Cumulative bondomers: a new concept in flux analysis from 2D [13C,1H] COSY NMR data

A well-established way of determining metabolic fluxes is to measure 2D [(13)C,(1)H] COSY NMR spectra of components of biomass grown on uniformly (13)C-labeled carbon sources. When using the entire set of measured data to simultaneously determine all fluxes in a proposed metabolic network model, the (13)C-labeling distribution in all measured compounds has to be simulated. This requires very large sets of isotopomer or cumomer balances. This article introduces the new concept of bondomers; entities that only vary in the numbers and positions of C-C bonds that have remained intact since the medium substrate molecule entered the metabolism. Bondomers are shown to have many analogies to isotopomers. One of these is that bondomers can be transformed to cumulative bondomers, just like isotopomers can be transformed to cumomers. Similarly to cumomers, cumulative bondomers allow an analytical solution of the entire set of balances describing a metabolic network. The main difference is that cumulative bondomer models are considerably smaller than corresponding cumomer models. This saves computational time, allows easier identifiability analysis, and yields new insights in the information content of 2D [(13)C,(1)H] COSY NMR data. We illustrate the theoretical concepts by means of a realistic example of the glycolytic and pentose phosphate pathways. The combinations of 2D [(13)C,(1)H] COSY NMR data that allow identification of all metabolic fluxes in these pathways are analyzed, and it is found that the NMR data contain less information than was previously expected.     

Flux quantification in central carbon metabolism of Catharanthus roseus hairy roots by 13C labeling and comprehensive bondomer balancing

Methods for accurate and efficient quantification of metabolic fluxes are desirable in plant metabolic engineering and systems biology. Toward this objective, we introduce the application of "bondomers", a computationally efficient and intuitively appealing alternative to the commonly used isotopomer concept, to flux evaluation in plants, by using Catharanthus roseus hairy roots as a model system. We cultured the hairy roots on (5% w/w U-(13)C, 95% w/w naturally abundant) sucrose, and acquired two-dimensional [(13)C, (1)H] and [(1)H, (1)H] NMR spectra of hydrolyzed aqueous extract from the hairy roots. Analysis of these spectra yielded a data set of 116 bondomers of beta-glucans and proteinogenic amino acids from the hairy roots. Fluxes were evaluated from the bondomer data by using comprehensive bondomer balancing. We identified most fluxes in a three-compartmental model of central carbon metabolism with good precision. We observed parallel pentose phosphate pathways in the cytosol and the plastid with significantly different fluxes. The anaplerotic fluxes between phosphoenolpyruvate and oxaloacetate in the cytosol and between malate and pyruvate in the mitochondrion were relatively high (60.1+/-2.5 mol per 100 mol sucrose uptake, or 22.5+/-0.5 mol per 100 mol mitochondrial pyruvate dehydrogenase flux). The development of a comprehensive flux analysis tool for this plant hairy root system is expected to be valuable in assessing the metabolic impact of genetic or environmental changes, and this methodology can be extended to other plant systems.     

Metabolic flux and metabolic network analysis of Penicillium chrysogenum using 2D [13C, 1H] COSY NMR measurements and cumulative bondomer simulation

At present two alternative methods are available for analyzing the fluxes in a metabolic network: (1) combining measurements of net conversion rates with a set of metabolite balances including the cofactor balances, or (2) leaving out the cofactor balances and fitting the resulting free fluxes to measured (13)C-labeling data. In this study these two approaches are applied to the fluxes in the glycolysis and pentose phosphate pathway of Penicillium chrysogenum growing on either ammonia or nitrate as the nitrogen source, which is expected to give different pentose phosphate pathway fluxes. The presented flux analyses are based on extensive sets of 2D [(13)C, (1)H] COSY data. A new concept is applied for simulation of this type of (13)C-labeling data: cumulative bondomer modeling. The outcomes of the (13)C-labeling based flux analysis substantially differ from those of the pure metabolite balancing approach. The fluxes that are determined using (13)C-labeling data are shown to be highly dependent on the chosen metabolic network. Extending the traditional nonoxidative pentose phosphate pathway with additional transketolase and transaldolase reactions, extending the glycolysis with a fructose 6-phosphate aldolase/dihydroxyacetone kinase reaction sequence or adding a phosphoenolpyruvate carboxykinase reaction to the model considerably improves the fit of the measured and the simulated NMR data. The results obtained using the extended version of the nonoxidative pentose phosphate pathway model show that the transketolase and transaldolase reactions need not be assumed reversible to get a good fit of the (13)C-labeling data. Strict statistical testing of the outcomes of (13)C-labeling based flux analysis using realistic measurement errors is demonstrated to be of prime importance for verifying the assumed metabolic model.     

An improved method for statistical analysis of metabolic flux analysis using isotopomer mapping matrices with analytical expressions

Analytical expressions were derived for calculating the sensitivities of isotopomer distribution vectors, the weighted output matrix with respect to the fluxes, and the covariance matrix for the metabolic flux analysis based on isotopomers mapping matrices (IMM). These expressions allow us to implement efficient statistical analysis, avoiding the time-consuming Monte Carlo techniques for estimating the confidence interval of the fluxes. The analytical expressions are also useful in implementing a faster design of experiment, which requires repetitive computation of the covariance matrix that is not straightforward to make in practice with the numerical techniques based on the conventional IMM. The proposed method was applied for analyzing the central carbon metabolism of the mixotrophically cultivated Synechocystis sp. PCC6803, and the confidence intervals of all its fluxes were computed based on the isotopomer distribution measured using NMR and GC-MS. It was found that the best feasible mixture for labeling experiment is 70% unlabeled, 10% [U-13C] and 20% [1,2-13C2] labeled glucose to obtain the most reliable metabolic fluxes.     

Quantitative analysis of metabolic fluxes in Escherichia coli, using two-dimensional NMR spectroscopy and complete isotopomer models.

Complete isotopomer models that simulate distribution of label in 13C tracer experiments are applied to the quantification of metabolic fluxes in the primary carbon metabolism of E. coli under aerobic and anaerobic conditions. The concept of isotopomer mapping matrices (IMMs) is used to simplify the formulation of isotopomer mass balances by expressing all isotopomer mass balances of a metabolite pool in a single matrix equation. A numerically stable method to calculate the steady-state isotopomer distribution in metabolic networks in introduced. Net values of intracellular fluxes and the degree of reversibility of enzymatic steps are estimated by minimization of the deviations between experimental and simulated measurements. The metabolic model applied includes the Embden-Meyerhof-Parnas and the pentose phosphate pathway, the tricarboxylic acid cycle, anaplerotic reaction sequences and pathways involved in amino acid synthesis. The study clearly demonstrates the value of complete isotopomer models for maximizing the information obtainable from 13C tracer experiments. The approach applied here offers a completely general and comprehensive analysis of carbon tracer experiments where any set of experimental data on the labeling state and extracellular fluxes can be used for the quantification of metabolic fluxes in complex metabolic networks.     

Optimization of 13C isotopic tracers for metabolic flux analysis in mammalian cells

Mammalian cells consume and metabolize various substrates from their surroundings for energy generation and biomass synthesis. Glucose and glutamine, in particular, are the primary carbon sources for proliferating cancer cells. While this combination of substrates generates static labeling patterns for use in (13)C metabolic flux analysis (MFA), the inability of single tracers to effectively label all pathways poses an obstacle for comprehensive flux determination within a given experiment. To address this issue we applied a genetic algorithm to optimize mixtures of (13)C-labeled glucose and glutamine for use in MFA. We identified tracer combinations that minimized confidence intervals in an experimentally determined flux network describing central carbon metabolism in tumor cells. Additional simulations were used to determine the robustness of the [1,2-(13)C(2)]glucose/[U-(13)C(5)]glutamine tracer combination with respect to perturbations in the network. Finally, we experimentally validated the improved performance of this tracer set relative to glucose tracers alone in a cancer cell line. This versatile method allows researchers to determine the optimal tracer combination to use for a specific metabolic network, and our findings applied to cancer cells significantly enhance the ability of MFA experiments to precisely quantify fluxes in higher organisms.     

Metabolic flux analysis at ultra short time scale: isotopically non-stationary 13C labeling experiments

A novel approach to (13)C metabolic flux analysis (MFA) is presented using cytosolic metabolite pool sizes and their (13)C labeling data from an isotopically non-stationary (13)C labeling experiment (INST-CLE). The procedure is demonstrated with an E. coli wild type strain grown at fed batch conditions. The intra cellular labeling dynamics are excited by a sudden step increase of the (13)C portion in the substrate feed. Due to unchanged saturation of the substrate uptake system, the metabolic fluxes remain constant during the following sampling time period of only 16s, in which 20 samples are taken by an automated rapid sampling device immediately stopping metabolism by methanol quenching. Subsequent cell disruptive sample preparation and LC-MS/MS enabled simultaneous determination of pool sizes and mass isotopomers of intra cellular metabolites requiring detection limits in the nM range. Based on this data the new computational flux analysis tool 13CFLUX/INST is used to determine the intra cellular fluxes based on a complex carbon labeling network model. The measured data is in good agreement with the model predictions, thus proving the applicability of the new isotopically non-stationary (13)C metabolic flux analysis (INST-(13)C-MFA) concept. Moreover, it is shown that significant new information with respect to flux identifiability, non-measurable pool sizes, data consistency, or large storage pools can be taken from the novel kind of experimental data. This offers new insight into the biological operation of the metabolic network in vivo.     

Bidirectional reaction steps in metabolic networks: II. Flux estimation and statistical analysis

Metabolic carbon labelling experiments enable a large amount of extracellular fluxes and intracellular carbon isotope enrichments to be measured. Since the relation between the measured quantities and the unknown intracellular metabolic fluxes is given by bilinear balance equations, flux determination from this data set requires the numerical solution of a nonlinear inverse problem. To this end, a general algorithm for flux estimation from metabolic carbon labelling experiments based on the least squares approach is developed in this contribution and complemented by appropriate tools for statistical analysis. The linearization technique usually applied for the computation of nonlinear confidence regions is shown to be inappropriate in the case of large exchange fluxes. For this reason a sophisticated compactification transformation technique for nonlinear statistical analysis is developed. Statistical analysis is then performed by computing appropriate statistical quality measures like output sensitivities, parameter sensitivities and the parameter covariance matrix. This allows one to determine the order of magnitude of exchange fluxes in most practical situations. An application study with a large data set from lysine-producing Corynebacterium glutamicum demonstrates the power and limitations of the carbon-labelling technique. It is shown that all intracellular fluxes in central metabolism can be quantitated without assumptions on intracellular energy yields. At the same time several exchange fluxes are determined which is invaluable information for metabolic engineering. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 118-135, 1997.     

Quantification of compartmented metabolic fluxes in developing soybean embryos by employing biosynthetically directed fractional (13)C labeling, two-dimensional [(13)C, (1)H] nuclear magnetic resonance, and comprehensive isotopomer balancing

Metabolic flux quantification in plants is instrumental in the detailed understanding of metabolism but is difficult to perform on a systemic level. Toward this aim, we report the development and application of a computer-aided metabolic flux analysis tool that enables the concurrent evaluation of fluxes in several primary metabolic pathways. Labeling experiments were performed by feeding a mixture of U-(13)C Suc, naturally abundant Suc, and Gln to developing soybean (Glycine max) embryos. Two-dimensional [(13)C, (1)H] NMR spectra of seed storage protein and starch hydrolysates were acquired and yielded a labeling data set consisting of 155 (13)C isotopomer abundances. We developed a computer program to automatically calculate fluxes from this data. This program accepts a user-defined metabolic network model and incorporates recent mathematical advances toward accurate and efficient flux evaluation. Fluxes were calculated and statistical analysis was performed to obtain sds. A high flux was found through the oxidative pentose phosphate pathway (19.99 +/- 4.39 micromol d(-1) cotyledon(-1), or 104.2 carbon mol +/- 23.0 carbon mol per 100 carbon mol of Suc uptake). Separate transketolase and transaldolase fluxes could be distinguished in the plastid and the cytosol, and those in the plastid were found to be at least 6-fold higher. The backflux from triose to hexose phosphate was also found to be substantial in the plastid (21.72 +/- 5.00 micromol d(-1) cotyledon(-1), or 113.2 carbon mol +/-26.0 carbon mol per 100 carbon mol of Suc uptake). Forward and backward directions of anaplerotic fluxes could be distinguished. The glyoxylate shunt flux was found to be negligible. Such a generic flux analysis tool can serve as a quantitative tool for metabolic studies and phenotype comparisons and can be extended to other plant systems.     

Parallel labeling experiments with [U-(13)C]glucose validate E. coli metabolic network model for (13)C metabolic flux analysis

(13)C-metabolic flux analysis (MFA) is a widely used method for measuring intracellular metabolic fluxes in living cells. (13)C MFA relies on several key assumptions: (1) the assumed metabolic network model is complete, in that it accounts for all significant enzymatic and transport reactions; (2) (13)C-labeling measurements are accurate and precise; and (3) enzymes and transporters do not discriminate between (12)C- and (13)C-labeled metabolites. In this study, we tested these inherent assumptions of (13)C MFA for wild-type E. coli by parallel labeling experiments with [U-(13)C]glucose as tracer. Cells were grown in six parallel cultures in custom-constructed mini-bioreactors, starting from the same inoculum, on medium containing different mixtures of natural glucose and fully labeled [U-(13)C]glucose, ranging from 0% to 100% [U-(13)C]glucose. Macroscopic growth characteristics of E. coli showed no observable kinetic isotope effect. The cells grew equally well on natural glucose, 100% [U-(13)C]glucose, and mixtures thereof. (13)C MFA was then used to determine intracellular metabolic fluxes for several metabolic network models: an initial network model from literature; and extended network models that accounted for potential dilution effects of isotopic labeling. The initial network model did not give statistically acceptable fits and produced inconsistent flux results for the parallel labeling experiments. In contrast, an extended network model that accounted for dilution of intracellular CO(2) by exchange with extracellular CO(2) produced statistically acceptable fits, and the estimated metabolic fluxes were consistent for the parallel cultures. This study illustrates the importance of model validation for (13)C MFA. We show that an incomplete network model can produce statistically unacceptable fits, as determined by a chi-square test for goodness-of-fit, and return biased metabolic fluxes. The validated metabolic network model for E. coli from this study can be used in future investigations for unbiased metabolic flux measurements.     

The thermodynamic meaning of metabolic exchange fluxes

Metabolic flux analysis (MFA) deals with the experimental determination of steady-state fluxes in metabolic networks. An important feature of the ¹³C MFA method is its capability to generate information on both directions of bidirectional reaction steps given by exchange fluxes. The biological interpretation of these exchange fluxes and their relation to thermodynamic properties of the respective reaction steps has never been systematically investigated. As a central result, it is shown here that for a general class of enzyme reaction mechanisms the quotients of net and exchange fluxes measured by ¹³C MFA are coupled to Gibbs energies of the reaction steps. To establish this relation the concept of apparent flux ratios of enzymatic isotope-labeling networks is introduced and some computing rules for these flux ratios are given. Application of these rules reveals a conceptional pitfall of ¹³C MFA, which is the inherent dependency of measured exchange fluxes on the chosen tracer atom. However, it is shown that this effect can be neglected for typical biochemical reaction steps under physiological conditions. In this situation, the central result can be formulated as a two-sided inequality relating fluxes, pool sizes, and standard Gibbs energies. This relation has far-reaching consequences for metabolic flux analysis, quantitative metabolomics, and network thermodynamics.     

Bioreaction network topology and metabolic flux ratio analysis by biosynthetic fractional 13C labeling and two-dimensional NMR spectroscopy

Biosynthetically directed fractional 13C labeling of the proteinogenic amino acids is achieved by feeding a mixture of uniformly 13C-labeled and unlabeled carbon source compounds into a bioreaction network. Analysis of the resulting labeling pattern enables both a comprehensive characterization of the network topology and the determination of metabolic flux ratios. Attractive features with regard to routine applications are (i) an inherently small demand for 13C-labeled source compounds and (ii) the high sensitivity of two-dimensional [13C,1H]-correlation nuclear magnetic resonance spectroscopy for analysis of 13C-labeling patterns. A user-friendly program, FCAL, is available to allow rapid data analysis. This novel approach, which recently also has been employed in conjunction with metabolic flux balancing to obtain reliable estimates of in vivo fluxes, enables efficient support of metabolic engineering and biotechnology process design.     

The relationships between the metabolic fluxes and 13C-labeled isotopomer distribution for the flux analysis of the main metabolic pathways

It has been known that ¹³C-labeling technique is quite useful in estimating the metabolic fluxes. Although the program-based flux analysis is powerful, it is not easy to be confident with the result obtained without experiences and exhaustive trial and errors based on statistical analysis for the confidence intervals in practice. It is, therefore, quite important to grasp the relationship between the fluxes and the ¹³C-labeled isotopomer distribution to get deeper insight into the metabolic flux analysis. In the present research, it was shown explicitly how the isotopomer distribution changes with respect to the fluxes in relation to the labeling patterns of the substrate, where either labeled glucose, acetate, or pyruvate was used as a carbon source. Some of the analytical expressions were derived based on the matrix representation, and they were utilized for analysis. It was shown that the isotopomer pattern does not necessarily change uniformly with respect to fluxes, but changes in a complicated way in particular for the case of using pyruvate as a carbon source where some isotopomers do not necessarily change monotonically. It was shown to be quite important to grasp how the isotopomer pattern changes with respect to fluxes and the labeling pattern of the substrate for flux determination and the experimental design. It was also shown that the mixture of [1-¹³C] acetate and [2-¹³C] acetate should not be used from the information index point of view. Some of the experimental data were evaluated from the present approach. It was also shown that the isotopomer distribution is less sensitive to the bidirectional fluxes in the reversible pathway.     

A priori analysis of metabolic flux identifiability from (13)C-labeling data

The (13)C-labeling technique was introduced in the field of metabolic engineering as a tool for determining fluxes that could not be found using the 'classical' method of flux balancing. An a priori flux identifiability analysis is required in order to determine whether a (13)C-labeling experiment allows the identification of all the fluxes. In this article, we propose a method for identifiability analysis that is based on the recently introduced 'cumomer' concept. The method improves upon previous identifiability methods in that it provides a way of systematically reducing the metabolic network on the basis of structural elements that constitute a network and to use the implicit function theorem to analytically determine whether the fluxes in the reduced network are theoretically identifiable for various types of real measurement data. Application of the method to a realistic flux identification problem shows both the potential of the method in yielding new, interesting conclusions regarding the identifiability and its practical limitations that are caused by the fact that symbolic calculations grow fast with the dimension of the studied system.     

Metabolic isotopomer labeling systems. Part II: structural flux identifiability analysis

Metabolic flux analysis using carbon labeling experiments (CLEs) is an important tool in metabolic engineering where the intracellular fluxes have to be computed from the measured extracellular fluxes and the partially measured distribution of 13C labeling within the intracellular metabolite pools. The relation between unknown fluxes and measurements is described by an isotopomer labeling system (ILS) (see Part I [Math. Biosci. 169 (2001) 173]). Part II deals with the structural flux identifiability of measured ILSs in the steady state. The central question is whether the measured data contains sufficient information to determine the unknown intracellular fluxes. This question has to be decided a priori, i.e. before the CLE is carried out. In structural identifiability analysis the measurements are assumed to be noise-free. A general theory of structural flux identifiability for measured ILSs is presented and several algorithms are developed to solve the identifiability problem. In the particular case of maximal measurement information, a symbolical algorithm is presented that decides the identifiability question by means of linear methods. Several upper bounds of the number of identifiable fluxes are derived, and the influence of the chosen inputs is evaluated. By introducing integer arithmetic this algorithm can even be applied to large networks. For the general case of arbitrary measurement information, identifiability is decided by a local criterion. A new algorithm based on integer arithmetic enables an a priori local identifiability analysis to be performed for networks of arbitrary size. All algorithms have been implemented and flux identifiability is investigated for the network of the central metabolic pathways of a microorganism. Moreover, several small examples are worked out to illustrate the influence of input metabolite labeling and the paradox of information loss due to network simplification.     

Collisional fragmentation of central carbon metabolites in LC-MS/MS increases precision of ¹³C metabolic flux analysis

Experimental determination of fluxes by (13)C-tracers relies on detection of (13)C-patterns in metabolites or by-products. In the field of (13)C metabolic flux analysis, the most recent developments point toward recording labeling patterns by liquid chromatography (LC)-mass spectrometry (MS)/MS directly in intermediates in central carbon metabolism (CCM) to increase temporal resolution. Surprisingly, the flux studies published so far with LC-MS measurements were based on intact metabolic intermediates-thus neglected the potential benefits of using positional information to improve flux estimation. For the first time, we exploit collisional fragmentation to obtain more fine-grained (13)C-data on intermediates of CCM and investigate their impact in (13)C metabolic flux analysis. For the case study of Bacillus subtilis grown in mineral medium with (13)C-labeled glucose, we compare the flux estimates obtained by iterative isotopologue balancing of (13)C-data obtained either by LC-MS/MS for solely intact intermediates or LC-MS/MS for intact and fragmented intermediates of CCM. We show that with LC-MS/MS data, fragment information leads to more precise estimates of fluxes in pentose phosphate pathway, glycolysis, and to the tricarboxylic acid cycle. Additionally, we present an efficient analytical strategy to rapidly acquire large sets of (13)C-patterns by tandem MS, and an in-depth analysis of the collisional fragmentation of primary intermediates. In the future, this catalogue will enable comprehensive in silico calculability analyses to identify the most sensitive measurements and direct experimental design.     

Computational tools for isotopically instationary 13C labeling experiments under metabolic steady state conditions

(13)C metabolic flux analysis (MFA) has become an important and powerful tool for the quantitative analysis of metabolic networks in the framework of metabolic engineering. Isotopically instationary (13)C MFA under metabolic stationary conditions is a promising refinement of classical stationary MFA. It accounts for the experimental requirements of non-steady-state cultures as well as for the shortening of the experimental duration. This contribution extends all computational methods developed for classical stationary (13)C MFA to the instationary situation by using high-performance computing methods. The developed tools allow for the simulation of instationary carbon labeling experiments (CLEs), sensitivity calculation with respect to unknown parameters, fitting of the model to the measured data, statistical identifiability analysis and an optimal experimental design facility. To explore the potential of the new approach all these tools are applied to the central metabolism of Escherichia coli. The achieved results are compared to the outcome of the stationary counterpart, especially focusing on statistical properties. This demonstrates the specific strengths of the instationary method. A new ranking method is proposed making both an a priori and an a posteriori design of the sampling times available. It will be shown that although still not all fluxes are identifiable, the quality of flux estimates can be strongly improved in the instationary case. Moreover, statements about the size of some immeasurable pool sizes can be made.     

High-throughput metabolic flux analysis based on gas chromatography-mass spectrometry derived 13C constraints

13C-constrained flux balancing analysis based on gas chromatography-mass spectrometry data is presented here as a simple and robust method for the estimation of intracellular carbon fluxes. In this approach, the underdetermined system of metabolite balances deduced from stoichiometric relations and measured extracellular rates is complemented with 13C constraints from metabolic flux ratio analysis. Fluxes in central carbon metabolism of exponentially growing Escherichia coli were estimated by 13C-constrained flux balancing from three different 13C-labeled glucose experiments. The best resolution of the network was achieved using 13C constraints derived from [U-13C]glucose and [1-13C]glucose experiments. The corresponding flux estimate was in excellent agreement with a solution that was independently obtained with a comprehensive isotopomer model. This new methodology was also demonstrated to faithfully capture the intracellular flux distribution in E. coli shake flasks and 1-ml deep-well microtiter plates. Due to its simplicity, speed, and robustness, 13C-constrained metabolic flux balancing is promising for routine and high-throughput analysis on a miniaturized scale.     

Strategies for investigating the plant metabolic network with steady-state metabolic flux analysis: lessons from an Arabidopsis cell culture and other systems

Steady-state (13)C metabolic flux analysis (MFA) is currently the experimental method of choice for generating flux maps of the compartmented network of primary metabolism in heterotrophic and mixotrophic plant tissues. While statistically robust protocols for the application of steady-state MFA to plant tissues have been developed by several research groups, the implementation of the method is still far from routine. The effort required to produce a flux map is more than justified by the information that it contains about the metabolic phenotype of the system, but it remains the case that steady-state MFA is both analytically and computationally demanding. This article provides an overview of principles that underpin the implementation of steady-state MFA, focusing on the definition of the metabolic network responsible for redistribution of the label, experimental considerations relating to data collection, the modelling process that allows a set of metabolic fluxes to be deduced from the labelling data, and the interpretation of flux maps. The article draws on published studies of Arabidopsis cell cultures and other systems, including developing oilseeds, with the aim of providing practical guidance and strategies for handling the issues that arise when applying steady-state MFA to the complex metabolic networks encountered in plants.     

Determination of metabolic fluxes in a non-steady-state system

Estimation of fluxes through metabolic networks from redistribution patterns of (13)C has become a well developed technique in recent years. However, the approach is currently limited to systems at metabolic steady-state; dynamic changes in metabolic fluxes cannot be assessed. This is a major impediment to understanding the behaviour of metabolic networks, because steady-state is not always experimentally achievable and a great deal of information about the control hierarchy of the network can be derived from the analysis of flux dynamics. To address this issue, we have developed a method for estimating non-steady-state fluxes based on the mass-balance of mass isotopomers. This approach allows multiple mass-balance equations to be written for the change in labelling of a given metabolite pool and thereby permits over-determination of fluxes. We demonstrate how linear regression methods can be used to estimate non-steady-state fluxes from these mass balance equations. The approach can be used to calculate fluxes from both mass isotopomer and positional isotopomer labelling information and thus has general applicability to data generated from common spectrometry- or NMR-based analytical platforms. The approach is applied to a GC-MS time-series dataset of (13)C-labelling of metabolites in a heterotrophic Arabidopsis cell suspension culture. Threonine biosynthesis is used to demonstrate that non-steady-state fluxes can be successfully estimated from such data while organic acid metabolism is used to highlight some common issues that can complicate flux estimation. These include multiple pools of the same metabolite that label at different rates and carbon skeleton rearrangements.