SEARCH

SEARCH BY CITATION

Keywords:

  • 13C labeling;
  • metabolic flux analysis;
  • pentose phosphate pathway;
  • transaldolase;
  • transketolase

Abstract

  1. Top of page
  2. Abstract
  3. Theory
  4. Results and Discussion
  5. Conclusion
  6. Experimental procedures
  7. Acknowledgements
  8. References
  9. Appendix

The currently applied reaction structure in stoichiometric flux balance models for the nonoxidative branch of the pentose phosphate pathway is not in accordance with the established ping-pong kinetic mechanism of the enzymes transketolase (EC 2.2.1.1) and transaldolase (EC 2.2.1.2). Based upon the ping-pong mechanism, the traditional reactions of the nonoxidative branch of the pentose phosphate pathway are replaced by metabolite specific, reversible, glycolaldehyde moiety (C2) and dihydroxyacetone moiety (C3) fragments producing and consuming half-reactions. It is shown that a stoichiometric model based upon these half-reactions is fundamentally different from the currently applied stoichiometric models with respect to the number of independent C2 and C3 fragment pools in the pentose phosphate pathway and can lead to different label distributions for 13C-tracer experiments. To investigate the actual impact of the new reaction structure on the estimated flux patterns within a cell, mass isotopomer measurements from a previously published 13C-based metabolic flux analysis of Saccharomyces cerevisiae were used. Different flux patterns were found. From a genetic point of view, it is well known that several micro-organisms, including Escherichia coli and S. cerevisiae, contain multiple genes encoding isoenzymes of transketolase and transaldolase. However, the extent to which these gene products are also actively expressed remains unknown. It is shown that the newly proposed stoichiometric model allows study of the effect of isoenzymes on the 13C-label distribution in the nonoxidative branch of the pentose phosphate pathway by extending the half-reaction based stoichiometric model with two distinct transketolase enzymes instead of one. Results show that the inclusion of isoenzymes affects the ensuing flux estimates.

Abbreviations
C2

glycolaldehyde moiety

C3

dihydroxyacetone moiety

e4p

erythrose 4-phosphate

f6p

fructose 6-phosphate

fbp

fructose 1,6-bisphosphate

g1p

glucose 1-phosphate

g6p

glucose 6-phosphate

g3p

glyceraldehyde 3-phosphate

MFA

metabolic flux analysis

p5p

pentose pool consisting of ribulose 5-phosphate, ribose 5-phosphate and xylulose 5-phosphate

PPP

pentose phosphate pathway

r5p

ribose 5-phosphate

s7p

sedoheptulose 7-phosphate

SSres

sum of squared residuals

S2res

estimated error variance

TA

transaldolase

TK

transketolase

TPP

thiamine pyrophosphate

x5p

xylulose 5-phosphate

During the past decade, 13C-labeling based metabolic flux analysis (MFA) has increasingly been used to understand the effect of genetic alterations [1,2], changes in external conditions [3,4] and different nutritional regimes [5,6] on the metabolism of micro-organisms. 13C-labeling based MFA relies on the feeding of 13C-labeled substrate to a biological system, allowing the labeled carbon atoms to distribute over the metabolic network, and subsequently measuring the 13C-label distributions of intracellular and/or secreted compounds by means of NMR spectroscopy or MS. The flux patterns within a metabolic network model can be calculated by iteratively fitting simulated 13C-label distributions for a chosen set of metabolic fluxes to the measured 13C-label distributions [7]. Apart from MFA, the information richness of 13C-labeling data also permits verification of the topology of metabolic network models. Furthermore, shortcomings in the stoichiometry of the metabolic network can be localized and alterations to the model can be hypothesized and validated [5,8,9].

A part of the metabolic network that has received relatively little attention from the MFA community with respect to model validation is the pentose phosphate pathway (PPP). This is rather surprising because the PPP plays several key roles in the cell metabolism. Apart from supplying the cell with precursors for amino acid and nucleotide biosynthesis, it also plays a crucial role in maintaining the cytosolic NADP+/NADPH balance. In order to maintain this balance, the flux through the oxidative branch of the PPP is usually much larger than the drain on PPP metabolites for the biosynthesis of building blocks, resulting in a significant recycling and redistribution of the carbon atoms via the nonoxidative branch. Incorrectly mapped carbon atom distributions, owing to, for example, an incomplete or incorrect metabolic model, can lead to erroneously predicted label distributions (and consequently flux estimates) for 13C-tracer experiments.

Practically all stoichiometric flux balance models of the nonoxidative branch of the PPP consist of three reversible reactions, namely two transketolase (TK) (EC 2.2.1.1) catalyzed reactions (r.1 and r.2) and one transaldolase (TA) (EC 2.2.1.2) catalyzed reaction (r.3) [6,10–14]:

  • image((r.1),)
  • image((r.2),)
  • image((r.3). )

van Winden et al. [15] argued that the nonoxidative branch of the PPP consists of more reactions than the three conventional reactions shown above. Supporting evidence from the literature was presented, indicating that six additional reactions can take place [16–19]. Furthermore, van Winden et al. [5] demonstrated that the incorporation of these reactions in the metabolic network model of Penicillium chrysogenum significantly increased the goodness-of-fit to measured 13C-label distribution data and also resulted in a changed flux distribution. The six additional reactions consist of five stoichiometric neutral reactions, two of which are catalyzed by TA (r.8 and r.9) and three of which are catalyzed by TK (r.5, r.6 and r.7), and one additional reversible TK-catalyzed reaction (r.4). Although the stoichiometric neutral reactions have no effect on the mass balances set up over the system, they do influence the labeling pattern of the metabolite pools and thus need to be incorporated into the metabolic network for 13C-based flux estimations [18,20]. The structure of reactions r.1–9 is such that a carbon fragment is transferred from one substrate to another, yielding two products. From hereon any nonoxidative PPP reactions abiding by this structure are denoted as traditional reactions:

  • image((r.4),)
  • image((r.5),)
  • image((r.6),)
  • image((r.7),)
  • image((r.8),)
  • image((r.9). )

In this article, results of genetic and kinetic studies into the nonoxidative branch of the PPP are analyzed and used to obtain a more realistic stoichiometric flux balance model. Based upon the kinetic mechanism of TA and TK, an alternative reaction structure for tracing the distribution of 13C through the nonoxidative branch of the PPP is proposed. It is shown that a stoichiometric flux balance model, based upon this new reaction structure, is fundamentally different from the current models with respect to 13C-label distribution and, consequently, can yield different flux patterns. Moreover, the new reaction structure facilitates the estimation of the metabolic fluxes from the 13C-labeling data as the result of a smaller number of parameters. Following genetic evidence, the presence of isoenzymes for TK and TA is incorporated to further refine the stoichiometric model. The effect of these model alterations on the estimated 13C-based flux patterns is examined using a recently published MFA for Saccharomyces cerevisiae based upon mass isotopomer measurements of 13C-labeled primary metabolites [21].

Theory

  1. Top of page
  2. Abstract
  3. Theory
  4. Results and Discussion
  5. Conclusion
  6. Experimental procedures
  7. Acknowledgements
  8. References
  9. Appendix

Kinetic mechanism of the nonoxidative branch of the PPP

The enzymes TK and TA catalyze the transfer of two- and three-carbon fragments from a ketose donor to an aldose acceptor. TK performs this glycolaldehyde (C2) transfer using a tightly bound thiamine pyrophosphate (TPP) as cofactor. The second carbon atom of the thiazole ring of TPP readily ionizes to give a carbanion, which can react with the carbonyl group of the ketose substrates: xylulose 5-phosphate (x5p), fructose 6-phosphate (f6p) or sedoheptulose 7-phosphate (s7p). The phosphorylated part of the ketose substrate splits off, leaving a negatively charged C2 attached to TPP. Resonance forms keep the glycolaldehyde unit attached to TPP until a suitable acceptor has been found in the form of ribose 5-phosphate (r5p), erythrose 4-phosphate (e4p) or glyceraldehyde 3-phosphate (g3p) [22]. In contrast to TK, TA does not contain a prosthetic group. Instead, a Schiff base is formed between the carbonyl group of the ketose substrate (f6p, s7p) and the ε-amino group of a lysine residue of the active site of the enzyme, leading to the formation of either g3p or e4p while leaving behind the bound dihydroxyacetone (C3). The nitrogen atom of the Schiff base (similar to the nitrogen atom in the thiazole ring of TK) stabilizes the dihydroxyacetone unit using resonance forms until a suitable aldose (g3p, e4p) acceptor is bound [22].

The kinetic mechanism employed by both enzymes has been characterized as a reversible ping-pong mechanism [23–25]. Bi-bi reactions use this mechanism to shuttle molecule fragments from one compound to another, epitomized by the fact that the first substrate is released from the holoenzyme before the second substrate binds. For the enzymes TK and TA this implies that the cleaved phosphorylated fragment of the ketose substrate is first detached from the enzyme before the stabilized carbon fragment (glycoaldehyde for TK and dihydroxyacetone for TA) is donated to a suitable aldose acceptor. This mechanism is in conflict with the traditional reactions. The structure of the traditional reactions is such that a C2 or C3 fragment is transferred from one specific donor to one specific acceptor molecule. This reaction structure is in agreement with a so-called ordered sequential kinetic mechanism. The difference between a sequential and a ping-pong kinetic mechanism is illustrated in Fig. 1. Whereas the correct ping-pong mechanism for TK and TA was adopted by several researchers in the 1990s to construct detailed kinetic models [20,26–28], this has been largely overlooked by the metabolic engineering community.

image

Figure 1. Schematic representation of the two kinetic mechanisms used for modeling the transketolase- and transaldolase-catalyzed reactions of the pentose phosphate pathway: (I) ping-pong mechanism and (II) (ordered) sequential mechanism. Depicted are the ketose substrate (K), the aldose acceptor (A), the transferred carbon-fragment (C), and the enzyme/cofactor complex (E).

Download figure to PowerPoint

In accordance with the ping-pong mechanism employed by TA and TK, the traditional reactions of the nonoxidative branch of the PPP can be represented as metabolite specific, reversible C2 and C3 fragments producing and consuming half-reactions for each of the metabolites s7p, f6p, x5p, r5p, e4p and g3p (r.10–14). Note that the C2 and C3 fragments remain bound to the holoenzyme (E) until they are transferred to an acceptor:

  • image((r.10),)
  • image((r.11),)
  • image((r.12),)
  • image((r.13),)
  • image((r.14). )

Using the above half-reactions, a C2 fragment-producing reaction (e.g. x5p[RIGHTWARDS ARROW]g3p + E − C2) can be coupled to a C2 fragment-consuming reaction (e.g. e4p + E − C2[RIGHTWARDS ARROW]f6p), leading to one of the traditional reactions (in this case r.2: x5p +e4p [RIGHTWARDS ARROW]f6p + g3p). In total, 13 different combinations of half-reactions are possible: the three C2 fragment-donating half-reactions can be combined with three C2 fragment-accepting half-reactions, and the two C3 fragment-donating half-reactions can be combined with the two C3 fragment-accepting half-reactions, leading to the three conventional reactions (r.1–3) and the six additional reactions (r.4–9).

Interestingly, the half-reactions r.10–14 can be used to show that a stoichiometric model for the nonoxidative branch of the PPP, based upon traditional reactions r.1–3, is, in essence, incomplete. In order to perform these three reactions in forward and backward directions, all five proposed half-reactions (r.10–14) are needed. The reversibility of the traditional reactions was argued by Follstad et al. [29], a claim supported by most textbooks [22,30]. However, recombination of the half-reactions into their traditional counterparts leads to nine reversible reactions (r.1–9), as shown in the previous paragraph. Therefore, given the reversibility of the TK- and TA-catalyzed reactions, and their demonstrated ping-pong mechanism, one has to conclude that in addition to traditional reactions r.1–3, one should also incorporate the other six traditional reactions (r.4–9) when constructing a stoichiometric model for the nonoxidative branch of the PPP.

Traditional vs. half-reactions: implications for 13C-labeling

From a labeling point of view, the main difference between modeling the stoichiometry of the nonoxidative branch of the PPP using either traditional reactions or half-reactions, is the number of independent C2 and C3 fragment pools that each approach generates. The traditional reactions will lead to separate C2 and C3 fragment pools for each of the nine possible reactions (r.1–9), while the half-reactions by definition lead to only one C2 and one C3 fragment pool, from which carbon fragments are retrieved and attached to any suitable acceptor (Fig. 2). As the number of nonoxidative PPP reactions increases, application of the traditional reactions leads to an increase in the number of distinct C2 and C3 fragment pools. As a result of these segregated pools, the 13C labeling of the C2 and C3 fragments (and, consequently, the labeling of the metabolites formed from these) can differ from the 13C labeling of the single C2 and C3 fragment pools generated by the half-reactions.

image

Figure 2. Number of glycolaldehyde (C2) and dihydroxyacetone (C3) fragment pools in the nonoxidative branch of the pentose phosphate pathway based upon a stoichiometric model constructed from traditional reactions (I) and half-reactions (II). The number of C2 and C3 fragment-producing reactions when applying the traditional reactions is denoted by n and m, respectively.

Download figure to PowerPoint

Genetic organization of the nonoxidative branch of the PPP

In recent years, the genes encoding the enzymes of the nonoxidative branch of the PPP have been sequenced and cloned for many micro-organisms. It was found that several micro-organisms, including Escherichia coli and S. cerevisiae, contain two TK genes, named tkl1 and tkl2 in S. cerevisiae[31,32] and tktA and tktB in E. coli[33]. The combined fact that several micro-organisms possess two TK genes and that most stoichiometric flux balance models of the nonoxidative branch of the PPP contain only two TK-catalyzed reactions (r.1–2), has led to the common misunderstanding that each reaction is catalyzed by a separate TK (either tkl1 or tkl2). In several publications it is assumed that the TK encoded by tkl1/tktA specifically catalyzes the reversible reaction r.1, while the TK encoded by tkl2/tktB catalyzes the reversible reaction r.2 [11,12,34–37]. In reality, the TK gene products in S. cerevisiae and E. coli are isoenzymes, each of which is capable of nonspecifically catalyzing both reactions r.1 and r.2 in the nonoxidative branch of the PPP [38–42]. As expected, the two isoenzymes of S. cerevisiae and E. coli show a strong resemblance with respect to amino acid residues; homology was measured to be 71%[32] and 74%[33], respectively.

The presence of isoenzymes for TA has been studied to a lesser extent. Microorganisms containing multiple genes with TA activity do exist, an example being E. coli, which contains two isoenzymes for TA (talA/talB) [38,40]. The talB gene of E. coli has been shown to encode a functional TA [43], while the functionality of the talA gene has not been shown, to date. S. cerevisiae contains one verified TA gene, named tal1[44]. Recently, a hypothetical ORF for a possible second TA was found [38,41].

Using this genetic information the stoichiometric model for the nonoxidative branch of the PPP can be further refined. Although homology between isoenzymes is normally quite high, differences in substrate affinity are common [45]. If evidence for isoenzymes of TK and/or TA exists, one can opt for a model with two sets of half-reactions, in which each set of half-reactions models the transfer of the C2 or C3 fragments for one isoenzyme. As a result of this modification, a second set of C2 and C3 fragment pools is created in the nonoxidative branch of the PPP. Note that genetic evidence alone is not sufficient proof for the actual expression of isoenzymes; this expression should be verified under relevant culture conditions. The literature shows that in S. cerevisiae, the activity of the tkl2-encoded TK appears to be very low when growing cells in batch on a synthetic mineral salts medium with glucose as the carbon source [32]. Furthermore, deletion mutants of tkl2 showed no changed phenotype, while deletion mutants of tkl1 were found to have a slower growth rate [46]. A similar trend was found for the isoenzymes of E. coli, where the tktA-encoded TK and talB-encoded TA accounted for the majority of the cellular activity [47–49].

Model construction and analysis

Using the five half-reactions (r.10–14), a new stoichiometric model for the combined glycolysis and PPP was constructed, as shown in Fig. 3II (from hereon referred to as the half-reaction model). Note that this model does not yet take into account the presence of isoenzymes for TK and TA, as it only contains a single C2 and C3 fragment pool. As a comparison, Fig. 3I shows the equivalent stoichiometric model based upon the traditional reactions (henceforth called the traditional model). Note that this model contains both the conventional nonoxidative PPP reactions (Fig. 3IA) as well as the six additional reactions proposed by van Winden et al. [15] (Fig. 3IB). The traditional model has previously been used to fit the metabolic fluxes of P. chrysogenum and S. cerevisiae[5,21].

image

Figure 3. Traditional (I) and half-reaction (II) stoichiometric flux balance models for the upper glycolysis and PPP. The nonoxidative pentose phosphate pathway reactions of the traditional model are split up into the three conventional reactions (r.1–3) (IA) and the six additional reactions (r.4–9) (IB). Closed arrows denote the direction of the forward flux in the case of reversible reactions.

Download figure to PowerPoint

The half-reaction model of Fig. 3II covers the complete range of possible reactions, yet it significantly reduces the number of free fluxes that have to be estimated from the 13C-labeling data during the flux fitting procedure. The model contains 12 reactions (n1–n12) and eight reversibilities, which are constrained by 10 mass balances over the intracellular metabolites in a (pseudo) steady state. When normalizing the rates relative to the uptake rate of glucose, nine free fluxes remain to be estimated from the 13C-labeling data. The corresponding traditional model (Fig. 3I) contains 16 reactions (v1–v16) and seven reversibilities. Under (pseudo) steady-state conditions, eight reaction rates are fixed by mass balances over the intracellular metabolites. Normalization of the fluxes to the glucose uptake rate thus leaves 14 free fluxes.

The half-reaction model can be extended with a second set of half-reactions to account for the possible presence of isoenzymes for TK (r.10–13) and/or TA (r.14–15). This extension will increase the number of free fluxes that have to be estimated from the 13C-labeling data. In the case of two actively expressed genes for TK, this will result in five additional free fluxes because the six additional half-reactions are constrained by one extra mass balance over the second C2 fragment pool. As a result, the total number of free fluxes (14) equals the number of free fluxes in the traditional model.

Results and Discussion

  1. Top of page
  2. Abstract
  3. Theory
  4. Results and Discussion
  5. Conclusion
  6. Experimental procedures
  7. Acknowledgements
  8. References
  9. Appendix

Traditional vs. half-reaction model: three theoretical cases

To illustrate the difference in 13C-labeling distribution when using either traditional reactions or half-reactions to model the nonoxidative branch of the PPP, three simplified metabolic networks were formulated (cases 1–3). Note that the three networks are oversimplified and are solely used to clarify the difference in 13C-label distribution that can occur between the two different modeling approaches.

For case 1 consider the traditional model of Fig. 3, but now containing only the conventional nonoxidative PPP reactions (Fig. 3IA). The reversibilities of the three bidirectional nonoxidative PPP reactions and the three bidireactional glycolytic reactions are set at zero, such that the PPP overall converts three p5p molecules (i.e. a pentose pool consisting of ribulose 5-phosphate, ribose 5-phosphate and xylulose 5-phosphate) into two f6p molecules and one g3p molecule. Consequently, only the forward reactions of the PPP (v8f, v9f, v14f) and the glycolysis (v2f, v3f, v5f) are active. Analogous to the traditional model, only the forward glycolytic reactions are included in the half-reaction model (n5f, n3f and n2f). Using the relations in Appendix I, the active nonoxidative PPP reaction rates in the traditional model are converted to the corresponding rates in the half-reaction model, resulting in substantial throughput for half-reactions n8f, n9b, n10b, n11b and n12f. Investigation of the acceptor and the donor of the C2 fragment in both models shows that the traditional model contains two C2 fragment pools created by reactions v8f and v9f, while the half-reaction model by definition contains one single C2 fragment pool that is solely formed by reaction n8f(Fig. 4). However, both C2 fragment pools in the traditional model are formed by the cleavage of p5p and can thus be lumped into a single pool, resulting in identical C2 fragment pools for both modeling approaches. Examination of the origin of the C3 fragment pools shows that both models contain only one C3 fragment-producing reaction, both with s7p as the donor (v14f, n12f). So, in essence, both models described in this case contain one C2 and one C3 fragment pool. As a result, the redistribution of 13C atoms in the PPP is identical for both models.

image

Figure 4. Route traversed by the glycolaldehyde (C2) fragments of the transketolase-catalyzed reactions present in the simplified traditional model (I) and half-reaction model (II) of cases 1 and 2 (see the main text). The colored spheres represent the carbon atoms from which the C2 fragment is constructed. A different 13C labeling of the C2 fragment is denoted by a different color. Consequently, the 13C labeling of the top two-carbon fragments of the p5p and f6p depicted in this figure is different.

Download figure to PowerPoint

For case 2 consider the same traditional model as used in case 1, supplemented with the stoichiometric neutral exchange reaction for e4p and f6p (v12 in Fig. 3IB). In the half-reaction model this means an increase in n9f and n9b (see Appendix I). As a result of this additional reaction, C2 fragments are now also produced from f6p, thus increasing the number of C2 fragment pools in the traditional model to three (Fig. 4). The absence of bidirectional reactions makes it impossible for the three C2 fragment pools, originating from either p5p or f6p, to efface their labeling differences. A different labeling of f6p (in comparison to p5p) therefore by necessity leads to two unique C2 fragment pools in the traditional model. The half-reaction model inherently contains one single C2 fragment pool that comprises all distinct C2 fragment pools of the traditional model, as shown in Fig. 4. From this single pool a C2 fragment is randomly retrieved and attached to any suitable acceptor. Consequently, the top two carbon atoms of s7p synthesized in the half-reaction model can originate from either f6p or p5p, while in the traditional model they can only originate from p5p. In a 13C-labeling experiment with 100%13C1 glucose this will result in the synthesis of unlabeled and 13C1-labeled s7p for the half-reaction model, in contrast to only unlabeled s7p for the traditional model.

For case 3 consider the same traditional and half-reaction model as used in case 2, but now with all bidirectional reactions set at maximum reversibility (99.9%). Owing to this reversibility assumption, the number of C2 fragment-producing reactions in the traditional model increases from two to four (v8f, v8b, v9f and v9b). However, the high reversibility of the bidirectional reactions also ensures that the label distributions of the C2 fragment pools (and also the C3 fragment pools) are fully exchanged, effacing the differences in labeling pattern amongst the separate pools. As a result, no difference in isotopomer distribution is observed between the two models under conditions of high reversibility.

The three cases discussed above show that the difference in 13C-label distribution amongst the two modeling approaches becomes more pronounced as the number of C2 and C3 fragment-producing reactions increases, while high reaction reversibilities diminish this difference. In reality the nonoxidative branch of the PPP contains multiple C2 and C3 fragment-producing reactions, thereby in essence creating different 13C-label distributions. As shown in case 3, these differences can be alleviated by high reversibilities for the nonoxidative PPP reactions. Even though the reversibility of these reactions was argued by Follstad & Stephanopoulos[29], it remains questionable whether these reversibilities are high enough to efface the difference in 13C-label distribution created by the multiple C2 and C3 fragment-producing reactions.

Application of the half-reaction model: flux patterns in S. cerevisiae

To investigate the actual difference in estimated flux patterns when applying either the traditional model or the half-reaction model shown in Fig. 3, measured mass isotopomers of 13C-labeled primary metabolites [21] were used to refit the fluxes in the glycolysis and the PPP of S. cerevisiae CEN.PK113-7D. Similarly to the previously published fit, only measured mass isotopomer fractions larger than 0.03 were included. Figures 5I,II and Table 1 show the previously estimated flux patterns for the traditional model, as well as the newly estimated flux patterns using the half-reaction model. In order to facilitate the comparison of the two flux sets in Table 1, the flux estimates for the traditional model have been converted into their corresponding half-reaction rates using the equations given in Appendix I. The difference in flux pattern is evident, although, in general, not very large. As expected, the largest differences are found for the PPP split-ratio and the fluxes of the nonoxidative branch of the PPP.

image

Figure 5. Fitted fluxes for the traditional model (I), the half-reaction model (II) and the ‘double transketolase’ half-reaction model (III), based upon the mass isotopomer measurements of 13C-labeled primary metabolites as presented in van Winden et al. [21]. Fluxes are normalized for the glucose-uptake rate. Values outside parentheses denote the net fluxes, while values inside parentheses represent the exchange fluxes. Solid arrowheads denote the direction of the net flux.

Download figure to PowerPoint

Table 1.  Comparison of the flux estimates for the traditional and half-reaction models presented in Fig. 5I,II. The pentose phosphate pathway fluxes in the traditional model have been converted to their corresponding fluxes in the half-reaction model using the equations in Appendix I.
Reaction no.Fluxes in the half-reaction modelConverted fluxes in the traditional modelRelative change (%)
n11001000
n2 net26260
n2 exchange13410521
n3 net565011
n3 exchange> 1000> 1000
n465633
n5 net65633
n5 exchange22119413
n61211192
n7182436
n8 net91348
n8 exchange410> 100
n9 net−3−567
n9 exchange10155> 100
n10 net−6−838
n10 exchange1244898> 100
n11 net−6−838
n11 exchange25244
n12 net6838
n12 exchange000

The minimized covariance-weighted sum of squared residuals (SSres) in these fits was calculated to be 20.9 and 6.5 for the half-reaction and traditional model, respectively. The SSres is distributed according to a χ2(n-p) distribution, with n-p being the degrees of freedom equal to the number of independent data points (n = 26) minus the number of free parameters (P = 14 and 9 for the traditional and the half-reaction model, respectively). Given the probabilities P2(12) > 6.5] = 0.89 and P[χ2(17) > 20.9] = 0.23, it follows that within the 95% confidence interval both models give statistically acceptable flux estimates. Even though both models are statistically acceptable, it must be noted that the discrepancy between the measured and the fitted mass isotopomers (SSres) is higher for the half-reaction model. One possible explanation for the higher SSres in the half-reaction model is an overparameterization of the traditional model. In an overparameterized model, some parameters are actually used to fit measurement errors, thereby underestimating the true SSres[50]. To determine the extent of this overparameterization, the estimated error variance (inline image) criterion can be used:

  • image

This criterion minimizes the variance of the sum of squared residuals by dividing the SSres of a model by its degrees of freedom. As the traditional model contains more parameters than the half-reaction model, this will result in a smaller denominator for inline image, thus compensating for any possible overparameterization. Nevertheless, the traditional model gives an inline image of 0.54 compared to 1.23 for the half-reaction model, implying that the traditional model performs better from a statistical point of view.

A second explanation for the higher SSres found for the half-reaction model might be the presence of isoenzymes for TK. As stated above, the genome of S. cerevisiae contains two genes encoding a TK, which adds a second C2 fragment pool to the metabolic network model. To test whether the introduction of an isoenzyme for TK in the metabolic network model results in a better fit, the half-reaction model in Fig. 3 was expanded with a second set of TK half-reactions (r.10–12) and subsequently used to fit the measured mass isotopomer fractions of S. cerevisiae. Figure 5III shows the estimated reaction rates for the so-called ‘double TK’ half-reaction model. The SSres for this model was 6.5, meaning that this model also adequately fitted the measured mass isotopomer fractions {P2(12) > 6.5] = 0.89}. Interestingly, exactly the same values for the minimized SSres and the number of free parameters (14) were found for both the ‘double TK’ half-reaction and the traditional model, making it impossible to distinguish the two models using the inline image criterion. Table 2 shows that the flux estimates for both models were also very similar. The resemblance between the two models can be understood when one realizes that both models, unlike the half-reaction model, have the ability to create separate C2 fragment pools. Considering the reported finding that tkl1 encodes the majority of the TK activity in S. cerevisiae cells grown in synthetic mineral medium on glucose, it was not anticipated that the addition of a TK isoenzyme to the metabolic network model would result in an increased goodness-of-fit. It must be noted that the prevalence of the tkl1-encoded TK was measured under excess glucose conditions, while the 13C-labeling experiment was performed in a chemostat under glucose-limiting conditions.

Table 2.  Comparison of the flux estimates for the traditional and the ‘double transketolase’ (‘double TK’) half-reaction model presented in Fig. 5II,III. The two separate fluxes for the transketolase-catalyzed half-reactions in the ‘double TK’ half-reaction model have been summed to allow for comparison with the converted fluxes of the traditional model shown in Table 1.
Reaction no.Converted fluxes in the ‘double TK’ half-reaction modelConverted fluxes in the traditional modelRelative change (%)
n11001000
n2 net26260
n2 exchange1031052
n3 net50501
n3 exchange> 1000> 1000
n463630
n5 net63630
n5 exchange1991943
n61181190
n725242
n8 net13133
n8 exchange10100
n9 net−5−54
n9 exchange10015555
n10 net− 8−83
n10 exchange114898> 100
n11 net−8−83
n11 exchange24242
n12 net883
n12 exchange000

Conclusion

  1. Top of page
  2. Abstract
  3. Theory
  4. Results and Discussion
  5. Conclusion
  6. Experimental procedures
  7. Acknowledgements
  8. References
  9. Appendix

This study shows that a good understanding of enzyme genetics and kinetics is crucial for a correct 13C-label distribution prediction in stoichiometric flux balance models. When comparing two models of the nonoxidative branch of the PPP based, respectively, on the traditional reactions and the kinetically derived half-reactions, it was demonstrated that the main difference between the two reaction structures is the number of independent C2 and C3 fragment pools present in the stoichiometric model. Whereas the traditional reactions lead to multiple independent pools, the half-reactions result in only one C2 and one C3 fragment pool. This difference in C2 and C3 fragment pools influences the ensuing label distribution when conducting 13C-tracer experiments. An additional advantage of using half-reactions is the decreased number of free parameters that have to be estimated by fitting 13C-labeling data to the stoichiometric model.

Mass isotopomer measurements from a previously published study on S. cerevisiae were used to compare the traditional and half-reaction model depicted in Fig. 3, resulting in statistically acceptable fits for both models. Different flux patterns were found for the two models, but no major rerouting of metabolic fluxes was observed. The incorporation of genetic knowledge into the metabolic network model for the nonoxidative branch of the PPP introduced the possibility of modeling the presence of isoenzymes for TK and TA. Extending the half-reaction model from one to two autonomously functioning TK enzymes resulted in a doubling of the number of C2 fragment pools. The fitting of measurement data to a ‘double TK’ half-reaction model yielded flux estimates and an SSres that were similar to those of the traditional model. The similarity of the flux estimates indicates that the presence of isoenzymes reduces the difference in 13C-label distribution between the two models and impedes their discrimination. This shows that for S. cerevisiae more accurate measurement techniques are needed to discriminate between the different stoichiometric models for the nonoxidative branch of the PPP, in combination with genetic and biochemical evidence on the number of active TK and TA isoenzymes under the experimental conditions used. In spite of their practical similarity, clear differences between the traditional and half-reaction models were illustrated by means of three theoretical cases. Therefore, considering the established ping-pong mechanism of TK and TA, we recommend the use of the half-reaction model when modeling the label distribution in the nonoxidative PPP, bearing in mind that isoenzymes for TK and TA may exist.

Experimental procedures

  1. Top of page
  2. Abstract
  3. Theory
  4. Results and Discussion
  5. Conclusion
  6. Experimental procedures
  7. Acknowledgements
  8. References
  9. Appendix

Metabolic network model

Apart from the variations in the stoichiometric model of the PPP discussed in this work, the other parts of the stoichiometric model used for fitting the fluxes of S. cerevisiae were identical to those presented by van Winden et al. [21]. For simplicity reasons the consumption of metabolites for the synthesis of biomass precursors and the reversible flux towards storage carbohydrates are not shown in the metabolic network model depicted in Fig. 3, but these were accounted for when fitting 13C-labeling data. The reversible reactions in Fig. 3 were modeled as separate forward and backward reactions and are referred to as net and exchange fluxes, where:

  • image
  • image

Flux-fitting procedure

The flux fitting procedure employed is described in detail by van Winden et al. [21]. In short, the procedure uses the cumomer balances and cumomer to isotopomer mapping matrices introduced by Wiechert et al. [51] to calculate the isotopomer distributions of metabolites in a predefined metabolic network model for a given flux set. The flux set that gives the best correspondence between the measured and simulated 13C-label distribution is determined by nonlinear optimization and denoted as the optimal flux fit. All calculations were performed in Matlab 6.1 (The Mathworks Inc., Natick, MA, USA).

Acknowledgements

  1. Top of page
  2. Abstract
  3. Theory
  4. Results and Discussion
  5. Conclusion
  6. Experimental procedures
  7. Acknowledgements
  8. References
  9. Appendix

This work was financially supported by the Dutch EET program (Project No. EETK20002) and DSM.

References

  1. Top of page
  2. Abstract
  3. Theory
  4. Results and Discussion
  5. Conclusion
  6. Experimental procedures
  7. Acknowledgements
  8. References
  9. Appendix
  • 1
    Wittmann C & Heinzle E (2002) Genealogy profiling through strain improvement by using metabolic network analysis: metabolic flux genealogy of several generations of lysine-producing corynebacteria. Appl Environ Microbiol 68, 58435859.
  • 2
    Van Dien SJ, Strovas T & Lidstrom ME (2003) Quantification of central metabolic fluxes in the facultative methylotroph Methylobacterium extorquens AM1 using 13C-label tracing and mass spectrometry. Biotechnol Bioeng 84, 4555.
  • 3
    Maaheimo H, Fiaux J, Cakar ZP, Bailey JE, Sauer U & Szyperski T (2001) Central carbon metabolism of Saccharomyces cerevisiae explored by biosynthetic fractional (13)C labeling of common amino acids. Eur J Biochem 268, 24642479.
  • 4
    Fiaux J, Andersson CIJ, Holmberg N, Bulow L, Kallio PT, Szyperski T, Bailey JE & Wuthrich K (1999) C-13 NMR flux ratio analysis of Escherichia coli central carbon metabolism in microaerobic bioprocesses. J Am Chem Soc 121, 14071408.
  • 5
    van Winden WA, van Gulik WM, Schipper D, Verheijen PJT, Krabben P, Vinke JL & Heijnen JJ (2003) Metabolic flux and metabolic network analysis of Penicillium chrysogenum using 2D [C-13, H-1] COSY NMR measurements and cumulative bondomer simulation. Biotechnol Bioeng 83, 7592.
  • 6
    Gombert AK, dos Santos MM, 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, 14411451.
  • 7
    Wiechert W (2001) 13C metabolic flux analysis. Metab Eng 3, 195206.
  • 8
    Christensen B & Nielsen J (2000) Metabolic network analysis of Penicillium chrysogenum using (13)C-labeled glucose. Biotechnol Bioeng 68, 652659.
  • 9
    Petersen S, de Graaf AA, Eggeling L, Mollney M, Wiechert W & Sahm H (2000) In vivo quantification of parallel and bidirectional fluxes in the anaplerosis of Corynebacterium glutamicum. J Biol Chem 275, 3593235941.
  • 10
    Marx A, de Graaf AA, 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, 111129.
  • 11
    Zhang HM, Shimizu K & Yao SJ (2003) Metabolic flux analysis of Saccharomyces cerevisiae grown on glucose, glycerol or acetate by C-13-labeling experiments. Biochem Eng J 16, 211220.
  • 12
    Schmidt K, Nielsen J & Villadsen J (1999) Quantitative analysis of metabolic fluxes in Escherichia coli, using two-dimensional NMR spectroscopy and complete isotopomer models. J Biotechnol 71, 175189.
  • 13
    dos Santos MM, Gombert AK, Christensen B, Olsson L & Nielsen J (2003) Identification of in vivo enzyme activities in the cometabolism of glucose and acetate by Saccharomyces cerevisiae by using 13C-labeled substrates. Eukaryotic Cell 2, 599608.
  • 14
    Wittmann C & Heinzle E (2001) Application of MALDI-TOF MS to lysine-producing Corynebacterium glutamicum– a novel approach for metabolic flux analysis. Eur J Biochem 268, 24412455.
  • 15
    van Winden W, Verheijen P & Heijnen S (2001) Possible pitfalls of flux calculations based on (13)C-labeling. Metab Eng 3, 151162.
  • 16
    Clark MG, Williams JF & Blackmore PF (1971) The transketolase exchange reaction in vitro. Biochem J 125, 381384 .
  • 17
    Williams JF, Blackmore PF & Clark MG (1978) New reaction sequences for the non-oxidative pentose phosphate pathway. Biochem J 176, 257282.
  • 18
    Flanigan I, Collins JG, Arora KK, Macleod JK & Williams JF (1993) Exchange-reactions catalyzed by group-transferring enzymes oppose the quantitation and the unraveling of the identity of the pentose pathway. Eur J Biochem 213, 477485.
  • 19
    Ljungdahl L, Wood HG, Couri D & Racker E (1961) Formation of unequally labeled fructose 6-phosphate by an exchange reaction catalyzed by transaldolase. J Biol Chem 236, 16221625.
  • 20
    Berthon HA, Bubb WA & Kuchel PW (1993) 13C n.m.r. isotopomer and computer-simulation studies of the nonoxidative pentose-phosphate pathway of human erythrocytes. Biochem J 296, 379387.
  • 21
    van Winden WA, van Dam JC, Ras C, Kleijn RJ, Vinke JL, van Gulik WM & Heijnen JJ (2005) Metabolic-flux analysis of Saccharomyces cerevisiae CEN.PK113–7D based on mass isotopomer measurements of (13)C-labeled primary metabolites. FEMS Yeast Res 5, 559568.
  • 22
    Stryer L (1995) Biochemistry, 4th edn. W.H. Freeman, New York.
  • 23
    Horecker BL, Cheng T & Pontremoli S (1963) Coupled reaction catalyzed by enzymes transketolase and transaldolase. II. Reaction of erythrose 4-phosphate and transaldolase–dihydroxyacetone complex. J Biol Chem 238, 34283431 .
  • 24
    Kato N, Higuchi T, Sakazawa C, Nishizawa T, Tani Y & Yamada H (1982) Purification and properties of a transketolase responsible for formaldehyde fixation in a methanol-utilizing yeast, Candida boidinii (Kloeckera Sp), 2201. Biochim Biophys Acta 715, 143150.
  • 25
    Wood T (1985) The Pentose Phosphate Pathway. Academic Press Inc., London.
  • 26
    Sabate L, Franco R, Canela EI, Centelles JJ & Cascante M (1995) A model of the pentose-phosphate pathway in rat liver cells. Mol Cell Biochem 142, 917.
  • 27
    Mcintyre LM, Thorburn DR, Bubb WA & Kuchel PW (1989) Comparison of computer simulations of the F-type and L-type non-oxidative hexose-monophosphate shunts with 31P-NMR experimental data from human erythrocytes. Eur J Biochem 180, 399420.
  • 28
    Melendez-Hevia E, Waddell TG & Montero F (1994) Optimization of metabolism – the evolution of metabolic pathways toward simplicity through the game of the pentose-phosphate cycle. J Theor Biol 166, 201219.
  • 29
    Follstad BD & Stephanopoulos G (1998) Effect of reversible reactions on isotope label redistribution – analysis of the pentose phosphate pathway. Eur J Biochem 252, 360371.
  • 30
    Nelson DL & Cox MM (2000) Lehninger Principles of Biochemistry, 3rd edn. Worth Publishers, New York.
  • 31
    Sundstrom M, Lindqvist Y, Schneider G, Hellman U & Ronne H (1993) Yeast TKL1 gene encodes a transketolase that is required for efficient glycolysis and biosynthesis of aromatic amino acids. J Biol Chem 268, 2434624352.
  • 32
    Schaaff-Gerstenschlager I, Mannhaupt G, Vetter I, Zimmermann FK & Feldmann H (1993) TKL2, a second transketolase gene of Saccharomyces cerevisiae. Cloning, sequence and deletion analysis of the gene. Eur J Biochem 217, 487492.
  • 33
    Sprenger GA (1995) Genetics of pentose-phosphate pathway enzymes of Escherichia coli K-12. Arch Microbiol 164, 324330.
  • 34
    Siddiquee KA, Arauzo-Bravo MJ & Shimizu K (2004) Metabolic flux analysis of pykF gene knockout Escherichia coli based on 13C-labeling experiments together with measurements of enzyme activities and intracellular metabolite concentrations. Appl Microbiol Biotechnol 63, 407417.
  • 35
    Fiaux J, Cakar ZP, Sonderegger M, Wuthrich K, Szyperski T & Sauer U (2003) Metabolic-flux profiling of the yeasts Saccharomyces cerevisiae and Pichia stipitis. Eukaryot Cell 2, 170180.
  • 36
    Zhao J & Shimizu K (2003) Metabolic flux analysis of Escherichia coli K12 grown on C-13-labeled acetate and glucose using GG-MS and powerful flux calculation method. J Biotechnol 101, 101117.
  • 37
    Sauer U, Lasko DR, Fiaux J, Hochuli M, Glaser R, Szyperski T, Wuthrich K & Bailey JE (1999) Metabolic flux ratio analysis of genetic and environmental modulations of Escherichia coli central carbon metabolism. J Bacteriol 181, 66796688.
  • 38
    Kanehisa M & Goto S (2000) KEGG: Kyoto encyclopedia of genes and genomes. Nucleic Acids Res 28, 2730.
  • 39
    Forster J, Famili I, Fu P, Palsson BO & Nielsen J (2003) Genome-scale reconstruction of the Saccharomyces cerevisiae metabolic network. Genome Res 13, 244253.
  • 40
    Karp PD, Riley M, Paley SM & Pelligrini Toole A (1996) EcoCyc: An encyclopedia of Escherichia coli genes and metabolism. Nucleic Acids Res 24, 3239.
  • 41
    Cherry JM, Adler C, Ball C, Chervitz SA, Dwight SS, Hester ET, Jia YK, Juvik G, Roe T, Schroeder M et al. (1998) SGD: Saccharomyces genome database. Nucleic Acids Res 26, 7379.
  • 42
    Daran-Lapujade P, Jansen MLA, Daran JM, van Gulik W, de Winde JH & Pronk JT (2004) Role of transcriptional regulation in controlling fluxes in central carbon metabolism of Saccharomyces cerevisiae– A chemostat culture study. J Biol Chem 279, 91259138.
  • 43
    Sprenger GA, Schorken U, Sprenger G & Sahm H (1995) Transaldolase-B of Escherichia coli K-12 – cloning of its gene, talB, and characterization of the enzyme from recombinant strains. J Bacteriol 177, 59305936.
  • 44
    Schaaff I, Hohmann S & Zimmermann FK (1990) Molecular analysis of the structural gene for yeast transaldolase. Eur J Biochem 188, 597603.
  • 45
    Moss DW (1982) Isoenzymes. Chapman & Hall Ltd, London.
  • 46
    Schaaff-Gerstenschlager I & Zimmermann FK (1993) Pentose-phosphate pathway in Saccharomyces cerevisiae– analysis of deletion mutants for transketolase, transaldolase, and glucose-6-phosphate-dehydrogenase. Curr Genet 24, 373376.
  • 47
    Iida A, Teshiba S & Mizobuchi K (1993) Identification and characterization of the Tktb gene encoding a 2Nd transketolase in Escherichia coli K-12. J Bacteriol 175, 53755383.
  • 48
    Zhao GS & Winkler ME (1994) An Escherichia coli K-12 tktA tktB mutant deficient in transketolase activity requires pyridoxine (vitamin B6) as well as the aromatic amino acids and vitamins for growth. J Bacteriol 176, 61346138.
  • 49
    Schorken U, Thorell S, Schurmann M, Jia J, Sprenger GA & Schneider G (2001) Identification of catalytically important residues in the active site of Escherichia coli transaldolase. Eur J Biochem 268, 24082415.
  • 50
    Burnham KP & Anderson DR (2002) Model Selection and Multimodel Inference: a Practical Information-Theoretic Approach, 2nd edn. Springer, New York.
  • 51
    Wiechert W, Mollney M, Isermann N, Wurzel M & de Graaf AA (1999) Bidirectional reaction steps in metabolic networks. III. Explicit solution and analysis of isotopomer labeling systems. Biotechnol Bioeng 66, 6985.

Appendix

  1. Top of page
  2. Abstract
  3. Theory
  4. Results and Discussion
  5. Conclusion
  6. Experimental procedures
  7. Acknowledgements
  8. References
  9. Appendix

Appendix I

Table 3.  Relations between the nonoxidative pentose phosphate pathway (PPP) fluxes of the traditional model and the half-reaction model. From the traditional and the half-reaction model of the nonoxidative PPP depicted in Fig. 3, linear dependencies can be derived relating the nonoxidative PPP fluxes of the two models. These nonredundant linear dependencies are given in A1–10.
  • image((A1) )
  • image((A2) )
  • image((A3) )
  • image((A4) )
  • image((A5) )
  • image((A6) )
  • image((A7) )
  • image((A8) )
  • image((A9) )
  • image((A10) )