In steady-state experiments the labeled precursor is supplied continuously, and the redistribution of the label is measured after the system reaches an isotopic and metabolic steady state. Experimental verification that these conditions are satisfied is crucial, and evidence should be presented whenever steady-state methods are used. Only when a suitable end-point has been identified through time-course observations is it legitimate to proceed to a steady-state analysis.
The steady-state approach is particularly suitable for the analysis of complex networks, such as the central pathways of carbon metabolism. Choosing a precursor for introducing the label into the network is usually straightforward; for example, there are many studies on plant and microbial systems that use glucose, but the labeling of the precursor needs to be chosen carefully. In one approach, the system is incubated with a mixture of uniformly labeled and unlabeled substrate (Ettenhuber et al., 2005; Glawischnig et al., 2001, 2002; Maaheimo et al., 2001; Sriram et al., 2004; Szyperski, 1995), while in an alternative approach the system is incubated with a specific isotopomer in which some, but not all, positions are labeled. The complexity of the network may make the optimal choice of isotopomer non-trivial (Roscher et al., 2000), and modeling the outcome in advance is the best way to ensure that precursors are chosen that will lead to an informative steady state (Schwender et al., 2004b; Wiechert et al., 2001). Ultimately, because the reliability of the calculated flux map is determined by the constraints on label redistribution within the network, conducting parallel experiments with different labeled precursors is the best way to ensure optimal determination of the fluxes.
Similarly, while the analysis of the steady-state labeling of just a handful of easily extractable metabolites may be sufficient to generate a flux map, complementary measurements of as many labeled components as possible, including macromolecules, will provide further constraints and increase confidence in the measured fluxes. Thus, while it may be sufficient to construct flux maps of central carbon metabolism in microbial systems by analyzing the redistribution of uniformly labeled glucose into protein (Szyperski, 1995, 1998), it is not yet clear that such an approach on its own will be sufficient to obtain reliable fluxes through the more complicated network of central carbon metabolism in plants. The approach is certainly technically feasible (Glawischnig et al., 2001; Sriram et al., 2004) but there is a strong case for using complementary labeling strategies to test the significance of the results obtained so far.
Information on the subcellular compartmentation of the metabolic network is obtained by analyzing the labeling of metabolites and end-products that are synthesized uniquely in one compartment (Ratcliffe and Shachar-Hill, 2005; Schwender et al., 2004b). For example, the labeling of starch reports on the plastidic hexose phosphate pool, and the labeling of the carboxyl end of long-chain (C20, C22) fatty acids reports on the cytosolic acetyl CoA pool. This approach is powerful, because it yields subcellular information with only minimal fractionation of the extract. However, given incomplete knowledge of the network, caution is required and assumptions about the subcellular location of particular steps may need to be revisited in the light of new information. Thus, new data on cytosolic ADP-glucose synthesis may force a re-evaluation of the compartmentation of the metabolic route to starch in photosynthesizing leaves (Baroja-Fernández et al., 2004, 2005; Neuhaus et al., 2005), emphasizing the point that fundamentally important features of the primary metabolic network are still being discovered. Recently it has been proposed that subcellular labeling information could be obtained by non-aqueous fractionation of labeled plant material before extraction (Fernie et al., 2005), and this would provide a useful method for testing assumptions about the subcellular compartmentation of the network. Finally, note that rapid exchange of intermediates between compartments may mean that apparently separate pools act as a functional unit (see below; Schwender et al., 2003).
Ideally the label distribution in the steady state should be characterized by both MS and NMR. Each method can provide sufficient isotopomeric information for network flux analysis on its own (Christensen and Nielsen, 1999; Schmidt et al., 1999), but neither approach has an overwhelming advantage, making it is advantageous to use data from both methods (Wiechert, 2001; Yang et al., 2002). Even when MS and NMR give entirely equivalent information, having independent measurements increases confidence in the eventual flux map, but in fact the information from the two techniques is often complementary (Box 4), creating a powerful argument for using the two techniques in tandem. For example, a detailed analysis of the validity of using MS for network flux analysis in C. glutamicum (Klapa et al., 2003) concluded that MS was better than NMR for analyzing the anaplerotic flux distribution, but that NMR was better than MS for elucidating the relative contribution of the parallel pathways of lysine synthesis. To date, most steady-state network flux analyses in plants have used NMR, with only one major application of MS (Schwender and Ohlrogge, 2002; Schwender et al., 2003, 2004b), but there is a strong case for following the microbial lead and using both techniques wherever possible.
MS and NMR characterize the labeling of specific molecules in terms of (i) the relative abundance of mass isotopomers, and (ii) the relative abundance of isotopomers and cumomers, including fractional enrichments at specific atomic positions (Box 1; Figure 2). In the analysis of experiments with uniformly labeled substrates, there is also the computationally efficient option of focusing on carbon–carbon bonds that remain intact during metabolism, and using NMR to characterize the redistribution of the label in terms of bondomers and cumulative bondomers (Box 1; Sriram and Shanks, 2004; van Winden et al., 2002). The labeling information is sufficient to generate flux ratios through different parts of the network, but to obtain a map of absolute fluxes it is also necessary to measure one or more input or output fluxes to calibrate the ratios. Thus, it is usual to measure substrate uptake and flux into end-products and/or biomass in parallel with the steady-state stable isotope analysis.
As with dynamic labeling, data interpretation hinges on setting up a mathematical representation of the network in steady state (Box 3), and then adjusting the model parameters to fit the data. The model parameters are the forward and reverse fluxes that link the branch points in the network, usually represented as the equivalent exchange fluxes and net fluxes, and the final output is a flux map for the whole network. The analysis depends on applying flux balancing to the labeling of individual carbon atoms, and, while simple in principle, this process is much more time-consuming than data acquisition, emphasizing the importance of obtaining a high-quality dataset at the outset.
Early applications of steady-state flux analysis to plant metabolism focused on obtaining an exact solution for a set of steady-state equations using the requisite number of positional fractional enrichments as inputs (Dieuaide-Noubhani et al., 1995; Edwards et al., 1998; Fernie et al., 2001; Rontein et al., 2002; Roscher et al., 2000). Although mathematically straightforward, this procedure has the disadvantage that it provides no indication as to the validity of the resulting flux map, because a solution can be found for any set of observed fractional enrichments. With this approach, therefore, the best way to test the map is to measure the positional fractional enrichments obtained with two different precursors, for example [1-13C]glucose and [2-13C]glucose. More recently, as documented elsewhere (Kruger et al., 2003), and drawing on developments in microbial network flux analysis (Schmidt et al., 1999; Wiechert, 2001; Wiechert et al., 2001), the emphasis has shifted to a full isotopomeric (cumomer) analysis in which a numerical fitting procedure is used to find the flux distribution that provides the best fit to the experimental data. In this scheme, the system is over-determined, allowing a statistical assessment of the quality of the fit and the confidence range of each fitted parameter.
Irrespective of the basis on which the analysis is carried out, most investigators have tended to set up their own routines for solving steady-state equations or for fitting data. This complicates the comparison of flux maps obtained on different systems by different groups, particularly if the more powerful approach of numerical fitting is used, and it also acts as a serious deterrent for new entrants into the field. Some of the software that has been developed is freely available (Box 4), for example 13C-FLUXTM (Wiechert et al., 2001), NMR2Flux (Sriram et al., 2004) and 4F (Ettenhuber et al., 2005), and this may ultimately lead to a standardized platform for steady-state network flux analysis. 13C-FLUXTM is a flexible program that has been used extensively on microbial systems, and it has recently been adopted by several plant groups, including our own. The mathematics on which it is based, and the program itself, are documented (Wiechert et al., 2001), and as well as accepting both NMR and MS data, 13C-FLUXTM also includes advanced fitting, simulation and statistical routines. The recently published NMR2Flux program operates on similar principles to 13C-FLUXTM, while 4F is a more specialized, rules-based program that calculates the underlying fluxes responsible for the isotopic equilibration of a uniformly labeled precursor, currently [13C6]glucose, when supplied in the presence of an excess of its unlabeled form (Ettenhuber et al., 2005).
One final point concerns the complexity of the model. It is always best to start with a simple representation of the network when performing a full isotopomeric analysis with numerical fitting, and then to develop this as the extent and quality of the labeling data increase. Increasing the scope of the data collection, for example by using more than one labeled precursor and/or by extending the subsequent analysis of the redistribution of the label, allows more complicated models to be compared with the initial one. If it then turns out that the more complicated model is no more satisfactory than the simple one, even though it is a more realistic representation of the molecular components that are thought to be present, then the possibility has to be considered that the network is functionally less complicated in flux terms than it actually appears.
Thus, to take a specific example, the decision as to whether to include one or two pentose phosphate pathways in models of heterotrophic carbon metabolism is pulled in one direction by the molecular evidence that at least some of the enzymes are present in both cytosol and plastid (Kruger and von Schaewen, 2003), and in the other direction by the difficulty in evaluating the relative merits of models with either one or two complete or incomplete pathways. For example, there is molecular evidence in oilseed rape embryos for the presence of the oxidative steps of the pathway in both the cytosol and the plastid. However, network flux analysis showed that a satisfactory fit could be obtained with a single pentose phosphate pathway, pointing to rapid exchange of intermediates between the plastid and cytosol. Thus, irrespective of the subcellular distribution of the enzymes, it appears that the compartmented pentose phosphate pathway operates as a single functional entity in oilseed rape embryos (Schwender et al., 2003).
Steady-state flux analysis generates detailed flux maps of central carbon metabolism (Krömer et al., 2004; Kruger et al., 2003). These maps highlight several features that are characteristic of metabolic networks, but are otherwise difficult to study, including bidirectional fluxes, substrate cycles (Portais and Delort, 2002), and subcellular compartmentation (Figure 1; Ratcliffe and Shachar-Hill, 2005). Each flux map provides a description of a fundamental cellular activity under the physiological conditions of the experiment and as such provides a definition of the metabolic phenotype of the organism.
Measuring multiple fluxes simultaneously provides new insights into the operation of plant metabolic networks. For example, the first large-scale application of steady-state analysis concluded that 70% of ATP turnover in maize root tips could be attributed to the synthesis and degradation of sucrose (Dieuaide-Noubhani et al., 1995). A similar process, responsible for 60% of ATP turnover, was found in a related study of cultured tomato cells during exponential growth (Rontein et al., 2002). While the recent discovery of a glucose 6-phosphatase activity in maize root tips (Alonso et al., 2005) suggests that the sink for ATP may actually be a cycle between glucose and glucose 6-phosphate rather than sucrose cycling, the point should not be lost that looking at the overall operation of the network in this way can lead to interesting conclusions about network efficiency. Thus, network analysis of developing oilseed embryos has defined the metabolic route from carbohydrate to storage lipid in unprecedented detail (Figure 9; Schwender et al., 2004b), revealing important information on the metabolic origin of the NADPH required for biosynthesis (Schwender et al., 2003) and leading to the discovery of a novel metabolic route operating in the production of seed oil (Schwender et al., 2004a).
Figure 9. Flux map of central carbon metabolism in developing Brassica napus seeds based on a combination of steady-state 13C labeling experiments and biomass accumulation measurements (Schwender et al., 2003, 2004b). Developing seeds were cultured in labeled medium for up to 14 days, with low-molecular-weight metabolites reaching isotopic steady state within 3 days, and oil and protein a week later. Net fluxes (nmol h−1 per embryo) are represented as arrows with a thickness proportional to the magnitude of the flux. The labeling measurements are consistent with several simplifications of the network in Figure 1, including: treating the hexose phosphates as one pool, and similarly the triose phosphates and the pentose phosphates; and combining cytosolic and plastidic metabolism between hexose phosphate and phosphoenolpyruvate (PEP). The overall pattern of fluxes is dominated by synthesis of oil, protein and carbohydrate. Note that this flux map does not include the activity of a recently discovered route involving Rubisco (Schwender et al., 2004a).
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The phenotypic value of flux maps is well established in the analysis of microbial metabolism (Krömer et al., 2004; Marx et al., 1999; Sauer et al., 1999) and similar applications can be expected in plants. The current plant focus on developing the methodology, without biological replication in some instances, should change as the field moves away from proof of concept mode. In particular, there is likely to be greater emphasis on the response of flux maps to physiological and genetic manipulation in future work. Examples of physiological studies already exist, including an analysis of the effect of hypoxia on the flux catalyzed by malic enzyme in maize root tips (Edwards et al., 1998), and a description of the response of central metabolism to progression through a cell culture cycle (Rontein et al., 2002). An analysis of the cycling between triose phosphate and hexose phosphate in transgenic tobacco lines, which demonstrated that pyrophosphate: fructose-6-phosphate 1-phosphotransferase is sensitive to physiologically relevant fluctuations of its effector in vivo (Fernie et al., 2001), is currently the only example of network flux analysis on transgenic plant material. However, it is clear from microbial work that flux maps can be invaluable tools for rational metabolic engineering (de Graaf et al., 2001; Petersen et al., 2001) and establishing the potential of a similar approach in plants must be a high priority as the methodology becomes established.
Although most steady-state flux maps describe the conversion of precursors into products, it is also possible to construct maps that focus exclusively on the recycling of particular metabolites (Ettenhuber et al., 2005). In the first application of this approach, glucose recycling was analyzed in tobacco seedlings, and it was concluded that the redistribution of label supplied as [13C6]glucose into a much larger number of glucose isotopomers could be attributed to the net effect of six metabolic loops. In contrast to the flux maps described above, the measured fluxes through these loops refer specifically to the conversion of glucose to glucose, which may or may not be the main function of any particular segment in the loop. For example, one loop involved metabolism of glucose down to the level of the Krebs cycle followed by gluconeogenesis (Ettenhuber et al., 2005). Clearly, this provides only limited information on flux through the Krebs cycle, because carbohydrate synthesis is unlikely to be the principal function of the cycle under most conditions. However, despite this limitation, the fluxes through these metabolic loops are diagnostic of the overall phenotype, and as such are likely to be useful in probing the metabolic response of the network to perturbation. A notable advantage of this recently proposed approach is that the scale of the numerical analysis is greatly reduced by focusing on the recycling of a single substrate.