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First published online July 30, 2008; 10.1104/pp.108.125195 Plant Physiology 148:704-718 (2008) © 2008 American Society of Plant Biologists OPEN ACCESS ARTICLE
Metabolic Network Fluxes in Heterotrophic Arabidopsis Cells: Stability of the Flux Distribution under Different Oxygenation Conditions1,[W],[OA]Department of Plant Sciences, University of Oxford, Oxford OX1 3RB, United Kingdom
Steady-state labeling experiments with [1-13C]Glc were used to measure multiple metabolic fluxes through the pathways of central metabolism in a heterotrophic cell suspension culture of Arabidopsis (Arabidopsis thaliana). The protocol was based on in silico modeling to establish the optimal labeled precursor, validation of the isotopic and metabolic steady state, extensive nuclear magnetic resonance analysis of the redistribution of label into soluble metabolites, starch, and protein, and a comprehensive set of biomass measurements. Following a simple modification of the cell culture procedure, cells were grown at two oxygen concentrations, and flux maps of central metabolism were constructed on the basis of replicated experiments and rigorous statistical analysis. Increased growth rate at the higher O2 concentration was associated with an increase in fluxes throughout the network, and this was achieved without any significant change in relative fluxes despite differences in the metabolite profile of organic acids, amino acids, and carbohydrates. The balance between biosynthesis and respiration within the tricarboxylic acid cycle was unchanged, with 38% ± 5% of carbon entering used for biosynthesis under standard O2 conditions and 33% ± 2% under elevated O2. These results add to the emerging picture of the stability of the central metabolic network and its capacity to respond to physiological perturbations with the minimum of rearrangement. The lack of correlation between the change in metabolite profile, which implied significant disruption of the metabolic network following the alteration in the oxygen supply, and the unchanging flux distribution highlights a potential difficulty in the interpretation of metabolomic data.
Although the complexity and plasticity of the metabolic network in plants allows them to adapt to fluctuating environmental conditions, the same properties also present a significant obstacle to metabolic engineering (Carrari et al., 2003a  ; Kruger and Ratcliffe, 2008; Sweetlove et al., 2008). The problem is particularly acute in primary metabolism, where there have been numerous instances of unsuccessful engineering, and reflects the current incomplete understanding of the way in which metabolic networks respond to environmental and genetic perturbations. Fluxes of central carbon metabolism are part of the missing information (Sweetlove et al., 2003), and although they are necessarily related to enzyme abundances, metabolite concentrations, and transcriptional responses (Carrari et al., 2006; Junker et al., 2007), their reliable prediction from the available data remains a non-trivial task (Sweetlove and Fernie, 2005). For this reason, the development and application of techniques for the measurement of flux in plants has become an important area of research (Schwender et al., 2004a; Fernie et al., 2005; Ratcliffe and Shachar-Hill, 2006).
Steady-state metabolic flux analysis (MFA) has the capacity to resolve parallel, cyclic, and reversible fluxes, making it a useful technique for quantifying metabolic fluxes and investigating the factors that control them in plants (Roscher et al., 2000
A key question in the regulation of central carbon metabolism is how the simultaneous demands of catabolic respiratory metabolism and anabolic biosynthetic metabolism are managed. The tricarboxylic acid (TCA) cycle is central to both processes, generating reducing equivalents for the mitochondrial electron transfer chain, and providing precursors for several biosynthetic pathways (Fernie et al., 2004 Thus, a quantitative picture is emerging of TCA cycle fluxes and the extent to which they vary depending on the need to generate precursors for biosynthesis and reductant for ATP synthesis. However, the factors that may control the rates of biosynthesis and respiration, and the balance between these two competing processes, have not been tested systematically. Accordingly, we varied the concentration of O2 in the medium of an Arabidopsis cell suspension culture with the aim of perturbing the operation of the TCA cycle. The effect of this manipulation on the flux map of central metabolism, and in particular the effect on the balance between respiratory and biosynthetic fluxes, was quantified using steady-state MFA.
Construction and Refinement of a Metabolic Model
The successful application of MFA requires the construction of a model that not only accurately reflects metabolism within the experimental system, but that also can be solved with the quantity and quality of data that are likely to be obtainable. To this end, we constructed an initial model of central carbon metabolism in heterotrophic Arabidopsis cell suspension cultures using a format compatible with the steady-state MFA software 13C-FLUX (Wiechert et al., 2001
The complexity of the network that can be analyzed is partly determined by the extent to which the redistribution of the 13C-label can be quantified after labeling to isotopic steady state. We used the statistical analysis component of 13C-FLUX, EstimateStat, to predict errors on optimized flux estimates for different network configurations and 13C-labeled precursors and, hence, refined the initial model to the point where it could be solved with the data obtainable from a steady-state labeling experiment. By this method, structurally nonidentifiable fluxes, i.e. those that can take any value without impacting on the observed label distribution (Wiechert et al., 2001
EstimateStat was also used to predict the optimal precursor for estimating TCA cycle fluxes in the refined model. Figure 1 suggests that [1-13C]Glc provides the best estimates of flux through the TCA cycle and elsewhere in the network. [1-13C]Glc and [U-13C6]Glc performed similarly well for TCA cycle fluxes, with predicted errors less than the magnitude of the flux estimates, but this analysis suggested that [1-13C]Glc provided the more accurate estimates of flux elsewhere in the network. [2-13C]Glc appeared to offer no advantage over [1-13C] or [U-13C6]Glc and is significantly more expensive. The analysis was repeated using several different models with more or less explicitly defined subcellular compartmentation of glycolysis and the oxidative pentose phosphate pathway (data not shown). Though the degree of compartmentation greatly affected the predicted relative errors, the qualitative finding that [1-13C]Glc would provide the smallest relative errors for the majority of fluxes remained the same. Post hoc analysis of the final model at the end of the investigation (data not shown) confirmed that labeling with 100% [1-13C]Glc provided the most reliable estimates of flux.
Elevated O2 Conditions Perturb Cell Suspension Culture Metabolism
As oxygen is required to support respiration, the availability of oxygen to the cell suspension cultures might be expected to influence overall rates of metabolism and/or the partitioning of carbon entering the TCA cycle between respiration and biosynthesis. To test this hypothesis, we established a system for culturing cells at elevated O2 concentration by replacing the aluminum foil used to seal the flasks with Miracloth. After 5 d of growth, there was consistently more oxygen dissolved in the medium of cultures covered with Miracloth (elevated O2) than those covered with foil (standard O2); in a representative experiment, the oxygen concentration of the culture medium was 161.5 ± 12.5 µM for elevated O2 cells and 76.0 ± 2.5 µM for standard O2 cells, both of which are lower than the 270 µM expected for air-saturated water at 21°C (Truesdale and Downing, 1954
Validation of Isotopic and Metabolic Steady State
Steady-state flux analysis requires isotopomer abundances to be measured when the system is at isotopic and metabolic steady state, i.e. when metabolic fluxes are constant and when the distribution of label throughout the network has stabilized (Ratcliffe and Shachar-Hill, 2006
The existence of an isotopic steady state suggests that any changes in metabolic fluxes over time must be relatively slow (Roscher et al., 2000 ). Stronger evidence for a metabolic steady state in our system is provided by the fact that the abundance of most soluble metabolites did not change from 4.5 to 5.5 d (Fig. 2). In particular, there were no significant changes in abundance between 5 and 5.5 d of growth, suggesting that the cells reached metabolic steady state after 5 d. In addition, the rate of Glc consumption and biomass increase was constant from 4.5 to 5.5 d (data not shown).
Cell cultures were labeled to isotopic steady state by growth on 100% [1-13C]Glc for 5 d under elevated O2 and standard O2 conditions. Quantitative 1D 13C NMR spectroscopy was used to obtain the label measurements necessary for estimation of metabolic fluxes from soluble metabolites, protein amino acids, and Glc digested from starch. The contributions to each assigned peak were analyzed by line-fitting (Fig. 4 , inset), and the resulting label measurements were combined appropriately to give relative cumomer abundances. This procedure yielded, from three biological replicates, a total of 389 relative cumomer abundance measurements for the standard O2 condition and 429 measurements for the elevated O2 condition. All measurements for a single biological replicate came from the same batch of cells. The complete measurement dataset is given in Supplemental Table S1.
To optimize flux estimates, 13C-FLUX minimizes the variance-weighted sum of squared differences between the experimental labeling data and simulated labeling data generated by 13C-FLUX using the flux estimates. The algorithm is therefore guided to an optimal flux solution by the size of the errors assigned to individual label measurements, and thus the accurate assignment of errors is likely to be important for the reproducible determination of the true flux solution. To accommodate this in the analysis, an empirical relationship was established between relative peak error and peak signal to noise ratio (SNR; Fig. 4). This formula was used to assign error estimates to individual 13C NMR labeling measurements and hence to relative cumomer abundances.
The 13C-FLUX implementation of the sequential quadratic programming algorithm Donlp2 (Peter Spellucci, Technische Universität Darmstadt, Germany) was used to fit the free net and exchange fluxes to the measured isotopomer data. Fluxes were fitted to all three biological replicates for a single treatment simultaneously to give a single solution that should represent the average flux state of the three replicates. To constrain the flux solution within known bounds, we used the rates of Glc consumption and biomass accumulation, and the biomass composition (Table I) to calculate input and output fluxes for cell suspensions grown under elevated and standard O2 (Sriram et al., 2006
The presence of phosphoenolpyruvate carboxykinase (PEPCK) in the cell cultures is supported by proteomic analysis (L. Miguet, unpublished data; Baerenfaller et al., 2008
The labeling data from amino acids synthesized from cytosolic (Ala; see Miyashita et al., 2007 ) and plastidic (Val, Ile, and Leu) pyruvate indicated that pyruvate in these compartments is not at isotopic equilibrium. This was modeled by introducing separate pools of pyruvate in the plastid and cytosol (ppyruvate and cpyruvate; Fig. 5). However, the introduction of an irreversible uptake of pyruvate into the plastid did not improve the fit of the data, suggesting that the labeling data contained little information on the uptake of pyruvate. A similar result was obtained with sunflower embryos (Alonso et al., 2007a), and a recent investigation, in which decreased plastidic pyruvate kinase produced severe decreases in lipid accumulation in Arabidopsis, is consistent with the hypothesis that uptake from the cytosol is not the main route by which the plastidic pyruvate pool is maintained (Andre et al., 2007).
Recent data also suggest that cytosolic and plastidic isoforms of NADP-malic enzyme (ME) are expressed constitutively in heterotrophic tissues of Arabidopsis (Gerrard Wheeler et al., 2008
The final network structure is shown in Figure 5, and in 13C-FLUX format, in Supplemental Table S3. The fitting procedure was initiated 150 times for both datasets with random initial flux estimates, and a feasible flux solution was found in over 85% of fits under both conditions. Some free fluxes converged to similar values in each run of the fitting algorithm, and for these fluxes the distribution of solutions was unimodal (Fig. 6 ). These fluxes included all the net fluxes, apart from flux through cytosolic aldolase under elevated O2 conditions, and all the exchange fluxes associated with the TCA cycle. In contrast, some of the remaining free fluxes did not converge to similar values in each run, with the solutions appearing to adopt a random distribution, suggesting that there is little information in the labeling data to constrain the fluxes to a particular value. The flux solution giving the lowest sum of squared weighted differences for each dataset was taken forward for further analysis and is referred to as the optimal flux solution.
Figure 7 shows that there was good agreement between the observed labeling data for the standard O2 and elevated O2 conditions and the labeling data predicted from the optimal flux solutions. Moreover, all measurements contributing more than 1% of the total sum of squared weighted differences could be removed from the fit (24 measurements contributing 40% of the residuum for standard O2 conditions and 21 measurements contributing 29% of the residuum for elevated O2 conditions) without altering the optimum flux solution, demonstrating that these poorly fitting measurements were not important in constraining the fit. It can be concluded that the optimal flux solutions provide adequate descriptions of the labeling data.
The errors for the optimal fluxes were derived using EstimateStat and are summarized in Table II . To ensure that biological error present within the replicate label measurements and biomass fluxes was translated into errors in the flux estimates, the labeling data, excluding the poorly fitting data described above, were reduced to a single set of measurements (see "Materials and Methods"). It was then possible to use EstimateStat in combination with replicate fitting experiments (Fig. 6) to define a list of fluxes that were statistically well determined (Wiechert et al., 2001 ).
Flux Maps of Central Carbon Metabolism under Standard and Elevated Oxygen Conditions Table II contains net and exchange fluxes together with errors calculated using EstimateStat for the optimal flux solutions under standard and elevated O2 conditions. Figure 8 shows the TCA cycle and its associated biosynthetic fluxes in detail. From Figure 8 and the data in Table II, it is clear that elevated O2 brings about an increase in flux through the TCA cycle and through the biosynthetic pathways associated with it. However, the proportion of carbon entering the TCA cycle that is used for biosynthesis is unaffected by the increased O2 concentration, with 38% ± 5% of carbon used for biosynthesis under standard O2 conditions and 33% ± 2% under elevated O2 conditions. Moreover, if the net fluxes throughout the network are expressed relative to the rate of Glc uptake, it is apparent that elevated O2 did not bring about a major rearrangement of the metabolic network, either at the level of the TCA cycle or at the level of the whole network (Fig. 9 ).
This study aimed to quantify multiple fluxes within the central carbon metabolism of Arabidopsis and to investigate the effect of an altered O2 concentration on the relationship between respiratory and biosynthetic fluxes around the TCA cycle. The flux maps reported here are the first, to our knowledge, to be obtained using steady-state MFA for Arabidopsis, and they show that while an elevated O2 concentration in a cell culture can increase fluxes throughout the metabolic network and alter the abundance of soluble metabolites, these changes do not require either a major reorganization of the network or a change in the balance between respiratory and biosynthetic flux.
Flux quantification was carried out using data obtained by 1D 13C NMR from three biological replicates of a [1-13C]Glc labeling experiment, leading to a set of statistically well-determined flux estimates that appears to represent the global optimum flux solution. The MFA protocol incorporated several refinements aimed at improving the precision and reliability of the flux estimates.
First, to increase the likelihood of being able to accurately quantify TCA cycle fluxes, we began our investigation by predicting the optimal 13C-labeled precursor to use for isotopic steady-state labeling experiments. While the approach used here considered fewer parameters than recent work in this area (Ghosh et al., 2006 Second, to quantify the biosynthetic capacity of the TCA cycle more completely than hitherto, measurements of organic and amino acids derived from the TCA cycle were incorporated into the model (Fig. 2, analysis of protein hydrolysate). While the list of quantified biomass components deriving from the TCA cycle is not exhaustive, accounting for these extra biosynthetic demands in the model should provide a more accurate picture of how the TCA cycle functions in respiration and biosynthesis. In contrast to previous work in this field, all of the biomass and labeling measurements were made on cell cultures initiated from the same stock cultures and grown concurrently. This should ensure that the labeling data and biomass data are consistent with each other, which may not otherwise be the case, particularly for soluble metabolites that show significant batch-to-batch variability. Finally, to avoid the need to calculate averages of relative cumomer abundances, which are nonlinear functions of metabolic fluxes, fluxes were fitted simultaneously to three separate biological replicates. This process was assisted by assigning specific errors to individual measurements on the basis of SNR (Fig. 4). Biological error was applied to the estimates of flux measurement precision (Table II) by assessing the relative error present in replicate cumomer abundance measurements. Repeated fitting of the model combined with statistical analysis then indicated fluxes that were both statistically well determined and which took similar values in each run. Fulfillment of both of these criteria is important, as statistically well-defined fluxes may not always have a single optimal value. In our investigation, this is the case for the net flux chex2 under elevated O2 conditions (Fig. 6), and, hence, biological conclusions made on the basis of consideration of a single flux solution, or indeed a subset of flux solutions, risk being erroneous.
The relative simplicity of the protocol developed in this study suggests that it may be possible to determine metabolic fluxes in heterotrophic tissue cultures of Arabidopsis reasonably easily, potentially allowing a wide range of genotypes and environmental conditions to be analyzed. The large datasets collected in this study will allow us, by exploiting the ability of 13C-FLUX to determine the sensitivity of individual label measurements to changes in fluxes (see Schwender et al., 2006
While the flux distribution centered on the TCA cycle in heterotrophic Arabidopsis cell suspensions under standard O2 conditions is qualitatively similar to flux distributions in other plant species (Rontein et al., 2002
In Arabidopsis under standard O2 conditions, 38% of carbon entering the TCA cycle was used for biosynthetic processes, including the synthesis of protein and accumulation of amino acids and organic acids (Fig. 8; Table II). Little to no carbon was withdrawn from the TCA cycle for plastidic fatty acid synthesis, consistent with the view that the main route of carbon supply for fatty acid synthesis is via plastidic pyruvate kinase and not via plastidic ME or uptake of pyruvate from the cytosol (Schwender et al., 2006
The increased rates of biomass accumulation and Glc consumption in the Arabidopsis cell suspension culture at elevated O2 concentrations were associated with increases in net fluxes throughout the metabolic network (Fig. 8; Table II). These higher fluxes corresponded to higher rates of ATP synthesis; calculations based on the optimal flux solutions, assuming that 2.5 molecules of ATP are produced for each NADH and 1.5 molecules produced for each FADH2 (Brand, 1994 While manipulation of O2 concentration brought about marked changes in absolute fluxes, expressing flux relative to the rate of Glc uptake showed that there was no major rearrangement of the metabolic network despite the associated changes in soluble metabolite levels (Fig. 2). In particular, MFA indicates that ratios of internal fluxes in the TCA cycle and elsewhere remained almost constant (Fig. 9), a result in keeping with the unchanged biomass proportions (Table I). Thus, the changes in levels of organic acids, amino acids, and sugars can be produced without major changes in relative fluxes within central metabolism. The fluxes that lead to the accumulation of soluble metabolites in this system are very small compared to fluxes though the core of carbon metabolism (Table II), so only small net changes in flux are required to produce large changes in the relative abundance of the soluble metabolites. For example, the 72% decrease in citrate accumulation relative to Glc uptake that occurred at elevated O2 could be produced with a change in citrate synthase flux of only 4%. Similarly, subtle changes in relative fluxes around oxaloacetate may be responsible for some of the changes in soluble metabolite abundances (Fig. 2). For example, under elevated O2 conditions, there was a detectable (22%) decrease in relative flux through PEPC (Figs. 8 and 9), while flux through PEPCK increased (Table II), possibly contributing to the decreased abundance of organic acids. However, in general, it appears that the differences in rates of accumulation of soluble metabolites arose from rearrangements of the central metabolic network that are smaller than can currently be detected using MFA. Overall, the O2 concentration did not exert significant control over the balance between respiration and biosynthesis under these conditions, even though it had a significant influence on the growth of the cells. Heterotrophic Arabidopsis cultures may therefore respond to changes in O2 concentration by altering rates of respiration, biosynthesis, and ultimately growth proportionally, such that the demand for ATP to support biosynthesis is balanced by the rate of respiratory processes that generate ATP.
Stability of relative fluxes in carbon metabolism has become a recurring theme in plant MFA studies. While certain environmental and genetic perturbations have been shown to alter the flux distribution in the central metabolic network (Spielbauer et al., 2006
The stability of the central metabolic network also complicates the interpretation of metabolite profiling data. The levels of most metabolites represent only a very small fraction of the total biomass, making it unlikely that changes in level will reflect significant changes in flux within the central network. Thus, the changes in metabolite abundance caused by altering the availability of oxygen (Fig. 2) do not lead to easily identifiable perturbations in the flux map (Fig. 8). Further improvements in the accuracy and precision of MFA may alleviate this problem, but it will also be important to complement MFA with the continued development of sophisticated models of plant metabolism (Sweetlove et al., 2008
A comprehensive description of the fluxes through the TCA cycle and associated pathways in an Arabidopsis cell suspension has been obtained using a robust steady-state stable isotope-labeling protocol. Increasing the concentration of dissolved oxygen increased fluxes throughout the network and caused changes in the soluble metabolite profile, while at the same time having no effect on the proportion of carbon entering the TCA cycle that was used for biosynthesis and no significant impact on the relative flux distribution in the central network. Ultimately, while the mechanism by which the cells respond to increased oxygen has yet to be established, the study demonstrates the utility of MFA as a tool for probing the impact of an environmental perturbation on the operation of the central metabolic network.
Experimental System
Cell suspensions of Arabidopsis (Arabidopsis thaliana) ecotype Landsberg erecta (May and Leaver, 1993
Measurements of dissolved oxygen concentration were made using a Clark type oxygen electrode at 21°C. Arabidopsis cell suspension (1 mL) was transferred to the electrode chamber, and oxygen consumption was monitored until the trace became linear. The linear portion was extrapolated to time zero to determine the oxygen concentration at the point of sample addition.
Cells were labeled to isotopic steady state by subculturing light-grown cell suspension into medium where a proportion of the unlabeled Glc was replaced with 13C-labeled Glc (Cambridge Isotope Laboratories and Sigma-Aldrich). This procedure has been shown to have no discernible effect on the flux distribution through the Arabidopsis metabolic network (Kruger et al., 2007b
Soluble metabolites were extracted from frozen tissue labeled to isotopic steady state using perchloric acid (Kruger et al., 2007b Protein was extracted by repeated washing of ground, lyophilized tissue with phosphate buffered saline (130 mM NaCl, 100 mM Na2HPO4/NaH2PO4, pH 7.0). Prior to hydrolysis, protein was precipitated using 12% TCA, washed with ice-cold acetone, and resuspended in 6 M HCl. Hydrolysis was carried out in Pierce hydrolysis tubes; samples were degassed and flushed with N2 three times, then heated at 95°C for 24 h under vacuum. Samples were freeze dried to remove HCl and redissolved in 10% 2H2O with 25 mM 1,4-dioxane, pH 7.5, for 13C NMR analysis.
Growth rate of cell suspensions was determined from fresh weight recorded during harvest and converted to change in dry weight by assuming that fresh cells contained 95% water by weight. This value was supported by experiments in which cell mass was determined before and after freeze drying. Measurements of the abundance of protein, amino acids, cell wall, starch, lipids, and soluble metabolites were made using either tissue labeled to isotopic steady state with [1-13C]Glc or tissue grown concurrently from the same stock cultures.
Protein extracted with phosphate buffered saline was quantified using the Bradford assay. The amino acid content of labeled protein hydrolysates was determined by HPLC (Bruckner et al., 1995
Starch was quantified by autoclaving duplicate samples of ground, unlabeled, lyophilized tissue for 1 h in 25 mM sodium acetate, pH 4.8. Fifteen units of
Cell wall was extracted by repeated washing of a known mass of unlabeled ground lyophilized tissue with a mixture of phenol, acetic acid, and water in the ratio 2:1:2 (Sriram et al., 2006
Lipids were extracted from a known mass of ground, labeled, lyophilized tissue using hexane and isopropanol according to an established protocol (Hara and Radin, 1978
Soluble metabolites were extracted with methanol as described elsewhere (Le Gall et al., 2003
Spectra were recorded on a Varian Unity Inova 600 spectrometer (Varian). 1D 13C NMR spectra were recorded at 150.9 MHz using either a 10-mm broadband or a 10-mm 13C/31P switchable probe, and in all experiments Waltz16 decoupling was applied during the detection period to decouple 1H signals. Spectra were referenced to 1,4-dioxane at 67.3 ppm. Where absolute quantification of labeling was not required, a recycle delay of 6 s was used, and the NOE was induced during the relaxation delay to increase SNR values. For quantitative data, the recycle delay was extended to 19 s and the nuclear Overhauser effect was not induced. Acquisition times of the order of 60 h (10,240 scans) were required to obtain suitable spectra from labeled samples for accurate line-fitting. Spectra were acquired in blocks of 1,024 scans that were manually summed following inspection to confirm that there was no significant degradation during acquisition. 1D 1H NMR spectra were recorded at 600 MHz using a 5-mm HCN triple resonance probe and the standard Varian pulse program. Presaturation was applied during the relaxation delay to suppress the water signal, and spectra were referenced to TSP at 0 ppm. Two-dimensional 1H/13C gHMBC and gHSQC spectra were recorded at 600 MHz (1H) and 150.9 MHz (13C) using a 5-mm HCN triple resonance probe and standard Varian pulse programs. WURST-40 or Garp1 decoupling was applied during the detection period to remove 13C-1H coupling. All spectra were processed and analyzed using NUTS (Acorn NMR). 1D 13C spectra were processed using a line-broadening of 2.5 Hz for spectra requiring line-fitting or 1 Hz for spectra requiring integration. 1D 1H spectra were processed using a line-broadening of 1 Hz. 1H and 13C assignments were based on literature values, comparison with pure standards, and the results of two-dimensional NMR experiments. Spectral deconvolution (line-fitting) of 1D 13C spectra was carried out using the line-fitting subroutine in NUTS. During line-fitting, resonance frequency, signal intensity, line-width, and fraction Lorentzian lineshape were varied to minimize the difference between the real and simulated spectra. The SNR values for the 1D 13C NMR signals from soluble extracts of cells labeled to isotopic steady state with [1-13C]Glc varied over more than two orders of magnitude between different metabolites and different experimental conditions. Variation in extraction efficiency and sample fresh weights also contributed to considerable variation in signal intensity for the same metabolites between biological replicates. Because instrumental precision depends on SNR, it would have been incorrect to assign the same relative error to every label measurement during optimization of fluxes. We therefore recorded replicate quantitative 1D 13C NMR spectra of standard samples of organic and amino acids (25 mM Ala, 50 mM citrate, 5 mM Glu, 0.5 mM Asp, and 1 mM malate) and [U-13C6]Glc. Signal intensities were measured by line-fitting, and the relative error of the same signal over three replicate spectra was correlated with the corresponding SNR (Fig. 4). An empirical relationship between SNR and relative peak error was determined (Fig. 4), and this formula was used to assign error estimates to 13C NMR labeling measurements.
Metabolic modeling was carried out using 13C-FLUX (version 20050329; Wiechert et al., 2001
The estimated flux errors produced by EstimateStat are sensitive to measurement configuration and relative measurement errors but do not depend on absolute label measurements (Wiechert et al., 2001
All indications of statistical significance are based on a Student's t test with P < 0.05 unless otherwise indicated.
The following materials are available in the online version of this article.
We thank Dr. W. Wiechert (Department of Simulation, University of Siegen, Germany) for permission to use 13C-FLUX. Received June 24, 2008; accepted July 28, 2008; published July 30, 2008.
1 This work was supported by the Biotechnology and Biological Sciences Research Council, United Kingdom. 
2 These authors contributed equally to the article. The author responsible for distribution of materials integral to the findings presented in this article in accordance with the policy described in the Instructions for Authors (www.plantphysiol.org) is: R. George Ratcliffe (george.ratcliffe{at}plants.ox.ac.uk).
[W] The online version of this article contains Web-only data.
[OA] Open Access articles can be viewed online without a subscription. www.plantphysiol.org/cgi/doi/10.1104/pp.108.125195 * Corresponding author; e-mail george.ratcliffe{at}plants.ox.ac.uk.
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ABSTRACT
RESULTS
-ketoglutarate dehydrogenase or via the 
-aminobutyrate (GABA) shunt, was considered as a single flux, because these parallel pathways produce identical distributions of label in their product, and Suc cycling was excluded from the model for the reasons discussed elsewhere (Kruger et al., 2007a
) or elevated (
) O2 conditions. Errors are ±1 SD (n = 2 or 3). "a" indicates statistically significant differences (Student's t test, P < 0.05) in metabolite abundances between the two conditions for that time point. "b" indicates statistically significant differences (Student's t test, P < 0.05) in metabolite abundance under a particular condition between the indicated time point and 4.5 d growth. No significant differences in abundance were detected between 5 and 5.5 d growth.
ppyruvate; 
0) or infinity (
,
1) is given. Where no exchange flux is given, the value was constrained to zero in the fit. See Supplemental Table S4 for the complete flux solution. DH, Dehydrogenase.
