Mesophyll conductance from measurements of C 18 OO photosynthetic discrimination and carbonic anhydrase activity

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1 Plant Physiology Preview. Published on August 13, 2018, as DOI: /pp Mesophyll conductance from measurements of C 18 OO photosynthetic discrimination and carbonic anhydrase activity Jérôme Ogée*, Lisa Wingate & Bernard Genty Institut National de la Recherche Agronomique (INRA), Bordeaux Sciences Agro, Unité Mixte de Recherche 1361, Interactions Sol-Plante-Atmosphère, 33140, Villenave d Ornon, France (J.O., L.W.) CNRS-CEA-Université Aix-Marseille, Unité Mixte de Recherche 7265, Biosciences and Biotechnologies Institute, 13108, Saint-Paul-lez-Durance, France (B.G.) * Address correspondence to jerome.ogee@inra.fr Short title: Mesophyll conductance in C 3 and C 4 plants Author contributions: J.O., B.G. and L.W. discussed the original idea, J.O. and B.G. developed the theory and performed the literature survey, and J.O. performed the analysis and wrote the article, with contributions from all the authors One-sentence summary A new model based on the relationship between C 18 OO photosynthetic discrimination and carbonic anhydrase activity is proposed for estimating mesophyll conductance in C 3 and C 4 plants ACKNOWLEDGMENTS This work was funded by the Agence Nationale de la Recherche (award no. ANR- 13-BS (project ORCA)) and the European Union s Seventh Framework Programme (FP7/ ) (grant agreements Nos (project SOLCA), (project 3to4) and (ERA-Net Plus project MODCARBOSTRESS)). Downloaded from on January 24, Published by Copyright 2018 by the American Society of Plant Biologists

2 Abstract Carbonic anhydrase (CA) activity in leaves catalyses the 18 O exchange between CO 2 and water during photosynthesis. This feature has been used to estimate the mesophyll conductance to CO 2 (g m) from measurements of online C 18 OO photosynthetic discrimination ( 18 O). Based on CA assays on leaf extracts, it has been argued that CO 2 in mesophyll cells should be in isotopic equilibrium with water in most C 3 species as well as many C 4 dicot species. However, this seems incompatible with 18 O data that would indicate a much lower degree of equilibration, especially in C 4 plants under high light intensity. This apparent contradiction is resolved here using a new model of C 3 and C 4 photosynthetic discrimination that includes competition between CO 2 hydration and carboxylation and the contribution of respiratory fluxes. This new modelling framework is used to revisit previously published datasets on C 3 and C 4 species, including CA-deficient plants. We conclude that (1) newly 18 O-derived g m values are usually close but significantly higher (typically 20% and up to 50%) than those derived assuming full equilibration and (2) despite the uncertainty associated with the respiration rate in light, or the water isotope gradient between mesophyll and bundle sheath cells, robust estimates of 18 O-derived g m can be achieved in both C 3 and C 4 plants. 49 2

3 Introduction Carbonic anhydrases (CAs) are a group of zinc metalloenzymes that catalyse the inter-conversion of CO 2 into bicarbonate with great efficiency (Moroney et al., 2001; Rowlett, 2010). In the mesophyll cells of C 3 plants, CA is most abundant in the stroma (Badger and Price, 1994), but CAs are also found in other compartments of the mesophyll such as the cytosol, the mitochondria or the plasma membrane (Fabre et al., 2007; DiMario et al., 2016). Chloroplastic CA in C 3 plants was first assumed to be required to provide CO 2 to RuBisCO in the stroma, given the alkalinity of this compartment (Badger and Price, 1994), but results of studies on antisense tobacco plants have not been conclusive (Price et al., 1994). In C 4 plants, CA is most abundant in the cytosol (Badger and Price, 1994), primarily because it is needed to increase the supply of bicarbonate to PEP carboxylase (Hatch and Burnell, 1990; Badger and Price, 1994). This idea was confirmed by experiments conducted on CA-deficient mutants, which showed that cytosolic CA was required to maintain high photosynthetic rate in Flaveria bidentis (von Caemmerer et al., 2004) and Zea mays, at least in low-co 2 environments (Studer et al., 2014). Irrespective of the exact functional role of CA in plants, CA catalyses the 18 O exchange between CO 2 and water so that CO 2 is commonly assumed to be near isotopic equilibrium with water in CA-containing mesophyll compartments. Consequently, a CO 2 partial pressure at the site of CA activity inside the mesophyll cells (p CA) can be derived from online 18O photosynthetic discrimination (Δ 18 O) measurements, provided that the 18 O/ 16 O ratio of leaf water at this CA site can be estimated (Gillon and Yakir, 2000a). However, sometimes CO 2 might not be in complete equilibration with water, especially 3

4 when CO 2 uptake rates are high, as this would result in relatively brief residence times for CO 2 molecules inside the mesophyll. This led Gillon and Yakir (2000a) to propose a formulation for Δ 18 O that incorporates the degree of CO 2-H 2O isotopic equilibrium θ (0 θ 1). Online Δ 18 O measurements and estimates of θ from in vitro CA assays indicated that, for three C 3 species, p CA always lay somewhere between the CO 2 partial pressure in the sub-stomatal cavity (p i) and that at the sites of carboxylation in the chloroplast stroma (p c), estimated separately from online 13 C photosynthetic discrimination (Δ 13 C) measurements (Gillon and Yakir 2000a). This finding was in line with the hypothesis that the outer limit of CA activity in C 3 plants was located at the chloroplast surface, and thus before the carboxylation site within the chloroplast stroma. This approach was later used in a follow-up study to estimate g m and θ in a number of C 3 plants but also in C 4 plants, that generally exhibited lower θ values than C 3 plants (Gillon and Yakir, 2001). In other studies (Gillon and Yakir, 2000b; Cousins et al., 2006a), a slightly different approach was adopted. Mesophyll conductance g m was derived from Δ 18 O measurements performed under low-light conditions, i.e. when the residence time of CO 2 inside the mesophyll was expected to be long enough to allow full CO 2-H 2O isotopic equilibration (θ = 1). Under higher light intensities, g m was assumed constant (for a given species) and θ was then estimated from the Δ 18 O data and usually found to be quite low, down to 0.1 (Gillon and Yakir, 2000b; Cousins et al., 2006a). Cousins et al. (2006a) noted that these Δ 18 O- derived θ values seemed incompatible with in vitro leaf CA assays that instead indicated full equilibration at all light conditions. These discrepancies between in vitro and Δ 18 O-derived θ estimates were hypothesised to arise from a spatial 4

5 mismatch between the CA site and the evaporation site in C 4 plants and an isotopically heterogeneous leaf water composition in the cytoplasm of mesophyll cells (Cousins et al., 2006a). Although it is not possible to completely rule out these hypotheses, there is growing evidence that water isotope gradients do not develop within the cytoplasm, and rather remain confined to the vascular tissues of the leaf (Holloway-Phillips et al., 2016). Furthermore, in vitro CA assays conducted in all recent studies, using ph and CO 2 concentrations close to those experienced in folio, seem to indicate that CO 2 should always be near full isotopic equilibration with leaf water (Cousins et al., 2007; Studer et al., 2014; Barbour et al., 2016; Ubierna et al., 2017). Consequently, a common practice now is to assume θ = 1 when estimating g m from online Δ 18 O measurements (Barbour et al., 2016; Ubierna et al., 2017), and to also perform a sensitivity analysis to predict how g m would be affected, had θ been set to lower values, noting that lower θ values always lead to higher g m values (Barbour et al., 2016; Ubierna et al., 2017). Most recently, alternative estimates of g m in C 4 plants using in vitro maximal PEP carboxylation rate measurements seem to support Δ 18 O-derived g m estimates assuming θ = 1 (Ubierna et al., 2017). This paper re-examines the relationship between carbonic anhydrase activity and isotopic equilibration during photosynthesis. To address this overlooked issue, we propose a steady-state modelling framework of Δ 18 O for both C 3 and C 4 plants. This new model explicitly accounts for the competition between CO 2 hydration and carboxylation, providing the possibility for incomplete CO 2-H 2O equilibration to occur inside the leaf. In addition, the new model accounts for the physical separation between mesophyll and bundle sheath cells in C 4 species, 5

6 and for the contribution of respiratory fluxes. Several factors motivated the derivation of this new model. First, as we will explain later, the current model describing the degree of isotopic equilibration θ (Gillon and Yakir, 2000a) is based on several assumptions that cannot be applied to steady-state leaf gasexchange measurements, thus preventing any conclusion to be drawn on whether or not isotopic equilibrium is reached based on in vitro CA activity assays. Additionally, the current practice of setting θ to unity or lower does not allow the study of the functional link between CA activity and Δ 18 O and how it varies between C 3 and C 4 species. A steady-state formulation of Δ 18 O by C 3 plants that includes the competition between carboxylation and CA-catalysed CO 2 hydration was proposed already by Farquhar and Lloyd (1993). This formulation constitutes the basis of our derivation that we extended to C 3 and C 4 photosynthesis pathways and mesophyll compartmentalisation. The new model also applies to conditions of high leaf-to-air vapour pressure deficit, that require ternary corrections on the CO 2 and C 18 OO assimilation rates (von Caemmerer and Farquhar, 1981; Farquhar and Cernusak, 2012). With this new modelling framework, we revisit a number of previously published datasets for C 3 and C 4 species, including CA-deficient mutants, and illustrate how to reconcile in vitro CA assays with online Δ 18 O measurements whilst, at the same time, estimating g m from Δ 18 O data Theory The gas-exchange view Throughout this paper, we will assume that CO 2 or C 18 OO gradients within the intercellular air space are negligible, and we will use the terms intercellular air space and stomatal cavity air space interchangeably. Under the assumption of 6

7 150 a well-identified CA site inside the mesophyll cells upstream of any carboxylation 7

8 site (Fig. 1, the gas exchange view ), the net leaf CO 2 flux can be written as the product of a conductance g m for CO 2 diffusion from the intercellular air space to the CA site, and the CO 2 drawdown along the same path: A = g m(p i - p CA)/P, where P is atmospheric pressure and p i and p CA are the CO 2 partial pressures in the intercellular air space and at the CA site, respectively. Similarly, the net C 18 OO flux can be defined as 18 A = 2g m 1+a w ( p i R i p CA R CA )/ P, where a w is the fractionation factor during CO 2 dissolution and diffusion from the sub-stomatal cavity to the CA site, and R i and R CA represent the 18 O/ 16 O ratios of CO 2 in the sub-stomatal cavity and at the CA site. The fractionation factor a w is quite small and usually taken as +0.8 at 25 C (Farquhar and Lloyd, 1993). These two flux-gradient relationships can be combined and re-arranged as follows: 162 Δ ci = Δ i a w 1+Δ i ε ci ( ) (1) where Δ ci = R CA/R i - 1, ε ci = p CA/(p i - p CA), Δ i = R i/r A - 1 and R A represents the 18O/ 16 O ratio of the net CO 2 flux ( = A/A), i.e., i represents 18 O, expressed relative to R i and not relative to the 18 O/ 16 O ratio of the CO 2 in the air surrounding the leaf (R a). Our current theoretical understanding of the C 18 OO photosynthetic discrimination has been drawn on the assumption that the CA site is located in a leaf water compartment with a homogeneous 18 O/ 16 O ratio that includes the evaporation site. This assumption is in accordance with recent studies showing that leaf water isotopic gradients seem to be limited to a small region around the leaf veins (Holloway-Phillips et al., 2016). In this case, the 18 O/ 16 O ratio of the water in the CA-containing compartment can be approximated as the 18 O/ 16 O ratio at the evaporation site within the mesophyll (noted R es hereafter), and thus 8

9 estimated from water vapour isotope and leaf gas-exchange measurements (Cernusak et al., 2004; Farquhar et al., 2007). From these estimates of R es, we can calculate the 18 O/ 16 O ratio of CO 2 in full isotopic equilibrium with leaf water at the CA site (noted Δ ei and expressed relative to R i): Δ ei = R esα wc R i 1, (2) where α wc denotes the temperature-dependent equilibrium isotopic fractionation between CO 2 and water (Brenninkmeijer et al., 1983). If we assume that CO 2 is fully equilibrated with leaf water at the CA site, then ci = ei and we can estimate ε ci from measurements of R es and R A using Eq. 1 (this requires knowledge of ia = R i/r a - 1, that can be estimated from measurements of A alongside CO 2 and water vapour fluxes, see Methods). However, because the residence time of CO 2 inside the mesophyll can be somewhat shorter than the time required for full isotopic equilibration with leaf water, Δ ci differs from Δ ei. The proportion of CO 2 in isotopic equilibrium with leaf water can be defined as (Gillon and Yakir, 2000a; Gillon and Yakir, 2000b): θ= Δ ci Δ ci0 Δ ei Δ ci0, (3) where Δ ci0 represents the value of Δ ci in the absence of any CA activity (or, more correctly, of any CO 2-H 2O oxygen isotope exchange). The latter is usually derived using an approach similar to that described for 13 C photosynthetic discrimination (Gillon and Yakir, 2000a), assuming no isotope fractionation during carboxylation by phosphoenolpyruvate carboxylase (PEPC; EC ) or RuBisCO or during respiration. The exact expression (see Appendix C, Eq. C28) shows that Δ ci0 depends on ε ci, and thus p CA. Therefore, it can be implicitly assumed that, despite the (putative) absence of CA activity, the carboxylation site 9

10 coincides with the (true) CA site. This can be problematic, especially in C 4 plants. However, in most cases, θ is expected to be close to unity and the exact knowledge of Δ ci0 becomes less critical. In fact, the knowledge of Δ ci0 is only required to compute θ. Because Gillon and Yakir (2000a; 2000b) proposed an independent expression for θ (see below) in terms of the residence time τ res (s) of CO 2 within the leaf mesophyll and the CAcatalysed CO 2-H 2O isotopic exchange rate k iso (s -1 ); they required knowledge of Δ ci0 to compute Δ ci and thus ε ci and g m. Another approach, adopted by Farquhar and Lloyd (1993), provided a direct expression for ci in terms of CA activity and carboxylation and respiratory fluxes. This expression, combined with Eq. 1 can be used to retrieve ε ci and g m, without the need to estimate the degree of equilibration θ, as demonstrated in some follow-up applications (Flanagan et al., 1994; Williams et al., 1996). These two approaches are reviewed below The biochemical view To derive an expression for θ, Gillon and Yakir (2000a; 2000b) revisited the work of Mills and Urey (1940), who showed that the 18 O/ 16 O ratio of CO 2 in closed aqueous solutions rapidly follows an ordinary differential equation, which can be re-written with the current notations as follows: 217 dδ ci dt = k iso ( Δ ci Δ ei ), (4) where k iso (s -1 ) is the CO 2-H 2O isotopic exchange rate. The leaf mesophyll is not a closed system, but Gillon and Yakir (2000a) assumed that Eq. 4 would adequately describe the dynamics of Δ ci. This is justified only if the CO 2-H 2O isotopic exchange rate is much greater than any C 18 OO carboxylation flux, which is unlikely under high light intensity or for CA-deficient leaves. Despite these 10

11 caveats, they proposed estimating θ (Eq. 3) by integrating Eq. 4 between time t = 0 and t = τ res, and assuming that Δ ci0 precisely represents the value of Δ ci at time t = 0 (Gillon and Yakir, 2000a): θ=1 exp( k iso τ res ). (5) This derivation is problematic as it uses a non steady-state formulation (integrated over the residence time τ res) to describe steady-state gas-exchange dynamics. Additionally, stating that Δ ci0 precisely represents the value of Δ ci at time t = 0 comes to assume that the leaf has been (initially) filled with unlabelled CO 2, which is not realistic even with a fluctuating environment because CA activity continuously resets Δ ci. Yet, Eq. 5 has been used in several studies to link CA activity to 18 O data (Gillon and Yakir, 2000a; e.g. Gillon and Yakir, 2000b; Gillon and Yakir, 2001; Cousins et al., 2006a; Cousins et al., 2006b; Cousins et al., 2007). To do so, the exchange rate constant k iso appearing in Eq. 5 is usually taken as one-third of the CA-catalysed CO 2 hydration rate k h, and the residence time τ res is taken as the ratio of the total amount of CO 2 inside the leaf to the one- way flux of CO 2 from the atmosphere into the leaf. However, the ratio k iso/k h equals one-third only in acidic conditions (see Appendix B, Eq. B8), and this definition of the residence time implicitly redefines the system boundaries to include not only the CA-containing leaf compartment but also other leaf compartments, including the inter-cellular air space. In this case, k iso should be replaced by a more complex expression that depends not only on ph but also on the volumes of the gas and liquid phases and the (total) transfer coefficient between these two phases, including g m (see Appendix B, Eq. B11). Finally, Eq. 5 does not account for the competition between CO 2 hydration and carboxylation, or for the contribution of respiratory fluxes. 11

12 For all these reasons, we adopted another approach that leads to a direct relationship between Δ ci and leaf CA activity at steady state, whilst simultaneously accounting for competition between hydration and carboxylation and for respiratory fluxes. The model of Farquhar and Lloyd (1993) forms the basis of this new approach, but is modified to account for the spatial separation of hydration and carboxylation sites, and their difference in leaf water isotopic composition, especially important in C 4 species. The CO 2 gas exchange rate A is the net result of CO 2 hydration, carboxylation, and respiration rates (Fig. 1, the biochemical view ). At steady state, isotopic equilibrium may not be reached, even at the CA site, if CO 2 carboxylation is large. Using the resistance scheme illustrated in Fig. 1, and assuming no isotopic fractionation during carboxylation by RuBisCO or PEPC, the isotope ratio of the net CO 2 flux is (see Appendix C for a derivation) determined as follows: 261 R A = V hm ( 3A R R m eq )+ V hc ( 3A R R c eq )+ V c A R F R c r mi R A = V hm ( 3A R m R eq )+ V c A R V c F r R mi φ r r A R mi for C 3 plants ( R mi ) for C 4 plants (6) where R eq = R esα wc, φ r is the fraction of respired CO 2 not recycled by the chloroplast stroma (C 3 plant) or not produced in the bundle sheath (C 4 plant) and F r is the ratio of the respiratory flux to the net flux: F r = (V r + 0.5V o)/a (all other symbols are defined in the caption of Fig. 1). Several lines of evidence [see Appendix C and also Farquhar and Cernusak (2012)] indicate that respired CO 2 should be fully equilibrated with mitochondrial water, suggesting R mi = R eq and R mi R x α wc, where R x is the isotope ratio of the water in the bundle sheath cells. Following arguments in favour of a strong homogeneity of water isotope ratios between the cytosol and 12

13 the chloroplast of single cells, we further assume that R m and R c should be closely related in C 3 species and equal to the CO 2 isotope ratio at the CA site (R CA). In C 4 species, we argue (see Appendix C) that R c (the 18 O/ 16 O ratio of CO 2 in the bundle sheath) should be closely related to R m/α cb R CA/α cb, where α cb is the isotope fractionation between CO 2 and bicarbonate (around at 25 C). With these simplifications, Eq. 6 can be re-written (see Appendix C): = 1+ 3ρF r 1+Δ i 3ρ 1 = 1+ 3ρF r 1+Δ i 3ρ ( Δ ci Δ ei )+1+Δ ci for C 3 plants ( Δ ci Δ ei )+ 1 a cbf r α cb V ( 1+Δ ci ) φ r r A Δ eq for C 4 plants (7) where ρ = ρ i(1 + ε ci)/ε ci, ρ i = A/(k CAp i), k CA is the measured leaf CA activity rate (expressed in µmol(co 2) m -2 s -1 Pa -1 ), a cb = α cb - 1 and eq = (R es/r x - 1)α cwr x/r i R es/r x 1. Equation 7 can be combined with Eq. 1 to eliminate ci and estimate ε ci (then p CA and g m) from measurements of k CA, Δ i, Δ ei and water vapour and CO 2 fluxes, provided that the respiratory terms (F r, V r/a, φ r) are known. Noting that F r also depends on ε ci (i.e. it can be expressed as a function of ε ci, V r/a and Γ * /C i where C i = p i/p and Γ * is the CO 2 compensation point in the absence of day respiration, see Eq. C17), this requires solving a quadratic (for C 3 plants) or a cubic (for C 4 plants) equation in ε ci (Eqs. C18 and C23, respectively, see Appendix C for a full derivation). If respiratory terms are negligible (F r = 0), then the solution for C 3 plants is similar to that proposed by Farquhar and Lloyd (1993). However, if respiratory terms are not negligible, the situation is different because here we assume that CO 2 respired by C 3 leaves is in equilibrium with mitochondrial (and thus cytoplasmic) water, while Farquhar and Lloyd did not (see Appendix C). 13

14 In the following, we solve Eq. 7 for ε ci using published datasets of k CA, Δ i, Δ ei and water vapour and CO 2 fluxes (Cousins et al., 2006a; Cousins et al., 2007; Barbour et al., 2016). For this, we set φ r = 0.5 and compute Γ * as a function of leaf temperature (Bernacchi et al., 2001). We then explore the possibility of using our new equation to estimate mesophyll conductance (g m) in C 3 and C 4 species, and estimate its sensitivity to the respiratory terms (V r/a) or the water isotope gradients between mesophyll and bundle sheath cells. For the sake of comparison with previous work, we also compute a degree of equilibration, as defined by Eq. 3. For this, we estimated ci0 by taking the limiting case of Eq. 6 when k CA tends to zero (i.e. V hm = V hc = 0) and assuming that, in absence of CA activity, the respiratory isotope ratios were equal to R a. Noting that V c/a = 1 + F r, this gives the following equation, for both C 3 and C 4 plants: R A ( 1+ F r )R c0 F r R a (8) k 0 CA where R c0 denotes R c in the absence of CA activity. Combined with flux-gradient relationships such as that in Eq. 1 (valid regardless of the CA activity), we obtain an expression for the ratio R c0/r a (see Appendix C, Eq. C28), from which we can derive ci0 (Eq. C29) and thus θ (Eq. 3) Results and discussion We first revisited the data from Cousins et al. (2006a), who measured online discrimination and the CA activity of C 3 and C 4 plants exposed to different light levels (see Table II in Cousins et al. 2006a). We estimated the effect of assuming or not assuming full CO 2-H 2O equilibration, and increasing the respiratory fraction (V r/a) on the light response of p CA/p a, g m and θ in F. bidentis leaves (Fig. 2). We see that the assumption of full 14

15 317 equilibration is almost valid at low light but as incident light increases, the 15

16 degree of equilibration decreases slowly (Fig. 2C) although not as sharply as the original θ values of Cousins et al. (2006a). This decrease in θ is slower when the respiratory fraction is high, as a consequence of the assumption that respired CO 2 is fully equilibrated. More interestingly, the retrieved mesophyll conductance responds very little to the increase in incident light, especially when compared to stomatal conductance (Fig. 2B). The new estimates of g m are also much lower (around 0.4 mol m -2 s -1 ) than the original value of 1 mol m -2 s -1 estimated by Cousins et al. (2006a), and only slightly higher (by around +15%) than the values we estimated assuming full equilibration (θ = 1). At first sight, it may seem surprising that, even for the lowest light level, our estimates of g m are much lower than the original estimate of Cousins et al. (2006a), despite the fact that in both cases, full isotopic equilibration is reached (an assumption in the case of Cousins et al. and a prediction in the present study). This apparent contradiction arises from the ternary corrections. Cousins et al. applied ternary corrections to estimate p i but not to interpret C 18 OO discrimination data, as it was common practice at the time. Farquhar and Cernusak (2012) have since shown that such a practice can lead to erroneous mesophyll conductance estimates. Indeed, when ternary corrections are only applied to compute p i, then the solution of Eq. 9 at low irradiance leads to the exact original g m value (1 mol m -2 s -1 ), but much lower g m values with increasing light (see Supplemental Figure S1). On the other hand, not applying ternary corrections at all leads to g m values almost identical to those shown in Fig. 2 (see Supplemental Figure S2), a result also predicted by Farquhar and Cernusak (2012). 16

17 The same analysis was also performed on the tobacco leaf datasets of Cousins et al. (2006a), and similar results were obtained (Fig. 3). The degree of equilibration decreased slowly with an increase in incident light but not as sharply as in the original publication (Fig. 3C), while the new estimates of g m were lower than originally estimated but slightly higher than the values obtained assuming full equilibration (+8-20%, depending on irradiance), and with less sensitivity to light levels than stomatal conductance (Fig. 3B). Compared to the results shown in Fig. 2, the sensitivity of g m to the respiratory fraction is also much lower. This is because, for C 3 species, V r/a only affects F r with little influence on i as long as ρ is small, whilst V r/a appears in two other terms in the C 18 OO discrimination model for C 4 species (Eq. 7). The above analysis demonstrates that, to explain the data from Cousins et al. (2006a), there is no need to evoke a spatial separation of the CA site and the evaporation site, nor an isotope heterogeneity of leaf water in the cytosol of mesophyll cells. By simply accounting for ternary corrections, competition between CO 2 hydration and carboxylation and the contribution of respiratory fluxes (Eq. 7) it is possible to reconcile the in vitro CA assays and the Δ 18 O measurements. Our new estimates of g m are lower than previous estimates, even when V r/a = 0 (Fig. 2 and Fig. 3). This is especially the case for F. bidentis, where g m is only slightly higher than the maximum stomatal conductance for CO 2 (g sc) (Fig. 2). As briefly explained above, this occurs because the estimation of g m as originally performed did not account for ternary corrections when interpreting isotopic discrimination. The difference between original and revised g m values is much lower when revisiting datasets where ternary corrections were fully accounted 17

18 367 for, such as those from Barbour et al. (2016). In this case, our new estimates of 18

19 368 g m tend to agree well with the original estimates but show consistently higher 19

20 values (by typically around 20% and up to 50% or more in some cases) than those estimated assuming full equilibration, and the sensitivity of g m and θ to the respiratory fraction V r/a is again very small in C 3 species and marginally small in C 4 species (Fig. 4). These results show that the degree of equilibration is expected to be near unity in all species (Fig. 4), and especially in C 3 plants, thus justifying a posteriori the assumption made by Barbour et al. (2016). However, accounting for incomplete equilibration between CO 2 and leaf water led to 18 O-derived g m values that are significantly higher than those obtained assuming full isotopic equilibration (Fig. 2, Fig. 3 and Fig. 4). Barbour et al. (2016) noticed that, in some C 3 plants, the 18 O-derived g m assuming full equilibration were sometimes of a magnitude similar to that of the mesophyll conductance estimated from 13 C discrimination. This was the case most notably in mature wheat leaves and seemed incompatible with the idea that the CA site was located at the chloroplast surface and, thus, upstream of the carboxylation site. Here, we show that accounting for incomplete equilibration increases the difference between 13 C- and 18 O-derived g m even in wheat (0.63 vs mol m -2 s -1 for mature leaves). Further, our modelling framework partly explains that the difference between 13 C- and 18 O-derived g m should not be so large because the CA site is now defined as the mean location of CA activity (Eq. C14), rather than its outer limit as originally defined in Gillon & Yakir (2000a). Ubierna et al. (2017) showed that PEPC-derived g m for C 4 plants agreed well with Δ 18 O-derived g m assuming θ = 1. Their reported PEPC-derived g m values for Zea mays and Setaria viridis agree well also with the Δ 18 O-derived g m reported by Barbour et al. (2016) assuming θ = 1, despite possible differences in plant 20

21 treatments and growth conditions between the two studies. For Z. mays and S. viridis, Barbour et al. (2016) report g m values of 0.5 and 1.1 mol m -2 s -1, respectively, at around 30 C, which is slightly lower but in relatively good agreement with the PEPC-derived g m estimates of Ubierna et al. (2017), of around 0.6 and 1.3 mol m -2 s -1, respectively (see Figure 2 of Ubierna et al. (2017). Our re-analysis shows that accounting for competition between CO 2 hydration and carboxylation would reconcile the two approaches even more, by leading 18 O-derived g m values of and mol m -2 s -1 for S. viridis and Z. mays, respectively (Fig. 4). Thus, our re-analysis indicates that imposing θ 1 to estimate g m is probably a fair approximation in many C 3 species and probably some C 4 species (Fig. 4). More importantly, our approach also provides a means to fully account for the role of competition between CO 2 hydration and carboxylation when estimating mesophyll conductance from online 18 O data. Another interesting dataset to revisit is that of Cousins et al. (2007) on mutants of Amaranthus edulis that exhibited a reduced PEPC activity but a CA activity similar to that of the wild-type. A re-analysis of their dataset using Eq. 7 is presented in Fig. 5. In the original analysis, g m was set to a constant value for all plants and the degree of equilibration was derived without fully accounting for ternary effects. This led to a rapid decrease in Δ 18 O-derived θ in response to increasing PEPC activity (Fig. 5). This feature seemed in contradiction with the observed in vitro CA activities that were similar amongst the different PEPC mutants (k CA = 60 ± 10 µmol m -2 s -1 Pa -1 ). Re-analysing their dataset with Eq. 7 led to quite different results, with a degree of equilibration much closer to unity, even in the wild-type, and much smaller values of g m that increased with PEPC activity (Fig. 5). Again, these new 18 O-derived g m estimates are very similar, 21

22 419 although slightly higher (up to +20%), than those estimated using full 22

23 equilibration (Fig. 5). Results shown in Fig. 5 may also help explain, at least qualitatively, the data from Stimler et al. (2011), who reported differences in Δ 18 O-derived θ between C 3 and C 4 species, despite no difference in CA activity between the two plant groups (estimated for the first time simultaneously on the same leaves, using carbonyl sulfide (COS) gas-exchange measurements). To reconcile the COS-derived CA activities with the Δ 18 O-derived θ values, Stimler et al. suggested that Eq. 5 should be re-visited. To explain the lower Δ 18 O values of C 4 plants relative to those of C 3 plants, they used Eq. 5 and hypothesised a reduction of k iso, of about 17% (Stimler et al., 2011). This reduction of k iso was attributed to PEPC activity that would deplete the bicarbonate pool of C 4 species to a point where it would affect CA activity (towards CO 2, but not OCS). Indeed, a depletion of bicarbonate would deplete p CA because the ratio of CO 2 to bicarbonate is fixed by ph, and this should lead to a decrease in the residence time of CO 2 and thus θ, to some extent. However, as explained above, Eq. 4 is ill-designed to describe steady-state gasexchange data. Our new formulation on the other hand (Eq. 7) is more suitable because it explicitly accounts for the competition between hydration and carboxylation rates whilst satisfying the steady-state mass balance. Results shown in Fig. 5C clearly demonstrate that differences in Δ 18 O (from 207 in the homozygous mutant to 16 in the wild type) are compatible with nearly full isotopic equilibration (θ 1) or with undetectable changes in CA activity deduced from other gas exchange techniques. In fact, CA activity (k CA) and the degree of equilibration (θ) are not intuitively related because large changes in k CA do not necessarily lead to large changes in θ (and g m). This is demonstrated in Fig. 6 that revisits data from Cousins et al. 23

24 445 (2006a) on wild-type and CA-deficient F. bidentis plants grown (and measured) 24

25 in ambient CO 2. Despite k CA values as low as 5 µmol m -2 s -1 Pa -1 and ρ values above unity in some CA-deficient plants, results using Eq. 7 indicate that g m remains relatively constant, and with values of wild-type plants and CA-deficient mutants being similar (Fig. 6B). Again, these g m values are higher than those estimated assuming full equilibration (Fig. 6). The degree of equilibration θ stays also relatively constant, between around 0.7 and 0.8 from low to high CA activity (Fig. 6C). In fact, in the datasets revisited here, the degree of equilibration θ will usually approach unity when ρ is below 0.01, and irrespective of whether it is a C 3 or C 4 species (Fig. 7). That θ is below 0.8 in Fig. 6 is primarily because ρ is not very low, even in the wild-type (mean value, 0.064). 25

26 Conclusion All the results presented here indicate that 18 O-derived g m values can be robustly estimated at steady state by considering the competition between CO 2 hydration and carboxylation, which determines the incomplete CO 2-H 2O equilibration inside the leaf. Even though CO 2 is in near-full equilibration with leaf water in most cases, the newly derived g m values are consistently higher (by typically around 20% and up to 50% or more in some cases) than those estimated assuming full equilibration. However, the physical meaning of this Δ 18 O-derived mesophyll conductance g m, and its significance for CO 2 assimilation, is still difficult to grasp, particularly for C 3 plants that exhibit CA activity in different mesophyll compartments. For both C 3 and C 4 plants, the contribution of the respiratory fluxes to the overall net C 18 OO discrimination (Fig. 1) complicates the classical view of g m as a pure diffusional property of the leaf mesophyll, a problem that also arises when interpreting 13 C discrimination data (Tholen et al., 2012). The new model formulation presented in this study by accounting for the compartmentalization of leaf water and CO 2 hydration, carboxylation and respiration sites is an attempt to bring more physical meaning to this leaf parameter. However, the gas exchange and biochemical views schematically presented in Fig. 1 are still far from being fully reconciled. Clearly, a more explicit representation of CO 2 and C 18 OO transport in the mesophyll and their exchange in the different compartments (cytosol, chloroplasts, mitochondria, etc.), with an explicit representation of their respective volumes, enzymatic activities and transfer resistances, is required to fully interpret Δ 18 O (and Δ 13 C) data in terms of the diffusional properties of the cell components. 26

27 481 27

28 482 28

29 Methods Literature data For the purpose of this study, three published datasets have been revisited (Cousins et al., 2006a; Cousins et al., 2007; Barbour et al., 2016). These datasets have been selected because they were the ones that gathered measurements of CA activity (k CA) using the 18 O exchange method (expected to provide more meaningful CA activities in vivo, see next section), isotopic discrimination ( A), leaf water isotope composition (R es), water vapour (E) and CO 2 (A) fluxes and stomatal (g sc) and boundary-layer (g bc) conductances for CO 2. Gas exchange and isotope data were available for all individual measurements, except for the datasets of Cousins et al. (2006a; 2007), where separate values of R a could not be retrieved and only mean values of R es, already expressed relative to R a (i.e., ea = R esα wc/r a - 1), could be assigned from the published tables. In addition, for consistency with the values of Barbour et al. (2016), these mean values of ea from Cousins et al. (2006a; 2007) were corrected using a fractionation factor for the diffusion of water vapour in still air of 28 (Merlivat, 1978), instead of 32 (Cappa et al., 2003). Finally, in Barbour et al. (2016), k CA values for G. hirsutum (cotton), T. aestivum (wheat) and Z. mays (corn) were not reported and were assumed here to be equal to those of tobacco plants (cotton and wheat) or taken from Cousins et al. (2006a) (corn) Estimating in vivo CO 2 hydration rates k CA from in vitro CA assays In all the studies that we revisited, CA activity was estimated by measuring the rate of 18 O loss of a sub-saturating, labelled C 18 O 2-buffered solution (Silverman, 1973; Badger and Price, 1994). The un-catalysed rate (k uncat,assay) was first measured and then leaf extracts were added to the solution to record the 29

30 catalysed rate (k cat,assay). CA activity (in units of mol(co 2) m -2 s -1 Pa -1 ) was then converted to its expected in vivo value (von Caemmerer et al., 2004): k CA = k cat,assay k uncat,assay k uncat,invivo K H V assay S leaf, (9) where k uncat,invivo (s -1 ) is the un-catalysed CO 2 hydration rate under the conditions in vivo (i.e. at physiological ph), K H (mol m -3 Pa -1 ) is the solubility of CO 2 in water, V assay (m 3 ) is the volume of the assay solution and S leaf (m 2 ) is the leaf area of the added leaf extracts in this volume. Compared to the ph method used in older studies (Gillon and Yakir, 2000a; Gillon and Yakir, 2000b; Gillon and Yakir, 2001), the CA assay using labelled CO 2 is less sensitive to the buffer solution used (Hatch and Burnell, 1990). More importantly, because the CO 2-H 2O isotopic exchange rate is somewhat slower than the hydration rate (Mills and Urey, 1940), measurements can be performed routinely at 25 C and near physiological ph and CO 2 concentrations, which is now the reason why this assay is preferred over the ph assay (von Caemmerer et al., 2004; Cousins et al., 2006a; Kodama et al., 2011; Studer et al., 2014; Barbour et al., 2016). A ph and CO 2 concentration correction still needs to be applied, which is done using Eq. 9. However, implicit to Eq. 9 is the assumption that the catalysed and un-catalysed rates respond similarly to ph, so that k uncat,invivo/k uncat,assay equals k cat,invivo/k cat,assay, where k cat,invivo would be the expected catalysed rate in vivo (i.e. at physiological ph). According to Rowlett et al. (2002) the ph dependence of k cat in wild-type Arabidopsis thaliana is well approximated by 1/( ph ). The ph response of k uncat usually used for CA assays is k uncat(ph) = /1011 ph (von Caemmerer et al., 2004). A modification of Eq. 9 was then applied here: k CA = k CA,orig k uncat ( ph assay ) k uncat ph invivo ( ) ph assay ph invivo, (10) 30

31 where k CA,orig is the original (reported) CA activity. For C 3 plants, Eq. 10 does not modify the reported CA activity because the compartment that contains most CA is the chloroplast stroma, whose ph is very close to the ph of the assay, typically around 8.0 (von Caemmerer et al., 2004). On the other hand, in C 4 plants, ph invivo is expected to be close to the ph of the cytosol and thus more acidic, around 7.4. In this case, Eq. 10 leads to CA activity levels of C 4 plants that are lower by about 20% than those reported in the literature Data analysis We define g tc as follows: g tc = 1/(1/g bc + 1/g sc). From p a, A, E and g tc, we computed p i according to (von Caemmerer and Farquhar, 1981): p i = 1 t 1+ t p a 1 1+ t AP g tc, (11) where t = 0.5E/g tc is the ternary correction factor. From p i and p a, we computed ε ia = p i/(p a - p i). Assuming no ternary effect (t = 0), the CO 2 isotope ratio in the intercellular air space, expressed relative to the ratio in the outside air, is derived as follows (see Appendix A for a derivation): Δ ia = Δ A a ε ia 1+Δ A ( ), (12) where a represents the weighted-mean isotope fractionation factor during CO 2 diffusion through the leaf boundary layer and the stomata. Including ternary effects (t 0) leads to (see Appendix A for a derivation): Δ ia = 1 Δ ia t a 1+ p a Δ A, (13) 1+ t a 1+ t a 1+Δ A where t a = t 1+ a the following: p i ( ) (Farquhar and Cernusak, 2012). From Δ ia, we then computed Δ i = ( 1+ Δ A )( 1+ Δ ia ) 1, (14) 31

32 555 and Δ ei = 1+ Δ ea 1+Δ ia 1, (15) Values of p i, k CA, i, ia and ei were used to compute ε ci using Eq. C18 (C 3 plants) or Eq. C23 (C 4 plants), from which we could compute p CA = p iε ci/(1 + ε ci) and g m = AP/(p i - p CA). We finally computed the ratio R CA0/R a (see Eq. C28), from which we derived ci0 (= R CA0/R a/(1 + ia) - 1) and thus θ. Supplemental Data Supplemental Figure 1. Ternary corrections applied to Figure 2 Supplemental Figure 2. No ternary correction applied to Figure 2 when computing both p i and p CA. Supplemental Figure 3. Isotope difference between C0 2 in equilibrium with the water at the evaporation site and in the intercellular air space. Supplemental Figure 4. Differences between the intercellular CO 2 in equilibrium with the water at the evaporation site and in the intercellular air space. Supplemental Figure S1. Same figure as Fig. 2 in the main text, but with ternary corrections applied only when computing the CO 2 partial pressure in the intercellular air space (p i) but not when estimating the CO 2 partial pressure at the CA site (p CA). Supplemental Figure S2. Same figure as Fig. 2 in the main text, but with no ternary correction applied when computing both p i and p CA. Supplemental Figure S3. Isotope difference between the CO 2 in equilibrium with the water at the evaporation site and that in the intercellular air space ( ei = Req/Ri - 1) and isotope difference between the CO2 in the intercellular air space and that in the outside air ( ia = R i/r a - 1), both plotted against the leaf-toair vapour pressure deficit (VPD) for the different experiments revisited in this study. Supplemental Figure S4. Differences between the intercellular CO 2 mixing ratio (C i = p i/p) or the stomatal conductance (g sw) re-calculated without assuming saturation of intercellular vapour pressure (e i) and those calculated by the LiCor portable photosynthesis system assuming saturation, both plotted against the relative humidity in the intercellular air spaces for the different experiments revisited in this study. 32

33 Acknowledgements We would like to thank very warmly Margaret Barbour and Asaph Cousins for kindly gathering and sharing with us the raw data corresponding to the published work that we revisited in this article. We also thank the editor, Professor Graham Farquhar, and the two reviewers, Lucas Cernusak and Nerea Ubierna, for their very constructive comments that helped us to greatly improve the final version of this paper. This study has received funding from the French Agence Nationale de la Recherche (ANR) [Grant Agreement No. ANR-13-BS (project ORCA)] and the European Union s Seventh Framework Programme (FP7/ ) [Grant Agreement Nos (ERC starting grant SOLCA), (project 3to4) and (ERA-Net Plus project MODCARBOSTRESS)]

34 Figure legends Figure 1. Resistance scheme of CO 2 and C 18 OO fluxes in C 3 and C 4 plants. From a gas-exchange point of view, the net CO 2 photosynthetic rate in the leaf (A) can be seen as driven by the CO 2 gradient between the intercellular air space (partial pressure p i, isotope ratio R i) and the leaf interior that, for C 18 OO, should correspond to the outer limit of CA activity (partial pressure p CA, isotope ratio R CA). From a biochemical point of view, we distinguish C 3 and C 4 photosynthetic pathways. For C 3 plants, the net CO 2 flux A is feeding CO 2 entirely to the cytoplasm of mesophyll cells while photorespiration (V o) and mitochondrial respiration (V r) are feeding CO 2 to the cytoplasm only partially (fraction φ r, isotope ratio R mi), and the other fraction is directly recycled by the chloroplast. For C 4 plants, A is also feeding CO 2 entirely to the cytoplasm of mesophyll cells, but RuBisCO-related photorespiration occurs only in the bundle sheath cells and mitochondrial respiration occurs in both mesophyll cells (fraction φ r, isotope ratio R mi) and bundle sheath cells (isotope ratio R mi). The CO 2 in the cytoplasm of mesophyll cells (mixing ratio C m, isotope ratio R m) can be hydrated (rate V hm), and the bicarbonate (concentration B m, isotope ratio R m) can be dehydrated (rate V dm). In C 4 plants, bicarbonate is also consumed through PEP carboxylase activity (rate V p). In C 3 plants, the CO 2 in the chloroplasts (mixing ratio C c, isotope ratio R c) can be hydrated (rate V hc) or consumed by RuBisCO (rate V c), and the bicarbonate (concentration B c, isotope ratio R c) can be dehydrated (rate V dc). In C 4 plants, the CO 2 in the bundle sheath cells can only be consumed by RuBisCO (rate V c). The exact correspondence between p CA and C m or C c will vary between C 3 and C 4 plants (see text) and the associated 18 O-related mesophyll conductance 34

35 to CO 2 (g m) is not simply a transfer resistance and may also incorporate a biochemical component Figure 2. Light response of gas-exchange parameters in Flaveria bidentis leaves exposed to increasing levels of photosynthetic photon flux density (PPFD). (A) CO 2 partial pressure ratio p CA/p a, (B) 18 O-derived mesophyll conductance (g m), (C) 18 O-derived degree of isotopic equilibrium (θ) and (D) the ratio ρ = A/(k CAp CA). Data taken from Cousins et al. (2006a). Original and revised values, with three different values of the respiratory fraction V r/a, or assuming full equilibration, are shown. The CO 2 partial pressure ratio p i/p a and the stomatal conductance to CO 2 (g sc) are also shown, in panels (A) and (B) respectively Figure 3. Light response of gas-exchange parameters in Nicotiana tabacum leaves exposed to increasing levels of photosynthetic photon flux density (PPFD). (A) CO 2 partial pressure ratio p CA/p a, (B) 18 O-derived mesophyll conductance (g m), (C) 18 O-derived degree of isotopic equilibrium (θ) and (D) the ratio ρ = A/(k CAp CA). Data taken from Cousins et al. (2006a). Original and revised values, with three different values of the respiratory fraction V r/a, or assuming full equilibration, are shown. The CO 2 partial pressure ratio p i/p a and the stomatal conductance to CO 2 (g sc) are also shown, in panels (A) and (B) respectively Figure 4. Degree of isotopic equilibrium (θ) and mesophyll conductance (g m) for three C 3 (left) and three C 4 (right) plants studied by Barbour et al. (2016). 35

36 Original and revised values, with three different values of the respiratory fraction V r/a, or assuming full equilibration, are shown. CA activity for Gossypium hirsutum (cotton) and Triticum aestivum (wheat) was assumed equal to that of Nicotiana tabacum (tobacco) and CA activity for Zea mays (corn) was taken from Cousins et al. (2006a). In cotton, wheat and corn, only mature leaves are shown here. For corn, one individual data point did not lead to a plausible solution to Eq. C23 (i.e. negative ε ci and g m) and has thus been discarded when computing the mean value. For consistency, we also discarded this individual data point when computing the mean g m value corresponding to full isotopic equilibrium. Had it not been discarded, we would have obtained the same g m value obtained by Barbour et al. (2016), as is the case for the other species Figure 5. Effect of PEPC activity (k PEPC) on gas-exchange parameters in wild-type (WT) and heterozygous (Pp) and homozygous (pp) PEPC-deficient Amaranthus edulis plants grown in elevated (0.98 kpa) CO 2. (A) CO 2 partial pressure ratio p CA/p a, (B) 18 O-derived mesophyll conductance (g m), (C) 18 O-derived degree of isotopic equilibrium (θ) and (D) the ratio ρ = A/(k CAp CA). Data taken from Cousins et al. (2007). Original and revised values, with three different values of the respiratory fraction V r/a, or assuming full equilibration, are shown. In (C) numbers in parentheses indicate isotopic discrimination 18 O Figure 6. Effect of leaf CA activity (k CA) on gas-exchange parameters in different wild-type and CA-deficient Flaveria bidentis leaves grown and measured at ambient CO 2 concentrations. (A) CO 2 partial pressure ratio p CA/p a, (B) 18 O- derived mesophyll conductance (g m), (C) 18 O-derived degree of isotopic 36