The thermodynamic meaning of metabolic exchange fluxes

Rethinking 13C-metabolic flux analysis - The Bayesian way of flux inference

Metabolic reaction rates (fluxes) play a crucial role in comprehending cellular phenotypes and are essential in areas such as metabolic engineering, biotechnology, and biomedical research. The state-of-the-art technique for estimating fluxes is metabolic flux analysis using isotopic labelling (13C-MFA), which uses a dataset-model combination to determine the fluxes. Bayesian statistical methods are gaining popularity in the field of life sciences, but the use of 13C-MFA is still dominated by conventional best-fit approaches. The slow take-up of Bayesian approaches is, at least partly, due to the unfamiliarity of Bayesian methods to metabolic engineering researchers. To address this unfamiliarity, we here outline similarities and differences between the two approaches and highlight particular advantages of the Bayesian way of flux analysis. With a real-life example, re-analysing a moderately informative labelling dataset of E. coli, we identify situations in which Bayesian methods are advantageous and more informative, pointing to potential pitfalls of current 13C-MFA evaluation approaches. We propose the use of Bayesian model averaging (BMA) for flux inference as a means of overcoming the problem of model uncertainty through its tendency to assign low probabilities to both, models that are unsupported by data, and models that are overly complex. In this capacity, BMA resembles a tempered Ockham's razor. With the tempered razor as a guide, BMA-based 13C-MFA alleviates the problem of model selection uncertainty and is thereby capable of becoming a game changer for metabolic engineering by uncovering new insights and inspiring novel approaches.

BayFlux: A Bayesian method to quantify metabolic Fluxes and their uncertainty at the genome scale

Metabolic fluxes, the number of metabolites traversing each biochemical reaction in a cell per unit time, are crucial for assessing and understanding cell function. 13C Metabolic Flux Analysis (13C MFA) is considered to be the gold standard for measuring metabolic fluxes. 13C MFA typically works by leveraging extracellular exchange fluxes as well as data from 13C labeling experiments to calculate the flux profile which best fit the data for a small, central carbon, metabolic model. However, the nonlinear nature of the 13C MFA fitting procedure means that several flux profiles fit the experimental data within the experimental error, and traditional optimization methods offer only a partial or skewed picture, especially in "non-gaussian" situations where multiple very distinct flux regions fit the data equally well. Here, we present a method for flux space sampling through Bayesian inference (BayFlux), that identifies the full distribution of fluxes compatible with experimental data for a comprehensive genome-scale model. This Bayesian approach allows us to accurately quantify uncertainty in calculated fluxes. We also find that, surprisingly, the genome-scale model of metabolism produces narrower flux distributions (reduced uncertainty) than the small core metabolic models traditionally used in 13C MFA. The different results for some reactions when using genome-scale models vs core metabolic models advise caution in assuming strong inferences from 13C MFA since the results may depend significantly on the completeness of the model used. Based on BayFlux, we developed and evaluated novel methods (P-13C MOMA and P-13C ROOM) to predict the biological results of a gene knockout, that improve on the traditional MOMA and ROOM methods by quantifying prediction uncertainty.

MYC overrides HIF-1α to regulate proliferating primary cell metabolism in hypoxia

Hypoxia requires metabolic adaptations to sustain energetically demanding cellular activities. While the metabolic consequences of hypoxia have been studied extensively in cancer cell models, comparatively little is known about how primary cell metabolism responds to hypoxia. Thus, we developed metabolic flux models for human lung fibroblast and pulmonary artery smooth muscle cells proliferating in hypoxia. Unexpectedly, we found that hypoxia decreased glycolysis despite activation of hypoxia-inducible factor 1α (HIF-1α) and increased glycolytic enzyme expression. While HIF-1α activation in normoxia by prolyl hydroxylase (PHD) inhibition did increase glycolysis, hypoxia blocked this effect. Multi-omic profiling revealed distinct molecular responses to hypoxia and PHD inhibition, and suggested a critical role for MYC in modulating HIF-1α responses to hypoxia. Consistent with this hypothesis, MYC knockdown in hypoxia increased glycolysis and MYC over-expression in normoxia decreased glycolysis stimulated by PHD inhibition. These data suggest that MYC signaling in hypoxia uncouples an increase in HIF-dependent glycolytic gene transcription from glycolytic flux.

Interpreting metabolic complexity via isotope-assisted metabolic flux analysis

Isotope-assisted metabolic flux analysis (iMFA) is a powerful method to mathematically determine the metabolic fluxome from experimental isotope labeling data and a metabolic network model. While iMFA was originally developed for industrial biotechnological applications, it is increasingly used to analyze eukaryotic cell metabolism in physiological and pathological states. In this review, we explain how iMFA estimates the intracellular fluxome, including data and network model (inputs), the optimization-based data fitting (process), and the flux map (output). We then describe how iMFA enables analysis of metabolic complexities and discovery of metabolic pathways. Our goal is to expand the use of iMFA in metabolism research, which is essential to maximizing the impact of metabolic experiments and continuing to advance iMFA and biocomputational techniques.

One-shot 13 C15 N-metabolic flux analysis for simultaneous quantification of carbon and nitrogen flux

Metabolic flux is the final output of cellular regulation and has been extensively studied for carbon but much less is known about nitrogen, which is another important building block for living organisms. For the tuberculosis pathogen, this is particularly important in informing the development of effective drugs targeting the pathogen's metabolism. Here we performed ¹³ C¹⁵ N dual isotopic labeling of Mycobacterium bovis BCG steady state cultures, quantified intracellular carbon and nitrogen fluxes and inferred reaction bidirectionalities. This was achieved by model scope extension and refinement, implemented in a multi-atom transition model, within the statistical framework of Bayesian model averaging (BMA). Using BMA-based ¹³ C¹⁵ N-metabolic flux analysis, we jointly resolve carbon and nitrogen fluxes quantitatively. We provide the first nitrogen flux distributions for amino acid and nucleotide biosynthesis in mycobacteria and establish glutamate as the central node for nitrogen metabolism. We improved resolution of the notoriously elusive anaplerotic node in central carbon metabolism and revealed possible operation modes. Our study provides a powerful and statistically rigorous platform to simultaneously infer carbon and nitrogen metabolism in any biological system.

Novel computational and experimental approaches for investigating the thermodynamics of metabolic networks

Thermodynamic analysis of metabolic networks has emerged as a useful new tool for pathway design and metabolic engineering. Understanding the relationship between the thermodynamic driving force of biochemical reactions and metabolic flux has generated new insights regarding the design principles of microbial carbon metabolism. This review summarizes the various lessons that can be obtained from the thermodynamic analysis of metabolic pathways, illustrates concepts of computational thermodynamic tools, and highlights recent applications of thermodynamic analysis to pathway design in industrially relevant microbes.

Glucose metabolism in Pseudomonas aeruginosa is cyclic when producing Polyhydroxyalkanoates and Rhamnolipids

Pseudomonas aeruginosa is an important chassis for production of polyhydroxyalkanoates (PHA) and rhamnolipids (RHL). Advances in the understanding of the biosynthesis metabolism of these biocompounds are crucial for increasing yield. ¹³C-Metabolic Flux Ratio Analysis (¹³C-MFA) is a technique to estimate in vivo metabolic fluxes ratios. PHA and RHL are essentially non-growth associated products of biotechnological interest and both contain hydroxyalkanoates (HAs), whose labeling patterns could be accessed by GC-MS. In this study, to reveal the relative contributions of the Entner-Doudoroff (ED) pathway and the non-oxidative Pentose Phosphate (PP) pathway to PHA and RHL production, ¹³C-MFA was performed in Pseudomonas aeruginosa LFM634 when supplied with labeled glucose. This bacterial strain lacks both functional EMP and the oxidative PP branch. Labeling patterns in HAs were measured. Experiments with [U-¹³C] glucose indicated a low flux though PP pathway. An optimal design of labeling experiment showed that [6-¹³C] glucose would be the best substrate to enable an estimation of the ED flux with high accuracy. Results of experiments performed with this isotope indicated that about two-thirds of glyceraldehyde 3-phosphate is recycled through a cyclic ED architecture, suggesting that P. aeruginosa utilizes that cycle to regulate the NADPH/Acetyl-CoA ratio for PHA and RHL biosynthesis.

Sulfate-dependent reversibility of intracellular reactions explains the opposing isotope effects in the anaerobic oxidation of methane

The anaerobic oxidation of methane (AOM) is performed by methanotrophic archaea (ANME) in distinct sulfate-methane interfaces of marine sediments. In these interfaces, AOM often appears to deplete methane in the heavy isotopes toward isotopic compositions similar to methanogenesis. Here, we shed light on this effect and its physiological underpinnings using a thermophilic ANME-1-dominated culture. At high sulfate concentrations, residual methane is enriched in both ¹³C and ²H (¹³α = 1.016 and ²α = 1.155), as observed previously. In contrast, at low sulfate concentrations, the residual methane is substantially depleted in ¹³C (¹³α = 0.977) and, to a lesser extent, in ²H. Using a biochemical-isotopic model, we explain the sulfate dependence of the net isotopic fractionation through the thermodynamic drive of the involved intracellular reactions. Our findings relate these isotopic patterns to the physiology and environment of the ANME, thereby explaining a commonly observed isotopic enigma.

Reversible jump MCMC for multi-model inference in Metabolic Flux Analysis

Motivation

The validity of model based inference, as used in systems biology, depends on the underlying model formulation. Often, a vast number of competing models is available, that are built on different assumptions, all consistent with the existing knowledge about the studied biological phenomenon. As a remedy for this, Bayesian Model Averaging (BMA) facilitates parameter and structural inferences based on multiple models simultaneously. However, in fields where a vast number of alternative, high-dimensional and non-linear models are involved, the BMA-based inference task is computationally very challenging.

Results

Here we use BMA in the complex setting of Metabolic Flux Analysis (MFA) to infer whether potentially reversible reactions proceed uni- or bidirectionally, using 13C labeling data and metabolic networks. BMA is applied on a large set of candidate models with differing directionality settings, using a tailored multi-model Markov Chain Monte Carlo (MCMC) approach. The applicability of our algorithm is shown by inferring the in vivo probability of reaction bidirectionalities in a realistic network setup, thereby extending the scope of 13C MFA from parameter to structural inference.

Supplementary information

Supplementary data are available at Bioinformatics online.

The Design of FluxML: A Universal Modeling Language for 13C Metabolic Flux Analysis

¹³C metabolic flux analysis (MFA) is the method of choice when a detailed inference of intracellular metabolic fluxes in living organisms under metabolic quasi-steady state conditions is desired. Being continuously developed since two decades, the technology made major contributions to the quantitative characterization of organisms in all fields of biotechnology and health-related research. ¹³C MFA, however, stands out from other "-omics sciences," in that it requires not only experimental-analytical data, but also mathematical models and a computational toolset to infer the quantities of interest, i.e., the metabolic fluxes. At present, these models cannot be conveniently exchanged between different labs. Here, we present the implementation-independent model description language FluxML for specifying ¹³C MFA models. The core of FluxML captures the metabolic reaction network together with atom mappings, constraints on the model parameters, and the wealth of data configurations. In particular, we describe the governing design processes that shaped the FluxML language. We demonstrate the utility of FluxML to represent many contemporary experimental-analytical requirements in the field of ¹³C MFA. The major aim of FluxML is to offer a sound, open, and future-proof language to unambiguously express and conserve all the necessary information for model re-use, exchange, and comparison. Along with FluxML, several powerful computational tools are supplied for easy handling, but also to maintain a maximum of flexibility. Altogether, the FluxML collection is an "all-around carefree package" for ¹³C MFA modelers. We believe that FluxML improves scientific productivity as well as transparency and therewith contributes to the efficiency and reproducibility of computational modeling efforts in the field of ¹³C MFA.

Cytosolic Aspartate Availability Determines Cell Survival When Glutamine Is Limiting

Mitochondrial function is important for aspartate biosynthesis in proliferating cells. Here, we show that mitochondrial aspartate export via the aspartate-glutamate carrier 1 (AGC1) supports cell proliferation and cellular redox homeostasis. Insufficient cytosolic aspartate delivery leads to cell death when TCA cycle carbon is reduced following glutamine withdrawal and/or glutaminase inhibition. Moreover, loss of AGC1 reduces allograft tumor growth that is further compromised by treatment with the glutaminase inhibitor CB-839. Together, these findings argue that mitochondrial aspartate export sustains cell survival in low-glutamine environments and AGC1 inhibition can synergize with glutaminase inhibition to limit tumor growth.

Isotopically nonstationary metabolic flux analysis (INST-MFA): putting theory into practice

Typically, ¹³C flux analysis relies on assumptions of both metabolic and isotopic steady state. If metabolism is steady but isotope labeling is not allowed to fully equilibrate, isotopically nonstationary metabolic flux analysis (INST-MFA) can be used to estimate fluxes. This requires solution of differential equations that describe the time-dependent labeling of network metabolites, while iteratively adjusting the flux and pool size parameters to match the transient labeling measurements. INST-MFA holds a number of unique advantages over approaches that rely solely upon steady-state isotope enrichments. First, INST-MFA can be applied to estimate fluxes in autotrophic systems, which consume only single-carbon substrates. Second, INST-MFA is ideally suited to systems that label slowly due to the presence of large intermediate pools or pathway bottlenecks. Finally, INST-MFA provides increased measurement sensitivity to estimate reversible exchange fluxes and metabolite pool sizes, which represents a potential framework for integrating metabolomic analysis with ¹³C flux analysis. This review highlights the unique capabilities of INST-MFA, describes newly available software tools that automate INST-MFA calculations, presents several practical examples of recent INST-MFA applications, and discusses the technical challenges that lie ahead.

Reverse engineering the cancer metabolic network using flux analysis to understand drivers of human disease

Metabolic dysfunction has reemerged as an essential hallmark of tumorigenesis, and metabolic phenotypes are increasingly being integrated into pre-clinical models of disease. The complexity of these metabolic networks requires systems-level interrogation, and metabolic flux analysis (MFA) with stable isotope tracing present a suitable conceptual framework for such systems. Here we review efforts to elucidate mechanisms through which metabolism influences tumor growth and survival, with an emphasis on applications using stable isotope tracing and MFA. Through these approaches researchers can now quantify pathway fluxes in various in vitro and in vivo contexts to provide mechanistic insights at molecular and physiological scales respectively. Knowledge and discoveries in cancer models are paving the way toward applications in other biological contexts and disease models. In turn, MFA approaches will increasingly help to uncover new therapeutic opportunities that enhance human health.

Metabolite concentrations, fluxes and free energies imply efficient enzyme usage

In metabolism, available free energy is limited and must be divided across pathway steps to maintain ΔG negative throughout. For each reaction, ΔG is log-proportional both to a concentration ratio (reaction quotient-to-equilibrium constant) and to a flux ratio (backward-to-forward flux). Here we use isotope labeling to measure absolute metabolite concentrations and fluxes in Escherichia coli, yeast, and a mammalian cell line. We then integrate this information to obtain a unified set of concentrations and ΔG for each organism. In glycolysis, we find that free energy is partitioned so as to mitigate unproductive backward fluxes associated with ΔG near zero. Across metabolism, we observe that absolute metabolite concentrations and ΔG are substantially conserved, and that most substrate (but not inhibitor) concentrations exceed the associated enzyme binding site affinity. The observed conservation of metabolite concentrations is consistent with an evolutionary drive to utilize enzymes efficiently given thermodynamic and osmotic constraints.

Fluxes through plant metabolic networks: measurements, predictions, insights and challenges

Although the flows of material through metabolic networks are central to cell function, they are not easy to measure other than at the level of inputs and outputs. This is particularly true in plant cells, where the network spans multiple subcellular compartments and where the network may function either heterotrophically or photoautotrophically. For many years, kinetic modelling of pathways provided the only method for describing the operation of fragments of the network. However, more recently, it has become possible to map the fluxes in central carbon metabolism using the stable isotope labelling techniques of metabolic flux analysis (MFA), and to predict intracellular fluxes using constraints-based modelling procedures such as flux balance analysis (FBA). These approaches were originally developed for the analysis of microbial metabolism, but over the last decade, they have been adapted for the more demanding analysis of plant metabolic networks. Here, the principal features of MFA and FBA as applied to plants are outlined, followed by a discussion of the insights that have been gained into plant metabolic networks through the application of these time-consuming and non-trivial methods. The discussion focuses on how a system-wide view of plant metabolism has increased our understanding of network structure, metabolic perturbations and the provision of reducing power and energy for cell function. Current methodological challenges that limit the scope of plant MFA are discussed and particular emphasis is placed on the importance of developing methods for cell-specific MFA.

Fluxome study of Pseudomonas fluorescens reveals major reorganisation of carbon flux through central metabolic pathways in response to inactivation of the anti-sigma factor MucA

Background

The bacterium Pseudomonas fluorescens switches to an alginate-producing phenotype when the pleiotropic anti-sigma factor MucA is inactivated. The inactivation is accompanied by an increased biomass yield on carbon sources when grown under nitrogen-limited chemostat conditions. A previous metabolome study showed significant changes in the intracellular metabolite concentrations, especially of the nucleotides, in mucA deletion mutants compared to the wild-type. In this study, the P. fluorescens SBW25 wild-type and an alginate non-producing mucA- ΔalgC double-knockout mutant are investigated through model-based ¹³C-metabolic flux analysis (¹³C-MFA) to explore the physiological consequences of MucA inactivation at the metabolic flux level. Intracellular metabolite extracts from three carbon labelling experiments using fructose as the sole carbon source are analysed for ¹³C-label incorporation in primary metabolites by gas and liquid chromatography tandem mass spectrometry.

Results

From mass isotopomer distribution datasets, absolute intracellular metabolic reaction rates for the wild type and the mutant are determined, revealing extensive reorganisation of carbon flux through central metabolic pathways in response to MucA inactivation. The carbon flux through the Entner-Doudoroff pathway was reduced in the mucA- ΔalgC mutant, while flux through the pentose phosphate pathway was increased. Our findings also indicated flexibility of the anaplerotic reactions through down-regulation of the pyruvate shunt in the mucA- ΔalgC mutant and up-regulation of the glyoxylate shunt.

Conclusions

Absolute metabolic fluxes and metabolite levels give detailed, integrated insight into the physiology of this industrially, medically and agriculturally important bacterial species and suggest that the most efficient way of using a mucA- mutant as a cell factory for alginate production would be to use non-growing conditions and nitrogen deprivation.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0148-0) contains supplementary material, which is available to authorized users.

Pool size measurements facilitate the determination of fluxes at branching points in non-stationary metabolic flux analysis: the case of Arabidopsis thaliana

Pool size measurements are important for the estimation of absolute intracellular fluxes in particular scenarios based on data from heavy carbon isotope experiments. Recently, steady-state fluxes estimates were obtained for central carbon metabolism in an intact illuminated rosette of Arabidopsis thaliana grown photoautotrophically (Szecowka et al., 2013; Heise et al., 2014). Fluxes were estimated therein by integrating mass-spectrometric data of the dynamics of the unlabeled metabolic fraction, data on metabolic pool sizes, partitioning of metabolic pools between cellular compartments and estimates of photosynthetically inactive pools, with a simplified model of plant central carbon metabolism. However, the fluxes were determined by treating the pool sizes as fixed parameters. Here we investigated whether and, if so, to what extent the treatment of pool sizes as parameters to be optimized in three scenarios may affect the flux estimates. The results are discussed in terms of benchmark values for canonical pathways and reactions, including starch and sucrose synthesis as well as the ribulose-1,5-bisphosphate carboxylation and oxygenation reactions. In addition, we discuss pathways emerging from a divergent branch point for which pool sizes are required for flux estimation, irrespective of the computational approach used for the simulation of the observable labeling pattern. Therefore, our findings indicate the necessity for development of techniques for accurate pool size measurements to improve the quality of flux estimates from non-stationary flux estimates in intact plant cells in the absence of alternative flux measurements.

Relevance of the MEK/ERK signaling pathway in the metabolism of activated macrophages: a metabolomic approach

The activation of immune cells in response to a pathogen involves a succession of signaling events leading to gene and protein expression, which requires metabolic changes to match the energy demands. The metabolic profile associated with the MAPK cascade (ERK1/2, p38, and JNK) in macrophages was studied, and the effect of its inhibition on the specific metabolic pattern of LPS stimulation was characterized. A [1,2-[(13)C](2)]glucose tracer-based metabolomic approach was used to examine the metabolic flux distribution in these cells after MEK/ERK inhibition. Bioinformatic tools were used to analyze changes in mass isotopomer distribution and changes in glucose and glutamine consumption and lactate production in basal and LPS-stimulated conditions in the presence and absence of the selective inhibitor of the MEK/ERK cascade, PD325901. Results showed that PD325901-mediated ERK1/2 inhibition significantly decreased glucose consumption and lactate production but did not affect glutamine consumption. These changes were accompanied by a decrease in the glycolytic flux, consistent with the observed decrease in fructose-2,6-bisphosphate concentration. The oxidative and nonoxidative pentose phosphate pathways and the ratio between them also decreased. However, tricarboxylic acid cycle flux did not change significantly. LPS activation led to the opposite responses, although all of these were suppressed by PD325901. However, LPS also induced a small decrease in pentose phosphate pathway fluxes and an increase in glutamine consumption that were not affected by PD325901. We concluded that inhibition of the MEK/ERK cascade interferes with central metabolism, and this cross-talk between signal transduction and metabolism also occurs in the presence of LPS.

Thermodynamic calculations for biochemical transport and reaction processes in metabolic networks

Thermodynamic analysis of metabolic networks has recently generated increasing interest for its ability to add constraints on metabolic network operation, and to combine metabolic fluxes and metabolite measurements in a mechanistic manner. Concepts for the calculation of the change in Gibbs energy of biochemical reactions have long been established. However, a concept for incorporation of cross-membrane transport in these calculations is still missing, although the theory for calculating thermodynamic properties of transport processes is long known. Here, we have developed two equivalent equations to calculate the change in Gibbs energy of combined transport and reaction processes based on two different ways of treating biochemical thermodynamics. We illustrate the need for these equations by showing that in some cases there is a significant difference between the proposed correct calculation and using an approximative method. With the developed equations, thermodynamic analysis of metabolic networks spanning over multiple physical compartments can now be correctly described.

Integrated stoichiometric, thermodynamic and kinetic modelling of steady state metabolism

The quantitative analysis of biochemical reactions and metabolites is at frontier of biological sciences. The recent availability of high-throughput technology data sets in biology has paved the way for new modelling approaches at various levels of complexity including the metabolome of a cell or an organism. Understanding the metabolism of a single cell and multi-cell organism will provide the knowledge for the rational design of growth conditions to produce commercially valuable reagents in biotechnology. Here, we demonstrate how equations representing steady state mass conservation, energy conservation, the second law of thermodynamics, and reversible enzyme kinetics can be formulated as a single system of linear equalities and inequalities, in addition to linear equalities on exponential variables. Even though the feasible set is non-convex, the reformulation is exact and amenable to large-scale numerical analysis, a prerequisite for computationally feasible genome scale modelling. Integrating flux, concentration and kinetic variables in a unified constraint-based formulation is aimed at increasing the quantitative predictive capacity of flux balance analysis. Incorporation of experimental and theoretical bounds on thermodynamic and kinetic variables ensures that the predicted steady state fluxes are both thermodynamically and biochemically feasible. The resulting in silico predictions are tested against fluxomic data for central metabolism in Escherichia coli and compare favourably with in silico prediction by flux balance analysis.

Metabolic fluxes during strong carbon catabolite repression by malate in Bacillus subtilis

Commonly glucose is considered to be the only preferred substrate in Bacillus subtilis whose presence represses utilization of other alternative substrates. Because recent data indicate that malate might be an exception, we quantify here the carbon source utilization hierarchy. Based on physiology and transcriptional data during co-utilization experiments with eight carbon substrates, we demonstrate that malate is a second preferred carbon source for B. subtilis, which is rapidly co-utilized with glucose and strongly represses the uptake of alternative substrates. From the different hierarchy and degree of catabolite repression exerted by glucose and malate, we conclude that both substrates might act through different molecular mechanisms. To obtain a quantitative and functional network view of how malate is (co)metabolized, we developed a novel approach to metabolic flux analysis that avoids error-prone, intuitive, and ad hoc decisions on (13)C rearrangements. In particular, we developed a rigorous approach for deriving reaction reversibilities by combining in vivo intracellular metabolite concentrations with a thermodynamic feasibility analysis. The thus-obtained analytical model of metabolism was then used for network-wide isotopologue balancing to estimate the intracellular fluxes. These (13)C-flux data revealed an extraordinarily high malate influx that is primarily catabolized via the gluconeogenic reactions and toward overflow metabolism. Furthermore, a considerable NADPH-producing malic enzyme flux is required to supply the biosynthetically required NADPH in the presence of malate. Co-utilization of glucose and malate resulted in a synergistic decrease of the respiratory tricarboxylic acid cycle flux.

Metabolic flux analysis in plants: coping with complexity

Theory and experience in metabolic engineering both show that metabolism operates at the network level. In plants, this complexity is compounded by a high degree of compartmentation and the synthesis of a very wide array of secondary metabolic products. A further challenge to understanding and predicting plant metabolic function is posed by our ignorance about the structure of metabolic networks even in well-studied systems. Metabolic flux analysis (MFA) provides tools to measure and model the functioning of metabolism, and is making significant contributions to coping with their complexity. This review gives an overview of different MFA approaches, the measurements required to implement them and the information they yield. The application of MFA methods to plant systems is then illustrated by several examples from the recent literature. Next, the challenges that plant metabolism poses for MFA are discussed together with ways that these can be addressed. Lastly, new developments in MFA are described that can be expected to improve the range and reliability of plant MFA in the coming years.