estimation of metabolic fluxes

8/14/2019 Estimation of Metabolic Fluxes

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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


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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


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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.



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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


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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.




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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.




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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.




8/12

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.




9/12

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.




10/12

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.




11/12

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