Revisiting the 13C-label distribution of the non-oxidative branch of the pentose phosphate pathway based upon kinetic and genetic evidence Roelco J Kleijn, Wouter A van Winden, Walter M van Gulik and Joseph J Heijnen Department of Biotechnology, Delft University of Technology, Delft, the Netherlands Keywords 13C labeling; metabolic flux analysis; pentose phosphate pathway; transaldolase; transketolase Correspondence R J Kleijn, Department of Biotechnology, Delft University of Technology, Julianalaan 67, 2628BC Delft, the Netherlands Fax: +31 15 2782355 Tel.: +31 15 2785025 E-mail: r.j.klein@tnw.tudelft.nl Website: http://www.bt.tudelft.nl/ (Received 24 June 2005, accepted August 2005) doi:10.1111/j.1742-4658.2005.04907.x 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 microorganisms, 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 halfreaction based stoichiometric model with two distinct transketolase enzymes instead of one Results show that the inclusion of isoenzymes affects the ensuing flux estimates 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 13 C-labeling based MFA relies on the feeding of C-labeled substrate to a biological system, allowing the labeled carbon atoms to distribute over the metabolic network, and subsequently measuring the 13 C-label distributions of intracellular and ⁄ or secreted 13 Abbreviations C2, glycolaldehyde moiety; C3, dihydroxyacetone moiety; e4p, erythrose 4-phosphate; f6p, fructose 6-phosphate; fbp, fructose 3;4;5 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 4970 FEBS Journal 272 (2005) 4970–4982 ª 2005 FEBS R J Kleijn et al Tracing compounds by means of NMR spectroscopy or MS The flux patterns within a metabolic network model can be calculated by iteratively fitting simulated 13 C-label distributions for a chosen set of metabolic fluxes to the measured 13C-label distributions [7] Apart from MFA, the information richness of 13 C-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) [6,1014]: TK x5p ỵ r5p $ s7p þ g3p TK x5p þ e4p $ f 6p þ g3p TA s7p ỵ g3p $ f 6p ỵ e4p ðr.1Þ; ðr.2Þ; ðr.3Þ: 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 FEBS Journal 272 (2005) 4970–4982 ª 2005 FEBS 13 C in the pentose phosphate pathway 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 influence the labeling pattern of the metabolite pools and thus need to be incorporated into the metabolic network for 13 C-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: TK f 6p ỵ r5p $ e4p ỵ s7p TK g3p ỵ x5p ! x5p ỵ g3p TK f 6p ỵ e4p ! e4p ỵ f 6p TK r5p ỵ s7p ! s7p ỵ r5p TA f 6p ỵ g3p ! g3p ỵ f 6p TA e4p ỵ s7p ! s7p ỵ e4p r.4ị; r.5ị; r.6ị; ðr.7Þ; ðr.8Þ; ðr.9Þ: 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 Kinetic mechanism of the nonoxidative branch of the PPP The enzymes TK and TA catalyze the transfer of twoand three-carbon fragments from a ketose donor to an 4971 Tracing 13 C in the pentose phosphate pathway R J Kleijn et al 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 e-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 A K A 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 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 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: A K C K E E I C C K C E K A K C A E C A E E A K C K II E A E K K C A E 4972 C C E K C E A A Fig 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) FEBS Journal 272 (2005) 4970–4982 ª 2005 FEBS R J Kleijn et al Tracing TK x5p $ g3p ỵ E C2 TK f 6p $ e4p ỵ E C2 TK s7p $ r5p ỵ E C2 TA f 6p $ g3p ỵ E C3 TA s7p $ e4p ỵ E C3 r.10ị; r.11ị; r.12ị; r.13ị; ðr.14Þ: Using the above half-reactions, a C2 fragment-producing reaction (e.g x5p fi g3p + E ) C2) can be coupled to a C2 fragment-consuming reaction (e.g e4p + E ) C2 fi f6p), leading to one of the traditional reactions (in this case r.2: x5p +e4p fi 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 13 C in the pentose phosphate pathway 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 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 microorganisms 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 Traditional vs half-reactions: implications for C-labeling 13 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 FEBS Journal 272 (2005) 4970–4982 ª 2005 FEBS Fig 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 4973 Tracing 13 C in the pentose phosphate pathway 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 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 halfreactions 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 tktAencoded 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 4974 R J Kleijn et al 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] 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 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 13 C-label distribution that can occur between the two different modeling approaches For case consider the traditional model of Fig 3, but now containing only the conventional nonoxidative FEBS Journal 272 (2005) 4970–4982 ª 2005 FEBS R J Kleijn et al Tracing 13 C in the pentose phosphate pathway Fig Traditional (I) and half-reaction (II) stoichiometric flux balance models for the 13 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 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 halfreaction 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 FEBS Journal 272 (2005) 4970–4982 ª 2005 FEBS 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 For case 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 4975 Tracing 13 C in the pentose phosphate pathway R J Kleijn et al Fig Route traversed by the glycolaldehyde (C2) fragments of the transketolasecatalyzed reactions present in the simplified traditional model (I) and half-reaction model (II) of cases and (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 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 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 halfreaction 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 13 C1-labeled s7p for the half-reaction model, in contrast to only unlabeled s7p for the traditional model For case consider the same traditional and halfreaction model as used in case 2, but now with all 4976 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 13 C-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 & FEBS Journal 272 (2005) 4970–4982 ª 2005 FEBS R J Kleijn et al 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 show the previously estimated flux patterns for the traditional model, as well as the newly estimated flux patterns using the half- Tracing 13 C in the pentose phosphate pathway 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 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 v2(n-p) distribution, with n-p being the degrees of freedom equal to the number of independent data points (n ¼ 26) minus the number of free parameters (P ¼ 14 and for the traditional and the half-reaction model, respectively) Given the probabilities P[v2(12) > 6.5] ¼ 0.89 and P[v2(17) > 20.9] ¼ 0.23, it follows that within the 95% Fig 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 arrow14 heads denote the direction of the net flux FEBS Journal 272 (2005) 4970–4982 ª 2005 FEBS 4977 Tracing 13 C in the pentose phosphate pathway R J Kleijn et al Table 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 15 equations in Appendix I Reaction no Fluxes in the half-reaction model Converted fluxes in the traditional model Relative change (%) n1 n2 net n2 exchange n3 net n3 exchange n4 n5 net n5 exchange n6 n7 n8 net n8 exchange n9 net n9 exchange n10 net n10 exchange n11 net n11 exchange n12 net n12 exchange 100 26 134 56 > 1000 65 65 221 121 18 )3 10 )6 124 )6 25 100 26 105 50 > 1000 63 63 194 119 24 13 10 )5 155 )8 4898 )8 24 0 21 11 – 3 13 36 48 > 100 67 > 100 38 > 100 38 38 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 (s2 ) criterres ion can be used: SSres : s2 ¼ res nÀp 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 s2 , thus res compensating for any possible overparameterization Nevertheless, the traditional model gives an s2 of 0.54 res compared to 1.23 for the half-reaction model, implying that the traditional model performs better from a statistical point of view 4978 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 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 {P[v2(12) > 6.5] ¼ 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 s2 criterion res Table 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 Conclusion 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 halfreactions, 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 FEBS Journal 272 (2005) 4970–4982 ª 2005 FEBS R J Kleijn et al Tracing Table 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 Reaction no Converted fluxes in the ‘double TK’ half-reaction model Converted fluxes in the traditional model Relative change (%) n1 n2 net n2 exchange n3 net n3 exchange n4 n5 net n5 exchange n6 n7 n8 net n8 exchange n9 net n9 exchange n10 net n10 exchange n11 net n11 exchange n12 net n12 exchange 100 26 103 50 > 1000 63 63 199 118 25 13 10 )5 100 )8 11 )8 24 100 26 105 50 > 1000 63 63 194 119 24 13 10 )5 155 )8 4898 )8 24 0 – 0 3 55 > 100 3 13 C in the pentose phosphate pathway 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 halfreaction model when modeling the label distribution in the nonoxidative PPP, bearing in mind that isoenzymes for TK and TA may exist Experimental procedures 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 were modeled as separate forward and backward reactions and are referred to as net and exchange fluxes, where: experiments An additional advantage of using halfreactions is the decreased number of free parameters vnet ¼ vforward À vbackward that have to be estimated by fitting 13C-labeling data to the stoichiometric model vexchange ¼ minðvforward ; vbackward Þ Mass isotopomer measurements from a previously published study on S cerevisiae were used to compare Flux-fitting procedure the traditional and half-reaction model depicted in Fig 3, resulting in statistically acceptable fits for both The flux fitting procedure employed is described in detail models Different flux patterns were found for the by van Winden et al [21] In short, the procedure uses the two models, but no major rerouting of metabolic cumomer balances and cumomer to isotopomer mapping fluxes was observed The incorporation of genetic matrices introduced by Wiechert et al [51] to calculate the knowledge into the metabolic network model for the isotopomer distributions of metabolites in a predefined nonoxidative branch of the PPP introduced the possimetabolic network model for a given flux set The flux set bility of modeling the presence of isoenzymes for TK that gives the best correspondence between the measured and simulated 13C-label distribution is determined by nonand TA Extending the half-reaction model from one linear optimization and denoted as the optimal flux fit All to two autonomously functioning TK enzymes resulcalculations were performed in Matlab 6.1 (The Mathworks ted in a doubling of the number of C2 fragment pools The fitting of measurement data to a ‘double 10 Inc., Natick, MA, USA) TK’ half-reaction model yielded flux estimates and an SSres that were similar to those of the traditional Acknowledgements model The similarity of the flux estimates indicates This work was financially supported by the Dutch that the presence of isoenzymes reduces the difference EET program 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isotopomer labeling systems Biotechnol Bioeng 66, 69–85 4981 Tracing 13 C in the pentose phosphate pathway R J Kleijn et al Appendix I 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 16 the nonoxidative PPP fluxes of the two models These nonredundant linear dependencies are given in A110 n8f ẳ v8f ỵ v9f ỵ v11 A1ị n8b ẳ v8b ỵ v9b ỵ v11 A2ị n9f ẳ v9b ỵ v10f ỵ v12 A3ị n9b ẳ v9f ỵ v10b ỵ v12 A4ị n10f ẳ v8b ỵ v10b ỵ v13 A5ị n10b ẳ v8f ỵ v10f ỵ v13 A6ị n11f ẳ v14b ỵ v15 A7ị n11b ẳ v14f ỵ v15 A8ị n12f ẳ v14f ỵ v16 A9ị n12b ẳ v14b ỵ v16 A10ị 4982 FEBS Journal 272 (2005) 49704982 ª 2005 FEBS ... based upon mass isotopomer measurements of 13C-labeled primary metabolites [21] Theory Kinetic mechanism of the nonoxidative branch of the PPP The enzymes TK and TA catalyze the transfer of twoand... 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. .. 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