Carbonic Anhydrase and Its Influence on Carbon Isotope Discrimination during C₄ Photosynthesis. Insights from Antisense RNA in Flaveria bidentis

Abstract

In C₄ plants, carbonic anhydrase (CA) facilitates both the chemical and isotopic equilibration of atmospheric CO₂ and bicarbonate (HCO₃⁻) in the mesophyll cytoplasm. The CA-catalyzed reaction is essential for C₄ photosynthesis, and the model of carbon isotope discrimination (Δ¹³C) in C₄ plants predicts that changes in CA activity will influence Δ¹³C. However, experimentally, the influence of CA on Δ¹³C has not been demonstrated in C₄ plants. Here, we compared measurements of Δ¹³C during C₄ photosynthesis in Flaveria bidentis wild-type plants with F. bidentis plants with reduced levels of CA due to the expression of antisense constructs targeted to a putative mesophyll cytosolic CA. Plants with reduced CA activity had greater Δ¹³C, which was also evident in the leaf dry matter carbon isotope composition (δ¹³C). Contrary to the isotope measurements, photosynthetic rates were not affected until CA activity was less than 20% of wild type. Measurements of Δ¹³C, δ¹³C of leaf dry matter, and rates of net CO₂ assimilation were all dramatically altered when CA activity was less than 5% of wild type. CA activity in wild-type F. bidentis is sufficient to maintain net CO₂ assimilation; however, reducing leaf CA activity has a relatively large influence on Δ¹³C, often without changes in net CO₂ assimilation. Our data indicate that the extent of CA activity in C₄ leaves needs to be taken into account when using Δ¹³C and/or δ¹³C to model the response of C₄ photosynthesis to changing environmental conditions.

Isotope analysis of atmospheric CO₂ is an important tool for monitoring changes in the global exchange of CO₂ (Flanagan and Ehleringer, 1998; Yakir and Sternberg, 2000). However, to interpret the atmospheric CO₂ isotopic signature requires an understanding of the isotopic fractionation steps associated with specific processes during leaf gas exchange (Yakir and Sternberg, 2000). Leaf level models of carbon isotope exchange (Δ¹³C) in C₄ plants have been used for many years to help interpret the response of C₄ plants to changing environmental conditions. However, only recently has the genetic manipulation of the C₄ photosynthetic apparatus provided an opportunity to reexamine the C₄ leaf level models of Δ¹³C (von Caemmerer et al., 1997a, 1997b).

Most C₄ plants utilize a compartmentalized CO₂-concentrating mechanism between the mesophyll and bundle sheath cells (BSC) to increase the CO₂ partial pressure (pCO₂) around the site of Rubisco in the BSC. The first enzymatic step in C₄ photosynthesis is the reversible hydration reaction catalyzed by carbonic anhydrase (CA), which converts CO₂ to bicarbonate (HCO₃⁻) in the mesophyll cytoplasm. Subsequently, HCO₃⁻ is fixed via phosphoenolpyruvate carboxylase (PEPC) into a four-carbon acid that diffuses to the BSC for decarboxylation (Kanai and Edwards, 1999). The specialized biochemistry and leaf anatomy of C₄ plants results in a pCO₂ around the site of Rubisco severalfold higher than current atmospheric levels, significantly reducing the rates of photorespiration (Hatch, 1987; Kanai and Edwards, 1999).

The carbon isotope discrimination during C₄ photosynthesis is determined by the fractionation that occurs during diffusion of CO₂ into the leaf, its conversion to HCO₃⁻ via CA, and the subsequent carboxylation reactions catalyzed by PEPC and Rubisco (Peisker, 1982; Farquhar, 1983; Peisker and Henderson, 1992; von Caemmerer et al., 1997a). The extent to which Rubisco can fractionate against CO₂ is determined by the amount of leakiness (φ), defined as the fraction of CO₂ fixed by PEPC that subsequently leaks out of the BSC. If the BSC were gas tight, then all of the CO₂ released into the BSC would be fixed by Rubisco and no fractionation would occur at this step. However, CO₂ can leak out of the BSC, allowing Rubisco to influence the overall discrimination during C₄ photosynthesis (Farquhar, 1983; Peisker and Henderson, 1992).

Differences in the ratio of CO₂ partial pressures between the intercellular airspace and the atmosphere (p_i/p_a) along with φ are the main factors attributed to variation in Δ¹³C in C₄ plants (Farquhar, 1983). The ratio p_i/p_a is primarily determined by stomatal conductance, whereas φ depends on the physical conductance of the BSC walls and the balance between the C₄ and C₃ cycles. Little change in φ was determined with gas exchange and Δ¹³C measurements in various C₄ plants under a variety of environmental conditions (Henderson et al., 1992). However, with the use of antisense technologies, it has been shown that Δ¹³C and φ increase when the capacity of the C₃ cycle is reduced relative to the C₄ cycle (von Caemmerer et al., 1997a, 1997b). Growth conditions (e.g. elevated CO₂ and water stress) have also been reported to influence the balance of the C₄ and C₃ cycles, leading to an altered isotopic composition of dry matter (Watling et al., 2000; Williams et al., 2001), although the influence on CA was not addressed in these studies.

There is limited research concerning the influence of CA activity on Δ¹³C in C₄ plants. Recent work indicates that CA activity in wild-type Flaveria bidentis is in excess and does not limit CO₂ assimilation under normal conditions (von Caemmerer et al., 2004). F. bidentis lines with reduced levels of CA, due to the expression of antisense constructs targeted to a putative mesophyll cytosolic CA, showed that rates of CO₂ assimilation were unaffected by a decrease in CA activity until activity was less than 20% of wild type (von Caemmerer et al., 2004). Although large changes in CA activity had little effect on photosynthetic rates, according to the Δ¹³C theory developed by Farquhar in 1983 (see “Materials and Methods”), the decrease in the hydration reaction of CO₂ (V_h) relative to the rate of PEPC carboxylation (V_p) should increase Δ¹³C potentially without a corresponding change in the rate of net CO₂ assimilation (Farquhar, 1983).

In this article, we use F. bidentis plants with low CA activity to examine the influence of the hydration reaction of CO₂ on Δ¹³C during C₄ photosynthesis. These results are discussed in relation to measurements of Δ¹³C made in F. bidentis under various irradiances, as well as plants with reduced levels of Rubisco.

RESULTS

Carbon Isotope Discrimination

Light Response Curves

In the mass spectrometric gas-exchange system used here for online Δ¹³C measurements, the leaf chamber gas outlet of a LI-6400 gas-exchange system (LI-COR) was directly coupled to a mass spectrometer (micromass ISOPRIME; Micromass Ltd.) via a gas-permeable silicone membrane (Fig. 1). This allowed the measurement of the ¹³C/¹²C ratio of the CO₂ in the airstream without prior purification of that CO₂. We measured rates of net CO₂ assimilation and Δ¹³C in F. bidentis wild-type plants in response to photon flux density (PFD) to test our online systems with previously published values of Δ¹³C from C₄ plants (Henderson et al., 1992). A summary of the symbols used in the text are shown in Table I. Net CO₂ assimilation increased with PFD to near-saturating rates (Fig. 2a). However, there was little change in Δ¹³C, p_i/p_a, and BSC CO₂ leakiness (φ), except at the two lowest light levels (Fig. 2, b–d). There was more uncertainty in the Δ¹³C measurements made at low light because of the higher ratio of the rate of CO₂ entry into the chamber to the rate of net CO₂ assimilation by the leaf (ξ; see Fig. 2, legend). Leakiness was calculated by rearranging Equation 2 (see equations in “Materials and Methods”) and substituting b₄ with Equation 3, with the assumption that the initial CO₂ carboxylation reaction catalyzed by PEPC to the rate of CO₂ hydration by CA (V_p/V_h) was zero. These gas-exchange and Δ¹³C measurements are similar to those previously reported for Amaranthus edulis and Zea mays under similar measurement conditions (Henderson et al., 1992).

Figure 1.

Arrangement of the gas flow controllers, the LI-6400 gas exchange system, and the mass spectrometer system used for simultaneous measurements of leaf gas exchange and carbon isotope discrimination. Switching between gas samples was controlled by a manual four-way valve. The zero and reference readings were made before and after each leaf measurement and averaged during the calculations.

Table I.

Symbols used in the text

Symbol	Description
A	Net CO2 assimilation
a	Fractionation during diffusion of CO2 from the chloroplast to the atmosphere (4.4‰)
al	Fractionation of CO2 diffusion through a liquid (0.7‰)
BSC	Bundle sheath cells
b3	Combined discrimination of Rubisco, respiration, and photorespiration (see Eq. 4)
b4	Combined discrimination of PEPC, respiration, and hydration/dehydration of CO2 (see Eq. 3 and Fig. 4)
bp	Discrimination by PEPC (2.2‰)
Δ13C	Carbon isotope discrimination
CA	Carbon anhydrase
e	Fractionation during respiration (3‰ or −6‰)
es	Fractionation as CO2 dissolves (1.1‰)
eb	Equilibrium fractionation factor for the catalyzed hydration/dehydration of CO2 (−9‰)
f	Discrimination during photorespiration (10‰ or −6.8‰)
φ	The fraction of CO2 fixed by PEPC that subsequently leaks out of the BSC
gw	The internal conductance to the diffusion of CO2 between the intercellular air space and the site of carboxylation in the mesophyll cytoplasm
h	Catalyzed fractionation during CO2 hydration (1.1‰)
kCA	Rate constant of carbonic anhydrase
Kc	Michaelis constant of Rubisco for CO2
Ko	Michaelis constant of Rubisco for O2
Kp	Michaelis constant of PEPC for CO2
Md	Rate of mitochondrial respiration
Mm	Rate of mitochondrial respiration in the mesophyll cells
Ms	Rate of mitochondrial respiration in the BSC
pCO2	Partial pressure of CO2
pe	pCO2 of dry air entering the leaf chamber
pi	pCO2 of the intercellular airspace
pm	pCO2 of the mesophyll cytoplasm
po	pCO2 of dry air leaving the leaf chamber
Re	13C/12C of the air entering the leaf chamber
Ro	13C/12C of the air leaving the leaf chamber
PFD	Photon flux density
PSII	PSII
ξ	pe/(pe − po)
s	Fractionation during the leakage of CO2 from the BSC (1.8‰)
Vc	Rate of Rubisco carboxylation
Vcmax	Maximal rate of Rubisco carboxylation
Vh	Rate of CO2 hydration
Vo	Rate of photorespiration
Vp	Rate of PEP carboxylation (A + Md)/(1 − φ) or (pmVpmax)/(pm + Kp)
Vpmax	Maximal rate of PEPC carboxylation

Figure 2.

a, Net CO₂ assimilation rate. b, Ratio of intercellular to ambient CO₂ partial pressures (p_i/p_a). c, Carbon isotope discrimination (Δ¹³C). d, Bundle sheath leakiness to CO₂ (φ) as a function of PFD (μmol quanta m⁻² s⁻¹). Measurements were made at a pCO₂ of 52 Pa, a pO₂ of 4.8 kPa, and a leaf temperature of 30°C. Shown are the means ± the se of measurements made on three to five leaves from two F. bidentis wild-type plants. Values for ξ (Eq. 1) were 29.9 ± 0.75, 15.7 ± 0.54, 7.11 ± 0.24, 5.5 ± 0.23, and 4.9 ± 0.17 at PFDs of 150, 300, 800, 1,400, and 2,000 μmol quanta m⁻² s⁻¹. φ was calculated from Equation 5, assuming V_p/V_h = 0.

Rubisco Small Subunit Plants

Net CO₂ assimilation in F. bidentis plants with reduced levels of Rubisco caused by antisense RNA constructs targeted to the nuclear-encoded gene for the small subunit of Rubisco (anti-SSu plants) had rates between 40% to 80% of wild-type plants (Table II). Additionally, the ratio of p_i/p_a, Δ¹³C, and φ were higher in the anti-SSu-plants as compared with wild-type plants (Table II). The parameter φ was determined from simultaneous gas-exchange and isotope measurements and solving for φ in Equation 2. Our measurements of Δ¹³C and leaf gas exchange are similar to previously published values by von Caemmerer et al. (1997b). The comparison of our results to previously published Δ¹³C values shows that our system can accurately and consistently monitor the influence of both environmental conditions and perturbations to the C₄ photosynthetic apparatus on instantaneous carbon isotope discrimination.

Table II.

CA rate constant (k_CA), net CO₂ assimilation rate (A), ratio of intercellular to atmospheric CO₂ partial pressure (p_i/p_a), online Δ¹³C discrimination, and leakiness of CO₂ out of the BSCs (φ) in the anti-SSu plants from the primary transformant 136-13

For calculation of φ, the V_p/V_h ratio was assumed to be zero. Measurements were made at a pCO₂ of 52 Pa, a pO₂ of 4.8 kPa, a PFD of 2,000 μmol quanta m⁻² s⁻¹, and a leaf temperature of 30°C. n = 4 for the wild-type plants.

	kCA	A	pi/pa	Δ13C	Leakiness φ
	mol m−2 s−1 Pa−1	μmol m−2 s−1		‰
136-13-11#1	52	17.0	0.67	6.1	0.43
136-13-12#4	88	19.5	0.64	6.5	0.45
136-13-12#3	62	27.9	0.72	6.0	0.42
136-13-11#2	81	29.9	0.71	5.4	0.39
Wild type	69 ± 2	37.6 ± 2.6	0.55 ± 0.02	2.5 ± 0.4	0.25 ± .02

CA Plants

Carbon isotope discrimination (Δ¹³C) increased as CA activity decreased in the F. bidentis plants containing the antisense RNA constructs targeted to the putative cytosolic CA (anti-CA plants; Fig. 3). CA activity, reported here as a rate constant (k_CA μmol m⁻² s⁻¹ Pa⁻¹), was determined on leaf extracts using mass spectrometry to measure the rates of ¹⁸O₂ exchange from doubly labeled ¹³C¹⁸O₂ to H₂¹⁶O (see “Materials and Methods”). Interestingly, Δ¹³C was more sensitive than net CO₂ assimilation to changes in CA activity as Δ¹³C increased in some anti-CA plants, whereas net CO₂ assimilation remained similar to wild-type plants (Fig. 3). In these anti-CA plants with reduced CA activity and wild-type rates of net CO₂ assimilation, Δ¹³C increased 1‰ to 2‰, which is a large shift for C₄ photosynthesis (Fig. 3c, inset; Table III). In the anti-CA plants, net CO₂ assimilation rates and p_i/p_a were similar to wild-type plants, except when CA activities were less than 20% of wild type (Fig. 3, a and b). Anti-CA plants with extremely low levels of CA activity (<5% of wild type) and low rates of net CO₂ assimilation had extremely high values of Δ¹³C (Fig. 3c).

Figure 3.

Net CO₂ assimilation rate, the ratio of intercellular to ambient pCO₂ (p_i/p_a), and carbon isotope discrimination (Δ¹³C) as a function of the rate constant of leaf CA (k_CA μmol m⁻² s⁻¹ Pa⁻¹). The inset in c shows the expanded scale of Δ¹³C where net CO₂ assimilation is relatively constant. Each point represents a measurement made on a different plant grown in a glasshouse at ambient CO₂ or in a growth cabinet at 1% CO₂: wild-type plants grown at ambient CO₂ (□); anti-CA plants grown at ambient CO₂ (▪); wild-type grown at 1% CO₂ (○, ▵); and anti-CA plants grown at 1% CO₂ (•, ▴). Measurements were made at 2,000 μmol quanta m⁻² s⁻¹, leaf temperature of 30°C, and an inlet CO₂ concentration of either 38 Pa in air (▵, ▴) or 52 Pa of CO₂ in a 90.5 kPa of N₂ and 4.8 kPa of O₂ gas mixture (□○, ▪•). The lines represent the best fit for all measurements (wild-type and anti-CA plants) made at either 38 or 52 Pa of CO₂.

Table III.

Net CO₂ assimilation rate (A), the ratio of intercellular to ambient pCO₂ (p_i/p_a), CA_leaf calculated as (k_CAp_m), Δ¹³C, and V_p/V_h for F. bidentis wild-type plants and anti-CA plants with low CA_leaf activity and wild-type-like net CO₂ assimilation rates

Measurements were made at a pCO₂ of 52 Pa, a pO₂ of 4.8 kPa, PFD of 2,000 μmol quanta m⁻² s⁻¹, and a leaf temperature of 30°C. V_p/V_h was estimated either by online Δ¹³C measurements* using Eqs. 3 and 5 (“Materials and Methods”) or estimated from V_p/CA_leaf**, where V_p was calculated as (A + M_d)/(1 − φ) and CA_leaf. g_w was assumed to be either 10 or 6 μmol m⁻² s⁻¹ Pa⁻¹, and φ was set at either 0.24 or 0.1. M_d is the daytime rate of respiration assumed to be 2 μmol m⁻² s⁻¹. n = 7 and 5 for anti-CA and wild-type plants, respectively.

	A	pi/pa	CAleaf	Δ13C		Vp/Vh
												gw = 10 φ = 0.24	gw = 6 φ = 0.24	gw = 10 φ = 0.1	gw = 6 φ = 0.1
	μmol m−2 s−1		μmol m−2 s−1	‰
Anti-CA	42 ± 0.6	0.48 ± 0.02	228 ± 37	4.4 + 0.2	Δ13C*	0.46 ± 0.06	0.55 ± 0.07	0.99 ± 0.08	1.1 ± 0.08
					In vitro**	0.29 ± 0.04	0.40 ± 0.04	0.24 ± 0.03	0.30 ± 0.04
Wild type	40 ± 0.1	0.47 ± 0.02	774 ± 48	3.3 ± 0.2	Δ13C*	0.07 ± 0.07	0.08 ± 0.08	0.61 ± 0.06	0.62 ± 0.08
					In vitro**	0.07 ± 0.01	0.09 ± 0.01	0.06 ± 0.01	0.07 ± 0.01

Nearly all of the measured values of Δ¹³C fall within the theoretical relationship of Δ¹³C to p_i/p_a as predicted from the model of C₄ carbon isotope discrimination developed by Farquhar (1983; Fig. 4; see “Materials and Methods”). Only in the anti-CA plants with extremely low CA activity do the measured values of Δ¹³C fall outside the predicted values (Fig. 4). The theoretical relationship of Δ¹³C and p_i/p_a was calculated with a φ value of 0.24, and the initial CO₂ carboxylation reaction catalyzed by PEPC relative to the CO₂ hydration by CA (V_p/V_h) was assumed to be either zero or 1 (as indicated in Fig. 4). The b₄ parameter, which is the combined fractionation associated with PEPC, respiration, and the isotopic equilibrium during the dissolution of CO₂ and conversion to HCO₃⁻, used in these calculations was determined with either the CA catalyzed (solid lines) or the spontaneous uncatalyzed (dotted lines) CO₂ and HCO₃⁻ hydration and dehydration fractionation factors (see “Materials and Methods”).

Figure 4.

Carbon isotope discrimination (Δ¹³C) as a function of the ratio of intercellular to ambient pCO₂ (p_i/p_a). The white symbols are wild-type plants and the black symbols are anti-CA plants. Other symbols and measurement conditions are as described in Figure 3. The lines represent the theoretical relationship of Δ¹³C and p_i/p_a, where φ = 0.24, the ratio of the PEPC carboxylation to the CO₂ hydration reaction (V_p/V_h) is either 0 or 1, and the b₄ parameter is calculated with the catalyzed (solid lines, b₄ = −5.7 + 7.9 V_p/V_h) and uncatalyzed (dotted lines, b₄ = −4.5 + 12.5 V_p/V_h) CO₂ and HCO₃⁻ hydration and dehydration fractionation factors. g_w was assumed to be large such that p_i = p_m.

To characterize the influence of CA activity on Δ¹³C, independent of changes in net CO₂ assimilation, we pooled the data of anti-CA plants with reduced CA activity and wild-type-like photosynthetic rates. Δ¹³C was higher in the anti-CA plants compared to the wild-type plants, whereas p_i/p_a was unchanged (Table III). The in vivo CA activity (CA_leaf), which is the product of k_CA and the pCO₂ in the mesophyll cytoplasm (p_m), was significantly less in the anti-CA relative to the wild-type plants (Table III). The value of p_m was calculated with an internal conductance to the diffusion of CO₂ between the intercellular airspace and the site of carboxylation in the mesophyll cytoplasm (g_w) of 10 mol m⁻² s⁻¹ Pa⁻¹. The ratio of V_p/V_h determined from the online measurements of Δ¹³C was approximately 6 times greater in the anti-CA plants than in the wild-type plants (Table III). It appears that a rather large decrease in leaf CA activity in F. bidentis can maintain the chemical equilibrium between CO₂ and HCO₃⁻ needed to sustain photosynthesis, but limits the isotopic equilibrium causing Δ¹³C to increase without changes in φ.

It should be noted that the absolute value of V_p/V_h determined this way is largely influenced by φ and slightly by g_w. For example, changing g_w from 6 to 10 mol m⁻² s⁻¹ Pa⁻¹ shifts calculations of V_p/V_h from 0.08 to 0.07 and 0.55 to 0.46 for wild-type and anti-CA plants, respectively. However, changing φ from 0.24 to 0.10, assuming a constant g_w of 10 mol m⁻² s⁻¹ Pa⁻¹, causes V_p/V_h to increase from 0.07 to 0.61 in the wild-type plants and from 0.46 to 0.99 in the anti-CA plants (Table III). In the anti-CA plants, which have a reduced capacity to concentrate CO₂ within the BSC, it is predicted from the C₄ photosynthetic model that φ will decrease relative to the wild-type plants (see below), which would increase the difference of V_p/V_h between the wild-type and the anti-CA plants. V_p/V_h can also be approximated from gas exchange and in vitro CA activity as V_p/CA_leaf, where CA_leaf is calculated as k_CAp_m and V_p is calculated as (A + M_d)/(1 − φ) (von Caemmerer, 2000). The parameter M_d is the daytime rate of mitochondrial respiration assumed to be 2 μmol m⁻² s⁻¹. The ratio of V_p/V_h determined from the in vitro assays of CA activity was approximately 4 times greater in the anti-CA plants than in the wild-type plants (Table III). The absolute value of V_p/V_h calculated in this manner is also influenced by changes in g_w and φ, although neither parameter has a large influence on the relative changes of V_p/V_h between wild-type and anti-CA plants.

Dry Matter δ¹³C

Leaf dry matter δ¹³C, the ratio of ¹³C/¹²C of the sample relative to the standard Vienna Pee Dee Belemnite (VPDB), was lower in plants with low levels of CA and correlated with increases in Δ¹³C (Fig. 5). Leaf δ¹³C was determined on plants germinated and grown in a glasshouse. After collecting an entire leaf for δ¹³C, the three plants with very low CA and photosynthetic rates were transferred after several weeks to the 1% CO₂ growth cabinets before leaf gas-exchange measurements were made. Otherwise, the leaf opposite to the one used for gas exchange was sampled for δ¹³C.

Figure 5.

Leaf dry matter δ¹³C, determined on the entire leaf opposite to the one used for gas exchange and enzyme analysis, plotted against changes in online carbon isotope discrimination (Δ¹³C). The white symbols are wild-type plants and the black symbols are anti-CA plants. All plants were germinated and grown in a glasshouse under ambient atmospheric CO₂ conditions. The plants with extremely low δ¹³C values (•) were transferred to the 1% CO₂ growth cabinets after tissue was collected for Δ¹³C analysis.

Photosynthetic and Carbon Isotope Discrimination Models

It has recently been shown that low leaf CA activity in F. bidentis reduces the capacity of the C₄ cycle by limiting the rate of PEPC carboxylation of HCO₃⁻ (V_p) (von Caemmerer et al., 2004). Here, we use the C₄ photosynthetic model developed by Berry and Farquhar (1978) and von Caemmerer (2000) to predict the response of net CO₂ assimilation, bundle sheath pCO₂, photorespiration (V_o), and φ to changes in the activity of PEPC due to a limitation in CA activity. In the C₄ photosynthetic model, the CA-mediated hydration/dehydration reaction of CO₂ within the mesophyll cytoplasm has not been incorporated. However, manipulating V_p within the model simulates the effect of changing CA activity and leads to a diminished ability to concentrate CO₂ within the BSC, which decreases both the photosynthetic rate and φ (Fig. 6, a and b).

Figure 6.

Modeling the response of net CO₂ assimilation (a); the pCO₂ in the BSC and BSC CO₂ leakiness, φ (b); and Δ¹³C (c) in response to changes in PEPC activity (V_p). The C₄ model used a V_cmax of 60 μmol m⁻² s⁻¹, a bundle sheath conductance to CO₂ per leaf area of 0.03 μmol m⁻² s⁻¹ Pa⁻¹, K_m of PEPC for CO₂ (K_p) of 8 Pa, K_m of Rubisco for CO₂ (K_c) and O₂ (K_o) of 65 Pa and 45 kPa, fraction of PSII in the BSC 0.2 and Rubisco specificity of 2,590 Pa/Pa in the gas phase, and mitochondrial respiration was 2 μmol m⁻² s⁻¹, one-half of which was assumed to occur in the mesophyll. The pO₂ in the mesophyll was assumed to be 20 kPa. Carbon isotope discrimination was calculated using the C₄ photosynthetic model output and a constant p_i/p_a of 0.4. V_h was set at 2,000 μmol m⁻² s⁻¹ and V_p/V_h varied between 0.001 and 0.1, causing only a 0.3‰ shift in Δ¹³C at a constant φ. The lines for Δ¹³C represent models determined with Equation 2 by substituting the b₄ and b₃ factors with Equations 3 and 4, respectively. The lines for Δ¹³C represent models using different fractionation factors for respiration (3‰ dotted line and −6‰ solid and dashed lines) and photorespiration (10‰ dashed line and −6.8‰ dotted and solid lines).

The outputs from the C₄ photosynthetic model, specifically the rates of Rubisco carboxylation (V_c), V_o, V_p, φ, and the pCO₂ in the BSC, were then incorporated into the model of C₄ carbon isotope discrimination (Δ¹³C) developed by Farquhar (1983). The Δ¹³C model was used to determine which photosynthetic parameters would influence Δ¹³C consistent with our experimental data and to demonstrate the influence of φ on Δ¹³C independent of changes in V_p/V_h. The model in Figure 6 included sufficient CA activity to keep V_p/V_h close to zero as V_p changes and p_i/p_a were held constant at 0.4. As shown in Figure 6c, when φ and the pCO₂ in the BSC are low, Δ¹³C decreases as the ability of Rubisco to fractionate is reduced. Additionally, the Δ¹³C model accounts for the effects of fractionation during respiration (e) and photorespiration (f); however, there is uncertainty in the specific values of factors e and f in the model (Gillon and Griffiths, 1997; Ghashghaie et al., 2003). Therefore, to test the influence of these parameters on the Δ¹³C model, various values of e (3‰ versus −6‰) and f (−6.8‰ versus 10‰) were used. Even at low CO₂ assimilation rates, relatively large changes in e and f had only a small influence on Δ¹³C (Fig. 6c).

DISCUSSION

Carbon isotope discrimination increased in the short term during leaf gas exchange (Δ¹³C) and the carbon isotope composition of leaf dry matter (δ¹³C) decreased in transformants containing reduced levels of leaf CA. As was previously reported (von Caemmerer et al., 2004), leaf CA activity appears to be in excess to maintain steady-state rates of net CO₂ assimilation in F. bidentis at high light. A nearly 80% decrease in leaf CA activity was needed before net CO₂ assimilation was affected when measured at a CO₂ partial pressure (pCO₂) of 52 Pa (Fig. 3a). The CA activity required to maintain wild-type-like photosynthetic rates increased when measurements were conducted at a lower pCO₂ of 38 Pa (Fig. 3a). This is in agreement with previously published work where reduced leaf cytosolic CA activity affected the initial slope of the CO₂ response curve in F. bidentis when the rate of CO₂ hydration limited the supply of HCO₃⁻ for PEPC carboxylation (von Caemmerer et al., 2004).

Carbon Isotope Discrimination and CA Activity

According to the C₄ photosynthetic model (von Caemmerer, 2000), a limitation in the supply of cytosolic HCO₃⁻ will lead to a decrease in the initial CO₂ carboxylation reaction catalyzed by PEPC and reduce the capacity of the C₄ pump to concentrate CO₂ within the BSC. A reduced pCO₂ in the BSC leads to a decrease in the rate of net CO₂ assimilation as well as a lower BSC CO₂ leakiness (φ). In the model of C₄ carbon isotope discrimination, the main factors that influence Δ¹³C are changes in the intercellular to ambient CO₂ partial pressures (p_i/p_a) and φ (Farquhar, 1983). When the ratio of PEPC carboxylation to the hydration reaction of CO₂ (V_p/V_h) is near zero (i.e. CA activity is high relative to PEPC carboxylation), the C₄ carbon isotope model predicts that Δ¹³C will decrease as φ decreases (Fig. 6). The Δ¹³C modeling illustrates that when the front end of the C₄ cycle is diminished (either by reduced CA and/or PEPC activity or anything else), φ decreases and Δ¹³C associated with φ also decreases (Fig. 6). However, in the anti-CA plants, which potentially reduced the ability to concentrate CO₂ in the BSC, Δ¹³C increased, which cannot be explained in the model by decreases in φ, but can be explained by changes in V_p/V_h.

Due to the high levels of mesophyll cytoplasmic CA activity in C₄ plants, it is generally assumed that CO₂ and HCO₃⁻ are in close chemical equilibrium. Under such conditions, the ratio of V_p/V_h in Equation 3 approaches zero and can be omitted from the calculation of b₄. However, when V_p/V_h tends away from zero, Equation 3 can be expressed with the fractionation factors provided in “Materials and Methods” as b₄ = −5.7 + 7.9 V_p/V_h at 25°C. The b₄ fractionation factor becomes more positive as V_p/V_h increases and Δ¹³C increases even without changes in p_i/p_a and φ. As shown in Figure 4, varying V_p/V_h between 0 and 1 can have a large impact on Δ¹³C, especially when p_i/p_a is high. Nearly all the variation in Δ¹³C in the anti-CA plants can be explained by changes in V_p/V_h (Fig. 4). Only when CA activity and photosynthetic rates decline dramatically do changes in V_p/V_h and p_i/p_a not accurately predict Δ¹³C (see below for further discussion).

Variation in the Ratio of PEPC Carboxylation to CO₂ Hydration by CA

The large change in V_p/V_h without changes in photosynthesis in the anti-CA plants (Table III) indicates that Δ¹³C is more sensitive to a reduction in CA activity than net CO₂ assimilation. The influence of V_p/V_h on Δ¹³C is predicted by the C₄ photosynthetic model for carbon isotope discrimination developed by Farquhar (1983), and here we demonstrate the influence of CA activity on Δ¹³C in a C₄ plant. In wild-type F. bidentis plants, CA appears to be in excess for supporting photosynthesis and V_p/V_h approaches zero. However, it has been reported that CA activity in most C₄ species is only just sufficient to support photosynthetic rates, especially in C₄ monocots (Hatch and Burnell, 1990; Gillon and Yakir, 2000, 2001), and the influence of V_p/V_h on Δ¹³C may be greater in these C₄ species. For example, we measured (A.B. Cousins, M. R. Badger, and S. von Caemmerer, unpublished data) CA activity in Z. mays as 266 ± 22 μmol m⁻² s⁻¹, which is similar to our anti-CA plants with wild-type photosynthetic rate (see Fig. 3c; Table III). Gillon and Yakir (2001) reported even lower CA activity for a number of C₄ grasses, which correspond to the low CA activities we measured in anti-CA plants shown in Figure 3c, inset. The values of V_p/V_h estimated from the CA activity and net CO₂ assimilation from this article indicate that Δ¹³C will differ in C₄ plants that have been reported to contain a range of CA_leaf activity (2–529 μmol m⁻² s⁻¹) with generally similar photosynthetic rates (Gillon and Yakir, 2001). However, a systematic investigation of the influence of V_p/V_h on Δ¹³C in a range of C₄ species needs to be conducted.

Changes in V_p/V_h and its influence on Δ¹³C also have important implications for interpreting physiological processes responsible for changes in Δ¹³C and δ¹³C during C₄ photosynthesis, particularly in response to changing environmental conditions. Water stress, reduced nitrogen availability, and atmospheric CO₂ availability have all been reported to increase Δ¹³C in C₄ plants by 1‰ to 3‰ (Meinzer et al., 1994; Ranjith et al., 1995; Buchmann et al., 1996; Saliendra et al., 1996; Meinzer and Saliendra, 1997; Meinzer and Zhu, 1998; Watling et al., 2000). Variation in Δ¹³C in these reports has been interpreted as changes in either p_i/p_a and/or φ, with the apparent assumption that V_p/V_h remains close to zero in all treatments. However, there are a few reports in the literature that suggest CA activity in C₄ plants is also influenced by environmental conditions, including nitrogen status, atmospheric CO₂ availability, and salt stress (Cervigni et al., 1971; Burnell et al., 1990; Brownell et al., 1991), implying that environmental conditions may also alter V_p/V_h and thus influence measured Δ¹³C. Because leaf CA activity in C₄ plants is largely dependent on the internal CO₂ partial pressures, conditions that influence CO₂ availability, such as water stress and growth under elevated atmospheric CO₂, will also alter V_p/V_h. C₄ photosynthesis generally operates near CO₂-saturating conditions at current atmospheric pCO₂ such that a reduction in p_i due to stomatal closure will cause V_p/V_h to increase. However, under such conditions, the ratio of p_i/p_a also decreases and the influence of V_p/V_h on Δ¹³C decreases as shown in Figure 4. Alternatively, it has been shown that, under well-watered conditions, C₄ photosynthesis generally does not respond to increases in atmospheric pCO₂ (McLeod and Long, 1999; Ghannoum et al., 2000; Wall et al., 2001; Ainsworth and Long, 2005; Leakey et al., 2006). However, because p_i/p_a is generally constant with changing atmospheric pCO₂ and CA has a very high K_m for HCO₃⁻, an increase in CO₂ availability will increase V_h, whereas PEPC is generally saturated around ambient pCO₂ and V_p will not change. This raises the possibility that growth under future atmospheric CO₂ conditions will alter Δ¹³C regardless of other environmental changes if CA is limiting.

Both online and in vitro measurements of V_p/V_h indicated that changes in CA activity have a significant influence on Δ¹³C without changes in p_i/p_a and φ. It must be noted that, although changes in g_w have a subtle effect on estimates of V_p/V_h, variation in φ can lead to large shifts in the absolute values of V_p/V_h when determined from the Δ¹³C measurements. There are no direct means of measuring φ, but it can be estimated using Δ¹³C measurements when V_p/V_h is assumed to be close to zero. The use of antisense technology targeted toward the C₄ PEPC enzyme would provide a range of V_p/V_h values and would allow an estimate of φ when V_p/V_h was known to be close to zero.

Low CA and Photosynthetic Mutants

In the majority of CA plants, the increase in Δ¹³C can be explained by changes in the ratio of V_p/V_h and p_i/p_a (Fig. 4). However, this explanation does not hold true for plants with very low leaf CA activity and photosynthetic rates. Potentially, the amount of direct fixation of atmospheric CO₂ in the BSC, leakage of HCO₃⁻ from the BSC, as well as photorespiration and respiration would influence Δ¹³C especially when net CO₂ assimilation is inhibited. Theoretically, CO₂ assimilation by direct diffusion of CO₂ from the atmosphere into the BSC would increase the Δ¹³C as the exchange of CO₂ between the atmosphere and the BSC would allow Rubisco to fractionate against the heavier carbon isotope. However, a low conductance of CO₂ diffusion across the BSC (g_w mmol m⁻² s⁻¹ Pa⁻¹) is an essential component of the C₄ CO₂-concentrating mechanism and limits the amount of direct fixation of CO₂ under ambient CO₂ concentrations (Jenkins et al., 1989; Brown and Byrd, 1993; He and Edwards, 1996; von Caemmerer, 2000; Kiirats et al., 2002). Therefore, even when the initial carboxylation reaction of the C₄ pump is limited by low CA activity or low light, there would be little, if any, direct fixation of CO₂ in the BSC and minimal influence on Δ¹³C.

Alternatively, because ¹³C concentrates in HCO₃⁻ and Rubisco preferentially fixes ¹²C, leakage of HCO₃⁻ out of the BSC would change the fractionation factor associated with CO₂ leakage from the BSC (s from Eq. 2). However, with the relatively low CA activity in the BSC, it is unlikely that CO₂ and HCO₃⁻ would be in full isotopic equilibrium and there would be little influence on s (Farquhar, 1983; von Caemmerer et al., 1997a; Ludwig et al., 1998). Additionally, the influence of respiration and photorespiration on the modeled value of Δ¹³C will increase as the rates of net CO₂ assimilation decrease. However, changing the fractionation effect of respiration (e in Eqs. 3 and 4) and photorespiration (f in Eq. 4) to a range of values reported in the literature (Ghashghaie et al., 2003) had only a slight influence on the modeled Δ¹³C even at low photosynthetic rates (Fig. 6c).

As previously mentioned, Equation 3 simplifies to b₄ = −5.7 + 7.9 V_p/V_h at 25°C when the catalyzed fractionation values for e_b of −9.0‰ and h of 1.1‰ are used. However, if the interconversion of CO₂ and HCO₃⁻ occurs via the spontaneous uncatalyzed reaction, e_b and h become −7.8‰ and 6.9‰, respectively, and Equation 3 is b₄ = −4.5 + 12.5 V_p/V_h, causing the b₄ value to become larger, leading to an increase in Δ¹³C (Fig. 4). The catalyzed and uncatalyzed values of e_b and h are taken from previously published work on the hydration and dehydration of CO₂ and HCO₃⁻ (Mook et al., 1974; Marlier and O'Leary, 1984; Paneth and O'Leary, 1985). The proportion of catalyzed to uncatalyzed hydration/dehydration reactions may have an influence on the Δ¹³C when the photosynthetic rates are extremely low, such as in the anti-CA plants with extremely low CA activity, but it would have little, if any, influence in wild-type plants.

Carbon Isotope Discrimination Increases at Low Light

The response of Δ¹³C in C₄ plants to various light levels has not been well characterized, but is an important factor to consider when interpreting dry matter δ¹³C of plants exposed to different light environments or leaves within a canopy. The increase in Δ¹³C and estimated values of φ in F. bidentis (Fig. 2) are similar to earlier reports that showed that Δ¹³C generally increases as the PFD decreases (Henderson et al., 1992; Peisker and Henderson, 1992; Tazoe et al., 2005). Buchmann et al. (1996) also showed that Δ¹³C, calculated from leaf δ¹³C values, in a number of C₄ plants was greater at low PFD. The low conductance of CO₂ diffusion across the BSC needed for C₄ photosynthesis would limit the direct fixation of CO₂ by Rubisco, even under low light, and its influence on Δ¹³C should be minimal. However, it has been demonstrated with the C₄ photosynthetic model that φ increases at low PFD as more electron transport is needed for recycling of photorespired CO₂ (von Caemmerer, 2000). The predicted change in φ at low PFD by the C₄ photosynthetic model is consistent with our current experimental evidence, as well as earlier published results (Henderson et al., 1992). The evidence from both online and dry matter isotope measurements indicates that growth light conditions need to be considered when interpreting carbon isotope discrimination in C₄ plants.

CONCLUSION

CA activity in wild-type F. bidentis appears to be in excess to maintain net CO₂ assimilation; however, reducing leaf CA activity had a relatively large influence on Δ¹³C, often without changes in net CO₂ assimilation. The influence of CA activity on Δ¹³C was also evident in the leaf dry matter δ¹³C. The model of Δ¹³C developed by Farquhar (1983) predicted the influence of changes in PEPC carboxylation relative to the hydration reaction of CO₂ (V_p/V_h) on Δ¹³C, except when photosynthetic rates and CA activity were dramatically reduced. It will be important to take the extent of CA activity in C₄ leaves into account when using Δ¹³C and/or δ¹³C to model leaf level and global C₄ photosynthesis in response to changing environmental influences. The influence of environmental conditions on leaf CA activity, V_p/V_h, and thus on Δ¹³C warrants further investigation.

Additionally, the amount of CA activity in a leaf plays an important role in determining C¹⁸OO discrimination during C₄ photosynthesis because CA enhances the rate of oxygen exchange between CO₂ and leaf H₂O and thus determines the extent of isotopic equilibrium. The anti-CA plants will be used to test whether changing leaf CA activity influences C¹⁸OO discrimination under similar environmental conditions and whether high CA activity, relative to photosynthetic rates, corresponds to complete isotopic equilibrium between CO₂ and leaf H₂O as predicted.

MATERIALS AND METHODS

Growth Conditions

Flaveria bidentis plants were previously transformed with antisense RNA constructs targeted to either the nuclear-encoded gene for the small subunit of Rubisco (anti-SSu plants) or a putative cytosolic CA (anti-CA plants; Furbank et al., 1996; von Caemmerer et al., 1997b, 2004). The segregating T₁ generations of anti-CA primary transformants with photosynthetic rates similar to wild type were grown during the summer months in a glasshouse under natural light conditions (27°C d/18°C night temperatures). Anti-CA and anti-SSu plants (segregating T₂ generation from primary transformant 136-13) with low photosynthetic capacities and wild-type plants were grown under 1% CO₂ in a controlled environment growth cabinet at a photosynthetic PFD of 400 μmol quanta m⁻² s⁻¹ at plant height and air temperature of 27°C during the day and 18°C at night with a 14-h daylength. Three plants with very low CA and photosynthetic rates were germinated and grown for several weeks in the glasshouse. Subsequently, these plants were transferred to the 1% CO₂ growth cabinets before leaf gas-exchange measurements were made. Plants were grown in 5-L pots in garden mix with 2.4 to 4 g Osmocote/L soil (15/4.8/10.8/1.2 N/P/K/Mg + trace elements: B, Cu, Fe, Mn, Mo, Zn; Scotts Australia Pty Ltd.) and watered daily.

Gas-Exchange Measurements

Plants from either the glasshouse or growth cabinet were transferred to the gas-exchange system, where one of the uppermost fully expanded leaves was placed into the leaf chamber of the LI-6400 and allowed to equilibrate at a leaf temperature of 30°C and 2,000 μmol quanta m⁻² s⁻¹ for a minimum of 1.5 h. Air entering the leaf chamber was prepared by using mass flow controllers (MKS Instruments) to obtain a gas mix of 90.5 kPa of dry nitrogen and 4.8 kPa oxygen (Fig. 1). A portion of the nitrogen/oxygen mixture was used to zero the mass spectrometer to correct for N₂O and other contaminates contributing to the 44 and 45 peaks. Pure CO₂ (δ¹³C = −29‰; VPDB) was added to the remaining airstream to obtain a CO₂ partial pressure of approximately 52 Pa. Alternatively, some measurements were made by mixing pure CO₂ with CO₂-free air and using the CO₂-free air as a zero.

The different gas mixtures had no apparent influence on leaf gas exchange or ¹³C isotope discrimination. Low oxygen (4.8 kPa) was use to minimize contamination of the 46 peak caused by the interaction of O₂ and N₂ to produce NO₂ with the mass spectrometer source element. This was important when looking at C¹⁸OO discrimination (A.B. Cousins, M.R. Badger, and S. von Caemmerer, unpublished data). The CO₂ used during the gas-exchange measurements had a similar isotopic signature to the CO₂ in the high CO₂ growth cabinet. This minimized the influence of respired CO₂ on the Δ¹³C measurements in plants with low photosynthetic rates.

The gas mixtures were fed to the inlet of the LI-6400 console and a flow rate of 200 μmol s⁻¹ was maintained over the leaf. The remaining airstream was vented or used to determine the isotopic composition of air entering the leaf chamber (Fig. 1). The efflux from the leaf chamber was measured by either replacing the match valve line with a line connected directly to the mass spectrometer or by placing a tee in the match valve line, allowing flow to both the mass spectrometer and the match valve simultaneously. Gas-exchange parameters were determined by the LI-6400, and pCO₂ leaving the chamber was subsequently corrected for the dilution of CO₂ by water vapor (von Caemmerer and Farquhar, 1981).

Isotopic Measurements

The efflux from the leaf chamber and the gas mix supplied to the LI-6400 system was linked to a mass spectrometer through an ethanol/dry ice water trap and a thin, gas-permeable silicone membrane, which was housed in a temperature-controlled cuvette. Masses 44 and 45 were monitored continuously and the carbon isotope discrimination during CO₂ exchange, Δ¹³C, was calculated from the ratio of mass 45 to 44 in the reference air, determined before and after each sample measurement, entering the chamber (R_e), and the composition of the sample air leaving the leaf chamber (R_o) as described by Evans et al. (1986):

(1)

where ξ = p_e/(p_e − p_o), and p_e and p_o are the CO₂ partial pressures of dry air entering and leaving the leaf chamber, respectively. A summary of the symbols used in the text is listed in Table I. Zero values for the 44 and 45 peaks were determined before and after the sample measurements were subtracted from both the sample and reference measurements prior to determining the mass ratios. The zero values were typically 1% of the 44 and 45 peaks at 4.8 kPa oxygen and 2% at 20 kPa oxygen.

Calculations of Carbon Isotope Discrimination

The model of C₄ carbon isotope discrimination (Δ¹³C) of Farquhar (1983) was used to determine which factors in the model would influence Δ¹³C consistent with our experimental data. The simplified model predicts that:

(2)

where a (4.4‰) is the fractionation during diffusion of CO₂ and s (1.8‰) is the fractionation during CO₂ leakage from the BSCs. The combined fractionation of PEPC, respiration, and the isotopic equilibrium during dissolution of CO₂ and conversion to HCO₃⁻ (b₄) is calculated as (Farquhar, 1983):

(3)

where b_p (2.2‰) is the fractionation by PEPC (O'Leary, 1981), e_s (1.1‰) is the fractionation as CO₂ dissolves (O'Leary, 1984), and e_b (−9‰) is the equilibrium fractionation factor of the catalyzed hydration/dehydration reactions of CO₂ and HCO₃⁻ (Mook et al., 1974). Alternatively, during the hydration/dehydration reactions, the uncatalyzed equilibrium fractionation factor e_b = −7.8‰ (Marlier and O'Leary, 1984). The fractionation when CO₂ and HCO₃⁻ are not at equilibrium is dependent on the rate of CO₂ hydration (V_h), the rate of PEPC (V_p), e_s, and the catalyzed fractionation during CO₂ hydration (h). The catalyzed hydration reaction has a fractionation factor of 1.1‰ (calculated by summing the catalyzed CO₂ and HCO₃⁻ equilibrium fractionation factor −9.0‰ and the catalyzed dehydration fractionation factor 10.1‰; Mook et al., 1974; Paneth and O'Leary, 1985), whereas the uncatalyzed reaction has a 6.9‰ fractionation factor (Marlier and O'Leary, 1984). The fractionation attributed to mitochondrial respiration is e at a rate of mesophyll CO₂ release of M_m.

The combined fractionation of Rubisco (30‰), respiration, and photorespiration (b₃) can be calculated as:

(4)

where V_c is the rate of Rubisco carboxylation reaction, M_s is the rate of BSC mitochondrial respiration, V_o is the rate of photorespiration, and f is the discrimination of photorespiration (Farquhar, 1983).

Equation 2 assumes that the internal conductance to the diffusion of CO₂ between the intercellular airspace and the site of carboxylation in the mesophyll cytoplasm (g_w) is large, such that p_i is equal to the pCO₂ at the site of PEPC carboxylation (p_c). If g_w is low, then Equation 2 can be modified to:

(5)

where A is the net rate of CO₂ assimilation and a_l (0.7‰) is the fractionation of CO₂ diffusion through a liquid (O'Leary, 1984).

CA Activity Measurements

CA activity was measured on leaf extracts using mass spectrometry to measure the rates of ¹⁸O₂ exchange from doubly labeled ¹³C¹⁸O₂ to H₂¹⁶O (Badger and Price, 1989; von Caemmerer et al., 2004). Measurements of leaf extracts were made at 25°C with a subsaturating total carbon concentration of 1 mm. The hydration rates were calculated from the enhancement in the rate of ¹⁸O loss over the uncatalyzed rate. We then applied this factor to the nonenzymatic first-order rate constant calculated at pH 7.4 appropriate for the mesophyll cytosol (Furbank et al., 1989) and report the CA activity as a first-order rate constant k_CA (mol m⁻² s⁻¹ Pa⁻¹). k_CAp_m then gives the in vivo CA activity at that particular cytosolic pCO₂. Leaf samples were collected after the gas-exchange measurements on the same leaf material and subsequently frozen in liquid nitrogen and stored at −80°C.

Dry Matter δ¹³C

The opposite leaf to the one used during gas exchange was collected and oven dried at 70°C, and ground with a mortar and pestle. A subsample of ground tissue was weighed and the isotopic composition determined by combustion in a Carlo Erba elemental analyzer; the CO₂ was analyzed by mass spectrometry. δ was calculated as [(R_sample − R_standard)/R_standard]1,000, where R_sample and R_standard are the ¹³C/¹²C of the sample and the standard VPDB, respectively. Dry matter δ¹³C was determined on glasshouse-grown plants only because there were large fluctuations in the carbon isotopic composition of the air in the growth cabinets.

Photosynthetic Model

The C₄ photosynthetic model developed by Berry and Farquhar (1978) and von Caemmerer (2000) was used to predict the response of net CO₂ assimilation, bundle sheath pCO₂, p_i/p_a, photorespiration, and φ to changes in the amount of PEPC activity (V_p). Manipulating V_p within the photosynthesis model was used to simulate the effect of changes in CO₂ hydration rates (V_h). The outputs from the C₄ photosynthetic model, specifically the rates of Rubisco carboxylation (V_c), V_o, V_p, φ, and the pCO₂ in the BSC, were incorporated into the model of C₄ carbon isotope discrimination (Δ¹³C) developed by Farquhar (1983). The Δ¹³C model was used to determine which photosynthetic parameters would influence Δ¹³C consistent with our experimental data.