Revisiting the
13
C-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
6
Department of Biotechnology, Delft University of Technology, Delft, the Netherlands
During the past decade,
13
C-labeling based metabolic
flux analysis (MFA) has increasingly been used to
understand the effect of genetic alterations [1,2], chan-
ges 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
13
C-labeled substrate to a biological system, allowing
the labeled carbon atoms to distribute over the meta-
bolic network, and subsequently measuring the
13
C-label distributions of intracellular and ⁄ or secreted
Keywords
8
13
C labeling; metabolic flux analysis;
pentose phosphate pathway; transaldolase;
transketolase
Correspondence
1

13
C-tra-
cer experiments. To investigate the actual impact of the new reaction struc-
ture on the estimated flux patterns within a cell, mass isotopomer
measurements from a previously published
13
C-based metabolic flux analy-
sis 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.
7
It is shown that the newly proposed stoichiometric model allows
study of the effect of isoenzymes on the
13
C-label distribution in the non-
oxidative 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
C
2
, glycolaldehyde moiety; C
3
, dihydroxyacetone moiety; e4p, erythrose 4-phosphate; f6p, fructose 6-phosphate; fbp, fructose
1,6-bisphosphate
3;4;5

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 conse-
quently flux estimates) for
13
C-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]:
x5p þ r5p $
TK
s7p þ g3p ðr.1Þ;
x5p þ e4p $
TK
f6p þ g3p ðr.2Þ;
s7p þ g3p $

TK
e4p þ s7p ðr.4Þ;
g3p þ x5p !
TK
x5p þ g3p ðr.5Þ;
f6p þ e4p !
TK
e4p þ f6p ðr.6Þ;
r5p þ s7p !
TK
s7p þ r5p ðr.7Þ;
f6p þ g3p !
TA
g3p þ f6p ðr.8Þ;
e4p þ s7p !
TA
s7p þ e4p 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 bal-
ance model. Based upon the kinetic mechanism of TA
and TK, an alternative reaction structure for tracing
the distribution of
13
C through the nonoxidative
branch of the PPP is proposed. It is shown that a stoi-
chiometric flux balance model, based upon this new
reaction structure, is fundamentally different from the
current models with respect to
13

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 carbani-
on, 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 C
2
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), eryth-
rose 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 di-
hydroxyacetone (C
3
). The nitrogen atom of the Schiff
base (similar to the nitrogen atom in the thiazole ring
of TK) stabilizes the dihydroxyacetone unit using res-
onance forms until a suitable aldose (g3p, e4p) accep-
tor is bound [22].
The kinetic mechanism employed by both enzymes
has been characterized as a reversible ping-pong mech-
anism [23–25]. Bi-bi reactions use this mechanism to

3
fragments
producing and consuming half-reactions for each of
the metabolites s7p, f6p, x5p, r5p, e4p and g3p (r.10–
14). Note that the C
2
and C
3
fragments remain bound
to the holoenzyme (E) until they are transferred to an
acceptor:
K
C
A
E
C
A
E
K
C
A
E
K
C
A
E
K
C
A
E

(ordered) sequential mechanism. Depicted
are the ketose substrate (K), the aldose
acceptor (A), the transferred carbon-frag-
ment (C), and the enzyme ⁄ cofactor complex
(E).
Tracing
13
C in the pentose phosphate pathway R. J. Kleijn et al.
4972 FEBS Journal 272 (2005) 4970–4982 ª 2005 FEBS
x5p $
TK
g3p þ E À C
2
ðr.10Þ;
f6p $
TK
e4p þ E À C
2
ðr.11Þ;
s7p $
TK
r5p þ E À C
2
ðr.12Þ;
f6p$
TA
g3p þ E À C
3
ðr.13Þ;
s7p $

ment-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 nonoxi-
dative branch of the PPP, based upon traditional reac-
tions 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 reversibil-
ity of the TK- and TA-catalyzed reactions, and their
demonstrated ping-pong mechanism, one has to con-
clude 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
13
C-labeling
From a labeling point of view, the main difference
between modeling the stoichiometry of the nonoxida-
tive branch of the PPP using either traditional reac-
tions or half-reactions, is the number of independent
C
2

fragments (and, consequently, the labeling of the
metabolites formed from these) can differ from the
13
C
labeling of the single C
2
and C
3
fragment pools gener-
ated 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 micro-
organisms possess two TK genes and that most stoichi-
ometric flux balance models of the nonoxidative
branch of the PPP contain only two TK-catalyzed
reactions (r.1–2), has led to the common misunder-
standing 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
Fig. 2. Number of glycolaldehyde (C
2
) and dihydroxyacetone (C
3

of the talA gene has not been shown, to date. S. cere-
visiae 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 isoen-
zymes 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 C
2
or C
3
fragments for one isoenzyme. As a result of this modi-
fication, a second set of C
2
and C
3
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]. Fur-
thermore, deletion mutants of tkl2 showed no changed

reduces the number of free fluxes that have to be esti-
mated from the
13
C-labeling data during the flux fitting
procedure. The model contains 12 reactions (n
1
–n
12
)
and eight reversibilities, which are constrained by 10
mass balances over the intracellular metabolites in a
(pseudo) steady state. When normalizing the rates rel-
ative to the uptake rate of glucose, nine free fluxes
remain to be estimated from the
13
C-labeling data. The
corresponding traditional model (Fig. 3I) contains 16
reactions (v
1
–v
16
) 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 sec-
ond 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

4974 FEBS Journal 272 (2005) 4970–4982 ª 2005 FEBS
PPP reactions (Fig. 3I
A
). 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 (v
8f
,v
9f
,v
14f
) and the
glycolysis (v
2f
,v
3f
,v
5f
) are active. Analogous to the tra-
ditional model, only the forward glycolytic reactions
are included in the half-reaction model (n
5f
,n
3f
and

2
fragment pool that is solely formed by reac-
tion n
8f
(Fig. 4). However, both C
2
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 C
2
fragment pools for both modeling approa-
ches. Examination of the origin of the C
3
fragment
pools shows that both models contain only one C
3
frag-
ment-producing reaction, both with s7p as the donor
(v
14f
,n
12f
). So, in essence, both models described in this
case contain one C
2
and one C
3
fragment pool. As a
result, the redistribution of

FEBS Journal 272 (2005) 4970–4982 ª 2005 FEBS 4975
increase in n
9f
and n
9b
(see Appendix I). As a result of
this additional reaction, C
2
fragments are now also
produced from f6p, thus increasing the number of C
2
fragment pools in the traditional model to three
(Fig. 4). The absence of bidirectional reactions makes
it impossible for the three C
2
fragment pools, origin-
ating 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 C
2
fragment pools in the traditional model. The half-reac-
tion model inherently contains one single C
2
fragment
pool that comprises all distinct C
2
fragment pools of
the traditional model, as shown in Fig. 4. From this
single pool a C
2

and v
9b
). However, the high reversibility of the bidirec-
tional reactions also ensures that the label distributions
of the C
2
fragment pools (and also the C
3
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 differ-
ence in
13
C-label distribution amongst the two mode-
ling approaches becomes more pronounced as the
number of C
2
and C
3
fragment-producing reactions
increases, while high reaction reversibilities diminish
this difference. In reality the nonoxidative branch of
the PPP contains multiple C
2
and C
3

C in the pentose phosphate pathway R. J. Kleijn et al.
4976 FEBS Journal 272 (2005) 4970–4982 ª 2005 FEBS
Stephanopoulos
9
[29], it remains questionable whether
these reversibilities are high enough to efface the dif-
ference in
13
C-label distribution created by the multiple
C
2
and C
3
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
13
C-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 iso-
topomer fractions larger than 0.03 were included.
Figures 5I,II and Table 1 show the previously estima-
ted 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

ble transketolase’ half-reaction model (III),
based upon the mass isotopomer measure-
ments of
13
C-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 arrow-
heads denote the direction of the net flux.
14
R. J. Kleijn et al. Tracing
13
C in the pentose phosphate pathway
FEBS Journal 272 (2005) 4970–4982 ª 2005 FEBS 4977
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 (SS
res
) is higher for the half-reac-
tion model. One possible explanation for the higher
SS
res
in the half-reaction model is an overparameteri-
zation of the traditional model. In an overparameter-
ized model, some parameters are actually used to fit
measurement errors, thereby underestimating the true

of 0.54
compared to 1.23 for the half-reaction model, implying
that the traditional model performs better from a sta-
tistical point of view.
A second explanation for the higher SS
res
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 C
2
fragment pool to the meta-
bolic network model. To test whether the introduct-
ion of an isoenzyme for TK in the metabolic
network model results in a better fit, the half-reac-
tion 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 SS
res
for this model was 6.5, meaning
that this model also adequately fitted the measured
mass isotopomer fractions {P[v
2
(12) > 6.5] ¼ 0.89}.
Interestingly, exactly the same values for the minim-
ized SS

13
C-label
distribution prediction in stoichiometric flux balance
models. When comparing two models of the nonoxida-
tive 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 C
2
and C
3
fragment pools present in the
stoichiometric model. Whereas the traditional reactions
lead to multiple independent pools, the half-reactions
result in only one C
2
and one C
3
fragment pool. This
difference in C
2
and C
3
fragment pools influences the
ensuing label distribution when conducting
13
C-tracer
Table 1. Comparison of the flux estimates for the traditional and
half-reaction models presented in Fig. 5I,II. The pentose phosphate

n
4
65 63 3
n
5 net
65 63 3
n
5 exchange
221 194 13
n
6
121 119 2
n
7
18 24 36
n
8 net
913 48
n
8 exchange
410>100
n
9 net
)3 )567
n
9 exchange
10 155 > 100
n
10 net
)6 )838

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 possi-
bility of modeling the presence of isoenzymes for TK
and TA. Extending the half-reaction model from one
to two autonomously functioning TK enzymes resul-
ted in a doubling of the number of C
2
fragment
pools. The fitting of measurement data to a ‘double
TK’ half-reaction model yielded flux estimates and an
SS
res
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
13
C-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 iso-
enzymes 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. There-

forward
; v
backward
Þ
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
13
C-label distribution is determined by non-
linear optimization and denoted as the optimal flux fit. All
calculations were performed in Matlab 6.1 (The Mathworks
Inc., Natick, MA, USA)
10
.
Acknowledgements
This work was financially supported by the Dutch
EET program (Project No. EETK20002) and DSM.
Table 2. Comparison of the flux estimates for the traditional and
the ‘double transketolase’ (‘double TK’) half-reaction model presen-
ted in Fig. 5II,III. The two separate fluxes for the transketolase-cat-
alyzed 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

63 63 0
n
5 exchange
199 194 3
n
6
118 119 0
n
7
25 24 2
n
8 net
13 13 3
n
8 exchange
10 10 0
n
9 net
)5 )54
n
9 exchange
100 155 55
n
10 net
) 8 )83
n
10 exchange
11 4898 > 100
n
11 net

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13
C in the pentose phosphate pathway

¼ v
9b
þ v
10f
þ v
12
ðA3Þ
n
9b
¼ v
9f
þ v
10b
þ v
12
ðA4Þ
n
10f
¼ v
8b
þ v
10b
þ v
13
ðA5Þ
n
10b
¼ v
8f
þ v

16
ðA10Þ
Tracing
13
C in the pentose phosphate pathway R. J. Kleijn et al.
4982 FEBS Journal 272 (2005) 4970–4982 ª 2005 FEBS