Advances in measurements and models of photosynthetic carbon isotope discrimination in C 3 plants

The scientific community has long recognized that the study of atmosphere–biosphere interactions is vital to understanding fields as varied as agriculture, ecology and global change. Measurements of CO2 and H2O exchange are potentially enhanced by measurements of the minor isotopologues of those species (e.g. 13C16O2), because of the extra information revealed about mechanisms limiting the fluxes. In the past, it was difficult to add the minor isotopologues to these ecosystem fluxes because samples had to be analysed in an isotope ratio mass spectrometer in a laboratory setting. Nowadays, optical isotope analysers (lasers and Fourier transform infrared spectroscopy) allow for rapid measurement of isotope ratios with sufficient precision, and in field settings. This has motivated a series of innovative studies both in the laboratory and in the field that combine measurements and models of photosynthetic fluxes and isotope exchange. Absorption spectroscopy methods have increased the rate at which measurements can be taken in the laboratory, allowing us to gain a better understanding of the dynamic responses of mesophyll conductance (Tazoe et al. 2011; Evans & von Caemmerer 2013), value for photorespiratory fractionation (Evans & von Caemmerer 2013), respiratory effects and their impact on photosynthetic discrimination calculations (Barbour et al. 2007; Stutz et al. 2014) and calculations of leakiness in C4 species (Ubierna et al. 2011). Field applications that traditionally have used isotope records from atmospheric flask samples or tree ring chronologies will benefit from the large data sets that are starting to become available with optical isotope analysers. Example of these are isotope-constrained carbon budgets (Ballantyne et al. 2010), partitioning of oceanic and terrestrial fluxes (Ciais et al. 1995; Fung et al. 1997), or confirmation of simulations of 13C discrimination by the terrestrial biosphere (Suits et al. 2005). Some other examples of field applications that have already used optical analysers include partitioning of net ecosystem exchange (Bowling et al. 2001; Zobitz et al. 2008) and the testing of the predictive ability of different discrimination models (Wingate et al. 2007; Bickford et al. 2009). In this issue of Plant, Cell & Environment, Gentsch et al. (2014) collect the largest available field data set of instantaneous measurements of observed discrimination (60 d of records with a half-hour interval) and use it to test different formulations of the 13C photosynthetic discrimination model (Δ13C). They demonstrate that both simple and ‘comprehensive’ models of Δ13C were able to predict flux-weighted discrimination equally well. Herein, we build upon the work of Gentsch et al. (2014), comment on the errors that may result when using different formulations of Δ13C and give some recommendations about what formulation should be chosen for different applications. One common debate in these kinds of studies is the degree of complexity that should be included in the mathematical models of 13C photosynthetic discrimination (Δ13C). The original model for Δ13C (Farquhar et al. 1982b), extended to include ternary effects (Farquhar & Cernusak 2012), includes several parameters that are difficult to measure or estimate and therefore often sacrificed for easier formulations (Fig. 1a). In the last few years, as the reliability of data and of parameter values has improved, detailed studies have shifted from the use of the very simplified formulation to the use of the full equation. (a) ‘Comprehensive’ model of Δ13C photosynthetic discrimination (Farquhar & Cernusak 2012) and several simplifications. (b) Division of the ‘Comprehensive’ model of Δ13C into the components that account for the major fractionations that ambient CO2 undergoes until its fixation in recent photosynthate. The term called stomatal contribution includes both stomatal and boundary layer effects, and could easily be decomposed into Δgs and Δgb, but boundary layer conductance is often large and thus a small contribution to the total discrimination. Ca, Cs, Ci and Cc (μmol mol−1) are the mol fractions in the ambient air, leaf surface, leaf intercellular spaces and chloroplast, respectively. ab, as, am, b, e and f are the fractionations associated with diffusion through the boundary layer (2.8‰), in air (4.4‰), in water (1.8‰), by Rubisco carboxylation (30‰), during respiration (0 to −5‰) and photorespiration (8–16‰), respectively. The terms αb, αe and αf are 1 + b, 1 + e and 1 + f, respectively. A and Rd are the photosynthetic and day respiration rates (μmol m−2 s−1), respectively. Γ* is the CO2 compensation point in the absence of day respiration (μmol mol−1). The ternary effect is t = αacE/2gac, where E is transpiration rate (mol m−2 s−1), gac is the conductance to diffusion of CO2 in air (mol m−2 s−1) and the fractionation for the isotopologues of CO2 diffusing in air is , where . Example of the contribution to total 13C discrimination during photosynthesis of Rubisco fractionation (Δb), stomatal and mesophyll conductances (Δgs and Δgm, respectively), respiration (Δe) and photorespiration (Δf). Equations for each component are presented in Fig. 1b. The values used for calculations were high or low photosynthetic rate (A = 20 or 3 μmol m−2 s−1), large or small mesophyll conductance (gm = 0.5 or 0.1 mol m−2 s−1), gs = 0.3 mol m−2 s−1, Rd = 1 μmol m−2 s−1 and E = 4 mmol m−2 s−1. All other parameters involved in the calculation of Δ13C were either derived from these previous values or from known constants (see Fig. 1 caption). Figure 2 illustrates that the largest moderators of Rubisco fractionation are Δgs and Δgm. When both A and gm were large, the diminutions of Δb (Rubisco fractionation) by gs and gm were 8 and 3‰, respectively. Under current ambient conditions [21% O2, [CO2] = 400 μmol mol−1], photorespiration represents a constant contribution of 1.1‰ at 25 °C. The effect of day respiration is modulated by the ratio Rd/(A + Rd). Thus, the respiratory contribution to discrimination is larger whenever Rd is large in proportion to A. The estimated value of fractionation during day respiration, e, varies between 0 and −5‰ (Tcherkez et al. 2004, 2010, 2011). In our example with e = −5‰, Δe reached a contribution to total Δ13C of −1.1‰ when A was low. Occasionally, a much larger apparent respiratory fractionation can occur when the substrate for respiration has a very different δ13C value from that of recent assimilates. This typically occurs in experiments that use a depleted tank for gas exchange/isotope measurements or when there is a shift in respiratory substrates, for example, at dusk or dawn (Wingate et al. 2007; Gentsch et al. 2014; Stutz et al. 2014). Nevertheless when weighted by carbon assimilation, under most conditions the respiratory contribution to daytime discrimination will be small and negligible. Notice (Fig. 2) that photorespiration and respiration contributions to total discrimination partially cancel each other out because of the opposite sign of the fractionation factors f (positive) and e (negative). If the terms Δb–Δgs are lumped together and ternary and boundary layer conductance effects are considered negligible, it results in the familiar, simple expression of Δsim [= as + (b − as)Ci/Ca]. If the value of b in Δsim is reduced (let us call it ) to account for the drop in discrimination by Δgm, then Δcom is essentially approximated by , with the remaining error (<1‰) attributed to photorespiration. The inconsistency between reported values of Cc/Ci and can be explained by the combination of two factors: (1) the difference between discrimination derived from δ13C of plant bulk material (Δp) and from observed instantaneous measurements of gas and isotopic exchange during photosynthesis (Δobs; Evans et al. 1986), and (2) differences in the method of calculation of gm. Firstly, the value of was developed from observations of Δp. However, Δp is often larger than Δobs, for example, by 2‰ in the study by von Caemmerer & Evans (1991). The reason behind the differences is unclear, but may be related to the different integration times of the isotopic signal and to the fact that bulk material contains fractions that are more depleted than sugars, such as lipids or lignin and possibly reflects nocturnal respiratory fractionations that are not captured in daytime Δobs (Cernusak et al. 2009). A 2‰ difference in discrimination would translate into a change in Cc/Ci of ≈ 0.1. Secondly, values of gm are obtained with various methods, each of them with different associated errors (Pons et al. 2009). For example, the effect of photorespiration is occasionally ignored when using the isotope method to calculate gm leading to an underestimation of Cc/Ci of ≈ 0.05 at 25 °C and 21% O2. Apart from methodological differences among studies, the ratio Cc/Ci is likely to vary among species and environmental conditions. It has been demonstrated that the slope of the relationship between A and gm is species specific (von Caemmerer & Evans 1991; Loreto et al. 1992; Hanba et al. 2001; Singsaas et al. 2004; Ubierna & Marshall 2011). Undoubtedly, Eqn 5 does not account for all observations, and clearly a better fit between observations and a particular model of Δ13C will be found as more fitting variables are used in the model. In model selection, it should be kept in mind that there should be a trade-off between the goodness of fit and the complexity of the model: appropriate statistical procedures should be used to ensure that there is no over fitting. One typical example from field studies where Eqn 5 might not suffice is the large discrimination values measured at dawn and dusk when photosynthetic rates are low. In these situations, the respiratory term is used as a fitting parameter between modelled and measured discrimination (Wingate et al. 2007; Gentsch et al. 2014). Of course, data collected when fluxes are low have to be interpreted with caution because of the large error associated with the calculation of Δobs. Despite the fact that models and measurements can be forced to match with this approach, we still know little about the processes that result in these observations. In order to decide what equation to choose, the user needs to ponder the application. If the objective is to derive gm or other parameters from measurements and models of discrimination, the detailed equation is required. Alternatively, for crude applications, such as using Δ13C to correct 14C data (Drake 2014), it would seem pointless going beyond the simplest model. As illustrated by Gentsch et al. (2014), the diurnal variation in Δobs was mostly explained by the contributions of stomatal and mesophyll conductances and photorespiration, which could be approximated by . For ecosystem or global scale applications such as isotope-constrained C-budgets, or whenever discrimination needs to be forecast but with no large data set of Δobs available, it will be advantageous to use the simplified equation introduced here. The ‘comprehensive’ model requires many estimated parameters, some of them with compensating effects (Gentsch et al. 2014) and in the absence of data sets to test the model prediction, it will likely result in larger model uncertainty and instability. A simplified model can introduce more error in the prediction of diurnal patterns, but C cycle models are more concerned with longer term C flux estimates. Technological advances and additional improvements to field studies should help increase the precision of data collected and our understanding of the factors contributing to photosynthetic discrimination at different temporal scales. G.D.F. acknowledges the Australian Research Council for a Discovery Grant DP1097276.