Mathematical modelling of metabolism

Hybrid metabolic flux analysis: combining stoichiometric and statistical constraints to model the formation of complex recombinant products

Background

Stoichiometric models constitute the basic framework for fluxome quantification in the realm of metabolic engineering. A recurrent bottleneck, however, is the establishment of consistent stoichiometric models for the synthesis of recombinant proteins or viruses. Although optimization algorithms for in silico metabolic redesign have been developed in the context of genome-scale stoichiometric models for small molecule production, still rudimentary knowledge of how different cellular levels are regulated and phenotypically expressed prevents their full applicability for complex product optimization.

Results

A hybrid framework is presented combining classical metabolic flux analysis with projection to latent structures to further link estimated metabolic fluxes with measured productivities. We first explore the functional metabolic decomposition of a baculovirus-producing insect cell line from experimental data, highlighting the TCA cycle and mitochondrial respiration as pathways strongly associated with viral replication. To reduce uncertainty in metabolic target identification, a Monte Carlo sampling method was used to select meaningful associations with the target, from which 66% of the estimated fluxome had to be screened out due to weak correlations and/or high estimation errors. The proposed hybrid model was then validated using a subset of preliminary experiments to pinpoint the same determinant pathways, while predicting the productivity of independent cultures.

Conclusions

Overall, the results indicate our hybrid metabolic flux analysis framework is an advantageous tool for metabolic identification and quantification in incomplete or ill-defined metabolic networks. As experimental and computational solutions for constructing comprehensive global cellular models are in development, the contribution of hybrid metabolic flux analysis should constitute a valuable complement to current computational platforms in bridging the metabolic state with improved cell culture performance.

A systematic investigation of Escherichia coli central carbon metabolism in response to superoxide stress

Background

The cellular responses of bacteria to superoxide stress can be used to model adaptation to severe environmental changes. Superoxide stress promotes the excessive production of reactive oxygen species (ROS) that have detrimental effects on cell metabolic and other physiological activities. To antagonize such effects, the cell needs to regulate a range of metabolic reactions in a coordinated way, so that coherent metabolic responses are generated by the cellular metabolic reaction network as a whole. In the present study, we have used a quantitative metabolic flux analysis approach, together with measurement of gene expression and activity of key enzymes, to investigate changes in central carbon metabolism that occur in Escherichia coli in response to paraquat-induced superoxide stress. The cellular regulatory mechanisms involved in the observed global flux changes are discussed.

Results

Flux analysis based on nuclear magnetic resonance (NMR) and mass spectroscopy (MS) measurements and computation provided quantitative results on the metabolic fluxes redistribution of the E. coli central carbon network under paraquat-induced oxidative stress. The metabolic fluxes of the glycolytic pathway were redirected to the pentose phosphate pathway (PP pathway). The production of acetate increased significantly, the fluxes associated with the TCA cycle decreased, and the fluxes in the glyoxylate shunt increased in response to oxidative stress. These global flux changes resulted in an increased ratio of NADPH:NADH and in the accumulation of α-ketoglutarate.

Conclusions

Metabolic flux analysis provided a quantitative and global picture of responses of the E. coli central carbon metabolic network to oxidative stress. Systematic adjustments of cellular physiological state clearly occurred in response to changes in metabolic fluxes induced by oxidative stress. Quantitative flux analysis therefore could reveal the physiological state of the cell at the systems level and is a useful complement to molecular systems approaches, such as proteomics and transcription analyses.

Modeling with a view to target identification in metabolic engineering: a critical evaluation of the available tools

The state of the art tools for modeling metabolism, typically used in the domain of metabolic engineering, were reviewed. The tools considered are stoichiometric network analysis (elementary modes and extreme pathways), stoichiometric modeling (metabolic flux analysis, flux balance analysis, and carbon modeling), mechanistic and approximative modeling, cybernetic modeling, and multivariate statistics. In the context of metabolic engineering, one should be aware that the usefulness of these tools to optimize microbial metabolism for overproducing a target compound depends predominantly on the characteristic properties of that compound. Because of their shortcomings not all tools are suitable for every kind of optimization; issues like the dependence of the target compound's synthesis on severe (redox) constraints, the characteristics of its formation pathway, and the achievable/desired flux towards the target compound should play a role when choosing the optimization strategy.

Metabolic effects of the initial glucose concentration on microbial production of hyaluronic acid

The objective of the present work was to evaluate the metabolic effects induced by the initial glucose concentration (IGC) on the cultivation of Streptococcus zooepidemicus for the production of hyaluronic acid (HA). These effects were monitored along non-controlled pH cultivations, carried out in 250-mL Erlenmeyer flasks (natural aeration) and in a 3-L bioreactor (forced aeration) as well. Effects of the IGC were observed with focus on the main metabolites, cell growth, production, and average molecular weight of HA. The absence of glucose resulted in a mixed acid metabolism independent of the oxygen supply, while, for IGCs ranging from 5 to 90 g L(-1), the homolactic metabolism was prevalent. The IGC had no influence on the amounts of either biomass or HA produced in the cultivations carried out in flasks; however, cultivations in 3-L bioreactor were found to be strongly dependent on it. The highest concentration of HA (1.21 g L(-1)) was obtained from 25 g L(-1) IGC, the only cultivation where the conversion of glucose to HA was higher than the one of glucose to biomass. Average molecular weight of HA increased concomitant with the IGC, independently of aeration; nevertheless, it decreased along cultivation under forced aeration, due to the shear imparted by stirring.

Making the right connections: biological networks in the light of evolution

Our understanding of how evolution acts on biological networks remains patchy, as is our knowledge of how that action is best identified, modelled and understood. Starting with network structure and the evolution of protein-protein interaction networks, we briefly survey the ways in which network evolution is being addressed in the fields of systems biology, development and ecology. The approaches highlighted demonstrate a movement away from a focus on network topology towards a more integrated view, placing biological properties centre-stage. We argue that there remains great potential in a closer synergy between evolutionary biology and biological network analysis, although that may require the development of novel approaches and even different analogies for biological networks themselves.

Recent developments in parameter estimation and structure identification of biochemical and genomic systems

The organization, regulation and dynamical responses of biological systems are in many cases too complex to allow intuitive predictions and require the support of mathematical modeling for quantitative assessments and a reliable understanding of system functioning. All steps of constructing mathematical models for biological systems are challenging, but arguably the most difficult task among them is the estimation of model parameters and the identification of the structure and regulation of the underlying biological networks. Recent advancements in modern high-throughput techniques have been allowing the generation of time series data that characterize the dynamics of genomic, proteomic, metabolic, and physiological responses and enable us, at least in principle, to tackle estimation and identification tasks using 'top-down' or 'inverse' approaches. While the rewards of a successful inverse estimation or identification are great, the process of extracting structural and regulatory information is technically difficult. The challenges can generally be categorized into four areas, namely, issues related to the data, the model, the mathematical structure of the system, and the optimization and support algorithms. Many recent articles have addressed inverse problems within the modeling framework of Biochemical Systems Theory (BST). BST was chosen for these tasks because of its unique structural flexibility and the fact that the structure and regulation of a biological system are mapped essentially one-to-one onto the parameters of the describing model. The proposed methods mainly focused on various optimization algorithms, but also on support techniques, including methods for circumventing the time consuming numerical integration of systems of differential equations, smoothing overly noisy data, estimating slopes of time series, reducing the complexity of the inference task, and constraining the parameter search space. Other methods targeted issues of data preprocessing, detection and amelioration of model redundancy, and model-free or model-based structure identification. The total number of proposed methods and their applications has by now exceeded one hundred, which makes it difficult for the newcomer, as well as the expert, to gain a comprehensive overview of available algorithmic options and limitations. To facilitate the entry into the field of inverse modeling within BST and related modeling areas, the article presented here reviews the field and proposes an operational 'work-flow' that guides the user through the estimation process, identifies possibly problematic steps, and suggests corresponding solutions based on the specific characteristics of the various available algorithms. The article concludes with a discussion of the present state of the art and with a description of open questions.

Towards the automated engineering of a synthetic genome

The development of the technology to synthesize new genomes and to introduce them into hosts with inactivated wild-type chromosome opens the door to new horizons in synthetic biology. Here it is of outmost importance to harness the ability of using computational design to predict and optimize a synthetic genome before attempting its synthesis. The methodology to computationally design a genome is based on an optimization that computationally mimics genome evolution. The biggest bottleneck lies on the use of an appropriate fitness function. This fitness function, usually cell growth, relies on the ability to quantitatively model the biochemical networks of the cell at the genome scale using parameters inferred from high-throughput data. Computational methods integrating such models in a common multilayer design platform can be used to automatically engineer synthetic genomes under physiological specifications. We describe the current state-of-the-art on automated methods for engineering or re-engineering synthetic genomes. We restrict ourselves to global models of metabolism, transcription and DNA structure. Although we are still far from the de novo computational genome design, it is important to collect all relevant work towards this goal. Finally, we discuss future perspectives about the practicability of an automated methodology for such computational design of synthetic genomes.

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.

Modeling metabolic networks in C. glutamicum: a comparison of rate laws in combination with various parameter optimization strategies

BACKGROUND

To understand the dynamic behavior of cellular systems, mathematical modeling is often necessary and comprises three steps: (1) experimental measurement of participating molecules, (2) assignment of rate laws to each reaction, and (3) parameter calibration with respect to the measurements. In each of these steps the modeler is confronted with a plethora of alternative approaches, e. g., the selection of approximative rate laws in step two as specific equations are often unknown, or the choice of an estimation procedure with its specific settings in step three. This overall process with its numerous choices and the mutual influence between them makes it hard to single out the best modeling approach for a given problem.

RESULTS

We investigate the modeling process using multiple kinetic equations together with various parameter optimization methods for a well-characterized example network, the biosynthesis of valine and leucine in C. glutamicum. For this purpose, we derive seven dynamic models based on generalized mass action, Michaelis-Menten and convenience kinetics as well as the stochastic Langevin equation. In addition, we introduce two modeling approaches for feedback inhibition to the mass action kinetics. The parameters of each model are estimated using eight optimization strategies. To determine the most promising modeling approaches together with the best optimization algorithms, we carry out a two-step benchmark: (1) coarse-grained comparison of the algorithms on all models and (2) fine-grained tuning of the best optimization algorithms and models. To analyze the space of the best parameters found for each model, we apply clustering, variance, and correlation analysis.

CONCLUSION

A mixed model based on the convenience rate law and the Michaelis-Menten equation, in which all reactions are assumed to be reversible, is the most suitable deterministic modeling approach followed by a reversible generalized mass action kinetics model. A Langevin model is advisable to take stochastic effects into account. To estimate the model parameters, three algorithms are particularly useful: For first attempts the settings-free Tribes algorithm yields valuable results. Particle swarm optimization and differential evolution provide significantly better results with appropriate settings.

Metabolic flux model for an anchorage-dependent MDCK cell line: characteristic growth phases and minimum substrate consumption flux distribution

Up to now cell-culture based vaccine production processes only reach low productivities. The reasons are: (i) slow cell growth and (ii) low cell concentrations. To address these shortcomings, a quantitative analysis of the process conditions, especially the cell growth and the metabolic capabilities of the host cell line is required. For this purpose a MDCK cell based influenza vaccine production process was investigated. With a segregated growth model four distinct cell growth phases are distinguished in the batch process. In the first phase the cells attach to the surface of the microcarriers and show low metabolic activity. The second phase is characterized by exponential cell growth. In the third phase, preceded by a change in oxygen consumption, contact inhibition leads to a decrease in cell growth. Finally, the last phase before infection shows no further increase in cell numbers. To gain insight into the metabolic activity during these phases, a detailed metabolic model of MDCK cell was developed based on genome information and experimental analysis. The MDCK model was also used to calculate a theoretical flux distribution representing an optimized cell that only consumes a minimum of carbon sources. Comparing this minimum substrate consumption flux distribution to the fluxes estimated from experiments unveiled high overflow metabolism under the applied process conditions.

Integration of metabolic modeling and phenotypic data in evaluation and improvement of ethanol production using respiration-deficient mutants of Saccharomyces cerevisiae

Flux balance analysis and phenotypic data were used to provide clues to the relationships between the activities of gene products and the phenotypes resulting from the deletion of genes involved in respiratory function in Saccharomyces cerevisiae. The effect of partial or complete respiratory deficiency on the ethanol production and growth characteristics of hap4Delta/hap4Delta, mig1Delta/mig1Delta, qdr3Delta/qdr3Delta, pdr3Delta/pdr3Delta, qcr7Delta/qcr7Delta, cyt1Delta/cyt1Delta, and rip1Delta/rip1Delta mutants grown in microaerated chemostats was investigated. The study provided additional evidence for the importance of the selection of a physiologically relevant objective function, and it may improve quantitative predictions of exchange fluxes, as well as qualitative estimations of changes in intracellular fluxes. Ethanol production was successfully predicted by flux balance analysis in the case of the qdr3Delta/qdr3Delta mutant, with maximization of ethanol production as the objective function, suggesting an additional role for Qdr3p in respiration. The absence of similar changes in estimated intracellular fluxes in the qcr7Delta/qcr7Delta mutant compared to the rip1Delta/rip1Delta and cyt1Delta/cyt1Delta mutants indicated that the effect of the deletion of this subunit of complex III was somehow compensated for. Analysis of predicted flux distributions indicated self-organization of intracellular fluxes to avoid NAD(+)/NADH imbalance in rip1Delta/rip1Delta and cyt1Delta/cyt1Delta mutants, but not the qcr7Delta/qcr7Delta mutant. The flux through the glycerol efflux channel, Fps1p, was estimated to be zero in all strains under the investigated conditions. This indicates that previous strategies for improving ethanol production, such as the overexpression of the glutamate synthase gene GLT1 in a GDH1 deletion background or deletion of the glycerol efflux channel gene FPS1 and overexpression of GLT1, are unnecessary in a respiration-deficient background.

Diverse metabolic model parameters generate similar methionine cycle dynamics

Parameter estimation constitutes a major challenge in dynamic modeling of metabolic networks. Here we examine, via computational simulations, the influence of system nonlinearity and the nature of available data on the distribution and predictive capability of identified model parameters. Simulated methionine cycle metabolite concentration data (both with and without corresponding flux data) was inverted to identify model parameters consistent with it. Thousands of diverse parameter families were found to be consistent with the data to within moderate error, with most of the parameter values spanning over 1000-fold ranges irrespective of whether flux data was included. Due to strong correlations within the extracted parameter families, model predictions were generally reliable despite the broad ranges found for individual parameters. Inclusion of flux data, by strengthening these correlations, resulted in substantially more reliable flux predictions. These findings suggest that, despite the difficulty of extracting biochemically accurate model parameters from system level data, such data may nevertheless prove adequate for driving the development of predictive dynamic metabolic models.

Investigation of metabolic objectives in cultured hepatocytes

Using optimization based methods to predict fluxes in metabolic flux balance models has been a successful approach for some microorganisms, enabling construction of in silico models and even inference of some regulatory motifs. However, this success has not been translated to mammalian cells. The lack of knowledge about metabolic objectives in mammalian cells is a major obstacle that prevents utilization of various metabolic engineering tools and methods for tissue engineering and biomedical purposes. In this work, we investigate and identify possible metabolic objectives for hepatocytes cultured in vitro. To achieve this goal, we present a special data-mining procedure for identifying metabolic objective functions in mammalian cells. This multi-level optimization based algorithm enables identifying the major fluxes in the metabolic objective from MFA data in the absence of information about critical active constraints of the system. Further, once the objective is determined, active flux constraints can also be identified and analyzed. This information can be potentially used in a predictive manner to improve cell culture results or clinical metabolic outcomes. As a result of the application of this method, it was found that in vitro cultured hepatocytes maximize oxygen uptake, coupling of urea and TCA cycles, and synthesis of serine and urea. Selection of these fluxes as the metabolic objective enables accurate prediction of the flux distribution in the system given a limited amount of flux data; thus presenting a workable in silico model for cultured hepatocytes. It is observed that an overall homeostasis picture is also emergent in the findings.

Hybrid semi-parametric mathematical systems: bridging the gap between systems biology and process engineering

Systems biology is an integrative science that aims at the global characterization of biological systems. Huge amounts of data regarding gene expression, proteins activity and metabolite concentrations are collected by designing systematic genetic or environmental perturbations. Then the challenge is to integrate such data in a global model in order to provide a global picture of the cell. The analysis of these data is largely dominated by nonparametric modelling tools. In contrast, classical bioprocess engineering has been primarily founded on first principles models, but it has systematically overlooked the details of the embedded biological system. The full complexity of biological systems is currently assumed by systems biology and this knowledge can now be taken by engineers to decide how to optimally design and operate their processes. This paper discusses possible methodologies for the integration of systems biology and bioprocess engineering with emphasis on applications involving animal cell cultures. At the mathematical systems level, the discussion is focused on hybrid semi-parametric systems as a way to bridge systems biology and bioprocess engineering.

Genome-scale analysis of Mannheimia succiniciproducens metabolism

Mannheimia succiniciproducens MBEL55E isolated from bovine rumen is a capnophilic gram-negative bacterium that efficiently produces succinic acid, an industrially important four carbon dicarboxylic acid. In order to design a metabolically engineered strain which is capable of producing succinic acid with high yield and productivity, it is essential to optimize the whole metabolism at the systems level. Consequently, in silico modeling and simulation of the genome-scale metabolic network was employed for genome-scale analysis and efficient design of metabolic engineering experiments. The genome-scale metabolic network of M. succiniciproducens consisting of 686 reactions and 519 metabolites was constructed based on reannotation and validation experiments. With the reconstructed model, the network structure and key metabolic characteristics allowing highly efficient production of succinic acid were deciphered; these include strong PEP carboxylation, branched TCA cycle, relative weak pyruvate formation, the lack of glyoxylate shunt, and non-PTS for glucose uptake. Constraints-based flux analyses were then carried out under various environmental and genetic conditions to validate the genome-scale metabolic model and to decipher the altered metabolic characteristics. Predictions based on constraints-based flux analysis were mostly in excellent agreement with the experimental data. In silico knockout studies allowed prediction of new metabolic engineering strategies for the enhanced production of succinic acid. This genome-scale in silico model can serve as a platform for the systematic prediction of physiological responses of M. succiniciproducens to various environmental and genetic perturbations and consequently for designing rational strategies for strain improvement.

Modeling of the role of a Bax-activation switch in the mitochondrial apoptosis decision

We performed in silico modeling of the regulatory network of mitochondrial apoptosis through which we examined the role of a Bax-activation switch in governing the mitochondrial apoptosis decision. Two distinct modeling methods were used in this article. One is continuous and deterministic, comprised of a set of ordinary differential equations. The other, carried out in a discrete manner, is based on a cellular automaton, which takes stochastic fluctuations into consideration. We focused on dynamic properties of the mitochondrial apoptosis regulatory network. The roles of Bcl-2 family proteins in cellular responses to apoptotic stimuli were examined. In our simulations, a self-amplification process of Bax-activation is indicated. Further analysis suggests that the core module of Bax-activation is bistable in both deterministic and stochastic models, and this feature is robust to noise and wide ranges of parameter variation. When coupling with Bax-polymerization, it forms a one-way-switch, which governs irreversible behaviors of Bax-activation even with attenuation of apoptotic stimulus. Together with the growing biochemical evidence, we propose a novel molecular switch mechanism embedded in the mitochondrial apoptosis regulatory network and give a plausible explanation for the all-or-none, irreversible character of mitochondrial apoptosis.

Flux balance analysis of a genome-scale yeast model constrained by exometabolomic data allows metabolic system identification of genetically different strains

A systems approach to biology requires a principled approach to pathway identification. In this study, the two nuclear petite yeast mutants K1Deltapet191a and K1Deltapet191ab and their parental industrial strain K1 were cultured in glucose-containing microaerobic chemostats. Exometabolomic profiles were used to infer the differences in the fermentation characteristics and respiration capacity of the strains. The ability of the metabolite measurement information to describe genetically different strains was investigated using a genome-scale yeast model. Flux balance analysis (FBA) of the model reveals that the objective function of minimal oxygen consumption enables the identification of the effect of genotypic differences when combined with the knowledge of the extracellular state of metabolism. The predicted decrease in oxygen consumption flux of K1Deltapet191a and K1Deltapet191ab strains with respect to the parental strain is about 80% and 100%, respectively, which coincides with the respiratory deficiencies of the strains. The expected increase in ethanol production rates in response to the decrease in the respiratory capacity was also predicted to be very close to the experimental values. This study shows the predictive power of the integrated analysis of genome-scale models with exometabolomic profiles, since accurate predictions could be made without any information about the respiration capacity of the strains. The FBA approach thereby enables identification of responsive pathways and so permits the elucidation of the genetic characteristics of strains in terms of expressed metabolite profiles.

Minimization of glycerol production during the high-performance fed-batch ethanolic fermentation process in Saccharomyces cerevisiae, using a metabolic model as a prediction tool

On the basis of knowledge of the biological role of glycerol in the redox balance of Saccharomyces cerevisiae, a fermentation strategy was defined to reduce the surplus formation of NADH, responsible for glycerol synthesis. A metabolic model was used to predict the operating conditions that would reduce glycerol production during ethanol fermentation. Experimental validation of the simulation results was done by monitoring the inlet substrate feeding during fed-batch S. cerevisiae cultivation in order to maintain the respiratory quotient (RQ) (defined as the CO2 production to O2 consumption ratio) value between 4 and 5. Compared to previous fermentations without glucose monitoring, the final glycerol concentration was successfully decreased. Although RQ-controlled fermentation led to a lower maximum specific ethanol production rate, it was possible to reach a high level of ethanol production: 85 g.liter-1 with 1.7 g.liter-1 glycerol in 30 h. We showed here that by using a metabolic model as a tool in prediction, it was possible to reduce glycerol production in a very high-performance ethanolic fermentation process.

A kinetic model of oxygen regulation of cytochrome production in Escherichia coli

Recent experimental work has identified the principal components arrayed by Escherichia coli in its sensing of, and response to, varying levels of oxygen. This apparatus may be leveraged/modified by the metabolic engineer to identify nonuniform oxygen and glucose regimens that deliver better yields than their uniform counterparts. Toward this end we build and analyse a mathematical model that captures the role played by oxygen in the regulation of cytochrome production in E. coli.

Modeling brain energy metabolism and function: a multiparametric monitoring approach

Mathematical modeling of brain function is an important tool needed for a better understanding of experimental results and clinical situations. In the present study, we are constructing and testing a mathematical model capable of simulating changes in brain energy metabolism that develop in real time under various pathophysiological conditions. The model incorporates the following parameters: cerebral blood flow, partial oxygen pressure, mitochondrial NADH redox state, and extracellular potassium. Accordingly, all the model variables are only time dependent (;point-model' approach). Numerical runs demonstrate the ability of the model to mimic pathological conditions, such as complete and partial ischemia, cortical spreading depression under normoxic and partial ischemic conditions. They also show that, when properly tuned, a model of this type permits the monitoring of only one or two crucial variables and the computation of the remaining variables in real time during clinical or experimental procedures.

Thoughts on the teaching of metabolism

Systems biology, metabolomics, metabolic engineering, and other recent developments in biochemistry suggest that future biochemists will require a detailed familiarity with the compounds and pathways of intermediary metabolism and their biochemical control. The challenge to the biochemistry instructor is the presentation of metabolic pathways in a manner that allows student creativity in learning the pathways and their components. One approach that does permit the use of problem solving for the study of metabolic pathways involves following the fate of (13) C, (14) C, or (15) N labels, presented originally in the structure of an important metabolic starting compound, through relevant metabolic pathways. This method allows the presentation and study of problems in which such an isotopic label can be traced through two or more metabolic pathways, thus illustrating how these pathways are interconnected. The understanding that all the pathways of intermediary metabolism are interconnected provides opportunities to discuss their metabolic control by such mechanisms as signaling, feedback inhibition, location in organelles, coenzyme levels, and coenzyme recycling rates. The method is illustrated by following the fate of (14) C labels through anaerobic glycolysis, gluconeogenesis, and fatty acid transport, β-oxidation, and ketone body formation. Cholesterol biosynthesis and heme formation are used to show that presentations of long and complex pathways can demonstrate important biochemical concepts by following the fate of an isotopic label using only the most important intermediates. Problems based on tracing radioactive labels through one or more metabolic pathways allow the use of cooperative learning techniques.

Metabolic network analysis on Phaffia rhodozyma yeast using 13C-labeled glucose and gas chromatography-mass spectrometry

Carotenoid production by microorganisms, as opposed to chemical synthesis, could fulfill an ever-increasing demand for 'all natural' products. The yeast Phaffia rhodozyma has received considerable attention because it produces the red pigment astaxanthin, commonly used as an animal feed supplement. In order to have a better understanding of its metabolism, labeling experiments with [1-(13)C]glucose were conducted with the wildtype strain (CBS5905T) and a hyper-producing carotenoid strain (J4-3) in order to determine their metabolic network structure and estimate intracellular fluxes. Amino acid labeling patterns, as determined by GC-MS, were in accordance with a metabolic network consisting of the Embden-Meyerhof-Parnas pathway, the pentose phosphate pathway, and the TCA cycle. Glucose was mainly consumed along the pentose phosphate pathway ( approximately 65% for wildtype strain), which reflected high NADPH requirements for lipid biosynthesis. Although common to other oleaginous yeast, there was no, or very little, malic enzyme activity for carbon-limited growth. In addition, there was no evidence of phosphoketolase activity. The central carbon metabolism of the mutant strain was similar to that of the wildtype strain, though the relative pentose phosphate flux was lower and the TCA cycle flux in accordance with the biomass yield being lower.

Integration of gene expression data into genome-scale metabolic models

A framework for integration of transcriptome data into stoichiometric metabolic models to obtain improved flux predictions is presented. The key idea is to exploit the regulatory information in the expression data to give additional constraints on the metabolic fluxes in the model. Measurements of gene expression from chemostat and batch cultures of Saccharomyces cerevisiae were combined with a recently developed genome-scale model, and the computed metabolic flux distributions were compared to experimental values from carbon labeling experiments and metabolic network analysis. The integration of expression data resulted in improved predictions of metabolic behavior in batch cultures, enabling quantitative predictions of exchange fluxes as well as qualitative estimations of changes in intracellular fluxes. A critical discussion of correlation between gene expression and metabolic fluxes is given.

Use of genome-scale microbial models for metabolic engineering

Metabolic engineering serves as an integrated approach to design new cell factories by providing rational design procedures and valuable mathematical and experimental tools. Mathematical models have an important role for phenotypic analysis, but can also be used for the design of optimal metabolic network structures. The major challenge for metabolic engineering in the post-genomic era is to broaden its design methodologies to incorporate genome-scale biological data. Genome-scale stoichiometric models of microorganisms represent a first step in this direction.

Understanding in vivo benzenoid metabolism in petunia petal tissue

In vivo stable isotope labeling and computer-assisted metabolic flux analysis were used to investigate the metabolic pathways in petunia (Petunia hybrida) cv Mitchell leading from Phe to benzenoid compounds, a process that requires the shortening of the side chain by a C(2) unit. Deuterium-labeled Phe ((2)H(5)-Phe) was supplied to excised petunia petals. The intracellular pools of benzenoid/phenylpropanoid-related compounds (intermediates and end products) as well as volatile end products within the floral bouquet were analyzed for pool sizes and labeling kinetics by gas chromatography-mass spectrometry and liquid chromatography-mass spectrometry. Modeling of the benzenoid network revealed that both the CoA-dependent, beta-oxidative and CoA-independent, non-beta-oxidative pathways contribute to the formation of benzenoid compounds in petunia flowers. The flux through the CoA-independent, non-beta-oxidative pathway with benzaldehyde as a key intermediate was estimated to be about 2 times higher than the flux through the CoA-dependent, beta-oxidative pathway. Modeling of (2)H(5)-Phe labeling data predicted that in addition to benzaldehyde, benzylbenzoate is an intermediate between l-Phe and benzoic acid. Benzylbenzoate is the result of benzoylation of benzyl alcohol, for which activity was detected in petunia petals. A cDNA encoding a benzoyl-CoA:benzyl alcohol/phenylethanol benzoyltransferase was isolated from petunia cv Mitchell using a functional genomic approach. Biochemical characterization of a purified recombinant benzoyl-CoA:benzyl alcohol/phenylethanol benzoyltransferase protein showed that it can produce benzylbenzoate and phenylethyl benzoate, both present in petunia corollas, with similar catalytic efficiencies.

Metabolic engineering: advances in modeling and intervention in health and disease

The field of metabolic engineering encompasses a powerful set of tools that can be divided into (a) methods to model complex metabolic pathways and (b) techniques to manipulate these pathways for a desired metabolic outcome. These tools have recently seen increased utility in the medical arena, and this paper aims to review significant accomplishments made using these approaches. The modeling of metabolic pathways has been applied to better understand disease-state physiology in a variety of cellar, subcellular, and organ systems, including the liver, heart, mitochondria, and cancerous cells. Metabolic pathway engineering has been used to generate cells with novel biochemical functions for therapeutic use, and specific examples are provided in the areas of glycosylation engineering and dopamine-replacement therapy. In order to document the potential of applying both metabolic modeling and pathway manipulation, we describe pertinent advances in the field of diabetes research. Undoubtedly, as the field of metabolic engineering matures and is applied to a wider array of problems, new advances and therapeutic strategies will follow.

Modelling of Mammalian cells and cell culture processes

Mammalian cell cultures represent the major source for a number of very high-value biopharmaceutical products, including monoclonal antibodies (MAbs), viral vaccines, and hormones. These products are produced in relatively small quantities due to the highly specialised culture conditions and their susceptibility to either reduced productivity or cell death as a result of slight deviations in the culture conditions. The use of mathematical relationships to characterise distinct parts of the physiological behaviour of mammalian cells and the systematic integration of this information into a coherent, predictive model, which can be used for simulation, optimisation, and control purposes would contribute to efforts to increase productivity and control product quality. Models can also aid in the understanding and elucidation of underlying mechanisms and highlight the lack of accuracy or descriptive ability in parts of the model where experimental and simulated data cannot be reconciled. This paper reviews developments in the modelling of mammalian cell cultures in the last decade and proposes a future direction - the incorporation of genomic, proteomic, and metabolomic data, taking advantage of recent developments in these disciplines and thus improving model fidelity. Furthermore, with mammalian cell technology dependent on experiments for information, model-based experiment design is formally introduced, which when applied can result in the acquisition of more informative data from fewer experiments. This represents only part of a broader framework for model building and validation, which consists of three distinct stages: theoretical model assessment, model discrimination, and model precision, which provides a systematic strategy from assessing the identifiability and distinguishability of a set of competing models to improving the parameter precision of a final validated model.

Description and interpretation of adaptive evolution of Escherichia coli K-12 MG1655 by using a genome-scale in silico metabolic model

Genome-scale in silico metabolic networks of Escherichia coli have been reconstructed. By using a constraint-based in silico model of a reconstructed network, the range of phenotypes exhibited by E. coli under different growth conditions can be computed, and optimal growth phenotypes can be predicted. We hypothesized that the end point of adaptive evolution of E. coli could be accurately described a priori by our in silico model since adaptive evolution should lead to an optimal phenotype. Adaptive evolution of E. coli during prolonged exponential growth was performed with M9 minimal medium supplemented with 2 g of alpha-ketoglutarate per liter, 2 g of lactate per liter, or 2 g of pyruvate per liter at both 30 and 37 degrees C, which produced seven distinct strains. The growth rates, substrate uptake rates, oxygen uptake rates, by-product secretion patterns, and growth rates on alternative substrates were measured for each strain as a function of evolutionary time. Three major conclusions were drawn from the experimental results. First, adaptive evolution leads to a phenotype characterized by maximized growth rates that may not correspond to the highest biomass yield. Second, metabolic phenotypes resulting from adaptive evolution can be described and predicted computationally. Third, adaptive evolution on a single substrate leads to changes in growth characteristics on other substrates that could signify parallel or opposing growth objectives. Together, the results show that genome-scale in silico metabolic models can describe the end point of adaptive evolution a priori and can be used to gain insight into the adaptive evolutionary process for E. coli.

Metabolic switching in the sugar phosphotransferase system of Escherichia coli

Bacteria grown in a mixture of multiple sugars will first metabolize a preferred sugar until it is nearly depleted, only then turning to other carbon sources in the medium. This sharp switching of metabolic preference is characteristic of systems that optimize fitness. Here we consider the mechanism by which switching can occur in the Escherichia coli phosphotransferase system (PTS), which regulates the uptake and metabolism of several sugars. Using a model combining the description of fast biochemical processes and slower genetic regulation, we derive metabolic phase diagrams for the uptake of two PTS sugars, indicating regions of distinct sugar preference as a function of external sugar concentrations. We then propose a classification of bacterial phenotypes based on the topology of the metabolic phase diagram, and enumerate the possible topologically distinct phenotypes that can be achieved through mutations of the PTS. This procedure reveals that there is only one nontrivial switching phenotype that is insensitive to large changes in biochemical parameters. This phenotype exhibits diauxic growth, a manifestation of the winner-take-all dynamics enforced by PTS architecture. Winner-take-all behavior is implemented by the induction of sugar-specific operons, combined with competition between sugars for limited phosphoryl flux. We propose that flux-limited competition could be a common mechanism for introducing repressive interactions in cellular networks, and we argue that switching behavior similar to that described here should occur generically in systems that implement such a mechanism.

Constraints-based models: regulation of gene expression reduces the steady-state solution space

Constraints-based models have been effectively used to analyse, interpret, and predict the function of reconstructed genome-scale metabolic models. The first generation of these models used "hard" non-adjustable constraints associated with network connectivity, irreversibility of metabolic reactions, and maximal flux capacities. These constraints restrict the allowable behaviors of a network to a convex mathematical solution space whose edges are extreme pathways that can be used to characterize the optimal performance of a network under a stated performance criterion. The development of a second generation of constraints-based models by incorporating constraints associated with regulation of gene expression was described in a companion paper published in this journal, using flux-balance analysis to generate time courses of growth and by-product secretion using a skeleton representation of core metabolism. The imposition of these additional restrictions prevents the use of a subset of the extreme pathways that are derived from the "hard" constraints, thus reducing the solution space and restricting allowable network functions. Here, we examine the reduction of the solution space due to regulatory constraints using extreme pathway analysis. The imposition of environmental conditions and regulatory mechanisms sharply reduces the number of active extreme pathways. This approach is demonstrated for the skeleton system mentioned above, which has 80 extreme pathways. As regulatory constraints are applied to the system, the number of feasible extreme pathways is reduced to between 26 and 2 extreme pathways, a reduction of between 67.5 and 97.5%. The method developed here provides a way to interpret how regulatory mechanisms are used to constrain network functions and produce a small range of physiologically meaningful behaviors from all allowable network functions.

Determination of in vivo oxygen uptake and carbon dioxide evolution rates from off-gas measurements under highly dynamic conditions

In vivo kinetics of Saccharomyces cerevisiae are studied, in a time window of 150 s, by analyzing the response of O(2) and CO(2) in the fermentor off-gas after perturbation of chemostat cultures by metabolite pulses. Here, a new mathematical method is presented for the estimation of the in vivo oxygen uptake rate (OUR) and carbon dioxide evolution rate (CER) directly from the off-gas data in such perturbation experiments. The mathematical construction allows effective elimination of delay and distortion in the off-gas measurement signal under highly dynamic conditions. A black box model for the fermentor off-gas system is first obtained by system identification, followed by the construction of an optimal linear filter, based on the identified off-gas model. The method is applied to glucose and ethanol pulses performed on chemostat cultures of S. cerevisiae. The estimated OUR is shown to be consistent with the independent dissolved oxygen measurement. The estimated in vivo OUR and CER provide valuable insights into the complex dynamic behavior of yeast and are essential for the establishment and validation of in vivo kinetic models of primary metabolism.

Genome-scale reconstruction of the Saccharomyces cerevisiae metabolic network

The metabolic network in the yeast Saccharomyces cerevisiae was reconstructed using currently available genomic, biochemical, and physiological information. The metabolic reactions were compartmentalized between the cytosol and the mitochondria, and transport steps between the compartments and the environment were included. A total of 708 structural open reading frames (ORFs) were accounted for in the reconstructed network, corresponding to 1035 metabolic reactions. Further, 140 reactions were included on the basis of biochemical evidence resulting in a genome-scale reconstructed metabolic network containing 1175 metabolic reactions and 584 metabolites. The number of gene functions included in the reconstructed network corresponds to approximately 16% of all characterized ORFs in S. cerevisiae. Using the reconstructed network, the metabolic capabilities of S. cerevisiae were calculated and compared with Escherichia coli. The reconstructed metabolic network is the first comprehensive network for a eukaryotic organism, and it may be used as the basis for in silico analysis of phenotypic functions.

Sequence-based analysis of metabolic demands for protein synthesis in prokaryotes

Constraints-based models for microbial metabolism can currently be constructed on a genome-scale. These models do not account for RNA and protein synthesis. A scalable formalism to describe translation and transcription that can be integrated with the existing metabolic models is thus needed. Here, we developed such a formalism. The fundamental protein synthesis network described by this formalism was analysed via extreme pathway and flux balance analyses. The protein synthesis network exhibited one extreme pathway per messenger RNA synthesized and one extreme pathway per protein synthesized. The key parameters in this network included promoter strengths, messenger RNA half-lives, and the availability of nucleotide triphosphates, amino acids, RNA polymerase, and active ribosomes. Given these parameters, we were able to calculate a cell's material and energy expenditures for protein synthesis using a flux balance approach. The framework provided herein can subsequently be integrated with genome-scale metabolic models, providing a sequence-based accounting of the metabolic demands resulting from RNA and protein polymerization.

Genetic "code": representations and dynamical models of genetic components and networks

Dynamical modeling of biological systems is becoming increasingly widespread as people attempt to grasp biological phenomena in their full complexity and make sense of an accelerating stream of experimental data. We review a number of recent modeling studies that focus on systems specifically involving gene expression and regulation. These systems include bacterial metabolic operons and phase-variable piliation, bacteriophages T7 and lambda, and interacting networks of eukaryotic developmental genes. A wide range of conceptual and mathematical representations of genetic components and phenomena appears in these works. We discuss these representations in depth and give an overview of the tools currently available for creating and exploring dynamical models. We argue that for modeling to realize its full potential as a mainstream biological research technique the tools must become more general and flexible, and formal, standardized representations of biological knowledge and data must be developed.

Escherichia coli K-12 undergoes adaptive evolution to achieve in silico predicted optimal growth

Annotated genome sequences can be used to reconstruct whole-cell metabolic networks. These metabolic networks can be modelled and analysed (computed) to study complex biological functions. In particular, constraints-based in silico models have been used to calculate optimal growth rates on common carbon substrates, and the results were found to be consistent with experimental data under many but not all conditions. Optimal biological functions are acquired through an evolutionary process. Thus, incorrect predictions of in silico models based on optimal performance criteria may be due to incomplete adaptive evolution under the conditions examined. Escherichia coli K-12 MG1655 grows sub-optimally on glycerol as the sole carbon source. Here we show that when placed under growth selection pressure, the growth rate of E. coli on glycerol reproducibly evolved over 40 days, or about 700 generations, from a sub-optimal value to the optimal growth rate predicted from a whole-cell in silico model. These results open the possibility of using adaptive evolution of entire metabolic networks to realize metabolic states that have been determined a priori based on in silico analysis.

A functional genomics approach using metabolomics and in silico pathway analysis

In the field of functional genomics increasing effort is being undertaken to analyze the function of orphan genes using metabolome data. Improved analytical equipment allows screening simultaneously for a high number of metabolites. Such metabolite profiles are analyzed using multivariate data analysis techniques and changes in the genotype will in many cases lead to different metabolite profiles. Here, a theoretical framework that may be applied to identify the function of orphan genes is presented. The approach is based on a combination of metabolome analysis combined with in silico pathway analysis. Pathway analysis may be carried out using convex analysis and a change in the active pathway structure of deletion mutants expressed in a different metabolite profile may disclose the function or the functional class of an orphan gene. The concept is illustrated using a simplified model for growth of Saccharomyces cerevisiae.

Genome-scale metabolic model of Helicobacter pylori 26695

A genome-scale metabolic model of Helicobacter pylori 26695 was constructed from genome sequence annotation, biochemical, and physiological data. This represents an in silico model largely derived from genomic information for an organism for which there is substantially less biochemical information available relative to previously modeled organisms such as Escherichia coli. The reconstructed metabolic network contains 388 enzymatic and transport reactions and accounts for 291 open reading frames. Within the paradigm of constraint-based modeling, extreme-pathway analysis and flux balance analysis were used to explore the metabolic capabilities of the in silico model. General network properties were analyzed and compared to similar results previously generated for Haemophilus influenzae. A minimal medium required by the model to generate required biomass constituents was calculated, indicating the requirement of eight amino acids, six of which correspond to essential human amino acids. In addition a list of potential substrates capable of fulfilling the bulk carbon requirements of H. pylori were identified. A deletion study was performed wherein reactions and associated genes in central metabolism were deleted and their effects were simulated under a variety of substrate availability conditions, yielding a number of reactions that are deemed essential. Deletion results were compared to recently published in vitro essentiality determinations for 17 genes. The in silico model accurately predicted 10 of 17 deletion cases, with partial support for additional cases. Collectively, the results presented herein suggest an effective strategy of combining in silico modeling with experimental technologies to enhance biological discovery for less characterized organisms and their genomes.