Báo cáo Y học: C-labelling experiments potx

Analysis of flux estimates based on 13 C-labelling experiments Bjarke Christensen*, Andreas Karoly Gombert† and Jens Nielsen Center for Process Biotechnology, BioCentrum DTU, Technical University of Denmark, DK-2800 kg. Lyngby, Denmark Modelling of the fluxes in central metabolism can be performed by combining labelling experiments with meta- bolite balancing. Using this approach, multiple samples from a cultivation of Saccharomyces cerevisiae in metabolic and isotopic steady state were analysed, and the metabolic fluxes in central metabolism were estimated. In the various samples, the estimates of the central metabolic pathways, the tricarboxylic acid cycle, the oxidative pentose phosphate pathway and the anaplerotic pathway, showed an unprece- dented reproducibility. The high reproducibility was obtained with fractional labellings of individual carbon atoms as the calculational base, illustrating that the more complex modelling using isotopomers is not necessarily superior with respect to reproducibility of the flux estimates. Based on these results some general difficulties in flux estimation are discussed. Keywords: metabolic network analysis; GC-MS; labelling experiments; pentose phosphate pathway. Methods for quantifying intracellular fluxes are important for understanding the interactions of the pathways in metabolic networks, and such methods are therefore essential for the metabolic engineering approach to redi- recting the metabolism towards production of desired metabolites. Flux estimation methods may be based on metabolite balances over intracellular metabolites, labelling experiments, or a combination of metabolite balances and labelling experiments. Thus, much information has been obtained from metabolite balances, which have been used to study carbon flux distribution, redox metabolism and energetics of cellular metabolism [1]. This method is mathematically attractive, as the equation system arising from metabolite balancing is linear. The metabolite balan- cing approach leads to estimates of the individual fluxes, but if only relative activities of certain pathways are of interest, a method based exclusively on labelling experiments, so-called metabolic flux ratio analysis, can be used [2]. However, to extract the most information on a metabolic network, it is necessary to use a combination of metabolite balances and labelling experiments, as illustrated by the studies of Corynebacterium glutamicum and Penicillium chrysogenum [3,4]. The mathematical problem of estimating metabolic fluxes from a combination of metabolite balances and labelling experiments is complex [5,6] and analytical solu- tions to the problem are therefore difficult or impossible to obtain. Reversible reactions, in particular, add to the complexity of the system, as the degree of reversibility cannot be addressed by mass balances. Thus, to apply labelling balancing to such systems, it is necessary to use models that account for the transitions of carbon atoms that occur in reversible reactions [3]. In particular, the combina- tion of several reversible reactions that is encountered in the pentose phosphate pathway (PP pathway) constitutes a highly complex system that may seriously affect the estimation of the physiologically important flux through the oxidative PP pathway [7]. Considerable efforts have therefore been put into developing efficient numerical methods that can handle the complexity of the nonlinear equations derived from the labelling experiments [5,8]. The numerical methods may operate either with metabolite isotopomers, which give a complete description of the labelling state of a metabolite pool, or with fractional labellings of the individual carbon atom positions in a metabolite. There is a quite substantial difference in the complexity of these two approaches, and although the general approach, i.e. the isotopomer-based method, is intrinsically superior to the fractional labelling-based method, the latter is often applied because of its relative simplicity. The labelling experiments are typically performed as continuous cultures that are fed with labelled glucose as the sole carbon source. When isotopic steady state is reached, the hydrolysed biomass is analysed with respect to the labelling patterns of the amino acids and sometimes also glucose and other carbohydrates. The amino acids and carbohydrates are derived from central metabolites, and due to the isotopic steady state, the labelling patterns of the central metabolites (which are the labelling patterns used for flux estimation) are reflected by the labelling patterns of these compounds [3]. The labelling patterns may be analysed by either NMR spectroscopy or GC-MS [2–4]. Depending on the situation, the two techniques have different advantages. For instance, the NMR method has proved to be very useful for investigating aspects related to lysine biosynthesis [9], while the GC-MS technique has been shown to be well suited for studying the relative rates of amino acid biosynthesis and amino acid uptake from the medium [10,11]. While the two techniques are generally comparable with respect to the information on the labelling Correspondence to J. Nielsen, Center for Process Biotechnology, BioCentrum DTU, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark. Abbreviations: PP pathway, pentose phosphate pathway. *Present address: Novozymes A/S, Krogshøjvej 36, DK-2880 Bagsværd, Denmark Present address: Departamento de Engenharia Quı ´ mica, University of Sa ˜ o Paulo, Brazil. (Received 3 September 2001, revised 19 April 2002, accepted 26 April 2002) Eur. J. Biochem. 269, 2795–2800 (2002) Ó FEBS 2002 doi:10.1046/j.1432-1033.2002.02959.x patterns, a GC-MS method is favoured by a higher sensitivity, which is important as labelling experiments typically are carried out on a small scale. Thus, to obtain sufficient biomass for the NMR analysis to be feasible, the entire biomass content of the bioreactor is often needed, and the experiment therefore has to be terminated [2,3]. This means that statistical analysis of flux estimates based on the NMR analysis is based on a single sample, and the isotopic steady-state condition, i.e. the condition where a stationary state of isotope enrichment is reached, is therefore not experimentally verified. In this study, a GC-MS method was used to measure the labelling pattern of the biomass in the waste stream from the chemostat of Saccharomyces cere- visiae [12]. The labelling patterns that were measured in the chemostat of S. cerevisiae verified the isotopic steady state, and by performing the flux estimation on the basis of the labelling patterns of each sample, a measure of the reproducibility of the flux estimates was obtained. The isotopomer-based method is compared with the fractional labelling-based approach, and the flux estimates are discussed with respect to their reliability as indicators of physiological conditions. METHODS Cultivation The cultivation, which is identical to the chemostat cultiva- tion described by Gombert et al. [12], was carried out as a continuous cultivation in a bioreactor with a working volume of 150 mL and a dilution rate of 0.1Æh )1 . Cultivation was started as a batch culture containing naturally labelled glucose as the sole carbon source. After the batch phase, the culture was switched to continuous operation by starting feeding with medium identical to the medium used for the batch cultivation. The volume was kept constant by a continuously operating pump. When metabolic steady state had been reached, the feed was changed to a medium identical to the previous media, but containing [1- 13 C]glu- cose as the sole carbon source. Samples for the labelling analysis were taken by collecting waste over a time interval of 1 h, corresponding to a volume of  15 mL. Details on the cultivation conditions and sample treatment are given in Gombert et al.[12]. Labelling and flux analysis The flux analysis was based on the labelling patterns of derivatives of the glucose and the amino acids that were obtained from acid hydrolysis of the biomass. Thus, one glucose derivative, glucose pentaacetate, and two different amino acid derivatives, N-ethoxycarbonyl amino acid ethyl esters and N-(N¢,N¢-dimethyl)methylene amino acid ethyl esters, were synthesized and analysed by GC-MS [4,13]. The mass spectra obtained from the GC-MS analysis were converted into so-called summed fractional labellings, which were used in the flux estimation procedure. The summed fractional labelling of a molecule or of a fragment hereof is identical to the sum of the fractional labellings of the carbon atoms contained in the molecule or fragment. Summed fractional labellings are very useful in combination with GC-MS, as they can be calculated directly from the mass isotopomer distribution [4]. The flux estimation was based on a combination of labelling balances and metabolite balances, where the set of fluxes giving the best fit to the measured labelling and metabolite data is found by an iterative process [4]. Thus, the estimated flux distribution for each sample will be affected by all types of variations that could possibly be associated with the steady-state assump- tion, the sampling and measurement process and the flux estimation, which are issues that have been put forward as potential shortcomings of flux estimation methods that are based on GC-MS measurements [14]. In the flux calcula- tions, a standard deviation of 1% 13 C-labelling was used. RESULTS AND DISCUSSION Central metabolic pathways Table 1 shows the summed fractional labellings of six samples taken from the waste stream of the bioreactor in metabolic steady state. The fact that there are only small variations, typically in the order of < 1% 13 C-labelling, indicates that an isotopic steady state was reached. These measurements were used to calculate the flux distribution in the metabolic network (Appendix A). For each individual sample, a flux distribution was estimated, yielding a total of six completely independent estimates of the flux distribu- tion. Thus, this procedure allows for a maximum of variation of the flux estimates, as all steps from sampling to flux estimation were carried out separately for each individual sample, and the procedure is therefore well suited for testing the reproducibility of the flux estimates. The key results are summarized in Table 2, where it can be seen that there are only small standard deviations in the estimates of the central fluxes, such as the flux through the PP pathway, the Embden–Meyerhof–Parnas pathway, and the tricarb- oxylic acid cycle. With relative standard deviations of < 3%, the standard deviations for these three central fluxes are remarkably low, showing that the completely indepen- dent sets of labelling measurements that were used for the calculations give rise to very consistent estimates of the activities of the central metabolic pathways. The estimate of the flux through the oxidative part of the PP pathway is particularly interesting, as this pathway accounts for a large part of the NADPH production needed for the anabolism. The data in Table 3 illustrate that the applied method, which is based on GC-MS measurements of summed fractional labellings, gives estimates that lie in a relatively narrow interval compared with the results from other studies. The main reason for the high reproducibility is to be found in the fact that the set of labelling measurements include a measurement of the glucose 6-phosphate-derived carbohydrate compounds, e.g. glycogen, glucan and treha- lose. The low labelling of the glucose 6-phosphate pool shows that there is a high degree of reversibility between the fructose 6-phosphate and the glucose 6-phosphate pool, and with this reversibility being estimated as ÔhighÕ,itis numerically much easier to estimate the flux through the oxidative PP pathway. Leaving out this measurement, the precise value of which is not very crucial, causes great fluctuations in the estimates of the PP pathway. In contrast with the high reproducibility of the estimates of the net-fluxes, the extents of reversibility in the reactions in the nonoxidative part of the PP pathway could not be estimated with any satisfactory consistency. In spite of this 2796 B. Christensen et al. (Eur. J. Biochem. 269) Ó FEBS 2002 seemingly important shortcoming of the method, the net fluxes, including the oxidative PP pathway flux, through the central metabolic pathways could still be estimated very reproducibly, Fig. 1, showing that the precise estimates of the reversibilities of those reactions are not necessarily essential for the estimation of the net-fluxes. To this end, it should be added that inclusion of the exchange reactions, the omission of which were recently pointed out by van Winden et al. to be a possible pitfall of the flux calculations based on 13 C-labelling experiments, had no effect on the net- flux estimates of either the oxidative PP-pathway flux or the fluxes of the other main pathways in the central metabolism (Table 2) [21]. The reactions that were omitted were exchange reactions, where exchange refers to the original Table 1. Summed fractional labellings. Residence times Fragment a C-atoms b 5.12 5.69 7.44 7.84 8.24 9.18 Ser175 1, 2 3.7 3.5 2.7 2.2 2.7 3.5 Ser132 2, 3 34.6 34.7 33.5 33.3 33.5 33.6 Gly175 1, 2 6.0 5.9 5.6 5.9 5.7 5.5 Gly144 1, 2 5.9 5.9 6.4 5.7 6.1 6.3 Gly85 2 3.8 3.6 3.8 3.7 3.6 3.5 Ala116 2, 3 36.0 35.9 36.1 36.3 36.3 36.1 Ala99 2, 3 36.1 35.8 36.1 36.0 36.1 35.9 Ala158 1, 3 38.0 38.7 38.2 39.5 38.8 38.1 Leu158 2, 6 106.3 105.8 105.0 106.4 107.3 106.1 Val144 2, 5 72.9 73.1 73.1 73.8 73.7 73.5 Val143 1, 2 7.3 7.1 7.3 7.0 7.0 6.7 Val127 2, 5 73.7 72.8 72.8 73.3 72.7 72.9 Val186 1, 5 74.1 74.5 75.3 73.5 76.0 75.0 Asp188 2, 4 57.0 56.9 57.1 57.5 57.3 57.1 Asp115 2 12.2 11.8 11.9 12.5 11.6 12.0 Asp216 1, 4 64.5 63.8 64.7 64.8 64.6 64.5 Ile158 2, 6 93.4 94.0 94.5 93.4 93.4 93.5 Thr175 1, 2 17.5 18.9 17.9 17.7 17.3 18.5 Thr146 2, 4 55.0 54.2 53.7 52.5 56.0 54.8 Pro142 2, 5 86.2 85.4 85.6 85.4 85.8 85.6 Lys156 2, 6 117.2 116.8 117.6 117.5 117.1 117.2 Glu143 1, 2 40.1 39.6 41.0 40.2 40.6 39.4 Glu230 1, 5 99.8 99.2 100.0 101.2 98.9 100.9 Phe192 2, 9 93.2 91.4 89.4 87.5 85.9 91.9 Phe143 1, 2 3.1 3.0 3.0 3.0 2.9 2.9 Glucose331 1, 6 92.0 92.3 91.2 92.8 91.9 91.2 a Refers to the metabolite that was measured, where the three-letter code corresponds to standard amino acid abbreviations, and the number corresponds to the mass of the (unlabelled) fragment. b ÔC-atomsÕ lists the carbon atoms of the amino acids or glucose that are present in the fragment. For instance, the sum of the fractional labelling of C2, the fractional labelling of C3 and the fractional labelling of C4 of threonine (Thr146) was measured to 55.0% after 5.12 residence times of labelled feed. For the flux calculations, a standard deviation of 1% 13 C- labelling was used for each fragment. Thus, e.g. for the Thr146 fragment measured after 5.12 residence times, the mean ± SD defines an interval of 54.0–56.0%. The time for the samples is given as residence times. With a dilution rate of D ¼ 0.1Æh )1 , a residence time is equivalent to 10 h. Table 2. Flux estimates and standard deviation of central metabolic pathways in S. cerevisiae. Flux calculations were performed with a network that includes the exchange reactions (marked with an asterisk) in Appendix A, which were mentioned by van Winden et al. [21]. The remaining flux calculations were performed with a network without these reactions. The flux estimates derived from the extended metabolic network are not included in the calculation of the average values and the standard deviations. ÔC4 decarboxylationÕ is a flux representing the combined contribution of decarboxylation of malate and decarboxylation of oxaloacetate. The time for the samples is given as residence times. With a dilution rate of D ¼ 0.1Æh )1 , a residence time is equivalent to 10 h. Residence times 5.12 5.69 7.44 7.84 8.24 9.18 9.18* Average SD PP pathway 43.2 44.4 44.3 41.5 42.4 43.8 43.9 43.3 1.0 Embden–Meyerhof–Parnas pathway 34.6 33.4 33.6 36.3 35.4 34.0 33.9 34.5 1.0 Tricarboxylic acid cycle 60.1 60.9 60.3 60.2 59.9 58.7 59.2 60.0 0.7 Pyruvate carboxylation 25.4 29.3 23.3 24.3 25.7 24.7 25.9 25.5 1.9 C4 decarboxylation 4.7 8.8 2.8 3.5 4.8 4.0 4.6 4.8 1.9 Net anaplerosis 20.7 20.5 20.5 20.9 20.9 20.7 21.3 20.7 0.2 Ó FEBS 2002 Flux analysis based on C-13 data (Eur. J. Biochem. 269) 2797 meaning of exchanging C 2 -andC 3 -units in transketolase and transaldolase reactions [17], and not in the sense that was introduced by Wiechert et al. [5] as a means to include reversibility of the reactions in the network. Reversibility of all reactions in the nonoxidative PP pathway was included in all calculations. Flux dependent influence on the reproducibility of the flux estimations Similar to the reversibilities of the reactions in the nonoxi- dative PP pathway, the transport reactions across the mitochondrial membrane are examples of reactions that may be difficult to estimate. Thus, the transport of acetyl- CoA from the cytosol to the mitochondrion is estimated to somewhere between 5.1 and 52.7, and also the estimate of the transport of pyruvate from the cytosol to the mito- chondria varies substantially. The reason for this is to be found in the labelling patterns of alanine and valine, which are assumed to be synthesized from cytosolic and mito- chondrial pyruvate, respectively. Under the conditions of the experiment, the labelling patterns of alanine and valine are almost identical, and the labelling patterns of cytosolic and mitochondrial pyruvate are consequently close to being identical. Acetyl-CoA may be derived from both mitoch- ondrial and cytosolic pyruvate, and as these two pools of pyruvate do not exhibit compartmental variations, the labelling patterns of the cytosolic and mitochondrial acetyl- CoA pools will be labelled almost identically. When metabolites of a certain type are located in different compartments, but still have identical labelling patterns, the pools of these metabolites can be lumped together. From a modelling point of view, any flux between such identical pools is meaningless, which is reflected by the large variations in the flux estimates (Fig. 1). Since the difficulties in estimating the transport fluxes are caused by the lack of differences in labelling patterns, information on the isotop- omer distributions would not give improved resolution of the fluxes. The difficulties in estimating acetyl-CoA transport fluxes are caused by the low flux through the malic enzyme catalysed reaction, which is a mitochondrial reaction. Therefore, if this reaction had taken place to a greater extent, the mitochondrial and cytosolic pools of pyruvate would be labelled differently, and the labelling patterns of the acetyl-CoA pools would now differ, enabling calculation of the exchange flux between these pools. Thus, there may be a strong coupling between the precision of the flux estimates and the magnitudes of the fluxes in the network. Flux estimates based on the labelling patterns of proteinogenic amino acids Quite interestingly, if the transport of acetyl-CoA across the mitochondrial membrane had not been included in the network, much more reproducible flux estimates would have been found. Thus, an erroneous network may lead to highly reproducible, yet incorrect, flux estimates, illustrating that reproducibility should not be taken to be a measure of the precision. This result is even more interesting when the very base of the calculations, the amino acid labelling patterns, is taken into consideration. The proteinogenic amino acids are derived from several different central metabolites, and their labelling patterns are taken to reflect the labelling patterns of their respective precursors. How- ever, it is important to realise that the labelling patterns of proteinogenic amino acids reflect the flux distribution at the time that the protein pool was synthesized, highlighting that there is an implicit assumption of proportionality between glucose uptake and protein biosynthesis. This is true for the Fig. 1. Metabolic flux distribution in S. ce revisiae growinginameta- bolic and isotopic steady state chemostat culture at dilution rate D ¼ 0.1Æh )1 and with glucose as the sole carbon source. Five different samples were taken during the steady state, and based on the labelling patterns of each of these samples, a flux distribution was estimated, leading to five different sets of fluxes. The pair of values represents the lowest and the highest estimates that were found in the five different flux distributions. Table 3. Pentose phosphate pathway flux estimates from the literature. The pentose phosphate pathway fluxes are scaled with respect to the glucose uptake flux, which was arbitrarily set to 100. Thus, for every 100 mol of glucose taken up by the cells, the fluxes indicate how many moles of glucose 6-phosphate were converted through the oxidative pentose phosphate pathway. Estimate (lower limit–upper limit) Marx et al. [15] 67 (53–78) Marx et al. [16] 76.3 (56.8–95.9) Schmidt et al. [17] 72.0 (66.3–74.9) Sauer et al. [18] 72.0 (64.8–79.2) Dauner et al. [19] 20 (11–29) Dauner et al. [19] 34 (16–52) This study 43.3 (41.5–44.4) 2798 B. Christensen et al. (Eur. J. Biochem. 269) Ó FEBS 2002 average culture in metabolic steady state, but as the labelling patterns are generated on a microscopic scale in individual cells that undergo, for instance, cell cycle-dependent meta- bolic phenomena, the average behaviour of the cells may differ materially from the behaviour of the individual cells, and the metabolism of the cells producing the most protein – and not necessarily metabolizing the most substrate ) will therefore have a dominating impact on fluxes calculated for the entire culture. Thus, when protein labelling patterns are used for flux estimations, it is assumed that glucose consumption is directly coupled to protein biosynthesis, which is an assumption that is unlikely to be true for all microbial systems. CONCLUSIONS Using a simple approach based on summed fractional labelling data, we have obtained highly reproducible estimates of the central fluxes in S. cerevisiae. The technique is therefore likely to be sensitive to small metabolic variations caused by changes in growth conditions or genetic make-up of the microorganism. It was not possible to find reproducible estimates of the reversible fluxes in the PP pathway, but quite interestingly, this had no influence on the estimate of the oxidative PP pathway flux. Summed fractional labelling data, which are readily available from GC-MS measurements, therefore render the effects of reversibilities in the PP pathway unimportant for the estimation of the flux through the oxidative PP pathway. As was the case for the reversible fluxes of the PP pathway, the estimates of the transport flux of acetyl-CoA between the cytosolic and mitochondrial compartments could not be estimated with any satisfactory consistency. This shortcoming was due to low malic enzyme activity, demonstrating that the magnitude of certain fluxes in the network may seriously affect the precision with which other fluxes can be estimated. This result also implies that the validity of simulations showing that a given set of measurements holds sufficient information for estimating the fluxes in a network is difficult to assess. With the above discussion we have also tried to illustrate that a metabolic network is a mathematical abstraction whose properties, i.e. network structure and flux distribu- tion, may not necessarily be a good description of the actual physiological state, no matter how precisely the fluxes are estimated. For instance, it is important to realise that when the labelling patterns of the proteinogenic amino acids are used as the basis for the calculations, the estimated fluxes represent the metabolic fluxes during protein biosynthesis, and not necessarily during the production of a metabolite of interest in a given situation. Thus, the flux values estimated for the various reactions may be affected by a number of physiological phenomena that are not accounted for in the model. These observations lead to the conclusion that at a certain stage, any greater precision that may be gained in the flux estimates by using complex isotopomer modelling lose meaning with respect to physiological interpretations, leaving the impression that the value of the isotopomer balancing approach lies in identifying unknown structural features of metabolic networks, and not in more precise estimates of the flux distribution. Thus, the strength of the detailed isotopomer modelling is that the superior informa- tion content of the measurements can be used for detecting inconsistencies between the measurements and the model structure, and thereby isotopomer modelling can function as an excellent tool for discriminating between different metabolic networks. REFERENCES 1. van Gulik, W.M. & Heijnen, J.J. (1995) A metabolic network stoichiometry analysis of microbial growth and product forma- tion. Biotechnol. Bioeng. 48, 681–698. 2. Sauer, U., Lasko, D.R., Fiaux, J., Hochuli, M., Glaser, R., Szyperski, T., Wu ¨ thrich, K. & Bailey, J.E. (1999) Metabolic flux ratio analysis of genetic and environmental modulations of Escherichia coli central carbon metabolism. J. Bacteriol. 181, 6679–6688. 3. Marx, A., de Graf, A.A., Wiechert, W., Eggeling, L. & Sahm, H. (1996) Determination of the fluxes in the central metabolism of Corynebacterium glutamicum by nuclear magnetic resonance spectroscopy combined with metabolite balancing. Biotechnol. Bioeng. 49, 111–129. 4. Christensen, B. & Nielsen, J. (2000) Metabolic network analysis of Penicillium chrysogenum using 13 C-labeled glucose. Biotechnol. Bioeng. 68, 652–659. 5. Wiechert, W. & de Graaf, A.A. (1997) In vivo stationary flux analysis by 13 C labeling experiments. Adv. Biochem. Eng. Bio- technol. 54, 109–154. 6. Schmidt, K., Carlsen, M., Nielsen, J. & Villadsen, J. (1997) Modeling isotopomer distributions in metabolic networks using isotopomer mapping matrices. Biotechnol. Bioeng. 55, 831–840. 7. Follstad, B.D. & Stephanopoulos, G. (1998) Effect of reversible reactions on isotope label redistribution. Analysis of the pentose phosphate pathway. Eur. J. Biochem. 252, 360–371. 8. Wiechert, W., Mo ¨ llney, M., Petersen, S. & de Graaf, A.A. (2001) A universal framework for 13 C metabolic flux analysis. Metabol. Eng. 3, 265–283. 9. Sonntag, K., Eggeling, L., de Graaf, A.A. & Sahm, H. (1993) Flux partitioning in the split pathway of lysine synthesis in Cor- ynebacterium glutamicum. FEBS 213, 1325–1331. 10. Christiansen, T., Christensen, B. & Nielsen, J. (2002) Metabolic network analysis of Bacillus clausii on minimal and semi-rich medium using 13 C-labeled glucose. Metabol. Eng.,inpress 11. Jensen, N.B.S., Christensen, B., Nielsen, J. & Villadsen, J. (2002) The simultaneous biosynthesis and uptake of amino acids by Lactococcus lactis studied by 13 C labelling experiments. Bio- technol. Bioeng. 78, 11–16. 12. Gombert, A.K., dos Santos, M.M., Christensen, B. & Nielsen, J. (2001) Network identification and flux quantification in the central metabolism of Saccharomyces cerevisiae under different conditions of glucose repression. J. Bacteriol. 183, 1441–1451. 13. Christensen, B. & Nielsen, J. (1999) Isotopomer analysis using GC-MS. Metabol. Eng. 1, 282–290. 14. Mo ¨ llney, M., Wiechert, W., Kownatzki, D. & de Graaf, A.A. (1999) Bidirectional reaction steps in metabolic networks. IV. Optimal design of isotopomer labeling experiments. Biotechnol. Bioeng. 66, 86–103. 15. Marx, A., Eikmans, B.J., Sahm, H., de Graaf, A.A. & Eggeling, L. (1999) Response of the central metabolism in Corynebacterium glutamicum to the use of an NADH-dependent glutamate dehy- drogenase. Metabol. Eng. 1, 35–48. 16. Marx, A., Striegel, K., de Graaf, A.A., Sahm, H. & Eggeling, L. (1997) Response of the central metabolism of Corynebacterium glutamicum to different flux burdens. Biotechnol. Bioeng. 56, 168–180. 17. Schmidt, K., Nørregaard, L.C., Pedersen, B., Meissner, A., Duus, J.Ø., Nielsen, J. & Villadsen, J. (1999) Quantification of Ó FEBS 2002 Flux analysis based on C-13 data (Eur. J. Biochem. 269) 2799 intracellular metabolic fluxes from fractional enrichment and 13 C- 13 C coupling constraints on the isotopomer distribution in labeled biomass components. Metabol. Eng. 1, 166–179. 18. Sauer, U., Hatzimanikatis, V., Bailey, J.E., Hochuli, M., Szyper- ski, T. & Wu ¨ thrich, K. (1997) Metabolic fluxes in riboflavin-pro- ducing Bacillus subtilis. Nat. Biotechnol. 15, 448–452. 19. Dauner, M., Bailey, J.E. & Sauer, U. (2001) Metabolic flux ana- lysis with a comprehensive isotopomer model in Bacillus subtilis. Biotechnol. Bioeng. 76, 144–156. 20. Flanigan, I., Collins, J.G., Arora, K.K., MacLeod, J.K. & Wil- liams, J.P. (1993) Exchange reactions catalyzed by group-tran- ferring enzymes oppose the quantitation and the unravelling of the identity of the pentose phosphate pathway. J. Biochem. 213, 477–485. 21. van Winden, W., Verheijen, P. & Heijnen, S. (2001) Possible pit- falls of flux calculations based on 13 C-labeling. Metabol. Eng. 3, 151–162. APPENDIX A Glucose uptake Glucose fi glucose 6-P EMP-pathway Glucose 6-P fi fructose 6-P (reversible) Fructose 6-P fi 2 glyceraldehyde 3-P Glyceraldehyde 3-P fi phosphoenolpyruvate Phosphoenolpyruvate fi pyruvate (cytosolic) PP-pathway Glucose 6-P fi pentose 5-P +CO 2 2Pentose5-Pfi sedoheptulose 7-P + glyceraldehyde 3-P (reversible) Sedoheptulose 7-P + glyceraldehyde 3-P fi fructose 6-P + erythrose 4-P (reversible) Pentose 5-P + Erythrose 4-P fi fructose 6-P + glyceral- dehyde 3-P (reversible) *Pentose 5-P + glyceraldehyde 3-P fi pentose 5-P + gly- ceraldehyde 3-P *Fructose 6-P + erythrose 4-P fi fructose 6-P + eryth- rose 4-P *Sedoheptulose 7-P + pentose 5-P fi sedoheptulose 7- P + Pentose 5-P *Fructose 6-P + glyceraldehyde 3-P fi fructose 6-P + glyceraldehyde 3-P *Sedoheptulose 7-P + erythrose 4-P fi sedoheptulose 7-P + erythrose 4-P Ethanol, acetate and glycerol formation Pyruvate (cytosolic) fi ethanol CO 2 Acetaladehyde fi acetate Glyceraldehyde 3-P fi glycerol Formation of Acetyl-CoA in the cytosol Acetate fi acetyl-CoA (cytosolic) Anaplerotic reaction (cytosolic) Pyruvate (cytosolic) + CO 2 fi oxaloacetate (cytosolic) TCA-cycle (considering scrambling around fumarate) Pyruvate (mitochondrial) fi acetyl-CoA (mitochon- drial) + CO 2 Oxaloacetate (mitochondrial) + acetyl-CoA (mitochon- drial) fi isocitrate Isocitrate fi 2-oxoglutarate + CO 2 2-Oxoglutarate fi fumarate + CO 2 Oxaloacetate (mitochondrial) fi fumarate (reversible, scrambling included) Transports Oxaloacetate (mitochondrial) fi oxaloacetate (cytosolic) (reversible) Acetyl-CoA (cytosolic) fi acetyl-CoA (mitochondrial) Pyruvate (cytosolic) fi pyruvate (mitochondrial) Threonine/serine/glycine metabolism (all enzymes assumed to be cytoplasmic) Glyceraldehyde 3-P fi serine Serine fi glycine+C 1 -tetrahydrofolate (reversible) Oxaloacetate (cytosolic) fi threonine Threonine fi glycine + acetaldehyde (reversible) Malic enzyme (oxaloacetate decarboxylation, mitochondrial) Oxaloacetate (mitochondrial) fi pyruvate (mitochond- rial) + CO 2 Drain of intermediates to macromolecules In the model, the following intracellular metabolites are used for biosynthesis of macromolecules: glucose 6-P, pentose 5-P, erythrose 4-P, glyceraldehyde 3-P, phosphoe- nolpyruvate, pyruvate (mitochondrial), pyruvate (cytosolic), oxaloacetate (cytosolic), 2-oxoglutarate, acetyl-CoA (cyto- solic), acetyl-CoA (mitochondrial), serine, glycine, C 1 -tetrahydrofolate and threonine. Excreted products The model includes fluxes representing the production of the following metabolite: ethanol, acetate, glycerol and CO 2 . Note Thereactionsaremarkedwithanasteriskareso-called exchange reactions, and these reactions were omitted in some of the flux estimations, see text. The reactions followed by ÔreversibleÕ are reversible reactions, and both the forward and the reverse direction of the reaction were included in the calculations. 2800 B. Christensen et al. (Eur. J. Biochem. 269) Ó FEBS 2002 . CO 2 Acetaladehyde fi acetate Glyceraldehyde 3-P fi glycerol Formation of Acetyl-CoA in the cytosol Acetate fi acetyl-CoA (cytosolic) Anaplerotic reaction (cytosolic) Pyruvate (cytosolic) + CO 2 fi. 6-P EMP-pathway Glucose 6-P fi fructose 6-P (reversible) Fructose 6-P fi 2 glyceraldehyde 3-P Glyceraldehyde 3-P fi phosphoenolpyruvate Phosphoenolpyruvate fi pyruvate (cytosolic) PP-pathway Glucose. N-ethoxycarbonyl amino acid ethyl esters and N-(N¢,N¢-dimethyl)methylene amino acid ethyl esters, were synthesized and analysed by GC-MS [4,13]. The mass spectra obtained from the GC-MS analysis