Carbon isotope discrimination as a diagnostic tool for C4 photosynthesis in C3-C4 intermediate species

Highlight Combined gas exchange and carbon isotope discrimination measurement and modeling is used to detect and estimate the contribution of the C4 cycle in the C3-C4 intermediate species.


Introduction
C 4 photosynthesis is a highly efficient carbon fixation system characterized by the presence of a biochemical carbon pump with the capacity of increasing the CO 2 partial pressure (pCO 2 ) at the site of ribulose 1,5-bisphosphate carboxylase/ oxygenase (Rubisco) to concentrations higher than ambient air (Hatch et al., 1967;Hatch, 1987;Ehleringer et al., 1991). This increases photosynthetic rates and reduces photorespiration, potentially improving nitrogen and water use efficiency (Hibberd et al., 2008;Langdale, 2011). Most C 4 species show a common anatomical pattern, called Kranz anatomy, that leads to the separation of enzyme functions in two compartments, the mesophyll and the bundle sheath cell (Brown, 1975). CO 2 is first hydrated into bicarbonate in the mesophyll cell cytoplasm in a reversible reaction catalyzed by carbonic anhydrase (CA) (Badger and Price, 1994). Carbon is then fixed by phosphoenol pyruvate carboxylase (PEPC), localized exclusively in the mesophyll, into four-carbon acids that diffuse to the internally adjacent bundle sheath cell, where they are decarboxylated and the released CO 2 is refixed by Rubisco.
The most productive crops, such as maize, sorghum and sugar cane, are C 4 plants, exemplifying the higher efficiency of this system over the C 3 photosynthetic pathway present in most plant species, including major crops like wheat and rice. For this reason, there is currently a strong interest in implementing the advantages of C 4 photosynthesis in to C 3 crops with the aim of increasing yield, to keep pace with the food needs of a growing world population Karki et al., 2013;Leegood, 2013). This kind of approach is boosting research on genetic, biochemical and physiological aspects of C 4 photosynthesis. However, the initial phases of these initiatives are not expected to produce fully functional C 4 plants, but plants showing incomplete C 4 phenotypes like those observed in C 3 -C 4 intermediate species, which have been considered remnants of the evolution from C 3 ancestors to C 4 plants (Rawsthorne, 1992;Sage et al., 2011). They show Kranz or Kranz-like leaf anatomy, but the activity of C 4 -related enzymes, such as PEPC, is lower compared to strict C 4 plants, and enzyme compartmentation is incomplete, with Rubisco and PEPC present in both the mesophyll and the bundle sheath cells (Cheng et al., 1988;Brown and Hattersley, 1989;Byrd et al., 1992). These factors reduce the efficiency of the carbon concentrating mechanism. In intermediate plants, a photorespiratory CO 2 pump, also known as the C 2 cycle or glycine shuttle, transports glycine formed during mesophyll photorespiration to the bundle sheath where it is decarboxylated and the CO 2 refixed, thus increasing overall CO 2 assimilation rate and reducing the effect of photorespiration (Monson et al., 1984;Sage et al., 2012;Schulze et al., 2013;Keerberg et al., 2014). The genus Flaveria has been the focus of numerous studies in the past because it comprises C 3 , C 4 and C 3 -C 4 intermediate species, the later showing different degrees of C 4 activity (Ku et al., 1983;McKown et al., 2005).
The C 4 cycle contribution to growth has been difficult to quantify in intermediate species. In these plants, a steeper initial slope in the CO 2 response of the CO 2 assimilation rate compared to a strict C 3 plantis expected. However, this trait is also affected by Rubisco content and its kinetic properties, so conclusions are not straightforward (von Caemmerer, 2000;von Caemmerer and Quick, 2000). Another important manifestation of C 4 activity in intermediate species is a reduction of the O 2 sensitivity of CO 2 assimilation and the compensation point (Γ) due to a proportion of Rubisco being contained in the bundle sheath (BS) and thus not in direct contact with air (Byrd and Brown, 1989;Dai et al., 1996). With the photorespiratory pump causing a similar effect, separating and quantifying the contribution of each biochemical pathway through this approach is not possible. The C 4 cycle activity relative to overall photosynthesis in intermediates has been estimated in the past by metabolite profiling, but recent reports indicate that metabolite accumulation is strongly dependent on the leaf zone sampled and its developmental stage (Monson et al., 1986;Leegood and von Caemmerer, 1994;Wang et al., 2014).
In order to develop a deeper understanding of the physiology of both natural and artificial C 3 -C 4 intermediates, better tools are needed to evaluate the contribution of C 4 photosynthesis to overall assimilation. One signature of the activity of PEPC as the initial CO 2 fixation enzyme is a change in carbon isotopic discrimination (Δ) during photosynthesis. Whereas Rubisco has a strong preference for the lighter isotope, 12 C, over the heavier isotope, 13 C, PEPC is less discriminating, which causes an important difference in the biochemical fractionation between C 3 and C 4 plants (O'Leary, 1981;Farquhar, 1983). Incomplete C 4 photosynthesis in C 3 -C 4 intermediates is also reflected in Δ, with both PEPC and mesophyll Rubisco acting as the initial CO 2 fixing enzymes and their relative activities determining the resulting Δ. Mathematical models describing CO 2 assimilation and isotopic discrimination in these plants have been previously developed (von Caemmerer and Hubick, 1989;von Caemmerer, 1992). However, attempts to characterize Flaveria intermediate species by studying carbon-isotope ratios in dry matter resulted in C 3 -like profiles, and were interpreted as having little or no contribution of the C 4 system to plant growth, which was in contradiction to results from metabolite analysis (Monson et al., 1988;Byrd et al., 1992).
Tunable diode laser (TDL) absorption spectroscopy allows relatively rapid measurements of Δ concurrently with gas exchange, and has been used to analyze and compare C 3 and C 4 species (Tazoe et al., 2011;von Caemmerer et al., 2014). The present work uses this technique, combined with mathematical modeling, as a tool to determine the presence and contribution of C 4 photosynthesis in C 3 -C 4 intermediate plants. An updated mathematical model of carbon isotope discrimination for C 3 -C 4 intermediate species is proposed, which considers the effect of mesophyll conductance and allows the calculation of the biochemical fractionation. The strategy was applied to the study of Flaveria bidentis (C 4 ), F. pringlei (C 3 ), F. floridana (C 3 -C 4 ) and F. brownii (C 4 -like). F. floridana has been described as a C 2 plant with elevated PEPC activity, but it was unclear if a C 4 cycle is actually contributing to total carbon assimilation in this species (Monson et al., 1986(Monson et al., , 1988Leegood and von Caemmerer, 1994;Dai et al., 1996). F. brownii, on the other hand, was initially considered a C 4 species, but later experiments proved incomplete enzyme compartmentation, with a small proportion of Rubisco activity present in the mesophyll cells, and it was then reclassified as a C 4 -like intermediate species (Holaday et al., 1984;Monson et al., 1987;Moore et al., 1989). In the present study, concurrent Δ and gas exchange measurement and modeling allowed the detection and estimation of the C 4 cycle in the intermediate species, proving itself as a powerful diagnostic tool for C 4 photosynthesis.

Plant material and growth conditions
Flaveria bidentis was propagated from seeds and F. pringlei, F. brownii and F. floridana were propagated from cuttings (Brown and Hattersley, 1989;Whitney et al., 2011). Plants were grown in 30 l pots in a garden soil mix fertilized with Osmocote (Scotts, Australia) in a glasshouse under natural light conditions, at 28/18°C day/night temperatures, respectively. Pots were watered daily.
Responses of CO 2 assimilation rate and CO 2 compensation point to O 2 partial pressure Two Li-Cor 6400XTs (Li-Cor, USA) were used to measure CO 2 assimilation at a range of reference pCO 2 (388, 0, 24, 48, 73, 97, 145, 194, 291, 388, 485, 582 and 776 μbar). N 2 and O 2 were mixed in different ratios by mass flow controllers (Omega Engineering Inc., USA) to generate a range of O 2 partial pressures (pO 2 ; 20, 50, 100, 200 and 300 mbar) supplied to the LI-6400s. Response curves of CO 2 assimilation rate (A) to intercellular pCO 2 (C i ), A/C i curves, were repeated sequentially at each pO 2 . The measurements were made at 25°C, a flow rate of 500 μmol s −1 and 1500 μmol quanta m −2 s −1 , inside a growth cabinet at 25°C. Four plants from each species were analyzed. The compensation point (Γ) was calculated from the A/C i curves at each pO 2 , as the intercellular CO 2 concentration where net CO 2 assimilation is zero.
To study the inhibitory effect of O 2 on assimilation rate, we compared the CO 2 assimilation rate at a reference pCO 2 of 380 μbar at each pO 2 .
Concurrent gas exchange and Δ measurements and calculations of mesophyll conductance Two Li-Cor 6400XTs (Li-Cor, USA) coupled to a tunable-diode laser absorption spectroscope (TDLAS, model TGA100A, Campbell Scientific, Inc., USA) as described in Tazoe et al. (2011) were used for concurrent measurements of gas exchange and carbon isotope discrimination (Bowling et al., 2003;Griffis et al., 2004;Pengelly et al., 2012;Evans and von Caemmerer, 2013). Plants were transferred from the glasshouse to a growth cabinet with fluorescence lights (TRIL1175, Thermoline Scientific Equipment, Australia) at 25°C and one young fully expanded leaf was placed in each of the 6 cm 2 leaf chambers. Measurements were made at a leaf temperature of 25°C, a flow rate of 200 μmol s −1 , 1500 μmol quanta m −2 s −1 and 20 mbar pO 2 . The desired pO 2 was achieved as described above and supplied to the Li-Cors 6400. Reference pCO 2 was changed stepwise to 392,980,686,490,294,196,98,49 and 392 μbar and measurements were made every 4 min for at least 30 min at each pCO 2 . Dark respiration (R d ) was measured at the end of an A/C i curve at 392 μbar pCO 2 and 20 mbar pO 2 by switching off the Li-Cor lamp. Three or four plants from each species were analyzed. Δ was calculated as previously described (Evans et al., 1986;Evans and von Caemmerer, 2013).
Mesophyll conductance (g m ) was calculated for F. pringlei from concurrent gas exchange and Δ measurements at the above range of reference pCO 2 and 19 mbar pO 2 , applying the equations previously described and including the ternary effects of transpiration rate (Farquhar and Cernusak, 2012;Evans and von Caemmerer, 2013). This method is only valid for C 3 species. For intermediate and C 4 species, we assumed the same CO 2 response of g m found in F. pringlei, and scaled the absolute value at ambient pCO 2 to obtain the best fit of the A and Δ models for the observed results (see Results section).

Mathematical models
The overall rate of net CO 2 assimilation (A) for C 3 -C 4 intermediate plants was previously described (von Caemmerer, 1992previously described (von Caemmerer, , 2013: where A m is the assimilation in the mesophyll and A s is the assimilation in the bundle sheath, which are defined as: so: where V p is PEPC carboxylation and β is the fraction of the CO 2 produced from photorespiration in the mesophyll (F m ) that is released in the bundle sheath. For simplification, bundle sheath respiration and photorespiration are not taken into account in eq. 4. The term L is the leak rate of CO 2 out of the bundle sheath, and can be expressed as: and where φ (leakiness) is the ratio of the leak rate of CO 2 out of the bundle sheath and the supply rate of CO 2 to the bundle sheath When pO 2 is low, F m can be considered 0. V m and R m are Rubisco carboxylation and day respiration in the mesophyll, respectively. V p and V m are calculated as described in von Caemmerer (2000): and where C m and C i are mesophyll and intercellular pCO 2 , respectively. K c and K o are the Michaelis-Menten constants for CO 2 and O 2 respectively, expressed as a partial pressure. Although the pCO 2 in the cytosol (site of PEPC carboxylation) and the chloroplast (site of Rubisco carboxylation) of the mesophyll cell are presumably different due to diffusional limitations, the same value (C m ) was assumed in both compartments (von Caemmerer, 2000(von Caemmerer, , 2013Tholen and Zhu, 2011). When the rate of PEP regeneration is limiting, V p =V pr , where V pr is a constant. V m,max is the maximum Rubisco carboxylation in the mesophyll, and V p,max is the maximum PEPC carboxylation (Table 1). When RuBP becomes limiting, V m in eq. 6 can be given by an electron transport limited rate (W j ), as previously described (von Caemmerer, 2000(von Caemmerer, , 2013. Theory developed by Farquhar et al. (1982) and Farquhar (1983) showed that photosynthetic carbon isotope discrimination can be described by equations having diffusion and biochemistry dependent terms. The equation of Δ presented by (Griffiths et al., 2007), which takes into account the effect of g m , was modified to incorporate the ternary effects of transpiration rate as suggested by Farquhar and Cernusak (2012): where a l is the fractionations during diffusion in water and b s is the fractionation as CO 2 enters solution. The term t a E , where E denotes the transpiration rate and g ac t the total conductance to CO 2 diffusion including boundary layer and stomatal conductance. The symbol aʹ denotes the combined fractionation during diffusion in the boundary layer and in air, and is calculated as: where a is the fractionation during diffusion in air, a b is the fractionation during diffusion in the boundary layer, and C a , C l , C i are the pCO 2 in the air, leaf surface and intercellular space respectively.

Table 1. Values assigned to variables for model fitting purposes
When fitting F. brownii as a strict C 4 and F. floridana as a strict C 3 species, values were assigned to obtain the best fitting without considering measured enzyme activities. n.a., not applicable. The biochemical fractionation, Δ bio , is the integrated net biochemical discrimination, and depends on the biochemistry of net CO 2 uptake (Griffiths et al., 2007). When Δ and g m are known, Δ bio can be solved from equation 10, resulting in: Because g m was obtained from combined measurement of Δ and gas exchange in the C 3 species F. pringlei, Δ and g m are not independent and we could not estimate Δ bio from eq. 12. For the intermediate and C 4 species, g m was calculated independently of the Δ measurements as described in the Materials and Methods section, so Δ bio could be estimated from eq. 12 for F. floridana, F. brownii and F. bidentis. For modeling purposes, or when Δ is unknown, Δ bio can be derived from von Caemmerer's (1992) equation A17: where R i and R p are the molar abundance ratios of 13 C/ 12 C in the intercellular space and the photosynthetic product, respectively. Thus: The factor b 3 is the Rubisco fractionation, and b 4 is the combined fractionation of PEP carboxylation and the preceding isotope equilibrium during dissolution of CO 2 and conversion to bicarbonate; s is the fractionation during leakage of CO 2 out of the bundle sheath; e is the fractionation during mitochondrial respiration; f is the fractionation during photorespiration; R m and R s are the mitochondrial respiration rates in the mesophyll and the bundle sheath in the light, respectively. It was assumed that R d =R m +R s , and R m =R s =0.5R d . The factors F m and F s are the photorespiration rates derived from Rubisco oxygenation in the mesophyll and the bundle sheath, respectively. When pO 2 is low, F m and F s are close to 0, so equation 13 simplifies to: The parameter e needs to account for differences between the isotopic composition of CO 2 during plant growth and during the measurements, because the substrates used during respiration are most likely carbohydrates assimilated before the experiment (Wingate et al., 2007). No fractionation during mitochondrial respiration was assumed in this work, so e was calculated as the difference between δ 13 C in the CO 2 cylinder used during the experiments and δ 13 C in the atmosphere during growth conditions (e=δ 13 C cylinder -δ 13 C atmosphere ) (Tazoe et al., 2009;Pengelly et al., 2010). In this work, δ 13 C cylinder was between −4.12‰ and −5.14‰, and δ 13 C atmosphere was assumed to be −8‰ (Table 1).
In vitro enzyme activity assays Leaf discs (0.5 cm 2 ) were collected from the leaves used for gas exchange experiments and frozen in liquid nitrogen immediately after the experiment. Soluble protein was extracted by grinding one frozen leaf disc in a cold Tenbroeck homogenizer with 0.5 ml extraction buffer [50mM HEPES, 1mM EDTA, 0.1% (v/v) Triton X-100, 10mM DTT, 1% (w/v) PVPP, 1% (v/v) protease inhibitor cocktail (Sigma), pH 7.8]. Extracts were centrifuged at 13 000rpm for 30 s. Spectrophotometric assays were performed to determine Rubisco and PEPC activities as described in Pengelly et al. (2010). CA activity was measured in the same extract used for PEPC and Rubisco activity measurements, using a membrane inlet mass spectrometer to measure the rates of 18 O exchange from labeled 13 C 18 O 2 to H 2 16 O at 25°C with a subsaturating total carbon concentration of 1 mM (Badger and Price, 1989;von Caemmerer et al., 2004;Cousins et al., 2008). The hydration rates were calculated from the enhancement in the rate of 18 O loss over the uncatalyzed rate, and the nonenzymatic first-order rate constant was applied at pH 7.4 (k c =6.22x10 −11 /[H + ]+3.8x10 −2 =0.0396), appropriate for the mesophyll cytosol, at a CO 2 concentration of 8μM, which is approximately the CO 2 concentration in the mesophyll of F. bidentis (Jenkins et al., 1989;von Caemmerer et al., 2004). When CA is in the chloroplast, which is tipically the case in C 3 plants like F. pringlei, our calculations underestimate its in planta activity by ~10% due to the effect of the higher chloroplastic pH on k c (k c =0.0442 at pH 8).

O 2 response of CO 2 assimilation rate and compensation point
The effect of pO 2 on CO 2 assimilation rate and the compensation point (Γ) was measured at 380 μbar reference CO 2 , an irradiance of 1500 μmol quanta m −2 s −1 and 25 °C (Fig. 1).
In F. pringlei, increasing pO 2 caused a decrease in CO 2 assimilation rate, a response typical of a C 3 plant. Consistent with this, the Γ increased with increasing pO 2 , ranging from 5.6 ubar at 19 mbar O 2 to 53 µbar at 285 mbar O 2 .
In the C 4 species F. bidentis, the effect of oxygen was very small, with only a 5% decrease in CO 2 assimilation rate at the highest tested pO 2 . Γ in these plants barely changed with pO 2 , and ranged from 0.2 to 1.2 μbar.
The effect of O 2 on Γ in F. brownii was also very small and similar to the C 4 species F. bidentis, ranging from 1.3 to 3.1 μbar (Fig. 1b). However, the inhibitory effect of O 2 on CO 2 assimilation rate was more pronounced, and resulted in an intermediate response of CO 2 assimilation rate to increasing pO 2 (Fig. 1a).
The O 2 response of Γ in F. floridana was intermediate between C 3 and C 4 species (2.3-18 μbar; Fig. 1b), as has been previously shown (Ku et al., 1991). However, in our experiments the inhibitory effect of O 2 on photosynthesis was smaller than that previously reported by these authors and strikingly similar to that in F. brownii when pO 2 was 200 mbar or lower, despite the important differences in the enzyme compartmentation between these two species (Fig. 1a). Only at 290 mbar O 2 the inhibition of photosynthesis was higher for F. floridana, with a reduction of a 22%, compared to that in F. brownii (15% inhibition).
Stomatal conductance and C i increased slightly with pO 2 , with the exception of F. bidentis, which remained stable, and were considerably higher in the C 3 species F. pringlei at any pO 2 ( Supplementary Fig. S1 at JXB online).
The relative activity of PEPC to Rubisco was lowest in F. pringlei and highest in F. bidentis (Fig. 2b). F. floridana showed a PEPC:Rubisco ratio 3.4 times greater than the C 3 species, and F. brownii was closer to the C 4 species.

CO 2 assimilation rate and carbon isotope discrimination
Measurements of carbon isotope discrimination concurrently with gas exchange were performed under a range of CO 2 concentrations at 19 mbar O 2 on 3-4 plants from each species (Fig. 3). At this low pO 2 , photorespiration is greatly reduced and the effect of the C 2 cycle is negligible. Thus, small differences in the level of C 4 activity or mesophyll Rubisco activity are easier to detect.
F. pringlei and F. bidentis showed the typical C 3 and C 4 response of CO 2 assimilation rate to increasing C i , respectively (Fig. 3a). The initial slope of the A/C i curve in F. floridana was closer to that in the C 3 species, F. pringlei, whereas that of F. brownii was more similar to that of the C 4 species, F. bidentis, although in both intermediate species the sharp saturation typical of the C 4 species was missing. The maximum apparent assimilation rates in both intermediates were higher than those of the C 3 and C 4 species.
Carbon isotope discrimination measured over the defined range of pCO 2 provided clear differences between the four species (Fig. 3b). Δ was greatest in F. pringlei at any C i , ranging from 16‰ to 24.4‰. Discrimination in F. floridana followed a similar trend than that in the C 3 species, with Δ generally increasing with C i , but Δ was lower than in F. pringlei across the whole experimental range, ranging from 12.2‰ to 18.6‰. The response of C i /C a to CO 2 concentration was parallel to that of Δ in F. pringlei and F. floridana, reflecting the strong dependence of Δ on the ratio C i /C a in C 3 species and also in    F. floridana (Fig. 3c). The initial decrease of Δ in F. pringlei is also caused by a drop in C i /C a , which is in turn driven by a reduction of stomatal conductance with increasing C i when C i is lower than 200μbar.
In F. bidentis, as expected from a C 4 plant, discrimination was low (2-4‰) and decreased slightly with increasing C i . Δ in F. brownii was similar to F. bidentis at C i under 95 μbar (3.5-2.6‰), but above that the value of Δ increased with increasing C i , to a maximum of 6.1‰.
Measured Δ is shown with respect to C i /C a in Fig. 4. The theoretical lines assume infinite mesophyll conductance, which explains why both F. pringlei and F. floridana fell below the theoretical response for C 3 plants, with Δ and C i /C a generally lower in F. floridana. In F. bidentis, the result was as predicted by a theoretical CO 2 response of Δ for a C 4 plant when φ = 0 25 . , whereas F. brownii only fitted the expected response at low C i /C a , with Δ higher than predicted at high C i /C a .

Modeling CO 2 assimilation rate and carbon isotope discrimination in C 3 -C 4 intermediate species
In order to evaluate the contribution of the C 4 cycle to overall photosynthesis in the intermediate species F. floridana and F. brownii, the mathematical models proposed here for A and Δ responses to C i (eqs 6 and 10, respectively) were fitted concurrently to the observed results (Fig. 5). By simultaneously fitting both models using the same set of parameters, the accuracy of the predictions increases because some combinations of assigned constants that may result in a good fit for one of the models are unacceptable for the other. For comparison, the same strategy was also applied to the C 3 and C 4 species (see Supplementary Fig. S2). Table 1 shows the values assigned for fitting purposes and their source. Rubisco K C and K O (Michaelis-Menten constants for CO 2 and O 2 , respectively) in the four Flaveria ( . ) C C i a ; (Roeske and O'Leary, 1984;Evans et al., 1994). Dashed line represents the theoretical response of Δ to C i /C a in species analyzed here have been previously reported (Kubien et al., 2008), and V c,max and V p,max are from our own in vitro experiments. We assigned reasonable values for maximum electron transport (J max ). Leakiness ( ) φ was assigned so that the sum of the squares of the variances between the measured and modeled A, and between the measured and modeled Δ, was minimum. The distribution of Rubisco between the mesophyll and the bundle sheath in the intermediate species can be adjusted in the models by the assigned V m,max (maximum rate of Rubisco carboxylation in the mesophyll) value. When V m,max equals the V c,max observed in vitro, all Rubisco is in the mesophyll. A lower asigned V m,max indicates that part of the Rubisco activity is contained in the bundle sheath cells.
Mesophyll conductance (g m ) for F. pringlei was calculated from concurrent gas exchange and carbon isotope discrimination measurements at 19 mbar O 2 and a range of reference pCO 2 as previously described (Tazoe et al., 2011;Farquhar and Cernusak, 2012;Evans and von Caemmerer, 2013). Results show that g m decreases from 0.62 ± 0.1 to 0.33 ± 0.03 mol m -2 s -1 bar -1 with increasing C i when atmospheric pCO 2 is lower than ambient, and then remains stable at higher pCO 2 (Fig. 6). The CO 2 dependence of g m in F. pringlei is described by the polinomial function g m =10 -6 ·C i 2 −0.0013·C i +c, where c=0.666. In C 4 and C 3 -C 4 intermediate species, g m cannot be obtained from concurrent gas exchange and Δ 13 C measurements, so the same CO 2 dependence of g m was assumed for F. bidentis, F. brownii and F. floridana, and the constant c was calculated from model fitting so that the sum of variances between the measured and modeled A, and between the measured and modeled Δ, was minimum ( Table 1). The resulting g m are shown in Fig. 6. Methods for obtaining g m in C 4 and C 3 -C 4 intermediate species, based on 18 O discrimination measurements, are currently being developed (S. von Caemmerer, unpublished results).
The A and Δ responses to increasing C i predicted with this strategy were reasonably close to the measured values for F. pringlei and F. bidentis (Supplementary Fig. S2). Comparison between modeled and measured responses of CO 2 assimilation rate, A, and carbon isotope discrimination, Δ, to variation in intercellular pCO 2 , C i , in the C 3 -C 4 intermediate species F. floridana and F. brownii. Measured A (a) and Δ (b) as a function of C i in F. floridana (empty triangles), compared with the modeled responses predicted by C 3 -C 4 photosynthetic model assuming an active C 4 cycle (solid lines) or no C 4 cycle activity (dashed lines). Measured A (c) and Δ (d) as a function of C i in F. brownii (white squares), compared with the modelled responses using the C 3 -C 4 models assuming Rubisco activity in the mesophyll cells (solid lines) or a strict compartmentalization of Rubisco in the bundle sheath cells (dashed lines). Parameters used for model simulations are presented in Table 1.  Fig. 6. Response of mesophyll conductance (g m ) to changes in atmospheric pCO 2 . In F. pringlei, g m was calculated from concurrent gas exchange and Δ measurements made at 19 mbar pO 2 . The values for F. floridana, F. brownii and F. bidentis were assigned assuming the same response of g m to C i as observed in F. pringlei, scaled from model fitting.
In an exercise to prove the predictive value of these models for the presence of low levels of activity of the C 4 component, we attempted to fit the models for F. floridana under two different premises. In one case, we assumed a certain level of effective C 4 cycle contribution to overall carbon assimilation (Fig. 5a, b, solid lines). In the second case, we considered no C 4 activity and values were assigned to obtain the best possible fitting ignoring the measured enzyme activities (Fig. 5a, b, dashed lines). The models could only be fitted to the measured values of Δ and A if some C 4 activity, specified by a V p,max close to our in vitro measurements, was assumed.
A similar approach was used with F. brownii. In one case, the models were fitted assuming the presence of Rubisco in the mesophyll, and in the other case the model was fitted as if it were a strict C 4 plant (Fig. 5c, d). The predicted responses approached the measured values only if ~30% of Rubisco activity was located in the mesophyll (V m,max =15 μmol m −2 s −1 ; observed in vitro V c,max =50 μmol m −2 s −1 ).
A comparison of Δ and Δ bio highlights the fact that CO 2 diffusion processes have a large influence on Δ (Figs 3, 7). Δ bio was calculated from eq. 12 using gas exchange and Δ measured values. Calculation of Δ bio factors out the contribution from CO 2 diffusion and shows that the biochemical fractionations are different in the species analyzed. In F. floridana, Δ bio was high and increasing with C i . In F. brownii, Δ bio also increased with increasing C i , whereas in the C 4 species F. bidentis Δ bio generally decreases with C i .
The A and Δ responses to C i could be modeled assuming a constant g m without important differences (data not shown). However, the calculation of biochemical fractionation (Δ bio ) from eq. 12 is dependent on g m , and thus the dependence of g m on C i must have an effect on Δ bio . To show the magnitude of this effect, the C i response of Δ bio was calculated from eq. 12 and the gas exchange and Δ measurements, assuming either variable g m , assigned as previously explained in this section, or constant g m , calculated as the average of the variable g m values obtained for each species (see Supplementary Fig. S3). As a reference, the C i response of Δ bio was calculated from eq. 14 (modelled Δ bio ) after fitting the models for the C i responses of A and Δ using variable g m .

Estimation of the C 4 (bundle sheath) photosynthesis contribution to total photosynthesis
The relative contribution of the bundle sheath to total photosynthesis in the intermediate species was estimated from A s in eq. 2, after fitting the models to our observed results (Fig. 8). Because the experiments were performed under low O 2 , photorespiration is greatly reduced and it can be assumed that all the CO 2 assimilated in the bundle sheath is transported by the C 4 cycle. The contribution of the bundle sheath to total photosynthesis in both F. floridana and F. brownii decreased with increasing C i . In F. brownii, almost all carbon was fixed by Rubisco in the bundle sheath at very low C i , but up to 25% of fixation occurred via Rubisco in the mesophyll at high C i . In F. floridana, the maximum estimated contribution of the bundle sheath photosynthesis via the C 4 cycle was 21% at very low C i and it dropped to 12% at the highest C i analyzed.

Effect of O 2 on carbon assimilation and compensation point
The oxygen responses of CO 2 assimilation and the compensation point have been used in the past as a tool to identify and characterize C 3 -C 4 intermediate species (Sayre and Kennedy, 1977;Monson et al., 1984;Dai et al., 1996;Vogan et al., 2007). As only mesophyll Rubisco is exposed to air oxygen, its effect on CO 2 assimilation and Γ decreases with increasing proportions of the enzyme allocated to the bundle sheath.
However, it is difficult to separate and quantify the effects of the C 2 and C 4 cycles from studies on the O 2 response of CO 2 assimilation, as both cycles contribute to reduce the negative effect of photorespiration in carbon assimilation and the compensation point. Moreover, the efficiency of the C 2 cycle varies between different intermediate species, as does the contribution of the C 4 cycle (Cheng et al., 1988;Keerberg et al., 2014). In this work, the O 2 response of carbon assimilation, and especially Γ, in F. brownii was very close to that of the C 4 species F. bidentis. A highly efficient C 2 cycle would have a greater impact on the O 2 sensitivity of Γ than on carbon assimilation and that, combined with high in vitro PEPC and CA activities at the same level as the C 4 species F. bidentis, eliminates the effect of pO 2 on Γ almost completely (Cheng et al., 1988;Ku et al., 1991). Previous studies initially classified F. brownii as a C 4 species, but it was later demonstrated that the enzyme compartmentation is incomplete in this plant (Monson et al., 1987;Ku et al., 1991). The small proportion of Rubisco present in the mesophyll is reflected in the sensitivity of assimilation rate to pO 2 .
CA activity in F. floridana is similar to F. pringlei but PEPC activity is four times higher (13.8 μmol m −2 s −1 ), consistent with Ku et al. (1991) and supporting the hypothesis of an active C 4 cycle. However, PEPC activity is still low when compared with F. bidentis (91.8 μmol m −2 s −1 ), indicating that the activity of the C 4 cycle in this plant is small. In our experiments, the O 2 sensitivity of Γ in F. floridana is intermediate, and the O 2 response of CO 2 assimilation rate is remarkably close to that of F. brownii.
Previous studies have reported a C 3 -like O 2 response in F. floridana (Dai et al., 1996;Monson et al., 1986), which differs from our observations. Although the reason for this discrepancy is not known, it must be noted that O 2 sensitivity measurements are affected by variation of parameters like temperature or stomatal conductance between measurements at different pO 2 . These interactions increase the difficulty of estimating the activity of the C 4 cycle from O 2 response experiments.

Signature of C 4 photosynthesis in the CO 2 response of Δ in intermediate species
The different CO 2 responses of Δ in the intermediate C 3 -C 4 species, relative to the C 3 or C 4 species, can be attributed to the different ratios of PEPC/Rubisco activity in the mesophyll. The lower Δ observed in F. floridana, relative to F. pringlei, is partially attributable to a lower C i /C a , but their different Δ bio indicates an influence of the PEPC to Rubisco ratio, especially at low C i .
Interestingly, F. brownii and F. bidentis show similar Δ at low C i , but it increases in F. brownii with increasing pCO 2 instead of decreasing as in the C 4 plant. This particular response can be attributed to the activity of the small fraction of Rubisco in the mesophyll that would have a stronger influence at high pCO 2 . In F. floridana, Rubisco is abundant in the mesophyll but PEPC activity is low, and as a consequence the greatest effect of the C 4 cycle activity is observed at very low pCO 2 , with a greater reduction of Δ compared to the C 3 species. Both results indicate that the contribution of mesophyll Rubisco to overall assimilation is more important under high pCO 2 , and of the C 4 cycle at low pCO 2 . The fact that environmental conditions affect the contribution of C 4 photosynthesis may explain ambiguous results on previous analyses of dry matter δ 13 C in F. floridana and other intermediates, which showed C 3 -like ratios (Monson et al., 1988;Byrd et al., 1992). δ 13 C is a result of carbon discrimination during the leaf growth, thus it integrates the effect of variable environmental conditions. In the online experiments presented here, instant discrimination is measured under controlled conditions, highlighting their influence. By performing the analyses under low pO 2 , the effect of photorespiration and subsequent refixation through the C 2 cycle is greatly reduced, emphasizing the differences in biochemical fractionation caused by the presence of C 4 activity.
Although the CO 2 response of A is also influenced by different relative activities of mesophyll Rubisco and PEPC, the effect of each enzyme in this case is difficult to separate. The greater initial slope of the A/C i curve in F. floridana, compared with F. pringlei, reflects the slightly greater PEPC activity detected in our in vitro assays, but could also be attributed to higher Rubisco activity. In the same sense, the initial slope of the A/C i curve in F. brownii and F. bidentis are similar and typically C 4 , whereas their Δ are different.

Concurrent model fitting reveals C 4 activity in F. floridana
The strategy to evaluate the contribution of the C 4 cycle to total carbon assimilation in intermediate species presented in this work is based on concurrently measuring and model-fitting the CO 2 responses of carbon assimilation and discrimination.
Mathematical modeling has proved to be a powerful tool to get a deeper insight into the biochemical and physiological basis of the observed responses of carbon assimilation and discrimination, and it has been used to estimate parameters such as the maximum carboxylase activity of Rubisco in vivo (V C,max ) and g m in C 3 species, or V P,max and leakiness in C 4 systems (Tazoe et al., 2011;Ubierna et al., 2011;Walker et al., 2013;Sharwood and Whitney, 2014). However, in most cases there is more than one unknown variable in the equations that represent those responses. This is especially problematic in intermediate species, where the number of factors affecting those responses is greater than in C 3 or C 4 plants. By concurrently fitting the CO 2 responses of A and Δ in each experiment with the same set of constants, the range of values that can be assigned to these variables to obtain a satisfactory fitting is reduced. In this work, the activities of photosynthetic enzymes were analyzed in vitro to further reduce the number of unknowns, providing more accurate predictions. This method confirmed the presence of Rubisco activity in the mesophyll of F. brownii, which was already known (Cheng et al., 1988), but more interestingly indicated that F. floridana harbors an active C 4 cycle. This C 4 activity causes a change in the biochemical fractionation, compared to F. pringlei, which is evident at any C i analyzed. This is consistent with the increased activity of PEPC and previous observations based on 14 CO 2 pulse-chase experiments (Monson et al., 1986;von Caemmerer and Hubick, 1989). It is important to note that other studies based on δ 13 C analyses, metabolite dynamics and O 2 response of carbon assimilation and Γ were unable to conclusively prove a contribution of the C 4 cycle to overall photosynthesis in F. floridana, and the presence of a futile C 4 cycle was proposed where most or all the CO 2 released in the bundle sheath is not fixed and leaks back to the mesophyll (Monson et al., 1988;Leegood and von Caemmerer, 1994;Dai et al., 1996). However, other authors have already indicated that in F. floridana the C 4 cycle may contribute up to 50% of the total CO 2 fixation (Ku et al., 1991). In this work, the contribution of the mesophyll and the bundle sheath Rubisco to overall carbon assimilation was calculated for F. brownii and F. floridana. In both intermediate species, the contribution of the C 4 cycle, or bundle sheath Rubisco, is highest at very low pCO 2 , and decreases with increasing pCO 2 . This reflects the lower apparent K c of PEPC compared to that of Rubisco (Bauwe, 1986;Kubien et al., 2008).

An improved equation describing CO 2 response of Δ in intermediate species
An equation describing photosynthetic carbon isotope discrimination (Δ) that is applicable for C 3 , C 4 and C 3 -C 4 photosynthesis is provided and applied in this study. It allows the calculation of the biochemical fractionation occurring for the different photosynthetic pathways as a function of C i and takes into account g m and the ternary effects of transpiration rate. The biological relevance of g m , and its influence on Δ, has been reported extensively and incorporated in mathematical models for C 3 species (Evans et al., 1986;von Caemmerer and Evans, 1991;Tazoe et al., 2011). When mesophyll conductance is considered in C 3 species, C c (pCO 2 at the site of Rubisco) can be estimated and is lower than C i , and this affects the estimates of Rubisco carboxylations. The same applies in intermediate species, where assimilation and discrimination by mesophyll Rubisco is dependent on the concentration of CO 2 diffusing from the intercellular space. For model fitting purposes, the calculated C c was used as the available CO 2 for both PEPC and mesophyll Rubisco in the case of the intermediate species. The models presented in this work assume that pCO 2 is the same in the cytosol and the chloroplast.
The effect of pCO 2 on g m has been studied by other authors, with results depending on the species analyzed. Whereas previous results showed that g m is not affected by pCO 2 in wheat (Tazoe et al., 2009), other authors reported an inverse correlation in several C 3 species (Flexas et al., 2007;Tazoe et al., 2011). We observed that g m is dependent on pCO 2 in the C 3 F. pringlei, and assumed that the same is true for the C 4 and intermediate species analyzed. Although the effect of using either constant or variable g m on the models of the CO 2 responses of carbon assimilation and discrimination has only a minor effect at low C i , it is important for the calculation of Δ bio and thus the contribution of the C 4 and C 3 cycles to overall carbon assimilation, especially at low C i . The fact that Δ bio is similar when calculated using either constant or variable g m in F. brownii and F. bidentis reflects the lower relevance of g m when the CO 2 concentrating mechanism is expressed at high levels.

Conclusion
Concurrent Δ and gas exchange measurements and modeling provide a powerful diagnostic tool for C 4 photosynthesis. Performing the measurements under controlled environmental conditions, especially low pO 2 , allows the detection and estimation of the C 4 cycle activity in C 3 -C 4 intermediate species even when it is low. This approach confirmed the presence of active Rubisco in the mesophyll of F. brownii, and revealed a contribution of the C 4 cycle to total carbon assimilation in F. floridana. However, the carbon isotope signal is complex and not all its components are well understood, so some caution is required. We show for example that a CO 2 dependence of g m affects the calculation of the biochemical fractionation, and thus the contribution of the C 4 cycle to overall CO 2 assimilation.

Supplementary data
Supplementary data are available from JXB online. Figure S1. Responses of C i and stomatal conductance to changes in atmospheric pO 2 . Figure S2. Models of CO 2 response of assimilation rate and carbon isotope discrimination in the C 3 and C 4 species. Figure S3. Effect of assuming constant or variable g m in the calculation of the biochemical fractionation.