strategies for metabolic ﬂux analysis in plants using...

Journal of Biotechnology 77 (2000) 81–102

Strategies for metabolic flux analysis in plants using isotopelabelling

Albrecht Roscher, Nicholas J. Kruger, R. George Ratcliffe *Department of Plant Sciences, Uni6ersity of Oxford, South Parks Road, Oxford OX1 3RB, UK

Received 5 March 1999; received in revised form 1 July 1999; accepted 6 July 1999

Abstract

Flux measurements through metabolic pathways generate insights into the integration of metabolism, and there isincreasing interest in using such measurements to quantify the metabolic effects of mutation and genetic manipula-tion. Isotope labelling provides a powerful approach for measuring metabolic fluxes, and it gives rise to severaldistinct methods based on either dynamic or steady-state experiments. We discuss the application of these methodsto photosynthetic and non-photosynthetic plant tissues, and we illustrate the different approaches with an analysis ofthe pathways interconverting hexose phosphates and triose phosphates. The complicating effects of the pentosephosphate pathway and the problems arising from the extensive compartmentation of plant cell metabolism areconsidered. The non-trivial nature of the analysis is emphasised by reference to invalid deductions in earlier work. Itis concluded that steady-state isotopic labelling experiments can provide important information on the fluxes throughprimary metabolism in plants, and that the combination of stable isotope labelling with detection by nuclear magneticresonance is particularly informative. © 2000 Elsevier Science B.V. All rights reserved.

Keywords: Carbohydrate metabolism; Compartmentation; Metabolic network analysis; Nuclear magnetic resonance; Pentosephosphate pathway; Positional labelling

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1. Introduction

The techniques of molecular biology allow thecreation of transgenic plants in which theamounts of specific enzymes can be altered fromtheir wild type levels. This approach is of greatvalue to plant biochemists, who might wish tounderstand the operation of particular pathways

or steps, and to plant biotechnologists, who mightwish to manipulate the productivity of a plant foragronomic or industrial purposes. Unfortunatelythe systemic character of metabolism (Fell, 1997)means that the metabolic effects of genetic manip-ulation are by no means predictable, and so eachnew genotype has to be characterised empirically.

The measurement of metabolic fluxes is oneaspect of this characterisation, and since differentfluxes are interdependent, it is often necessary toextend the analysis to include all the major fluxesof primary metabolism. The easiest way of assess-

* Corresponding author. Fax: +44-1865-275074.E-mail address: [email protected] (R.G. Rat-

cliffe)

0168-1656/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved.

PII: S 0168 -1656 (99 )00209 -6

A. Roscher et al. / Journal of Biotechnology 77 (2000) 81–10282

ing metabolic fluxes is to measure the depletion ofgiven substrate(s) and/or the accumulation of spe-cific end product(s). It is then possible, knowingthe topology of the metabolic pathways and as-suming a steady-state for the metabolic intermedi-ates, to calculate the fluxes through differentpathways, a technique known as metabolite fluxbalancing. This approach is most readily appliedto relatively simple metabolic networks, such asthose operating in some micro-organisms, buteven here it is usually necessary to make furtherassumptions to obtain an unequivocal set offluxes (Bonarius et al., 1997).

Metabolite flux balancing is unlikely to be par-ticularly useful in plants for several reasons. First,plants accumulate large and diverse stores of sub-strate in order to meet the fluctuating demandsthat arise during diurnal, seasonal and reproduc-tive cycles, as well as to survive the fluctuatingconditions of their habitat. Thus metabolite fluxbalancing is likely to involve the measurement ofsmall changes in substrates and products that arepresent in large amounts, and there is also uncer-tainty about the availability of endogenous sub-strates. Secondly, plant metabolism is extensivelycompartmented, with many steps occurring inboth the cytosol and plastids, and this makesmetabolite flux balancing ambiguous. Finally, themore complex topography of the metabolic net-work in plants opens up many more possibilitiesfor substrate cycles, but these cannot be allowedfor by metabolite flux balancing, since the analysisis based on a consideration of net fluxes. Howeversince substrate cycles can play an important regu-latory role, as well as having an impact on theenergy balance of the cell, it is necessary to use amore powerful technique for analysing metabolicfluxes in complex networks.

The solution to these problems is to base themeasurement of metabolic fluxes on the redistri-bution of an isotopic label that is supplied with anexternal substrate. This approach requires analyti-cal methods for detecting isotopes and their chem-ical speciation. Mass spectrometry (MS) andnuclear magnetic resonance (NMR) are the ana-lytical techniques that are generally used for thedetection of stable isotopes; while radiotracingand MS are used for unstable isotopes. The chem-

ical identification of the labelled compounds canbe obtained directly by NMR; whereas with theother methods the information can only be ob-tained indirectly, e.g. by fractionation andderivatisation of the labelled compound prior toanalysis by gas chromatography MS.

The aim of this article is to describe the way inwhich the isotope labelling approach can be usedto measure metabolic fluxes in plants. While theanalysis presented here is largely independent ofthe analytical techniques that are used to detectthe redistribution of the label, the combination ofstable isotope labelling with NMR detection ap-pears to be particularly suitable for the determina-tion of metabolic fluxes (London, 1988). Theincreasing need to characterise transgenic plantmaterial at the metabolic level (Bouchez andHofte, 1998), coupled with the existing interest inthe biochemical and physiological applications ofNMR in plants (Ratcliffe, 1994), provide the con-text for this analysis. It is concluded that isotopiclabelling experiments should be capable of provid-ing detailed information on the consequences ofgenetic manipulation.

2. Results and discussion

2.1. O6er6iew of isotope labelling techniques

The first point to consider when devising anisotope labelling experiment is whether to usedynamic or steady-state labelling. Dynamic la-belling experiments involve sampling the time-course as the label moves from an initial substrateinto different metabolites. They can be performedwith either radioactive or stable isotopes, and thesubstrate can be fully, positionally, or bond-la-belled (see below for definitions). The choice ofthe label depends on the pathway to be studiedand the possibilities for analysis. The timecourseis usually constructed by analysing a series oftissue extracts, but an interesting alternative,which avoids the problems associated with samplevariability, is the use of in vivo NMR spec-troscopy for the direct detection of isotopes with anuclear spin (e.g. 2H, 13C, 15N). However, thistechnique only works for sufficiently concentrated

A. Roscher et al. / Journal of Biotechnology 77 (2000) 81–102 83

intermediates and for timecourses that are not toofast.

The analysis of the timecourse from a dynamiclabelling experiment allows the absolute fluxes foreach pathway to be calculated (Sims and Folkes,1964). Such an analysis is relatively straightfor-ward for metabolites that are very close to thepoint of entry of the labelled substrate, but be-comes increasingly complex with each additionalreaction step. Moreover, the timecourse is de-scribed by a set of linear differential equationsthat cannot be separated if there is the possibilityof cyclic flux within the network. To thesedifficulties should be added the experimentaldifficulty of sampling the necessary timepoints.The rate constants k (or characteristic times t=k−1) for the reactions in a metabolic network candiffer greatly. Thus it is necessary to have goodtime resolution in order to describe the fasterreactions, while sampling over a sufficiently longperiod to gain information on slower steps. How-ever, even then it is difficult to get precise infor-mation on a relatively fast reaction stepdownstream of a much slower step.

The alternative to dynamic labelling experi-ments is the detection of label at isotopic steady-state, when the rate of incorporation of label intoa metabolic intermediate equals its rate ofoutflow. In this approach, the parameter of inter-est is not the absolute amount of label in ametabolite but the relative amount, i.e. the pro-portion of metabolite molecules that are labelled.This dimensionless quantity is usually called thefractional enrichment, f, and it is linearly relatedto the specific radioactivity that is conventionallyused in the analysis of radiolabelling experiments.The fractional enrichment of a metabolite is deter-mined by the ratio of the fluxes coming fromdifferent source metabolites and by the fractionalenrichment of the source molecules. It followsthat steady-state labelling only allows determina-tion of the relative fluxes, and this set of relativefluxes, or flux ratios, has to be calibrated by oneabsolute flux (e.g. the consumption of substrate)to calculate the absolute flux values for eachreaction in the network. One major advantage ofthe steady-state approach over dynamic labellingis that there is no problem with having reactions

in the network that operate on very differenttimescales, as long as the fluxes are of comparablemagnitude.

The fractional enrichment of a metabolite atisotopic steady-state only contains useful informa-tion if it is determined by the relative strength ofcompeting influxes from sources with differentfractional enrichments. It follows that the experi-ments depend on feeding substrates that containboth labelled and unlabelled components. Thiscan be achieved in three ways: (i) by using twochemically different substrates, only one of whichis labelled; (ii) by using a substrate that is labelledin some specific atomic positions but not others(positional labelling); and (iii) by using a substratein which some, but not all, of the molecules havebeen uniformly labelled (bond-labelling). Thesethree strategies are discussed in the followingparagraphs.

The first possibility for introducing a mixedlabelled/unlabelled substrate is to give two chemi-cally different substrates, of which only one isisotopically labelled. The measured fractional en-richment for a metabolite that can be derivedfrom either of the substrates will give the relativecontributions of each substrate to the flux into theobserved metabolite. Note that one of the sub-strates can also be an endogenous storagemetabolite, e.g. starch in plants, and this indicatesa potential problem with the method. The dilutionof isotope enrichment, which is at the heart of thistechnique, can come from multiple endogenoussources, and these may be difficult to identify andto quantify. A second problem is that the analysisis restricted to metabolites that have two distinctroutes of synthesis, one originating from the la-belled substrate (a in Fig. 1) and the other fromthe unlabelled substrate (b). This is the case formetabolites C, D, and E in Fig. 1 (note that

Fig. 1. A schematic metabolic network in which the substratesa and b are metabolised through the steady-state intermediatesA–J.


although the net flux through D can only followone pathway, each molecule of D can derive fromeither B or E). In contrast, metabolism cannot beanalysed in regions of metabolism that deriveexclusively from one of the substrates (A and B inFig. 1) nor in regions (like F and its downstreamproducts) that are fed through a common inter-mediate (E) where the fluxes from both substratesmerge.

The second possibility for introducing labelledand unlabelled substrate simultaneously is to usea substrate that is labelled at some, but not all, ofthe positions in the molecule. It is the metabolicfate of the different atomic positions of the sub-strate molecule that is important in this approach,and so the method is called positional labelling.Exchange between label and naturally abundantisotope occurs whenever the flux from the sub-strate to the observed metabolite can follow twodifferent routes that lead to differential incorpora-tion of labelled and unlabelled substrate atomsinto a particular position in the metabolite, e.g. ifcarbon i of the metabolite is derived from carbonj of the substrate via the first route, but fromcarbon k via the second route. The metabolitesthat can be analysed include not only those situ-ated at intersections of metabolism but also thoseinvolved in bidirectional reactions. For examplein Fig. 1, if the labelling in G can be scrambled bycycling through H and J, then the relative fluxesfrom E and G into F can be quantified due to theexchange reaction with G. This information can-not be gained from two-substrate feeding. Thepositional labelling method depends on being ableto analyse the quantity of label at each atomicposition within a metabolite. This is readily doneby NMR, since chemically distinct atoms usuallygive separate signals in NMR spectra. In contrast,radioanalysis and MS both require a cumbersomechemical sample preparation in which themetabolite is cleaved into fragments that are sepa-rately analysed. With MS, this can also be doneby analysing several derivatives with differentfragmentation patterns (e.g. Beylot et al., 1993).

The third possibility is to supply a substrate inwhich only a fraction of the molecules has beenuniformly labelled whereas the rest are unlabelled.This type of experiment, which is called bond-la-

belling, is most informative with substrates inwhich the carbon skeleton is uniformly labelled(e.g. [U-13C6]-glucose (Szyperski, 1995, 1998)).For example, assume in Fig. 1 that substrate a issupplied on its own as a mixture of 10% uni-formly carbon-labelled and 90% uniformly unla-belled molecules, and that no rearrangements ofthe carbon skeleton occur in the metabolic stepsto metabolite G. The subsequent cleavage of Ginto H and J is reversible. If a uniformly labelledmolecule G is cleaved, it will give uniformly la-belled H and J, whereas the cleavage of unlabelledG will give unlabelled H and J. However, for thereverse reaction, a labelled molecule H has a 90%probability of reacting with an unlabelledmolecule J and only a 10% probability of forminga fully labelled molecule G. So for the G-molecules that are labelled in the H-moiety, thefraction of them that are not labelled in theJ-moiety, divided by the 90% probability, is adirect measure of the exchange flux relative to thesum of the exchange flux and the net flux into G.

Molecules that contain different distributions ofisotopic label but are otherwise identical arecalled isotopomers. Isotopomers formed of stableisotopes can be detected by MS or by NMR. MSprovides a direct measurement of sets of isoto-pomers with the same number of isotope labelatoms in them, but it is much harder to obtaininformation about the positional distribution ofthe isotope label with this technique. In contrast,it is straightforward to obtain information aboutneighbouring label isotopes with NMR since theresonance peak stemming from one atomic posi-tion is split into a multiplet if there is a magneti-cally inequivalent NMR-active isotope in anadjacent position. The frequency difference be-tween the multiplet peaks is due to a scalar cou-pling that is mediated by the chemical bonds.However, this coupling becomes much smaller ifmore than one bond is involved, so while thedetection of neighbouring labelled atoms is usu-ally straightforward, labelled atoms further apartcan only be correlated with some experimentaleffort (e.g. Wendisch et al., 1997; Carvalho et al.,1998).

If a substrate is used that is labelled in severalpositions but not uniformly, then it is possible to


do a hybrid experiment that exploits both bond-labelling and positional labelling. This allows thesimultaneous analysis of both the positional redis-tribution of label and the isotopomer distributionreflecting the cleavage of labelled bonds. Possibili-ties include the use of substrates where contiguoussections of the carbon skeleton are labelled (e.g.[1,2-13C2]-glucose (Kunnecke and Seelig, 1991),the labelling of heteronuclear bonds (e.g. [13C-15N]-bonds (Schaefer et al., 1981; Hutton et al.,1998)) and the detection of long-range bonds byMS (e.g. feeding with [1,6-13C2, 6,6%-2H2]-glucose(Ross et al., 1994)). In contrast to the pure bond-labelling experiment, there is no need to feed apercentage of unlabelled substrate as the naturalisotope dilution can come from within the par-tially labelled substrate molecule, as in positionallabelling experiments.

2.2. Measuring fluxes between hexose phosphatesand triose phosphates in plants

To illustrate the use of the different labellingtechniques, we consider their application in deter-mining unidirectional flux between hexose phos-phates and triose phosphates in plant cells. This isof relevance to two questions in plant metabolism:the first is the relative contribution of hexosephosphates and triose phosphates to carbontransport across the plastid envelope for starchsynthesis in heterotrophic tissues; and the secondis the metabolic role of the readily reversiblereaction catalysed by pyrophosphate:fructose 6-phosphate 1-phosphotransferase (PFP), and theregulation of PFP by fructose 2,6-bisphosphate(Fru-2,6-P2). Measuring the flux from hexosephosphates to triose phosphates and back tohexose phosphates, and into their products, is thekey to answering both questions. In the first in-stance, the parameter of interest is the proportionof hexose phosphate incorporated into starch thathas been re-synthesised from triose phosphates. Inthe second case, the same parameter is measuredin a cytosolic product (e.g. sucrose) since PFP andFru-2,6-P2 are confined to the cytosol in hetero-trophic tissues.

The information needed to address these ques-tions is difficult to obtain from dynamic labelling

Fig. 2. Metabolites and fluxes relevant for labelling analysis offluxes between hexose phosphates and triose phosphates. Allfluxes are expressed in hexose units. The fluxes are: 6H, influxof substrate into the hexose phosphate pool; 6T, influx ofsubstrate into the triose phosphate pool; 6C, efflux out of thehexose phosphate pool, mainly into carbohydrate synthesis;6G, efflux out of the triose phosphate pool, mainly into glycol-ysis; 61, forward, and 6-1, reverse flux between hexose andtriose phosphates.

experiments since it would require interpretingsubtle differences in the timecourse for the la-belling of pathway intermediates in terms of com-peting fluxes. In contrast, all three steady-statelabelling techniques described above can be em-ployed advantageously. However, each approachmeasures the flux ratios in a different way, andeach relies on different assumptions andconditions.

First, consider the feeding of two different sub-strates that enter the metabolic section understudy at different ends. One possibility, as used byTrethewey and ap Rees (1994) to study the con-version of starch to sucrose in darkened leaves, isto supply glucose and glycerol, one of which islabelled. Suppose the glucose is labelled with afractional enrichment fGlc. Assuming bothmetabolic and isotopic steady-state for the hexosephosphate and triose phosphate pools, a simplecalculation (as presented in Appendix A) usingthe metabolic scheme in Fig. 2 gives the fractionalenrichments for hexose phosphate, fHexP, and fortriose phosphate, fTriP:

fHexP=a(6T+61) and fTriP=a61 with

a= fGlc

6H6H6T+6H61+6T6-1

(1)

fHexP and fTriP can be determined from measure-ments on a metabolite that is derived exclusivelyfrom the relevant pools. In selecting a suitablemetabolite, it is important that the measured pooldoes not contain molecules that were synthesisedbefore the labelling had reached steady-state.


Knowing fGlc, fHexP and fTriP, it is possible tocalculate the flux ratios:

616T

=fTriP

fHexP− fTriP

and6-16H

=fGlc− fHexP

fHexP− fTriP

(2)

However, the determination of the ratio (or abso-lute values) of the forward and backward fluxbetween hexose phosphates and triose phosphates(61 and 6-1, respectively) requires supplementaryinformation, namely the ratio between (or theabsolute values of) the influx 6H into the hexosephosphate pool and the influx 6T into the triosephosphate pool. These parameters can be ob-tained by studying the uptake of label from eitherglucose or glycerol. However, these two feedingexperiments can give additional information thatallows a more robust determination of 6-1/61. Bydetermining the proportion of label supplied viaglucose that enters a given hexose phosphatederived metabolite, say sucrose, LHexP�Suc, andthen doing the same for label provided via glyc-erol, giving LTriP�Suc, then, as argued byTrethewey and ap Rees (1994), the ratio:

LTriP�Suc

LHexP�Suc

=6-1

6-1+6G=

6-161+6T

(3)

gives the proportion of flux out of triose phos-phates, which flows into hexose phosphates. If6T�61 can be assumed, e.g. if the cells are hexose-fed and glycerol is only used as a tracer in verylow concentration, then this ratio provides a di-rect measure for 6-1/61. Otherwise Eqs. (1) and (3)have to be combined:

6-161

=LTriP�Suc

LHexP�Suc

fHexP

fTriP

(4)

Unfortunately, measurements of LHexP�Suc andLTriP�Suc alone do not provide information onthe relation between 6H and 6T or between 61 and6-1, and thus cannot be used to estimate therelative rates of export of three-carbon and six-carbon intermediates from the chloroplast in thedark as attempted by Trethewey and ap Rees(1994). Note that the metabolic assumptions madefor the measurement of the fractional enrichmentsfHexP and fTriP, namely that the measured metabo-lite pool (e.g. sucrose) is in isotopic equilibriumwith the source pool (e.g. hexose phosphates) and

that there is no unlabelled fraction that existedfrom before the labelling experiment, are not nec-essary for measuring LHexP�Suc and LTriP�Suc. Inthe latter case, the only requirement is that theconditions in the two labelling experiments areidentical, and that 6T�61 if the fractional enrich-ment information is not used.

The second possible approach involves feedingwith positionally labelled substrate. This has beenexploited by several groups to measure the fluxbetween hexose phosphates and triose phosphatesand to determine the substrate for starch synthesisin different heterotrophic plant tissues or cell cul-tures. The studies have generally used NMR todetect the positional redistribution of label afterincubation with [1-13C]- or [6-13C]-glucose (Keel-ing et al., 1988; Viola et al., 1991; Dieuaide-Noub-hani et al., 1995; Kosegarten et al., 1995; Krooket al., 1998), although in one study, analysis wasrestricted to the proportion of label that wasrecovered in triose moieties derived from the firstthree and last three carbon atoms of hexose afterlabelling with [1-14C]- or [6-14C]-glucose (Hatzfeldand Stitt, 1990). The analysis of the labelling canbe done using the flux model of Fig. 2, butassuming negligible influx into triose phosphates(6T=0). However, instead of balancing only theinflux and efflux of label for each intermediarymetabolite at steady-state, it is now necessary todo this for each carbon position of the intermedi-ary metabolites. The relevant atoms are carbons 1and 6 of hexose phosphates and carbon 3 of triosephosphates as the other carbons cannot be la-belled in this simple metabolic scheme. The calcu-lation assumes that the reaction catalysed bytriose phosphate isomerase is very rapid. If thiswere not the case, it would be necessary to incor-porate it explicitly into the metabolic scheme.From this scheme, the expected fractional enrich-ments fHexP

C1 , fHexPC6 and fTriP

C3 can then be calculatedas a function of the fluxes and the fractionalenrichments fGlc

C1 or fGlcC6 of the substrate (see Ap-

pendix A for details). Eliminating fTriPC3 , this

leaves:

fHexPC1 =

6-1 fHexPC6 +26H fGlc

C1

26H+6-1and


fHexPC6 =

6-1 fHexPC1 +26H fGlc

C6

26H+6-1(5)

Eq. (5) can be transformed to:

6-16H

=2fHexP

C6 − fGlcC6

fHexPC1 − fHexP

C6 =2fHexP

C1 − fGlcC1

fHexPC6 − fHexP

C1 (6)

This corresponds to Eq. (2) found for the two-substrate labelling, as can be seen by insertinginto it the expression:

fTriPC3 =

12

( fHexPC1 + fHexP

C6 ) (7)

Again, supplementary information about absolutefluxes is necessary for the determination of 6-1/61.

The first advantage of this method over thetwo-substrate feeding experiment is that it is notnecessary to create the relatively unusual situationin which there is an appreciable influx (6T) at thetriose phosphate level. However, the second andmain advantage is that it is not necessary tomeasure fractional enrichments, but only the rela-tive amounts of label in positions 1 and 6 ofhexose phosphates if fGlc

C6 or fGlcC1 can be neglected

or approximated. For this, the first form of Eq.(6) is used when feeding C1-labelled glucose andthe second when feeding C6-labelled glucose asthe required parameter is then very small. Indeed,it would be zero when feeding 14C-labelled glu-cose, since [1-14C]-glucose, for example, shouldnot contain any 14C in position 6. However,Hatzfeld and Stitt (1990) found that this is notentirely true for commercially available com-pounds. In contrast, 13C-compounds are availablewithout noticeable contamination due to theirsynthesis. However, they do contain the 1.1%natural abundance of 13C in the unlabelled posi-tions, but this can be taken into account in vari-ous ways with sufficient accuracy, e.g. bydetection of the NMR signals from the unlabelledcarbons 2–5. After this correction, there is noproblem if either the measured metabolite (e.g.starch) contains a high level of natural-abundancematerial or if the influx of label is diluted to anunknown extent by endogenous substrate lower-ing the fractional enrichment of the labelled posi-tion, fGlc

C1 or fGlcC6 . The main drawback of the

positional labelling technique is that it does notreally detect the flux from hexose phosphates to

triose phosphates and back, but the cyclic fluxhexose phosphate to glyceraldehyde 3-phosphateto dihydroxyacetone phosphate to hexose phos-phate or vice versa, and this only allows a directquantification of the flux between hexose andtriose phosphates if the triose phosphate iso-merase has a very high activity. This is oftenassumed but is more difficult to verify. Finally,note the symmetry of the results regarding C1- orC6-labelling reflecting the symmetry of themetabolic network under consideration.

The third type of labelling experiment, namelybond-labelling, has not yet been used for elucidat-ing flux between hexose phosphates and triosephosphates in plants. The cleavage of hexosephosphates to triose phosphates results in therupture of the chemical bond between carbons 3and 4. If a proportion pf (typically pf�10%(Szyperski, 1995)) of fully labelled [U-13C6]-glu-cose is fed with the remaining 1−pf being unla-belled glucose (but containing 13C at naturalabundance), then any labelled triose phosphatethat reforms a hexose phosphate molecule has aprobability 1−pf of doing so with an unlabelledtriose phosphate resulting in a hexose phosphatein which only one moiety is labelled. It is thusnecessary to detect the relative amounts of fullylabelled hexose phosphates and hexose phos-phates with only one labelled moiety. This can bedone either by MS or by NMR, and the analysisof the results depends on the detection method.Note that this bond-labelling technique detectsthe cleavage of the C3–C4 bond by aldolasewithout the need for equilibration of label bytriose phosphate isomerase demanded by the posi-tional labelling technique.

MS detects hexose phosphate derived hexoseunits with either six 13C-atoms, fHexP

6C , or with onlythree 13C-atoms, fHexP

3C . Since the probability offinding three 13C-atoms from natural abundancein the same hexose is very low (2.6×10−5) andcan be ignored, the detected fractions are (seeAppendix A for a detailed derivation):

fHexP6C =

pf6H+p f26-1

6-1+6Hand

fHexP3C =

2pf(1−pf)6-16-1+6H

(8)


Note that the factor of 2 in the expression forfHexP

3C occurs because it comprises molecules la-belled in either triose moiety. Eq. (8) can betransformed into:

6-16H

=pf− fHexP

6C

fHexP6C −p f

2=fHexP

3C

2pf(1−pf)− fHexP6C

=fHexP

3C

2fHexP6C −pf(2fHexP

6C + fHexP3C )

(9)

The latter form of this expression does not dependon the absolute values of fHexP

6C and fHexP3C but only

on their ratio, as is the case for Eq. (6) if naturalabundance can be neglected.

NMR allows determination of the relative pro-portions of a given labelled carbon atom, e.g. C4,attached to either a labelled C3, f [C4]HexP

C3 or anunlabelled C3, (1− f [C4]HexP

C3 ). The relative isoto-pomer populations containing a (3-13C, 4-13C) ora (3-12C, 4-13C) fragment are thus measured. Sincethe presence of only one neighbouring atom isdetected, natural abundance pn=0.011 cannot beneglected. With an overall 13C-abundance of:

p1=pf+ (1−pf)pn (10)

the proportion of labelled C3–C4 bonds (relativeto the proportion p1 of molecules containing aC4-label) can then be calculated (see Appendix Afor details):

f [C4]HexPC3 =

(pf+ (1−pf)pn2)6H+p1

26-1p1(6H+6-1)

(11)

This equation can be transformed to give:

6-16H

=pf+ (1−pf)pn

2−p1 f [C4]HexPC3

p1 f [C4]HexPC3 −p1

2 (12)

This is the same expression as obtained with MSexcept that pn is not negligible and except for thefactor 2 in Eq. (9). Note that pn could be reducedto zero by using [U-12C6]-glucose as source ofunlabelled glucose (Rinehart et al., 1982). How-ever the associated cost would seem rather highfor the simplification gained. With respect toNMR detection, it is important to note that thebond-labelling technique was originally proposedwith the labelling analysis of amino acids in mind(Szyperski, 1995). In contrast to amino acids,sugars have a less favourable spread of 13C chem-

ical shifts, and it is not always possible to avoidstrong coupling effects. C4 is more favourablethan C3 in this respect, so the example above isbased on the detection of C4. In fact strongcoupling can safely be neglected for the C4 ofb-glucose at magnetic fields as low as 4.7 T,whereas a field of at least 7.0 T is advisable forthe first-order analysis of the C4 resonance of theglucosyl moiety of sucrose, and 8.5 T for thefructosyl moiety. A still higher field is required forthe analysis of the C3 of the main fructoseanomer, the b-pyranose form, and C4 will bestrongly coupled to C5 at even the highest fields.Incidentally, the near degeneracy of the carbon-carbon coupling constants is a further complicat-ing factor in the analysis.

A comparison of the different labelling tech-niques shows that the result is always of the form:

6-16H

=ax

b−xwhere x=

redistributed labeloriginal label

(13)

This equation holds regardless of the actual na-ture of the label, as long as signal from naturalabundance is neglected. Clearly, the accuracy ofthe result is greatest when x is large enough to bedetectable without gross error, but not too close

Fig. 3. Dependence of the flux ratio 6-1/6H on the ratio ofredistributed label over original label (Eq. (13)), here given asratio of fractional enrichments fHexP

C6 /fHexPC1 measured after

incubation with C1-labelled glucose. The interval lines showhow the error in flux ratio obtained from a constant absoluteerror in the measured ratio of fractional enrichments, increaseswith increasing label redistribution.


to its asymptotic value b (Fig. 3). In the lattercase, the exchange flux dominates the influx intohexose phosphates, equilibrating the hexose phos-phate and triose phosphate pools, and leading toa situation where the exact flux value is hard todetermine. Whenever such a situation occurs, themain interest is to know that the exchange fluxbetween the pools is much higher than the net fluxthrough them, but it is rarely necessary to knowthe exact numbers. Such would be the case forexample, if substrate for starch synthesis wereimported into the plastid only via the triose phos-phate translocator, in which case the label instarch would be completely redistributed.

2.3. Influence of the pentose phosphate pathwayon flux measurements between hexose phosphatesand triose phosphates

All three labelling methods discussed in theprevious section would seem to be suitable for thetask of measuring flux between hexose phosphatesand triose phosphates in plants, although theNMR-detected bond-labelling may pose problemsdue to strong coupling effects and degeneracy ofcoupling constants. However, as generally recog-nised by the researchers who have used positionallabelling techniques, the pentose phosphate path-way and its influence on label redistribution can-not be neglected a priori. This pathway cancontribute in several ways to the labelling ob-served after feeding a positionally labelled sub-strate (Fig. 4). First, there is the possibility ofcyclic flux through the oxidative pentose phos-phate pathway in order to provide reducingequivalents. In this case, all the C1 atoms fromglucose 6-phosphate entering the pathway are lostas CO2, whereas one out of every three C6 atomsis directly recycled into the C6 of fructose 6-phos-phate. The two remaining C6 atoms are incorpo-rated as glyceraldehyde 3-phosphate in the C3position of triose phosphates. One triose phos-phate is then used by the transaldolase reaction toreform a second molecule of fructose 6-phos-phate. Secondly, the transaldolase reaction alsolinks the C6 of hexose phosphates with the C3 oftriose phosphates via a simple forward–backwardexchange reaction that leaves the C1 of hexose

Fig. 4. Metabolites and fluxes relevant for labelling analysis offluxes between hexose phosphates and triose phosphates in-cluding the fluxes through the oxidative pentose phosphatepathway. (A) The flux topology: 6oppp, cyclic oxidative fluxfrom hexose phosphates to pentose phosphates, from there inthree branches to the hexose and triose phosphate pools withrecycling of one of the triose phosphates to hexose phosphate;6noppp, cyclic flux through the non-oxidative reactions, startingfrom hexose and triose phosphates through all branches topentose phosphates and back; 6TA, exchange flux catalysed bytransaldolase, from hexose phosphates to triose phosphatesand back; 6E4P, recycling of a triose phosphate to hexosephosphate during net synthesis of erythrose 4-phosphate; otherfluxes as in Fig. 2. (B) The flux stoichiometry: nC designatesn-carbon sugar phosphates (glucose- and fructose 6-phos-phate, 6C; ribulose-, ribose- and xylulose 5-phosphate, 5C;sedoheptulose 7-phosphate, 7C; erythrose 4-phosphate, 4C;glyceraldehyde 3-phosphate, 3C).

phosphates unaffected. Thirdly, cyclic fluxesaround the reversible non-oxidative section of thepentose phosphate pathway can rearrange label inthe following fashion:

2 HexP C1�HexP C1+HexP C3;

2 HexP C6�2 TriP C3;

3 TriP C3�TriP C3+2 HexP C6.

Finally, the pentose phosphate pathway can act ina non-cyclic form fed by either the oxidative orthe non-oxidative end in order to provide ribose5-phosphate for nucleotide synthesis or erythrose


4-phosphate for synthesis of aromatic com-pounds. Synthesis of the former only contributesto the total efflux from the hexose phosphate andtriose phosphate pools and thus does not affectthe labelling other than through the concomitantincrease in 6H. Synthesis of erythrose 4-phosphatevia the oxidative reactions consumes two glucose6-phosphate molecules of which one is recycled.Label in C1 is lost as CO2, while one of the C6atoms goes into erythrose 4-phosphate and theother enters the triose phosphate pool, which inturn is the source of the C6 for the recycledfructose 6-phosphate. In contrast, from the non-oxidative direction, the transketolase reactiontransforms one fructose 6-phosphate and onetriose phosphate into one erythrose 4-phosphateand one xylulose 5-phosphate. The latter can thenbe epimerised and isomerised into ribose 5-phos-phate for nucleotide synthesis. Otherwise, threeerythrose 4-phosphate molecules can be synthe-sised from two fructose 6-phosphate and twotriose phosphate molecules, concomitantly recy-cling one fructose 6-phosphate in the same way asin the oxidative reaction.

From this information rather complex expres-sions can be calculated for the fractional enrich-ments fHexP

C1 and fHexPC6 :

fHexPC1 =

6H fGlcC1 +

1+a2+a

6-1 fHexPC6

6H+236oppp+6E4P+

1+a2+a

6-1

and

fHexPC6 =

6H fGlcC6 +

12+a

(6-1+6ex)fHexPC1

6H+1

2+a(6-1+6ex)

with 6ex=136oppp+6TA+6E4P+6noppp and

a=6ex+

136oppp

61(14)

where 6oppp denotes the cyclic oxidative pentosephosphate pathway flux, 6TA the flux of thetransaldolase exchange reaction, 6noppp the cyclicflux in the non-oxidative pentose phosphate path-way (all expressed in hexose equivalents flowing

into the respective pathways) and 6E4P the rate ofre-synthesis of fructose 6-phosphate during netsynthesis of erythrose 4-phosphate. Note that thiscalculation does not take into account recycling oflabel from C3 to C1 in the operation of thenon-oxidative pentose phosphate cycle. If 6noppp istoo large for this simplification, as can be inde-pendently judged from the redistribution of labelfrom C1 to C3, then it actually becomes necessaryto make label balances for all carbon atoms asthey are all interconnected by these differentfluxes.

Eq. (14) shows that the symmetry between fHexPC1

and fHexPC6 is lost due to the asymmetric structure

of most of the reactions associated with the pen-tose phosphate pathway. Asymmetry between theredistribution of C1 and C6 label in hexose phos-phates thus indicates the presence of at least oneof these reactions but it is not sufficient for quan-tification in the way attempted by Hatzfeld andStitt (1990) since too many unknown parametersare involved. Without further information, it isonly possible to determine: (i) an aggregate rela-tive recycling flux, (6-1+6ex)/((2+a)6H), from theanalysis of label redistribution from C1 to C6;and (ii) the parameter ((1+a)6-1)/((2+a)(6H+2/36oppp+6E4P)) from the analysis of label redistri-bution from C6 to C1, provided fGlc

C1 can beneglected or 2/3 6oppp+6E4P�6H. These measure-ments allow variations in the recycling flux to beassessed under different conditions but they donot provide true relative fluxes. It is neverthelessinteresting to note that 6TA, 6E4P and vnoppp lead toa higher label redistribution from C1 to C6 com-pared to the redistribution from C6 to C1 pro-vided that there is a net glycolytic flux, 6-1B61.Under most but not all flux conditions, 6oppp hasthe same effect. In addition to the reactions of thepentose phosphate pathway, there are furthercomplications, including sucrose cycling(Dieuaide-Noubhani et al., 1995), incomplete ran-domisation between glucose 6-phosphate andfructose 6-phosphate by glucose 6-phosphate iso-merase and the effects of compartmentation be-tween the cytosol and the plastid (see below). Onthe whole, the system is underdetermined andneeds additional information to elucidate all thefluxes that contribute to the labelling pattern. This


information can be derived either from the la-belling of other metabolites, or from other la-belling experiments (e.g. with [2-13C]-glucose,which is particularly suited for examining theoxidative pentose phosphate pathway), or fromflux balancing.

Additional labelling information is automati-cally obtained when NMR is used to detect iso-topic labelling. First, there is the informationfrom other atoms derived from hexose phosphate(e.g. C3 as mentioned above), and secondly, aspectrum from an unfractionated cell extract canprovide labelling information not only for solublesugars but also for a range of metabolites linkedto primary metabolism, essentially amino acidsand organic acids but potentially also abundantsecondary metabolites. Thus, NMR detected posi-tional 13C-labelling is able to provide much moreinformation for a given experimental effort thanmixed substrate labelling or the use of other de-tection techniques for positional labelling, and itbecomes the preferred technique for analysing thefluxes in large metabolic networks. Bond-labellinggives comparable and even supplementary infor-mation (e.g. about transketolase catalysed fluxes(Szyperski, 1995)). Its drawbacks are mainly theproblem of quantifying the (potentially strong)13C–13C couplings in the crowded spectral regioncontaining most of the sugar resonances in thecase of NMR detection, and the need for goodchemical separation and identification if analysinga crude cell extract by MS.

2.4. Deri6ing fluxes from obser6ed labelling in acomplex network

The multiple labelling information derived fromthe analysis of different metabolites has to beinterpreted in terms of fluxes. The first step is towrite the isotope balance equation for each car-bon atom in every metabolite that can be synthe-sised from at least two differentially labelledprecursors. However in full metabolic networks,the number of different routes from the substrateto a given metabolite is enormous since one ex-change reaction or metabolic cycle at any point inthe network can add a possible route. Manualanalysis in the way used above quickly becomes

too laborious and error prone, and it is necessaryto resort to a more formal analysis. A convenientapproach is to use atom mapping matrices whichdescribe the transfer of carbon atoms from theirposition in a substrate to their new position in aproduct for each reaction in the metabolic net-work (Zupke and Stephanopoulos, 1994). Theycan be readily expanded to produce isotopomermapping matrices describing the transformationof any given combination of substrate isoto-pomers into product isotopomers (Schmidt et al.,1997). These matrices only have to be establishedonce, and then they can be used with metabolicnetworks of different topology. After choosing anetwork topology, the balance equations for eachmetabolite are established by hand or in an auto-mated fashion (Wiechert and de Graaf, 1997;Wiechert et al., 1997). The matrix formalism thenallows the automatic calculation of the carbonisotope or isotopomer balances. Thus, in contrastto an unformalised carbon-by-carbon analysis,this approach allows changes in the network to-pology or the trial of different topologies withoutcomplete recalculation.

The balance equations describe a bilinear rela-tion between the fluxes and the fractional enrich-ments or the isotopomer distributions. They canbe used to calculate the expected fractional en-richments or isotopomer distributions for a givenflux state in a labelling experiment. This computa-tion is rather straightforward and can be used formetabolic simulations (Wiechert and de Graaf,1997). Conversely, the balance equations can givethe flux distribution from a known set of frac-tional enrichments or isotopomer distributions.This is certainly of more practical interest but it iscomputationally more demanding and needs pre-cautions. The most obvious approach to this cal-culation is to measure a set of fractionalenrichments that corresponds exactly to the num-ber of undetermined fluxes. These enrichments,together with the relevant balance equations,which must be linearly independent, form a sys-tem of linear equations that can be solved. Inplants, this has only been done for maize root tips(Dieuaide-Noubhani et al., 1995). These authorsactually reduced the dimension of the system tobe solved by dividing the network into several


subnetworks, some of which are treated sepa-rately. The drawback of this approach is that itdoes not take into account the precision in themeasured fractional enrichments. Some of thefractional enrichments can indeed play a pivotalrole, and small errors in these numbers can inducelarge errors in the resulting fluxes, whereas otherfractional enrichments may be less informative.This suggests that it would be useful to attempt asensitivity analysis in order to choose the set offractional enrichments that gives the most robustflux measurement.

An alternative and more rewarding approach isto exploit one of the strengths of NMR, namelythe large number of fractional enrichments andisotopomer distributions that can be determinedfrom the same experiment. This extra informa-tion, although in some cases quite imprecise, al-lows a large overdetermination of the flux system.The idea is then to resort to a non-linear, leastsquares fitting procedure that tries to iterate theflux distribution until finding the one that pro-duces fractional enrichments and isotopomer dis-tributions that are in closest agreement with theexperimental results. This procedure allows theinclusion of further constraints, e.g. limiting a fluxto a value consistent with enzyme activity mea-surements. It also opens the possibility of using amixture of fractional enrichment and isotopomerdistribution data for determining fluxes. However,the calculation of fractional enrichments and thefitting of fluxes by this method require somecomputational precautions as analysed in detailby Wiechert et al. (1997). In particular, it is usefulto transform the forward and backward flux co-ordinates of an exchange reaction into net fluxand exchange flux co-ordinates, and then torescale the exchange flux to avoid numerical prob-lems resulting from very high exchange fluxes(Wiechert and de Graaf, 1997). The non-linearfitting procedure then allows for a detailed errorand sensitivity analysis of the results (Wiechert etal., 1997) which is necessary for establishing notonly the precision of the results but also theiraccuracy. The analysis of labelling studies involv-ing a large set of metabolic fluxes, especially inplants with their more complex metabolism com-pared to prokaryotes, would certainly profit fromsuch a formalised computer-aided procedure.

2.5. Labelling strategies in photosynthetic andnon-photosynthetic plant tissues

Metabolism in higher plants can be broadlydivided into three categories: autotrophicmetabolism in photosynthetic tissues in the light,heterotrophic metabolism in the same tissues inthe dark, and heterotrophic metabolism in thenon-photosynthetic tissues (roots, flowers, seeds,etc.). The implications of these three types ofmetabolism for studies of metabolic flux by la-belling techniques are considered in the followingparagraphs.

In non-photosynthetic tissue, metabolism de-pends on provision of substrate, usually sucrose,by the leaves. It follows that 13C-labelling experi-ments can be performed by simply cutting off thesupply of carbohydrate from the leaves (e.g. byexcision of the studied tissue) and replacing it byan exogenous supply of labelled substrate. Al-though sucrose is the standard translocated sugar,it can be replaced by labelled glucose or fructosesince sucrose is cleaved by cell-wall bound inver-tases into glucose and fructose in many tissues,and then imported by hexose transporters or sim-ple diffusion. Feeding labelled glucose or fructosehas the advantages of commercial availability anda simpler analysis since there is the uptake of onlyone labelled substrate. The other hexose can begiven at natural abundance if necessary (Krook etal., 1998), although at the expense of label dilu-tion and with the need to account for a furtherunknown flux.

The metabolism of photosynthetic tissue in thedark relies on the degradation of accumulatedphotosynthate, mainly sucrose in the cytosol andvacuole, and starch in the chloroplasts. Labellingexperiments requiring high initial fractional en-richments, especially positional labelling experi-ments with stable isotopes, are thus only feasibleafter the tissue has been depleted of the reservesaccumulated during the photoperiod. Themetabolic situation when the starved tissue issubsequently supplied with labelled sugar is notexactly the same as in a normal dark period:during labelling, the carbohydrate enters the cyto-sol, is phosphorylated and then partly transferredto the chloroplasts; whereas under normal condi-


tions chloroplasts are net exporters of glucose,maltose, triose phosphates and sometimes alsohexose phosphates (Emes and Neuhaus, 1997).Labelling experiments that require only relativelylow fractional enrichments (e.g. positional la-belling or mixed substrate labelling with radioac-tive isotopes, bond-labelling with stable isotopes)can be performed with unstarved photosynthetictissue in the dark. The labelled substrate has to besupplied with a high enrichment that is subse-quently diluted by the endogenous reserves. How-ever, the dilution proceeds in an uncontrolledfashion and can come from different sources. Thelabelled and unlabelled material enter metabolismat different points with unknown fluxes, and thiscomplicates the data analysis considerably.

Photosynthesis relies on CO2 as the only carbonsubstrate, and steady-state positional labellingwith a one-carbon substrate is impossible. How-ever, dynamic positional labelling by supplying13CO2 is feasible (Schaefer et al., 1980; Bartlett etal., 1989; Ito and Mitsumori, 1992), since the 13Cwill first be fixed in specific positions during theoperation of the Calvin cycle, and analysing thelabelling time courses allows the determination ofmetabolic fluxes. An alternative to labelling viathe CO2 supply is to feed the tissue with a posi-tionally or bond-labelled substrate at high enrich-ment that will be diluted by ongoingphotosynthetic carbon fixation (Ito and Mit-sumori, 1992). This situation is comparable to thelabelling of unstarved photosynthetic tissue in thedark, and is naturally encountered in meristematicleaf tissue that cannot yet fulfil all its carbonrequirements by photosynthesis and needs to im-port some carbohydrate.

Working with whole plants, Schaefer et al.(1975) found an ingenious way to use photosyn-thetic bond-labelling for analysing metabolism inthe sink tissue. They exposed only one trifoliolateleaf of an intact soybean plant to 13CO2, and theresulting bond-labelled sucrose was then dilutedin the sink tissue, the developing ovule, by unla-belled sucrose from other leaves. This createdconditions for studying ovule metabolism, in par-ticular the importance of the pentose phosphatepathway during lipid synthesis, by analysing thelabelled bonds.

A variation of this experiment, using temporalinstead of spatial separation of 12CO2 and 13CO2

feeding, could also be used to analyse themetabolism of photosynthetic tissue in the darkby bond-labelling of endogenous sources. Forthis, the plant has to be supplied with 13CO2

during just a part of the photoperiod resulting inthe formation of reserves containing a mixture oflabelled and unlabelled material. Triose phos-phates formed during photosynthesis would essen-tially be fully labelled after a few turns of theCalvin cycle following the switch to 13CO2. Thisisotopic equilibration time should be sufficientlyshort for bond-labelling (Schaefer et al., 1975).Depending on the carbohydrate status at the startof the labelling period, the C3-C4 bond in sucrosewould not necessarily be fully labelled due toturnover of sucrose and the hexose phosphate-triose phosphate cycle. In contrast, the same bondin chloroplastic starch should become labelled tothe same extent as the triose phosphate bonds.However, during the mobilisation of the reserves,the proportion of labelled over unlabelled mate-rial might vary with time since starch is depositedin granules so that the most recently depositedmaterial will be mobilised first. It might thus benecessary to alternate periods of 13CO2 and 12CO2

supply that are long enough to allow for isotopicequilibration of the Calvin cycle but short enoughto allow for a constant proportion of labelledmaterial during starch breakdown.

In conclusion, while metabolism in hetero-trophic plant tissue can be analysed by feeding asuitable isotope labelled substrate (usually glucoseor fructose), this type of analysis is more difficultin photosynthetic tissue and needs moreprecautions.

2.6. Impact of metabolic compartmentation on theinterpretation of labelling experiments

Compartmentation is an integral aspect ofplant metabolism (ap Rees, 1988), and conse-quently transport of intermediates between thedifferent compartments needs to be included inthe metabolic network. Similar considerations ap-ply to animal cells, but the only non-cytosolicsection of carbon metabolism that is usually con-


sidered in current models of mammalianmetabolism is the tricarboxylic acid cycle in themitochondria. This pathway is linked to cytosoliccarbon metabolism by import of pyruvate andexport of malate and citrate (Mancuso et al.,1994). However, provided that cytosolic pyruvateis the only precursor for mitochondrial pyruvate,and that mitochondrial malate and citrate are theonly precursors for the respective cytosolic poolsof these intermediates, then compartmentationhas no influence on label redistribution within themetabolites. Thus each metabolite may be consid-ered to be in a single pool, and there is noinformation on compartmentation.

However, metabolism in plants has greater re-dundancy and is more highly compartmentedthan in other organisms. Thus, for example, thereare alternative routes for the synthesis of two ofthe organic acids considered above. Cytosolicmalate may originate from the mitochondrial poolor be synthesised directly in the cytosol fromphosphoenolpyruvate (PEP) using PEP carboxy-lase and malate dehydrogenase. Similarly, mito-chondrial pyruvate can be derived directly fromthe cytosolic pool, or be synthesised from mito-chondrial malate by malic enzyme. The availableevidence suggests that fluxes through these addi-tional pathways of malate and pyruvate produc-tion are significant in plants (Bryce and ap Rees,1985; Hill, 1997). Since these alternative routesresult in differences in the distribution of labelwithin both pyruvate and malate, it is not permis-sible to consider either metabolite as forming asingle metabolic pool within a plant cell.

A far greater problem is presented by the dupli-cation of all, or nearly all, of the enzymes ofglycolysis and the oxidative pentose phosphatepathway in the cytosol and plastids (ap Rees,1985). This means that many plant cells are ableto oxidise carbohydrates by two distinct, spatiallysegregated glycolytic and pentose phosphate path-way sequences. In heterotrophic cells, these path-ways can communicate by the exchange of hexosephosphates as well as various three-carbon phos-phate esters. Even if hexose phosphate exchange isconfined to a unidirectional import into the plas-tid, usually in the form of glucose 6-phosphate,but also glucose 1-phosphate and ADPglucose in

some tissues (Emes and Neuhaus, 1997), thencytosolic and plastidic hexose phosphates have tobe considered as separate pools since plastidichexose phosphate molecules could be derivedfrom both import and the reactions of the plas-tidic pentose phosphate pathway. The corollary ofthe subcellular organisation of the pathways ofcarbohydrate oxidation is that flux through gly-colysis and the oxidative pentose phosphate path-way must be determined separately for thecytosolic and plastidic pathways in cells in whichthe subcellular distribution of the enzyme activi-ties indicate that both compartments have thecapacity to catalyse these pathways.

Distinguishing between fluxes through parallelcytosolic and plastidic pathways requires metabo-lites that are confined to one compartment andare amenable to labelling analysis. At the hexoselevel, the obvious candidates are sucrose andstarch. Although starch, as a storage polymer,presents some problems for analysis (see below),the analysis of label redistribution in thesemetabolites can give the desired information onthe flux through the oxidative and non-oxidativesections of the pentose phosphate pathway rela-tive to glycolysis. The difference in labelling dueto different flux ratios in the two compartmentswill however be attenuated if there is an apprecia-ble exchange of hexose phosphate via the hexosephosphate transporter instead of just a unidirec-tional import into the plastid.

To appreciate this effect, consider a simplifiedmetabolic scheme in which C2-labelled glucosecontaining no natural abundance of label isotopeis fed. Activity of the cyclic oxidative pentosephosphate pathway redistributes 2/3 of the labelfrom C2 into C1 and one third into C3. For theclarity of the argument, suppose that in this par-ticular network, as shown in Fig. 5, all the label isredistributed from C2 to C1, and a subsequentpassage through this cycle releases the label, nowin C1, as CO2. The label is analysed in the hexoseunits of starch and sucrose since these metabolitesreflect the labelling of the hexose phosphate poolsfrom which they were derived.Solving the balance equations gives the fractionalenrichments:


fSucC2 = f c-HexP

C2 =6H fGlc

C2 +6ex fp-HexPC2

6c-in

=6p-in6H fGlc

C2

6c-in6p-in− (6net+6ex)6ex

=6ex=0 6H fGlc

C2

6H+566c-oppp

(15)

fStarchC2 = fp-HexP

C2 =(6net+6ex)f c-HexP

C2

6p-in

=(6net+6ex)6H fGlc

C2


=6ex=0

6H6net fGlcC2�

6H+566c-oppp

��6net+

566p-oppp

� (16)

fSucC1 = f c-HexP

C1 =6c-oppp f c-HexP

C2 +6ex fp-HexPC1

6c-in

=6p-in6c-oppp f c-HexP

C2 +6ex6p-oppp fp-HexPC2


=6ex=0

6c-oppp6H fGlcC2�

6H+566c-oppp

�2 (17)

fStarchC1 = fp-HexP

C1 =6p-oppp fp-HexP

C2 + (6net+6ex)f c-HexPC1

6p-in

=6c-in6p-oppp fp-HexP

C2 + (6net+6ex)6c-oppp f c-HexPC2


=6ex=0

6H6net fGlcC2�

6H+566c-oppp

��6net+

566p-oppp

�: 6c-oppp

6H+566c-oppp

+6p-oppp

6net+566p-oppp

;(18)

as a function of the fluxes across the plastidenvelope, the cyclic fluxes through the cytosolicand plastidic oxidative pentose phosphate path-way, 6c-oppp and 6p-oppp, respectively, and theinfluxes into the two compartments: 6c-in=6H+6ex+ (5/6)6c-oppp and 6p-in=6net+6ex+ (5/6)6p-oppp.Note that the fraction of 5/6 occurs because onecarbon is lost from each hexose phosphate enter-ing the oxidative pentose phosphate cycle. Thiscarbon loss has to be compensated by the fluxes6H and 6net, respectively. The flux of hexose phos-phate over the plastid envelope is split into a netflux, 6net, and an exchange flux, 6ex, in order tohighlight the influence of a bidirectional exchangeof hexose phosphate on the fractional enrich-ments. Indeed, as is shown in Fig. 6, the effect of6ex is to draw the fractional enrichments of cyto-solic and plastidic hexose phosphate closer to-gether until they converge asymptotically. It iseasily proven that a non-zero flux through theplastidic oxidative pentose phosphate pathway,6p-oppp\0, always results in the inequalities:

fp-HexPC2 B f c-HexP

C2 andfp-HexP

C1

fp-HexPC2 \

f c-HexPC1

f c-HexPC2 (19)

However, there is no similar relationship betweenfp-HexP

C1 and f c-HexPC1 as can be seen from the crossing

lines for these enrichments in the inset of Fig.6(E). Furthermore, it can be shown that while thefour measurable fractional enrichments allow anunambiguous determination of fluxes 6c-oppp and6ex relative to 6H, the ratio of 6p-oppp to 6net+6ex isoverdetermined, as can be seen from the twolinearly independent expressions for it:

6p-oppp

6net+6ex

=f c-HexP

C2

fp-HexPC2

�fp-HexPC1

fp-HexPC2 −

f c-HexPC1

f c-HexPC2

�and

Fig. 5. Compartmented carbohydrate flux between the plantcytosol and plastid. The flux between the cytosolic hexosephosphate pool, c-HexoseP, and the plastidic hexose phos-phate pool, p-HexoseP, across the plastid envelope is split intoa net import flux, 6net, and a bidirectional exchange flux, 6ex.The flux through the compartmented pentose phosphate path-way, for which only a simplified cyclic oxidative scheme isconsidered, 6c-oppp and 6p-oppp, leads to redistribution of labelfrom the C2-position of hexose into the C1-position, and fromthe C1-position into CO2. Cytosolic hexose phosphate unitsare incorporated into sucrose, and plastidic ones into starch.


Fig. 6. Influence of the exchange flux across the plastid envel-ope, 6ex, on the label redistribution in the metabolic scheme ofFig. 5 during incubation with C2-labelled glucose. The chosenparameters are: 6H=1.0 and 6net=0.5, with 6c-oppp=6p-oppp

=0.1 in the left-hand panels (A–C), and 6c-oppp=6p-oppp=1.0in the right-hand panels (D–F). The upper two panels (A, D)show the fractional enrichments in the C2-position of hexosephosphates, f C2, the middle ones (B, E) the fractional enrich-ments in the C1-position, f C1, and the lower panels (C, F) givethe ratio f C1/f C2. The solid lines represent the cytosolic pooland the dashed lines the plastidic pool. Note that the relationsof Eq. (19) are fulfilled for the upper and lower panels,whereas the lines in panel E cross, as highlighted in the insert.

metabolic flux network containing the actual la-belling pathways, even though the relations be-tween fractional enrichments and relative fluxesare then far more complex and therefore moreeasily analysed in a formalised way as advocatedabove.

In contrast to 6ex, 6net cannot be related to vH;so it is not possible to compare the fluxes in thecytoplasmic and the plastidic oxidative pentosephosphate pathway. In fact, 6net+6ex plays thesame reference role for the plastid as 6H for thewhole cell. The problem is that, whereas the abso-lute value of 6H can be determined relatively easilyby measuring the uptake of substrate, this is muchmore difficult for the plastid in situ. 6net can onlybe assessed by metabolic flux balancing, using thefluxes into end products of plastidic metabolism.This is straightforward for the main endproductssuch as starch or fatty acids, but the numeroussmaller fluxes into products such as amino acidsand secondary metabolites are more difficult tomeasure and to attribute to the plastid eventhough their overall contribution could well besignificant. Accordingly any determination of 6net

must be regarded as yielding a lower limit for 6net,both in this simple system and in more complexnetworks.

Despite the more detailed information obtain-able from labelling experiments using C2-glucose,most studies have been based on C1-labelling, inwhich the oxidative pentose phosphate pathwayleads to the loss of label as CO2. This results infractional enrichments at C1 in sucrose and starchof the same form as Eqs. (15) and (16). It followsthat a decrease in the fractional enrichments inthe C1-positions of sucrose and starch with re-spect to that of the fed glucose can be attributedto the operation of the oxidative pentose phos-phate pathway, provided label dilution by endoge-nous sources can be excluded, and ifredistribution of label to other carbons by thedifferent reactions and pathways shown in Fig. 4is accounted for. Furthermore, on the basis of thefirst part of Eq. (19), a difference in these frac-tional enrichments indicates an active plastidicoxidative pentose phosphate pathway. However,the second form of Eq. (19), which is only usablewith C2-labelling, is much more robust, as the

6p-oppp

6net+6ex

=65�f c-HexP

C2

fp-HexPC2 −1

�(20)

In both expressions, the determination of (6p-oppp)/(6net+6ex) hinges on the differences between themeasured fractional enrichments in the cytosoland the plastid, and it fails when 6ex is so largethat the fractional enrichments in the two com-partments are the same within experimental error.This problem persists when analysing a full


ratio of the fractional enrichments used in theequation is less susceptible to the effect of labeldilution from endogenous sources at natural iso-tope abundance. Further conclusions from C1-la-belling experiments, as drawn by Krook et al.(1998), are only possible on the assumption thatthere is no flux of hexose phosphates from theplastid to the cytosol, i.e. 6ex=0. If this assump-tion can be verified independently, then the fluxratios 6c-oppp/6H and 6p-oppp/6net can be calculated.Otherwise, without further labelling data it isimpossible to distinguish a reduction in f c-HexP

C1

caused by a cytoplasmic oxidative pentose phos-phate pathway activity from one due to the plas-tidic pathway coupled to an exchange over theplastid envelope. Thus, any serious attempt tounravel the compartmentation of the oxidativepentose phosphate pathway is critically dependenton a C2-labelling experiment.

The situation encountered here is not unique tocompartmented systems but could also occur withreactions in a single compartment, where a strongexchange flux can mask labelling differences be-tween two metabolites. However, compartmentedsystems present two particular difficulties. First,compartmented pools of a chemically identicalmetabolite cannot be distinguished in an extract,since the compartmentation information is lost,and it is only possible to determine the fractionalenrichment of the combined pools. Supplemen-tary information can sometimes be obtained byanalysing two chemically different metabolitesthat can each be assigned to one compartment, aswith sucrose and starch. Secondly, parallelmetabolic pathways in two compartments, asfound in the cytosol and the plastid, or to a lesserextent in the cytosol and the mitochondrion, giverise to the same possibilities for label redistribu-tion. Thus the number of independent fluxes dou-bles for a parallel pathway, whereas the numberof independent labelling measurements remainsthe same.

2.7. Labelling studies in slow growing tissues withhigh polymer content

Labelling to isotopic steady-state for lowmolecular weight metabolic intermediates takes

an appreciable time even for metabolically activemeristematic tissue, e.g. 12 h for maize root tipsthat had been depleted of carbohydrate by pre-starving for 4 h (Dieuaide-Noubhani et al., 1995).During this time, maize root tips typically doublein fresh weight, partly due to elongation andpartly due to cell division. Thus, only a propor-tion of the cell polymers (starch, cell wall, lipids,DNA, RNA, proteins) are newly synthesised dur-ing the incubation period, and any analysis ofthese compounds has to work against a highbackground of natural abundance material.

Polymers that were synthesised prior to theincubation period can be accounted for by includ-ing a pseudo-flux from a hypothetical pool of thepolymer at natural abundance in the metabolicflux network. This flux has no meaning but conve-niently mimics the dilution effect. Furthermore, itis also necessary to take into account the fact thatthe label detected in a polymer pool is an integralover the total incubation time, including the pe-riod necessary for establishing isotopic steady-state. Thus using this labelling informationrequires a retrospective analysis of the time courseof label accumulation by simulating the time-course of the approach to the steady-state usingthe flux velocities determined from the steady-state analysis. Such an analysis might be usefullycomplemented by sampling the labelling state atdifferent time points during the incubation period,although such a determination carries the incon-venience of dynamic labelling techniques.

However, the labelling analysis of starch isfacilitated by its structural and metabolic proper-ties. Keeling et al. (1988) introduced a techniqueinvolving partial hydrolysis of the starch grain ofwheat endosperm and used it to analyse the mostrecently synthesised outer layers separately fromthe older inner layers. The fractional enrichmentin the outer starch fraction is much higher thanthat of the inner layers with their high naturalabundance background, and it reflects moreclosely the fractional enrichment of the plastidichexose phosphates incorporated into starch dur-ing the incubation period. Another technique,presented by Dieuaide-Noubhani et al. (1995), isuseful on heterotrophic tissues that do not accu-mulate very large amounts of starch. They pre-


starved excised maize root tips for 4 h prior toincubation with labelled glucose. This treatment isexpected to reduce the starch content considerably(Saglio and Pradet, 1980), so that nearly all thestarch has been synthesised during the labellingperiod. A corollary of this method is that thesoluble carbohydrate content of the root tips isalso greatly reduced, and this is replenished imme-diately after addition of glucose to the incubationmedium. It follows that significant polymer syn-thesis only occurs after a lag phase during whichthe more rapidly turning over pools of solublemetabolites can approach isotopic steady-state(Dieuaide-Noubhani et al., 1997).

When using a label that has a negligible naturalbackground such as 14C-label or 13C-labelledbonds, the polymer pool present prior to theincubation period can be neglected since the ratiosof fractional enrichments are independent of thesize of the natural-abundance pool. In contrast,the time between the start of incorporation oflabel into the polymer and the establishment ofisotopic steady-state of its precursor has to beincluded in the analysis. Regarding 13C-bond-la-belling, it is worthwhile to re-emphasise that poly-mer analysis has been restricted to the hydrolysedcellular protein fraction in most investigations(e.g. Szyperski (1995) for micro-organisms andFlogel et al. (1997) for mammalian cells). How-ever, this fraction only contains restricted infor-mation on sugar metabolism, and for this purposea labelling-analysis of polymers containing sugarresidues (starch, cell wall, DNA/RNA) would beworthwhile in plants, although, as indicated ear-lier, NMR analysis of multiple 13C labelling insugars is more difficult than the same type ofanalysis with amino acids.

The situation regarding the labelling of poly-mers is different with plant cell cultures, where thecells can be grown for several generations onlabelled substrate, thus leading to an isotopicsteady-state even in slowly turning over polymers.In continuous cell cultures, maintained in ametabolic steady-state, the labelling state of thepolymers reflects the isotopic steady-state corre-sponding to the metabolic steady-state. Howeverin batch cultures, the metabolic state of the cellsshifts with the developmental state of the cell and

the decline in available substrate, and this isreflected in the isotopic state which follows theshifting metabolic state (Krook et al., 1998). Thelabelling in metabolite pools with turnover ratesthat are high compared to the rate of change ofthe metabolic state can still be analysed using anapproximate steady-state assumption. In contrast,the labelling in polymers that turn over slowlyreflects the history of isotopic states, and can onlybe analysed usefully when these dynamics can betaken into account by recording a timecourse ofthe labelling.

2.8. Impact of cellular and temporal heterogeneityof metabolism

As is usual in metabolic studies, it is necessaryto be aware of the underlying cellular andtemporal heterogeneity of metabolism. A plantorgan is not comprised of a single homogeneouscell type, and any metabolic analysis will thus bea mean over different cell types. If there are widedifferences in metabolism in cell populations ofcomparable size, then the metabolic analysiswill fail, or at least give a false picture. Thisfailure point is hard to predict or even to de-tect. Dieuaide-Noubhani et al. (1995) showed thatone set of fluxes can describe the labelling ob-tained in the morphologically heterogeneousmaize root tip but the transposability of this resultis unclear.

Moreover, a growing tissue is not strictly in ametabolic steady-state. Its metabolism will evolveover time even within the time frame of an incu-bation experiment that aims to achieve isotopicsteady-state. However it is necessary to bear inmind that a steady-state analysis of isotope la-belling does not need to assume a metabolicsteady-state during the whole labelling ex-periment. It is sufficient if the metabolic statechanges slowly enough for the isotopic state to‘catch up’. Thus the assumption of metabolicsteady-state only has to be valid during a periodthat allows for the pools of metabolic intermedi-ates to turn over several times. In contrast,metabolite pools that do not fulfil this conditionhave to be analysed like pools of accumulatingpolymers.


3. Conclusion

Steady-state isotope labelling experiments offerseveral powerful methods for measuringmetabolic fluxes in plants. However, in contrast tomicro-organisms and animals, it is necessary tomake due allowance for effects arising from thecompartmentation and greater complexity of thepathways of primary metabolism in plant mate-rial. A combination of 13C-labelling and NMRanalysis is the preferred analytical approach inmany cases, and with suitable precautions it ispossible to generate quantitative metabolic mod-els that highlight the integration of plantmetabolism. There is now considerable scope forusing this NMR approach for the characterisationof mutants and transgenic plants at the metaboliclevel, and this is likely to lead to an increasedunderstanding of the factors that control fluxthrough biotechnologically important pathways.

Acknowledgements

This work was supported by the Biotechnologyand Biological Sciences Research Council of theUnited Kingdom.

Appendix A

Formulation of the equations relating fluxesand fractional enrichments of reactants proceedsfrom the assumption of metabolic and isotopicsteady-state. This is exemplified by derivation ofEq. (1). Under isotopic steady-state, the influxand efflux of each isotope must balance for eachintermediate metabolite pool in the metabolicscheme of Fig. 2, i.e. hexose phosphates and triosephosphates:

6H fGlc+6-1 fTriP= (61+6C)fHexP and

6T fGro+61 fHexP= (6-1+6G)fTriP (A1)

Assuming metabolic steady-state, the rate of syn-thesis and degradation of a metabolic intermedi-ate will be equal. This condition allows the totalefflux from the hexose phosphate and triose phos-

phate pools to be replaced by the total influx intothe same pools, reducing the number of un-knowns in the equations:

6H fGlc+6-1 fTriP= (6H+6-1)fHexP and

6T fGro+61 fHexP= (6T+61)fTriP (A2)

This system of two linear equations can now beresolved for the two unknowns fHexP and fTriP. Eq.(1) is obtained by inserting the experimental con-dition fGro=0.

The same reasoning applies to the derivation ofEq. (5) for the positional labelling experiments.However, in contrast to uniform two-substratelabelling, each carbon position in each intermedi-ate metabolite has to be considered separately.Thus the isotopic and metabolic steady-state con-ditions for the carbons 1 and 6 of hexose phos-phates as well as for carbon 3 of triose phosphatesgive:

6H fGlcC1 +6-1 fTriP

C3 = (6C+61)fHexPC1

= (6H+6-1)fHexPC1 ,

6H fGlcC6 +6-1 fTriP

C3 = (6C+61)fHexPC6

= (6H+6-1)fHexPC6 , and

61 fHexPC1 +61 fHexP

C6 = (26G+26-1)fTriPC3

=261 fTriPC3 . (A3)

The third line gives an expression for fTriPC3 which

can be substituted into the first two lines. Rear-rangement of the resulting equations gives theexpressions for fHexP

C1 and fHexPC6 in Eq. (5).

The derivation of Eq. (8) for mass spectroscopydetected bond-labelling follows the same princi-ple, but it is complicated by the fact that thebalance equations are not linear in the fractionalenrichments since the formation of a given isoto-pomer depends on the fractional enrichments ofall its precursors. In this special case where hexosephosphates can be synthesised from two triosephosphates, this means that square terms of thefractional enrichment of triose phosphates appear:

6H fGlc6C +6-1( fTriP

3C )2= (6C+61)fHexP6C

= (6H+6-1)fHexP6C ,

6H fGlc3C +26-1 fTriP

3C (1− fTriP3C )= (6C+61)fHexP

3C


= (6H+6-1)fHexP3C and

261 fHexP6C +61 fHexP

3C = (26G+26-1)fTriP3C

=261 fTriP3C . (A4)

Using the experimental conditions fGlc6C =pf and

fGlc3C =0 (i.e. neglecting natural abundance), the

first two lines of Eq. (A4) can be combined toeliminate the ( fTriP

3C )2 term, and then be insertedinto the third line, yielding:

fTriP3C = fGlc

6C =pf (A5)

This result is expected since fTriP3C is not affected by

the bond splitting of the aldolase reaction, andthus should be equal to the enrichment in three-carbon fractions in the glucose flowing into themetabolic system. Inserting Eq. (A5) into the firsttwo lines of Eq. (A4) leads directly to Eq. (8). Thederivation of Eq. (11) for NMR detected bond-labelling again follows the same principles,but more isotopomers have to be taken into ac-count since natural abundance 13C cannot beneglected. The balance equation for the hexosephosphate isotopomer pool containing a labelledC3–C4 fragment can be established in the usualway:

6H f GlcC3-C4+6-1( fTriP

C1 )2= (6C+61)f HexPC3-C4

= (6H+6-1)f HexPC3-C4 (A6)

A C3–C4 fragment in glucose can either formpart of a uniformly labelled molecule (probabilitypf) or consist of two natural abundance neigh-bours (probability pn

2) in an unlabelled molecule(probability 1−pf). The probability of finding a13C in the first position of triose phosphatesequals the probability of finding one in the thirdor fourth position of hexose phosphates and thus,in turn, in the third or fourth position of glucose,the source molecule of the metabolic network.This probability is the joint probability of eitherhaving a uniformly labelled molecule (pf), or anunlabelled molecule (1−pf) with uniformly butrandomly distributed natural abundance (pn),which is called p1 (Eq. (10)). It is the same for allsix carbon positions:

fTriPC1 =

12

( fHexPC3 + fHexP

C4 )= fHexPC3

= fHexPC4 = fGlc

C3 = fGlcC4 =p1 (A7)

Thus, Eq. (A6) can be rewritten as:

6H(pf+ (1−pf)pn2)+6-1p1

2= (6H+6-1)f HexPC3-C4 (A8)

However the proposed NMR method doesnot give information about the total proportionof molecules containing a labelled C3–C4 frag-ment but detects for a given labelled position,e.g. C4, the proportion of it attached to alabelled C3-atom. Knowing that a proportion p1

is labelled in C4 (Eq. (A7)), the required relationis:

f HexPC3-C4= fHexP

C4 f [C4]HexPC3 =p1 f [C4]HexP

C3 (A9)

Using this relation, Eq. (A8) can be transformedinto Eq. (11).

References

ap Rees, T., 1985. The organization of glycolysis andthe oxidative pentose phosphate pathway in plants. In:Douce, R., Day, D.A. (Eds.), Encyclopaedia of PlantPhysiology, vol. 18. Springer-Verlag, Berlin, pp. 391–417.

ap Rees, T., 1988. Compartmentation of plant metabolism. In:Davies, D.D. (Ed.), The Biochemistry of Plants, Vol. 12:Physiology of Metabolism. Academic Press, London, pp.87–115.

Bartlett, M.R.E., Collins, J.G., Flanigan, I., MacLeod, J.K.,Williams, J.F., 1989. CO2 labelling of octulose bisphos-phates during photosynthesis. An NMR study using intactspinach leaves. Biochem. Int. 18, 35–46.

Beylot, M., Previs, S.F., David, F., Brunengraber, H., 1993.Determination of the 13C-labelling pattern of glucose bygas chromatography-mass spectrometry. Anal. Biochem.212, 526–531.

Bonarius, H.P.J., Schmid, G., Tramper, J., 1997. Flux analysisof underdetermined metabolic networks: the quest for themissing constraints. Trends Biotechnol. 15, 308–314.

Bouchez, D., Hofte, H., 1998. Functional genomics in plants.Plant Physiol. 118, 725–732.

Bryce, J.H., ap Rees, T., 1985. Rapid decarboxylation of theproducts of dark fixation of CO2 in roots of Pisum andPlantago. Phytochemistry 24, 1635–1638.

Carvalho, R.A., Jeffrey, F.M.H., Sherry, A.D., Malloy,C.R., 1998. 13C isotopomer analysis of glutamate by het-eronuclear multiple quantum coherence-total correlationspectroscopy (HMQC-TOCSY). FEBS Lett. 440, 382–386.

Dieuaide-Noubhani, M., Raffard, G., Canioni, P., Pradet, A.,Raymond, P., 1995. Quantification of compartmentedmetabolic fluxes in maize root tips using isotope distribu-


tion from 13C- or 14C-labeled glucose. J. Biol. Chem. 270,13147–13159.

Dieuaide-Noubhani, M., Canioni, P., Raymond, P., 1997.Sugar-starvation-induced changes of carbon metabolismin excised maize root tips. Plant Physiol. 115, 1505–1513.

Emes, M., Neuhaus, H.E., 1997. Metabolism and transport innon-photosynthetic plastids. J. Exp. Bot. 48, 1995–2005.

Fell, D.A., 1997. Understanding the Control of Metabolism.Portland Press, London.

Flogel, U., Willker, W., Leibfritz, D., 1997. Determination ofde novo synthesized amino acids in cellular proteins revis-ited by 13C NMR spectroscopy. NMR Biomed. 10, 50–58.

Hatzfeld, W.D., Stitt, M., 1990. A study of the rate ofrecycling of triose phosphates in heterotrophicChenopodium rubrum cells, potato tubers, and maize en-dosperm. Planta 180, 198–204.

Hill, S.A., 1997. Carbon metabolism in mitochondria. In:Dennis, D.T., Turpin, D.H., Lefebvre, D.D., Layzell, D.B.(Eds.), Plant Metabolism. Longman, Harlow, pp. 181–199.

Hutton, W.C., Likos, J.J., Gard, J.K., Garbow, J.R., 1998.Triple resonance isotope-edited (TRIED): a powerful newNMR technique for studying metabolism. J. Label.Compd. Radiopharm. 41, 87–95.

Ito, O., Mitsumori, F., 1992. Transformation and transloca-tion of photoassimilated 13CO2 and glycine-2-13C insunflower leaves detected by 13C-NMR. Soil Sci. PlantNutr. 38, 347–360.

Keeling, P.L., Wood, J.R., Tyson, R.H., Bridges, I.G., 1988.Starch biosynthesis in developing wheat grain. Evidenceagainst the direct involvement of triose phosphates in themetabolic pathway. Plant Physiol. 87, 311–319.

Kosegarten, H., Kalinowski, H.-O., Mengel, K., 1995. Long-term 13C labelling of starch and sucrose during the courseof amyloplast development in intact suspension-culturedstorage cells of potato (Solanum tuberosum). J. Plant Phys-iol. 146, 405–410.

Krook, J., Vreugdenhill, D., Dijkema, C., van der Plas,L.H.W., 1998. Sucrose and starch metabolism in carrot(Daucus carota L.) cell suspensions analysed by 13C-la-belling: indications for a cytosol and a plastid-localizedoxidative pentose phosphate pathway. J. Exp. Bot. 49,1917–1924.

Kunnecke, B., Seelig, J., 1991. Glycogen metabolism as de-tected by in vivo and in vitro 13C NMR spectroscopy using[1,2-13C2]glucose as substrate. Biochim. Biophys. Acta1095, 103–113.

London, R.E., 1988. 13C labeling in studies of metabolicregulation. Prog. NMR Spectrosc. 20, 337–383.

Mancuso, A., Sharfstein, S.T., Tucker, S.N., Clark, D.S.,Blanch, H.W., 1994. Examination of primary metabolicpathways in a murine hybridoma with carbon-13 nuclearmagnetic resonance spectroscopy. Biotechnol. Bioeng. 44,563–585.

Ratcliffe, R.G., 1994. In vivo NMR studies of higher plantsand algae. Adv. Bot. Res. 20, 43–123.

Rinehart, K.L., Potgieter, M., Wright, D.A., 1982. Use ofD-[13C6]-labeled glucose together with 13C-depleted glucoseand homonuclear 13C decoupling to identify the labelingpattern by this precursor of the ‘m-C7N’ unit of gel-danamycin. J. Am. Chem. Soc. 104, 2649–2652.

Ross, B.D., Kingsley, P.B., Ben-Yoseph, O., 1994. Measure-ment of the pentose phosphate pathway activity in a singleincubation with [1,6-13C2, 6,6-2H2]glucose. Biochem. J.302, 31–38.

Saglio, P.H., Pradet, A., 1980. Soluble sugars, respiration, andenergy charge during aging of excised maize root tips.Plant Physiol. 66, 516–519.

Schaefer, J., Stejskal, E.O., Beard, C.F., 1975. Carbon-13nuclear magnetic resonance analysis of metabolism in soy-bean labeled by 13CO2. Plant Physiol. 55, 1048–1053.

Schaefer, J., Kier, L.D., Stejskal, E.O., 1980. Characterizationof photorespiration in intact leaves using 13Carbon dioxidelabeling. Plant Physiol. 65, 254–259.

Schaefer, J., Skokut, T.A., Stejskal, E.O., McKay, R.A.,Varner, J.E., 1981. Asparagine amide metabolism in devel-oping cotyledons of soybean. Proc. Natl. Acad. Sci. USA78, 5978–5982.

Schmidt, K., Carlsen, M., Nielsen, J., Villadsen, J., 1997.Modeling isotopomer distributions in biochemical net-works using isotopomer matrices. Biotechnol. Bioeng. 55,831–840.

Sims, A.P., Folkes, B.F., 1964. A kinetic study of the assimila-tion of [15N]-ammonia and the synthesis of amino acids inan exponentially growing culture of Candida utilis. Proc. R.Soc. Lond. B. Biol. Sci. 159, 479–502.

Szyperski, T., 1995. Biosynthetically directed fractional 13C-la-beling of proteinogenic amino acids. An efficient analyticaltool to investigate intermediary metabolism. Eur. J.Biochem. 232, 433–448.

Szyperski, T., 1998. 13C-NMR, MS and metabolic flux balanc-ing in biotechnology research. Q. Rev. Biophys. 31, 41–106.

Trethewey, R.N., ap Rees, T., 1994. The role of the hexosetransporter in the chloroplasts of Arabidopsis thaliana L.Planta 195, 168–174.

Viola, R., Davies, H.V., Chudeck, A.R., 1991. Pathways ofstarch and sucrose biosynthesis in developing tubers ofpotato (Solanum tuberosum L.) and seeds of faba bean(Vicia faba L.). Elucidation by 13C-nuclear-magnetic-reso-nance spectroscopy. Planta 183, 202–208.

Wendisch, V.F., de Graaf, A.A., Sahm, H., 1997. Accuratedetermination of 13C enrichments in non-protonated car-bon atoms of isotopically enriched amino acids by 1Hnuclear magnetic resonance. Anal. Biochem. 245, 196–202.

Wiechert, W., de Graaf, A.A., 1997. Bidirectional reactionsteps in metabolic networks: I. modeling and simulationcarbon isotope labeling experiments. Biotechnol. Bioeng.55, 101–117.

Wiechert, W., Siefke, C., de Graaf, A.A., Marx, A., 1997.Bidirectional reaction steps in metabolic networks: II. flux.


estimation and statistical analysis. Biotechnol. Bioeng. 55,118–135.

Zupke, C., Stephanopoulos, G., 1994. Modeling of isotope

distributions and intracellular fluxes in metabolic networksusing atom mapping matrices. Biotechnol. Prog. 10, 489–498.

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