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8/14/2019 Estimation of Metabolic Fluxes
1/12
TECHNICAL ADVANCE
Estimation of metabolic fluxes, expression levels and meta-bolite dynamics of a secondary metabolic pathway in potato
using label pulse-feeding experiments combined with kineticnetwork modelling and simulation
Elmar Heinzle1,2,*, Fumio Matsuda3, Hisashi Miyagawa2,3, Kyo Wakasa3,4 and Takaaki Nishioka2
1Biochemical Engineering Institute, Saarland University, D-66123 Saarbrucken, Germany,2Division of Applied Life Sciences, Agricultural Department, Kyoto University, Kyoto 606-8502, Japan,3Plant Functions and Their Control, CREST, Japan Science and Technology Agency, 3-4-5 Nihonbashi, Chuo, Tokyo 103-0027,
Japan, and4Department of Agriculture, Tokyo University of Agriculture, 1737 Funako, Atsugi, Kanagawa 243-0034, Japan
Received 16 July 2006; revised 13 November 2006; accepted 23 November 2006.*For correspondence (fax +49 681 302 4572; e-mail [email protected]).
Summary
In this paper we present a method that allows dynamic flux analysis without a priorikinetic knowledge. This
method was developed and validated using the pulse-feeding experimental data obtained in our previous
study (Matsuda et al., 2005), in which incorporation of exogenously applied L-phenylalanine-d5 into seven
phenylpropanoid metabolites in potato tubers was determined. After identification of the topology of the
metabolic network of these biosynthetic pathways, the system was described by dynamic mass balances in
combination with power-law kinetics. After the first simulations, some reactions were removed from the
network because they were not contributing significantly to network behaviour. As a next step, the exponents
of the power-law kinetics were identified and then kept at fixed values during further analysis. The model was
tested for statistical reliability using Monte Carlo simulations. Most fluxes could be identified with highaccuracy. The two test cases, control and after elicitation, were clearly distinguished, and with elicitation
fluxes toN-p-coumaroyloctopamine (pCO) andN-p-coumaroyltyramine (pCT) increased significantly, whereas
those for chlorogenic acid (CGA) and p-coumaroylshikimate decreased significantly. According to the model,
increases in the first two fluxes were caused by induction/derepression mechanisms. The decreases in the
latter two fluxes were caused by decreased concentrations of their substrates, which in turn were caused by
increased activity of the pCO- and pCT-producing enzymes. Flux-control analysis showed that, in most cases,
flux control was changed after application of elicitor. Thus the results revealed potential targets for improving
actions against tissue wounding and pathogen attack.
Keywords: metabolic flux analysis, metabolic control analysis, pulse-feeding experiment, kinetic network
modelling, phenylpropanoid pathway, potato.
Introduction
Plants, as major primary producers of biochemical sub-
stances, have enormous biosynthetic potential that could be
explored more fully using methods of metabolic engineer-
ing, as indicated by a series of recent reviews (Hanson and
Shanks, 2002; Rontein et al., 2002). The basis for rational
design of metabolic paths is a thorough quantitative
understanding of the paths, including an understanding of
their kinetics and their regulation at the levels of genes,
proteins and metabolites (Bailey, 1998; Giersch, 2000; Niel-
sen, 1998; Stephanopoulos et al., 1998). Metabolic flux
176 2007 The AuthorsJournal compilation 2007 Blackwell Publishing Ltd
The Plant Journal (2007) 50, 176187 doi: 10.1111/j.1365-313X.2007.03037.x
8/14/2019 Estimation of Metabolic Fluxes
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analysis is a major tool in this field, providing quantitative
data about reaction rates. Relative to their importance, such
quantitative analyses have notbeen applied widely in plants.
This is probably due to the fact that the wide range of
methods developed for microbial systems and also mam-
malian cells in recent years (Dauner and Sauer, 2000; Hel-
lerstein, 2004; Hellerstein and Neese, 1999; Wahlet al., 2004;
Wiechert, 2001; Wiechertet al., 2001; Wittmann, 2002; Witt-
mann and Heinzle, 1999, 2001a,b) have been adapted only
partially for plant systems (Ratcliffe and Shachar-Hill, 2006;
Roscher et al., 2000). Several reasons can be identified to
explain this: (i) plant genetics are more complex than
microbial genetics, and the Arabidopsis and rice genomes
have been sequenced in their entirety only relatively re-
cently; (ii) experimentation with plants is generally more
complex and less suited to well defined laboratory experi-
ments compared with microbial systems; (iii) under most
relevant photosynthetic conditions, plants assimilate carbon
dioxide, which is not well suited for classical metabolic flux
analysis methods using 13
C-label distribution measure-ments; (iv) plants are usually highly compartmented, which
complicates metabolic flux analysis; and (v) it is difficult to
carry out experiments in plants under steady-state condi-
tions (such as those used in the chemostat technique for
microbial cultures), which are desirable for metabolic flux
analysis methods based on well-established metabolic
stoichiometry.
While quantitative flux analyses of central pathways and
polymeric reactions using13C-labelled precursor substances
in plantsundersteady-stateconditionshave been carried out
quite extensively in recent years (Glawischniget al., 2002;
Hellersteinand Neese, 1999;Krugerand vonSchaewen,2003;
Ratcliffe and Shachar-Hill, 2006; Schwender et al., 2003),
there is little information available on the metabolic fluxes of
secondary metabolism in plants.
At first glance, it may seem relatively easy to analyse
linear-type secondary metabolic pathways with limited
branching. This is true if starting and final rates can be
measured adequately and if intracellular concentrations are
known. Unfortunately, this is usually not the case. Precur-
sors entering the pathway may be produced by metabolic
pathways at unknown rates, and product accumulation may
be unable to be measured because appropriate experimen-
tal techniques are unavailable, or because the products
undergo further reactions. In such cases, dynamic tech-niques have to be applied. These take into account the
accumulation of compounds, and are most successfully
applied if preliminary kinetic information is already avail-
able. Rohwer andBotha (2001) analysed the accumulation of
sucrose in sugarcane culms using in vitro kinetic data.
McNeil et al. (2000) identified key constraints in an engin-
eered pathway producing glycine betaine. Labelling tech-
niques combined with simple first-order kinetic models can
be used to determine metabolic rates, as shown earlier by
Sims and Folkes (1964). Recently, Matsuda et al. (2003)
modified this method and applied it to L-phenylalanine (Phe)
metabolism in potato tubers, to allow determination of flux
partitioning at the p-coumaroyl CoA branch point. This
method is particularly attractive because of its simplicity and
clear definition. It relies, however, on a series of assump-
tions, square-step input, first-order kinetics and constant
rates during the labelling experiment, which limits its use.
Boatrightet al.(2004) studiedin vivobenzenoid metabolism
in petunia petal tissue using dynamic labelling experiments
combined with mass spectrometric analysis of labelling.
They did, however, assume constant rates throughout their
experiment. Therefore they could not directly extract kinetic
information using their method. Full kinetic models with
MichaelisMenten kinetics were applied by Nuccio et al.
(2000) to determine glycine betaine synthesis in tobacco. In
their work they used 14C as the labelling isotope. It is
certainly preferable to use established kinetic equations, but
these are often not easily available, for example for secon-
dary metabolite pathways. In such cases it seems best toapply generally applicable kinetic equations such as power-
law kinetics, which allow many kinetic dependencies
observed in biological systems, within a certain range, to
be mimicked (Voit, 2000). The application of dynamic
models for flux analysis has a significant advantage because
kinetic models allow straightforward further analysis. It is
generally possible to obtain hints about expression levels
and to calculate flux-control coefficients using the models
(McNeilet al., 2000). Another way of obtaining flux-control
coefficients is by modifying enzyme activity and measure-
ment of flux responses, as was done by Ramli et al. (2002)
using radioactive tracer substances. Basic information on
the methodology and techniques of network modelling and
flux analysis can be found in textbooks (e.g. Stephanopou-
loset al., 1998). A useful detailed overview is provided in a
recent comprehensive review of metabolic flux analysis in
plants, in which important technical terms are also
explained (Ratcliffe and Shachar-Hill, 2006).
Here we investigate a method for the determination of
metabolic fluxes, expression levels of enzymes at each
reaction step, concentrations of unmeasured intermediates,
and control coefficients of secondary metabolic pathways in
plants without a priorikinetic knowledge. First-order and
power-law kinetics are applied to describe changes in
metabolitesand metabolitelabelling.A morecomplexmodelis reduced to a simpler one, which is used for statistical
analysis using Monte Carlo simulations and for calculating
flux-control coefficients. Experimental data used in the
present study are derived from pulse-labelling experiments
carried out in our previous study (Matsuda et al., 2005), in
which incorporation of exogenously applied L-phenylalan-
ine-d5 into seven phenylpropanoid metabolites in potato
tubers was determined. In potato (Solanum tuberosum) the
following metabolites are derived from the phenylpropanoid
Method for metabolic flux and control analysis 177
2007 The AuthorsJournal compilation 2007 Blackwell Publishing Ltd, The Plant Journal, (2007), 50, 176187
8/14/2019 Estimation of Metabolic Fluxes
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pathway: one hydroxycinnamic acid ester with quinate
(chlorogenic acid, CGA) and six amides with tyramine,
octopamine and putrescine: N-p-coumaroyloctopamine
(p-CO), N-p-coumaroyltyramine (p-CT), N-feruloyloctopam-
ine (FO), N-feruloyltyramine (FT); caffeoylputrescine (CafP)
and feruloylputrescine (FP) (Figure 1). p-CO, FO, p-CTandFT
accumulation is induced by pathogen infection (Clarke, 1982;
Kelleret al., 1996), wounding of tissues and treatment with
elicitors (Miyagawaet al., 1998; Negrelet al., 1993; Schmidt
et al., 1999). Regulation of these pathways is thus of great
interest, and a better understanding of the pathways could
lead to the development of plants with improved defence
responses. Although the metabolic flux of metabolite bio-
synthesis has been estimated roughly from the amounts of
metabolites (Schmidt et al., 1998), the activities of biosyn-
thesis-related enzymes (Matsuda et al., 2000; Negrel et al.,
1993), the transcription levels of the genes encoding these
enzymes (Schmidt et al., 1999), and the regulatory mecha-
nisms of the pathways are poorly understood due to meth-
odological limitations. Recently, direct determination of the
metabolic fluxes of this pathway was achieved using pulsefeeding combined with simple metabolic models. Using this
method, regulation of the phenylpropanoid pathway in
control plants and those treated with ab-1,3-glucooligosac-
charide elicitor (laminarin) has been characterized in some
detail (Matsuda et al., 2003, 2005). However, the metabolic
model used in that study was too simple to analyse the
complex metabolic network shown in Figure 1.
In the present work we develop a method to answer the
following questions: (i) Is it possible to determine the
metabolic flux of all reaction steps shown in Figure 1? (ii)
Are the results obtained earlier by Matsuda et al. (2005) in
agreement withthe network model results? (iii) Which fluxes
are modified significantly upon application of the b-1,3-
glucooligosaccharide elicitor? (iv) Is it possible to generate
hypotheses about induction repression based on kinetic
metabolic flux analysis? (v) Is it possible to predict levels of
unmeasured intermediate metabolites based on simula-
tions? (vi) What are the rate-controlling reactions in the
control and elicitor experiments?
Results and discussion
Model formulation and simplification
Model development began from the reaction scheme shown
in Figure 1. The appropriateness of the pathway was dis-
cussed in our previous work (Matsudaet al., 2005). In a first
model with only first-order kinetics, it was found that the
reactionsfrom phenylalanine to pCACoAcan be lumped into
one reaction without influencing the results significantly.This is so because the concentrations of intermediates are
very low, below the detection limit of the HPLCMS method,
allowing the assumption of steady state for these metabo-
lites. Additionally, reactions from pCACoA to CGA and those
from pCACoA to caffeoyl CoA (CafCoA) via p-coumaroyls-
hikimate and caffeoylshikimate couldbe lumped together for
the same reason. The uptake of Phe added was described
betterby a reversible reactionthat reflects a diffusionprocess
ina simpleway.In additionto thereactionsdepicted inFigure 1,
COOH
NH2
COOH
NH2
COCoA
HO
COCoA
HO
COCoA
HO
HO
H3CO
HO
N
O
H
OH
HO
N
O
H
OH
OH
HO
N
O
H
OH
HO
N
O
H
OH
OH
H3CO
H3CO
HO
N NH2
O
H
H3CO
HO
N NH2
O
H
HO
HO
O
OHO
OH
OH
HO COOH
p-coumaric acid
Cinnamic acid
L-phenylalanine
p-coumaroyl CoA
caffeoyl CoA
feruloyl CoA
chlorogenic acid
p-coumaroyloctopamine
p-coumaroyltyramine
feruloyloctopamine
feruloyltyramine feruloylputrescine
caffeoylputrescine
p-coumaroylshikimatep-coumaroylquinate
caffeoylshikimate
PAL
THT
THT
C4H
4CL
CQT CST
CST
CQT
CCoAOMT
PHT
PHT
C3'H
kDPhe
kPAL
k4CL
kTHTpCO
kTHTpCT
kpCOdeg
kpCTdeg
kCST1kCQT1
kCQT2
kCST2
kPHTCafP
kPHTFP
kTHTFO
kTHTFT
kFOdeg
kFTdeg kFPdeg
kCafPdeg
C3'HkC3'HCGA
kCCoAOMT
Phe
Pheex
pCACoApCO
pCT
FO
FT
CafP
FP
CGA
kC4H
CafCoA
FCoA
kCGAdeg
kC3'HCafS
Figure 1. Reaction schemeof themetabolic path-
ways in potato that start from L-phenylalanine
(Phe).
Enzymes are abbreviated as follows: 4CL, 4-hydroxy-
cinnamic acid:CoA ligase; Phe, phenylalanine ammo-
nia lyase; PHT, putrescine hydroxycinnamoyl
transferase;CQT, quinatehydroxycinnamoyl-CoA:qui-
nate hydroxycinnamoyltransferase; THT, tyramine
hydroxycinnamoyl-CoA:tyramine hydroxycinnamoyl-
transferase; C3H, 5-O-(4-hydroxycinnamoyl)quinate3-hydroxylase; C4H, cinnamic acid 4-hydroxylase;
CST, shikimate hydroxycinnamoyl-CoA:shikimate
hydroxycinnamoyltransferase.
178 E. Heinzleet al.
2007 The AuthorsJournal compilation 2007 Blackwell Publishing Ltd, The Plant Journal, (2007), 50, 176187
8/14/2019 Estimation of Metabolic Fluxes
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three hypothetical reactions from hydroxycinnamoyl CoAs
(pCACoA, CafCoA and FCoA) into other metabolites or poly-
mers were introduced as indicated by their corresponding
rateconstants, kpCACoAdeg, kCafCoAdeg and kFCoAdeg (Figure 2a),
as the hydroxycinnamoyl CoAs could serve as precursors forthe synthesis of other defence-related polymers, including
lignin, which might be upregulated on elicitor treatment.
From this, the so called first-order model was obtained (Fig-
ure 2a). Using this model and the experimental data from
Matsudaet al.(2005), we found that the reactions indicated
by the rate constants kpCACoAdeg, kCafCoAdeg and kFCoAdeg were
always negligibly small. These were therefore eliminated
from further studies, resulting in the scheme shown in
Figure 2(b), which we named the power-law model.
In the next step, all parameters (11 initial concentrations,
20 rate constants and 11 exponents of power-law kinetics)
were estimated using weighted least squares. Initial values
were estimated for all concentrations, also for those that
were experimentally observed, because they also had an
experimental error of about 20%. Details of weighting are
given in Experimental procedures. The whole calculation
procedure is summarized schematically in Figure 3.
Using Berkeley Madonna, these parameters were fitted to
the 68 experimental points of each experiment for the
control and elicitor treatments (Tables S1S3). It was poss-
ible to fit the experimental data very well, as can be seen in
Figure 4 for the labelling data.
Each estimation required about 500010 000 runs, which
were finished in
8/14/2019 Estimation of Metabolic Fluxes
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including JPAL, JCQT2, JCGAdeg, JCST1 and JCCoAMT, which
could not be determined in our previous study due to excess
simplification of the metabolic model. This improvement is
an obvious advantage of the present method, by which a
more detailed flux distribution in the metabolic network was
determined. Moreover, the estimated values of metabolic
fluxes showed good agreement with those determined in
our previous study (Table 1; Matsuda et al., 2005), except for
the degradation steps includingJpCOdeg,JpCTdeg,JpFOdegand
JpFTdeg. One possible reason for the discrepancy is that
degradation reactions are generally predicted with higher
uncertainty (Table 1; Figure 5).
In the control case, 74% of Phe is converted to pCACoA,
and most of it ends up in FO (45%), although 19% is
converted to FP, 10% to CafP and about 4% to FT. Only 16%
of Phe is converted to pCO, and 6% to pCT. Only FO and FP
seem to be converted to further species, but the estimations
of these fluxes are characterized by high standard devia-
tions. In the potato tuber disks to which elicitor was applied,
the fluxes JPAL, JTHTpCO, JTHTpCT and JCGAdeg increased
significantly. The mean values of fluxes from pCO and pCT
to other products, JpCOdeg and JpCTdeg, also increased
significantly. Other reaction rates, JCQT1, JCST1, JCCoAOMT,JPHTCafP, JTHTFO and JPHTFO, clearly decreased. This means
that, after elicitor treatment, the metabolism is shifted to
pCO and pCT biosynthesis, compounds that are further
converted to polymer compounds to form a physical barrier
against pathogen intrusion (Schmidt et al., 1998). These
results also suggest that the role of pCO in defence response
is more important than that of other compounds, which
generally agrees with the results of our previous study
(Matsudaet al., 2005).
Kinetic analysis and expression
A second set of answers obtained from the model is based
on its kinetic properties. Figure 6 shows the rate constants.
These are the product of enzyme concentration and the
actual rate constant, and might also be influenced generally
Figure 3. Procedures for modelling and param-
eter estimation.Q is the weighted least squares,
yithe experimental value, Pthe parameter vec-
tor,xithe independent variable,f(xi,P) are model
values, andwi= 1/ri is the weighting factor.
Phe pCO pCT CGA
0 5
CafP
0 5
FO
0 5
FT
0 5
FP
Phe pCO pCT CGA
0 5
CafP
0 5
FO
0 5
FT
0 5
FP
Time (h)
Isotopeabundance
Isotopeabundance
Time (h)
(b)
(a)
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
0.8
0
0.2
0.4
0.6
0.8
0
0.2
0.4
0.6
0.8
Figure 4. Fractional 13C enrichment calculated by the model compared with
experimental data (symbols) using the data set obtained from control (a) and
elicitor-treated (b) samples.
180 E. Heinzleet al.
2007 The AuthorsJournal compilation 2007 Blackwell Publishing Ltd, The Plant Journal, (2007), 50, 176187
8/14/2019 Estimation of Metabolic Fluxes
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by other metabolites. First, it can be seen that these con-
stants are determined with relatively small errors, and vary
over orders of magnitude. Assuming that the effects of other
metabolites are negligible, predictions of expression-
induction phenomena can be made directly. This can be
done at each metabolic branch point, for example at pCA-
CoA, CafCoA and FCoA (Figure 7), by observing the relative
changes. Even if the estimation of the concentration of each
starting metabolite was not very precise, the relative
magnitudes of the rate constants clearly indicate induction-
repression phenomena. These can be seen in comparative
linear plots ofkTHTpCO, kTHTCpT, kCQT1 and kCST1 in Figure 7(a).
Both constants kTHTpCO and kTHTpCT increased significantly,
18- and 10-fold, respectively, whereas bothkCQT1and kCST1remained constant. The activation of THT activity in b-1,3-
gluco-oligosaccharide elicitor-treated potato tubers has
been observed earlier in independent experiments (Matsuda
et al., 2000), and thus supports our findings. At the same
time, the corresponding fluxes JTHTpCO and JTHTpCT also in-
creased, whereas JCQT1 and JCST1 both decreased signifi-
cantly, as shown in Figure 5. This can be explained by the
estimated reduced concentration of pCACoA, as shown in
Figure 8. The branch point at CafCoA showed a significant
increase in kCCoAOMT, whereas kPHTCafP remained nearly
constant (Figure 7b). Both associated fluxes, JPHT1CafP and
JCCoAOMT, decreased upon elicitation, as shown in Figure 5.
The third branch point studied, the reactions starting from
FCoA, showed increases ofkTHTFO and kTHTFT, which were,
however, not significant considering the large degree of
error, and a significant decrease ofkPHTFP as shown in Fig-
ure 7(c). The fluxes JTHTFO and JPHTFP decreased, whereasJTHTFT remained about constant (Figure 5). These results
clearly show the regulation effects in thismetabolic network.
Flux-control analysis
The model was also used further for flux-control analysis
(Table 2). The concept of flux-control coefficients (Fell, 1997;
Kacser and Burns, 1973) was introduced to estimate
quantitatively the contribution of each metabolic step to
Table 1 Estimated absolute and relative metabolic fluxes, Ji, and their standard deviations for the control and for the case with elicitor
application
Control Elicitor
Mean flux
[nmol (g FW)1 h1]
Relative flux
(%)
Flux determined
by Matsuda et al.
(2005) [nmol (g FW)1 h1]
Mean flux
[nmol (g FW)-1 h1]
Relative flux
(%)
Flux determined
by Matsuda et al.
(2005) [nmol (g FW)1 h1]
JPAL 8.59 0.41 100 0.0 nda 11.87 0.89 100 0.0 nd
JTHTpCO 1.41 0.22 16.4 2.8 0.98 7.6 0.6 64.0 0.3 8.7
JpCOdeg 0.00 0.00 0.0 0.0 0.98 2.69 1.73 21.2 17.2 7.4
JTHTpCT 0.75 0.24 8.6 2.7 0.34 2.14 0.15 18.0 0.3 2.5
JpCTdeg 0.00 0.00 0.0 0.0 0.33 1.07 0.37 9.1 3.7 2.3
JCQT1 0.34 0.03 4.0 0.3 0.38 0.12 0.01 1.0 0.0 0.14
JCGAdeg 0.03 0.00 0.3 0.0 nd 0.16 0.01 1.4 0.1 nd
JCQT2 0.23 0.33 2.6 3.8 nd 0.47 0.2 4.1 1.9 nd
JCST1 6.10 0.41 71 3.2 nd 2.01 0.16 17.0 0.4 nd
JCCoAOMT 5.54 0.55 64.4 5.6 nd 2.42 0.2 20.7 1.8 nd
JPHTCafP 0.79 0.08 9.2 0.8 1.14 0.05 0.01 0.4 0.0 0.14
JCafPdeg 0.12 0.20 1.4 2.5 0.49 0.55 0.27 4.5 2.6 0.11
JPHTFP 1.63 0.19 19.0 2.3 1.22 0.11 0.02 0.9 0.2 0.14
JFPdeg 0.04 0.07 0.5 0.8 0.13 0.12 0.19 1.2 1.8 0.04
JTHTFO 3.59 0.41 41.7 4.1 3.4 2.05 0.19 17.4 1.4 3.4
JFOdeg 0.42 0.83 4.8 9.4 3.3 0.79 0.68 7.4 6.5 3.3
JTHTFT 0.33 0.08 3.9 0.9 0.26 0.26 0.04 2.3 0.5 0.59
JFTdeg 0.00 0.00 0.0 0.0 0.24 0.01 0.02 0.1 0.2 0.52
Metabolic flux values determined from the same data set using a different method by Matsuda et al.(2005). a, not determined.
Phe
pCACoA
CGA
CafCoA
FCoA
CafP
FP
pCOpCT
JCST1
JPAL
rCQT1
JCQT2
JpCOdeg
JpCTdeg
JTHTpCO
JTHTpCT
FOFT
JFOdeg
JFTdeg
JTHTFO
JTHTFT
JCGAdeg
JPHTcafP
JPHTFP
JcafPdeg
JFPdeg
JCCoAOMT3.6 0.4/ 2.0 0.20.4 0.8/0.8 0.7
0.0/0.01 0.02 0.1/0.3 0.00.3
1.6 0.2/0.1 0.0
5.5 0.6/2.4 0.2
0.04 0.07/0.1 0.2
0.1 0.2/ 0.6 0.30.8 0.1/ 0.1 0.0
6.1 0.4 / 2.0 0.2
0.2 1.7/ 0.5 0.2
0.03 0.00/0.2 0.0
0.3 0.0/0.1 0.0
0.8 0.2/ 2.1 0.2
1.4 0.2/ 7.6 0.60.0 / 2.7 1.7
0.0 / 1.1 0.4
8.6 0.4 / 11.9 0.9
Control/elicitor
(nmol(g FW)1 h1)
Figure 5. Absolute fluxes for the control and elicitor cases. Values for the
control and for the case with elicitor application are shown at the corres-
ponding reaction steps (control/elicitor), in nmol (g FW)1 h1.
Method for metabolic flux and control analysis 181
2007 The AuthorsJournal compilation 2007 Blackwell Publishing Ltd, The Plant Journal, (2007), 50, 176187
8/14/2019 Estimation of Metabolic Fluxes
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controlling a metabolic flux in a pathway. For JTHTpCOof the
control sample (Table 2), control coefficients of the steps for
kDPheandkTHTpCOhad large positive values. This means that
the increase inkTHTpCO(in other words, the activation of the
enzyme responsible for this step) is mainly responsible for
the increase in JTHTpCO. In contrast, control coefficients for
kTHTpCT, kCQT1 and kCST1 were negative, indicating that an
increase in their values caused a decrease in JTHTpCO.
However, the step ofkCST1is more important thankTHTpCTand kCQT1 for controlling the metabolic flux ofJTHTpCO, asthe
control coefficient ofkCST1()73) was much smaller than the
control coefficients of kTHTpCT and kCQT1 ()13 and )5,
respectively). In Table 2, the sum of the values of the controlcoefficients in each row is always 100. It is obvious that the
supply ofL-phenylalanine was important for most reactions
of the system, as it is the only input. Only for minor
metabolic activities where accumulation played a dominant
role (e.g. JCGAdeg, JCQT2, JCafPdeg, JFPdeg, JFOdegand JFTdeg)
was it less important. Most interesting here is a comparison
of control and elicitor cases to determine whether flux
control has moved to other reactions after elicitor applica-
tion. JTHTpCO was mostly controlled by itself and was in
competition withJCST1. The competition was smaller for the
elicitor case. JTHTpCT was mostly in competition with the
reaction via p-coumaroylshikimate and, after elicitor appli-
cation, with the reaction to pCO. Significant changes were
observed for JCQT1. Competition from the reaction to pCO,
JTHTpCO, increased and competition from JCST1 decreased.
JCQT2was influenced primarily by kCQT2. The flux JCST1was
increasingly in competition with JTHTpCO after elicitor
Figure 6. Estimated kinetic constants of the power-law model (Figure 2) with
fixed values for exponents of power-law kinetics as specified in the text. The k
values represent the rate constants of each reaction step as defined by Eqn 3
in Experimental procedures. Error bars, standard deviations derived from
Monte Carlo simulations.
0
5
10
15
20
25
30
kTHTFO kTHTFT kPHTFP
Control
Elicitor
0
50
100
150
200
250
300
350
400
450
500
kTHTpCO kTHTpCT kCQT1 kCST1
Control
Elicitor
0
200
400
600
800
1000
1200
1400
kPHTCafP kCCoAOMT
Rateconstant(h1)
Rateconsta
nt(h1)
Rateconstant(h
1)
Control
Elicitor
(a)
(b)
(c)
Figure 7. Comparison of kinetic constants around various nodes.
(a) p-coumaroyl CoA (pCCoA); (b) caffeoyl CoA (CafCoA); (c) feruloyl CoA
(FCoA). Kinetic constants are defined in Figure 2. Error bars, standard
deviations derived from Monte Carlo simulations.
182 E. Heinzleet al.
2007 The AuthorsJournal compilation 2007 Blackwell Publishing Ltd, The Plant Journal, (2007), 50, 176187
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application. The reaction to CafP, JPHTCafP, was primarily in
competition with the reaction to FCoA, to a slightly lesser
extent with the reaction to pCO, and to an even lesser extent
with the reaction to pCT; however, it was stimulated by
JCST1, especially after elicitation, when kCQT2 also had a
stimulating effect. The reactions to THTFO and THTFT were
similarly influenced by all preceding reactions, but were
main competitors with each other. To a lesser extent, JPHT2
was also a competitor. The degradation reactions weregenerally predicted with higher uncertainty (Table 1;
Figure 5). Therefore information about their control is also
generally less accurate. Their control coefficients did not
change very much upon elicitation.
The results of the metabolic control analysis revealed
potential targets for rational metabolic engineering. As
elicitation simulates the plants defences against pathogen
infection (Clarke, 1982; Keller et al., 1996) and wounding of
tissues (Miyagawaet al., 1998; Negrel et al., 1993; Schmidt
et al., 1999), amplification ofJpCOdegis desirable. This could
be accomplished by amplification ofp-coumaroyloctopam-
ine-synthesizing and -degrading enzymes, characterized by
kTHTpCOandkpCOdeg, which both have a highly positive flux-
control coefficient for JpCOdeg. A reduction of the flux
towardsp-coumaroyltyramine would also be beneficial.
Conclusions
We have shown in the present study that flux analysis using
labelled precursors is possible, even under dynamic condi-
tions, withouta prioriknowledge of kinetics. This is possible
by using power-law kinetics, which can describe almost any
kinetics with sufficient accuracy. The analysis completely
answers the questions introduced in the Introduction.
Dynamic tracer experiments not only allow the estimation of
metabolic fluxrates (Table 1) and the distribution of network
activities (Figure 5), but also permit further direct analysis,
for example of flux-control coefficients (Table 2). Flux-con-
trol coefficients can be used to identify targets for engin-
eering plant metabolism. In the present study, suggestions
for improved plant self-protection could be elaborated. The
application of dynamic models in combination with statis-
tical model evaluation allows additional interpretation, for
example, prediction of unmeasured intermediate concen-
trations (Figure 8) and prediction of expression/repression
phenomena (Figures 6 and 7). Such dynamic models can be
applied even for rather complex systems using the fast and
reliable computational tools available.
We believe this methodology will also be very useful for
large-scale quantitative analysis of metabolic networks after
the application of pulses or step changes of labelled water,carbon dioxide or ammonia (e.g. 2H2O, H2
18O, 13CO2 or15NH3). Then it would be possible to analyse simultaneously
a whole set of sub-networks using the methodology pre-
sented here, provided corresponding metabolite analysis is
available (Soga et al., 2002). The method of metabolic
analysis demonstrated in this study is also expected to be
a powerful tool for investigation of plant metabolic func-
tions, as well as for rational metabolic engineering.
Experimental procedures
Model formulation
The pathway investigated here is depicted in Figure 1, and is des-
cribed elsewhere in greater detail (Matsuda et al., 2003, 2005).
Starting from this reaction network, the model equations were set
up using standard techniques described in textbooks (e.g. Dunn
et al., 2003). In all formulations, a well-mixed system is assumed.
Material balances were formulated for the constant volume system
for each labelled and non-labelled species:
dCj;k
dt Xn
j1
Jj;k 1
where Cis concentration, i indicates the component, k indicates
whether the component is a labelled or non-labelled species, Ji s
metabolic flux or reaction rate, and j indicates reactions producingand consuming component i.
The balance for labelled pCACoA of the power-law model
(Figure 2b) is, for example:
dCpCACoA;i
dt JPAL;i JTHTpCO;i JTHTpCT;i JCQT1;i JCST1;i 2
whereJrepresents the reaction rates of fluxes each formulated as:
Jj kjCaji k
0jC
ajE;jC
aji 3
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
pCACoA CafCoA FCoa
Concentration(nmol(gFW)1)
Control
Elicitor
Figure 8. Estimated average concentrations of unmeasured compounds p-coumaroyl CoA(pCCoA),caffeoyl CoA(CafCoA)and feruloyl CoA(FCoA), with
error bars derived from Monte Carlo simulations.
Method for metabolic flux and control analysis 183
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Here jindicates the reaction, i the reacting component and E the
enzyme. For the reactions indicated by thin lines in Figure 2(b), only
first-order kinetics were used (ai= 1). For the reactions indicated by
thick lines in Figure 2(b), power-law kinetics were applied. In this
simplified formulation, it is assumed that influences from other
substances, either co-substrates or other compounds allosterically
Table 2Flux-control coefficients estimated using the model
KDPhe kPAL kTHTpCO kpCOdeg kTHTpCT kpCTdeg kCQT1 kCGAdeg kCQT2 kCST1 kCCoAOMT kPHTCafP kCafPdeg kPHTFP kFPdeg kTHTFO kFOdeg kTHTFT kFTdeg
JPAL
C 97 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
E 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
JTHTpCO
C 105 4 84 0 )
13 0 )
5 0 0 )
74 0 0 0 0 0 0 0 0 0E 101 0 35 0 )19 0 )1 0 0 )17 0 0 0 0 0 0 0 0 0
JpCOdeg
C 84 5 69 96 )11 0 )4 0 0 )60 0 0 0 0 0 0 0 0 0
E 51 1 18 79 )10 0 )1 0 0 )9 0 0 0 0 0 0 0 0 0
JTHTpCT
C 105 4 )16 0 87 0 )5 0 0 )74 0 0 0 0 0 0 0 0 0
E 101 0 )65 0 81 0 )1 0 0 )17 0 0 0 0 0 0 0 0 0
JpCTdeg
C 96 5 )15 0 81 100 )5 0 0 )69 0 0 0 0 0 0 0 0 0
E 65 1 )44 0 55 57 )1 0 0 )12 0 0 0 0 0 0 0 0 0
JCQT1
C 116 4 )18 0 )15 0 95 0 0 )82 0 0 0 0 0 0 0 0 0
E 113 0 )72 0 )21 0 99 0 0 )19 0 0 0 0 0 0 0 0 0
JCGAdeg
C 8 0 )
1 0 )
1 0 7 100 0 )
6 0 0 0 0 0 0 0 0 0E 5 0 )3 0 )1 0 5 93 )13 )1 0 0 0 0 0 0 0 0 0
JCQT2
C 7 0 )1 0 )1 0 6 0 100 )5 0 0 0 0 0 0 0 0 0
E 5 0 )3 0 )1 0 4 )6 88 )1 0 0 0 0 0 0 0 0 0
JCST1
C 93 3 )14 0 )12 0 )4 0 0 34 0 0 0 0 0 0 0 0 0
E 90 0 )58 0 )17 0 )1 0 0 85 0 0 0 0 0 0 0 0 0
JCCoAOMT
C 91 3 )14 0 )11 0 )4 0 0 33 15 )12 0 0 0 0 0 0 0
E 77 0 )49 0 )14 0 0 )1 13 72 2 )2 0 0 0 0 0 0 0
JPHTCafP
C 109 4 )16 0 )14 0 )5 0 0 40 )102 85 0 0 0 0 0 0 0
E 92 0 )59 0 )17 0 0 )1 16 86 )117 98 0 0 0 0 0 0 0
JCafPdeg
C 22 1 )
3 0 )
3 0 )
1 0 0 8 )
21 18 86 0 0 0 0 0 0E 2 0 )2 0 0 0 0 0 0 2 )3 2 66 0 0 0 0 0 0
JPHTFP
C 106 5 )16 0 )13 0 )5 0 0 40 18 )15 0 62 0 )73 0 )8 0
E 97 0 )62 0 )18 0 0 )1 17 90 3 )3 0 94 0 )105 0 )15 0
JFPdeg
C 28 2 )4 0 )3 0 )1 0 0 10 5 )4 0 17 99 )19 0 )2 0
E 4 0 )3 0 )1 0 0 0 1 4 0 0 0 4 98 )5 0 )1 0
JTHTFO
C 79 4 )12 0 )10 0 )4 0 0 30 13 )11 0 )29 0 46 0 )6 0
E 73 0 )47 0 )13 0 0 )1 13 68 2 )2 0 )5 0 22 0 )12 0
JFOdeg
C 67 4 )10 0 )8 0 )3 0 0 25 11 )9 0 )24 0 39 99 )5 0
E 32 1 )21 0 )6 0 0 0 6 31 1 )1 0 )2 0 10 74 )5 0
JTHTFT
C 106 5 )
16 0 )
13 0 )
5 0 0 40 18 )
15 0 )
38 0 )
73 0 92 0E 97 0 )62 0 )18 0 0 )1 17 90 3 )3 0 )6 0 )105 0 85 0
JFTdeg
C 60 3 )9 0 )8 0 )3 0 0 23 10 )8 0 )22 0 )41 0 53 100
E 33 1 )22 0 )6 0 0 0 6 32 1 )1 0 )2 0 )37 0 30 92
Control coefficients are given as percentages. C, control experiment; E, elicitor treatment.
184 E. Heinzleet al.
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influencing rates, are constant throughout one experiment. These
influences would then be summarized in the value ofkj. The rates of
the labelled and non-labelled compounds were calculated by:
Jj;kJjCi;k
Ci4
with variables as defined above.
Flux experiments
All experiments were carried out by Matsuda et al. (2003, 2005)
and are described in detail there. Here we describe only essentials
for setting up the model. Disk-shaped slices of potato tubers were
incubated in the dark at 18C. After 24 h the elicitor laminarin was
applied to a subset of disks. After a further 12 h, labelled L-phe-
nyl-d5-alanine was added to all disks. For concentration and
labelling analysis, three potato tuber disks were analysed by li-
quid chromatographymass spectroscopy (LCMS). Labelling data
were used directly for parameter estimation. Additional experi-
mental data used were initial concentrations (concentrations at
the time when labelling was applied, 36 h after preparation of
disks). To take into consideration the past time-course of the
concentration changes, initial rates of concentration changes
were calculated from the slopes of concentration at time zero in
the labelling experiment (36 h after disk preparation and 12 h
after elicitor application). Experimental data are given in
Tables S1S3.
Simulation and parameter estimation
The calculation procedures are summarized schematically in
Figure 3. Initial simulations were carried out using Berkeley Ma-
donna (http://www.berkeleymadonna.com; Dunn et al., 2003).
This software is fast and allowed quick parameter estimation
using available integrators for stiff systems. Rate constants and
initial concentrations were constrained to values 0, and expo-
nents of power-law equations were constrained to 0.2 < a < 1.5.
Weighting was carried out using experimentally identified stan-dard deviations. These were: concentrations, 20%; initial rates,
10%; fractional labelling, 10%. For initial rates the error was
calculated as a percentage of the initial concentrations. Data used
are specified in Table S1. It was found that parameter estimation
depended quite strongly on the initial conditions. Calculations
with initial conditions far from the final values did not always
converge to the global minimum. This lack of convergence could,
however, be seen easily from graphical comparison of simulation
results and experimental data, and also from the calculated
weighted sum of square deviations. Under conditions where all
experimental data fitted reasonably well, the identified minima
were very close.
In the first set of simulations, all initial concentrations, initial
rates and kinetic constants could be fitted simultaneously. This
was necessary because initial conditions and initial rates were
also corrupted by experimental errors and had to be estimated.
Convergence was usually obtained after 5000 to 10 000 simula-
tions. In later simulations, initial conditions and exponents of the
power-law kinetics were fixed and only rate constants were
estimated. The results found were confirmed by simulation using
MATLAB. MATLAB simulations used the ode15 s integrator and
fminsearch (unconstrained optimization) or fmincon (constrained
optimization) as optimizers. The MATLAB simulations were con-
siderably slower than those carried out using Berkeley Madonna.
Also, in the MATLAB optimizations convergence depended on the
choice of initial conditions: having initial conditions sufficiently
close to the final values always gave very similar results. MATLAB
was also used for further analysis of parameter estimation
results. These included the sensitivities of estimation for param-
eter values, as well as pairwise contour plots of the sum of
weighted square deviations as a function of two parameters to
check for parameter correlation. Final statistical analysis of the
model and results was carried out using Monte Carlo simula-
tions. All measurement data were varied according to theirindividual error ranges using the nrmrnd function of MATLAB. In
these runs, exponents of power-law kinetics were fixed and only
rate constants were estimated. Starting values for estimated
parameters and initial values were those identified in Berkeley
Madonna simulations.
Flux-control analysis
Flux-control coefficients were originally introduced by Kacser and
Burns (1973) and later described in more detail by Fell (1997):
CJkj @Jk
@Ej
Ej
Jk
@lnJk
@lnEj5
Fluxes as defined in Eqn 3 are identical to reaction rates. Assuming
that the rate constants k defined in Eqn 3 are proportional to en-
zyme concentration, we obtain:
CJkj @Jk
@Ej
Ej
Jk
@Jk
@Kj
Kj
Jk6
Thederivative Jk/kj was calculated numerically by calculatingfluxes at a total of nine equally spaced parameter values 20%around the optimal value. After smoothing using the csapsspline
tool of MATLAB, the derivative was calculated at the optimal
parameter value and was eventually estimated as a percentage. The
whole MATLABcode necessary to calculate flux-control coefficients
is contained in the Supplementary material. This also includes the
kinetic model, as well as all data used for the calculations.
Acknowledgements
The first author would like to express his deep gratitude for the
generous offer of being a guest professor in the Agricultural
Department of Kyoto University. This work was supported in part by
a grant from the Ministry of Education, Culture, Sports, Science, and
Technology of Japan (T.N.),and by the CREST programof the Japan
Science and Technology Organization.
Supplementary material
The following supplementary material is available for this article
online:Table S1 Label data for metabolites determined by LCMS taken
from Matsudaet al. (2005).
Table S2 Label time-course forphenylalanine determined by LCMS
(Matsudaet al., 2005).
Table S3 Initial concentration and initial rates taken from Matsuda
et al.(2005).
Appendix S1 Set ofMATLABm-files for the calculation of flux-control
coefficients.
This material is available as part of the online article from http://
www.blackwell-synergy.com.
Method for metabolic flux and control analysis 185
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