Lack of leaf carbonic anhydrase activity eliminates the C4 carbon-concentrating mechanism requiring direct diffusion of CO2 into bundle sheath cells.

Carbonic anhydrase (CA) performs the first enzymatic step of C4 photosynthesis by catalysing the reversible hydration of dissolved CO2 that diffuses into mesophyll cells from intercellular airspaces. This CA-catalysed reaction provides the bicarbonate used by phosphoenolpyruvate carboxylase to generate products that flow into the C4 carbon-concentrating mechanism (CCM). It was previously demonstrated that the Zea mays ca1ca2 double mutant lost 97% of leaf CA activity, but there was little difference in the growth phenotype under ambient CO2 partial pressures (pCO2 ). We hypothesise that since CAs are among the fastest enzymes, minimal activity from a third CA, CA8, can provide the inorganic carbon needed to drive C4 photosynthesis. We observed that removing CA8 from the maize ca1ca2 background resulted in plants that had 0.2% of wild-type leaf CA activity. These ca1ca2ca8 plants had reduced photosynthetic parameters and could only survive at elevated pCO2 . Photosynthetic and carbon isotope analysis combined with modelling of photosynthesis and carbon isotope discrimination was used to determine if ca1ca2ca8 plants had a functional C4 cycle or were relying on direct CO2 diffusion to ribulose 1,5-bisphosphate carboxylase/oxygenase within bundle sheath cells. The results suggest that leaf CA activity in ca1ca2ca8 plants was not sufficient to sustain the C4 CCM.

Whole-tree mesophyll conductance reconciles isotopic and gas-exchange estimates of water-use efficiency.

Photosynthetic water-use efficiency (WUE) describes the link between terrestrial carbon (C) and water cycles. Estimates of intrinsic WUE (iWUE) from gas exchange and C isotopic composition (δ13 C) differ due to an internal conductance in the leaf mesophyll (gm ) that is variable and seldom computed. We present the first direct estimates of whole-tree gm , together with iWUE from whole-tree gas exchange and δ13 C of the phloem (δ13 Cph ). We measured gas exchange, online 13 C-discrimination, and δ13 Cph monthly throughout spring, summer, and autumn in Eucalyptus tereticornis grown in large whole-tree chambers. Six trees were grown at ambient temperatures and six at a 3°C warmer air temperature; a late-summer drought was also imposed. Drought reduced whole-tree gm . Warming had few direct effects, but amplified drought-induced reductions in whole-tree gm . Whole-tree gm was similar to leaf gm for these same trees. iWUE estimates from δ13 Cph agreed with iWUE from gas exchange, but only after incorporating gm . δ13 Cph was also correlated with whole-tree 13 C-discrimination, but offset by -2.5 ± 0.7‰, presumably due to post-photosynthetic fractionations. We conclude that δ13 Cph is a good proxy for whole-tree iWUE, with the caveats that post-photosynthetic fractionations and intrinsic variability of gm should be incorporated to provide reliable estimates of this trait in response to abiotic stress.

Two-Source δ18O Method to Validate the CO18O-Photosynthetic Discrimination Model: Implications for Mesophyll Conductance.

Theoretical models of photosynthetic isotopic discrimination of CO2 (13C and 18O) are commonly used to estimate mesophyll conductance (g m). This requires making simplifying assumptions and assigning parameter values so that g m can be solved for as the residual term. Uncertainties in g m estimation occur due to measurement noise and assumptions not holding, including parameter uncertainty and model parametrization. Uncertainties in the 13C model have been explored previously, but there has been little testing undertaken to determine the reliability of g m estimates from the 18O model (g m18). In this study, we exploited the action of carbonic anhydrase in equilibrating CO2 with leaf water and manipulated the observed photosynthetic discrimination (Δ18O) by changing the oxygen isotopic composition of the source gas CO2 and water vapor. We developed a two-source δ18O method, whereby two measurements of Δ18O were obtained for a leaf with its gas-exchange characteristics otherwise unchanged. Measurements were performed in broad bean (Vicia faba) and Algerian oak (Quercus canariensis) in response to light and vapor pressure deficit. Despite manipulating the Δ18O by over 100‰, in most cases we observed consistency in the calculated g m18, providing confidence in the measurements and model theory. Where there were differences in g m18 estimates between source-gas measurements, we explored uncertainty associated with two model assumptions (the isotopic composition of water at the sites of CO2-water exchange, and the humidity of the leaf internal airspace) and found evidence for both. Finally, we provide experimental guidelines to minimize the sensitivity of g m18 estimates to measurement errors. The two-source δ18O method offers a flexible tool for model parameterization and provides an opportunity to refine our understanding of leaf water and CO2 fluxes.

Directional change in leaf dry matter δ 13C during leaf development is widespread in C3 plants.

BACKGROUND AND AIMS: The stable carbon isotope ratio of leaf dry matter (δ 13Cp) is generally a reliable recorder of intrinsic water-use efficiency in C3 plants. Here, we investigated a previously reported pattern of developmental change in leaf δ 13Cp during leaf expansion, whereby emerging leaves are initially 13C-enriched compared to mature leaves on the same plant, with their δ 13Cp decreasing during leaf expansion until they eventually take on the δ 13Cp of other mature leaves. METHODS: We compiled data to test whether the difference between mature and young leaf δ 13Cp differs between temperate and tropical species, or between deciduous and evergreen species. We also tested whether the developmental change in δ 13Cp is indicative of a concomitant change in intrinsic water-use efficiency. To gain further insight, we made online measurements of 13C discrimination (∆ 13C) in young and mature leaves. KEY RESULTS: We found that the δ 13Cp difference between mature and young leaves was significantly larger for deciduous than for evergreen species (-2.1 ‰ vs. -1.4 ‰, respectively). Counter to expectation based on the change in δ 13Cp, intrinsic water-use efficiency did not decrease between young and mature leaves; rather, it did the opposite. The ratio of intercellular to ambient CO2 concentrations (ci/ca) was significantly higher in young than in mature leaves (0.86 vs. 0.72, respectively), corresponding to lower intrinsic water-use efficiency. Accordingly, instantaneous ∆ 13C was also higher in young than in mature leaves. Elevated ci/ca and ∆ 13C in young leaves resulted from a combination of low photosynthetic capacity and high day respiration rates. CONCLUSION: The decline in leaf δ 13Cp during leaf expansion appears to reflect the addition of the expanding leaf's own 13C-depleted photosynthetic carbon to that imported from outside the leaf as the leaf develops. This mixing of carbon sources results in an unusual case of isotopic deception: less negative δ 13Cp in young leaves belies their low intrinsic water-use efficiency.

Diurnal variation in mesophyll conductance and its influence on modelled water-use efficiency in a mature boreal Pinus sylvestris stand.

Mesophyll conductance (gm) is a critical variable for the use of stable carbon isotopes to infer photosynthetic water-use efficiency (WUE). Although gm is similar in magnitude to stomatal conductance (gs), it has been measured less often, especially under field conditions and at high temporal resolution. We mounted an isotopic CO2 analyser on a field photosynthetic gas exchange system to make continuous online measurements of gas exchange and photosynthetic 13C discrimination (Δ13C) on mature Pinus sylvestris trees. This allowed the calculation of gm, gs, net photosynthesis (Anet), and WUE. These measurements highlighted the asynchronous diurnal behaviour of gm and gs. While gs declined from around 10:00, Anet declined first after 12:00, and gm remained near its maximum until 16:00. We suggest that high gm played a role in supporting an extended Anet peak despite stomatal closure. Comparing three models to estimate WUE from ∆13C, we found that a simple model, assuming constant net fractionation during carboxylation (27‰), predicted WUE well, but only for about 75% of the day. A more comprehensive model, accounting explicitly for gm and the effects of daytime respiration and photorespiration, gave reliable estimates of WUE, even in the early morning hours when WUE was more variable. Considering constant, finite gm or gm/gs yielded similar WUE estimates on the diurnal scale, while assuming infinite gm led to overestimation of WUE. These results highlight the potential of high-resolution gm measurements to improve modelling of Anet and WUE and demonstrate that such gm data can be acquired, even under field conditions.

Critical review: incorporating the arrangement of mitochondria and chloroplasts into models of photosynthesis and carbon isotope discrimination.

The arrangement of mitochondria and chloroplasts, together with the relative resistances of cell wall and chloroplast, determine the path of diffusion out of the leaf for (photo)respired CO2. Traditional photosynthesis models have assumed a tight arrangement of chloroplasts packed together against the cell wall with mitochondria located behind the chloroplasts, deep inside the cytosol. Accordingly, all (photo)respired CO2 must cross the chloroplast before diffusing out of the leaf. Different arrangements have recently been considered, where all or part of the (photo)respired CO2 diffuses through the cytosol without ever entering the chloroplast. Assumptions about the path for the (photo)respiratory flux are particularly relevant for the calculation of mesophyll conductance (gm). If (photo)respired CO2 can diffuse elsewhere besides the chloroplast, apparent gm is no longer a mere physical resistance but a flux-weighted variable sensitive to the ratio of (photo)respiration to net CO2 assimilation. We discuss existing photosynthesis models in conjunction with their treatment of the (photo)respiratory flux and present new equations applicable to the generalized case where (photo)respired CO2 can diffuse both into the chloroplast and through the cytosol. Additionally, we present a new generalized Δ13C model that incorporates this dual diffusion pathway. We assess how assumptions about the fate of (photo)respired CO2 affect the interpretation of photosynthetic data and the challenges it poses for the application of different models.

The response of mesophyll conductance to short-term variation in CO2 in the C4 plants Setaria viridis and Zea mays.

Mesophyll conductance (gm) limits rates of C3 photosynthesis but little is known about its role in C4 photosynthesis. If gm were to limit C4 photosynthesis, it would likely be at low CO2 concentrations (pCO2). However, data on C4-gm across ranges of pCO2 are scarce. We describe the response of C4-gm to short-term variation in pCO2, at three temperatures in Setaria viridis, and at 25 °C in Zea mays. Additionally, we quantified the effect of finite gm calculations of leakiness (ϕ) and the potential limitations to photosynthesis imposed by stomata, mesophyll, and carbonic anhydrase (CA) across pCO2. In both species, gm increased with decreasing pCO2. Including a finite gm resulted in either no change or increased ϕ compared with values calculated with infinite gm depending on whether the observed 13C discrimination was high (Setaria) or low (Zea). Post-transitional regulation of the maximal PEP carboxylation rate and PEP regeneration limitation could influence estimates of gm and ϕ. At pCO2 below ambient, the photosynthetic rate was limited by CO2 availability. In this case, the limitation imposed by the mesophyll was similar or slightly lower than stomata limitation. At very low pCO2, CA further constrained photosynthesis. High gm could increase CO2 assimilation at low pCO2 and improve photosynthetic efficiency under situations when CO2 is limited, such as drought.

Temperature response of mesophyll conductance in three C4 species calculated with two methods: 18 O discrimination and in vitro Vpmax.

Mesophyll conductance (gm ) is an important factor limiting rates of C3 photosynthesis. However, its role in C4 photosynthesis is poorly understood because it has been historically difficult to estimate. We use two methods to derive the temperature responses of gm in C4 species. The first (Δ18 O) combines measurements of gas exchange with models and measurements of 18 O discrimination. The second method (in vitro Vpmax ) derives gm by retrofitting models of C4 photosynthesis and 13 C discrimination with gas exchange, kinetic constants and in vitro Vpmax measurements. The two methods produced similar gm for Setaria viridis and Zea mays. Additionally, we present the first temperature response (10-40°C) of C4 gm in S. viridis, Z. mays and Miscanthus × giganteus. Values for gm at 25°C ranged from 2.90 to 7.85 µmol m-2  s-1  Pa-1 . Our study demonstrated that: the two described methods are suitable to calculate gm in C4 species; gm values in C4 are similar to high-end values reported for C3 species; and gm increases with temperature analogous to reports for C3 species and the response is species specific. These results improve our mechanistic understanding of C4 photosynthesis.

The coordination of C4 photosynthesis and the CO2-concentrating mechanism in maize and Miscanthus x giganteus in response to transient changes in light quality.

Unequal absorption of photons between photosystems I and II, and between bundle-sheath and mesophyll cells, are likely to affect the efficiency of the CO2-concentrating mechanism in C4 plants. Under steady-state conditions, it is expected that the biochemical distribution of energy (ATP and NADPH) and photosynthetic metabolite concentrations will adjust to maintain the efficiency of C4 photosynthesis through the coordination of the C3 (Calvin-Benson-Bassham) and C4 (CO2 pump) cycles. However, under transient conditions, changes in light quality will likely alter the coordination of the C3 and C4 cycles, influencing rates of CO2 assimilation and decreasing the efficiency of the CO2-concentrating mechanism. To test these hypotheses, we measured leaf gas exchange, leaf discrimination, chlorophyll fluorescence, electrochromatic shift, photosynthetic metabolite pools, and chloroplast movement in maize (Zea mays) and Miscanthus × giganteus following transitional changes in light quality. In both species, the rate of net CO2 assimilation responded quickly to changes in light treatments, with lower rates of net CO2 assimilation under blue light compared with red, green, and blue light, red light, and green light. Under steady state, the efficiency of CO2-concentrating mechanisms was similar; however, transient changes affected the coordination of C3 and C4 cycles in M. giganteus but to a lesser extent in maize. The species differences in the ability to coordinate the activities of C3 and C4 cycles appear to be related to differences in the response of cyclic electron flux around photosystem I and potentially chloroplast rearrangement in response to changes in light quality.

Constraining 3-PG with a new δ13C submodel: a test using the δ13C of tree rings.

A semi-mechanistic forest growth model, 3-PG (Physiological Principles Predicting Growth), was extended to calculate δ(13)C in tree rings. The δ(13)C estimates were based on the model's existing description of carbon assimilation and canopy conductance. The model was tested in two ~80-year-old natural stands of Abies grandis (grand fir) in northern Idaho. We used as many independent measurements as possible to parameterize the model. Measured parameters included quantum yield, specific leaf area, soil water content and litterfall rate. Predictions were compared with measurements of transpiration by sap flux, stem biomass, tree diameter growth, leaf area index and δ(13)C. Sensitivity analysis showed that the model's predictions of δ(13)C were sensitive to key parameters controlling carbon assimilation and canopy conductance, which would have allowed it to fail had the model been parameterized or programmed incorrectly. Instead, the simulated δ(13)C of tree rings was no different from measurements (P > 0.05). The δ(13)C submodel provides a convenient means of constraining parameter space and avoiding model artefacts. This δ(13)C test may be applied to any forest growth model that includes realistic simulations of carbon assimilation and transpiration.

Bundle-sheath leakiness in C4 photosynthesis: a careful balancing act between CO2 concentration and assimilation.

Crop species with the C4 photosynthetic pathway are generally characterized by high productivity, especially in environmental conditions favouring photorespiration. In comparison with the ancestral C3 pathway, the biochemical and anatomical modifications of the C4 pathway allow spatial separation of primary carbon acquisition in mesophyll cells and subsequent assimilation in bundle-sheath cells. The CO2-concentrating C4 cycle has to operate in close coordination with CO2 reduction via the Calvin-Benson-Bassham (CBB) cycle in order to keep the C4 pathway energetically efficient. The gradient in CO2 concentration between bundle-sheath and mesophyll cells facilitates diffusive leakage of CO2. This rate of bundle-sheath CO2 leakage relative to the rate of phosphoenolpyruvate carboxylation (termed leakiness) has been used to probe the balance between C4 carbon acquisition and subsequent reduction as a result of environmental perturbations. When doing so, the correct choice of equations to derive leakiness from stable carbon isotope discrimination (Δ(13)C) during gas exchange is critical to avoid biased results. Leakiness responses to photon flux density, either short-term (during measurements) or long-term (during growth and development), can have important implications for C4 performance in understorey light conditions. However, recent reports show leakiness to be subject to considerable acclimation. Additionally, the recent discovery of two decarboxylating C4 cycles operating in parallel in Zea mays suggests that flexibility in the transported C4 acid and associated decarboxylase could also aid in maintaining C4/CBB balance in a changing environment. In this paper, we review improvements in methodology to estimate leakiness, synthesize reports on bundle-sheath leakiness, discuss different interpretations, and highlight areas where future research is necessary.

Using Carbon Stable Isotopes to Study C3 and C4 Photosynthesis: Models and Calculations.

Stable carbon isotopes are a powerful tool to study photosynthesis. Initial applications consisted of determining isotope ratios of plant biomass using mass spectrometry. Subsequently, theoretical models relating C isotope values to gas exchange characteristics were introduced and tested against instantaneous online measurements of 13C photosynthetic discrimination. Beginning in the twenty-first century, laser absorption spectroscopes with sufficient precision for determining isotope mixing ratios became commercially available. This has allowed collection of large data sets at lower cost and with unprecedented temporal resolution. More data and accompanying knowledge have permitted refinement of 13C discrimination model equations, but often at the expense of increased model complexity and difficult parametrization. This chapter describes instantaneous online measurements of 13C photosynthetic discrimination, provides recommendations for experimental setup, and presents a thorough compilation of equations available to researchers. We update our previous 2018 version of this chapter by including recently improved descriptions of (photo)respiratory processes and associated fractionations. We discuss the capabilities and limitations of the diverse 13C discrimination model equations and provide guidance for selecting the model complexity needed for different applications.

Environmental and physiological determinants of carbon isotope discrimination in terrestrial plants.

Stable carbon isotope ratios (δ(13) C) of terrestrial plants are employed across a diverse range of applications in environmental and plant sciences; however, the kind of information that is desired from the δ(13) C signal often differs. At the extremes, it ranges between purely environmental and purely biological. Here, we review environmental drivers of variation in carbon isotope discrimination (Δ) in terrestrial plants, and the biological processes that can either damp or amplify the response. For C3 plants, where Δ is primarily controlled by the ratio of intercellular to ambient CO2 concentrations (ci /ca ), coordination between stomatal conductance and photosynthesis and leaf area adjustment tends to constrain the potential environmentally driven range of Δ. For C4 plants, variation in bundle-sheath leakiness to CO2 can either damp or amplify the effects of ci /ca on Δ. For plants with crassulacean acid metabolism (CAM), Δ varies over a relatively large range as a function of the proportion of daytime to night-time CO2 fixation. This range can be substantially broadened by environmental effects on Δ when carbon uptake takes place primarily during the day. The effective use of Δ across its full range of applications will require a holistic view of the interplay between environmental control and physiological modulation of the environmental signal.

The efficiency of C4 photosynthesis under low light conditions in Zea mays, Miscanthus x giganteus and Flaveria bidentis.

The efficiency of C(4) photosynthesis in Zea mays, Miscanthus x giganteus and Flaveria bidentis in response to light was determined using measurements of gas exchange, (13) CO(2) photosynthetic discrimination, metabolite pools and spectroscopic assays, with models of C(4) photosynthesis and leaf (13) CO(2) discrimination. Spectroscopic and metabolite assays suggested constant energy partitioning between the C(4) and C(3) cycles across photosynthetically active radiation (PAR). Leakiness (φ), modelled using C(4) light-limited photosynthesis equations (φ(mod)), matched values from the isotope method without simplifications (φ(is)) and increased slightly from high to low PAR in all species. However, simplifications of bundle-sheath [CO(2)] and respiratory fractionation lead to large overestimations of φ at low PAR with the isotope method. These species used different strategies to maintain similar φ. For example, Z. mays had large rates of the C(4) cycle and low bundle-sheath cells CO(2 ) conductance (g(bs)). While F. bidentis had larger g(bs) but lower respiration rates and M. giganteus had less C(4) cycle capacity but low g(bs), which resulted in similar φ. This demonstrates that low g(bs) is important for efficient C(4) photosynthesis but it is not the only factor determining φ. Additionally, these C(4) species are able to optimize photosynthesis and minimize φ over a range of PARs, including low light.

The influence of light quality on C4 photosynthesis under steady-state conditions in Zea mays and Miscanthus×giganteus: changes in rates of photosynthesis but not the efficiency of the CO2 concentrating mechanism.

Differences in light quality penetration within a leaf and absorption by the photosystems alter rates of CO(2) assimilation in C(3) plants. It is also expected that light quality will have a profound impact on C(4) photosynthesis due to disrupted coordination of the C(4) and C(3) cycles. To test this hypothesis, we measured leaf gas exchange, (13) CO(2) discrimination (Δ(13) C), photosynthetic metabolite pools and Rubisco activation state in Zea mays and Miscanthus × giganteus under steady-state red, green, blue and white light. Photosynthetic rates, quantum yield of CO(2) assimilation, and maximum phosphoenolpyruvate carboxylase activity were significantly lower under blue light than white, red and green light in both species. However, similar leakiness under all light treatments suggests the C(4) and C(3) cycles were coordinated to maintain the photosynthetic efficiency. Measurements of photosynthetic metabolite pools also suggest coordination of C(4) and C(3) cycles across light treatments. The energy limitation under blue light affected both C(4) and C(3) cycles, as we observed a reduction in C(4) pumping of CO(2) into bundle-sheath cells and a limitation in the conversion of C(3) metabolite phosphoglycerate to triose phosphate. Overall, light quality affects rates of CO(2) assimilation, but not the efficiency of CO(2) concentrating mechanism.

Physiological responses to low CO2 over prolonged drought as primers for forest-grassland transitions.

Savannahs dominated by grasses with scattered C3 trees expanded between 24 and 9 million years ago in low latitudes at the expense of forests. Fire, herbivory, drought and the susceptibility of trees to declining atmospheric CO2 concentrations ([CO2]a) are proposed as key drivers of this transition. The role of disturbance is well studied, but physiological arguments are mostly derived from models and palaeorecords, without direct experimental evidence. In replicated comparative experimental trials, we examined the physiological effects of [CO2]a and prolonged drought in a broadleaf forest tree, a savannah tree and a savannah C4 grass. We show that the forest tree was more disadvantaged than either the savannah tree or the C4 grass by the low [CO2]a and increasing aridity. Our experiments provide insights into the role of the intrinsic physiological susceptibility of trees in priming the disturbance-driven transition from forest to savannah in the conditions of the early Miocene.

Estimation of canopy average mesophyll conductance using δ(13) C of phloem contents.

Conductance to CO(2) inside leaves, known as mesophyll conductance (g(m)), imposes large limitations on photosynthesis. Because g(m) is difficult to quantify, it is often neglected in calculations of (13)C photosynthetic discrimination. The 'soluble sugar method' estimates g(m) via differences between observed photosynthetic discrimination, calculated from the δ(13)C of soluble sugars, and discrimination when g(m) is infinite. We expand upon this approach and calculate a photosynthesis-weighted average for canopy mesophyll conductance ((c) g(m)) using δ(13)C of stem phloem contents. We measured gas exchange at three canopy positions and collected stem phloem contents in mature trees of three conifer species (Pseudotsuga menziesii, Thuja plicata and Larix occidentalis). We generated species-specific and seasonally variable estimates of (c)g(m) . We found that (c)g(m) was significantly different among species (0.41, 0.22 and 0.09 mol m(-2) s(-1) for Larix, Pseudotsuga and Thuja, respectively), but was similar throughout the season. Ignoring respiratory and photorespiratory fractionations ((c)Δ(ef)) resulted in ≈30% underestimation of (c)g(m) in Larix and Pseudotsuga, but was innocuous in Thuja. Substantial errors (~1-4‰) in photosynthetic discrimination calculations were introduced by neglecting (c)g(m) and (c)Δ(ef) . Our method is easy to apply and cost-effective, captures species variation and would have captured seasonal variation had it existed. The method provides an average canopy value, which makes it suitable for parameterization of canopy-scale models of photosynthesis, even in tall trees.

The efficiency of C(4) photosynthesis under low light conditions: assumptions and calculations with CO(2) isotope discrimination.

Leakiness (Φ), the proportion of carbon fixed by phosphoenolpyruvate carboxylation that leaks out of the bundle-sheath cells, determines C(4) photosynthetic efficiency. Large increases in Φ have been described at low irradiance. The underlying mechanisms for this increase remain uncertain, but changes in photorespiration or the energy partitioning between the C(4) and C(3) cycles have been suggested. Additionally, values of Φ at low light could be magnified from assumptions made when comparing measured photosynthetic discrimination against (13)C (Δ) with the theoretical formulation for Δ. For example, several simplifications are often made when modelling Δ to predict Φ including: (i) negligible fractionation during photorespiration and dark respiration; (ii) infinite mesophyll conductance; and (iii) CO(2) inside bundle-sheath cells (C(s)) is much larger than values in mesophyll cells (C(m)). Theoretical models for C(4) photosynthesis and C(4) Δ were combined to evaluate how these simplifications affect calculations of Δ and Φ at different light intensities. It was demonstrated that the effects of photorespiratory fractionations and mesophyll conductance were negligible at low light. Respiratory fractionation was relevant only when the magnitude of the fractionation factor was artificially increased during measurements. The largest error in estimating Φ occurred when assuming C(s) was much larger than C(m) at low light levels, when bundle-sheath conductance was large (g(s)), or at low O(2) concentrations. Under these conditions, the simplified equation for Δ overestimated Φ, and compromised comparisons between species with different g(s), and comparisons across O(2) concentrations.