Estimating Mesophyll Conductance from Measurements of ... · Estimating Mesophyll Conductance from Measurements of C18OO Photosynthetic Discrimination and Carbonic Anhydrase Activity1[OPEN]

Estimating Mesophyll Conductance from Measurementsof C18OO Photosynthetic Discrimination and CarbonicAnhydrase Activity1[OPEN]

Jérôme Ogée,a,2 Lisa Wingate,a and Bernard Gentyb,3

aInstitut National de la Recherche Agronomique, Bordeaux Sciences Agro, Unité Mixte de Recherche 1361,Interactions Sol-Plante-Atmosphère, 33140 Villenave d’Ornon, FrancebCentre National de la Recherche Scientifique-Commissariat à l’Energie Atomique-Université Aix-Marseille,Unité Mixte de Recherche 7265, Biosciences and Biotechnologies Institute, 13108 Saint-Paul-lez-Durance, France

ORCID IDs: 0000-0002-3365-8584 (J.O.); 0000-0003-1921-1556 (L.W.)

Carbonic anhydrase (CA) activity in leaves catalyzes the 18O exchange between CO2 and water during photosynthesis. Thisfeature has been used to estimate the mesophyll conductance to CO2 (gm) from measurements of online C18OO photosyntheticdiscrimination (Δ18O). Based on CA assays on leaf extracts, it has been argued that CO2 in mesophyll cells should be in isotopicequilibrium with water in most C3 species as well as many C4 dicot species. However, this seems incompatible with Δ18O datathat would indicate a much lower degree of equilibration, especially in C4 plants under high light intensity. This apparentcontradiction is resolved here using a new model of C3 and C4 photosynthetic discrimination that includes competition betweenCO2 hydration and carboxylation and the contribution of respiratory fluxes. This new modeling framework is used to revisitpreviously published data sets on C3 and C4 species, including CA-deficient plants. We conclude that (1) newly Δ18O-derived gmvalues are usually close but significantly higher (typically 20% and up to 50%) than those derived assuming full equilibrationand (2) despite the uncertainty associated with the respiration rate in light, or the water isotope gradient between mesophyll andbundle sheath cells, robust estimates of Δ18O-derived gm can be achieved in both C3 and C4 plants.

Carbonic anhydrases (CAs) are a group of zinc me-talloenzymes that catalyze the interconversion of CO2into bicarbonate with great efficiency (Moroney et al.,2001; Rowlett, 2010). In the mesophyll cells of C3 plants,CA is most abundant in the stroma (Badger and Price,1994), but CAs also are found in other compartments ofthe mesophyll such as the cytosol, the mitochondria, orthe plasmamembrane (Fabre et al., 2007; DiMario et al.,2016). Chloroplastic CA in C3 plants was first assumedto be required to provide CO2 to Rubisco in the stroma,given the alkalinity of this compartment (Badger andPrice, 1994), but results of studies on antisense tobacco(Nicotiana tabacum) plants have not been conclusive

(Price et al., 1994). In C4 plants, CA is most abundant inthe cytosol (Badger and Price, 1994), primarily becauseit is needed to increase the supply of bicarbonate tophosphoenolpyruvate carboxylase (PEPC; Hatch andBurnell, 1990; Badger and Price, 1994). This idea wasconfirmed by experiments conducted on CA-deficientmutants, which showed that cytosolic CAwas requiredto maintain high photosynthetic rate in Flaveria bidentis(von Caemmerer et al., 2004) and Zea mays, at least inlow-CO2 environments (Studer et al., 2014).

Irrespective of the exact functional role of CA inplants, CA catalyzes the 18O exchange between CO2and water, so that CO2 is commonly assumed to benear isotopic equilibrium with water in CA-containingmesophyll compartments. Consequently, CO2 partialpressure at the site of CA activity inside the mesophyllcells (pCA) can be derived from online 18O photosyn-thetic discrimination (D18O) measurements, providedthat the 18O/16O ratio of leaf water at this CA site can beestimated (Gillon and Yakir, 2000b). However, some-times CO2 might not be in complete equilibration withwater, especially when CO2 uptake rates are high, asthis would result in relatively brief residence times forCO2 molecules inside the mesophyll. This led Gillonand Yakir (2000b) to propose a formulation for D18Othat incorporates the degree of CO2-H2O isotopicequilibrium, u (0 # u # 1). Online D18O measurementsand estimates of u from in vitro CA assays indicatedthat, for three C3 species, pCA always lay somewherebetween the CO2 partial pressure in the substomatal

1This work was funded by the Agence Nationale de la Recherche(award no. ANR-13-BS06-0005-01 [project ORCA]) and the EuropeanUnion’s Seventh Framework Programme (FP7/2007-2013; grantagreements nos. 338264 [project SOLCA], 289582 [project 3to4], and618105 [ERA-Net Plus project MODCARBOSTRESS]).

2Author for contact: [email protected] author.The author responsible for distribution of materials integral to the

findings presented in this article in accordance with the policy de-scribed in the Instructions for Authors (www.plantphysiol.org) is:Jérôme Ogée ([email protected]).

J.O., B.G., and L.W. discussed the original idea; J.O. and B.G. de-veloped the theory and performed the literature survey; J.O. per-formed the analysis and wrote the article, with contributions fromall the authors.

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cavity (pi) and that at the sites of carboxylation in thechloroplast stroma (pc), estimated separately fromonline 13C photosynthetic discrimination (D13C) mea-surements (Gillon and Yakir, 2000b). This finding wasin line with the hypothesis that the outer limit of CAactivity in C3 plants was located at the chloroplastsurface, and thus before the carboxylation site withinthe chloroplast stroma. This approach was later used ina follow-up study to estimate mesophyll conductance(gm) and u in a number of C3 plants but also in C4 plants,which generally exhibited lower u values than C3 plants(Gillon and Yakir, 2001).In other studies (Gillon and Yakir, 2000a; Cousins

et al., 2006b), a slightly different approachwas adopted.gm was derived from D18O measurements performedunder low-light conditions (i.e. when the residence timeof CO2 inside the mesophyll was expected to be longenough to allow full equilibration [u = 1]). Under higherlight intensities, gm was assumed constant (for a givenspecies), and u was then estimated from the D18O dataand usually found to be quite low, down to 0.1 (Gillonand Yakir, 2000a; Cousins et al., 2006b). Cousins et al.(2006b) noted that these D18O-derived u values seemedincompatible with in vitro leaf CA assays that, instead,indicated full equilibration at all light conditions. Thesediscrepancies between in vitro and D18O-derived uestimates were hypothesized to arise from a spatialmismatch between the CA site and the evaporation sitein C4 plants and an isotopically heterogenous leafwater composition in the cytoplasm of mesophyll cells(Cousins et al., 2006b).Although it is not possible to completely rule out

these hypotheses, there is growing evidence that waterisotope gradients do not develop within the cytoplasmand, rather, remain confined to the vascular tissues ofthe leaf (Holloway-Phillips et al., 2016). Furthermore,in vitro CA assays conducted in all recent studies, usingpH and CO2 concentrations close to those experiencedin folio, seem to indicate that CO2 should always benear full isotopic equilibration with leaf water (Cousinset al., 2007; Studer et al., 2014; Barbour et al., 2016;Ubierna et al., 2017). Consequently, a common practicenow is to assume u = 1 when estimating gm from onlineD18Omeasurements (Barbour et al., 2016; Ubierna et al.,2017) and also to perform a sensitivity analysis to pre-dict how gm would be affected had u been set tolower values, noting that lower u values always lead tohigher gm values (Barbour et al., 2016; Ubierna et al.,2017). Most recently, alternative estimates of gm inC4 plants using in vitro maximal phosphoenolpyruvate(PEP) carboxylation rate measurements seem to supportD18O-derived gm estimates assuming u = 1 (Ubierna et al.,2017).This article reexamines the relationship between CA

activity and isotopic equilibration during photosyn-thesis. To address this overlooked issue, we propose asteady-state modeling framework of D18O for both C3and C4 plants. This new model explicitly accountsfor the competition between CO2 hydration and car-boxylation, providing the possibility for incomplete

CO2-H2O equilibration to occur inside the leaf. In ad-dition, the new model accounts for the physical sepa-ration between mesophyll and bundle sheath cells in C4species and for the contribution of respiratory fluxes.Several factors motivated the derivation of this newmodel. First, as we will explain later, the current modeldescribing the degree of u (Gillon and Yakir, 2000b) isbased on several assumptions that cannot be applied tosteady-state leaf gas-exchange measurements, thuspreventing any conclusion to be drawn on whetherisotopic equilibrium is reached based on in vitro CAactivity assays. Additionally, the current practice ofsetting u to unity or lower does not allow the study ofthe functional link between CA activity and D18O andhow it varies between C3 and C4 species. A steady-stateformulation of D18O by C3 plants that includes thecompetition between carboxylation and CA-catalyzedCO2 hydration was proposed already by Farquharand Lloyd (1993). This formulation constitutes thebasis of our derivation that we extended to C3 and C4photosynthesis pathways and mesophyll compart-mentalization. The new model also applies to condi-tions of high leaf-to-air vapor pressure deficit thatrequire ternary corrections on the CO2 and C18OOassimilation rates (von Caemmerer and Farquhar,1981; Farquhar and Cernusak, 2012). With this newmodeling framework, we revisit a number of previ-ously published data sets for C3 and C4 species, in-cluding CA-deficient mutants, and illustrate how toreconcile in vitro CA assays with online D18O mea-surements while, at the same time, estimating gmfrom D18O data.

THEORY

The Gas-Exchange View

Throughout this article, we will assume that CO2 orC18OO gradients within the intercellular air space arenegligible, and we will use the terms intercellular airspace and stomatal cavity air space interchangeably.Under the assumption of a well-identified CA site in-side themesophyll cells upstream of any carboxylationsite (Fig. 1, gas-exchange view), the net leaf CO2 fluxcan be written as the product of a conductance gm forCO2 diffusion from the intercellular air space to theCA site and the CO2 drawdown along the same path:A = gm(pi 2 pCA)/P, where P is atmospheric pressureand pi and pCA are the CO2 partial pressures in theintercellular air space and at the CA site, respectively.Similarly, the net C18OO flux can be defined as18A ¼ 2gm

1þawðpiRi 2 pCARCAÞ=P, where aw is the fraction-

ation factor during CO2 dissolution and diffusion fromthe substomatal cavity to the CA site and Ri and RCArepresent the 18O/16O ratios of CO2 in the substomatalcavity and at the CA site. The fractionation factor awis quite small and usually taken as +0.8‰ at 25°C(Farquhar and Lloyd, 1993). These two flux-gradientrelationships can be combined and rearranged asfollows:

Plant Physiol. Vol. 178, 2018 729

Mesophyll Conductance in C3 and C4 Plants

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Dci ¼ Di 2 aw«cið1þ DiÞ ð1Þ

where Dci = RCA/Ri 2 1, «ci = pCA/(pi 2 pCA), Di = Ri/RA 2 1, and RA represents the 18O/16O ratio of thenet CO2 flux (=0.518A/A); that is, Δi representsΔ18O, expressed relative to Ri and not relative tothe 18O/16O ratio of the CO2 in the air surrounding theleaf (Ra).

Our current theoretical understanding of the C18OOphotosynthetic discrimination has been drawn onthe assumption that the CA site is located in a leafwater compartment with a homogenous 18O/16O ratiothat includes the evaporation site. This assumption isin accordance with recent studies showing that leafwater isotopic gradients seem to be limited to a smallregion around the leaf veins (Holloway-Phillips et al.,2016). In this case, the 18O/16O ratio of the water in theCA-containing compartment can be approximated asthe 18O/16O ratio at the evaporation site within the

mesophyll (noted Res hereafter) and, thus, estimatedfrom water vapor isotope and leaf gas-exchangemeasurements (Cernusak et al., 2004; Farquhar et al.,2007). From these estimates of Res, we can calculate the18O/16O ratio of CO2 in full isotopic equilibriumwith leafwater at the CA site (noted Dei and expressed relativeto Ri):

Dei ¼ Resawc

Ri2 1 ð2Þ

where awc denotes the temperature-dependent equi-librium isotopic fractionation between CO2 and water(Brenninkmeijer et al., 1983).

If we assume that CO2 is fully equilibrated withleaf water at the CA site, then Δci = Δei and we canestimate «ci from measurements of Res and RA usingEquation 1 (this requires knowledge of Δia = Ri/Ra 2 1,which can be estimated from measurements of ΔAalongside CO2 and water vapor fluxes; see “Materialsand Methods”).

Figure 1. Resistance scheme of CO2 and C18OO fluxes in C3 and C4 plants. From a gas-exchange point of view, the net CO2

photosynthetic rate in the leaf (A) can be seen as driven by the CO2 gradient between the intercellular air space (partial pressure pi,isotope ratio Ri) and the leaf interior that, for C18OO, should correspond to the outer limit of CA activity (partial pressure pCA,isotope ratio RCA). From a biochemical point of view, we distinguish C3 and C4 photosynthetic pathways. For C3 plants, the netCO2 flux A is feeding CO2 entirely to the cytoplasm of mesophyll cells, while photorespiration (Vo) and mitochondrial respiration(Vr) are feeding CO2 to the cytoplasm only partially (fraction fr, isotope ratio Rmi) and the other fraction is recycled directly by thechloroplast. For C4 plants,A also is feeding CO2 entirely to the cytoplasm of mesophyll cells, but Rubisco-related photorespirationoccurs only in the bundle sheath cells and mitochondrial respiration occurs in both mesophyll cells (fraction fr, isotope ratio Rmi)and bundle sheath cells (isotope ratio R9mi). The CO2 in the cytoplasm of mesophyll cells (mixing ratioCm, isotope ratio Rm) can behydrated (rate Vhm), and the bicarbonate (concentration Bm, isotope ratio R9m) can be dehydrated (rate Vdm). In C4 plants, bicar-bonate also is consumed through PEPC activity (rateVp). In C3 plants, the CO2 in the chloroplasts (mixing ratioCc, isotope ratioRc)can be hydrated (rate Vhc) or consumed by Rubisco (rate Vc), and the bicarbonate (concentration Bc, isotope ratio R9c) can bedehydrated (rate Vdc). In C4 plants, the CO2 in the bundle sheath cells can only be consumed by Rubisco (rate Vc). The exactcorrespondence between pCA and Cm or Cc will vary between C3 and C4 plants (see text), and the associated D18O-derivedmesophyll conductance to CO2 (gm) is not simply a transfer resistance but also may incorporate a biochemical component.

730 Plant Physiol. Vol. 178, 2018

Ogée et al.



However, because the residence time of CO2 insidethe mesophyll can be somewhat shorter than the timerequired for full isotopic equilibration with leaf water,Dci differs from Dei. The proportion of CO2 in isotopicequilibrium with leaf water can be defined as (Gillonand Yakir, 2000a, 2000b):

u ¼ Dci 2Dci0

Dei 2Dci0ð3Þ

where Dci0 represents the value of Dci in the absenceof any CA activity (or, more correctly, of any CO2-H2Ooxygen isotope exchange). The latter is usually de-rived using an approach similar to that described for13C photosynthetic discrimination (Gillon and Yakir,2000b), assuming no isotope fractionation duringcarboxylation by PEPC (EC 4.1.1.31) or Rubisco orduring respiration. The exact expression (see Appen-dix C, Eq. C28) shows that Dci0 depends on «ci and,thus, pCA. This comes to assume that, despite the(putative) absence of CA activity, the carboxylationsite coincides with the (true) CA site. This can beproblematic, especially in C4 plants. However, in mostcases, u is expected to be close to unity and the exactknowledge of Dci0 becomes less critical.In fact, the knowledge of Dci0 is only required to

compute u. Because Gillon and Yakir (2000a, 2000b)proposed an independent expression for u (see below)in terms of the residence time tres (s) of CO2 within theleaf mesophyll and the CA-catalyzed CO2-H2O isotopicexchange rate kiso (s21), they required knowledge ofDci0 to compute Dci and, thus, «ci and gm. Another ap-proach, adopted by Farquhar and Lloyd (1993), pro-vided a direct expression for Δci in terms of CA activityand carboxylation and respiratory fluxes. This ex-pression, combined with Equation 1, can be usedto retrieve «ci and gm without the need to estimatethe degree of equilibration u, as demonstrated insome follow-up applications (Flanagan et al., 1994;Williams et al., 1996). These two approaches arereviewed below.

The Biochemical View

To derive an expression for u, Gillon and Yakir(2000a, 2000b) revisited the work of Mills and Urey(1940), who showed that the 18O/16O ratio of CO2 inclosed aqueous solutions rapidly follows an ordinarydifferential equation, which can be rewritten with thecurrent notations as follows:

dDci

dt¼ 2 kisoðDci 2DeiÞ ð4Þ

where kiso (s21) is the CO2-H2O isotopic exchange rate.

The leafmesophyll is not a closed system, but Gillon andYakir (2000b) assumed that Equation 4 would ade-quately describe the dynamics ofDci. This is justified onlyif the CO2-H2O isotopic exchange rate is much greater

than any C18OO carboxylation flux, which is unlikelyunder high light intensity or for CA-deficient leaves.Despite these caveats, they proposed estimating u(Eq. 3) by integrating Equation 4 between time t =0 and t = tres and assuming that Dci0 precisely repre-sents the value of Dci at time t = 0 (Gillon and Yakir,2000b):

u ¼ 12 expð2 kisotresÞ ð5ÞThis derivation is problematic, as it uses a non-

steady-state formulation (integrated over the resi-dence time tres) to describe steady-state gas-exchangedynamics. Additionally, stating that Dci0 precisely rep-resents the value of Dci at time t = 0 assumes that the leafhas been (initially) filled with unlabeled CO2, which isnot realistic even with a fluctuating environment, be-cause CA activity continuously resets Dci. Yet, Equation5 has been used in several studies to link CA activityto Δ18O data (Gillon and Yakir, 2000a, 2000b, 2001;Cousins et al., 2006a, 2006b, 2007). To do so, the ex-change rate constant kiso appearing in Equation 5 usu-ally is taken as one-third of the CA-catalyzed CO2hydration rate kh and the residence time tres is taken asthe ratio of the total amount of CO2 inside the leaf to theone-way flux of CO2 from the atmosphere into the leaf.However, the ratio kiso/kh equals one-third only in acidicconditions (see Appendix B, Eq. B8), and this definitionof the residence time implicitly redefines the systemboundaries to include not only the CA-containing leafcompartment but also other leaf compartments, in-cluding the intercellular air space. In this case, kisoshould be replaced by a more complex expression thatdepends not only on pH but also on the volumes of thegas and liquid phases and the (total) transfer coeffi-cient between these two phases, including gm (seeAppendix B, Eq. B11). Finally, Equation 5 does notaccount for the competition between CO2 hydrationand carboxylation or for the contribution of respira-tory fluxes.

For all these reasons, we adopted another ap-proach that leads to a direct relationship between Dciand leaf CA activity at steady state while simulta-neously accounting for competition between hydra-tion and carboxylation and for respiratory fluxes.The model of Farquhar and Lloyd (1993) forms thebasis of this new approach but is modified to ac-count for the spatial separation of hydration andcarboxylation sites, and their difference in leaf waterisotopic composition, especially important in C4species.

The CO2 gas-exchange rate A is the net result ofCO2 hydration, carboxylation, and respiration rates(Fig. 1, biochemical view). At steady state, isotopicequilibrium may not be reached, even at the CA site, ifCO2 carboxylation is large. Using the resistance schemeillustrated in Figure 1, and assuming no isotopic frac-tionation during carboxylation by Rubisco or PEPC, theisotope ratio of the net CO2 flux (see Appendix C for aderivation) is determined as follows:





where Req = Resawc, fr is the fraction of respired CO2not recycled by the chloroplast stroma (C3 plant) or notproduced in the bundle sheath (C4 plant), and Fr is theratio of the respiratory flux to the net flux: Fr = (Vr +0.5Vo)/A (all other symbols are defined in the legend ofFig. 1).

Several lines of evidence (see Appendix C and alsoFarquhar and Cernusak [2012]) indicate that respiredCO2 should be fully equilibrated with mitochondrialwater, suggesting Rmi = Req and R9

mi �Rxawc, where Rxis the isotope ratio of the water in the bundle sheathcells. Following arguments in favor of a strong homo-geneity of water isotope ratios between the cytosol andthe chloroplast of single cells, we further assume thatRm and Rc should be closely related in C3 speciesand equal to the CO2 isotope ratio at the CA site(RCA). In C4 species, we argue (see Appendix C) that Rc(the 18O/16O ratio of CO2 in the bundle sheath) shouldbe closely related to Rm/acb�RCA/acb, where acb is theisotope fractionation between CO2 and bicarbonate(around 1.0095 at 25°C). With these simplifications,Equation 6 can be rewritten (see Appendix C):

where r = ri(1 + «ci)/«ci, ri = A/(kCApi), kCA is themeasured leaf CA activity rate [expressed in mmol(CO2) m

22 s21 Pa21], acb = acb 2 1, and Δeq = (Res/Rx 2 1)acwRx/Ri� Res/Rx – 1. Equation 7 can be combined withEquation 1 to eliminate Δci and estimate «ci (then pCAand gm) from measurements of kCA, Di, Dei, and watervapor and CO2 fluxes, provided that the respiratoryterms (Fr, Vr/A, and fr) are known. Noting that Fr alsodepends on «ci (i.e. it can be expressed as a function of«ci, Vr/A, and G*/Ci, where Ci = pi/P and G* is the CO2compensation point in the absence of day respiration;see Eq. C17), this requires solving a quadratic (for C3plants) or a cubic (for C4 plants) equation in «ci (Eqs. C18and C23, respectively; see Appendix C for a full deri-vation). If respiratory terms are negligible (Fr = 0), thenthe solution for C3 plants is similar to that proposed byFarquhar and Lloyd (1993). However, if respiratory

terms are not negligible, the situation is different be-cause, here, we assume that CO2 respired by C3 leaves isin equilibrium with mitochondrial (and thus cytoplas-mic) water, while Farquhar and Lloyd (1993) did not(see Appendix C).

In the following, we solve Equation 7 for «ci us-ing published data sets of kCA, Di, Dei, and watervapor and CO2 fluxes (Cousins et al., 2006b, 2007;Barbour et al., 2016). For this, we set fr = 0.5 andcompute G* as a function of leaf temperature(Bernacchi et al., 2001). We then explore the pos-sibility of using our new equation to estimate gm inC3 and C4 species and estimate its sensitivity tothe respiratory terms (Vr/A) or the water isotopegradients between mesophyll and bundle sheathcells.

For the sake of comparison with previous work, wealso compute a degree of equilibration, as defined byEquation 3. For this, we estimated Δci0 by taking thelimiting case of Equation 6 when kCA tends to zero (i.e.Vhm = Vhc = 0) and assuming that, in the absence of CAactivity, the respiratory isotope ratios were equal to Ra.

Noting that Vc/A = 1 + Fr, this gives the followingequation for both C3 and C4 plants:

RA →kCA→0

ð1þ FrÞRc0 2 FrRa ð8Þ

where Rc0 denotes Rc in the absence of CA activity.Combined with flux-gradient relationships such as thatin Equation 1 (valid regardless of the CA activity), weobtain an expression for the ratio Rc0/Ra (see AppendixC, Eq. C28), fromwhichwe can derive Δci0 (Eq. C29) andthus u (Eq. 3).

RESULTS AND DISCUSSION

We first revisited the data fromCousins et al. (2006b),who measured online discrimination and the CA

8>><>>:

RA ¼ Vhm

3A

�Rm 2Req

�þ Vhc

3A

�Rc 2Req

�þ Vc

ARc 2 FrRmi for C3 plants

RA ¼ Vhm

3A

�Rm 2Req

�þ Vc

ARc 2 FrRmi 2fr

Vr

AðRmi 2R9

miÞ for C4 plantsð6Þ

8>>><>>>:

11þ Di

¼ 1þ 3rFr3r

ðDci 2DeiÞ þ 1þ Dci for C3 plants

11þ Di

¼ 1þ 3rFr3r

ðDci 2DeiÞ þ 12 acbFracb

ð1þ DciÞ2frVr

ADeq for C4 plants

ð7Þ


Ogée et al.



activity of C3 and C4 plants exposed to different lightlevels (see Table II in Cousins et al., 2006b).We estimated the effect of assuming or not assuming

full CO2-H2O equilibration and increasing the respira-tory fraction (Vr/A) on the light response of pCA/pa, gm,and u in F. bidentis leaves (Fig. 2). We see that the as-sumption of full equilibration is almost valid at lowlight but, as incident light increases, the degree ofequilibration decreases slowly (Fig. 2C), although notas sharply as the original u values of Cousins et al.(2006b). This decrease in u is slower when the respira-tory fraction is high, as a consequence of the assump-tion that respired CO2 is fully equilibrated. Moreinterestingly, the retrieved gm responds very little to theincrease in incident light, especially when comparedwith stomatal conductance (Fig. 2B). The new estimatesof gm also are much lower (around 0.4 mol m22 s21)than the original value of 1 mol m22 s21 estimated byCousins et al. (2006b) and only slightly higher (byaround +15%) than the values we estimated assumingfull equilibration (u = 1).At first sight, it may seem surprising that, even for the

lowest light level, our estimates of gm are much lowerthan the original estimate of Cousins et al. (2006b),despite the fact that, in both cases, full isotopic equili-bration is reached (an assumption in the case of Cousinset al. [2006b] and a prediction in this study). This ap-parent contradiction arises from the ternary corrections.Cousins et al. (2006b) applied ternary corrections toestimate pi but not to interpret C18OO discriminationdata, as was common practice at the time. Farquhar andCernusak (2012) have since shown that such a practicecan lead to erroneous gm estimates. Indeed, when ter-nary corrections are only applied to compute pi, thenthe solution of Equation 9 at low irradiance leads to theexact original gm value (1 mol m22 s21) but much lowergm values with increasing light (Supplemental Fig. S1).On the other hand, not applying ternary corrections atall leads to gm values almost identical to those shown inFigure 2 (Supplemental Fig. S2), a result also predictedby Farquhar and Cernusak (2012).The same analysis also was performed on the tobacco

leaf data sets of Cousins et al. (2006b), and similar re-sults were obtained (Fig. 3). The degree of equilibrationdecreased slowly with an increase in incident light butnot as sharply as in the original publication (Fig. 3C),while the new estimates of gm were lower than esti-mated originally but slightly higher than the valuesobtained assuming full equilibration (+8%–20%,depending on irradiance) and with less sensitivity tolight levels than stomatal conductance (Fig. 3B). Com-pared with the results shown in Figure 2, the sensitivityof gm to the respiratory fraction also is much lower. Thisis because, for C3 species,Vr/A only affects Fr with littleinfluence on Δi as long as r is small, whileVr/A appearsin two other terms in the C18OO discrimination modelfor C4 species (Eq. 7).The above analysis demonstrates that, to explain the

data from Cousins et al. (2006b), there is no need toevoke a spatial separation of the CA site and the

evaporation site, nor an isotope heterogeneity of leafwater in the cytosol of mesophyll cells. By simply ac-counting for ternary corrections, competition betweenCO2 hydration and carboxylation, and the contributionof respiratory fluxes (Eq. 7), it is possible to reconcile thein vitro CA assays and the D18O measurements.

Figure 2. Light response of gas-exchange parameters in F. bidentisleaves exposed to increasing levels of photosynthetic photon fluxdensity (PPFD). A, CO2 partial pressure ratio pCA/pa. B, Δ

18O-derivedmesophyll conductance (gm). C, Δ18O-derived degree of isotopicequilibrium (u). D, Ratio r = A/(kCApCA). Data were taken from Cousinset al. (2006b). Original and revised values, with three different values ofthe respiratory fraction Vr/A, or assuming full equilibration, are shown.The CO2 partial pressure ratio pi/pa and the stomatal conductance toCO2 (gsc) also are shown, in A and B, respectively.




http://www.plantphysiol.org/cgi/content/full/pp.17.01031/DC1



Our new estimates of gm are lower than previousestimates, even when Vr/A = 0 (Figs. 2 and 3). This isespecially the case for F. bidentis, where gm is onlyslightly higher than the maximum stomatal conduc-tance for CO2 (gsc; Fig. 2). As briefly explained above,this occurs because the estimation of gm as originally

performed did not account for ternary correctionswheninterpreting isotopic discrimination. The difference be-tween original and revised gm values is much lowerwhen revisiting data sets where ternary correctionswere fully accounted for, such as those from Barbouret al. (2016). In this case, our new estimates of gm tend toagree well with the original estimates but show con-sistently higher values (typically around 20% and up to50% or more in some cases) than those estimated as-suming full equilibration, and the sensitivity of gm and uto the respiratory fractionVr/A is again very small in C3species and marginally small in C4 species (Fig. 4).

These results show that the degree of equilibration isexpected to be near unity in all species (Fig. 4), and

Figure 4. Degree of isotopic equilibrium (u) and mesophyll conduc-tance (gm) for three C3 (left) and three C4 (right) plants studied by Barbouret al. (2016). Original and revised values, with three different values ofthe respiratory fraction Vr/A, or assuming full equilibration, are shown.CA activity for Gossypium hirsutum (cotton) and Triticum aestivum(wheat) was assumed to be equal to that of tobacco, and CA activity forZ. mays (corn) was taken from Cousins et al. (2006b). For cotton, wheat,and corn, only data for mature leaves are shown here. For corn, oneindividual data point did not lead to a plausible solution to EquationC23 (i.e. negative «ci and gm) and, thus, was discardedwhen computingthe mean value. For consistency, we also discarded this individual datapoint when computing the mean gm value corresponding to full isotopicequilibrium. Had it not been discarded, we would have obtained thesame gm value obtained by Barbour et al. (2016), as is the case for theother species.

Figure 3. Light response of gas-exchange parameters in tobacco leavesexposed to increasing levels of photosynthetic photon flux density(PPFD). A, CO2 partial pressure ratio pCA/pa. B, Δ

18O-derived mesophyllconductance (gm). C, Δ

18O-derived degree of isotopic equilibrium (u).D, Ratio r = A/(kCApCA). Data were taken from Cousins et al. (2006b).Original and revised values, with three different values of the respiratoryfraction Vr/A, or assuming full equilibration, are shown. The CO2 partialpressure ratio pi/pa and the stomatal conductance to CO2 (gsc) also areshown, in A and B, respectively.


Ogée et al.



especially in C3 plants, partially justifying a posteriorithe assumption made by Barbour et al. (2016). How-ever, accounting for incomplete equilibration betweenCO2 and leaf water led to Δ18O-derived gm values thatare significantly higher than those obtained assumingfull isotopic equilibration (Figs. 2–4). Barbour et al.(2016) noticed that, in some C3 plants, the Δ

18O-derivedgm assuming full equilibration were sometimes of amagnitude similar to that of the gm estimated from Δ13Cdiscrimination. This was the case most notably in ma-ture wheat (Triticum aestivum) leaves and seemed in-compatible with the idea that the CA site was located atthe chloroplast surface and, thus, upstream of the car-boxylation site. Here, we show that accounting for in-complete equilibration increases the difference betweenΔ13C- and Δ18O-derived gm even in wheat (0.63 versus0.75 mol m22 s21 for mature leaves). Furthermore, ourmodeling framework partly explains that the differencebetween Δ13C- and Δ18O-derived gm should not be solarge because the CA site is now defined as the meanlocation of CA activity (Eq. C14) rather than its outerlimit, as defined originally by Gillon and Yakir (2000b).Ubierna et al. (2017) showed that PEPC-derived gm

for C4 plants agreed well with D18O-derived gm as-suming u = 1. Their reported PEPC-derived gm valuesfor Z. mays and Setaria viridis agree well also with theD18O-derived gm reported by Barbour et al. (2016) as-suming u = 1, despite possible differences in planttreatments and growth conditions between the twostudies. For Z. mays and S. viridis, Barbour et al. (2016)report gm values of 0.5 and 1.1 mol m22 s21, respec-tively, at around 30°C, which is slightly lower but inrelatively good agreement with the PEPC-derived gmestimates of Ubierna et al. (2017), of around 0.6 and1.3 mol m22 s21, respectively (see Fig. 2 of Ubierna et al.[2017]). Our reanalysis shows that accounting forcompetition between CO2 hydration and carboxylationwould reconcile the two approaches even more, byleading to Δ18O-derived gm values of 0.55 to 0.65 and1 to 1.3 mol m22 s21 for S. viridis and Z. mays, respec-tively (Fig. 4).Another interesting data set to revisit is that of

Cousins et al. (2007) on mutants of Amaranthus edulisthat exhibited a reduced PEPC activity but a CA activitysimilar to that of the wild type. A reanalysis of their dataset using Equation 7 is presented in Figure 5. In theoriginal analysis, gm was set to a constant value for allplants and the degree of equilibration was derivedwithout fully accounting for ternary effects. This led toa rapid decrease in D18O-derived u in response to in-creasing PEPC activity (Fig. 5). This feature seemed incontradiction with the observed in vitro CA activitiesthat were similar among the different PEPC mutants(kCA = 60 6 10 mmol m22 s21 Pa21). Reanalyzing theirdata set with Equation 7 led to quite different results,with a degree of equilibration much closer to unity, evenin the wild type, and much smaller values of gm that in-creased with PEPC activity (Fig. 5). Again, these new Δ18

O-derived gm estimates are slightly higher (up to +20%),than those estimated using full equilibration (Fig. 5).

The results shown in Figure 5 also may help explain,at least qualitatively, the data from Stimler et al. (2011),who reported differences in D18O-derived u betweenC3 and C4 species, despite no difference in CA activ-ity between the two plant groups (estimated for thefirst time simultaneously on the same leaves, usingcarbonyl sulfide [COS] gas-exchange measurements).

Figure 5. Effects of PEPC activity (kPEPC) on gas-exchange parameters inwild-type (WT) and heterozygous (Pp) and homozygous (pp) PEPC-deficientA. edulis plants grown in elevated (0.98 kPa) CO2. A, CO2 partial pressureratio pCA/pa. B, Δ

18O-derived mesophyll conductance (gm). C, Δ18O-derived

degree of isotopic equilibrium (u). D, Ratio r = A/(kCApCA). Data were takenfrom Cousins et al. (2007). Original and revised values, with three differentvalues of the respiratory fraction Vr/A, or assuming full equilibration, areshown. InC, numbers in parentheses indicate isotopic discrimination (Δ18O).





To reconcile the COS-derived CA activities with theD18O-derived u values, Stimler et al. (2011) suggestedthat Equation 5 should be revisited. To explain thelower D18O values of C4 plants relative to those of C3plants, they used Equation 5 and hypothesized a re-duction of kiso of about 17% (Stimler et al., 2011). Thisreduction of kiso was attributed to PEPC activity thatwould deplete the bicarbonate pool of C4 species to apoint where it would affect CA activity (towards CO2but not COS). Indeed, a depletion of bicarbonate woulddeplete pCA because the ratio of CO2 to bicarbonateis fixed by pH, and this should lead to a decrease inthe residence time of CO2 and thus u, to some extent.However, as explained above, Equation 4 is ill designedto describe steady-state gas-exchange data. Our newformulation (Eq. 7), on the other hand, is more suitablebecause it explicitly accounts for the competition be-tween hydration and carboxylation rates while satis-fying the steady-state mass balance. The results shownin Figure 5C clearly demonstrate that differences inD18O (from 207‰ in the homozygous mutant to 16‰in the wild type) are compatible with nearly full iso-topic equilibration (u � 1) or with undetectablechanges in CA activity deduced from other gas-exchange techniques.

In fact, CA activity (kCA) and the degree of equili-bration (u) are not intuitively related, because largechanges in kCA do not necessarily lead to large changesin u (and gm). This is demonstrated in Figure 6, whichrevisits data from Cousins et al. (2006b) on wild-typeand CA-deficient F. bidentis plants grown (and mea-sured) in ambient CO2. Despite kCA values as low as5 mmol m22 s21 Pa21 and r values above unity in someCA-deficient plants, the results using Equation 7 indi-cate that gm remains relatively constant, with values ofwild-type plants and CA-deficient mutants being sim-ilar (Fig. 6B). Again, these gm values are higher thanthose estimated assuming full equilibration (Fig. 6). Thedegree of equilibration u also stays relatively constant,between around 0.7 and 0.8 from low to high CA ac-tivity (Fig. 6C). In fact, in the data sets revisited here, thedegree of equilibration u will usually approach unitywhen r is below 0.01, irrespective of whether it is a C3 orC4 species (Fig. 7). That u is below 0.9 in Figure 6 isprimarily because r is not very low, even in the wildtype (mean value, 0.064).

CONCLUSION

All the results presented here indicate that Δ18O-derived gm values can be estimated robustly at steadystate by considering the competition between CO2 hy-dration and carboxylation, which determines the in-complete CO2-H2O equilibration inside the leaf. Eventhough CO2 is in nearly full equilibration with leafwater in most cases, the newly derived gm values areconsistently higher (typically around 20% and up to50% or more in some cases) than those estimated as-suming full equilibration. However, the physicalmeaning of this D18O-derived gm, and its significance

for CO2 assimilation, are still difficult to grasp, partic-ularly for C3 plants that exhibit CA activity in differentmesophyll compartments. For both C3 and C4 plants,the contribution of the respiratory fluxes to the overallnet C18OO discrimination (Fig. 1) complicates the clas-sical view of gm as a pure diffusional property of the leaf

Figure 6. Effects of leaf CA activity (kCA) on gas-exchange parameters indifferent wild-type and CA-deficient F. bidentis leaves grown andmeasured at ambient CO2 concentrations. A, CO2 partial pressure ratiopCA/pa. B, Δ

18O-derived mesophyll conductance (gm). C, Δ18O-derived

degree of isotopic equilibrium (u). D, Ratio r = A/(kCApCA). Data weretaken from Cousins et al. (2006b). Values, with three different values ofthe respiratory fraction Vr/A, or assuming full equilibration, are shown.Dashed lines indicate second-order polynomial fits to the individualdata points.


Ogée et al.



mesophyll, a problem that also arises when interpretingΔ13C discrimination data (Tholen et al., 2012). The newmodel formulation presented in this study, by ac-counting for the compartmentalization of leaf waterand CO2 hydration, carboxylation, and respirationsites, is an attempt to bring more physical meaning tothis leaf parameter. However, the gas-exchange and bi-ochemical views schematically presented in Figure 1 arestill far from being fully reconciled. Clearly, a more ex-plicit representation of CO2 and C18OO transport in themesophyll and their exchange in the different compart-ments (cytosol, chloroplasts, mitochondria, etc.), with anexplicit representation of their respective volumes, en-zymatic activities, and transfer resistances, is required tofully interpret D18O (and D13C) data in terms of the dif-fusional properties of the cell components.

MATERIALS AND METHODS

Literature Data

For the purpose of this study, three published data sets have been revisited(Cousins et al., 2006b, 2007; Barbour et al., 2016). These data sets have beenselected because they were the ones that gathered measurements of CA activity(kCA) using the

18O-exchangemethod (expected to providemoremeaningful CAactivities in vivo; see next section), isotopic discrimination (ΔA), leaf waterisotope composition (Res), water vapor (E) andCO2 (A) fluxes, and stomatal (gsc)and boundary layer (gbc) conductances for CO2.

Gas-exchange and isotope data were available for all individual measure-ments, except for the data sets of Cousins et al. (2006b, 2007), where separatevalues of Ra could not be retrieved and only mean values of Res, already

expressed relative to Ra (i.e. Δea = Resawc/Ra 2 1), could be assigned from thepublished tables. In addition, for consistency with the values of Barbour et al.(2016), these mean values of Δea from Cousins et al. (2006b, 2007) were correctedusing a fractionation factor for the diffusion of water vapor in still air of 28‰(Merlivat, 1978) instead of 32‰ (Cappa et al., 2003). Finally, in Barbour et al.(2016), kCA values for Gossypium hirsutum (cotton), Triticum aestivum (wheat),and Zea mays (corn) were not reported and were assumed here to be equal tothose of tobacco plants (cotton and wheat) or taken from Cousins et al.(2006b) for corn.

Estimating in Vivo CO2 Hydration Rates kCA from in VitroCA Assays

In all the studies that we revisited, CA activity was estimated by measuring therate of 18O loss of a subsaturating, labeled C18O2-buffered solution (Silverman, 1973;Badger and Price, 1994). The uncatalyzed rate (kuncat,assay) was first measured, andthen leaf extracts were added to the solution to record the catalyzed rate (kcat,assay).CA activity [in units of mol(CO2) m

22 s21 Pa21] was then converted to its expectedin vivo value (von Caemmerer et al., 2004):

kCA ¼ kcat;assaykuncat;assay

kuncat;invivoKHVassay

Sleafð9Þ

where kuncat,invivo (s21) is the uncatalyzed CO2 hydration rate under theconditions in vivo (i.e. at physiological pH), KH (mol m23 Pa21) is the solubilityof CO2 in water, Vassay (m

3) is the volume of the assay solution, and Sleaf (m2) is

the leaf area of the added leaf extracts in this volume. Compared with the pHmethod used in older studies (Gillon and Yakir, 2000a, 2000b, 2001), the CAassay using labeled CO2 is less sensitive to the buffer solution used (Hatch andBurnell, 1990). More importantly, because the CO2-H2O isotopic exchange rateis somewhat slower than the hydration rate (Mills and Urey, 1940), measure-ments can be performed routinely at 25°C and near physiological pH and CO2concentrations, which is now the reason why this assay is preferred over the pHassay (von Caemmerer et al., 2004; Cousins et al., 2006b; Kodama et al., 2011; Studeret al., 2014; Barbour et al., 2016).ApHandCO2 concentration correction still needs tobe applied, which is done using Equation 9. However, implicit to Equation 9 is theassumption that the catalyzed and uncatalyzed rates respond similarly to pH, sothat kuncat,invivo/kuncat,assay equals kcat,invivo/kcat,assay, where kcat,invivo would be the ex-pected catalyzed rate in vivo (i.e. at physiological pH). According to Rowlett et al.(2002), the pH dependence of kcat in wild-type Arabidopsis thaliana is well ap-proximated by 1/(1 + 107.2 2 pH). The pH response of kuncat usually used for CAassays is kuncat(pH) = 0.038 + 6.22/1011– pH (von Caemmerer et al., 2004). A mod-ification of Equation 9 was then applied here:

kCA ¼ kCA;origkuncat

�pHassay

�kuncatðpHinvivoÞ3

1þ 107:22 pHassay

1þ 107:22 pHinvivoð10Þ

where kCA,orig is the original (reported) CA activity. For C3 plants, Equation10 does not modify the reported CA activity because the compartment thatcontains the most CA is the chloroplast stroma, whose pH is very close to the pHof the assay, typically around 8 (von Caemmerer et al., 2004). On the other hand,inC4 plants, pHinvivo is expected to be close to the pHof the cytosol and, thus,moreacidic, around 7.4. In this case, Equation 10 leads to CA activity levels of C4 plantsthat are lower by about 20% than those reported in the literature.

Data Analysis

We define gtc as follows: gtc = 1/(1/gbc + 1/gsc). From pa, A, E, and gtc, wecomputed pi according to von Caemmerer and Farquhar (1981):

pi ¼ 12 t9

1þ t9pa 2

11þ t9

APgtc

ð11Þ

where t9 = 0.5E/gtc is the ternary correction factor.From pi and pa, we computed «ia = pi/(pa 2 pi). Assuming no ternary effect

(t9 = 0), the CO2 isotope ratio in the intercellular air space, expressed relativeto the ratio in the outside air, is derived as follows (see Appendix A for aderivation):

D9ia ¼ DA 2�a9

«iað1þ DAÞ ð12Þ

where �a9 represents the weighted-mean isotope fractionation factor duringCO2 diffusion through the leaf boundary layer and the stomata. Includingternary effects (t9 � 0) leads to (see Appendix A for a derivation):

Figure 7. Degree of equilibration (u) as a function of the ratio of netphotosynthesis to CA hydration rate for the different experimentsrevisited in this study (Figs. 2 and 3, light response; Fig. 4, interspeciesdifferences; Fig. 5, PEPC response; and Fig. 6, CA response) and theremaining data set of Barbour et al. (2016) testing the effect of leaf ageon mesophyll conductance. Only values for Vr/A = 0 are shown forclarity. Increasing Vr/A tends to lift the curve up, with all u values above0.6 for Vr/A = 0.6.





Dia ¼ 11þ ta

D9ia 2

ta1þ ta

�1þ pa

pi

�DA

1þ DAð13Þ

where ta ¼ t9ð1þ �a9Þ (Farquhar and Cernusak, 2012). From Dia, we thencomputed the following:

Di ¼ ð1þ DAÞð1þ DiaÞ2 1 ð14Þ

and

Dei ¼ 1þ Dea

1þ Dia2 1 ð15Þ

Values of pi, kCA, Δi, Δia, and Δei were used to compute «ci using EquationC18 (C3 plants) or Equation C23 (C4 plants), from which we could computepCA = pi«ci/(1 + «ci) and gm = AP/(pi 2 pCA). We finally computed the ratioRCA0/Ra (see Eq. C28), from which we derived Δci0 [=RCA0/Ra/(1 + Δia) 2 1]and thus u.

Supplemental Data

The following supplemental materials are available.

Supplemental Figure S1. Ternary corrections applied to Figure 2.

Supplemental Figure S2. No ternary correction applied to Figure 2 whencomputing both pi and pCA.

Supplemental Figure S3. Isotope difference between CO2 in equilibriumwith the water at the evaporation site and in the intercellular air space.

Supplemental Figure S4. Differences between the intercellular CO2 inequilibrium with the water at the evaporation site and in the intercellularair space.

ACKNOWLEDGMENTS

We thank Margaret Barbour and Asaph Cousins for kindly gatheringand sharing with us the raw data corresponding to the published work thatwe revisited in this article. We also thank the editor, Graham Farquhar, andthe two reviewers, Lucas Cernusak and Nerea Ubierna, for their veryconstructive comments that helped us to greatly improve the final versionof this article.

Received July 26, 2017; accepted July 26, 2018; published August 13, 2018.

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APPENDIX A: TERNARY EFFECTS AND C18OO PHOTOSYNTHETIC DISCRIMINATION

Derivation of Equation 12

Neglecting ternary effects, the net CO2 flux into the leaf also can be expressed as A9 = gtc/P (pa – pi) (with the primeindicating that ternary effects are neglected).Writing a similar equation for the C18OO flux, the ratioRA = 18A9/A9 (wedo not have a prime on RA because it is a measured quantity that does not depend on whether ternary effects areaccounted for or not) can be expressed as:

RA ¼ 11þ �a9

Rapa 2R9ipi

pa 2 piðA1Þ

where R9i denotes Ri when ternary effects are neglected. Using DA = Ra/RA 2 1 and defining D9

ia ¼ R9i=Ra 2 1,

Equation A1 then becomes:

ð1þ DAÞ2 1 ¼ 11þ �a9

�12D9

iapi

pa 2 pi

�ðA2Þ

which can be easily rearranged into Equation 12 in the main text.

Derivation of Equation 13

If we now account for ternary effects, EquationA1 needs to be rewritten. As demonstrated by Farquhar andCernusak(2012), this leads to (see their last equation on page 1223):

Ri ¼ 11þ ta

R9i þ ta

1þ ta

��1þ pa

pi

�RA 2Ra

papi

�ðA3Þ

This can be rewritten as:

Dia ¼ 11þ ta

ð1þ D9iaÞ þ ta

1þ ta

��1þ pa

pi

�ð1þ DAÞ2 1 2

papi

�2 1 ðA4Þ

which easily leads to Equation 13 in the main text.

APPENDIX B: DYNAMICS OF 18O EXCHANGE DURING CO2 HYDRATION AND BICARBONATE DEHYDRATIONIN CLOSED AND OPEN SYSTEMS

Rationale

The dynamics of 18O exchange between CO2 and water in closed solutions has been described previously (Mills andUrey, 1940; Uchikawa and Zeebe, 2012). However, because these studies were designed primarily to estimate theCA-catalyzed hydration rate by means of 18O labelling techniques, kinetic and equilibrium isotopic effects wereignored as a first approximation (e.g. no distinction was made between hydration rate constants for CO2 andC18OO). In this situation, the isotope ratio of dissolved CO2 at equilibrium with the surrounding water (Rc,eq)would simply equal that of the water (Rw). In practice, we know this is not the case, as an equilibrium frac-tionation aCO2ðaq:Þ2H2O of 1.0413 at 25°C exists between aqueous CO2 and water (Beck et al., 2005; Zeebe, 2007). Abrief description of the kinetic isotope effects during CO2 hydration and bicarbonate dehydration is presentedbelow.

Kinetic Isotope Effects during CO2 Hydration and Bicarbonate Dehydration

Using the same notation as in previous studies (Mills and Urey, 1940; Uchikawa and Zeebe, 2012), that is, [66] forC16O2 concentration, [68] for C

16O18O concentration, [6] for H216O concentration, [668] for H2C

16O2

18O concen-tration., and neglecting doubly labeled species at natural abundance, only three hydration-dehydration reac-tions need to be considered:


Ogée et al.



½66� þ ½6�16kh→

16kd← ½666�

½68� þ ½6�18kh→

18kd← ½668�

½66� þ ½8�18k9h→

18kd← ½668�

8>>>>>>>>>>>>>><>>>>>>>>>>>>>>:

ðB1Þ

The rates of change of [666], [68], and [668] are then:8>>>>>>><>>>>>>>:

d½666�dt

¼ 16kh½6�½66�2 16kd½666�d½68�dt

¼ 2 18kh½6�½68� þ 2318kd½668�

d½668�dt

¼ 18kh½6�½68� þ 18k9h½8�½66�2 18kd½668�

ðB2Þ

The factor 2/3 in the middle equation comes from the fact that the 18O in [668] also can be transferred to the watermolecule, assuming that the three oxygen atoms in carbonic acid are distributed stochastically (but see Zeebe, 2014).At equilibrium, these rates approach zero and we have:

16kh½6�½66�eq ¼ 16kd½666�eq18kh½6�½68�eq ¼ 2

318kd½668�eq

18k9h½8�½66�eq ¼ 18kd½668�eq 2 18kh½6�½68�eq ¼ 1

318kd½668�eq

8>>>>><>>>>>:

ðB3Þ

where the subscript eq indicates that it is the equilibrium concentration. Noting that Rc,eq = [68]eq/(2[66]eq) andRw = [8]/[6], taking the ratio of the second and third equalities in Equation B3 leads to:

18k9h18kh

¼ Rc;eq

Rw¼ aCO2ðaq:Þ2H2O ðB4Þ

Now, inserting Equation B4 and the second equality in Equation B3 into Equation B2 leads to:

8>><>>:

d½68�dt

¼ 218kh½6�½66��aCO2ðaq:Þ-H2CO3Rb 2Rc

d½668�dt

¼ 18kh½6�½66��2Rc þ aCO2ðaq:Þ-H2ORw 2 3aCO2ðaq:Þ-H2CO3Rb

ðB5Þ

where we have defined Rc = [68]/(2[66]), Rb = [668]/(3[666]), and:

aCO2ðaq:Þ2H2CO3 ¼Rc;eq

Rb;eqðB6Þ

whereRb,eq is the value ofRb at equilibrium. FollowingUchikawa and Zeebe (2012), wewill assume that carbonic acidand bicarbonate are isotopically inseparable and that their oxygen isotopic ratios are equal. In this case, we have:

aCO2ðaq:Þ2H2CO3 ¼ aCO2ðaq:Þ2HCO23¼ aCO2ðaq:Þ2H2O

aHCO23 2H2O

ðB7Þ

According to Beck et al. (2005), at 25°C, this ratio is equal to 1.0413/1.0315 = 1.0095. Note that, as long as H2CO3 andHCO3

2 (and H2O and OH2) are isotopically inseparable, Equation B5 remains valid even when CA activity is lowand CO2 hydroxylation dominates 16kh (and

18kh.).





Analysis of the Dynamics of the System

Equation B5 describes the rate of change of C18O16O and H2C18O16O2 in a closed aqueous solution and can be used to

estimate how fast it takes to reach isotopic steady state (i.e.Rc =Rc,eq andRb =Rb,eq) in the case of a labeling experiment(i.e. a step change in 18O in either the dissolved CO2 or bicarbonate pool). The time needed to recover steady state willbe dictated by the dynamics of the coupled differential equations in Equation B5. The mathematical analysis of thedynamics of such coupled equations has been done elsewhere, in the case of multiply labeled species (more ap-propriate for highly enriched labeling) but ignoring kinetic and equilibrium isotopic effects (Mills and Urey, 1940;Silverman, 1982; Uchikawa and Zeebe, 2012). In this case, the coupled differential equations resemble Equation B5but with atom fractions instead of isotope ratios and no fractionation factors (the a’s). The analysis of the dynamics ofthis coupled system shows that bothRc andRb rapidly follow a single exponential decay functionwith a characteristictime scale t given by (Mills and Urey, 1940; Silverman, 1982; Uchikawa and Zeebe, 2012):

t2 1 ¼ 0:518kh½H2O�8<:1þ acb

½CO2�S

2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ 2

3acb

½CO2�S

þ�acb

½CO2�S

�2s 9=

; ðB8Þ

where S = [H2CO3] + [HCO32] + [CO

3

22] and acb is provided by Equation B6. To a good approximation, we canassume that the ratio [CO2]/S is close to its equilibrium value (this assumption is actually required to derive Eq. B8),and in this case, t21 (corresponding to kiso in Eq. 4) is only a function of temperature and pH.

For pH , 4.5, the ratio [CO2]/S becomes large and the square root term in Equation B8 can be approximated asacb[CO2]/S + 1/3, so that t21 (=kiso) approaches

18kh[H2O]/3 at any temperature. For pH = 7.4, a more realisticvalue for the cytoplasm of mesophyll cells (Jenkins et al., 1989), t21 is much smaller and approaches 0.02818kh[H2O] (i.e. it takes 10 times longer to reach the isotopic equilibrium at pH 7.4 than it takes at pH 4.5). This featurehas been used to precisely measure 18kh and, thus, CA activity in vivo using 18O labeling techniques and graphicalestimation of the decay rate t (Silverman, 1982). This is the technique used currently to measure leaf CA activityin vitro (Badger and Price, 1989; von Caemmerer et al., 2004), although for historical reasons (i.e. by analogy with thepH method), not one but two decay rates t are measured, before (t1) and after (t2) the addition of leaf extracts inthe reactor, and CA activity then is computed as (t1/t2)kh,uncat (see also Eq. 10), where kh,uncat is the expecteduncatalyzed hydration rate at 0.1 M ionic strength (von Caemmerer et al., 2004).

Mathematically, Equation B8 can be simplified to a good approximation to:

t2 1 �18kh3

½H2O� 11þ S

½CO2�ðB9Þ

This is because from Equation B5, we can see that:

½CO2� dRc

dtþ ½H2CO3� dRb

dt¼

18kh3

½H2O�½CO2��aCO2ðaq:Þ-H2ORw 2Rc

ðB10Þ

and if we further assume dRb/dt � dRc/dt, then we end up with a first-order ordinary differential equation whosedecay rate is given by Equation B9.

When the labeling is performed in vivo, the approximation of a uniform solution is not valid anymore. Gerster(1971a, 1971b) developed equations to include an extra gas phase where gaseous CO2 can exchange with the solutionat a rate characterized by a transfer coefficient. In a leaf, this transfer coefficient is similar to a total leaf conductanceand, therefore, includes gm. Other authors also have considered a compartmentalized solution by means of a bio-logicalmembrane (Silverman et al., 1981). In both cases, themass balance of the different isotope species in each phaseleads to a system of differential equations that resembles Equation B5 but with a third differential equation for the gasphase (or the second liquid compartment) and extra terms that involve the transfer coefficient between the gas andliquid phases (or through the biological membrane). Measurements of the decay rates of multiply labeled CO2 speciesthen are required to estimate simultaneously the hydration rate and the transfer coefficient. In the case of the liquid-gas phase example, the decay rates for the C18O2 fraction and the 18O in the CO2 atom fraction are (Gerster, 1971a):

t2 1 � kh3

1

1þ S½CO2� þ VG

�1

BVLþ kh=3SGpt

�

t9 2 1 � 2kh3

1

1þ S½CO2� þ VG

�1

BVLþ 2kh=3

SGpt

�

8>>>>>>><>>>>>>>:

ðB11Þ


Ogée et al.



where VG and VL are the volumes of the gas and liquid phases, B is the dimensionless CO2 solubility, pt (m s21) is thetransfer coefficient between the gas and liquid phases, and SG is the surface area of the gas-liquid interface.We can seeeasily that, in the absence of a gas phase (VG = 0), Equation B11 simplifies to Equation B9 (with the notation kh =

18kh[H2O]). The introduction of a gas phase makes the system dynamics slower, to an extent that will increase with alarger volume of the gas phase VG and a smaller liquid volume VL and transfer coefficient pt. Because the latter isexpected to covary with total leaf conductance, which includes stomatal and mesophyll components, t21 = kiso is afunction not only of temperature and pH but also of gsc and gm.

Application to Model the 18O Discrimination during Leaf Photosynthesis

The rates of change of [68] and [668] (right-hand side of Equation B5) can be used to compute the steady-state massbalance of 18O in CO2 and bicarbonate in folio. However, in this case, other CO2 fluxes (carboxylation, respiration,and atmosphere) competing with CA activity will maintain the CO2 and bicarbonate slightly out of isotopicequilibrium (i.e. Rc � Rc,eq and Rb � Rb,eq), even at steady state, and this degree of disequilibrium will varydepending on the competition between hydration and carboxylation (term r in Farquhar and Lloyd, 1993). Thissituation is described in Appendix C.

APPENDIX C: DERIVING A NEW MODEL FOR C18OO PHOTOSYNTHETIC DISCRIMINATION IN C3 AND C4SPECIES

Rationale

Asmentioned already, the 18O photosynthetic discriminationmodel proposed by Farquhar and Lloyd (1993; denotedFL93 hereafter) was developed for C3 plants only. It also neglects CA activity in the cytosol, and there is growingevidence that CA is present and rather abundant in the cytosol and plasmalemma of the mesophyll cells (Fabre et al.,2007). Additionally, the derivation of the FL93 model was never presented, which renders the identification of thedifferent assumptions difficult. In the following, we will derive a new model for C18OO discrimination duringphotosynthesis that is applicable to both C3 and C4 plants and takes into account CA activity in the cytosol.

Mass Balance Equations

Let us consider the C flux diagram shown in Figure 1. At steady state, there is no accumulation of CO2 in the cy-toplasm of mesophyll cells, so that the CO2 flux A entering the cytosol must balance the CO2 flux out:

�A ¼ Vhm 2Vdm þ gchðCm 2CcÞ2frðVr þ 0:5VoÞ for C3 plants

A ¼ Vhm 2Vdm þ gshðCm 2CcÞ2frVr for C4 plants ðC1Þ

Similarly, there is no accumulation of bicarbonate in the cytoplasm of mesophyll cells:

�0 ¼ Vhm 2Vdm for C3 plantsVp ¼ Vhm 2Vdm for C4 plants ðC2Þ

and no accumulation of CO2 in the chloroplasts of C3 plants or the bundle sheath cells of C4 plants:

�gchðCm 2CcÞ ¼ Vhc 2Vdc 2 ð12frÞðVr þ 0:5VoÞ þ Vc for C3 plantsgshðCm 2CcÞ ¼ 2Vp 2 ð12frÞVr 2 0:5Vo þ Vc for C4 plants ðC3Þ

where Vp is assumed to represent well the rate of CO2 that is released from C4 acids. The mass balance of bicarbonatein the chloroplasts of C3 plants leads to Vhc = Vdc, so that, for both C3 and C4 plants, the sum of Equations C1 to C3gives A = Vc 2 0.5Vo 2 Vr.Similar mass balances can be written for the 18O in CO2 and bicarbonate, where the net leaf photosynthetic

uptake of C18OO, 18A, must balance all the C18OO flux out of the cytoplasm of the mesophyll cells. Using EquationB5 above to explicate the hydration-dehydration terms, and writing Vhm = khmCm and Vdm = kdmBm, this gives:

8>>><>>>:

18A ¼ 218khmCmðRm 2aCO2 2H2CO3R9mÞ þ 2gch

1þ achðCmRm 2CcRcÞ2 2frðVr þ 0:5VoÞRmi for C3 plants

18A ¼ 218khmCmðRm 2aCO2 2H2CO3R9mÞ þ 2gsh

1þ ashðCmRm 2CcRcÞ2 2frVrRmi for C4 plants

ðC4Þ





where 18khm is the hydration rate for C18OO (Zeebe, 2014), ach and ash are fractionation factors during CO2diffusion across the chloroplast and bundle sheath cells, respectively, aCO2 2H2CO3 is the equilibrium oxygenisotope fractionation factor between CO2 and carbonic acid, and Rm and R9

m are the oxygen isotope compositionof dissolved CO2 and bicarbonate in the cytoplasm of mesophyll cells. The factor 2 on the right-hand side comesfrom the fact that, by definition of the isotope ratios, [C18OO] = 2[CO2]R.

Similarly, the mass balance of HCO218O2 in the cytoplasm of mesophyll cells gives (see Eq. B5):

8><>:

0 ¼ 18khmCmð2Rm þ aCO2 2H2ORw 2 3aCO2-H2CO3R9mÞ for C3 plants

3Vp

1þ bPEPCR9

m ¼ 18khmCmð2Rm þ aCO2 2H2ORw 2 3aCO2-H2CO3R9mÞ for C4 plants

ðC5Þ

whereRw is the oxygen isotope ratio of thewater at the site of hydration in the cytoplasm ofmesophyll cells (Rw�Res)and bPEPC is the oxygen isotope fractionation factor during PEP carboxylation by PEPC.

For C3 plants, a similar equation can be derived for the mass balance of HCO218O2 in the chloroplasts of

mesophyll cells. If we assume that Rw, the isotope ratio of water at the hydration sites in the cytosol, repre-sents well the isotope ratio of chloroplastic water, then the mass balance of HCO

2

18O2 in the chloroplasts ofmesophyll cells gives: 2Rc þ aCO2 2H2ORw ¼ 3aCO2-H2CO3R

9c.

Finally, the budget of 18O in CO2 in the chloroplasts of C3 plants or in the bundle sheath cells of C4 plants leads to:

8>>><>>>:

2gch1þ ach

ðCmRm 2CcRcÞ ¼ 218khcCcðRc 2aCO2-H2CO3R9cÞ2 2ð12frÞðVr þ 0:5VoÞRmi þ 2Vc

1þ bRc for C3 plants

2gch1þ ach

ðCmRm 2CcRcÞ ¼ 22Vp

ð1þ bPEPCÞRp 2 2ðð12frÞVr þ 0:5VoÞR9mi þ 2Vc

1þ bRc for C4 plants

ðC6Þ

where b is the isotope fractionation during Rubisco-catalyzed carboxylation andRp corresponds to the isotope ratio ofthe CO2 released from C4 acids in the bundle sheath of C4 plants.

Model Simplifications for C3 and C4 Plants

The value of b is unknown, but noting that the oxygen atoms of CO2 do not bind to the active sites of Rubisco, we willassume that oxygen isotope effects are small and b = 0 (Farquhar and Lloyd, 1993). In addition, in the net reactionHCO3

2 + PEP→ CO2 + Pi + pyruvate, out of the three oxygens from the bicarbonate, one is lost to phosphate (Pi) andthe other two are released as CO2 without binding to any of the active sites of the different enzymes involved (PEPC,MDH, NAD-ME, or NADP-ME). Therefore, we should not expect a strong oxygen isotope effect through this netreaction, and bPEPC = 0 and Rp ¼ R9

m seems a fair assumption. Then, combining Equations C4 to C6 leads to:

8>>><>>>:

1218A ¼

18khmCm

3

�Rm 2Req

�þ 18khcCc

3

�Rc 2Req

�þ VcRc

1þ b2

�Vr þ 1

2Vo

�Rmi for C3 plants

1218A ¼

18khmCm

3

�Rm 2Req

�þ VcRc

1þ b2

�Vr þ 1

2Vo

�Rmi 2frVrðRmi 2R9

miÞ for C4 plants

ðC7Þ

where we have defined Req ¼ aCO2 2H2ORes (and kept the fractionation factor b for reasons explained below).Equation C7 corresponds to Equation 6 in the main text (because RA = 0.518A/A and assuming b = 0).

The pH of mammalian mitochondria has been found to be rather alkaline, with a resting pH around 8 (Llopiset al., 1998), and it was suggested that the same situation occurred in plants (Tholen and Zhu, 2011). An alkalinepH favors high CA activity, whose pKa is usually found around 7.2 (Rowlett et al., 2002), and the expression ofCA in mitochondria also has been demonstrated, at least for C3 plants (Fabre et al., 2007) but also algae (Giordanoet al., 2003). To our knowledge, the existence of mitochondrial CA in C4 plants has never been shown, but giventhe relatively small efflux of CO2 from the mitochondria, we will assume that respired CO2 is in fullisotopic equilibrium with mitochondrial water in both mesophyll and bundle sheath cells and thatmitochondrial water has the same isotopic composition as cytosolic water: Rmi �Req ¼ aCO2 2H2ORes andR9

mi �R9eq ¼ aCO2 2H2ORx, where Rx is the oxygen isotope ratio of the water in the cytoplasm of bundle sheath cells.

Farquhar and Cernusak (2012) revisited 18O discrimination measurements on Ricinius communis performed in thedark (Cernusak et al., 2004) and concluded that respired CO2 by this plant was in full isotopic equilibrium withleaf water at the evaporation site. This result provides indirect evidence that Rmi = Req is a good approximation,although the presence of CA in the cytosol and the plasmalemma (Fabre et al., 2007) could be responsible for thereset of Rmi to Req during the diffusion of respired CO2 out of the leaf.


Ogée et al.



Model Simplifications Specific to C3 Plants

A last simplification may arise regarding the distinction made between Rm and Rc. Could these isotope ratios beequal? In C4 plants, it seems quite unlikely, because they represent CO2 pools physically well separated betweenthe mesophyll and the bundle sheath. On the other hand, given the rather small oxygen isotope fractionation byRubisco (b � 0) and CO2 diffusion (aw � 0.8‰), we could expect in C3 plants the CO2 isotope ratio in the cytosoland chloroplasts of individual mesophyll cells to be closely related, even if different from the surrounding water.If Rm = Rc in C3 plants, then Equation C7 simplifies even further and leads to:

1218A ¼ 1

3

�18khmCm þ 18khcCc

��Rc 2Req

�þ VcRc

1þ b2

�Vr þ 1

2Vo

�Rmi ðC8Þ

which can be rearranged:

RA ¼ Rc 2Req

3rcð12G=CcÞ þ1

12G=Cc

�Rc

1þ b2G=CcRmi

�ðC9Þ

where Vr + 0.5Vo = VcG/Cc and rc = Vc/(18khmCm + 18khcCc). If we assume Rmi � Req, then Equation C9 becomes:

RA ¼ Rc 2Req

3r∗þ Rc

1þ b9ðC10Þ

where we have defined r* = rc(1 2 G/Cc)/(1 + 3rcG/Cc) and b9 = b/[12G/Cc(1 + b)]. Dividing Equation C10 by Rileads to:

11þ Di

¼ Dci 2Dei

3r∗þ 1þ Dci

1þ b9ðC11Þ

By eliminating Δci in Equation C11 using Equation 1 (thus defining the CA site such that RCA = Rc) and neglectingsecond-order terms related to b9 (i.e. bΔi, baw,.), we obtain an equation that relates the observed variables Δi and Δei to«ci and r*:

ð1þ 3r∗ÞðDi – awÞ=«ci ¼ 2 3r∗ðDi – b9Þ þ Deið1þ DiÞ: ðC12ÞEquation C12 can be rearranged to express Δi as a function of «ci, r*, and Δei:

Di ¼ awð1þ 3r∗Þ þ «ciðDei þ 3r∗b9Þ12 «ciDei þ 3r∗ð1þ «ciÞ ðC13Þ

If we assume G = 0, then r* = rc and b9 = b and Equation C13 reduces to the one reported by Farquhar and Lloyd(1993), with the only differences that their Equation 34 contained an (obvious) typo in the expressions of «ci and 1 + «ciand that all variables here are expressed relative to the intracellular air space partial pressure (pi) and isotope ratio (Ri)rather than to those in the outside air. Later publications (Flanagan et al., 1994) corrected the typo but introducedanother one by writing 3r*«ci instead of 3r*(1 + «ci) in the denominator. Thus, we felt it important to give the exactexpression here.The similarity between Equation C13 and the formulation proposed by Farquhar and Lloyd (1993) is surprising

because those authors had not made the distinction between Cm and Cc, nor had they accounted for CO2 hydration inthe cytosol. An important implication is that rc is not simply related to a single CO2 partial pressure anymore. If wedefine pCA such that 18khmCm + 18khcCc = kCApCA, then Equation C13 can be used to retrieve pCA from online CO18Odiscrimination measurements, but this will correspond to a partial pressure that lies between PCm and PCc, dependingon the relative activity of cytosolic versus chloroplastic CA. Indeed, noting that kCA, as estimated from the CA assay,should correspond to (18khm + 18khc)/P, we should have:

pCA ¼ P18khmCm þ 18khcCc

18khm þ 18khcðC14Þ

In other words, the CA site is not defined here as the outer limit of CA activity (Gillon and Yakir, 2000b) but as themean point of CA activity within the mesophyll cells. Given themore alkaline pH and higher CA concentration in thechloroplast stroma compared with the cytosol (pH 7.4 and [CA] around 0.1 mM for the cytosol and pH 8 and [CA]around 0.3 mM for the stroma; Tholen and Zhu, 2011), however, we should expect 18khc .. 18khm, kCA � 18khc/P, andpCA � PCc.





Another difference with the formulation of Farquhar and Lloyd (1993), and an extra complication, comes from therespiratory term. We argue here that Rmi should be closely related to Req rather than Rc. In contrast, in the originalFL93model that includes respiratory terms,Rmiwas expressed asRc(1 +Dmc), so that Equation C9 could simplify to anequation similar to Equation C13 with the correspondence r* → rc(1 2 G/Cc) and:

b9→G=CcDmcð1þ b9Þ þ b9

12G=Ccð1þ DmcÞð1þ b9Þ�G=CcDmc þ b12G=Cc

ðC15Þ

Here, we assume Rmi � Req and r* keeps its original definition: r* = rc(12 G/Cc)/(1 + 3rcG/Cc). The latter also can beexpressed as r/(1 + 3rFr), where r = rc(12 G/Cc) =A/(kCApCA) and Fr is the ratio of the respiratory flux to the net flux:Fr = (Vr + 0.5Vo)/A. In other words, the respiratory terms tend to reduce r*, bringing the CO2 closer to full equili-bration. With these notations and now assuming b = 0, Equation C11 becomes:

11þ Di

¼ 1þ 3rFr3r

ðDci 2DeiÞ þ 1þ Dci ðC16Þ

Noting that r = A/(kCApCA) also can be reexpressed as ri(1 + «ci)/«ci, where ri = A/(kCApi), Equation C16 can becombined with Equation 1 to eliminate Δci and estimate «ci (then pCA and gm) frommeasurements of pi, ri, RA, and Res.However, a complication arises from the fact that Fr depends on G/Cc that we do not know. Thus, we need to makeassumptions on the compensation point G and the CO2 mixing ratio in the chloroplast Cc. As explained above, pCAshould relate closely to PCc and, at least for the respiratory terms, which are only correction factors, we could assumethat they are equal:Cc� pCA/P =Ci«ci/(1 + «ci). We can further split the compensation point into photorespiration (G*)and nonphotorespiration components, leading to:

Fr ¼ Vr=A«ci þ ð1þ «ciÞG∗=Ci

«ci 2 ð1þ «ciÞG∗=CiðC17Þ

Combining Equations C16 and C17with Equation 1 is a bit tedious but leads to a cubic equation that degenerates intoa quadratic equation, whose positive solution is «ci:

a2«2ci þ a1«ci þ a0 ¼ 0 ðC18Þwith: 8<

:a2 ¼ DiA1 2Deið1þ DiÞA2

a1 ¼ DiB1 2Deið1þ DiÞB2 þ ðDi 2 awÞðA1 þ A2Þa0 ¼ DiC1 2Deið1þ DiÞC2 þ ðDi 2 awÞðB1 þ B2Þ

ðC19Þ

and: 8>>>>>><>>>>>>:

A1 ¼ 2 3riðG∗=Ci 2 1ÞB1 ¼ 2 3rið2G∗=Ci 2 1ÞC1 ¼ 2 3riG

∗=CiA2 ¼ þ3riðG∗=Ci þ Vr=AÞ þ 12G∗=Ci

B2 ¼ þ3rið2G∗=Ci þ Vr=AÞ2G∗=Ci

C2 ¼ þ3riG∗=Ci

ðC20Þ

Equation C18 has two unknown parameters, the compensation point G* and the ratio Vr/A. The compensation pointcan be estimated from leaf temperature, using literature data (von Caemmerer et al., 2009), and a sensitivity analysiscan be performed on Vr/A. Likely values for Vr/A should lie within the range 0.05 to 0.25, but we explored here alarger range, from zero to 0.6. From the values of «ci and pi, we can calculate pCA and then gm.

Summary of C3 Model Simplifications

To summarize, for C3 plants, (1) if the respiratory terms are known (Fr or at least Vr/A), (2) if the respired CO2 has anisotope ratio in equilibriumwith leaf water at the evaporation site (Rmi� Req), and (3) if the CO2 in the cytosol and thechloroplasts have similar isotope ratios (Rm � Rc), then we can compute a gm from 18O discrimination measurementsthat will correspond to the CO2 transfer resistance between the intercellular air space (partial pressure pi) and a lo-cation between the cytosol and the chloroplast (partial pressure pCA). The definition of pCA in C3 plants (Eq. C14) issuch that it should correspond more closely to the CO2 partial pressure in the chloroplast (pCA � PCc).


Ogée et al.



Model Simplifications Specific to C4 plants (a Correction to this section has been posted, see at the end of Appendix C)

For C4 plants, the situation is somewhat simpler, because CA activity is located only in themesophyll (pCA = PCm). Onthe other hand, the physical separation of the mesophyll and the bundle sheath cells makes it difficult to assume Rm =Rc. If Rmi = Req and R9

mi �R9eq in C4 plants, then Equation C7 can be rewritten:

RA ¼ 1þ 3rFr3r

�Rm 2Req

�þ ð1þ FrÞRc 2 FrRm 2frVr

A

�Req 2R9

eq� ðC21Þ

The main CO2 source in the bundle sheath comes from the decarboxylation of the C4 acid with an isotope ratioRp �R9

m (see discussion above). A possible approximation then would be to assume that Rc is close to thisisotope ratio. Because the CA activity is high in the mesophyll cells, we also should expect the CO2 and bi-carbonate in this compartment to be close to isotopic equilibrium: Rm �acbR9

m, where acb is the isotopicfractionation between CO2 and bicarbonate (around 1.0095 at 25°C; see Appendix B). In other words, Rm/acbseems a reasonable approximation for Rc. Equation C21 then can be simplified to:

RA ¼ 1þ 3rFr3r

�Rm 2Req

�þ ð12 acbð1þ FrÞÞRm 2frVr

A

�Req 2R9

eq� ðC22Þ

where acb = acb 2 1. Combining Equation C22 with Equations C17 and 1 is a bit tedious but leads to a quadratic equationthat degenerates into a cubic equation in «ci:

b3«3ci þ b2«2ci þ b1«ci þ b0 ¼ 0 ðC23Þwith:

8>><>>:

b3 ¼ A991A1 2YA1A2

b2 ¼ A991B1 2YA1B2 þ ðA1X2C1YÞA2 þ

�C1Z9 2A9

1X�A1

b1 ¼ A991C1 2YA1C2 þ ðA1X2C1YÞB2 þ

�C1Z9 2A9

1X�B1 þ C1XðA1 þ A2Þ

b0 ¼ ðA1X2C1YÞC2 þ�C1Z9 2A9

1X�C1 þ C1XðB1 þ B2Þ

ðC24Þ

and where we have defined:

8>>>>>><>>>>>>:

X ¼ Di 2 awY ¼ Deið1þ DiÞZ9 ¼ Di 2frVr=AðDei 2D9

eiÞð1þ DiÞD2 ¼ 3riðG∗=Ci þ Vr=AÞA9

1 ¼ A1 2 acbðA1 þD2ÞA99

1 ¼ A1Z9 2 acbðA1 þD2Þð1þ DiÞ

ðC25Þ

We can verify that, when fr = 0 and acb = 0, Equation C23 simplifies to Equation C18 (with b = 0), because then theexpression forRA is the same for C3 andC4 plants (i.e. Eqs. C10 andC22 are the same). In this study,we setfr = 0.5 andacb = 9.5‰ and made the approximation Dei 2D9

ei �Res 2Rtrans, where Rtrans represents the isotope ratio of thetranspired water vapor, a good proxy for the source (xylem) water (Song et al., 2015) and, thus, for bundle sheathwater. When not available, Rtrans was taken as the isotopic ratio of irrigation water. As was done for C3 plants, asensitivity analysis was performed on Vr/A, with values in the range 0 to 0.6. From the values of «ci and pi, we couldcalculate pCA and then gm.In the majority (i.e. 86%) of the situations that we tested, the cubic equation (Eq. C23) has three real roots, and the

most positive solution is always the plausible one (i.e. the only one greater than the value of «ci computed assumingfull equilibrium, the other two solutions being close to zero or negative). However, we also found combinations (i.e.14%) where Equation C23 has only one real and two complex solutions. In these situations, the single real solution istaken, except in 2% of the cases (i.e. three individual Z. mays leaves out of 147 measurements) where this single realsolution was unrealistic (i.e. negative «ci and gm), so that no solution could be found.These problematic situations may arise because of uncertainties in CA activity measurements. Indeed, because CA

activity measurements are all performed on leaf extracts, it is possible that they are not fully representative of thein vivo activity at the time of the leaf C18OO discrimination measurements. In fact, the CA activity of corn leaves wasnot measured by Barbour et al. (2016), and we had to estimate its value from the literature. We set kCA to 34 mmol m22

s21 Pa21 according to Cousins et al. (2006b) but noticed also that Studer et al. (2014) had measured CA activity in Z.mays about 2 to 3 times higher. We thus explored the effect of an increase of kCA on the estimation of «ci from EquationC23.We found that, for the problematic casesmentioned above, a 6.5-fold increase of kCAwas required to start findinga plausible solution to Equation C23. To our knowledge, a kCA value of 220 mmol m22 s21 Pa21 has never been





reported, especially in C4 plants. Therefore, the uncertainty on kCA cannot be the only reason why Equation C23sometimes has no solution.

The problem alsomay have theoretical origins. For example, the assumption that the air in the substomatal cavity issaturated in water vaporwas challenged recently by Cernusak et al. (2018), who collected field data where the d18O ofCO2 in the intercellular air space did not lie between the d18O of CO2 in the air and that in equilibrium with theevaporation site (i.e. Δei, 0 while Δia$ 0). They explained this behavior by letting the air in the substomatal cavity besubsaturated in water vapor (which implies recalculating the stomatal conductance gsw and the CO2 partial pressurepi from the leaf gas-exchange data) and finding the substomatal vapor pressure that led to Δci = Δei (i.e. full equi-librium). In all the data sets that are revisited here, the situation described by Cernusak et al. (2018) was not found (i.e.we always had Δei . 0 and Δia $ 0; Supplemental Fig. S3). We also recalculated the vapor pressure deficit that wouldbe needed to reach full equilibrium (Δci = Δei) and did not find departures of more than 0.3%, leading to absolutechanges in pi/P and in gsw of less than 1.5mmolmol21 and 8mmolm22 s21 (Supplemental Fig. S4). Thus, subsaturatedair in the substomatal cavity does not seem to be the reason why sometimes Equation C23 does not have a plausiblesolution.

Another uncertain parameter is leaf temperature. Leaf temperature is commonly monitored using a fine-wirethermocouple appraised against the leaf lower surface. However, because the contact between the thermocouplejunction and the leaf surface is not perfect and there is heat conduction by thermocouple wires, the leaf temperaturereading is amixture between leaf and air temperatures and, therefore, overestimates leaf temperaturewhen the leaf istranspiring. We thus explored the effect of an overestimation of leaf temperature on the retrieval of «ci from EquationC23. This required recalculating the stomatal conductance gsw and the CO2 partial pressure pi from the leaf gas-exchange data and the isotopic composition of leaf water at the evaporation site (Res). We found that a 1K overes-timation of leaf temperature was enough to always find a plausible solution to Equation C23, leading to higherstomatal conductance (sometimes up to 50mmolm22 s21) and lower gm (typically by 200–300mmolm22 s21). Becausean overestimation of leaf temperature by 1K is very possible, we recommend systematically performing a sensitivityanalysis of the solution to leaf temperature (and maybe also kCA) in order to determine the robustness of the results.

Summary of C4 Model Simplifications

To summarize, for C4 plants, (1) if the respiratory terms (fr and Vr/A) are known, (2) if respired CO2 is in isotopicequilibriumwith mitochondrial water, (3) if mitochondrial water has the isotopic composition of the evaporation sitein themesophyll (Rmi�Req) and the transpired vapor in the bundle sheath (R9

mi �R9eq), and (4) if the CO2 in the bundle

sheath cytosol is in isotopic equilibriumwith the bicarbonate in the mesophyll (Rc � Rm/acb), then we can compute agm from 18O discrimination measurements that will correspond to the CO2 transfer resistance between the intercel-lular air space (partial pressure pi) and the CO2 hydration site in the mesophyll cytosol (partial pressure pCA � PCm).

Limiting Case in the Absence of CA Activity

As explained in the main text, in the limiting case where kCA tends to zero, the isotope ratio at the carboxylation site (Rc0)becomes very simply related to RA and Ra (Eq. 8). However, because RA is a measured quantity, we cannot use it toestimate a hypothetical Rc0 corresponding to the situation when kCA would tend to zero. Thus, we need to find an ex-pression for Rc0 independent of RA.

By combining the two flux-gradient relationships that led to Equation 1, we can easily show that, whether kCA tendsto zero or not, we also have:

RA ¼ 11þ aw

Ri0pi 2RCA0pCApi 2 pCA

ðC26Þ

where Ri0 and RCA0 denote Ri and RCA in absence of CA activity. Using flux-gradient relationships between pi and pa,while accounting for ternary effects in the gas phase, Farquhar and Cernusak (2012) also showed that (see their Eq.14 on page 1223):

RA ¼ Rapa 2Ri0pi 2 t�Rapa þ Ri0pi

�ð1þ a9Þ�pa 2 pi

�2 t

�pa þ pi

� ðC27Þ

Like Equation C26, this equation is valid irrespective of the level of CA activity. By inserting Equation 8 into EquationC26 and assuming that RCA0 = Rc0 in the absence of CA activity, we obtain an expression for Ri0pi that we can injectinto Equation C27 together with Equation 8 to obtain an expression that relates RCA0/Ra to pa, pi, and pCA:

RCA0

Ra¼ ð12 tÞpa þ Fr

��1þ a9

��pa 2 pi

�2 t

�pa þ pi

�þ ð1þ awÞð1þ tÞ�pi 2 pCA�

ð1þ FÞ�ð1þ a9Þ�pa 2 pi�2 t

�pa þ pi

�þ ð1þ tÞð1þ awÞ�pi 2 pCA

� þ ð1þ tÞpCAðC28Þ


Ogée et al.





From this expression, Dci0 is computed as:

Dci0 ¼ RCA0

Ri2 1 ¼ RCA0

Ra3

11þ Dia

2 1 ðC29Þ

If we further assume that Fr = 0, we obtain the same expression as Ubierna et al. (2017) in their Equation 14.Note that Fr andRCA0/Ra are computed using the value of pCA deduced from 18O discriminationmeasurements (i.e.

in the presence of CA activity). This is problematic, especially in C4 plants, where the carboxylation and CA sites arephysically well separated. This demonstrates the limited meaningfulness of the degree of equilibration u, as definedby Equation 3.

Correction to Appendix C (February 2019)

Note that a correction to Appendix C, including a new derivation for C4 species, is available as a new Supplementalfile on the Plant Physiology website. In particular Eqs. (C23) and (C24) have been updated. As shown in this newSupplemental file, the results of this new derivation do not change the conclusions of the paper.





Table D1. List of symbols

Symbol Definition (and First Appearance in the Text) Unit

�a9 Isotope fractionation factor during CO2 diffusion through the leaf boundary layerand the stomata (Eq. 12)

‰

ach, ash Isotope fractionation factor during CO2 diffusion across the chloroplast (ach;C3 plant) or the bundle sheath cells (ash; C4 plant) (Eq. C4)

‰

acb Isotope fractionation factor between CO2 and bicarbonate at equilibrium(i.e. acb = acb 2 1) (Eq. 7)

‰

aw Isotope fractionation factor during CO2 dissolution and diffusion from thesubstomatal cavity to the CA site (Eq. 1)

‰

A, 18A Net total CO2 and C18OO flux (Eq. 1) mol m22 s21

b, bPEPC Isotope fractionation factor during Rubisco and PEPC carboxylation(Appendix C)

‰

B Dimensionless solubility of CO2 in water (i.e. 8.314KHT, where T is temperature)(Eq. B11)

m3 m23

Cc, Bc CO2 and bicarbonate concentrations at the Rubisco site (chloroplast stroma inC3 plants, bundle sheath in C4 plants) (Fig. 1)

mol mol21

Cm, Bm CO2 and bicarbonate concentrations in the cytoplasm of mesophyll cells (Fig. 1) mol mol21

E Transpiration rate (Eq. 11) mol m22 s21

Fr Ratio of respiratory to net CO2 flux [i.e. (Vr + 0.5Vo)/A] (Eq. 6) Unitlessgbc, gsc, gtc Boundary layer, stomatal, and total conductance to CO2 (Eq. 11) mol m22 s21

gch, gsh Conductance to CO2 from the CA site to the Rubisco site (i.e. across the chloroplast[gch; C3 plant] or the bundle sheath cells [gsh; C4 plant])

mol m22 s21

gm Mesophyll conductance to CO2 from the intercellular air space to the CAsite (Fig. 1)

mol m22 s21

kCA Leaf CA activity rate (Eqs. 7 and 9) mol m22 s21 Pa21

kCA,orig Leaf CA activity rate, before applying the pH correction (Eq. 10) mol m22 s21 Pa21

kcat,assay, kuncat,assay CA-catalyzed and uncatalyzed CO2 hydration rates under CA assay conditions(Eq. 9)

s21

18kd,16kd H2C

18OO2 and H2C16O3 dehydration rates (Eq. B1) s21

KH Solubility of CO2 in water (Eq. 9) mol m23 Pa21

kh,16kh,

18kh,18k9h CO2 hydration rate (introduction, after Eq. 5) and CO2-H2O, C18OO-H2O, and

CO2-H218O reaction rates (Eq. B1)

s21

18khm,18khc C18OO-H2O reaction rate in the mesophyll and the chloroplast, respectively

(Eqs. C4 and C6)s21

kiso CO2-H2O isotopic exchange rate (Eq. 4) s21

kuncat,invivo Uncatalyzed CO2 hydration rate under in vivo conditions (Eq. 9) s21

P Atmospheric pressure (Fig. 1) Papa, pi, pCA CO2 partial pressure in outside air, intercellular air space, and at the CA site

(Fig. 1)Pa

pHassay, pHinvivo pH of the assay solution and of the leaf CA-containing compartment (Eq. 10) UnitlessRA Isotope ratio of net CO2 flux (=0.518A/A) UnitlessR9i Isotope ratio of CO2 in intercellular air space when ternary effects are neglected

(Eq. A1)Unitless

Ra, Ri, RCA Isotope ratio of CO2 in outside air, intercellular air space, and at the CAsite (Fig. 1)

Unitless

Rb Isotope ratio of bicarbonate (Eq. B5) UnitlessRb,eq Isotope ratio of bicarbonate in equilibrium with water (Eq. B5) UnitlessRc, R9c Isotope ratio of CO2 and bicarbonate at the Rubisco site (Fig. 1) UnitlessRc Isotope ratio of CO2 (Eq. B5) UnitlessRc,eq Isotope ratio of CO2 in equilibrium with water (i.e. Rwawc) (Eq. B4) UnitlessReq Isotope ratio of CO2 in equilibrium with water at the evaporation site (i.e. Resawc)

(Eq. 6)Unitless

R9eq Isotope ratio of CO2 in equilibrium with water in bundle sheath cells (i.e. Rxawc)(Eq. 6)

Unitless

Res Isotope ratio of water at the evaporation site (Eq. 2) UnitlessRi0, RCA0, Rc0 Ri, RCA, and Rc in the absence of CA activity (Eqs. 8 and C26) UnitlessRm, R9m Isotope ratio of CO2 and bicarbonate in the cytoplasm of mesophyll cells

(Fig. 1)Unitless

Rmi, R9mi Isotope ratio of CO2 produced in mitochondria of mesophyll and bundle sheathcells (Fig. 1)

Unitless

(Table continues on following page.)

APPENDIX D: LIST OF SYMBOLS AND ACRONYMS


Ogée et al.



Table D1. (Continued from previous page.)

Symbol Definition (and First Appearance in the Text) Unit

Rp Isotope ratio of CO2 released from C4 acids in bundle sheath cells(Eq. C6)

Unitless

Rtrans Isotope ratio of transpired water vapor (Appendix C) UnitlessRx Isotope ratio of water in bundle sheath cells (Eq. 6) UnitlessRw Isotope ratio of water (Eq. B4) UnitlessS Total bicarbonate species (i.e. [H2CO3] + [HCO3

2] + [CO3

22]) (Eq. B8) mol m23

SG Surface area of the gas-liquid interface (Eq. B11) m2

Sleaf Leaf area used for the CA assay (Eq. 9) m2

t Time (Eq. 4) st9 Ternary correction factor (Eq. 11) Unitlessta Ternary correction factor for CO2 isotopes (Eq. 13) UnitlessVassay Volume of the CA assay solution (Eq. 9) m3

Vc Rubisco carboxylase activity rate in the chloroplast stroma of C3 plants orbundle sheath cells of C4 plants (Fig. 1)

mol m22 s21

VG, VL Volumes of the gas and liquid phases (Eq. B11) m3

Vhc, Vdc CO2 hydration and dehydration rates in the chloroplast stroma of C3

plants (Fig. 1)mol m22 s21

Vhm, Vdm CO2 hydration and dehydration rates in the cytoplasm of mesophyllcells (Fig. 1)

mol m22 s21

Vo, Vr Photorespiration and mitochondrial respiration rates (Fig. 1) mol m22 s21

Vp PEPC activity rates in the cytoplasm of C4 mesophyll cells (and CO2 release ratefrom C4 acid in bundle sheath cells) (Fig. 1)

mol m22 s21

aCO2ðaq:Þ2H2O,acw Isotope fractionation between CO2 and water at equilibrium (i.e. Rc,eq/Rw)(Eqs. 2 and B4)

Unitless

aCO2ðaq:Þ2H2CO3, acb Isotope fractionation between CO2 and bicarbonate at equilibrium(i.e. Rc,eq/Rb,eq) (Eq. B6)

Unitless

G* CO2 compensation point in the absence of mitochondrial respiration(Appendix C)

mol mol21

ΔA Photosynthetic C18OO discrimination (i.e. Ra/RA 2 1) (Eq. 12) ‰

Δci Isotope ratio of CO2 at the CA site, expressed relative to that in the intercellularair space (i.e. RCA/Ri 2 1) (Eq. 1)

‰

Δci0 Δci in the absence of CA activity (Eq. 3) ‰

Δea Isotope ratio of CO2 in equilibrium with the evaporation site, expressed relativeto that in air (i.e. Req/Ra 2 1) (Eq. 11)

‰

Δei Isotope ratio of CO2 in equilibrium with the evaporation site, expressed relativeto that in the intercellular air space (i.e. Req/Ri 2 1) (Eq. 2)

‰

Δeq Isotope ratio of the evaporation site, expressed relative to that of bundle sheathcell water (i.e. Res/Rx 2 1) (Eq. 7)

‰

Δi Photosynthetic C18OO discrimination, expressed relative to the isotope ratio ofCO2 in the intercellular air space (i.e. Ri/RA 2 1) (Eq. 1)

‰

Δia Isotope ratio of CO2 in the intercellular air space, expressed relative to that inthe outside air (i.e. Ri/Ra 2 1) (Eq. A4)

‰

Δ9ia Δia without ternary corrections (Eq. 11) ‰

Δmc Isotope fractionation factor between respired CO2 and CO2 at the Rubiscocarboxylation site (i.e. Rmi/Rc 2 1) (Appendix C)

‰

«ci pCA/(pi – pCA) (Eq. 1) Unitless«ia pi/(pa – pi) (Eq. 11) Unitlessu Degree of isotopic equilibration (Eq. 3) Unitlesspt Transfer coefficient between the gas and liquid phases (Eq. B11) m s21

r Ratio of net CO2 flux to CA activity [i.e. A/(kCApCA)] (Eq. 7) Unitlessri Ratio of net CO2 flux to kCApi (Eq. 7) Unitlesst Time scale of CO2-H2O isotopic exchange dynamics (Eq. B8) st9 Decay rate of 18O in the CO2 atom fraction (Eq. B11) st1, t2 C18O2 decay rates before and after leaf extract addition during the CA assay

(Appendix B)s

tres Residence time of CO2 inside the leaf mesophyll (Eq. 5) sfr Fraction of respired CO2 not recycled by the chloroplast stroma (C3 plant)

or not produced in the bundle sheath (C4 plant) (Fig. 1)Unitless





Table D2. List of acronyms

Acronym Definition

CA Carbonic anhydrasePEPC Phosphoenolpyruvate carboxylasePPFD Photosynthetic photon flux density


Ogée et al.



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