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*C-Labeled metabolic flux analysis of a fed-batch culture of elutriated Saccharomyces cerevisiae

Roeland Costenoble, Dirk Müller, Timo Barl, Walter M. Van Gulik, Wouter A. Van Winden, Matthias Reuss, Joseph J. Heijnen
DOI: http://dx.doi.org/10.1111/j.1567-1364.2006.00199.x 511-526 First published online: 1 June 2007


This study addresses the question of whether observable changes in fluxes in the primary carbon metabolism of Saccharomyces cerevisiae occur between the different phases of the cell division cycle. To detect such changes by metabolic flux analysis, a *C-labeling experiment was performed with a fed-batch culture inoculated with a partially synchronized cell population obtained through centrifugal elutriation. Such a culture exhibits dynamic changes in the fractions of cells in different cell cycle phases over time. The mass isotopomer distributions of free intracellular metabolites in central carbon metabolism were measured by liquid chromatography–mass spectrometry. For four time points during the culture, these distributions were used to obtain the best estimates for the metabolic fluxes. The obtained flux fits suggested that the optimally fitted split ratio for the pentose phosphate pathway changed by almost a factor of 2 up and down around a value of 0.27 during the experiment. Statistical analysis revealed that some of the fitted flux distributions for different time points were significantly different from each other, indicating that cell cycle-dependent variations in cytosolic metabolic fluxes indeed occurred.

  • synchronized culture
  • *C-labeling experiment
  • Saccharomyces cerevisiae
  • LC-MS analysis
  • metabolic flux analysis
  • cell division cycle


When metabolic flux analysis (MFA) is applied to a culture of microorganisms growing in, for instance, a chemostat, the mass balances for the metabolites in the system are used as flux constraints. For a steady-state situation, this implies that the accumulation term in the mass balance for each of the extracellular and intracellular metabolites are set to zero (Stephanopoulos, 1998). Furthermore, it is assumed that the steady-state culture is homogeneous, and that the behavior of the whole culture is therefore representative of the behavior of every individual cell in that culture. However, it is very possible that metabolic fluxes and metabolite levels in individual cells vary in time and/or between cells. Most notable in this respect are metabolic changes in relation to the cell division cycle. Because a chemostat culture consists of a large, stable population of cells distributed over all phases of the cell cycle, time-invariant fluxes and metabolite concentrations averaged for the entire population will be measured. Whereas measuring the average behavior of a population suffices for describing the productivity of a bioreactor, it may not reveal the intracellular regulation of metabolism during the cell cycle at the level of the individual cell. For instance, it is known that in Saccharomyces cerevisiae, the storage carbohydrates glycogen and trehalose accumulate intracellularly during the growth phase and are subsequently broken down at the time when the bud emerges, which in this case is closely associated with the beginning of the next phase of the cell cycle (Küenzi & Fiechter, 1969). When MFA is performed on a chemostat culture, this cyclic synthesis and degradation will appear as a futile cycle, whereas, with respect to the cell cycle, it is not.

Insights into cell cycle-dependent behavior can be obtained from cultures in which a large proportion of the cells is in the same phase of the cell cycle at the same time. One way to obtain these synchronized cell cultures for S. cerevisiae is using centrifugal elutriation (Creanor & Mitchison, 1979). In such cultures, the distribution of the cell population over the four phases of the cell cycle (G1, S, G2 and M) is not stable, and this is reflected in the macroscopic behavior of the broth. Combined measurement of the distribution of the population over the cell cycle phases and the macroscopic uptake and production rates can be used to study the time-varying, cell cycle-based metabolic activities of the subpopulations of cells. In such studies, one has to assume that the turnover of all free intracellular metabolite pools is considerably faster than the rate with which the metabolism of the cell population changes. In other words, the intracellular metabolites of the culture have to be assumed to be in pseudo-steady state at any time. This assumption would satisfy the requirements for application of MFA as discussed above (Wiechert & Nöh, 2005).

One of the recognized problems of MFA is the occurrence of underdetermined systems, due to the presence of parallel, bidirectional and/or cyclic reaction pathways (Savinell & Palsson, 1992; Vallino & Stephanopoulos, 1993; Bonarius, 1997). Furthermore, MFA relies in many cases on cofactor balances that can include a number of uncertain sources and sinks (van Winden, 2001). MFA based on *C-labeling experiments (*C-MFA) has been introduced to overcome both of these problems (Zupke & Stephanopoulos, 1995; Marx, 1996; Sauer, 1997; Schmidt, 1997). It relies on the specific distribution of *C atoms (superposed on the natural 1% abundance of *C) throughout the carbon-containing metabolites when a culture is fed with a specifically *C-labeled substrate. This method allows the application of mass balances for the individual carbon atoms of the metabolites as additional constraints. Several different techniques for *C-MFA are available (Szyperski, 1996; Christensen & Nielsen, 2000; Wittmann & Heinzle, 2001; van Winden, 2005), of which three have been reported for yeast: through measurement of the (mass) isotopomer distributions of the protein-bound amino acids by nuclear magnetic resonance (NMR) (Maaheimo, 2001) or GC-MS analysis (Gombert, 2001), and through direct measurement of the mass isotopomer distributions (MIDs) of free, intracellular metabolites in central carbon metabolism by liquid chromatography–mass spectrometry (LC-MS) analysis (van Winden, 2005). In all cases, application of *C-MFA requires (pseudo) steady-state conditions throughout the period during which the distribution of the *C label in the analyzed compounds is shifting from the natural *C-labeling pattern to the pattern as imposed by the *C label in the substrate feed. When the analyzed compounds are biomass constituents such as protein-bound amino acids, this requires the metabolic fluxes to be constant during time periods that are inversely related to the growth rate (Wiechert & Nöh, 2005). When one is interested in the cell cycle-dependent variations of metabolic fluxes during a time period of only one or two cell divisions, this leads to an obvious conflict.

Therefore, the application of *C-MFA to synchronized cultures critically depends on the possibility of measuring the labeling patterns of the free intracellular metabolites. Their short turnover times lead to a much faster equilibration of the *C-label distribution than for biomass constituents. It has recently been demonstrated that the *C-labeling of intermediates of the primary carbon metabolism of S. cerevisiae can be inferred from mass isotopomer measurements using LC-MS analysis (van Winden, 2005).

Several experimental methods exist for synchronization of (yeast) cultures (Futcher, 1999). In the present study, centrifugal elutriation was employed as the synchronization method, as it has the least effect on the cells' metabolism and yields sufficient amounts of biomass with which to inoculate a culture, from which a number of samples can subsequently be taken in a short period of time. Because, in particular, LC-MS analysis requires higher amounts of the analyzed metabolites compared to, for instance, GC-MS analysis to yield reliable results, it was important to start the culture with a substantial amount of biomass. As an additional advantage, elutriation yields cell age synchronization, whereas this is not the case for, for instance, synchronization through chemical block and release of cell cycle progression (Futcher, 1999). In the present study, *C-MFA is applied for the first time to elutriated cells to determine cell cycle-related changes in metabolic fluxes.

Materials and methods

Strain and media

The yeast strain used in this study was S. cerevisiae CBS 7336 (ATCC 32167).

All media used were synthetic mineral media adjusted to pH 5.0 (Theobald, 1993). All media used in the elutriation procedure resembled the fed-batch medium, but with lower glucose concentrations and extra NaCl to prevent physiologic changes of the cells due to changes in medium osmolarity (Table 1).

View this table:

Media used in this study

Mediumd-Glucose (g L*)NaCl (g L*)
Medium for continuous culture30
Pre-elutriation medium0.02
Elutriation medium0.028.4
Postelutriation medium0.023.6
Fed-batch medium3.52.2
  • * *C-labeled glucose.

The fed-batch medium contained 3.5 g L* glucose with the following labeling pattern: 25% naturally labeled d-glucose, 50% [U-*C]d-glucose (99.0% isotopomeric purity, Campro Scientific GmbH, Berlin, Germany) and 25% [1-*C]d-glucose (99.61%, isotopomeric purity, identical supplier). For all other media, only naturally labeled d-glucose was used.

Preparation of the inoculum

A 200-mL sample, containing c. 3 g dry weight of biomass and with a low budding index, was withdrawn from an oscillating continuous culture [30°C, pH=5.0, dilution rate (D)=0.1 h* (Theobald, 1997)] and centrifuged (5000 g, 10 min, 4°C). The cells were resuspended in 75 mL of pre-elutriation medium at 4°C. Cell clumps were dispersed by sonication for 15 s (320 W, Sonorex Super RK510 H, Bandelin electronic GmbH, Berlin, Germany). The cells were loaded into a spinning elutriation rotor (40-mL standard chamber, 3600 r.p.m., 4°C, rotor JE-5.0 in a J6-MC centrifuge, Beckman Inc., Palo Alto, CA) with a flow rate of 27 mL min* of elutriation medium. The cell suspension was allowed to equilibrate in the elutriation chamber for 20 min. A 500-mL fraction of small daughter cells, eluting at a flow rate of 45 mL min*, was collected on ice. The collected cell suspension was centrifuged (5000 g, 10 min, 4°C), resuspended in 200 mL of postelutriation medium, sonicated for 15 s, and transferred to the fed-batch reactor.

Culture conditions and analyses

With the elutriated cell suspension, a fed-batch culture (μaverage=0.15 h*, T=30°C, pH 5.0) was started by transferring it to a continuously stirred tank reactor, which is described elsewhere (Müller, 2003). Sampling, determination of dry weight, budding index and cell number, and the analysis of extracellular ethanol were performed as described elsewhere (Müller, 2003). Extracellular glucose, glycerol and acetate were determined enzymatically (r-biopharm, Darmstadt, Germany, Cat. No. 10716251035, 10148270035 and 10148261035 respectively). O2, CO2 and *CO2 mole fractions in the outflowing gas stream were determined online on a mass spectrometer (VGProLab, Thermo Onix, Weesp, the Netherlands). For determination of cell cycle phases, 4,6-diamidino-2-phenylindone (DAPI) fluorescent staining was used as described elsewhere (Müller, 2003). On the basis of the nuclear morphology revealed by the staining, four cell classes were distinguished: cells in G1 phase (single cells without a bud), cells in S/G2 phase (budded cells with a single nucleus), cells in early M phase (budded cells with migrating nuclei), and cells in late M phase (binucleated cells) (van Doorn, 1988; Müller, 2003).

Samples for analysis of the intracellular metabolites were handled essentially as described in Mashego (2004). Six-milliliter broth samples were rapidly transferred to 30 mL of 60% (v/v) cold (−40°C), unbuffered methanol solution, vortexed and centrifuged [5 min, −20°C, 1500 g, in a precooled (−40°C) centrifuge rotor]. The pellet was washed once with 30 mL of 60% (v/v) cold (−40°C) methanol. The metabolites were extracted by adding 5 mL of boiling, unbuffered, aqueous, 75% (v/v) ethanol solution to the pellet, vortexing, and quickly warming the suspension in an oil bath (175°C) up to c. 75°C. After this, the suspension was incubated for 3.0 min in a water bath (96°C) with frequent mixing. After extraction, the samples were cooled on ice and freeze-dried for 48 h at −70°C and 0.02 mbar. The dried pellets were dissolved in 100 μL of double-distilled water. Cell debris was removed by centrifugation (5 min, 11 000 g, 4°C), and the supernatant was stored at −80°C until analysis.

LC-MS analysis

Quantification of the mass isotopomers of the reported intracellular metabolites was done using the LC-MS system and methods as described elsewhere (van Winden, 2005).

MIDs for all reported metabolites were calculated as relative abundances of the different possible mass isotopomers of a certain metabolite (pool) (van Winden, 2005). Reported MIDs and SDs are based on three independent analyses of one separately processed sample.

13 CO2 calibration gas

A *CO2 calibration gas (consisting of 2% CO2 and 98% N2, with a *CO2/*CO2 ratio of 1 : 2) for calibration of the mass spectrometer used for online gas analysis was prepared as follows. One gram of unlabeled and 0.5 g of *C-labeled K2CO3 (Cambridge Isotope Laboratories, Andover, MA) were dissolved in 50 mL of water. The solution was brought to pH 1 by addition of 10 mL of 4 M HCl, and subsequently heated to 50°C. The escaping 0.22 L of CO2 gas was collected in a gas bag (Ritter Apparatebau GmbH, Bochum, Germany), diluted with N2 gas (5.0 purity grade), and analyzed with the gas analysis system.

Macroscopic conversion rates

The consumption and production rates of biomass, glycerol, acetate, ethanol and glucose were obtained from their respective mass balances in the broth, using concentration measurements and the flow rate of the fed-batch medium. The CO2 production rate was obtained from a balance over the gas phase using the measured mole fraction and correcting this for changes in the overall gas flow rate through the inert nitrogen gas balance. All macroscopic rates were balanced through data reconciliation (Wang & Stephanopoulos, 1983; van der Heijden, 1994) in which the O2 consumption rate was considered to be not measured after detection of a gross error in its measurement.

In the metabolic network model used for the flux fit, biomass formation is defined by a set of fluxes originating from several different pools of metabolites that serve as molecular precursors of biomass components. To calculate these fluxes for each sample point, the following procedure was followed. For each of the four discernible cell cycle phases, a macromolecular composition of S. cerevisiae grown aerobically with a μaverage of 0.15 h* was estimated (Müller, 2006) (Table 2) and used to calculate the phase-specific, stoichiometric requirements for key metabolites serving as biomass precursors. These calculations were done with the help of a software tool for metabolic network analysis (mna pr3.0, SPAD-it, Nijmegen, The Netherlands) with a detailed, compartmented metabolic network of S. cerevisiae containing 147 reactions and 164 metabolites (Lange, 2002). With the obtained phase-specific stoichiometric precursor needs, combined with the macroscopic biomass formation rate, the fluxes towards biomass starting from key metabolites in the glycolysis pathway, the pentose phosphate pathway (PPP) and the tricarboxylic acid (TCA) cycle between two sample points were calculated, whereby the distribution of the cell population over the different cell cycle phases at each sample point as well as the total increase in biomass between two sample points were taken into account.

View this table:

Estimated macromolecular biomass compositions during different cell cycle phases for Saccharomyces cerevisiae grown aerobically at μ=0.15 h* under glucose limitation

Cell cycle phase
G1S/G2Early MLate MElemental composition on C-mol basis
Mass fractions (w/w) [g·(g biomass)*]
Nuclear RNA0.0560.0570.0590.059C1H1.232N0.390O0.737P0.105
Mitochondrial RNA0.0190.0190.0200.020C1H1.232N0.390O0.737P0.105
Mitochondrial DNA0.00040.00040.00050.0005C1H1.255N0.378O0.612P0.102
Nuclear DNA0.0040.0050.0060.006C1H1.255N0.378O0.612P0.102
  • * From Lange & Heijnen (2001).

  • All these compounds, except for nuclear DNA, trehalose and glycogen, were assumed to maintain constant ratios among themselves during the whole cell cycle. Intracellular concentrations were calculated for each phase on the basis of concentration data for cell number and biomass dry weight in combination with mean cell volumes for the respective cell cycle phase (Mauch, 2000; Müller, 2006).

  • The compound ‘lipids’ consists of neutral lipids, phospholipids, sterols, sterol esters, and free fatty acids (Müller, 2006).

Metabolic network model and flux fitting

The metabolic network and the flux-fitting procedure used here have been described elsewhere (van Winden, 2005), and were applied with a few modifications. Only the following metabolites from glycolysis and the PPP are involved in reactions that result in rearrangements of the carbon skeleton (and hence the label distribution), and therefore only these were included in the *C-MFA network model: glucose 6-phosphate (g6p), glucose 1-phosphate (g1p), fructose 6-phosphate (f6p), fructose 1,6-bisphosphate (fbp), erythrose 4-phosphate (e4p), and seduheptulose 7-phosphate (s7p). Because the carbon skeletons of ribose 5-phosphate, ribulose 5-phosphate and xylulose 5-phosphate are unaffected by interconversion of these metabolites, these pentose 5-phosphates were included as a single, lumped pool (p5p). This holds also for dihydroxyacetone phosphate, glyceraldehyde 3-phosphate, 2,3-bisphosphoglycerate, 2-phosphoglycerate, 3-phosphoglycerate, and phosphoenolpyruvate, which were included as a single triose phosphate pool (t3p).

Fluxes and MIDs of metabolites further down the catabolic route than phosphoenolpyruvate (pep), as well as the MIDs of trehalose 6-phosphate, were not considered in the flux-fitting procedure (see ‘Results and Discussion’). The PPP was modeled according to a ping-pong mechanism in which two-carbon and three-carbon fragments (C2 and C3) are transferred between the participating metabolites (Kleijn, 2005).

The g1p, f6p, p5p, e4p and t3p pools were modeled as the precursor molecules for biomass formation. All precursor molecules for the synthesis of the biomass constituents glucan, glycogen and trehalose were modeled as a g1p efflux. In reality, one out of two hexoses forming trehalose is a g6p unit, but due to the chosen modeling method, this has no effect on the outcome of this study.

The elutriated cells used for the inoculation of the fed-batch culture are recently budded-off daughter cells, and although they have not had much time to take up glucose, they can still contain substantial amounts of unlabeled storage carbohydrates after elutriation. Turnover of glycogen yields mainly g1p units. Turnover of trehalose yields directly two glucose molecules. Owing to the chosen modeling method with a high assumed reversibility of phosphoglucomutase, these two storage carbohydrate pools are indistinguishable as a source of unlabeled carbon. The inflow of extra, unlabeled carbon was therefore accounted for by incorporating a flow of unlabeled g1p into the metabolic network (g1p_unlab) combined with an equal flow of (label-averaged) g1p out of it towards biomass formation.

The resulting network model consisted of 12 fitted fluxes, of which eight were modeled as reversible, and six fixed fluxes that were constrained by the macroscopic conversion rates discussed earlier: glucose inflow and the biomass precursor fluxes. The measured MIDs of 10 metabolite pools were used as input for the optimization routine: g6p, g1p, f6p, mannose 6-phosphate (m6p), fbp, the 2-phosphoglycerate and 3-phosphoglycerate pool (2/3pg), pep, 6-phosphogluconate (6pg), p5p and s7p. Although some of them are redundant, as they should be identical as imposed by the metabolic network applied (e.g. 2/3pg and pep, or f6p and m6p), these MIDs can be used as a data consistency check. In total, the MIDs from these metabolite pools contained 54 independent data points. The *C-MFA software tool used in this study simulates the MIDs of the mentioned components based on the estimated fluxes. It finds the fluxes that minimize the variance-weighted squared sum of residuals between simulated and measured MIDs (SSres) (van Winden, 2005).

Results and discussion


The results presented here were obtained from a fed-batch culture of S. cerevisiae for which the inoculum had been obtained by centrifugal elutriation. Samples were taken during a time period during which the partially synchronized culture went through two complete cell cycles. This corresponded to 6.5 h of growth on *C-labeled medium in a carbon-limited, fed-batch mode. In the following, t=0 h corresponds to the start of the feed of the *C-labeled medium to the freshly elutriated cells. From the elutriation, a total amount of biomass of 162 mg dry weight, consisting of recently budded-off daughter cells, was collected and transferred to the fed-batch reactor.

Elutriation does not, in general, yield a completely synchronized culture (Futcher, 1999; Walker, 1999). Subpopulations of one of the four discernible cell classes were therefore quantified at each of the sample time points by DAPI staining of broth samples (van Doorn, 1988; Müller, 2003). From this analysis, distributions of subpopulations of cells for each sample point were obtained (Fig. 1). From Fig. 1, it can be seen that, for almost every sample point during the cultivation, the majority of the cells were in the G1 phase. At certain time points, however, substantial numbers of cells went through one of the three other discernible phases of cell division.


Fig. 1. Distribution of cell cycle phase-related subpopulations in the reported elutriated fed-batch culture of Saccharomyces cerevisiae according to DAPI staining. The first culture cycle ranged from t=1.2 h to 4.1 h, and the second from t=4.5 h to 6.3 h.

It can be inferred from the measured cell cycle distributions (Fig. 1) that the synchronicity of the cell culture during the second (culture) cell cycle (t=4.5 h and later) in the experiment was better than during the first cycle. This is also reflected by the budding index of the culture, which reached a higher value during the second cycle (Fig. 2), indicating that a substantial proportion of the cells did not divide during the first cycle of the culture. This might indicate the triggering of a stress response as a result of the shift to a higher growth rate after elutriation (from 0.1 h* in the continuous culture preceding elutriation, to 0.15 h* in the fed-batch culture). The fact that not all cells divided during each cycle also explains the apparent discrepancy between the duration of one cell cycle (c. 2.5 h in this experiment) and the growth rate of 0.15 h* that, if all cells divide, would agree with a doubling time of 4.6 h.


Fig. 2.Budding index during the reported elutriated fed-batch culture of Saccharomyces cerevisiae given as the percentage of cells carrying a bud. Cell viability was at least 90% for all samples.

Macroscopic fluxes

The time courses of the balanced, macroscopic, biomass-specific conversion rates of the substrates and products during the elutriated fed-batch culture are shown in Fig. 3. It can be seen that the rates for ethanol and acetate, in particular, showed cyclic behavior, with consecutive net production and uptake of these compounds during the different cell cycle phases. This phenomenon has also been observed in metabolically oscillating continuous cultures (Porro, 1988; Strässle, 1989; Duboc, 1996; Hans, 2003; Müller, 2003), and is coupled to the limited capacity of the cells to respire glucose during parts of the cell cycle (Porro, 1988; Strässle, 1988). Around the time when the bud emerges, which in S. cerevisiae coincides with the beginning of S phase, cells rapidly degrade their storage carbohydrates, leading to increased glycolytic ATP production coupled to the production of ethanol and acetate. These products are subsequently taken up again during the following cell cycle phases. After mitosis, the growing cells increase their uptake of glucose, part of which is accumulated again as storage carbohydrates. These sequential cyclic processes of ethanol and acetate production and consumption, as well as switching between respirative and respirofermentative metabolism, were qualitatively visible in the time courses of the macroscopic conversion rates and the respiration quotient (Fig. 3).


Fig. 3. Balanced macroscopic fluxes in the reported elutriated fed-batch culture of Saccharomyces cerevisiaeaverage=0.15 h*). (a) ⋄, ethanol; △, acetate; ◻, glycerol. (b) ▪, CO2; ♦, glucose; ▲, O2; x, biomass. (c) ●, respiratory quotient (RQ). Error bars indicate mean±SD.


The greatest advantage of the LC-MS method employed is its favorable time resolution, which is due to the fact that it measures the labeling patterns of the free metabolite pools in primary metabolism instead of the labeling patterns of biomass components derived therefrom, such as protein-bound amino acids. In this study, samples taken as closely apart as 30 min already showed changes in the MIDs of these free metabolites, as can be seen in Fig. 4, which gives the MIDs for all measured metabolites as a function of time.


Fig. 4.Mass isotopomer distributions of several metabolites during the reported elutriated fed-batch culture of Saccharomyces cerevisiae. Mass isotopomers are indicated as the molar mass of the unlabeled molecule (M+0) increased by the number of labeled carbon atoms present (1–12). In the upper left part, the MID of the used isotopic mixture of the carbon substrate (glucose) is given. Ribose 5-phosphate, ribulose 5-phosphate and xylulose 5-phosphate are not separated in the chromatography procedure, and are therefore presented as one pool. The same holds for 2-phosphoglycerate and 3-phosphoglycerate, and for citrate and isocitrate. Error bars indicate mean±SD based on three independent measurements of one sample.

It is observed that certain metabolite pools had MID patterns very similar to a metabolically coupled neighboring pool during the whole experiment. This indicates that the corresponding enzymatic reaction step between the two pools operates close to equilibrium under in vivo growth conditions. This was the case for the known equilibria between g6p and f6p, 2/3pg and pep, and g6p and g1p (Teusink, 2000; Wittmann, 2005; Wu, 2006a). Because f6p and m6p also showed similar MID patterns throughout the whole experiment, it is likely that the phosphofructomutase enzyme, which interconverts these two pools, also works close to equilibrium in vivo.

The metabolite pair of g6p and 6pg is known to be far from equilibrium, because this reaction is practically irreversible, due to the rapid hydrolysis of the lactone intermediate. However, these two metabolites still had very similar MID patterns, because g6p is the unique precursor for 6pg, and no rearrangements of the carbon skeleton occur in the reaction. Other metabolite pairs that are known to be far from equilibrium actually showed differences in their MID patterns, e.g. f6p and fbp, and pep and pyruvate (Teusink, 2000). These differing MIDs indicate the inflow of differently labeled metabolite molecules into the pool of the reaction product.

The MIDs of succinate and malate were found to differ considerably. Given the earlier observation that malate is close to equilibrium with fumarate (Wittmann, 2005; Wu, 2006b), it can be concluded that succinate and fumarate are not close to equilibrium under the in vivo conditions that apply and assuming that all three metabolite pools are not compartmentalized.

When the measured mass fractions of the trehalose 6-phosphate precursors g1p and g6p were combined to calculate the MID of trehalose 6-phosphate, the calculated result had a considerably lower unlabeled (M+0) fraction than the measured MIDs of trehalose 6-phosphate for all time points, as shown in Fig. 4 (Table 3). To explain this overrepresentation of the M+0 fraction in the measured MID of trehalose 6-phosphate, it had to be assumed that there was a varying inflow of unlabeled metabolite into this pool. Naturally labeled storage carbohydrates present intracellularly at the beginning of the fed-batch experiment could be the source of this. However, the storage carbohydrate trehalose is normally degraded directly to two glucose units, and trehalose 6-phosphate is thus not a regular intermediate in the degradation of trehalose (Kalf & Rieder, 1958). The major breakdown products of the other main storage carbohydrate in S. cerevisiae, glycogen, are g1p units. If unlabeled g1p units from this source constituted the missing inflow of unlabeled material, this would have been reflected in the MID of g1p; this was, however, not the case. A hypothetical explanation that the measured MID of trehalose 6-phosphate was correct and the MID of g1p contained a gross measurement error was discarded after testing with the flux-fitting method (results not shown). It is therefore unlikely that the unlabeled trehalose 6-phosphate originated from a pool of naturally labeled storage carbohydrates. As it thus could be seen a priori that the proposed metabolic model could not explain the labeling state of the M+0 fraction of trehalose 6-phosphate, it was decided to omit its MIDs from the flux-fitting procedure to prevent systematic errors in the estimation of the fluxes.

View this table:

Measured M+0 mass fractions of trehalose 6-phosphate (t6p), and expected, calculated fractions based on the combination of the measured M+0 fractions of one glucose 1-phosphate and one glucose 6-phosphate during the reported elutriated fed-batch experiment

t (h)
Measured M+0 fraction of t6p0.470.370.
Calculated M+0 fraction of t6p0.

Six minutes after the start of the (*C-labeled) glucose feed, the first sample was taken. This sample is indicated by ‘pre’ in Fig. 4, because it mirrors the inflow of labeled glucose into cellular metabolism. Owing to the low amount of biomass present at this time point and a correspondingly low amount of intracellular metabolites, no MID could be determined for some of these metabolites. It can be clearly seen that metabolites appearing later in the catabolic pathway [pyruvate, (iso)citrate, succinate and malate] still had large M+0 fractions at this time point and had thus not yet reached isotopic pseudo-steady state. In the succeeding samples, this M+0 fraction quickly decreased relative to the higher mass fractions, indicating the inflow of the labeled carbon into metabolism.

Dynamic changes other than the initial decrease of the M+0 fraction and the concomitant increase of the higher mass fractions were observed for the TCA cycle intermediates 2-oxoglutarate and succinate. These pools showed a remarkably elevated M+0 fraction at time points t=5.2 h and 5.7 h, indicating a significant inflow of unlabeled material into those pools at those time points that, given the prevailing conditions, could only have its origin in the conversion of unlabeled amino acids and/or protein. The 2-oxoglutarate pool in S. cerevisiae is known to be directly enzymatically coupled to the amino acid pool of glutamate. Unlabeled carbon from amino acid and/or protein turnover could therefore enter this pool. As can be deduced from the course of the budding index of the culture (Fig. 2), it can be safely assumed that a significant proportion of the cells present in the broth at the mentioned time points were cells that also constituted the freshly elutriated inoculum at the start-up of the fed-batch culture. These cells would probably still contain a large amount of unlabeled protein [and possibly also unlabeled free amino acid pools (Grotkjaer, 2004)], because they were grown on medium containing only naturally labeled substrate before elutriation. However, as under the experimental conditions the TCA cycle is known to operate as a cycle in the mitochondria, it is hard to understand why the MIDs of malate and citrate did not show this elevated M+0 fraction. This can only be explained by speculating that the measured mass signals for succinate and 2-oxoglutarate at the given time points were dominated by nonmitochondrial pools of these metabolites that were not interconverted in a cyclic mode but were processed via separate cytosolic pathways, involved in amino acid metabolism. Varying absolute amounts of intracellular 2-oxoglutarate as well as of a number of free amino acid pools have been observed during cell cycle-related, metabolic oscillations of S. cerevisiae in continuous cultures (Hans, 2003; Wittmann, 2005). The applied mass isotopomer analysis is, however, independent of the absolute amounts of the intracellular metabolites, and it was therefore not possible to confirm these observations for the experiments presented here.

*C metabolic flux analysis

*C-MFA for the whole primary carbon metabolism of S. cerevisiae is complicated by:

  • 1. The turnover of unlabeled metabolite storage pools such as glycogen (Paalman, 2003) or the large pool of free glutamate (Hans, 2003; Grotkjaer, 2004);

  • 2. Compartmentalization of pyruvate and several TCA cycle intermediates;

  • 3. The periodic influx of carbon-containing substrates such as ethanol and acetate during the cell cycle (Porro, 1988).

Because the storage carbohydrate pools were expected to be already substantially labeled in the second cycle of the experiment, only MIDs from this cycle were used in the flux-fitting procedure. Flux fits were therefore performed for samples taken at t=4.5 h, 4.9 h, 5.2 h and 5.7 h. On the basis of the measured macroscopic conversion rates (Fig. 3), the phase-specific macromolecular biomass compositions (Table 2), and the distribution of the cell population over the different cell cycle phases (Fig. 1), the stoichiometric requirements for biomass precursor molecules were calculated for the selected time points as described in ‘Materials and methods’. To facilitate comparison, all numbers were normalized to a glucose uptake of 100 (arbitrary units) (Table 4). It can be seen that the biomass precursor requirements vary only slightly for the four sample points considered (Table 5).

View this table:

Stoichiometric fate of 100 mol of glucose during the four considered time intervals (see text) in the presented fed-batch experiment (μaverage=0.15 h*)

Time interval (h)Biomass (C-mol)Ethanol (mol)Acetate (mol)Glycerol (mol)Carbon dioxide (mol)
  • Negative numbers indicate net uptake of the component during the respective time interval. Time intervals are indicated as time passed since the start of the fed-batch feed and correspond to time periods between two sampling points.

View this table:

Detailed description of the biomass formation (amounts taken from Table 4) in the form of reaction formulas

Time interval (h)Glucose 1- phosphate (mol)Fructose 6- phosphate (mol)Dihydroxyacetone phosphate (mol)3-phosphoglycerate (mol)Phosphoenolpyruvate (mol)Pyruvate (mol)Ribulose 5-phosphate (mol)Erythrose 4-phosphate (mol)Acetyl CoA (cyt) (mol)2-Oxoglutarate (cyt) (mol)2-Oxoglutarate (mit) (mol)Oxaloacetate (cyt) (mol)Carbon dioxide (mol)Glyceraldehyde 3-phosphate (mol)Biomass (C-mol)
  • Numbers indicate number of moles of respective key metabolites needed to build the indicated amount of biomass. Numbers in bold typeface were included in the flux-fitting procedure as constraining fluxes at the sample point at the start of the respective time interval.

  • * cyt, cytosolic; mit, mitochondrial.

  • * Concurrent with biomass formation in the current model, CO2 and glyceraldehyde 3-phosphate are produced as the net result. Under normal conditions, the glyceraldehyde 3-phosphate is then further metabolized in glycolysis.

Furthermore, only the glycolytic and the PPP fluxes were fitted, because both pathways take place uniquely in the cytoplasm. Because this part of metabolism was selected, the periodic inflow of labeled carbon resulting from the small periodic consumption of (labeled) acetate and ethanol did not influence the results any more, because carbon from these sources would enter catabolic metabolism at the level of acetyl-CoA (Boubekeur, 2001). The MIDs of CO2 were not used, because these result partially from CO2 formed by decarboxylating enzymes in areas of metabolism that were excluded from the current model.

The fluxes within the resulting network (see ‘Materials and methods’) were then fitted to the measured MIDs (Fig. 4) using the calculated fluxes of the biomass precursor molecules (Table 5) as partial constraints. The resulting fitted flux distributions are given in Fig. 5a–d for the four sample points in the second cell cycle of the fed-batch culture. Figure 6 shows the measured and simulated MIDs for each sample point. In Table 6, the absolute macroscopic glucose conversion rate, the PPP split ratio (the flux from g6p to p5p relative to the glucose influx), and the SSres for each of the four sample points, are given. The SSres value is a measure of the goodness of fit of the fitted flux patterns, and indicates whether the differences between measured and fitted MIDs are statistically acceptable or not. If not, this would mean that there is either a systematic error in the network model or an underestimation of the measurement error in the measured MIDs (Antoniewicz, 2006). For the presented network model (54 independent data points and 10 degrees of freedom), the boundary value at which the SSres can be accepted with 95% confidence lies at [χ*(44)>0.05]=61. The values for t=4.9 h and t=5.7 h (Table 6) are thus accepted, whereas those for t=4.5 h and t=5.2 h are not. Because the network model and the range of SDs of the measurements are the same for all four samples, the experimental data for t=4.5 h and t=5.2 h may contain small, but significant, systematic errors.


Fitted metabolic flux distributions for the four selected time points of the reported elutriated fed-batch culture of Saccharomyces cerevisiae normalized to a glucose influx of 100 (arbitrary units). Dashed lines indicate constraining fluxes towards biomass formation; C2 indicates two-carbon fragment transferred in transketolase-catalyzed reactions; C3 indicates three-carbon fragment transferred in transaldolase-catalyzed reactions (dotted lines are only used to prevent visual confusion); large-sized numbers indicate the net flux of a reaction in the direction of the arrow; negative large-sized numbers indicate net fluxes against the direction of the arrow; small-sized numbers in italics indicate exchange fluxes of the reversible reactions in the direction of the arrow. (a) Fluxes at time point t=4.5 h. (b) Fluxes at time point t=4.9 h. (c) Fluxes at time point t=5.2 h. (d) Fluxes at time point t=5.7 h. For abbreviated metabolite names, see text. Apparent discrepancies in mass balances are caused by round-off errors.


Simulated (‘sim’) and measured (‘meas’, from Fig. 4) mass isotopomer distributions of intracellular metabolites during the reported elutriated fed-batch culture of Saccharomyces cerevisiae. (a) MIDs at time point t=4.5 h. (b) MIDs at time point t=4.9 h. (c) MIDs at time point t=5.2 h. (d) MIDs at time point t=5.7 h. For abbreviations, see text. for colour-coding see Fig. 4.

View this table:

Summarized results of the flux fits for the four selected time points

Sample time pointAbsolute glucose uptake rate [mmol·(C-mol biomass)* h*]PPP split ratio (arbitrary units)Global, variance-weighted minimized squared sum of residuals (SSres)
t=4.5 h390.14 (0.015–0.31)205
t=4.9 h420.43 (0.39–0.46)50
t=5.2 h430.53 (0.27–0.77)98
t=5.7 h430.28 (0.18–0.36)38
  • * The pentose phosphate pathway (PPP) split ratio is defined as the flux from glucose 6-phosphate to the pentose 5-phosphate pool divided by the normalized glucose influx (=100 arbitrary units). Numbers in parentheses are 95% confidence intervals (see text).

Figure 6 shows that a good correspondence existed between the measured and simulated MIDs and that none of the considered metabolites or mass fractions was clearly misfitted. As can be seen in Fig. 5 and Table 6, the flux fits suggested that during the considered time period, the PPP split ratio changed by a factor 1.9, both up and down, around a value of 0.27 (arbitrary units), from 0.14 at t=4.5 h to 0.53 at t=5.2 h. Furthermore, it can be seen that for none of the considered sample points was an influx of unlabeled carbon in the form of g1p_unlab fitted. This does not mean, however, that glycogen was not degraded at all. If the glycogen already contained labeled glucose units at the ends of its branches, polymerized during the first cycle and the G1 phase of the second cycle, these would be spliced off first upon glycogen turnover, and in that way contribute to the labeling state of the pool of free g1p.

PPP split ratio and confidence intervals

It is remarkable that although the MIDs and the biomass precursor fluxes of these four sample points show only small changes (Fig. 4 and Table 5), clearly different flux patterns are fitted. Apparently, small changes in MIDs can already give rise to large changes in fitted flux patterns. It was therefore decided to further investigate the significance of these changes.

The fitted network model has 10 degrees of freedom: eight net fluxes of the reversible reactions, the inflow flux of g1p_unlab, and the PPP split ratio. It was decided to focus on the PPP split ratio, as the ‘gp1_unlab’ flux equals zero for all four selected time points, and the eight exchange fluxes of the reversible reactions are hard to estimate individually, because they are largely interdependent (Christensen, 2002). The PPP split ratio depends not only on the cell cycle phase, but also very much on the exact growth conditions (van Winden, 2005). A broad range of values has been reported for it (Table 7). The fact that large differences in the PPP split ratios are fitted with only slightly changing MIDs and biomass precursor needs, and the broad range of reported split ratios, instigated the determination of the reliability of the fitted estimations of the PPP split ratio reported here.

View this table:

Values of the pentose phosphate pathway split ratios reported in the literature for aerobic, continuous cultures of Saccharomyces cerevisiae determined by *C-MFA

ReferenceReported split ratioExperimental conditions
van Winden (2005)0.24 (0.05–0.52)30°C, pH 5, D=0.10 h*, CEN.PK-113.7D, 1.0 g L* ethanol present in medium, LC-MS
Kleijn (2005)0.18
Fiaux (2003)0.41 ± 0.0230°C, pH 5.5, D=0.1 h*, CEN.PK-113.7D, NMR
Gombert (2001)0.44230°C, pH 5, D=0.11 h*, CEN.PK-113.7D, GC-MS
Christensen (2002)0.415–0.444
This study0.14 (0.015–0.31)30°C, pH 5.0, fed-batch after elutriation, μ=0.15 h*,
0.28 (0.18–0.36)CBS7336, LC-MS
0.43 (0.39–0.46)
0.53 (0.27–0.77)
  • * Ninety per cent confidence interval based on a χ*(16.0, 17) distribution.

  • * *Reported results in these references are based on the same dataset as for the preceding reference; the different results are due to improved data handling.

  • * Mean ± SD.

  • * *Lower and upper limit of the results of MFA of five independent samples taken from the same steady-state culture.

  • * Ninety-five per cent confidence interval based on an F(1,44) distribution.

First, it was investigated whether the observed changes in the measured MIDs between two consecutive samples were significantly larger than the differences between the measured and simulated MIDs for the individual time points. If not, one should expect measurement noise to obscure any variation in the true metabolic fluxes. The SSres values of the measured and simulated MIDs for the separate time points are given in Table 6. The squared differences of the measured MIDs for the three pairs of consecutive samples were weighted by the variances of the paired datasets. These sums of squared differences were 705 (for the change from t=4.5 h to t=4.9 h), 2075 (t=4.9 h to t=5.2 h), and 1009 (t=5.2 h to t=5.7 h). Thus, the variations between the measurements of consecutive time points were an order of magnitude larger than those between measurements and simulated results. From this, we conclude that the measured MIDs indicate, at least qualitatively, that the considered metabolic fluxes changed in consecutive samples.

To investigate whether the observed changes in the fitted PPP split ratios were significant, the following procedure was applied to determine their confidence intervals (van Winden, 2005; Antoniewicz, 2006; Kleijn, 2006). For each time point, the split ratio was varied around the value obtained in the original flux fit. With each of these new split ratios, a new flux-fitting procedure was performed, now with one degree of freedom less, yielding a new value for SSres. The results are plotted in Fig. 7. Boundary values for the reliability of SSres were determined using the following formula: Embedded Image in which: SSres,sr is the minimized squared sum of residuals at a set split ratio (sr); SSres is the global, minimized squared sum of residuals; p′ is the number of fitted parameters for which the confidence intervals are calculated; Embedded Image is the estimator for the variance of the error (=SSres/np); F is the F-distribution; α is the confidence level; n is the number of independent data points used in the fitting procedure; and p is the number of fitted parameters (=degrees of freedom in the original flux fit).


Minimized squared sum of residuals as a function of the pentose phosphate pathway (PPP) split ratio; ⋄, at time point t= 4.5 h; ◻, t=4.9 h; △, t=5.2 h; x, t=5.7 h. Horizontal solid lines indicate the 95% confidence boundary value of the F(1,44)-distributed sum of squared residuals for the fitted flux pattern at the indicated time point.

The boundary values calculated for p′=1, α=95%, n=54 and p=10 are indicated in Fig. 7 by horizontal lines; their cutoffs with the SSres graphs indicate the confidence intervals for the PPP split ratios. It can be seen in Fig. 7 that only the flux fit for the t=4.9 h sample point was well defined. The 95% confidence interval of the PPP split ratio for this point allowed it to vary by only 9% around its original value of 0.43. The global SSres for the sample point at t=5.7 h had a lower absolute value but also a broader confidence interval (−36% and +29% around its original value of 0.28) for the PPP split ratio. Despite this broader confidence interval, it still did not overlap with the confidence interval for the t=4.9 h sample point. This leads to a probability of less than 5% that the differences in the fitted PPP split ratios for these two sample points were caused by measurement errors alone. The difference in the fitted split ratio for these two sample points must therefore have been the result of differences in the measured MIDs, which in turn are most likely the result of a changing metabolic flux towards the PPP for these two sample points.

The confidence intervals for the other two sample points were less well defined, indicating that the observed MIDs could result from a broad range of flux distributions with different PPP split ratios. However, even with these broad confidence intervals, the interval for the t=4.5 h sample point still did not overlap with that for the t=4.9 h sample point. Thus, these two fitted split ratios also probably resulted from different intracellular fluxes.

Cell cycle metabolism

Because significant differences in the fitted PPP split ratios between two of the samples were observed, it was safe to assume that the metabolic flux towards the PPP (and, in consequence, all other fluxes in cytosolic central carbon metabolism) changed over time. Given the course of the macroscopic conversion rates of substrate and products, which clearly resulted from cyclic physiologic events in the cells, it was plausible to assume that these changing metabolic fluxes were also connected to the observed changing distribution of the cell population over the different cell cycle phases.

Because of the current error margins, care should, however, be taken when relating these changes in the fitted, normalized flux patterns to changes in the absolute sizes of the fluxes and to cell cycle-related metabolism in general. When considering the question of how the relatively small changes in the cell population distribution yield the observed pronounced changes in the fitted flux patterns, and whether these changes will become even stronger when 100% pure subpopulations are used, one should bear in mind that the results are biased by the subpopulation with the largest absolute amounts of metabolites. As a consequence, a relatively small subpopulation with a relatively large amount of a given metabolite can still dominate the population-averaged MID for that metabolite.

Although the estimated flux patterns should not be overinterpreted, it can be observed that the flux towards the PPP was lowest for the sample at t=4.5 h, when 93% of the cells were in G1 phase. This was the case in both normalized and absolute terms, i.e. related to the absolute glucose uptake rates (Table 6). At the other three sample points, substantial proportions of the cell population went through cell division (34, 41 and 57%, respectively), which apparently led to a higher PPP flux. This change in the PPP split ratio would be in accordance with the postulated increased production of NADPH during the ‘reductive/charging phase’ of the metabolic cycle, as recently suggested by Tu (2005). By studying the genome-wide transcription of metabolically oscillating cultures of S. cerevisiae, these authors defined a conceptual relationship between the metabolic oscillation cycle and the cell division cycle, in which metabolism cycles between an oxidative phase during cell growth and a reductive phase during cell division (Klevecz, 2004; Tu, 2005; Reinke & Gatfield, 2006). The reductive/charging phase would in this concept putatively coincide with the early M phase as defined in this study. Samples that contained an early M-phase subpopulation (the samples at t=4.9, 5.2 and 5.7 h contain 9, 17 and 16% of cells in early M phase, respectively; see Fig. 1) should therefore be expected to have a higher PPP flux than samples not containing this subpopulation (t=4.5 h). This is indeed the case for the optimally fitted PPP split ratio. The course of the optimally fitted PPP split ratio was therefore, at least qualitatively, in agreement with the concept of the yeast metabolic cycle as suggested by Tu (2005), and Reinke & Gatfield (2006).

Another feature of interest in this respect would be the induction of proteasomal transcripts and the resulting protein catabolic activity during the reductive phase (Tu, 2005; Reinke & Gatfield, 2006). This feature could provide a tentative explanation for the source of the observed inflow of unlabeled material in the metabolite pools of the TCA cycle intermediates 2-oxoglutarate and succinate in the M-phase-enriched samples of t=5.2 and 5.7 h as discussed earlier.


This is the first time that *C-MFA has been applied to determine changes in metabolic fluxes in an elutriated culture of S. cerevisiae. Changing flux patterns have indeed been observed with respect to the flux towards the PPP, as the PPP split ratio was found to change from 0.14 (arbitrary units) (95% confidence intervals: 0.015–0.31) for an almost exclusively G1-phase-enriched cell population to 0.53 (95% confidence interval: 0.27–0.77) for a cell population 41% enriched in dividing cells (S/G2 and early M phase).

The microscopic method applied to identify the cell cycle phase of cells does not allow for distinction between cells in S phase and cells in G2 phase. Measurement of DNA distribution (Vanoni, 1983) would allow for this distinction, but, in turn, this method does not allow for distinction between cells in G2 phase and cells in M phase. The results of this study stress the importance of being able to distinguish S-phase cells from G2-phase cells. If this distinction could be made, it would become possible to pinpoint, using the presented *C-MFA method, where exactly in the cell cycle intracellular fluxes change due to the turnover of storage carbohydrates: in late G1 phase or early S phase. This information will be of importance in determining the contribution of metabolic activity to the commitment of the cell to division and timing of S-phase entry (Silljé, 1999; Jorgensen & Tyers, 2004; Futcher, 2006).

It can be concluded that clear changes in the fluxes of the primary, cytosolic carbon metabolism of S. cerevisiae occur in an elutriated culture in which the distributions of the cell population over the cell cycle phases vary. Including cell cycle dependency in a metabolic network model could therefore constitute an improvement when studying metabolic fluxes, especially when changing experimental conditions are applied that affect the growth rate of the individual cells and the culture as a whole. However, the sensitivity of the applied experimental method needs improvement. A way to achieve this is by obtaining higher degrees of synchronicity in the culture, which could yield better distinguishable flux patterns. These changes can be detected by the LC-MS analysis based *C-MFA presented here, but a thorough analysis of the error margins in this *C-MFA procedure will also be of importance (Antoniewicz, 2006).


The authors would like to thank Cor Ras for performance of the LC-MS analyses. This study was financially supported by the Kluyver Centre for Genomics of Industrial Fermentation (project 5.4) and the German Research Foundation (DFG, Sonderforschungsbereich 495).


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