# Theoretical considerations about carbon isotope distribution in glucose of C_{3} plants

Guillaume Tcherkez ^{A}

^{D}, Graham Farquhar

^{B}, Franz Badeck

^{C}and Jaleh Ghashghaie

^{A}

^{A} Laboratoire d'écophysiologie végétale, UMR 8079, Bât. 362, Centre scientifique d’Orsay, Université Paris XI, 91405 Orsay Cedex, France.

^{B} Research School of Biological Sciences, Institute of Advanced Studies, Australian National University, GPO Box 475 Canberra, ACT 2601, Australia.

^{C} Potsdam Institute for Climate Impact Research (PIK), PF 60 12 03, 14412 Potsdam, Germany.

^{D} Corresponding author; email: guillaume.tcherkez@ese.u-psud.fr

*Functional Plant Biology* 31(9) 857-877 https://doi.org/10.1071/FP04053

Submitted: 12 March 2004 Accepted: 20 July 2004 Published: 23 September 2004

## Abstract

The origin of the non-statistical intramolecular distribution of ^{13}C in glucose of C_{3} plants is examined, including the role of the aldolisation of triose phosphates as proposed by Gleixner and Schmidt (1997). A modelling approach is taken in order to investigate the relationships between the intramolecular distribution of ^{13}C in hexoses and the reactions of primary carbon metabolism. The model takes into account C–C bond-breaking reactions of the Calvin cycle and leads to a mathematical expression for the isotope ratios in hexoses in the steady state. In order to best fit the experimentally-observed intramolecular distribution, the values given by the model indicate that (i), the transketolase reaction fractionates against ^{13}C by 4–7‰ and (ii), depending on the photorespiration rate used for estimations, the aldolase reaction discriminates in favour of ^{13}C by 6‰ during fructose-1,6-bisphosphate production; an isotope discrimination by 2‰ against ^{13}C is obtained when the photorespiration rate is high. Additionally, the estimated fractionations are sensitive to the flux of starch synthesis. Fructose produced from starch breakdown is suggested to be isotopically heavier than sucrose produced in the light, and so the balance between these two sources affects the average intramolecular distribution of glucose derived from stored carbohydrates. The model is also used to estimate photorespiratory and day respiratory fractionations that appear to both depend only weakly on the rate of ribulose-1,5-bisphosphate oxygenation.

**Keywords:** Calvin cycle, isotope effects, photorespiration, respiration, starch.

## Acknowledgments

We thank to Gabriel Cornic for his advice on writing the manuscript. Graham Farquhar acknowledges the Autralian Research Council for its support through a Discovery Grant. This work was supported in part by the European Community's Human Potential Program under contract HPRN-CT 1999–00059, [NETCARB].

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## Appendix Model description

The modelled Calvin cycle is described in the Scheme 1. The flux of ribulose-1,5-bisphosphate (RuBP) carboxylation is *v*_{c} and it is supposed that *v*_{c} = 1 and the flux of photorespiratory RuBP oxygenation is *v*_{o} = Φ*v _{c}*. Assuming

*v*

_{c}= 1,

*v*

_{o}= Φ. The flux entering the glyceraldehyde-3-phosphate (G3P) is then 2+3Φ/2. The isomerisation flux to dihydroxyacetone-phosphate (DHAP) is 1+Φ/2 and the export flux is 1–Φ/2 so that all the other fluxes are equal to (1+Φ)/3 because of mass balance.

The compounds are abbreviated as follows:

As pointed out in *Assumptions and methods*, the variables used at first in the model are isotope ratios and inverse isotope effects. Inverse isotope effects are simpler to use through numerical calculations because they are simply multiplied by isotope ratios. The main parameters used in the model are listed below.

### General procedure

The procedure used for stable isotope ratios is detailed assuming that the exported molecule is DHAP and, initially, that there is no starch synthesis (*T* = 0). The isotope ratio ^{13}C / ^{12}C of a given molecule M at the *n*th round of the Calvin cycle is denoted as [M]_{n} and [M] in the steady state. The recurrence equations are derived from the procedure in *Assumption and methods*. For example, for G3P-C1, the amount of ^{13}C in G3P in position C1 is denoted as [G3P-C1]^{13} and has the following general expression:

where *s* (mol of C) is the flux of carbon through reactions for a given time interval. We divide by the carbon pool size *S* (which comprises ^{13}C and ^{12}C isotopomers) and then we have:

That is, neglecting the ratios, compared with 1:

In the steady state, we have the relationship:

which does not depend on the amount *S*. It should be noted that the relationship with isotope compositions (δ^{13}C) can then be derived from this equation. If *R*_{st} is the isotope ratio in the standard material, the previous equation is equivalent to:

that is,

If the discrimination in the ‘reaction’ consuming G3P-C1 is denoted as Δ(α) = α - 1, and neglecting the second order terms, then we have:

That said, we can write the equations in the steady state for the other compounds, including the effects of photorespiration. Then we have:

Using a substitution procedure the following relationships can be deduced:

where the notation *def* means that this relationship defines *ã*_{3}. Similarly,

When using *ã _{2}* and

*ã*we have:

_{3}And for photorespiratory CO_{2} :

Eventually, substituting RuBP ratios into G3P equations and rearranging gives:

The isotopic ratios in FBP when expressed as a function of [G3P-C1] are:

It should be noted that these isotopic ratios are not dependent on *t*_{3}, which then cannot be expressed as a function of FBP isotopic ratios. Moreover, we have the relationship: [FBP-C1]=[FBP-C6], which is consequence of isomerisation by triose-phosphate isomerase and the absence of secondary isotope effects on C-3 of trioses in the model. However, this equality does not occur in natural Glc (Rossmann *et al.* 1991) and the isotope ratios in C-1 to C-5 positions only are used for calculations of inverse isotope effects.

### Introducing starch synthesis

The same procedure can be used assuming that there is a net flux of FBP for transitory starch synthesis in the chloroplast (*T*), and that there is a trade-off between DHAP export and starch synthesis. In this case, the DHAP export flux is *T* can be calculated with the constraint *T*_{max}. Relationships giving isotopic ratios are very similar to those in section *a*, giving for FBP:

### Cytoplasmic FBP

Carbohydrates from storage organs may come from those supplied by leaves through light export of Suc or night degradation of transitory starch. Suc produced in light is synthesised in the cytoplasm from DHAP exported from the chloroplast (Scheme 1). The export flux of DHAP from the chloroplast is *E* = 1 / 3 - Φ / 6 – 2*T*. The DHAP molecules in the cytoplasm are isomerised to G3P and FBP is produced by aldolase. One part of the G3P is diverted to other metabolic purposes (like respiration) and the flux of Suc synthesis in the cytoplasm is *E* / 3. Thus the isotopic ratios in cytoplasmic FBP are as follows:

where [DHAP-Ci] are the isotopic ratios of DHAP *in the chloroplast*.

### Calculation of isotope effects

Glc from which Rossmann *et al.* (1991) measured isotope ratios result from storage (root storage in beet, grain storage in maize) and so are derived from both light-produced (cytosolic) and night-produced Suc (transitory starch). The proportion of Glc that comes from light-produced Suc in storage Glc is denoted as *L*. From the relationships given before, it is deduced that the isotope ratios in the Glc analysed by Rossmann *et al.* (1991) are the following:

where [G3P-C1] is the isotope ratio of G3P in the chloroplast and is given by the relationship shown in *Introducing starch synthesis*. Those expressions do not allow a direct resolution and a linearisation is more convenient. The inverse isotope effects are written as *a*_{i}=1+*o*(*a*_{i}) so that the isotope discrimination is then Δ(*a*_{i})=1 / / *a*_{i}-1 that is, –o(*a*_{i}). If the second order terms in the previous equations are neglected, the discriminations are given by:

with the relationships:

### Photorespiratory discrimination

Isotope discrimination occurring during photorespiration in on-line gas-exchange systems is defined using net assimilated carbon as a reference material (Farquhar *et al.* 1982) and is equal to *R _{A}* is the isotope ratio of the net assimilated carbon. This ratio can be simply derived from the assimilation equation:

where *A* is the net assimilation rate, *R*_{R} the carbon isotope ratio of day-respired CO_{2} and *R*_{d} the rate of day respiration. *C* is the isotope ratio in photorespired CO_{2} (see above). Rearranging, gives:

Assuming that G3P molecules entering glycolysis are completely degraded through respiration, *R*_{R} is the mean isotope ratio in cytoplasmic G3P. The value of *R _{d}* is positive and its maximal value is

*E*/ 3 (Scheme 1). With the relationship

*C*=2[RuBP-C2] / (2

*+ g*) (see above) and neglecting second order terms, we get the approximation

*ξ*is a term of the same order as

*f*(per mil). That is,

*f*is linearly related to

*g*/ 2. The day respiratory discrimination is calculated with the relationship