A high throughput gas exchange screen for determining rates of photorespiration or regulation of C4 activity

Summary A rapid approach to determine photorespiratory activity in plants suitable for analysis of photosynthetic mutants, C3–C4 intermediates, as well as lines with a weak glycine shuttle.


Introduction
In most photosynthetic organisms Ribulose Bisphosphate Carboxylase Oxygenase (RuBisCO) catalyses the first key step in carbon assimilation, reacting ribulose-1,5-bisphosphate with CO 2 to produce two molecules of 3-phosphoglycerate (PGA). Oxygen competitively inhibits this reaction and leads to the synthesis of the 2-carbon compound phosphoglycollate, which is recycled to PGA (consuming ATP, and then NADPH) and CO 2 by the photorespiratory cycle (Yoshimura et al., 2004;Sage et al., 2012). The result of photorespiration is a noticeable carbon loss and a consequent metabolic cost for carbon recapture and for the recycling of photorespiratory intermediates (Ehleringer and Pearcy, 1983;Pearcy and Ehleringer, 1984;Eckardt, 2005). Many plants have evolved strategies to reduce photorespiration by increasing the level of CO 2 around RuBisCO, including both crassulacean acid metabolism (CAM) and the C 4 photosynthetic pathway (Dodd et al., 2002;Sage, 2004;Sage et al., 2011;Osborne and Sack, 2012;Griffiths et al., 2013;Owen and Griffiths, 2013). C 4 photosynthesis is most often based on a two-celled carbon concentrating mechanism, where HCO 3 is first fixed into the four-carbon compound oxaloacetic acid (OAA) in the mesophyll by phosphoenolpyruvate carboxylase (PEPC). OAA is then reduced to malate or transaminated to aspartate and the resulting C 4 -(amino)acid is shuttled into the bundle sheath (BS), where it is decarboxylated, releasing CO 2 for refixation by RuBisCO (Hibberd and Covshoff, 2010;Bellasio and Griffiths, 2014c).
Although the enzymes catalysing the core C 4 carbon concentration mechanism (CCM) are well characterized (Kanai and Edwards, 1999), many of the genes responsible for the accompanying anatomical alterations or for generating and maintaining expression of the C 4 cycle genes (Hibberd et al., 2008;Langdale, 2011) have yet to be identified. One approach that is increasingly proving useful to identify candidate genes underlying the C 4 pathway is comparative transcriptomics of samples either undergoing C 3 or C 4 photosynthesis Gowik et al., 2011;John et al., 2014), or tissues in the process of inducing the full C 4 system (Li et al., 2010;Pick et al., 2011;Chang et al., 2012;Wang et al., 2013). Because stable transformation of C 4 species is typically time-consuming, introduction of RNA interference constructs via a transient Agrobacterium tumefaciens-based system would be very helpful in screening these candidates being generated from transcriptomics.
At present, techniques used to screen for mutants possessing defective, or enhanced CCM characteristics are time-consuming (Table 1). Analysing the response of assimilation (A) to decreasing CO 2 concentration in the substomatal cavity (C i ), as A/C i curves (Long and Bernacchi, 2003;Yin et al., 2011a) can take 45 minutes per replicate leaf, and an appropriate model, which may require a priori knowledge of species-specific limitations (Laisk and Edwards, 2000;von Caemmerer, 2000von Caemmerer, , 2013Yin et al., 2011b). 13 C/ 12 C discrimination during photosynthesis (Evans et al., 1986) can also be used, and a comparison with stomatal conductance allows the internal mesophyll conductance, or extent of CCM or PEPC activity, to be resolved (Meyer et al., 2008;Kromdijk et al., 2010;Pengelly et al., 2010;Bellasio and Griffiths, 2014a, b, c). However, this latter technique is sensitive, and requires either off-line sample preparation for mass spectrometric analyses or specialized laser equipment which is not readily available (Table 1).
In this paper we describe a novel method, and present the associated theory, to determine rates of photorespiration from instantaneous rates of RuBisCO carboxylation and oxygenation. The approach compares concurrent gas exchange and pulse-modulated chlorophyll fluorescence measurements under ambient and low O 2 . Under these non-photorespiratory conditions assimilation (A) increases, because RuBisCO competitive inhibition from O 2 is reduced. In contrast, Y(II) decreases because the demand for NADPH associated with photorespiratory by-product cycling (and reduction) is lower, and cannot entirely be offset by the increase in A. The new method combines developments in approaches using gas exchange (Sharkey, 1988;Long and Bernacchi, 2003;Ripley et al., 2007) and the quantitative interpretation of quantum yield (Yin et al., 2004(Yin et al., , 2011bStruik, 2009, 2012;Bellasio and Griffiths, 2014b). This new method can be performed with off-the-shelf commercial equipment, which is generally available in ecophysiology laboratories. The procedure takes as little as 6 minutes to perform if plants are pre-adapted, making it significantly faster than A/C i curves and potentially useful as a high-throughput approach for assessing C 4 activity in mutant screens, the progeny from C 3 -C 4 crosses or C 3 -C 4 intermediates.

Gas exchange measurements with concurrent PSII yield
Measurements were performed with an infra-red gas analyser (IRGA, a LI6400XT, LI-cor, USA), fitted with a 6400-40 leaf chamber fluorometer. The IRGA was fed with CO 2 (through the IRGA gas mixing unit) and ambient air. Gas flow was set at 150 μmol s -1 . Reference CO 2 was set at 200 μmol mol -1 ( Figure 1 and Table 1) or set alternatively at 400, 300, 200, 150, 100, and 50 μmol s -1 (Figure 3). Block temperature was controlled at 35 °C. The fluorometer was set to multiphase pulse with factory setting, target intensity=10 and ramp depth=40% (Loriaux et al., 2013). A portion of a light-adapted leaf was clamped in the cuvette. The leaf was allowed to reach stable photosynthetic conditions under PPFD=300 μmol m -2 s -1 (factory setting: 90% red, 10% blue). Photosynthesis was measured every 10 s for 30 s (the three values were then averaged) and a multiphase pulse was applied for the determination of Y(II). A humidified 2% O 2 /N 2 gas (pre-mixed, BOC, Guilford, UK) was switched to supply the inlet of the IRGA. The gas was allowed to completely flush the cuvette (c. 6 min). Photosynthesis was measured every 10 s for 30 s (the three values were then averaged) and a multiphase pulse was applied for the determination of Y(II). Light was turned off, the inlet was fed with ambient air, the reference CO 2 was set at 500 μmol mol -1 , similar to the lab CO 2 concentration (c. 550 μmol mol -1 ) to minimize the errors caused by CO 2 leakage (Boesgaard et al., 2013), and flow was set to 40 μmol s -1 . Once the cuvette had been flushed, and the signal stabilised (c. 5 min), respiration was measured every 10 s for 2 min (the values were then averaged). C a was not adjusted to account for changes in stomatal conductance or for the control of C i during this procedure. This avoided the need for IRGA recalibration as the Y(II) measurements are independent of C i . The measured A and Y(II) under low and ambient O 2 , together with an estimate of R LIGHT (see below), were used to determine RuBisCO rate of carboxylation (V C ), RuBisCO rate of oxygenation (V O ), and the rate of photorespiratory CO 2 evolution in the light (F).

Theory
RuBisCO catalyses two reactions: a carboxylase reaction whereby Ribulose BisPhosphate (RuBP) is carboxylated to form two molecules of phosphoglyceric acid (PGA), and an oxygenase reaction whereby RuBP is oxygenated to form one PGA and one glycollate molecule. Each carboxylase event requires 2 NADPH for the reduction of the 2 PGA molecules formed. Each oxygenase event requires 1 NADPH for the reduction of the PGA directly produced by RuBisCO, 0.5 NADPH to recycle glycollate, and 0.5 NADPH to reduce the PGA regenerated, which total 2 NADPH (Bellasio and Griffiths, 2014c). The overall NADPH demand, at steady-state, equals the total photosynthetic NADPH production rate J NADPH (Yin et al., 2004;Yin and Struik, 2012): (1) Where J NADPH is the total NADPH produced for photosynthesis, V C is RuBisCO carboxylation rate, and V O is RuBisCO oxygenation rate. Notably, this reducing power requirement is the same for all types of photosynthesis, as active types of CCM require additional ATP but not NADPH. In line with von Caemmerer (2000) equation 1 assumes that PGA is entirely reduced, and therefore the small quantity of PGA consumed by respiration ( in fact under growth light irradiance 2V C +2V O >> 1 3 R LIGHT , unless at very low irradiances, see equation 7 in Bellasio and Griffiths (2014c).
Although the carboxylation reaction of RuBisCO consumes CO 2 , the regeneration of glycollate releases 0.5 CO 2 for each oxygenase catalytic event. CO 2 is also produced by light respiration, a process which is active during photosynthesis to support basal metabolism. The net assimilation rate (A, which is the quantity measured through gas exchange) results from summing the CO 2 consumed by RuBisCO, the CO 2 produced by glycollate regeneration and the CO 2 produced by respiration: Where A is net CO 2 assimilation, R LIGHT is respiration in the light and other variables were previously defined. Notably, this equation is universal for all types of photosynthesis (von Caemmerer, 2013).
For the definition of gross assimilation (GA = A + R LIGHT ), equation 2 can be rearranged: Equation 1 and 3 can be combined to give: The rate of photorespiratory CO 2 evolution, F can be calculated as: (von Caemmerer, 2013) Under low O 2 , V O can be approximated to ≈0, hence, from equation 4: NADPH is produced through linear electron flow. Independently from where this reaction is located (e.g. in mesophyll cells), electrons are invariably extracted from water by PSII (Yin and Struik, 2012), therefore J NADPH is proportional to Y(II) (Yin and Struik, 2012). This allows J NADPH to be calculated under photorespiratory conditions using the information derived under non-photorespiratory conditions, and can be expressed as (Bellasio and Griffiths, 2014b): Where J NADPH and Y(II) refer to ambient O 2 conditions. Equation 7 has been validated in C 3 and C 4 plants (Yin et al., , 2011bBellasio and Griffiths, 2014b, c) but it is worth noting that equation 7 is a mathematical simplification and holds true when: (i) photorespiration is negligible under non-photorespiratory conditions, which is a widely used simplification; (ii) R LIGHT does not vary between low and ambient O 2 -this is also a fair assumption because any O 2 effect is generally negligible (Badger, 1985;Gupta et al., 2009); (iii) the allocation to alternative sinks (non-assimilatory and non-photorespiratory) is proportional to Y(II). This is the normal case in C 4 plants where the relationship between Y(II) and Y(CO 2 ) has a null intercept (Edwards and Baker, 1993). When that is not the case, for instance when the allocation to alternative sinks is constant, equation 7 would also hold true if the allocation to alternative sinks is small compared with Y(II). This is the normal case in C 3 plants (Valentini et al., 1995;Martins et al., 2013). Should the allocation to alternative sinks be large, equation 7 would still hold true mathematically when is close to the unity. The implications for method accuracy are detailed in the discussion. Equation 3, 4, 6, and 7 can be combined to obtain: Which expresses the RuBisCO rate of oxygenation relative to carboxylation. The influence on the quality of R LIGHT estimate on V O /V C is described in the discussion, together with the other factors influencing the results.

Modelling C 3 and C 4 V O /V C
The data obtained for tobacco and maize were compared with a simulated V O /V C based on the validated von Caemmerer models for C 3 and C 4 photosynthesis. Briefly, for tobacco, the response of A to C i was modelled using the quadratic equation (Table 3, equation 9) proposed by Ethier and Livingston (2004), which takes into account mesophyll conductance to CO 2 . The CO 2 concentration at the site of carboxylation C C was then calculated through the supply function of mesophyll (equation 10), and, finally V O /V C was simulated from the kinetic properties of RuBisCO and the ratio between C C and the O 2 concentration at the site of carboxylation (equation 11). For maize (Table 4), firstly we simulated the responses of V P and A to decreasing C i , using the equations for the enzyme-limited model for C 4 photosynthesis (equation 12 and 16, respectively). These were used to simulate the CO 2 and O 2 concentration in the bundle sheath (equation 13 and 14, respectively), the ratio of which, together with RuBisCO specificity, was used to simulate V O /V C (equation 15 and 17). Figure 1 displays a typical primary data profile for a C 3 tobacco leaf, showing the interaction between steady state assimilation (A) and quantum yield of PSII, Y(II), during the transition from ambient to low O 2 (21 to 2% O 2 ), with hatched areas indicating the steady state conditions under which readings were taken to derive V O /V C . Under nonphotorespiratory conditions, A increases because of the lower competitive inhibition of O 2 , whereas Y(II) decreases owing to the lower NADPH demand for photorespiratory by-product recycling and reduction. The experimental conditions were deliberately chosen to minimize reductions of quantum yield at saturating light (relatively low PPFD of 300 μmol m -2 s -1 ), and enhance photorespiratory responses to low O 2 partial pressure (measurements at 200 μmol mol -1 CO 2 ) ( Fig. 1 and Table 2). Subsequently, V O /V C was measured on C 3 tobacco and C 4 maize using different CO 2 concentrations in the reference gas: 400, 300, 200, 150, 100, and 50 μmol mol -1 (Fig. 2) and results were compared with simulated values of V O /V C generated with the validated von Caemmerer C 3 and C 4 models. To facilitate the comparison, data were plotted against the substomatal CO 2 concentration C i . As expected, under decreasing C i , V O /V C becomes progressively higher in tobacco but it is only marginally affected in maize. The measured data track the trend and magnitude of the theoretical curves in C 3 , whereas we could not capture the theoretical increase in V O /V C expected when C i was close to zero. This may be due to errors in the determination of C i at very low stomatal conductance or to the simplifications used to resolve equation 7. Our data slightly underestimate V O /V C derived using pulsed of 13 C enriched CO 2 (Busch et al., 2013), which, however, lay above the curve simulated with the von Caemmerer C 3 model (see Fig. 2).

Results
Additional measurements were undertaken with the IRGA, including a recalibration procedure to account for the changing sensitivity to water vapour pressure after the transition to low O 2 , but stomatal conductance was reduced on average by 1% and internal CO 2 concentration, C i , by 3 μmol mol -1 (data not shown). In the subsequent sections, primary data for V O /V C determinations using this new method (calculated from equation 4) are initially presented for three representatives of C 3 and C 4 species. We then undertake a systematic error analysis of the method, to include the impact of biological and environmental variables. These include physiological components (R LIGHT ) and Fm′, as well as light intensity and CO 2 concentration used during experimentation. Table 2 demonstrates that the method clearly discriminates between C 4 species, possessing a functional CCM, and C 3 species with higher rates of photorespiration. V O /V C ranged from 0.0435 to 0.0852 for the representative C 4 species, with coefficients of variation ranging from c. 15% down to 5% in C. gynandra (Table 2). For the C 3 species, V O /V C ranged from 0.522 to 0.569, with a low coefficient of variation in tobacco and rice around 6% ( Table 2). The magnitude of the offset between C 3 and C 4 systems, if being used as a rapid screen, would allow changes in expression of C 4 characteristics to be clearly resolved. Such an approach would then allow more detailed characterisation of selected transformants, C 2 , or C 3 -C 4 intermediates to be undertaken.

Accuracy of R LIGHT estimates
To account for the extent that R LIGHT affected the measurement of V O /V C, a sensitivity analysis was used to determine how R LIGHT influences V O /V C (Fig. 3). To do so, equation 8 was calculated for a realistic dataset (R LIGHT =1 μmol m -2 s -1 , V O /V C =0.2 and Y(II)=0.65) at variable assimilation values. Then, test values for V O /V C were calculated after R LIGHT was varied to 2 μmol m -2 s -1 (+100%), 1.5 μmol m -2 s -1 (+50%), 1.2 μmol m -2 s -1 (+20%), 0.8 μmol m -2 s -1 (-20%), 0.5 μmol m -2 s -1 (-50%), 0 μmol m -2 s -1 (-100%, GA=A). The deviation from the set V O /V C value (0.2) represented the effect of errors in the evaluation of R LIGHT on V O /V C . Figure 3 shows that V O /V C was relatively insensitive to R LIGHT : for assimilation rates higher than 4 μmol m -2 s -1 , R LIGHT values which differed ± 50% resulted in an error lower than 4% in relative terms. R LIGHT overestimation resulted in a lower error than R LIGHT underestimation. For these reasons there is generally no need for a high quality estimate of R LIGHT .

Accuracy of Fm′ measurements
Equations 7 and 8 require the photochemical yield of PSII, Y(II). This is determined according to the formula of Genty (Genty et al., 1989;Maxwell and Johnson, 2000;Kramer et al., 2004), whereby Y(II) is calculated as the difference between the light-saturated chlorophyll fluorescence signal (Fm′) minus the chlorophyll fluorescence signal measured during photosynthesis (Fs), expressed as relative to Fm′. Key to this technique is achieving full saturation of PSII in the determination of Fm′ (Earl and Ennahli, 2004;Loriaux et al., 2006;Harbinson, 2013;Loriaux et al., 2013). Sub-saturating light pulses result in the underestimation of Fm′; however, the degree of underestimation depends not only on the saturating pulse spectra and intensity, but also on the species, the growth light intensity, and the light intensity used during the measurements (Earl and Ennahli, 2004).
Here, we show how a given Fm′ underestimation influences the values for V O /V C (Fig. 4). To do so, equation 8 was set to physiologically realistic conditions (R LIGHT =1 μmol m -2 s -1 , V O /V C =0.2, and A=5 μmol m -2 s -1 ), at different Y(II) values. Underestimates of Fm′ were then introduced by multiplying the realistic Fm′ value by, successively, 0.99 (-1%), 0.98 (-2%), 0.97 (-3%), and 0.95 (-5%). The difference between the two values represented the effect of Fm′ underestimation on V O /V C . Figure 4 shows that V O /V C was sensitive to Fm′ underestimation; for instance the relative error of V O /V C was c. 20% when Y(II) was 0.15 and Fm′ was underestimated by 3%. The error increased hyperbolically at decreasing Y(II), and increased proportionally as the Fm′ underestimation was increased.

Light intensity and CO 2 concentration used for experimentation
High light intensities (e.g. PPFD>1000 μmol m -2 s -1 ) result in a low PSII yield, which may potentially amplify the systematic error from any Fm′ underestimation (see above). Similarly, small Y(II) could potentially lead to V O /V C underestimation when the allocation to alternative sinks is significant (see description   Table 2. Example of variability within populations and between populations displayed by plants with different pathways of assimilation V O /V C was measured on species (Miscanthus, Cleome gynandra, maize, wheat, tobacco, and rice) under photosynthetic photon flux density (PPFD) of 300 μmol m -2 s -1 , and C a =200 μmol mol -1 .  Table 3 and 4). With decreasing C i , V O /V C gets progressively higher in tobacco but it is only marginally affected in maize, CO 2 concentration can therefore be used to control the resolution of the method. All data shown, n=4. of equation 7). Further, high light conditions require longer timescales to reach stable photosynthetic conditions. On the other hand, depending on growth conditions, low light intensities (e.g. <100 μmol m -2 s -1 ) might lead to low assimilation rates, which could amplify the systematic errors in the estimation of R LIGHT (see Fig. 3

and above). For these reasons, intermediate light intensities represent the best solution, whereby Y(II) and
A are both high. For instance, values at the top end of the linear region of the light response curve would be ideal. These generally correspond to the growth light intensity. CO 2 concentration in the cuvette (C a ) can be used to manipulate photorespiration. Figure 2 shows the measured and predicted V O /V C of C 3 and C 4 plants under different CO 2 concentrations. Because of the CCM, V O /V C is low in maize, even at low C i , whereas in wheat V O /V C increases hyperbolically at decreasing C i . This contrasting behaviour allows the resolution of the method to be manipulated by changing the CO 2 concentration in the background gas. However, decreasing CO 2 concentration is disadvantageous because: (i) low C i results in quenching of PSII yield, which may potentially amplify the systematic error determined by Fm′ underestimation (see above); at the same time (ii) low Y(II) would amplify the magnitude of V O /V C underestimation owing to the partitioning of Y(II) to alternative sinks (see description of equation 7); (iii) under low C a , more time is required to reach stable photosynthetic conditions, which result in lower throughput; (iv) low C a increases the driving force for diffusion from outside of the cuvette, which may constitute a potential source of error, especially when assimilation is low (Boesgaard et al., 2013). For these reasons the optimal C a will depend on the purpose of the analysis, and on the desired resolution and speed.

Discussion
This method is based upon the difference in net assimilation (A) and photosystem II yield (Y(II)) observed when the gas supplied to an actively photosynthesizing leaf is switched from ambient O 2 to low O 2 . The goal was to develop a relatively quick, readily available method, which could be used to screen large numbers of transformants, C 3 -C 4 , C 2 , or photorespiratory refixation variants (Busch et al 2013;Oakley et al., 2014) in a given population of plants. The data show that the method readily distinguishes between V O /V C for typical C 3 and C 4 plants (Table 2), and, given the low coefficients of variation, should detect more subtle variations in C 4 repression or activation within a screen. It would then be possible to subject plants identified in this way to a more detailed, conventional gas exchange or stable isotope screen, to identify contributory morphological, metabolic or genetic factors. In the subsequent discussion, we explore the theoretical and practical limitations underpinning the accuracy of the method, and improvements that could be instituted to enhance the outputs, if high sample throughput was not a primary limitation.
Other methods have been proposed to determine the contribution of photorespiration in vivo through gas exchange measurements. The method proposed by Ripley et al. (2007) uses only the increase in assimilation under non-photorespiratory conditions, and therefore ignores the effect on Y(II). In our work we observed that Y(II) is generally influenced by changes in O 2 concentration (Figure 1), even in C 4 plants (see Fig. 2 in Bellasio and Griffiths, 2014b); therefore it is important to take into account the feedback from assimilation on photosystem II yield. Long and Bernacchi (Long and Bernacchi, 2003) proposed a comprehensive method to determine the partitioning of total electron transport rate between photorespiratory and assimilatory demand. Their protocol requires an initial light or A/C i response so as to fit a linear relationship between quantum yield for CO 2 fixation Y(CO 2 ) and quantum yield of photosystem II, Y(II).
deriving V O /V C from equation 8, both the numerator and the denominator are proportional to leaf area, a huge advantage for small or dissected leaves. The likelihood of triose phosphate limitation (Sharkey, 1988) is minimized under the relatively low light intensities and low C i , which are optimal for this protocol. The determination of V O /V C could take as little as c. 6 min, although the complete routine was longer (c. 40 min) as leaves were allowed to acclimate before measurement of both assimilation and dark respiration. Therefore, the run time can be minimized by measuring assimilation under growth conditions (e.g. at growth light intensity and CO 2 concentration), and either measuring respiration after all plants have been collectively dark-adapted, or estimating it separately (see below).

Other factors affecting accuracy of V O /V C determination
As shown in Fig. 3, the estimation of R LIGHT is important when calculating gross assimilation using eqn. 8 (GA=A+R LIGHT ) at low assimilation rates. R LIGHT can be determined with several methods; for instance, by linear regression of assimilation (A) versus irradiance (under very low irradiance e.g. <150 μmol photons m -2 s -1 ), by linear regression of A versus irradiance multiplied by Y(II) [under moderate irradiance, e.g. <400 μmol photons m -2 s -1 (Yin et al., 2011a)], by non-linear regression [throughout the light response curve (Prioul and Chartier, 1977;Dougherty et al., 1994)] or assumed to equal dark respiration [e.g. (Kromdijk et al., 2010;Ubierna et al., 2013)]. These methods do not necessarily yield the same R LIGHT values, and so, the degree of similarity between different R LIGHT estimates depends on the species and growth conditions. For instance, in Cocklebur (Xanthium strumarium L., Asteraceae), R LIGHT was significantly different from dark respiration (Tcherkez et al., 2008), whereas in maize R LIGHT is generally nonsignificantly different from dark respiration (C. Bellasio, unpublished data). The most suitable method to estimate R LIGHT should therefore be evaluated on a case-by-case basis (see Bellasio and Griffiths, 2014a), and for a uniform population (e.g. one species or set of transformants in a growth chamber), R LIGHT could be estimated on a subset of individuals, with one of the methods described above. If dark respiration is used as a proxy, the quality of the estimate can be increased using large chambers and low flow rates. In a diverse population, R LIGHT could be estimated by measuring   (Ethier and Livingston, 2004) dark respiration on each individual plant after the measurements in the light. As shown in Fig. 3, errors in the determination of Fm′ suggest that techniques such as the multiphase flash (Loriaux et al., 2013), or initial checks to ensure that the saturating pulse is saturating (see Bellasio and Griffiths, 2014b) are normally appropriate for this method. However, the use of our method is possible without a multiphase flash. Firstly, the underestimation of Fm′ introduces a systematic error, i.e. comparable plants will normally show similar V O /V C (see Bellasio et al., 2014), unless the extent of C 4 or C 2 activity has changed under these conditions. Thus, the precision and the resolution of the method, when comparing different phenotypes against a common genetic background, are not affected by a consistent underestimation of Fm′. Secondly, to improve accuracy, i.e. the capacity of the method to estimate the true V O /V C , other approaches could: (i) increase the saturating pulse intensity; (ii) reduce the distance between light source or fibre-optic probe and leaf (in some systems); (iii) decrease actinic light intensity (as shown in this study) to maximise Y(II); and (iv) CO 2 concentration can be increased, in order to maximise Y(II).

IRGA recalibration, matching Y(II), C i , and consideration of mesophyll conductance
As mentioned in the results, a slight effect on stomatal conductance and C i (under low O 2 ) could have been caused by not recalibrating the IRGA upon switching background gas (Bunce, 2002). Although that recalibration could have increased C i and g S accuracy (under low O 2 ), this procedure   α Fraction of PSII active in BS cells 0.15 (Edwards and Baker, 1993;von Caemmerer, 2000;Kromdijk et al., 2010) γ* Half of the reciprocal of the RuBisCO specificity 0.000193 (von Caemmerer, 2000) Γ* CO 2 compensation point in absence of dark respiration * * Γ BS = γ O (17) Equation 4.9 in (von Caemmerer, 2000) is liable to introduce operator error and extend the time taken for measurements; further, there are theoretical reasons why we need not account for these processes while carrying out such a simple comparative screen. Firstly, the data used to calculate equation 8 are measured by the CO 2 channel of the IRGA and the fluorometer, which are both unaffected by the background gas (Bunce, 2002). Secondly, the effect of C i on A (under low O 2 ) is, for the greatest part, accounted by the feedback on Y(II). Although C i decreases under low O 2 , there is a strong feedback between assimilation and Y(II), and therefore Y(II) decreases proportionally. In fact, the relationship between gross assimilation (or, better, between Y(CO 2 ), which is GA divided by PPFD) and Y(II) is strictly linear (Edwards and Baker, 1993;Valentini et al., 1995;Martins et al., 2013). In C 4 plants, this linear relationship has generally a zero intercept, (Edwards and Baker, 1993); therefore, for C 4 plants, there is no need for curve fitting and the relationship can be correctly estimated with a single point. In C 3 systems this relationship is still linear but the intercept is, although generally small, not zero. The intercept, which is the magnitude of engagemant of alternative sinks, can be estimated by linear curve fitting, although several data points are required (Valentini et al., 1995;Martins et al., 2013). Using the complete fitting of the Y(CO 2 )/Y(II) relationship, however, did not improve the estimate of V O /V C (data not shown): the complete curve fitting correctly estimates the intercept, but the datapoints are taken under conditions which differ from those under which V O /V C is measured. Another way to improve the estimate of V O /V C would be to adjust C a under low O 2 so as to match Y(II) measured under ambient O 2 with Y(II) measured under low O 2 . Alternatively, C a could be manipulated to deliver C i under low O 2 , which matches that under ambient. The advantages would be that the measured data would then probably fit the predicted C 3 and C 4 models more precisely when C i is limiting (see Fig. 2, Tables 3 and 4). However, these operations do not improve the capacity to screen between C 3 and C 4 photosynthesis and the additional manipulations increase time and likelihood of errors. We also note that such improvements would allow this method to be used to calculate the CO 2 concentration at the site of carboxylation (C C ) in C 3 plants through equation 11 (Table 3), as well as mesophyll conductance via equation 10, using C C , and the values for assimilation and C i measured under ambient conditions.

Conclusion
In this paper a simple method, and associated theory, have been presented, which allow the determination of both the oxygenation (V O ) and carboxylation (V C ) rate of RuBisCO and the rate of photorespiratory CO 2 evolution (F) based on gas exchange and variable chlorophyll fluorescence under ambient and low O 2 . This may be of particular interest for high throughput screening to identify C 4 mutants lacking a fully functional CCM, C 2 variants, or populations of C 3 -C 4 hybrids (Oakley et al., 2014).