Type and capacity of glucose transport influences succinate yield in two-stage cultivations.

BACKGROUND: Glucose is the main carbon source of E. coli and a typical substrate in production processes. The main glucose uptake system is the glucose specific phosphotransferase system (Glc-PTS). The PTS couples glucose uptake with its phosphorylation. This is achieved by the concomitant conversion of phosphoenolpyruvate (PEP) to pyruvate. The Glc-PTS is hence unfavorable for the production of succinate as this product is derived from PEP. RESULTS: We studied, in a systematic manner, the effect of knocking out the Glc-PTS and of replacing it with the glucose facilitator (Glf) of Zymomonas mobilis on succinate yield and productivity. For this study a set of strains derived from MG1655, carrying deletions of ackA-pta, adhE and ldhA that prevent the synthesis of competing fermentation products, were constructed and tested in two-stage cultivations. The data show that inactivation of the Glc-PTS achieved a considerable increase in succinate yield and productivity. On the other hand, aerobic growth of this strain on glucose was strongly decreased. Expression of the alternative glucose transporter, Glf, in this strain enhanced aerobic growth but productivity and yield under anaerobic conditions were slightly decreased. This decrease in succinate yield was accompanied by pyruvate production. Yield could be increased in both Glc-PTS mutants by overexpressing phosphoenolpyruvate carboxykinase (Pck). Productivity on the other hand, was decreased in the strain without alternative glucose transporter but strongly increased in the strain expressing Glf. The experiments were complemented by flux balance analysis in order to check the observed yields against the maximal theoretical yields. Furthermore, the phosphorylation state of EIIAGlc was determined. The data indicate that the ratio of PEP to pyruvate is correlating with pyruvate excretion. This ratio is affected by the PTS reaction as well as by further reactions at the PEP/pyruvate node. CONCLUSIONS: The results show that for optimization of succinate yield and productivity it is not sufficient to knock out or introduce single reactions. Rather, balancing of the fluxes of central metabolism most important at the PEP/pyruvate node is important.

Application of theoretical methods to increase succinate production in engineered strains.

Computational methods have enabled the discovery of non-intuitive strategies to enhance the production of a variety of target molecules. In the case of succinate production, reviews covering the topic have not yet analyzed the impact and future potential that such methods may have. In this work, we review the application of computational methods to the production of succinic acid. We found that while a total of 26 theoretical studies were published between 2002 and 2016, only 10 studies reported the successful experimental implementation of any kind of theoretical knowledge. None of the experimental studies reported an exact application of the computational predictions. However, the combination of computational analysis with complementary strategies, such as directed evolution and comparative genome analysis, serves as a proof of concept and demonstrates that successful metabolic engineering can be guided by rational computational methods.

Modeling the Interplay of Pseudomonas putida EIIA with the Potassium Transporter KdpFABC.

The nitrogen phosphotransferase system (PTS(Ntr)) of Pseudomonas putida is a key regulatory device that participates in controlling many physiological processes in a posttranscriptional fashion. One of the target functions of the PTS(Ntr) is the regulation of potassium transport. This is mediated by the direct interaction of one of its components with the sensor kinase KdpD of the two-component system controlling transcription of the kdpFABC genes. From a detailed experimental analysis of the activity of the kdpF promoter in P. putida wild-type and pts mutant strains with varying potassium concentrations, we had highly time-resolved data at hand, describing the influence of the PTS(Ntr) on the transcription of the KdpFABC potassium transporter. Here, this data was used to construct a mathematical model based on a black box approach. The model was able to describe the data quantitatively with convincing accuracy. The qualitative interpretation of the model allowed the prediction of two general points describing the interplay between the PTS(Ntr) and the KdpFABC potassium transporter: (1) the influence of cell number on the performance of the kdpF promoter is mainly by dilution by growth and (2) potassium uptake is regulated not only by the activity of the KdpD/KdpE two-component system (in turn influenced by PtsN). An additional controller with integrative behavior is predicted by the model structure. This suggests the presence of a novel physiological mechanism during regulation of potassium uptake with the KdpFABC transporter and may serve as a starting point for further investigations.

Interplay of the PtsN (EIIA(Ntr)) protein of Pseudomonas putida with its target sensor kinase KdpD.

The nitrogen phosphotransferase system (PTS(Ntr) ) of Pseudomonas putida is a multi-component regulatory device that participates in controlling a variety of physiological processes in a post-translational fashion. A general survey of genes regulated by PtsN exposed transcription of the kdpFABC operon is most conspicuously affected. Measurements of kdpFp promoter activity in different pts mutants showed that PtsN is responsible for repression of kdpFABC transcription. This effect could be assigned mainly to PtsN∼P, depending on the external K(+) concentration. Bacterial two-hybrid assays demonstrated that kdpFp regulation is implemented through direct interaction of the PtsN protein with the sensor kinase KdpD of the KdpD/KdpE two-component system. Interaction between KdpD and PtsN was detectable with a PtsN variant that imitates the non-phosphorylated form as well as with a PtsN type mimicking the phosphorylated form of PtsN. These results raise a regulatory scenario in which the Kdp system is regulated by the action of PtsN through direct interaction with the sensor kinase KdpD, and the outcome of such an interaction depends on the phosphorylation state of PtsN as well as on the external K(+) concentration.

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.

Optimal experimental design with the sigma point method.

Using mathematical models for a quantitative description of dynamical systems requires the identification of uncertain parameters by minimising the difference between simulation and measurement. Owing to the measurement noise also, the estimated parameters possess an uncertainty expressed by their variances. To obtain highly predictive models, very precise parameters are needed. The optimal experimental design (OED) as a numerical optimisation method is used to reduce the parameter uncertainty by minimising the parameter variances iteratively. A frequently applied method to define a cost function for OED is based on the inverse of the Fisher information matrix. The application of this traditional method has at least two shortcomings for models that are nonlinear in their parameters: (i) it gives only a lower bound of the parameter variances and (ii) the bias of the estimator is neglected. Here, the authors show that by applying the sigma point (SP) method a better approximation of characteristic values of the parameter statistics can be obtained, which has a direct benefit on OED. An additional advantage of the SP method is that it can also be used to investigate the influence of the parameter uncertainties on the simulation results. The SP method is demonstrated for the example of a widely used biological model.

A feed-forward loop guarantees robust behavior in Escherichia coli carbohydrate uptake.

MOTIVATION: In Escherichia coli, the phosphoenolpyruvate: carbohydrate phosphotransferase system acts like a sensory element which is able to measure the flux through glycolysis. Since the output of the sensor, the phosphorylated form of protein EIIA, is connected to the activity of the global transcription factor Crp, the kinetic and structural properties of the system are important for the understanding of the overall cellular behavior. RESULTS: A family of mathematical models is presented, varying with respect to their degree of complexity (number of reactions that are taken into account, number of parameters) that show a structurally and quantitatively robust behavior. The models describe a set of experimental data that relates the output of the sensor to the specific growth rate. A central element that is responsible for the structural robustness is a feed-forward loop in the glycolysis, namely the activation of the pyruvate kinase reaction by a metabolite of the upper part of the glycolysis. The robustness is shown for variations of the measured data as well as for variations of the parameters. AVAILABILITY: MATLAB files for model simulations are available on http://www.mpi-magdeburg.mpg.de/people/kre/robust/ A short description of the files provided on this site can be found in the Supporting information.

Systems biology--an engineering perspective.

The interdisciplinary field of systems biology has evolved rapidly over the last years. Different disciplines have aided the development of both its experimental and theoretical branches. One field, which has played a significant role is engineering science and, in particular chemical engineering. Here, we review and illustrate some of these contributions, ranging from modeling approaches to model analysis with a special focus on technique which have not yet been substantially exploited but can be potentially useful in the analysis of biochemical systems.

Comment on mathematical models which describe transcription and calculate the relationship between mRNA and protein expression ratio.

Mathematical models to describe transcription (Arnold et al. (2001); Biotech Bioeng 72:548-561) and translation (Mehra et al. (2003); Biotech Bioeng 84:822-841) in bacteria are modified in order to improve reaction kinetics and to include the number of polymerase molecules that are active on the DNA, as well as to include the number of ribosomes that are active on the nascent and on the completed mRNA, respectively.

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.

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.

Time hierarchies in the Escherichia coli carbohydrate uptake and metabolism.

The analysis of metabolic pathways with mathematical models contributes to the better understanding of the behavior of metabolic processes. This paper presents the analysis of a mathematical model for carbohydrate uptake and metabolism in Escherichia coli. It is shown that the dynamic processes cover a broad time span from some milliseconds to several hours. Based on this analysis the fast processes could be described with steady-state characteristic curves. A subsequent robustness analysis of the model parameters shows that the fast part of the system may act as a filter for the slow part of the system; the sensitivities of the fast system are conserved. From these findings it is concluded that the slow part of the system shows some robustness against changes in parameters of the fast subsystem, i.e. if a parameter shows no sensitivity for the fast part of the system, it will also show no sensitivity for the slow part of the system.

Modular modeling of cellular systems with ProMoT/Diva.

MOTIVATION: Need for software to setup and analyze complex mathematical models for cellular systems in a modular way, that also integrates the experimental environment of the cells. RESULTS: A computer framework is described which allows the building of modularly structured models using an abstract, modular and general modeling methodology. With this methodology, reusable modeling entities are introduced which lead to the development of a modeling library within the modeling tool ProMot. The simulation environment Diva is used for numerical analysis and parameter identification of the models. The simulation environment provides a number of tools and algorithms to simulate and analyze complex biochemical networks. The described tools are the first steps towards an integrated computer-based modeling, simulation and visualization environment Availability: Available on request to the authors. The software itself is free for scientific purposes but requires commercial libraries. SUPPLEMENTARY INFORMATION: http://www.mpi-magdeburg.mpg.de/projects/promot

The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models.

MOTIVATION: Molecular biotechnology now makes it possible to build elaborate systems models, but the systems biology community needs information standards if models are to be shared, evaluated and developed cooperatively. RESULTS: We summarize the Systems Biology Markup Language (SBML) Level 1, a free, open, XML-based format for representing biochemical reaction networks. SBML is a software-independent language for describing models common to research in many areas of computational biology, including cell signaling pathways, metabolic pathways, gene regulation, and others. AVAILABILITY: The specification of SBML Level 1 is freely available from http://www.sbml.org/

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

A mathematical model to describe carbon catabolite repression in Escherichia coli is developed and in part validated. The model is aggregated from two functional units describing glucose and lactose transport and degradation. Both units are members of the crp modulon and are under control of a global signal transduction system which calculates the signals that turn on or off gene expression for the specific enzymes. Using isogenic mutant strains, our model is validated by a set of experiments. In these experiments, substrate composition of the preculture and of the experimental culture are varied in order to stimulate the system in different ways. With the obtained measurements (three states in the liquid phase and one intracellular component) a part of the model parameters could be estimated. Therefore all experiments could be sufficiently described with a single set of parameters.

The organization of metabolic reaction networks. II. Signal processing in hierarchical structured functional units.

Based on the analysis of molecular interactions of proteins with DNA binding sites, a new approach to developing mathematical models describing gene expression is introduced. Detection of hierarchical structures in metabolic networks can be used to decompose complex reaction schemes. This will be achieved by assigning each regulator protein to one level in the hierarchy. Signals are then transduced from the top level to the lower level, but not vice versa. The method is shown by a simple example with two interacting proteins. A comparison of simulation results shows good agreement between a model taking all interactions into account and a model developed with the new approach. Finally, the method is applied to the crpA modulon in Escherichia coli, which controls uptake and metabolism for a number of carbohydrates. Here, RNA polymerase represents the top level, CrpA the second level, and the lactose-specific repressor LacI the lowest level, respectively. Besides the lactose operon, the method is applied to the adenylate cyclase gene and the gene for the regulator CrpA.

The organization of metabolic reaction networks: a signal-oriented approach to cellular models.

Complex metabolic networks are characterized by a great number of elements and many regulatory loops. The description of these networks with mathematical models requires the definition of functional units that group together several cellular processes. The approach presented here is based on the idea that cellular functional units may be assigned directly to mathematical modeling objects. Because the proposed modeling objects have defined inputs and outputs, they can be connected with other modeling objects until eventually the whole metabolism is covered. This modular approach guarantees a high transparency for biologists as well as for engineers. Three criteria are introduced to demarcate functional units. The criteria consider the physiological pathways, the organization of the corresponding genes, and the observation that cellular systems can be structured into units showing a hierarchy of signal transduction and processing. As an example, the carbon catabolic reactions in Escherichia coli are discussed as members of a functional unit catabolism.