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Methods for improving the visualization and deconvolution

of isotopic signals

GUILLAUME TCHERKEZ1,2, JALEH GHASHGHAIE2 & HOWARD GRIFFITHS3

1Plateforme Métabolisme-Métabolome, IFR 87, Bât. 630, 2Laboratoire d’écophysiologie végétale, CNRS UMR 8079, Bât. 362,

Université Paris Sud-XI, 91405 Orsay cedex, France and 3Department of Plant Sciences, University of Cambridge, CB2 3EA,

UK

ABSTRACT

Stable isotopes and their associated mechanistic frame-

works have provided the means to model biological trans-

formations from inorganic sources to organic sinks, and

their impact on long-term terrestrial carbon reservoirs.

However, stable isotopes have also the potential to diagnosethe mechanisms by which biological systems operate, when

using ‘multidimensional’ analyses of the isotopic outputs.

For this purpose, we suggest that isotopic signals may be

treated as mathematical vectors to reveal their interrela-

tionships. These visualizations may be achieved, thanks

to multidimensional representations (the ‘isotopology’

method), or by appreciating the colinearity of isotopic

vectors to develop a clustering analysis (the ‘isotopomic’

method) similar to that used in molecular biology. Both

methods converge to the same mathematical form, i.e. both

lead to a covariation approach. Using simple practical

examples, we argue that such procedures allow the decon-

volution of plant biological systems by revealing the hierar-chy of contributory physiological processes.

Key-words: stables isotopes; fractionation; vectors; array;

clustering analysis.

INTRODUCTION

Earth and plant systems biology requires an understanding

of both interannual biospheric processes and its contribu-

tory molecular mechanisms, and stable isotopes can be

used to integrate such geochemical and biological systems

(Yakir 2002). Systematic shifts in natural isotopic ratios

(such as 13C/12C or 18O/16O) are based on fractionation pro-

cesses which lead to discriminations between isotopes in

biological cornerstone reactions like photosynthesis [in

which ribulose-1,5-bisphosphate carboxylase/oxygenase

(Rubisco) discriminates against 13CO2] (Farquhar,

Ehleringer & Hubick 1989; Tcherkez, Farquhar & Andrews

2006), leaf and canopy transpiration (discrimination against

H218O and exchange as either C18O16O or water vapour)

(Farquhar, Barbour & Henry 1998; Helliker & Griffiths

2007) or plant nitrate assimilation (discrimination against

15NO3-) (Ledgard, Woo & Bergersen 1985; Werner &

Schmidt 2002; Tcherkez and Farquhar 2006).

There have been a number of recent reviews which have

evaluated biological and ecological stable isotope transfor-

mations, their impact on carbon reservoirs in the atmo-

sphere, plant and soil, and coupling with the hydrological

cycle (Griffiths 1998; Dawson et al. 2002;Flanagan,Pataki &Ehleringer 2005; Griffiths & Jarvis 2005). Most recently, it

has been suggested that transformations and isotopic distri-

butions can be viewed as‘isoscapes’ which trace interannual

variations or geographical linkages (West et al. 2006).

In this paper, we propose that isotope data should be

visualized more clearly to reveal the connectivity between

isotopic signals, and diagnose underlying mechanisms

within plant systems. This may be achieved with ‘isotopolo-

gies’, which represent multidimensional maps of observed

isotopic distributions, or ‘isotopomics’, in which systematic

isotopic enrichments and depletions (isotopic shifts) within

biological systems are correlated as vectors using multiar-

ray, differential displays and cluster analysis.

A MULTIDIMENSIONAL ‘ISOTOPOLOGY’

The clearest representation of a global isotopic output is the

annual dance of photosynthetic carbon uptake and seques-

tration in summer, followed by respiratory CO2 release in

winter, which drives seasonal variations in CO2 concentra-

tion. Particularly in the Northern Hemisphere, the hetero-

geneity and temporary disequilibrium in isotopic mass

balance of atmospheric CO2 lead to a striking intraannual

variation in 12C/13C isotope composition (denoted as d 13C).

This interaction is classically represented as a ‘rug’ or ‘flying

carpet’ diagram (whose data are available at the NOAACMDL Carbon Cycle Cooperative Global Air Sampling

Network website: http://wwwsrv.cmdl.noaa.gov/ccgg/iadv),

and encapsulates our vision of an isotopic landscape or an

‘isotopology’. We suggest that this kind of approach can be

used for other isotopic data,which are normally only shown

as one-dimensional isotopic diagrams.

Multiparametric representation: visualizing themultidependence of a given isotopic signal

To illustrate this point practically at the leaf level, we

start from a multidimensional representation of exportedCorrespondence: G. Tcherkez. E-mail: guillaume.tcherkez@

u-psud.fr

Plant, Cell and Environment (2007) 30, 887–891 doi: 10.1111/j.1365-3040.2007.01687.x

© 2007 The AuthorsJournal compilation © 2007 Blackwell Publishing Ltd 887

http://wwwsrv.cmdl.noaa.gov/ccgg/iadv

http://wwwsrv.cmdl.noaa.gov/ccgg/iadv



assimilates that are subsequently distributed in severalpools and could be used for respiration or growth (Fig. 1). It

shows how the time-course of the d 13C signal in phloem

sucrose depends on both circadian metabolic changes and

internal parameters (such as the rate of starch synthesis)

that are in turn modulated by environmental conditions.

Briefly, the fructose-producing aldolase reaction of the

chloroplast favours 13C (enriching starch in this isotope).

The remaining triose phosphates are used in the cytosol to

produce (13C-depleted) sucrose, so that sucrose found in the

phloem during the day is 13C-depleted, contrary to sucrose

produced during the night, simply because the latter comes

from depolymerization of starch. This example typifies how

the compartmentation of metabolic reactions (chloroplasticstarch synthesis versus cytoplasmic sucrose synthesis), when

associated with an isotope effect, scales up to the plant

level. Multidimensional representations involving isotopes

are useful to deconvolute the complexity of physiological

processes, and more importantly, challenge the common

interpretation of delta values; as can be seen from Fig. 1, a

given d 13C of sucrose may correspond to several possible

drivers (starch synthesis, relative time), as well as environ-

mental effects such as the impact of temperature on meta-

bolic processes.

Such diel variations will be, among others, a factor con-

tributing to the cellulose isotope signatures of tree rings,

which in turn integrate seasonal climatic conditions(Schleser et al. 1999; MacCarroll & Loader 2004). Thus,

as a further multidimensional representation, we provide a

simple conceptual framework depicting the physiological

complexity of ring deposition by the cambium (Fig. 2).

A physical analogy involving transfer functions has

also been proposed to improve the analyses of isotopic

signals in rings (Schleser et al. 1999). Cellulose deposition is

influenced by the (leaf) carbon source (as determined by

cc/ca, the ratio of intracellular/external CO2), and also by the

contribution that reserves make as substrate for cellulose

deposition (whether sucrose from starch in the dark, or

sucrose during the day) and respiratory losses (Fig. 2a).

When modelled as a three-dimensional representation(Fig. 2b), the deviation of the d 13C value of ring cellulose

from the d 13C value of fixed CO2 can be seen as a function

of the proportion of day sucrose (versus night sucrose) as a

carbon source (L) and the relative respiratory rate (r ),

assuming a fixed respiratory discrimination of -6‰. It is

clear that both parameters have an effect on the carbon

isotope signature of cellulose, and a quite large deviation is

obtained under certain conditions (Fig. 2b). For example,

the larger the respiratory losses (13C-enriched), the more13C depleted the remaining deposited material (so that

d *–d C increases). Further, the larger the contribution of

(13C-depleted) day sucrose to cellulose deposition, the

lower the isotope composition of cellulose (so thatd

*–d

Cincreases as well). This representation integrates the key

determinants of internal carbon signature, which may in

turn be changed by environmental conditions (e.g. the

increase of respiration with temperature, etc.).

The multidimensional representations of both Figs 1

and 2 are classical representations, in which the isotopic

signal is a function of physiological drivers. Still, they are

useful to deconvolute the complexity of physiological pro-

cesses, and visualize how a given isotopic signal value may

correspond to several possible values of the drivers. That

said, multidimensional representations plotting several iso-

topic signals are perhaps more useful for deconvoluting

interactions between bio(geo)chemical pathways, as wenow show.

Multiple isotopic signals: partitioningbiochemical pathways from isotopiccompositions

When partitioning occurs during metabolism, graphical rep-

resentations can be used to visualize the network of corre-

lations. This can also be allied with additional techniques

such as correlative clustering analysis, developed as follows.

It will become apparent that both analyses – graphical mul-

tidimensional and clustering – are similar in the way that

Figure 1. Multidimensional isotopic representation showing the

modelled time-course of phloem sucrose in a leaf, using a

sinusoïdal function of 13C-enriched sucrose by night and13C-depleted sucrose by day. Note that the exported carbon slips to

more 13C-depleted values when starch synthesis (in moles of

hexoses per mole of carbon fixed) increases. Calculations from

Tcherkez et al. (2004).

–22

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–19

–18

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–16

–15

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0.040.05

0.060.07

0.080.09

T i me ( h)

S t a r c h

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888 G. Tcherkez et al.

© 2007 The AuthorsJournal compilation © 2007 Blackwell Publishing Ltd, Plant, Cell and Environment, 30, 887–891



the final mathematical formalism converges, but differ in

terms of their visual realization.

As an example, we reanalyse data generated from the

isotope composition of different metabolites extracted

from a leaf during a series of labelling experiments

(Nogués et al. 2004). A conventional multidimensional

representation would show each compound on a separate

axis. However, to display the interrelationships betweencompounds in such a graphical presentation, such data can

be interpreted using a Bayesian analysis; for a given iso-

topic signal in compound number i, one may look at (the)

other compound(s) in the pathway which covary in asso-

ciation with that signal (Fig. 3). Thus, in mathematical

terms, two isotopic signals i and j are best correlated if

they follow each other in the graphical presentation, inde-

pendently of others (denoted here as n). This means that

signals n are in a perpendicular space, with the scalar

product of i and j maximal, and the scalar products of i

and any n, or j and any n, zero. In its general form, the

scalar product would be as follows:

x x x xk

K

i j ik jk, ==

∑1

(1)

where isotopic signal xik is that of compound i obtained

during the measurement (or experiment) number k. This is

very similar to what the similarity-based clustering analysis

discussed as follows gives.The associated visualization may be, however, compli-

cated when more than three isotopic signals are considered.

While a classical bidimensional graph may be used for all

the isotopic signals, a polar graph is, perhaps, a more con-

venient way to associate isotopic shifts in the different com-

pounds, and determine whether they follow the same

pathway. Figure 3 gives such an example using the data of

Nogués et al. (2004), collected during labelling experiments

allowing Phaseolus leaves to fix varying quantities of isoto-

pically defined CO2. We now plot the offset in isotopic

signals between respired CO2 (after illumination) and

compound-specific signals in sucrose, starch, organic acids,

ci /c

a

Fixed CO2 (d *)

Starch Suc

1− L L

Ring carbohydrates

Ring cellulose (d C)

Reserves CO2

e, r

Other

L e a v e s

Tree ring

(b)(a)

−8

−6

−4

−2

0

2

0.00

0.05

0.100.15

0.200.25

0.300.35

0.40

0.00.2

0.40.6

0.8

d ∗

−

d C

r

L

Figure 2. (a) The carbon isotope composition of cellulose in tree rings (d C) does not simply reflect that of fixed CO 2 [given by the

internal-to-external CO2 molar fraction ratio ci/ca (or cc/ca) denoted as d *], because of so many intermediary stages. Namely, the

proportion of sucrose produced by day (Suc) versus that at night (denoted as L) to feed the metabolism of ring cells, as well as

respiration (relative rate r ), which liberates CO2 that may be enriched or depleted (the fractionation is denoted as e). These internal

factors may in turn be influenced by external parameters (curved arrows): the respiration rate responds positively to temperature, the

allocation of fixed carbon to starch or sucrose during the day depends on ci, etc. (b) As an example, the difference between d * and d C is

plotted as a double function of L and r , with a fixed respiratory fractionation (e) of -6‰. Numbers were obtained using an extension of

the model of Tcherkez et al. (2004).

Improving the visualization and deconvolution of isotopic signals 889




proteins and lipids. The isotopic shifts are normalized to

100° (angular degrees) and plotted as angles (denoted as q

just below), and each labelling condition (experiment)

corresponds to a radial increment. This allows one to see

whether the isotopic pathways have the same shape, or

rather, diverge. From a quantitative point of view, we note

that two pathways A and B are exactly similar if the angles

(q A and q B) are similar for each radial increment, i.e. if the

corresponding cosine [cos(q

A- q

B)] value is 1, then thescalar product of the associated vectors is maximal. It can

be seen in Fig. 3 that the pathway followed by CO 2 is closer

to that of carbohydrates and correlates less well with other

compounds. In other words, this indicates that the origin of

CO2 respired by leaves after illumination is carbohydrates.

Less apparent is, however, the molecule from which CO2

is derived (starch or sucrose). Another representation,

coupled to a more quantitative correlative technique, is thus

described as follows.

ISOTOPOMICS

The isotopomics concept is illustrated by Fig. 4. Here, weshow how statistical methods derived from genomics can be

used to deconvolute isotope signals. Traditional cluster

analysis of gene transcription using microarrays (Eisen et al.

1998) indicates the abundance of many transcripts by

colours. The cluster analysis of genes, where correlation

coefficients or related mathematical parameters use simi-

larities in transcription patterns to detect the coregulation

of gene expression, can also be used to infer metabolic

interactions and associations (Gachon et al. 2005). Similarly,

arrays can be used to show isotopic modifications for dif-

ferent compounds of a biological system (in rows), induced

by different environmental conditions (in columns); the

clusters show the isotopic proximity of compounds or part-

ners within a network of fluxes comprising the particular

biological system of interest. This provides an effective

mean of seeing the correlative network between com-

pounds in the given biological system. In other words, we

use here isotopes not only as classical tracers, but addition-

ally as ‘correlators’. From a mathematical point of view, theprinciple is similar to the genetic clustering analysis, i.e. uses

correlations of isotopic shift vectors as calculated, for

example, by the normalized scalary product. If we denote x

as the vectors of isotopic shifts (array conditions or ‘experi-

ments’ are numbered from 1 to K ), the similarity (or colin-

earity) index (denoted as S) between two vectors i and j has

the following general form:

S

x x

x x

k

K

k

K

k

K ij

i k j k

ik jk

= =

= =

∑

∑ ∑

1

2

1

2

1

(2)

The xik values may be relative isotopic shifts in delta

values or ratios or % in 13C (in case of strong labelling), etc.

All the Sij values generate a matrix which may be in turn

treated by the clustering programme to generate clusters.

As a simple example,such an approach can be used at the

leaf scale with compound-specific isotope composition fol-

lowing isotopic labelling (Fig. 4). Again, data from Nogués

et al. (2004) (in which leaves were labelled with 13C-

depleted CO2) are used to generate a matrix of relative

isotopic shifts from the initial value. Array conditions

(columns) correspond to different labelling level (denoted

as Lab_i where i is the amount of carbon fixed during the

labelling period in Fig. 4). The colour brightness indicatesthe amplitude of the relative isotopic shift. The cluster

analysis can be used to generate a phylogenetic-style tree

indicated on the left-hand side of Fig. 4. In this particular

example, metabolic associations can be easily concluded

0

1

2

3

4

5

6

7

8

9

10

11

12

0

30

6090

CO2

Suc

Starch

OA

Lip

Prot

Experiments

Figure 3. Representation of the isotopic shifts in the

compound-specific d 13C values after labelling leaves with

industrial CO2 (data from Nogués et al. 2004), plotted as a polar

graph in which each increment corresponds to a different

experiment (increasing fixed C amount) and the angles (denoted

as q in the main text) represent the isotopic shifts normalized to

100 angular degrees. Suc, sucrose; OA, organic acids; Lip, lipids;

Prot, heat-precipitated proteins.

Figure 4. Example of isotopomics at the leaf level. The array

has been obtained with isotopic shifts in the compound-specific

d 13C values after labelling leaves with industrial CO2 (data from

Nogués et al. 2004). The array has been used to derive a cluster

analysis (left) indicating the correlations between isotopic shifts.

Each Lab_i indicates a different labelling experiment, in which i

is the amount of C net fixed (in mmol C m-2 s-1). The array and

the cluster have been generated with the Cluster and Treeview

softwares (M. Eisen, Standford University). Suc, sucrose; Prot,

heat-precipitated proteins; OA, organic acids; Lip, lipids.

890 G. Tcherkez et al.




with this technique: CO2 evolved in darkness correlates

more closely with starch and sucrose; and lipids, on the

other hand, show little correlation with other compounds

because of their slow turnover. Thus, starch appears to be

the most likely substrate feeding leaf respiration following

illumination.

PERSPECTIVES

At the outset, we emphasized the current use of isotopes to

understand the architecture of plant metabolism and com-

munities in ecosystems. Isotopes indeed provide a key to

these approaches, linking global carbon mass balance to

basic enzymatic discrimination (e.g. Rubisco and respira-

tory processes) via elementary physiological events, which

ultimately define the CO2 signature in the atmosphere.

However, more correlative approaches using isotopes,

which have been undertaken in genomic and metabolomic

approaches, have not been realistically conducted to date. If

integrative methods such as isotopomics and isotopologieswere to be adopted, this would help to understanding con-

nectivity between metabolite pools or drivers of ecosytem

dynamics.This would help to elucidate interactions between

biogeochemical factors controlling carbon sequestration

and respiratory release.

In the present paper, we have used leaf-scale data as an

example to explain the principle of the approaches. In a

similar manner, we propose that isotopomic approaches

could be extended to larger-scale studies, to investigate the

architecture of the carbon trafficking networks in soil or

ecosystem scales, showing, for example, transfer of carbon

from leaves to soil-respired CO2 (Bowling et al. 2002; Knohl

et al. 2005). We nevertheless recognize that this wouldrequire a large body of isotopic data associated with several

components of ecosystems. However, there is no doubt that

this may be overcome in the very near future, thanks to the

use of automated continuous-flow spectrometric measure-

ments or tunable diode laser techniques (as CO2 isotope

composition is concerned) (Bowling et al. 2002). Ultimately,

we suggest that by mapping the distribution of isotopic

signals in biological systems, these approaches will improve

our understanding of ecological processes by weighting the

contributory physiological processes, and provide a more

effective means to visualize their interrelationships.

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