Determination of elasticities, concentration and flux control coefficients from transient metabolite data using linlog kinetics

Performing in spite of starvation: How Saccharomyces cerevisiae maintains robust growth when facing famine zones in industrial bioreactors

In fed-batch operated industrial bioreactors, glucose-limited feeding is commonly applied for optimal control of cell growth and product formation. Still, microbial cells such as yeasts and bacteria are frequently exposed to glucose starvation conditions in poorly mixed zones or far away from the feedstock inlet point. Despite its commonness, studies mimicking related stimuli are still underrepresented in scale-up/scale-down considerations. This may surprise as the transition from glucose limitation to starvation has the potential to provoke regulatory responses with negative consequences for production performance. In order to shed more light, we performed gene-expression analysis of Saccharomyces cerevisiae grown in intermittently fed chemostat cultures to study the effect of limitation-starvation transitions. The resulting glucose concentration gradient was representative for the commercial scale and compelled cells to tolerate about 76 s with sub-optimal substrate supply. Special attention was paid to the adaptation status of the population by discriminating between first time and repeated entry into the starvation regime. Unprepared cells reacted with a transiently reduced growth rate governed by the general stress response. Yeasts adapted to the dynamic environment by increasing internal growth capacities at the cost of rising maintenance demands by 2.7%. Evidence was found that multiple protein kinase A (PKA) and Snf1-mediated regulatory circuits were initiated and ramped down still keeping the cells in an adapted trade-off between growth optimization and down-regulation of stress response. From this finding, primary engineering guidelines are deduced to optimize both the production host's genetic background and the design of scale-down experiments.

Metabolomics and modelling approaches for systems metabolic engineering

Metabolic engineering involves the manipulation of microbes to produce desirable compounds through genetic engineering or synthetic biology approaches. Metabolomics involves the quantitation of intracellular and extracellular metabolites, where mass spectrometry and nuclear magnetic resonance based analytical instrumentation are often used. Here, the experimental designs, sample preparations, metabolite quenching and extraction are essential to the quantitative metabolomics workflow. The resultant metabolomics data can then be used with computational modelling approaches, such as kinetic and constraint-based modelling, to better understand underlying mechanisms and bottlenecks in the synthesis of desired compounds, thereby accelerating research through systems metabolic engineering. Constraint-based models, such as genome scale models, have been used successfully to enhance the yield of desired compounds from engineered microbes, however, unlike kinetic or dynamic models, constraint-based models do not incorporate regulatory effects. Nevertheless, the lack of time-series metabolomic data generation has hindered the usefulness of dynamic models till today. In this review, we show that improvements in automation, dynamic real-time analysis and high throughput workflows can drive the generation of more quality data for dynamic models through time-series metabolomics data generation. Spatial metabolomics also has the potential to be used as a complementary approach to conventional metabolomics, as it provides information on the localization of metabolites. However, more effort must be undertaken to identify metabolites from spatial metabolomics data derived through imaging mass spectrometry, where machine learning approaches could prove useful. On the other hand, single-cell metabolomics has also seen rapid growth, where understanding cell-cell heterogeneity can provide more insights into efficient metabolic engineering of microbes. Moving forward, with potential improvements in automation, dynamic real-time analysis, high throughput workflows, and spatial metabolomics, more data can be produced and studied using machine learning algorithms, in conjunction with dynamic models, to generate qualitative and quantitative predictions to advance metabolic engineering efforts.

Bayesian inference of metabolic kinetics from genome-scale multiomics data

Modern biological tools generate a wealth of data on metabolite and protein concentrations that can be used to help inform new strain designs. However, learning from these data to predict how a cell will respond to genetic changes, a key need for engineering, remains challenging. A promising technique for leveraging omics measurements in metabolic modeling involves the construction of kinetic descriptions of the enzymatic reactions that occur within a cell. Parameterizing these models from biological data can be computationally difficult, since methods must also quantify the uncertainty in model parameters resulting from the observed data. While the field of Bayesian inference offers a wide range of methods for efficiently estimating distributions in parameter uncertainty, such techniques are poorly suited to traditional kinetic models due to their complex rate laws and resulting nonlinear dynamics. In this paper, we employ linear-logarithmic kinetics to simplify the calculation of steady-state flux distributions and enable efficient sampling and inference methods. We demonstrate that detailed information on the posterior distribution of parameters can be obtained efficiently at a variety of problem scales, including nearly genome-scale kinetic models trained on multiomics datasets. These results allow modern Bayesian machine learning tools to be leveraged in understanding biological data and in developing new, efficient strain designs.

Dynamic metabolic response of Aspergillus niger to glucose perturbation: evidence of regulatory mechanism for reduced glucoamylase production

Environmental gradient is an important common issue during scale-up process for protein production. To address the dynamic regulatory mechanism of Aspergillus niger being exposed to inhomogeneous glucose concentrations, glucose perturbation were experimented on the steady state of A. niger chemostat culture, and dynamic profiles of the intracellular metabolites in central carbon metabolism were tracked in a time scale of seconds. The upper glycolysis and pentose phosphate pathway showed sharp variations after glucose perturbation, while the lower glycolysis, TCA cycle and amino acid pools represented a moderate and prolonged response due to the allosteric regulation of enzymes and buffering function of metabolites with large pool sizes. Improved glucose-6-phosphate enhanced the metabolic flux to PP pathway remarkably, which provided not only more redox cofactors (NADPH) for protein synthesis but also more precursors (phosphoribosyl pyrophosphate and ribose-5-phosphate) for cell growth. Moreover, reduction of the total adenine nucleotides and major precursor amino acids indicated the upregulated RNA synthesis was required to produce stress proteins, and partially explained the drop of glucoamylase production when A. niger experienced a fluctuated glucose concentration environment. These findings would be valuable for improving bioreactor operation, design, and scale-up from engineering or genetic aspects.

Engineering Microbial Metabolite Dynamics and Heterogeneity

As yields for biological chemical production in microorganisms approach their theoretical maximum, metabolic engineering requires new tools, and approaches for improvements beyond what traditional strategies can achieve. Engineering metabolite dynamics and metabolite heterogeneity is necessary to achieve further improvements in product titers, productivities, and yields. Metabolite dynamics, the ensemble change in metabolite concentration over time, arise from the need for microbes to adapt their metabolism in response to the extracellular environment and are important for controlling growth and productivity in industrial fermentations. Metabolite heterogeneity, the cell-to-cell variation in a metabolite concentration in an isoclonal population, has a significant impact on ensemble productivity. Recent advances in single cell analysis enable a more complete understanding of the processes driving metabolite heterogeneity and reveal metabolic engineering targets. The authors present an overview of the mechanistic origins of metabolite dynamics and heterogeneity, why they are important, their potential effects in chemical production processes, and tools and strategies for engineering metabolite dynamics and heterogeneity. The authors emphasize that the ability to control metabolite dynamics and heterogeneity will bring new avenues of engineering to increase productivity of microbial strains.

Formulation, construction and analysis of kinetic models of metabolism: A review of modelling frameworks

Kinetic models are critical to predict the dynamic behaviour of metabolic networks. Mechanistic kinetic models for large networks remain uncommon due to the difficulty of fitting their parameters. Recent modelling frameworks promise new ways to overcome this obstacle while retaining predictive capabilities. In this review, we present an overview of the relevant mathematical frameworks for kinetic formulation, construction and analysis. Starting with kinetic formalisms, we next review statistical methods for parameter inference, as well as recent computational frameworks applied to the construction and analysis of kinetic models. Finally, we discuss opportunities and limitations hindering the development of larger kinetic reconstructions.

Robust identification of metabolic control for microbial l-methionine production following an easy-to-use puristic approach

The identification of promising metabolic engineering targets is a key issue in metabolic control analysis (MCA). Conventional approaches make intensive use of model-based studies, such as exploiting post-pulse metabolic dynamics after proper perturbation of the microbial system. Here, we present an easy-to-use, purely data-driven approach, defining pool efflux capacities (PEC) for identifying reactions that exert the highest flux control in linear pathways. Comparisons with linlog-based MCA and data-driven substrate elasticities (DDSE) showed that similar key control steps were identified using PEC. Using the example of l-methionine production with recombinant Escherichia coli, PEC consistently and robustly identified main flux controls using perturbation data after a non-labeled ¹²C-l-serine stimulus. Furthermore, the application of full-labeled ¹³C-l-serine stimuli yielded additional insights into stimulus propagation to l-methionine. PEC analysis performed on the ¹³C data set revealed the same targets as the ¹²C data set. Notably, the typical drawback of metabolome analysis, namely, the omnipresent leakage of metabolites, was excluded using the ¹³C PEC approach.

Construction of feasible and accurate kinetic models of metabolism: A Bayesian approach

Kinetic models are essential to quantitatively understand and predict the behaviour of metabolic networks. Detailed and thermodynamically feasible kinetic models of metabolism are inherently difficult to formulate and fit. They have a large number of heterogeneous parameters, are non-linear and have complex interactions. Many powerful fitting strategies are ruled out by the intractability of the likelihood function. Here, we have developed a computational framework capable of fitting feasible and accurate kinetic models using Approximate Bayesian Computation. This framework readily supports advanced modelling features such as model selection and model-based experimental design. We illustrate this approach on the tightly-regulated mammalian methionine cycle. Sampling from the posterior distribution, the proposed framework generated thermodynamically feasible parameter samples that converged on the true values, and displayed remarkable prediction accuracy in several validation tests. Furthermore, a posteriori analysis of the parameter distributions enabled appraisal of the systems properties of the network (e.g., control structure) and key metabolic regulations. Finally, the framework was used to predict missing allosteric interactions.

Biochemical Systems Theory: A Review

Biochemical systems theory (BST) is the foundation for a set of analytical andmodeling tools that facilitate the analysis of dynamic biological systems. This paper depicts major developments in BST up to the current state of the art in 2012. It discusses its rationale, describes the typical strategies and methods of designing, diagnosing, analyzing, and utilizing BST models, and reviews areas of application. The paper is intended as a guide for investigators entering the fascinating field of biological systems analysis and as a resource for practitioners and experts.

Testing biochemistry revisited: how in vivo metabolism can be understood from in vitro enzyme kinetics

A decade ago, a team of biochemists including two of us, modeled yeast glycolysis and showed that one of the most studied biochemical pathways could not be quite understood in terms of the kinetic properties of the constituent enzymes as measured in cell extract. Moreover, when the same model was later applied to different experimental steady-state conditions, it often exhibited unrestrained metabolite accumulation.

Here we resolve this issue by showing that the results of such ab initio modeling are improved substantially by (i) including appropriate allosteric regulation and (ii) measuring the enzyme kinetic parameters under conditions that resemble the intracellular environment. The following modifications proved crucial: (i) implementation of allosteric regulation of hexokinase and pyruvate kinase, (ii) implementation of V_max values measured under conditions that resembled the yeast cytosol, and (iii) redetermination of the kinetic parameters of glyceraldehyde-3-phosphate dehydrogenase under physiological conditions.

Model predictions and experiments were compared under five different conditions of yeast growth and starvation. When either the original model was used (which lacked important allosteric regulation), or the enzyme parameters were measured under conditions that were, as usual, optimal for high enzyme activity, fructose 1,6-bisphosphate and some other glycolytic intermediates tended to accumulate to unrealistically high concentrations. Combining all adjustments yielded an accurate correspondence between model and experiments for all five steady-state and dynamic conditions. This enhances our understanding of in vivo metabolism in terms of in vitro biochemistry.

Baker's yeast is widely applied in modern biotechnology, for instance for production of heterologous protein or biofuel. For such applications a thorough understanding of the central energy metabolism of the bug is crucial. Nevertheless, even for this well-known organism, attempts to build models ab initio, based on independently measured characteristics of the catalysts (the enzymes), seldom gives reliable results. A key problem in this field is that enzyme characteristics are often studied under non-physiological conditions that do not resemble the environment inside the cell. In this study we measured the enzyme characteristics under physiological conditions and assembled the results into a computational model of yeast energy metabolism. We show that this simple trick greatly improves the predictive value of the computational model. This allowed us to predict correctly how yeast cells adapt to nitrogen starvation, an industrially relevant situation, in which remodeling of the proteome strongly affects cellular energy metabolism.

Identification of informative metabolic responses using a minibioreactor: a small step change in the glucose supply rate creates a large metabolic response in Saccharomyces cerevisiae

In this study, a previously developed mini-bioreactor, the Biocurve, was used to identify an informative stimulus-response experiment. The identified stimulus-response experiment was a modest 50% shift-up in glucose uptake rate (qGLC) that unexpectedly resulted in a disproportionate transient metabolic response. The 50% shift-up in qGLC in the Biocurve resulted in a near tripling of the online measured oxygen uptake (qO2) and carbon dioxide production (qCO2) rates, suggesting a considerable mobilization of glycogen and trehalose. The 50% shift-up in qGLC was subsequently studied in detail in a conventional bioreactor (4 l working volume), which confirmed the results obtained with the Biocurve. Especially relevant is the observation that the 50% increase in glucose uptake rate led to a three-fold increase in glycolytic flux, due to mobilization of storage materials. This explains the unexpected ethanol and acetate secretion after the shift-up, in spite of the fact that after the shift-up the qGLC was far less than the critical value. Moreover, these results show that the correct in vivo fluxes in glucose pulse experiments cannot be obtained from the uptake and secretion rates only. Instead, the storage fluxes must also be accurately quantified. Finally, we speculate on the possible role that the transient increase in dissolved CO2 immediately after the 50% shift-up in qGLC could have played a part in triggering glycogen and trehalose mobilization.

Optimization-based metabolic control analysis

In this work, a novel optimization-based metabolic control analysis (OMCA) method is introduced for reducing data requirement for metabolic control analysis (MCA). It is postulated that using the optimal control approach, the fluxes in a metabolic network are correlated to metabolite concentrations and enzyme activities as a state-feedback control system that is optimal with respect to a homeostasis objective. It is then shown that the optimal feedback gains are directly related to the elasticity coefficients (ECs) of MCA. This approach requires determination of the relative "importance" of metabolites and fluxes for the system, which is possible with significantly reduced experimental data, as compared with typical MCA requirements. The OMCA approach is applied to a top-down control model of glycolysis in hepatocytes. It is statistically demonstrated that the OMCA model is capable of predicting the ECs observed experimentally with few exceptions. Further, an OMCA-based model reconciliation study shows that the modification of four assumed stoichiometric coefficients in the model can explain most of the discrepancies, with the exception of elasticities with respect to the NADH/NAD ratio.

Tradeoff between enzyme and metabolite efficiency maintains metabolic homeostasis upon perturbations in enzyme capacity

Substrate metabolite concentrations are inversely related to the in vivo capacity of their converting enzymes.

Local metabolite responses represent a passive mechanism to achieve metabolic homeostasis upon perturbations in enzyme capacity.

Enzyme capacity and metabolite concentration control the metabolic reaction rate.

Physiological behavior emerges from complex dynamic interactions between transcripts, enzymes, and metabolites, the constituents of metabolism, and its regulatory network (Sauer, 2006). Although large data sets can be generated on all these variables, data integration, in particular across different omics levels, is becoming the key challenge (Stitt and Fernie, 2003; Sauer et al, 2007). In this study, we identify a general relationship between substrates of an enzymatic reaction and enzymatic capacity in central carbon metabolism that allows the prediction of changes in metabolite concentration based on changes in enzyme capacity and vise versa. To elucidate whether general relationships exist between metabolite concentrations and enzyme capacities (i.e. the outcome of enzyme abundance combined with activity), we propose three hypothetical and alternative governing principles. The first hypothesis postulates a minimization of metabolite concentration at a given flux. In this case, no correlation between alterations in metabolite concentrations and enzyme capacities is expected. The second hypothesis postulates a tradeoff between metabolite concentration and enzyme capacity. In this case, a negative correlation between differences in concentrations of substrate metabolites and differences in enzyme capacity is expected. The third hypothesis postulates a minimization of enzyme capacity at a given flux. In this case, we expect a positive correlation between differences in concentrations of product metabolites and differences in enzyme capacity. As hypotheses I–III imply different relationships between enzyme capacities and metabolite concentrations, identification of the prevailing situation in microbial metabolism requires quantitative in vivo metabolite concentration and enzyme capacity data upon moderate changes in enzyme capacity. As a first test, we chose wild type Saccharomyces cerevisiae and an otherwise isogenic mutant with a complete deletion of the transcription factor Gcr2p, an activator of glycolysis (Chambers et al, 1995). This mutant exhibits altered transcript abundances, enzyme activities, and metabolite concentrations within closely connected reactions in glycolysis and in the tricarboxylic acid cycle (Uemura and Fraenkel, 1990, 1999; Sasaki and Uemura, 2005). To quantify the relationship between metabolite concentrations and enzyme capacities, we determined transcript, enzyme, and metabolite abundances in wild type and GCR2 mutant in batch culture on glucose minimal medium. Transcript and enzyme abundances are used as surrogates for enzyme capacities. The most significant correlation was observed for fold-changes in substrate metabolite concentrations with fold-changes in enzyme abundance. Not unexpectedly, enzyme abundances were a significantly better approximation for enzyme capacities than transcript abundances. A further improved correlation was achieved by considering all diverging enzymes that react upon a given substrate metabolite simultaneously rather than considering them as a separate reaction (Figure 4). The high correlation between substrate metabolite and enzyme fold-changes suggests a tradeoff between enzyme capacity and metabolite concentrations in central metabolism. To test the general validity for central carbon metabolism of the above-identified tradeoff between reaction substrate metabolite concentrations and enzyme abundances, we performed four independent validations: a statistical, a literature based, and two experimental ones. Statistically, we verified that the correlation between substrate metabolites and enzymes could not have been found by chance. On the basis of the literature data, we performed the above correlation analysis with literature data. All available data followed the proposed correlation, thus providing further evidence for the general validity of this relationship. As a more serious challenge of the identified correlation, we designed an experiment where the absolute flux alterations are large and additionally the flux directions are altered. We expected the substrate metabolites to occur at higher concentrations in the mutant than in the wild type. This expectation was fulfilled by the experimental data in all cases, thereby further corroborating the negative correlation between enzyme capacity and metabolite concentrations. So far, our experimental evidence was based on perturbing multiple enzyme abundances through a transcription factor mutant. To ensure that our findings are also valid for single-reaction perturbations, we modulated individual abundances of the four glycolytic enzymes Pgi1p, Tpi1p, Eno2p, and Cdc19p using strains whose endogenous genomic promotor was replaced by a Tet-controlled promotor (Mnaimneh et al, 2004) (Figure 7). Thus, we determined intracellular metabolites concentrations during exponential growth in the strains with modulated enzyme abundance. Our above-identified correlation predicts metabolite concentrations to increase only for the substrate of the such perturbed reaction and all other metabolite concentrations to remain constant. This prediction was verified. We demonstrate here that global or local alterations in enzyme abundance correlate negatively with enzyme reaction substrate concentration at least in central carbon metabolism. This implies a tradeoff between enzyme and metabolite efficiency in metabolic networks. These findings can be interpreted as a passive network mechanism to maintain close-to-wild-type homeostasis of central carbon metabolism upon perturbations that alter the enzyme capacity. The alterations are compensated by converse changes in reaction substrate concentrations, thereby minimizing the difference in metabolic flux that is caused by the alteration.

What is the relationship between enzymes and metabolites, the two major constituents of metabolic networks? We propose three alternative relationships between enzyme capacity and metabolite concentration alterations based on a Michaelis–Menten kinetic; that is enzyme capacities, metabolite concentrations, or both could limit the metabolic reaction rates. These relationships imply different correlations between changes in enzyme capacity and metabolite concentration, which we tested by quantifying metabolite, transcript, and enzyme abundances upon local (single-enzyme modulation) and global (GCR2 transcription factor mutant) perturbations in Saccharomyces cerevisiae. Our results reveal an inverse relationship between fold-changes in substrate metabolites and their catalyzing enzymes. These data provide evidence for the hypothesis that reaction rates are jointly limited by enzyme capacity and metabolite concentration. Hence, alteration in one network constituent can be efficiently buffered by converse alterations in the other constituent, implying a passive mechanism to maintain metabolic homeostasis upon perturbations in enzyme capacity.

Dynamics and control of the central carbon metabolism in hepatoma cells

BACKGROUND

The liver plays a major role in metabolism and performs a number of vital functions in the body. Therefore, the determination of hepatic metabolite dynamics and the analysis of the control of the respective biochemical pathways are of great pharmacological and medical importance. Extra- and intracellular time-series data from stimulus-response experiments are gaining in importance in the identification of in vivo metabolite dynamics, while dynamic network models are excellent tools for analyzing complex metabolic control patterns. This is the first study that has been undertaken on the data-driven identification of a dynamic liver central carbon metabolism model and its application in the analysis of the distribution of metabolic control in hepatoma cells.

RESULTS

Dynamic metabolite data were collected from HepG2 cells after they had been deprived of extracellular glucose. The concentration of 25 extra- and intracellular intermediates was quantified using HPLC, LC-MS-MS, and GC-MS. The in silico metabolite dynamics were in accordance with the experimental data. The central carbon metabolism of hepatomas was further analyzed with a particular focus on the control of metabolite concentrations and metabolic fluxes. It was observed that the enzyme glucose-6-phosphate dehydrogenase exerted substantial negative control over the glycolytic flux, whereas oxidative phosphorylation had a significant positive control. The control over the rate of NADPH consumption was found to be shared between the NADPH-demand itself (0.65) and the NADPH supply (0.38).

CONCLUSIONS

Based on time-series data, a dynamic central carbon metabolism model was developed for the investigation of new and complex metabolic control patterns in hepatoma cells. The control patterns found support the hypotheses that the glucose-6-phosphate dehydrogenase and the Warburg effect are promising targets for tumor treatment. The systems-oriented identification of metabolite dynamics is a first step towards the genome-based assessment of potential risks posed by nutrients and drugs.

Impact of thermodynamic principles in systems biology

It is shown that properties of biological systems which are relevant for systems biology motivated mathematical modelling are strongly shaped by general thermodynamic principles such as osmotic limit, Gibbs energy dissipation, near equilibria and thermodynamic driving force. Each of these aspects will be demonstrated both theoretically and experimentally.

Metabolic network discovery through reverse engineering of metabolome data

Reverse engineering of high-throughput omics data to infer underlying biological networks is one of the challenges in systems biology. However, applications in the field of metabolomics are rather limited. We have focused on a systematic analysis of metabolic network inference from in silico metabolome data based on statistical similarity measures. Three different data types based on biological/environmental variability around steady state were analyzed to compare the relative information content of the data types for inferring the network. Comparing the inference power of different similarity scores indicated the clear superiority of conditioning or pruning based scores as they have the ability to eliminate indirect interactions. We also show that a mathematical measure based on the Fisher information matrix gives clues on the information quality of different data types to better represent the underlying metabolic network topology. Results on several datasets of increasing complexity consistently show that metabolic variations observed at steady state, the simplest experimental analysis, are already informative to reveal the connectivity of the underlying metabolic network with a low false-positive rate when proper similarity-score approaches are employed. For experimental situations this implies that a single organism under slightly varying conditions may already generate more than enough information to rightly infer networks. Detailed examination of the strengths of interactions of the underlying metabolic networks demonstrates that the edges that cannot be captured by similarity scores mainly belong to metabolites connected with weak interaction strength. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s11306-009-0156-4) contains supplementary material, which is available to authorized users.

Towards the engineering of in vitro systems

Synthetic biology aims at rationally implementing biological systems from scratch. Given the complexity of living systems and our current lack of understanding of many aspects of living cells, this is a major undertaking. The design of in vitro systems can be considerably easier, because they can consist of fewer constituents, are quasi time invariant, their parameter space can be better accessed and they can be much more easily perturbed and then analysed chemically and mathematically. However, even for simplified in vitro systems, following a comprehensively rational design procedure is still difficult. When looking at a comparatively simple system, such as a medium-sized enzymatic reaction network as it is represented by glycolysis, major issues such as a lack of comprehensive enzyme kinetics and of suitable knowledge on crucial design parameters remain. Nevertheless, in vitro systems are very suitable to overcome these obstacles and therefore well placed to act as a stepping stone to engineering living systems.

Kinetic hybrid models composed of mechanistic and simplified enzymatic rate laws--a promising method for speeding up the kinetic modelling of complex metabolic networks

Kinetic modelling of complex metabolic networks - a central goal of computational systems biology - is currently hampered by the lack of reliable rate equations for the majority of the underlying biochemical reactions and membrane transporters. On the basis of biochemically substantiated evidence that metabolic control is exerted by a narrow set of key regulatory enzymes, we propose here a hybrid modelling approach in which only the central regulatory enzymes are described by detailed mechanistic rate equations, and the majority of enzymes are approximated by simplified(non mechanistic) rate equations (e.g. mass action, LinLog, Michaelis-Menten and power law) capturing only a few basic kinetic features and hence containing only a small number of parameters to be experimentally determined. To check the reliability of this approach, we have applied it to two different metabolic networks, the energy and redox metabolism of red blood cells, and the purine metabolism of hepatocytes, using in both cases available comprehensive mechanistic models as reference standards. Identification of the central regulatory enzymes was performed by employing only information on network topology and the metabolic data for a single reference state of the network [Grimbs S, Selbig J, Bulik S, Holzhutter HG & Steuer R (2007) Mol Syst Biol 3, 146, doi:10.1038/msb4100186].Calculations of stationary and temporary states under various physiological challenges demonstrate the good performance of the hybrid models. We propose the hybrid modelling approach as a means to speed up the development of reliable kinetic models for complex metabolic networks.

Determination of the cytosolic free NAD/NADH ratio in Saccharomyces cerevisiae under steady-state and highly dynamic conditions

The coenzyme NAD plays a major role in metabolism as a key redox carrier and signaling molecule but current measurement techniques cannot distinguish between different compartment pools, between free and protein-bound forms and/or between NAD(H) and NADP(H). Local free NAD/NADH ratios can be determined from product/substrate ratios of suitable near-equilibrium redox reactions but the application of this principle is often precluded by uncertainties regarding enzyme activity, localization and coenzyme specificity of dehydrogenases. In Saccharomyces cerevisiae, we circumvented these issues by expressing a bacterial mannitol-1-phosphate 5-dehydrogenase and determining the cytosolic free NAD/NADH ratio from the measured [fructose-6-phosphate]/[mannitol-1-phosphate] ratio. Under aerobic glucose-limited conditions we estimated a cytosolic free NAD/NADH ratio between 101(+/-14) and 320(+/-45), assuming the cytosolic pH is between 7.0 and 6.5, respectively. These values are more than 10-fold higher than the measured whole-cell total NAD/NADH ratio of 7.5(+/-2.5). Using a thermodynamic analysis of central glycolysis we demonstrate that the former are thermodynamically feasible, while the latter is not. Furthermore, we applied this novel system to study the short-term metabolic responses to perturbations. We found that the cytosolic free NAD-NADH couple became more reduced rapidly (timescale of seconds) upon a pulse of glucose (electron-donor) and that this could be reversed by the addition of acetaldehyde (electron-acceptor). In addition, these dynamics occurred without significant changes in whole-cell total NAD and NADH. This approach provides a new experimental tool for quantitative physiology and opens new possibilities in the study of energy and redox metabolism in S. cerevisiae. The same strategy should also be applicable to other microorganisms.

A method for estimation of elasticities in metabolic networks using steady state and dynamic metabolomics data and linlog kinetics

Background

Dynamic modeling of metabolic reaction networks under in vivo conditions is a crucial step in order to obtain a better understanding of the (dis)functioning of living cells. So far dynamic metabolic models generally have been based on mechanistic rate equations which often contain so many parameters that their identifiability from experimental data forms a serious problem. Recently, approximative rate equations, based on the linear logarithmic (linlog) format have been proposed as a suitable alternative with fewer parameters.

Results

In this paper we present a method for estimation of the kinetic model parameters, which are equal to the elasticities defined in Metabolic Control Analysis, from metabolite data obtained from dynamic as well as steady state perturbations, using the linlog kinetic format. Additionally, we address the question of parameter identifiability from dynamic perturbation data in the presence of noise. The method is illustrated using metabolite data generated with a dynamic model of the glycolytic pathway of Saccharomyces cerevisiae based on mechanistic rate equations. Elasticities are estimated from the generated data, which define the complete linlog kinetic model of the glycolysis. The effect of data noise on the accuracy of the estimated elasticities is presented. Finally, identifiable subset of parameters is determined using information on the standard deviations of the estimated elasticities through Monte Carlo (MC) simulations.

Conclusion

The parameter estimation within the linlog kinetic framework as presented here allows the determination of the elasticities directly from experimental data from typical dynamic and/or steady state experiments. These elasticities allow the reconstruction of the full kinetic model of Saccharomyces cerevisiae, and the determination of the control coefficients. MC simulations revealed that certain elasticities are potentially unidentifiable from dynamic data only. Addition of steady state perturbation of enzyme activities solved this problem.

Modelling strategies for the industrial exploitation of lactic acid bacteria

Lactic acid bacteria (LAB) have a long tradition of use in the food industry, and the number and diversity of their applications has increased considerably over the years. Traditionally, process optimization for these applications involved both strain selection and trial and error. More recently, metabolic engineering has emerged as a discipline that focuses on the rational improvement of industrially useful strains. In the post-genomic era, metabolic engineering increasingly benefits from systems biology, an approach that combines mathematical modelling techniques with functional-genomics data to build models for biological interpretation and--ultimately--prediction. In this review, the industrial applications of LAB are mapped onto available global, genome-scale metabolic modelling techniques to evaluate the extent to which functional genomics and systems biology can live up to their industrial promise.

Simulation of biochemical networks--cellular networks as dynamic control systems

It has been appreciated for at least a hundred years that biological organisms contain control systems that enable them to adapt to a changing environment and adjust their internal systems when they need to proliferate. Even so, we have little understanding of the role that many of the control systems play. It's only in recent years that mainstream science has begun to study biological systems qualitatively and to look specifically at dynamical responses. As a result it might be possible that future cancer therapies will operate by manipulating the control systems that have gone awry during uncontrolled proliferation. This is a long term goal because it would require a mind shift in the way some biologists approach such problems. In this short paper the author describes some of the main control elements found in biological systems and illustrate their use in biological networks. In addition the author discuss some of the strategies that one can use to build computational models.

Application of metabolome data in functional genomics: A conceptual strategy

A gene with yet unknown physiological function can be studied by changing its expression level followed by analysis of the resulting phenotype. This type of functional genomics study can be complicated by the occurrence of 'silent mutations', the phenotypes of which are not easily observable in terms of metabolic fluxes (e.g., the growth rate). Nevertheless, genetic alteration may give rise to significant yet complicated changes in the metabolome. We propose here a conceptual functional genomics strategy based on microbial metabolome data, which identifies changes in in vivo enzyme activities in the mutants. These predicted changes are used to formulate hypotheses to infer unknown gene functions. The required metabolome data can be obtained solely from high-throughput mass spectrometry analysis, which provides the following in vivo information: (1) the metabolite concentrations in the reference and the mutant strain; (2) the metabolic fluxes in both strains and (3) the enzyme kinetic parameters of the reference strain. We demonstrate in silico that changes in enzyme activities can be accurately predicted by this approach, even in 'silent mutants'.

Approximative kinetic formats used in metabolic network modeling

An overview is presented of the different approximative enzyme kinetic formats that have been proposed for use in metabolic modeling studies. It is considered that the following four general properties are relevant for approximative kinetics: the rate must be proportional to enzyme level; at high metabolite concentrations, there is downward concave behavior of rate versus concentration; the number of kinetic parameters should be as small as possible; analytical solutions of steady-state network balances are desirable. Six different approximative kinetic formats are evaluated (linear, logarithmic-linear, power law GMA, power law S-systems, thermokinetic, linear-logarithmic) and it is concluded that only the recently proposed linear-logarithmic approach combines all desired properties and therefore seems a most appropriate approximate kinetic format.