molecular and system-level approaches to biological research under the name of Systems Biology. It integrates many types of molecular knowledge, which can best be achieved by the synergistic use of models and experimental data. Many different types of modeling approaches are useful depending on the amount and quality of the molecular data available and the purpose of the model. Analysis of such models and the structure of molecular networks have led to the discovery of principles of cell functioning overarching single species. Two main approaches of systems biology can be distinguished. Top-down systems biology is a method to characterize cells using system-wide data originating from the Omics in combination with modeling. Those models are often phenomenological but serve to discover new insights into the molecular network under study. Bottom-up systems biology does not start with data but with a detailed model of a molecular network on the basis of its molecular properties. In this approach, molecular networks can be quantitatively studied leading to predictive models that can be applied in drug design and optimization of product formation in bioengineering. In this chapter we introduce analysis of molecular network by use of models, the two approaches to systems biology, and we shall discuss a number of examples of recent successes in systems biology.

Environmental selection of the feed-forward loop circuit in gene-regulation networks

Gene-regulation networks contain recurring elementary circuits termed network motifs. It is of interest to understand under which environmental conditions each motif might be selected. To address this, we study one of the most significant network motifs, a three-gene circuit called the coherent feed-forward loop (FFL). The FFL has been demonstrated theoretically and experimentally to perform a basic information-processing function: it shows a delay following ON steps of an input inducer, but not after OFF steps. Here, we ask under what environmental conditions might the FFL be selected over simpler gene circuits, based on this function. We employ a theoretical cost-benefit analysis for the selection of gene circuits in a given environment. We find conditions that the environment must satisfy in order for the FFL to be selected over simpler circuits: the FFL is selected in environments where the distribution of the input pulse duration is sufficiently broad and contains both long and short pulses. Optimal values of the biochemical parameters of the FFL circuit are determined as a function of the environment such that the delay in the FFL blocks deleterious short pulses of induction. This approach can be generally used to study the evolutionary selection of other network motifs.

How phosphotransferase system-related protein phosphorylation regulates carbohydrate metabolism in bacteria

The phosphoenolpyruvate(PEP):carbohydrate phosphotransferase system (PTS) is found only in bacteria, where it catalyzes the transport and phosphorylation of numerous monosaccharides, disaccharides, amino sugars, polyols, and other sugar derivatives. To carry out its catalytic function in sugar transport and phosphorylation, the PTS uses PEP as an energy source and phosphoryl donor. The phosphoryl group of PEP is usually transferred via four distinct proteins (domains) to the transported sugar bound to the respective membrane component(s) (EIIC and EIID) of the PTS. The organization of the PTS as a four-step phosphoryl transfer system, in which all P derivatives exhibit similar energy (phosphorylation occurs at histidyl or cysteyl residues), is surprising, as a single protein (or domain) coupling energy transfer and sugar phosphorylation would be sufficient for PTS function. A possible explanation for the complexity of the PTS was provided by the discovery that the PTS also carries out numerous regulatory functions. Depending on their phosphorylation state, the four proteins (domains) forming the PTS phosphorylation cascade (EI, HPr, EIIA, and EIIB) can phosphorylate or interact with numerous non-PTS proteins and thereby regulate their activity. In addition, in certain bacteria, one of the PTS components (HPr) is phosphorylated by ATP at a seryl residue, which increases the complexity of PTS-mediated regulation. In this review, we try to summarize the known protein phosphorylation-related regulatory functions of the PTS. As we shall see, the PTS regulation network not only controls carbohydrate uptake and metabolism but also interferes with the utilization of nitrogen and phosphorus and the virulence of certain pathogens.

The nature of systems biology

The advent of functional genomics has enabled the molecular biosciences to come a long way towards characterizing the molecular constituents of life. Yet, the challenge for biology overall is to understand how organisms function. By discovering how function arises in dynamic interactions, systems biology addresses the missing links between molecules and physiology. Top-down systems biology identifies molecular interaction networks on the basis of correlated molecular behavior observed in genome-wide "omics" studies. Bottom-up systems biology examines the mechanisms through which functional properties arise in the interactions of known components. Here, we outline the challenges faced by systems biology and discuss limitations of the top-down and bottom-up approaches, which, despite these limitations, have already led to the discovery of mechanisms and principles that underlie cell function.

Bacterial gene regulation in diauxic and non-diauxic growth

When bacteria are grown in a batch culture containing a mixture of two growth-limiting substrates, they exhibit a rich spectrum of substrate consumption patterns including diauxic growth, simultaneous consumption, and bistable growth. In previous work, we showed that a minimal model accounting only for enzyme induction and dilution captures all the substrate consumption patterns [Narang, A., 1998a. The dynamical analogy between microbial growth on mixtures of substrates and population growth of competing species. Biotechnol. Bioeng. 59, 116-121, Narang, A., 2006. Comparitive analysis of some models of gene regulation in mixed-substrate microbial growth, J. Theor. Biol. 242, 489-501]. In this work, we construct the bifurcation diagram of the minimal model, which shows the substrate consumption pattern at any given set of parameter values. The bifurcation diagram explains several general properties of mixed-substrate growth. (1) In almost all the cases of diauxic growth, the "preferred" substrate is the one that, by itself, supports a higher specific growth rate. In the literature, this property is often attributed to the optimality of regulatory mechanisms. Here, we show that the minimal model, which accounts for induction and growth only, displays the property under fairly general conditions. This suggests that the higher growth rate of the preferred substrate is an intrinsic property of the induction and dilution kinetics. It can be explained mechanistically without appealing to optimality principles. (2) The model explains the phenotypes of various mutants containing lesions in the regions encoding for the operator, repressor, and peripheral enzymes. A particularly striking phenotype is the "reversal of the diauxie" in which the wild-type and mutant strains consume the very same two substrates in opposite order. This phenotype is difficult to explain in terms of molecular mechanisms, such as inducer exclusion or CAP activation, but it turns out to be a natural consequence of the model. We show furthermore that the model is robust. The key property of the model, namely, the competitive dynamics of the enzymes, is preserved even if the model is modified to account for various regulatory mechanisms. Finally, the model has important implications for the problem of size regulation in development. It suggests that protein dilution may be the mechanism coupling patterning and growth.

Finding one of a kind: advances in single-protein production

An ultimate goal for any protein production system is to express only the protein of interest without producing other cellular proteins. To date, there are only two established methods that will allow the successful expression of only the protein of interest: the cell-free in vitro protein synthesis system and the in vivo single-protein production (SPP) system. Although single-protein production can be achieved in cell-free systems, it is not easy to completely suppress the production of cellular proteins during the production of a protein of interest in a living cell. However, the finding of a unique sequence-specific mRNA interferase in Escherichia coli led to the development of the SPP system by converting living cells into a bioreactor that produces only a single protein of interest without producing any cellular proteins. This technology not only provides a new high expression system for proteins, but also offers a novel avenue for protein structural studies.

Exploiting the bootstrap method for quantifying parameter confidence intervals in dynamical systems

A quantitative description of dynamical systems requires the estimation of uncertain kinetic parameters and an analysis of their precision. A method frequently used to describe the confidence intervals of estimated parameters is based on the Fisher-Information-Matrix. The application of this traditional method has two important shortcomings: (i) it gives only lower bounds for the variance of a parameter if the solution of the underlying model equations is non-linear in parameters. (ii) The resulting confidence interval is symmetric with respect to the estimated parameter. Here, we show that by applying the bootstrap method a better approximation of (possibly) asymmetric confidence intervals for parameters could be obtained. In contrast to previous applications devoted to non-parametric problems, a dynamical model describing a bio-chemical network is used to evaluate the method.

Qualitative simulation of the carbon starvation response in Escherichia coli

In case of nutritional stress, like carbon starvation, Escherichia coli cells abandon their exponential-growth state to enter a more resistant, non-growth state called stationary phase. This growth-phase transition is controlled by a genetic regulatory network integrating various environmental signals. Although E. coli is a paradigm of the bacterial world, it is little understood how its response to carbon starvation conditions emerges from the interactions between the different components of the regulatory network. Using a qualitative method that is able to overcome the current lack of quantitative data on kinetic parameters and molecular concentrations, we model the carbon starvation response network and simulate the response of E. coli cells to carbon deprivation. This allows us to identify essential features of the transition between exponential and stationary phase and to make new predictions on the qualitative system behavior following a carbon upshift.

Comparative analysis of some models of gene regulation in mixed-substrate microbial growth

Mixed-substrate microbial growth is of fundamental interest in microbiology and bioengineering. Several mathematical models have been developed to account for the genetic regulation of such systems, especially those resulting in diauxic growth. In this work, we compare the dynamics of three such models (Narang, 1998a. The dynamical analogy between microbial growth on mixtures of substrates and population growth of competing species. Biotechnol. Bioeng. 59, 116-121; Thattai and Shraiman, 2003. Metabolic switching in the sugar phosphotransferase system of Escherichia coli. Biophys. J. 85(2), 744-754; Brandt et al., 2004. Modelling microbial adaptation to changing availability of substrates. Water Res. 38, 1004-1013). We show that these models are dynamically similar--the initial motion of the inducible enzymes in all the models is described by the Lotka-Volterra equations for competing species. In particular, the prediction of diauxic growth corresponds to "extinction" of one of the enzymes during the first few hours of growth. The dynamic similarity occurs because in all the models, the inducible enzymes possess properties characteristic of competing species: they are required for their own synthesis, and they inhibit each other. Despite this dynamic similarity, the models vary with respect to the range of dynamics captured. The Brandt et al. model always predicts the diauxic growth pattern, whereas the remaining two models exhibit both diauxic and non-diauxic growth patterns. The models also differ with respect to the mechanisms that generate the mutual inhibition between the enzymes. In the Narang model, mutual inhibition occurs because the enzymes for each substrate enhance the dilution of the enzymes for the other substrate. The Brandt et al. model superimposes upon this dilution effect an additional mechanism of mutual inhibition. In the Thattai and Shraiman model, the mutual inhibition is entirely due to competition for the phosphoryl groups. For quantitative agreement with the data, all models must be modified to account for specific mechanisms of mutual inhibition, such as inducer exclusion.

Plasticity of the cis-regulatory input function of a gene

The transcription rate of a gene is often controlled by several regulators that bind specific sites in the gene's cis-regulatory region. The combined effect of these regulators is described by a cis-regulatory input function. What determines the form of an input function, and how variable is it with respect to mutations? To address this, we employ the well-characterized lac operon of Escherichia coli, which has an elaborate input function, intermediate between Boolean AND-gate and OR-gate logic. We mapped in detail the input function of 12 variants of the lac promoter, each with different point mutations in the regulator binding sites, by means of accurate expression measurements from living cells. We find that even a few mutations can significantly change the input function, resulting in functions that resemble Pure AND gates, OR gates, or single-input switches. Other types of gates were not found. The variant input functions can be described in a unified manner by a mathematical model. The model also lets us predict which functions cannot be reached by point mutations. The input function that we studied thus appears to be plastic, in the sense that many of the mutations do not ruin the regulation completely but rather result in new ways to integrate the inputs.

A few point mutations in the lac operon of Escherichia coli are sufficient to change the nature of the transcriptional computation.

A quantitative approach to catabolite repression in Escherichia coli

A dynamic mathematical model was developed to describe the uptake of various carbohydrates (glucose, lactose, glycerol, sucrose, and galactose) in Escherichia coli. For validation a number of isogenic strains with defined mutations were used. By considering metabolic reactions as well as signal transduction processes influencing the relevant pathways, we were able to describe quantitatively the phenomenon of catabolite repression in E. coli. We verified model predictions by measuring time courses of several extra- and intracellular components such as glycolytic intermediates, EII-ACrr phosphorylation level, both LacZ and PtsG concentrations, and total cAMP concentrations under various growth conditions. The entire data base consists of 18 experiments performed with nine different strains. The model describes the expression of 17 key enzymes, 38 enzymatic reactions, and the dynamic behavior of more than 50 metabolites. The different phenomena affecting the phosphorylation level of EIIACrr, the key regulation molecule for inducer exclusion and catabolite repression in enteric bacteria, can now be explained quantitatively.

Optimality and evolutionary tuning of the expression level of a protein

Different proteins have different expression levels. It is unclear to what extent these expression levels are optimized to their environment. Evolutionary theories suggest that protein expression levels maximize fitness, but the fitness as a function of protein level has seldom been directly measured. To address this, we studied the lac system of Escherichia coli, which allows the cell to use the sugar lactose for growth. We experimentally measured the growth burden due to production and maintenance of the Lac proteins (cost), as well as the growth advantage (benefit) conferred by the Lac proteins when lactose is present. The fitness function, given by the difference between the benefit and the cost, predicts that for each lactose environment there exists an optimal Lac expression level that maximizes growth rate. We then performed serial dilution evolution experiments at different lactose concentrations. In a few hundred generations, cells evolved to reach the predicted optimal expression levels. Thus, protein expression from the lac operon seems to be a solution of a cost-benefit optimization problem, and can be rapidly tuned by evolution to function optimally in new environments.

Auto-induction medium for the production of [U-15N]- and [U-13C, U-15N]-labeled proteins for NMR screening and structure determination

Protocols have been developed and applied for the high-throughput production of [U-15N]- or [U-13C-, U-15N]-labeled proteins using the conditional methionine auxotroph Escherichia coli B834. The large-scale growth and expression uses a chemically defined auto-induction medium containing salts and trace metals, vitamins including vitamin B12, and glucose, glycerol, and lactose. The results from nine expression trials in 2-L of the auto-induction medium (500 mL in each of four polyethylene terephthalate beverage bottles) gave an average final optical density at 600 nm of approximately 5, an average wet cell mass yield of approximately 9.5 g L(-1), and an average yield of approximately 20 mg of labeled protein in the six instances in which proteolysis of the fusion protein was observed. Correlations between the cell mass recovered, the level of protein expression, and the relative amounts of glucose, glycerol, and lactose in the auto-induction medium were noted. Mass spectral analysis showed that the purified proteins contained both 15N and 13C at levels greater than 95%. 1H-15N heteronuclear single quantum correlation spectroscopy as well as 13C; 15N-edited spectroscopy showed that the purified [U-15N]- and [U-13C, U-15N]-labeled proteins were suitable for structure analysis.

Analysis of two-component signal transduction by mathematical modeling using the KdpD/KdpE system of Escherichia coli

A mathematical model for the KdpD/KdpE two-component system is presented and its dynamical behavior is analyzed. KdpD and KdpE regulate expression of the kdpFABC operon encoding the high affinity K+ uptake system KdpFABC of Escherichia coli. The model is validated in a two step procedure: (i) the elements of the signal transduction part are reconstructed in vitro. Experiments with the purified sensor kinase and response regulator in presence or absence of DNA fragments comprising the response regulator binding-site are performed. (ii) The mRNA and molecule number of KdpFABC are determined in vivo at various extracellular K+ concentrations. Based on the identified parameters for the in vitro system it is shown, that different time hierarchies appear which are used for model reduction. Then the model is transformed in such a way that a singular perturbation problem is formulated. The analysis of the in vivo system shows that the model can be separated into two parts (submodels which are called functional units) that are connected only in a unidirectional way. Hereby one submodel represents signal transduction while the second submodel describes the gene expression.

Modeling and experimental validation of the signal transduction via the Escherichia coli sucrose phospho transferase system

Bacterial signal processing was investigated concerning the sucrose phosphotransferase system (sucrose PTS) in the bacterium Escherichia coli as an example. The about 20 different phosphotransferase systems (PTSs) of the cell fulfill besides the transport of various carbohydrates, also the function of one signal processing system. Extra- and intracellular signals are converted within the PTS protein chain to important regulatory signals affecting, e.g. carbon metabolism and chemotaxis. A detailed dynamical model of the sucrose PTS was developed describing transport and signal processing function. It was formulated using a detailed description of complex formation and phosphate transfer between the chain proteins. Model parameters were taken from literature or were identified with own experiments. Simulation studies together with experimental hints showed that the dynamic behavior of phosphate transfer in the PTS runs within 1 s. Therefore a description of steady state characteristics is sufficient for describing the signaling properties of the sucrose PTS. A steady state characteristic field describes the degree of phosphorylation of the PTS protein EIIACrr as a function of the input variables extracellular sucrose concentration and intracellular phosphoenolpyruvate (PEP):pyruvate ratio. The model has been validated with different experiments performed in a CSTR using a sucrose positive E. coli W3110 derivative. A method for determining intracellular metabolite concentrations has been developed. A sample preparation technique using a boiling ethanol buffer solution was successfully applied. The PTS output signal degree of phosphorylation of EIIACrr was also measured. Steady state conditions with varying dilution rate and dissolved oxygen concentration and dynamical variations applying different stimuli to the culture were considered. Pulse, and stop feeding experiments with limiting sucrose concentrations were performed. Simulation and experimental results matched well. The same holds for the expanded sucrose PTS and glycolysis model.