Characterization of the metabolic shift between oxidative and fermentative growth in Saccharomyces cerevisiae by comparative 13C flux analysis
© Frick and Wittmann; licensee BioMed Central Ltd. 2005
Received: 29 September 2005
Accepted: 03 November 2005
Published: 03 November 2005
One of the most fascinating properties of the biotechnologically important organism Saccharomyces cerevisiae is its ability to perform simultaneous respiration and fermentation at high growth rate even under fully aerobic conditions. In the present work, this Crabtree effect called phenomenon was investigated in detail by comparative 13C metabolic flux analysis of S. cerevisiae growing under purely oxidative, respiro-fermentative and predominantly fermentative conditions.
The metabolic shift from oxidative to fermentative growth was accompanied by complex changes of carbon flux throughout the whole central metabolism. This involved a flux redirection from the pentose phosphate pathway (PPP) towards glycolysis, an increased flux through pyruvate carboxylase, the fermentative pathways and malic enzyme, a flux decrease through the TCA cycle, and a partial relocation of alanine biosynthesis from the mitochondrion to the cytosol. S. cerevisiae exhibited a by-pass of pyruvate dehydrogenase in all physiological regimes. During oxidative growth this by-pass was mainly provided via pyruvate decarboxylase, acetaldehyde dehydrogenase, acetyl-CoA synthase and transport of acetyl-CoA into the mitochondrion. During fermentative growth this route, however, was saturated due to limited enzyme capacity. Under these conditions the cells exhibited high carbon flux through a chain of reactions involving pyruvate carboxylase, the oxaloacetate transporter and malic enzyme. During purely oxidative growth the PPP alone was sufficient to completely supply NADPH for anabolism. During fermentation, it provided only 60 % of the required NADPH.
We conclude that, in order to overcome the limited capacity of pyruvate dehydrogenase, S. cerevisiae possesses different metabolic by-passes to channel carbon into the mitochondrion. This involves the conversion of cytosolic pyruvate either into acetyl CoA or oxaloacetate followed by intercompartmental transport of these metabolites. During oxidative growth mainly the NAD specific isoforms of acetaldehyde dehydrogenase and isocitrate dehydrogenase catalyze the corresponding reactions in S. cerevisiae, whereas NADPH supply under fermentative conditions involves significant contribution of sources other than the PPP such as e. g. NADPH specific acetaldehyde dehydrogenase or isocitrate dehydrogenase.
The budding yeast S. cerevisiae is an important biotechnological organism e.g. for production of ethanol , recombinant proteins , antibiotics  or biomass . Additionally it is relevant as a model system to study metabolism due to its high homology with other eukaryotic organisms [5, 6]. This explains the high interest in understanding metabolic function and regulation in this organism. S. cerevisiae is able to perform simultaneous respiration and fermentation at high growth rates even under fully aerobic conditions [7, 8]. This Crabtree effect called phenomenon is visualized in chemostat culture of S. cerevisiae by a shift from biomass formation towards fermentative products at increased dilution rates . Also other yeast species show this behavior . Despite many studies in the past [10–12], a clear and univocal explanation of this phenomenon has not yet been provided [13, 14]. The Crabtree effect has important consequences for industrial processes aiming at the production of yeast biomass, where the formation of fermentative by-products is undesired [15, 16]. A powerful approach to investigate metabolic systems is 13C metabolic flux analysis which allows the quantification of in vivo activity of pathways and reactions [17–19]. In recent studies, which took the spatial arrangement of metabolic reactions in the compartments cytosol and mitochondrion into account, metabolic flux analysis was successfully applied to S. cerevisiae and related yeast strains [20–27]. In the present work we investigated the metabolic shift from oxidative to fermentative growth in S. cerevisiae by quantifying metabolic fluxes through the underlying reactions in the central metabolism at these different physiological states. For this purpose chemostat cultures with [1-13C] glucose as substrate were grown at different growth rates under aerobic glucose-limited conditions to metabolic and isotopic steady-state. The use of a continuous culture hereby allowed the precise adjustment of the physiological state of the cells, i.e. the relative activity of the fermentative pathways.
Growth and product formation of S. cerevisiae
Tracer experiments with [1-13C] glucose as sole carbon source
Anabolic demand of Saccharomyces cerevisiae during aerobic glucose-limited chemostat culture at different dilution rates. The data are given in μmol (g cell dry mass)-1 and are calculated from the cellular composition.
D = μ = 0.15 h-1
D = μ = 0.30 h-1
D = μ = 0.40 h-1
Phosphoglycerate (for lipids, nucleotides)
Phosphoglycerate (for serine + cysteine)
Phosphoglycerate/Oxaloacetate (for glycine)a
Oxaloacetate (for threonine, methionine, isoleucine)
Oxaloacetate (for others)
Pyruvate (for alanine)b
Pyruvate (mitochondrial, for others)
Specific growth, substrate consumption, product formation rates and carbon balance of Saccharomyces cerevisiae cultured on [1-13C] glucose in chemostat at different growth rates for metabolic flux analysis.
Specific rate (C mmol h-1)
Purely Oxidative Growth (μ = 0.15 h-1)
Respiro-Fermentative Growth (μ = 0.30 h-1)
Mainly Fermentative Growth (μ = 0.40 h-1)
sum of substrates
sum of products
carbon recovery [%]
13C labeling patterns of amino acids in cell hydrolysates of Saccharomyces cerevisiae cultivatedon [1-13C] glucose in chemostat under aerobic glucose-limited conditions at different growth rates.
Purely Oxidative Growth (μ = 0.15 h-1)
Respiro-Fermentative Growth (μ = 0.30 h-1)
Mainly Fermentative Growth (μ = 0.40 h-1)
Alanine (m/z 260, C1–3)
Alanine (m/z 232, C2–3)
Glycine (m/z 246, C2)
Valine (m/z 186, C2–5)
Valine (m/z 260, C2–5)
Valine (m/z 288, C2–5)
Serine (m/z 288, C2–3)
Serine (m/z 362, C2–3)
Serine (m/z 390, C1–3)
Threonine (m/z 376, C2–4)
Threonine (m/z 404, C1–4)
Aspartate (m/z 418, C1–4)
Arginine (m/z 414, C1–5)
Phenylalanine (m/z 336, C1–9)
Phenylalanine (m/z 302, C1–2)
Tyrosine (m/z 466, C1–9)
Tyrosine (m/z 302, C1–2)
Glutamate (m/z 432, C1–5)
PPP and glycolysis
The metabolic shift of S. cerevisiae was accompanied by a substantial decrease of the relative flux through the PPP (Figure 3). The decreasing contribution of the PPP with increasing growth rate has direct consequences for the supply of NADPH, required in various anabolic reactions, and certain anabolic precursors. Taking into account that two molecules NADPH are generated in the oxidative part of the PPP, the relative supply of NADPH is 110 % (normalized to the glucose uptake rate) at μ = 0.15 h-1. In comparison only 60 % and 30 % NADPH, respectively, are formed at μ = 0.30 h-1 and μ = 0.4 h-1. A similar trend can be seen for erythrose 4-phosphate and ribose 5-phosphate. The supply of these anabolic precursors was substantially lower under fermentative conditions.
Fluxes around the pyruvate node
Distinct flux changes were observed for the pathways utilizing cytosolic pyruvate, i. e. pyruvate carboxylase, pyruvate decarboxylase, and the pyruvate transporter into the mitochondrion. A surprising result was the increase of flux through pyruvate carboxylase with increasing growth rate. This reaction was thought to mainly serve for the supply of cytosolic oxaloacetate for anabolism. Under fermentative conditions at higher growth rate, however, the anabolic demand for this precursor was much lower as compared to purely oxidative growth (Table 2). Accordingly the increase of flux through pyruvate carboxylase was not driven by an increased anabolic demand. It was in fact linked to increased transport of oxaloacetate into the mitochondrion. Interestingly, pyruvate decarboxylase, the entry step towards the fermentative metabolism, exhibited in vivo activity not only during the formation of fermentative by-products. Significant flux through this pathway was also observed under conditions of purely oxidative growth, i.e. in the absence of overflow metabolism. Accordingly a high production of acetaldehyde resulted for all physiological states. Under purely oxidative growth, the formed acetaldehyde was completely utilized for the synthesis of cytosolic acetyl CoA. This was then either transported into the mitochondrion or directly channeled into anabolic pathways located in the cytoplasm. During the switch to fermentation the acetaldehyde formed was mainly channeled into the fermentative by-products. The highest flux through pyruvate decarboxylase was observed at maximum production of ethanol and acetate. The ingoing flux through the lower glycolytic chain was higher during fermentative growth as compared to purely oxidative growth (Figure 3).
A substantial transport of carbon from the cytosol into the mitochondrion resulted for all growth rates (Figure 3). Hereby the relative contribution of the different transporters depended on the physiological state. Under purely oxidative growth acetyl CoA, formed in high amounts via the fermentative routes, was the dominating metabolite transported into the mitochondrion. The acetyl CoA transport was strongly decreased under conditions of respiro-fermentative growth. During mainly fermentative metabolism the transport net flux practically decreased to zero. The flux of oxaloacetate transport increased with increasing growth rate. This is linked, as described above, with the increased flux through pyruvate carboxylase. Interestingly the activity of the oxaloacetate transporter correlated with the flux through malic enzyme. This might suggest that sufficient intercompartmental oxaloacetate transport is important for the activity of malic enzyme. The picture observed for the pyruvate transport was more complex. The relative transport flux increased from purely oxidative to respiro-fermentative growth. With further increase of the specific growth rate it substantially decreased. The total flux of carbon into the mitochondrion, as sum of the single transport reactions, was highest during purely oxidative growth.
Overall, the metabolic shift from pure oxidation to fermentation was linked to a strong decrease of the TCA cycle flux (Figure 3). Under purely oxidative growth citrate synthase, the entry enzyme of this pathway, exhibited a relative flux of 73.1 %. The relative activity of this enzyme was 54 % at μ = 0.30 h-1 which indicates that the TCA cycle still contributed to a large extent to the metabolic activity. At μ = 0.40 h-1 the TCA cycle still operated as a cycle, but only at a relatively low activity. The observed flux changes include a shift of the relative contribution of fumarase and the oxaloacetate transporter to the supply of the mitochondrial malate/oxaloacetate pool.
Under purely oxidative growth both pathways for glycine biosynthesis were active, whereby the major fraction of glycine was formed via the serine pathway (Figure 3). The simultaneous in vivo activity of both pathways was maintained under fermentative conditions. An interesting finding resulted for the biosynthesis of alanine for biomass production. Whereas alanine was exclusively synthesized via the mitochondrial route at purely oxidative growth, cells partly switched to cytosolic alanine formation during the metabolic shift towards fermentation (Figure 3). Under mainly fermentative conditions the cytosolic pathway even provided the major fraction of proteinogenic alanine.
Goodness of fit and statistical flux evaluation
Statistical evaluation of metabolic fluxes of Saccharomyces cerevisiae cultured in chemostat under aerobic, glucose-limited conditions at μ = 0.15 h-1, μ = 0.30 h-1, and μ = 0.40 h -1.
Interval for 90 % Confidencea (μ = 0.15 h-1)
Interval for 90 % Confidence (μ = 0.30 h-1)
Interval for 90 % Confidence (μ = 0.40 h-1)
glucose 6-phosphate isomerase
fructose 1,6-bisphosphate aldolase
glyceraldehyde 3-phosphate dehydrogenase
glucose 6-phosphate dehydrogenase
acetyl CoA synthase
intercompartmental pyruvate transport
intercompartmental oxaloacetate transport
intercompartmental acetyl CoA transport
overall intercompartmental transport
cytosolic alanine synthesis
mitochondrial alanine synthesis
glycine synthesis via serine
glycine synthesis via threonine
NADPH supply by PPP
NADPH demand for anabolism
Flux Reversibility b
glucose 6-phosphate isomerase
intercompartmental oxaloacetate transport
intercompartmental acetyl CoA transport
In the present work comparative 13C metabolic flux analysis of S. cerevisiae at different defined physiological states revealed that the transition from oxidative to fermentative utilization of glucose is reflected by substantial flux changes throughout the whole central carbon metabolism. The different physiological conditions, i. e. purely oxidative, mixed respiro-fermentative and mainly fermentative growth were established by variation of the dilution rate in chemostat culture. Hereby, the extent of the fermentation could be precisely adjusted and run into metabolic and isotopic steady-state.
We observed the previously described transition from respiration to fermentation as indicated by the redirection of flux from the TCA cycle towards the fermentation pathways . It becomes, however, clear from the present study, that the regulatory changes linked to the metabolic transition were not restricted to these reactions, but affected a number of additional pathways.
(ii) Pyruvate decarboxylase, the key enzyme of fermentative metabolism, was found to already operate at a high activity under conditions in which alcoholic fermentation was absent (Figure 3). The substantial amount of acetaldehyde formed under these conditions was completely converted into cytosolic acetyl CoA which is either used for anabolism or transported into the mitochondrion. These findings disprove the common perception that only a small fraction of pyruvate is channeled through the fermentative by-pass at low glycolytic flux , but rather support previous speculations on fluxes around the pyruvate node linked to the Crabtree effect in S. cerevisiae . Based on enzyme profiles, substrate affinities and intracellular pyruvate level studied in chemostat cultivation of S. cerevisiae at varied dilution rate it was previously supposed that pyruvate decarboxylase might be active even during purely oxidative metabolism leading to the formation of cytosolic acetyl CoA and its transport into the mitochondrion. The increased pyruvate level observed during fermentative growth  could also be an explanation for the observed flux redirection from mitochondrial to cytosolic alanine biosynthesis.
(iii) We found evidence for substantial in vivo activity of malic enzyme, as was previously reported for S. cerevisiae [29, 35]. Additionally we could show a strong flux increase for malic enzyme, when the cells switched from pure oxidation to fermentative metabolism. The flux through malic enzyme increased almost linearly with increasing growth rate (Figure 4C). Although the present work and previous studies differ, concerning e.g. the investigated strain, the pH value or the nutrient status, the flux through malic enzyme is generally increased at high growth rate. As exception only a minor flux of 7 % was observed for malic enzyme in a batch culture of S. cerevisiae grown on glucose . This might arise from the above mentioned differences in the experimental setup or the generally high uncertainty for the quantification of this flux parameter (Table 5). The exact physiological role of malic enzyme in S. cerevisiae so far remained quite intriguing . Also this study does not really provide a satisfying insight into the function of malic enzyme. What at least can be stated is that the flux through malic enzyme seems to be related to the flux through the cytosolic pyruvate carboxylase and the oxaloacetate transporter. One might conclude that the increased activity of malic enzyme results indirectly from the flux redirection at the cytosolic pyruvate node.
Macromolecular composition of Saccharomyces cerevisiae in glucose-limited chemostat culture at different dilution rates. The data given in g (g cell dry mass)-1 are calculated from literature data [27, 47-49].
D = μ = 0.15 h-1
D = μ = 0.30 h-1
D = μ = 0.40 h-1
During purely oxidative growth the PPP alone can account for the total anabolic NADPH demand. Under these conditions an additional NADPH supply by other reactions seems not necessary. Because no intercompartmental transport system for NADPH has been described for S. cerevisiae, it is likely that also mitochondrial enzymes are involved in the supply of NADPH. A potential candidate is mitochondrial NADPH specific isocitrate dehydrogenase . This enzyme can, however, account only for a certain fraction of the total flux through the TCA cycle. An exclusive activity of NADPH specific isocitrate dehydrogenase can be excluded. Assuming this the total amount of NADPH supplied would be almost twice as high as the anabolic demand. Thus we conclude that to large extent mitochondrial NADH specific isoenzymes of isocitrate dehydrogenase contribute to the TCA cycle flux during oxidative growth of S. cerevisiae.
Under predominantly fermentative utilization of glucose only about 60 % of the totally required NADPH was provided by the PPP. This is an indication for an additional cytosolic NADPH source required during fermentative metabolism in S. cerevisiae. S. cerevisiae possesses several isoenzymes for acetaldehyde dehydrogenase with different specificity for NADH and NADPH . Possibly the relative contribution of the different isoenzymes changes with the on-set of fermentation, so that instead of mainly NADH under oxidative growth, also NADPH is formed. Recently it was found that especially the NADPH dependent acetaldehyde dehydrogenase isoforms are involved in anaerobic fermentation of S. cerevisiae . The increased NADPH formation by acetaldehyde dehydrogenase would probably lead to an increased level of intracellular NADPH, known to inhibit the PPP enzymes glucose 6-phosphate dehydrogenase and 6-phosphogluconate dehydrogenase . The reduction of the PPP flux might therefore not only be caused by the reduced anabolic demand, but also by the activation of alternative cytosolic pathways for NADPH supply.
Summarizing, the regulatory changes linked to the metabolic transition affect a number of pathways throughout the whole central metabolism of S. cerevisiae. It is known that yeast undergoes various changes involving e. g. change of enzyme levels, tolerance to stress, or morphology, when the metabolism switches from respirative to fermentative growth. These changes are controlled complex regulatory systems of transcriptional control as well as post-transcriptional control . One of the important primary signals for the regulation of yeast metabolism under different nutrient conditions is the concentration of glucose . As shown the glucose concentration in the medium indeed increased with increasing growth rate (Figure 2). The on-set of the glucose repression system was probably the major signal that triggered the observed changes in the intracellular carbon fluxes. This includes the observed decrease of flux through the TCA cycle with increasing growth rate, which probably results from direct repression of TCA cycle genes on the transcriptional level by the glucose repression system . Similarly the strong increase of the specific glucose uptake rate and the glycolytic flux is probably a direct result of transcriptional induction of the corresponding genes . Recent studies on fluxes and transcriptional levels revealed that a number of intracellular pathways in S. cerevisiae is probably regulated on the post-transcriptional level . Metabolic flux analysis alone on itself as performed in the present study cannot distinguish between flux changes directly controlled or indirectly affected e.g. by regulation of interconnected reactions. However, it appears as a valuable tool to quantitatively assess metabolic changes in great detail and to provide important data leading to a deeper understanding of the metabolism of S. cerevisiae.
Organism and cultivation
S. cerevisiae ATCC 32167 was purchased from the American Type Strain and Culture Collection (Manassas, USA). The mineral medium used for cultivation contained 2 g/L glucose, 0.5 g/L (NH4)2HPO4, 1.0 g/L (NH4)2SO4, 0.05 g/L MgSO4 ·7 H2O, 0.025 g/L citric acid, 0.5 g/L KCl, 0.03 g/L CaCl2·2 H2O, 3 mg/L FeCl3·6 H2O, 2.1 mg/L MnSO4·H2O, 1.8 mg/L ZnSO4·7 H2O, 0.5 mg/L CuSO4·5 H2O, 60.3 mg/L myo-inositol, 30 mg/L Ca-panthotenate, 6 mg/L thiamin·HCl, 1.5 mg/L pyridoxine·HCl, 0.03 mg/L biotin, and 50 mmol/L phosphate buffer (pH 6.2). All chemicals were of analytical grade and purchased from Fluka (Buchs, Switzerland), Merck (Darmstadt, Germany), or Sigma (St. Louis, USA). In tracer studies normal glucose was replaced by an equal molar concentration of 99% [1-13C] glucose (Campro, Veenendal, Netherlands). Cultivations were performed in a continuously operated bioreactor (Meredos, Bovenden, Germany) with a culture volume of 100 ml at 30°C and 500 rpm. The aeration rate was kept at 100 mL/min by a mass flow controller (WMR Compact 4, Brooks Instruments, Veenendal, Netherlands). Composition of inlet and exhaust gas was determined on-line by mass spectrometry as described previously . For flux quantification the culture was operated with the tracer substrate for five residence times, including on-line verification by a constant CO2 concentration in the exhaust gas, so that metabolic and isotopic steady-state could be assumed. Samples were then taken continuously from the outlet of the reactor and harvested at 4°C. Supernatant, obtained by centrifugation (16000 g, 5 min, Biofuge Pico, Heraeus, Hanau, Germany), was used for analysis of extracellular metabolites. The cell pellet was used for 13C labeling analysis by GC-MS.
Analysis of biomass and extracellular metabolites
Optical density (OD660) was measured at 660 nm (Novaspec II, Pharmacia, Freiburg, Germany). Cell dry mass (CDM) was determined gravimetrically after two-fold washing, centrifugation (10 min, 4°C, 3940 g; Labofuge 400 R, Heraeus, Hanau, Germany), and drying at 80°C until constant weight. A linear relationship of OD660 = 0.52 [g CDM /L] was obtained. Enzymatic test-kits were used for quantification of glucose, glycerol, acetate (Boehringer Mannheim, Mannheim, Germany) and ethanol (Sigma Diagnostics, St. Louis, USA) in the supernatant. Concentrations of 2-oxoglutarate, pyruvate, succinate, and fumarate in the supernatant were analyzed by HPLC . Amino acid composition of the cell protein of S. cerevisiae was quantified by HPLC  after hydrolysis with 6 M HCl for 24 h at 105°C. The mean relative error of the stoichiometric measurements, i.e. the quantification of the yield coefficients, was 3.7 % (biomass yield), 4.0 % (ethanol yield), 9.3 % (acetate yield) and 11.3 % (glycerol yield).
GC-MS analysis of proteinogenic amino acids
Measurement of amino acid labeling patterns from cell hydrolysate was carried out by GC-MS in selective ion monitoring mode . For a number of ion clusters all mass isotopomer fractions from the non-labeled (x0) to the fully 13C labeled (xn) variant could be measured with good signal intensity and accuracy (Table 4). Accordingly, a comprehensive data set was available for calculation of the metabolic fluxes. The relative measurement error for a mass isotopomer fraction from the four replicates at each dilution rate was typically below 1 %. It must be mentioned that some amino acids could not be considered for the flux calculation. These were tryptophan, methionine, cysteine and histidine, which did not yield suitable GC/MS signals, proline, which exhibited isobaric overlay, and leucine and isoleucine with ambiguous fragmentation pathways due to similarity of the amino acid side chain and the derivatization agent.
Metabolic network of S. cerevisiae
Cytosolic Metabolite Pools
Glucose 6-phosphate: ν1 - ν2 - ν3 + ν4 - ν5 = 0 (1)
Fructose 6-phosphate: ν3 - ν4 - ν6 + ν8 - ν9 + ν10 - ν11 = 0 (2)
Pentose phosphate: ν2 - ν7 - ν8 + ν9 - 2ν12 + 2ν13 = 0 (3)
Erythrose 4-phosphate: - ν8 + ν9 + ν10 - ν11 - ν14 = 0 (4)
Sedoheptulose 7-phosphate: ν12 - ν13 - ν10 + ν11 - ν5 = 0 (5)
Glyceraldehyde 3-phosphate: ν6 - ν10 + ν11 + ν8 - ν9 + ν12 - ν13 + ν16 - ν17 - ν18 = 0 (6)
Dihydroxyacetone-phosphate: ν6 - ν15 - ν16 = 0 (7)
3-Phosphoglycerate: ν17 - ν19 - ν20 - ν24 = 0 (8)
Serine: ν20 - ν21 - ν22 = 0 (9)
Glycine: ν22 - ν23 + ν29 = 0 (10)
Threonine: ν28 - ν29 - ν30 = 0 (11)
Phosphoenolpyruvate: ν24 - ν25 - ν26 = 0 (12)
Pyruvatecyt: ν26 - ν27 - ν32 - ν33 - ν34 = 0 (13)
Acetaldehyde: ν32 - ν37 - ν38 = 0 (14)
Acetate: ν38 - ν39 - ν40 = 0 (15)
Acetyl CoAcyt: ν40 - ν41 - ν47 + ν48 = 0 (16)
Alaninecyt: ν33 - ν42 = 0 (17)
Oxaloacetatecyt: ν27 - ν28 - ν31 - ν35 + ν36 = 0 (18)
Mitochondrial Metabolite Pools
Pyruvatemit: ν34 - ν43 - ν44 + ν50 - ν51 = 0 (19)
Alaninemit: ν43 - ν45 = 0 (20)
Acetyl CoAmit: ν44 - ν46 + ν47 - ν48 - ν49 = 0 (21)
2-Oxoglutarate: ν49 - ν52 - ν53 = 0 (22)
Succinate: ν53 - ν54 + ν55 = 0 (23)
Oxaloacetate/Malatemit: ν35 - ν36 - ν49 - ν50 + ν54 - ν55 = 0 (24)
For each examined physiological state a different, growth rate dependent, cellular composition of S. cerevisiae was considered (Table 1). The macromolecular composition of a yeast cell in relation to the growth rate was calculated from literature data [47–49]. The composition of each macromolecule, however, was assumed to be identical for the different growth conditions . The content and composition of lipids, nucleic acids, and carbohydrates was taken from the literature [48, 49]. The amino acid composition of the cell protein was experimentally determined in this work. Based on these data and the stoichiometry of the anabolic pathways in yeast the demand for the different precursor metabolites could be calculated (Table 2) and used as measured fluxes in the flux estimation routine as described previously .
Mathematical modeling and flux analysis
Flux calculations were carried out with Matlab 6.1 and Simulink 3.0 (Mathworks Inc., Nattick, USA) combining metabolite balancing and isotopomer modeling. The performed approach utilized metabolite balancing (see mass balances given above) during each optimization step considering stoichiometric data on anabolic demand for biomass precursors (Table 2) and product secretion (Table 3). The set of fluxes that gave minimum deviation between experimental and simulated mass isotopomer fractions was taken as best estimate for the intracellular flux distribution. As error criterion a weighted sum of least squares was used . Since the non-linear structure of isotopomer models may potentially lead to local minima, multiple parameter initializations were used to assure that the obtained flux distributions represented a global optimum. Statistical analysis of the obtained flux parameters was carried out by Monte-Carlo analysis, whereby random, normal-distributed noise was added to the measurement data [41, 50].
We acknowledge the advice of Michael Hans in the performed tracer studies.
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