CASE STUDY 1.1  Development of A:pi curves

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Susanne von Caemmerer and Graham Farquhar

Component processes underlying CO2 assimilation are amenable to analysis at a whole-leaf level. Under strong illumination, CO2-assimilation clearly predominates over CO2-generating processes (both mitochondrial and photorespiration), and in those circumstances the inward flux of CO2 can be taken as a net reaction rate for CO2 assimilation via Rubisco as primary catalyst. However, if whole-leaf photosynthesis is to be analysed in biochemical terms, the effective concentration of this primary substrate at fixation sites must also be known. How then can these substrate levels be defined in an actively photosynthesising leaf? Moreover, knowing that CO2 assimilation is energy dependent, and that both ATP and reducing power (NADPH) are being generated concurrently, how can photosynthetic electron flow be described in terms relevant to CO2 assimilation?

Early models of leaf gas exchange had been developed as electrical analogues of resistances, and proved useful in making a distinction between stomatal and mesophyll limitations on CO2 assimilation. Mesophyll, or ‘residual’, resistance (rmc) was a collective term that was meant to embody non-stomatal diffusive factors, and included both physical and biochemical constraints. Further refinement would depend upon a reliable estimate of CO2 partial pressure at fixation sites within leaves, and those estimates came with improvements in diffusive models for leaves, but, in particular, development of high- precision gas exchange systems with a capacity for fast data analysis (either by interfacing measuring devices with computers, or via chart recorder and human agency!). CO2 response curves emerged as a valuable tool to analyse photo-synthesis in vivo.

In this essay A:ci refers to CO2 assimilation rate (A) as a function of intercellular CO2 concentration (ci) expressed in terms of µL of CO2 per litre of gas (µL L–1) or µg of CO2 per litre of gas (µg L–1). In strict biophysical terms, intercellular CO2 partial pressure (pi) rather than gaseous concentration (ci) is a more relevant determinant of CO2 assimilation, and where leaf chamber atmospheric pressure is known, an A:pi curve can be constructed. CO2 assimilation rate (A) is then referenced to intercellular partial pressure (pi) expressed as µbar where pi = chamber pressure × ci. At one bar atmospheric pressure, pi is numerically equivalent to ci.

Physical concepts of leaf gas exchange

Penman and Schofield (1951) put diffusion of CO2 and water vapour through stomata on a firm physical basis. Their ideas were taken up at Wageningen by Pieter Gaastra in the 1950s and modern analytical gas exchange is often attributed to this seminal work (Gaastra 1959) where he even constructed his own infrared gas analyser and other equipment necessary to make measurements of CO2 and water vapour exchange. His work was a landmark because it examined CO2 assimilation and water vapour exchange rates of individual leaves under different environmental conditions, and he distinguished between stomatal and internal resistances. Gaastra calculated resistances to water vapour and CO2 diffusion from two equations (here in our simplified notation) which are based on Fick’s Law for the diffusion of gases.


where E and A are the fluxes of water vapour and CO2 and wi and ci and wa and ca are the mole fractions of water vapour and CO2 in intercellular air spaces and ambient air respectively. The denominator terms, rsw and rsc, represent stomatal resistances to H2O and CO2 diffusion respectively. Gaastra calculated wi from the saturated vapour pressure at the measured leaf temperature and since both E and wa were measured variables this allowed rsw to be calculated. Knowing that resistances to CO2 and water vapour are related by the ratio of their diffusivities, he calculated stomatal resistance to CO2 diffusion, rsc. Gaastra realised that the diffusion path for CO2 is longer than that of water vapour, as CO2 had to diffuse from the intercellular airspaces through the cell wall across membranes to the chloroplast stroma where CO2 fixation by Rubisco takes place. He therefore extended the equation for CO2 assimilation to:


where cchl represented CO2 concentration at chloroplasts.

Gaastra analysed the dependence of CO2 assimilation rate on light, CO2 and temperature, and observed that at low CO2 concentrations the rate of CO2 assimilation was independent of temperature whereas it was strongly influenced by temperature at higher CO2. This led him to conclude that the rate of CO2 uptake was completely limited by CO2 diffusion processes at low CO2 and that biochemical processes became limiting only at high CO2. The belief that CO2 diffusion was limiting gave rise to the assumption that chloroplastic CO2 concentration was close to zero. This led to the erroneous simplification of the above equation such that the total resistance to CO2 diffusion could be calculated from CO2 assimilation rate and the ambient CO2 concentration alone. Since stomatal resistances could be calculated from measurements of water vapour diffusion, it was also possible to calculate mesophyll resistance to CO2 diffusion. In Australia particularly there was a great interest in determining the relative importance of stomatal and mesophyll resistance in limiting CO2 assimilation rates under adverse conditions of high temperature and frequent water stresses, and in global terms much of the pioneering work was undertaken in this country (see, for example, Bierhuizen and Slatyer 1964).


Figure 1 An early A:ci curve showing the CO2 assimilation rate of cotton at a range of cell wall CO2 concentrations (redrawn from Troughton (1969) and Troughton and Slayter (1969) and retaining original units for CO2 flux). For comparative purposes, 10 × 10-8 g cm-2 s-1 would be equivalent to 22.27 µmol CO2 m-2 s-1, and 1 µg L-1 would be equivalent to 0.54 µL L-1 (assuming a gram molecular weight of 44 for CO2, and measurements at normal temperature and pressure). (a) Leaf temperature influences the overall shape of CO2 response curves (measured in O2-free air) but has no effect on the initial slope where response to CO2 is limited by Rubisco activity. This family of curves comes from repeated measurements of gas exchange by the same leaf at five different temperatures (values shown) and indicated in the figure by five different symbols. (b) CO2 response curves for two leaves of cotton measured in O2-free air at 25°C and three levels of relative water content. Legend:  leaf 1, 92% water content; O leaf 1, 56%; leaf 2, 92%; leaf 2, 69%. Identical slopes regardless of treatment mean that variation in relative water content over this range is without effect on CO2 assimilation within mesophyll tissues. By implication, reduction in CO2 uptake as commonly observed on whole leaves under moisture stress would be attributable to stomatal factors.

Calculation of intercellular CO2, ci and the first A versus ci curves

Although CO2 concentration in intercellular airspaces, ci, was explicit in Gaastra’s equations, this term was first specifically calculated by Moss and Rawlings in 1963, and the first extensive use of the parameter was made by Whiteman and Koller in 1967, who examined stomatal responses to CO2 and irradiance, concluding that stomata were more likely to respond to ci rather than ca. The first bona fide response curves of CO2 assimilation rate to ci rather than ca were those of Troughton (1969) and Troughton and Slatyer (1969) (Figure 1). In Figure 1(a), ci was derived from measurements of CO2 uptake in an assimilation chamber where air passed through a leaf, rather than over both surfaces concurrently (as became commonplace in subsequent designs), and such estimates would differ slightly. More importantly, those measurements were made at different temperatures and confirmed that CO2 assimilation was not greatly affected by temperature at low ci. Later, this lack of temperature dependence was explained by the kinetics of Rubisco (von Caemmerer and Farquhar 1981). Figure 1(b) shows the initial slope of CO2 response curves measured at different stages of water stress. In this case, water stress has affected stomatal resistance (as the ci obtained at air levels of CO2 occur at progressively lower ci) but not the relationship between CO2 assimilation rate and ci. A versus ci response curves thus provided an unambiguous distinction between stomatal and non-stomatal effects on CO2 assimilation and, provided stomata respond uniformly across both leaf surfaces, that distinction can be made quantitative.

Before we head further into a discussion of our 1990s understanding and interpretation of more comprehensive CO2 response curves, we must take an important digression into development of mathematical models of C3 photosynthesis.

Biochemistry of photosynthesis and leaf models

Gas exchange studies focused initially on physical limitations to diffusion, but it was not long before persuasive arguments were being brought forward to show that leaf biochemistry must influence the rate of CO2 fixation even at low CO2 concentrations. Björkman and Holmgren (1963) made careful gas exchange measurements of sun and shade ecotypes of Solidago growing in Sweden, and noted strong correlations between photosynthetic rate measured at high irradiance and ambient CO2 and the nitrogen content of leaves, and later also related it to different concentrations of Rubisco (then called carboxydismutase). Anatomical studies implied that thin shade leaves would not have larger internal diffusion resistance to CO2 than thicker sun leaves where cells were more densely packed. Furthermore, following earlier discoveries of the O2 sensitivity of photosynthesis, namely a low-O2 enhancement of CO2 assimilation rate, Gauhl and Björkman (1969), then at Stanford, showed very elegantly that while O2 concentration did affect CO2 assimilation rate, water vapour exchange was not affected (i.e. stomata had not responded). Clearly, the increase in CO2 assimilation rates seen with a decrease in O2 concentration could not be explained via a limitation on CO2 diffusion.

Central importance of Rubisco

Early mathematical models of leaf photosynthesis were extensions of Gaastra’s resistance equation, and could not accommodate the O2 sensitivity of CO2 assimilation. They were quickly followed by development of more biochemical models in the early 1970s and the discoveries by Bowes et al. (1971) that Rubisco was responsible for both carboxylation and oxygenation of RuBP (a five-carbon phosphorylated sugar, regenerated by the PCR cycle of chloroplasts). This crucial observation of dual function put Rubisco at centre stage. Laing et al. (1974) were first to compare the gas exchange of soybean leaves with the in vitro kinetics of Rubisco and suggested the following equation for the net CO2 assimilation rate:

where Vc and Vo are the rates of Rubisco carboxylation and oxygenation (later on a term for mitochondrial respiration was added to most models). Laing et al. related a ratio of the rates of carboxylation to oxygenation of RuBP to the con-centration of its substrates, CO2, C, and O2, O, and showed that:

where Kc, Ko, Vcmax, Vomax are the corresponding Michaelis Menten constants and maximal activities of carboxylase and oxygenase functions respectively and Γ∗ is the CO2 compensation point in the absence of mitochondrial respiration.

A note on Γ: illuminated leaves held in a closed circuit of recirculating air will reduce CO2 to a ‘compensation point’ where uptake and generation of CO2 are balanced; this is commonly 50–100 ppm for C3 plants and referred to as Γ. A CO2 response curve for leaf photosynthesis will show a similar value as an intercept on the abscissa. Γ can thus be measured empirically, and will be an outcome of interactions between photosynthesis, photorespiration and dark (mitochondrial) respiration (Rd). If allowance is made for Rd, the CO2 compensation point would then be slightly lower, and is termed Γ∗. As with measured Γ, this inferred CO2 compensation point, Γ∗, is linearly related to O2, an observation that intrigued earlier observers but was easily reconciled with the dual function of Rubisco. Laing et al. (1974) used Equations 3 and 4 to predict this linear dependence of Γ∗ on O2, and with subsequent confirmation Rubisco became a key player in photosynthetic models. (Equation 3 assumes that for each oxygenation, 0.5 CO2 are evolved in the subsequent photorespiratory cycle, although there has been some debate over this stoichiometry.) If the enzyme reaction is ordered with RuBP binding first, the rate of carboxylation in the presence of the competitive inhibition by O2 at saturating RuBP concentration can be given by

When combined with Equation 3 this gave a simple expression of net CO2 fixation rate:

which depends on the maximal Rubisco activity and provided the quantitative framework for comparing rates of CO2 assimilations with the amount of Rubisco present in leaves (von Caemmerer and Farquhar 1981). Difference in CO2 assimilation rates observed under different growth con-ditions could then be explained according to variations in the amount of Rubisco present in leaves. In Figure 2 the dotted line shows a CO2 response curve modelled by Equation 6. Chloroplast CO2 partial pressure was then assumed to be similar to that in the intercellular airspaces. Using on-line discrimination between 13CO2 and 12CO2, and deriving an estimate of CO2 partial pressure at fixation sites within chloroplasts, we subsequently learned that a further draw down can occur, but the general applicability of Equation 6 was not compromised. As an aside, these equations became basic to most photosynthetic models long before the order of the reaction mechanism of Rubisco had been unequivocally established. Had CO2 and O2 bound to Rubisco before RuBP, or the reaction not been ordered, our equations would have been much more complex with both Km(CO2) and Km(O2) dependent upon RuBP concentration.


Figure 2 Comparison of measured and modelled CO2 response curves. (a) CO2 assimilation rate v. intercellular CO2 partial pressure in Phaseolus vulgaris measured at two irradiances and a leaf temperature of 28°C. Arrows indicate points obtained at an external CO2 partial pressure of 330 µbar. (b) Modelled CO2 response curves. The dotted line and its extension represent the Rubisco-limited rate of CO2 assimilation . The dashed lines and their extensions represent the electron-transport-limited rates of CO2 assimilation at the two irradiances . For further details see von Caemmerer and Farquhar (1981). (c) CO2 assimilation rate v. intercellular CO2 concentration in Phaseolus vulgaris measured at two O2 concentrations at a leaf temperature of 28°C. Arrows indicate points obtained at an external CO2 partial pressure of 330 µbar. (d) Modelled CO2 response curves for conditions applied in (c). (Method details in (b)) .

 Regeneration of RuBP and electron transport rate

Equation 6 could mimic CO2 assimilation rate at low ci , as well as O2 effects on CO2 uptake, but measured rates of CO2 assimilation saturated much more abruptly at high CO2 concentrations than could be predicted from Rubisco kinetics (Figure 2). Using a highly novel approach in Estonia, Laisk and Oja (1974) proposed that CO2 assimilation was limited by RuBP regeneration rate at high ci. They had fed brief pulses of CO2 to leaves that had been previously exposed to low CO2 (conditions under which RuBP concentrations were presumably high), and obtained rates up to 10 times higher than the steady-state rates of CO2 assimilation! Lilley and Walker (1975) at Sheffield reached a similar conclusion after comparing the CO2 responses of illuminated isolated chloroplasts with those obtained upon lysing chloroplasts in a medium containing saturating RuBP.

In our model of C3 photosynthesis (Farquhar et al. 1980) the way we handled rate limitation by RuBP regeneration was probably the most important decision made in that context. Both ATP and NADPH were required for RuBP regeneration, and this fundamental need formed a connection with light in our model. From a mathematical perspective there were two options: (1) RuBP and CO2 could always colimit the rate of carboxylation, and this we would express in a double Michaelis Menten equation, or (2) carboxylation rate could be limited by either RuBP or else saturated and thus independent of RuBP. The in vivo kinetics of Rubisco suggest the second option.

Peisker (1974) and Farquhar (1979) pointed out that Rubisco was unusual in that it was present in the chloroplast at very high concentrations. Given such a low Km(RuBP), this meant that the in vivo kinetics with respect to chloroplastic RuBP were those of a tight binding substrate. That is, the rate of Rubisco would depend linearly on RuBP concentration when chloroplastic RuBP concentration was below Rubisco catalytic site concentration, and once RuBP exceeded Rubisco site concentration carboxylase would be RuBP saturated. We also knew that irradiance affected CO2 assimilation rate mainly at high intercellular CO2. This supported option 2 (see Figure 2a, b). Given these insights, the more complex link between chloroplastic electron transport rate and RuBP pools used by Farquhar et al. (1980) was quickly simplified to a description of CO2 assimilation that was limited by RuBP regeneration, and utilisation of ATP and NADPH for photosynthetic carbon reduction or oxygenation. RuBP regeneration was in turn driven by the electron transport rate, J (dependent on irradiance and its own maximal capacity), and stoichiometry of ATP or NADPH use by the photosynthetic carbon reduction and oxygenation cycle. For example, when electron transport rate, J, was limiting (in view of ATP use) carboxylation rate could proceed at:


Dashed lines in Figure 2 give modelled electron-transport-limited rates of CO2 fixation according to:

This simplified formulation of C3 photosynthesis (Equations 6 and 8) now provides a meaningful framework for analysis of leaf photosynthesis, and has focused our interpretation of CO2 response curves on leaf biochemistry. For example, von Caemmerer and Farquhar (1981) related the initial slopes of CO2 response curves to in vitro Rubisco activity, and the CO2-saturated rates of A:ci curves to in vitro measurements of electron transport rates. Such studies validate Equations 6 and 8, demonstrating that CO2 response curves could be used as a meaningful and non-invasive tool to quantify these biochemical components under a wide variety of conditions. Subsequent comparisons between wild-type tobacco and transgenic tobacco with a reduced amount of Rubisco have confirmed our concepts. When Rubisco alone is reduced in transgenic plants, RuBP regeneration capacity remains unchanged and no longer limits the rate of CO2 assimilation at high CO2. Rubisco then constitutes the sole limitation (Figure 3).


Figure 3 Transgenic tobacco with reduced amount of Rubisco shows no limitation by the rate of RuBP regeneration. CO2 assimilation response curves in wild-type tobacco, , and in transgenic tobacco with reduced amount of Rubisco, , were measured at a photon irradiance of 1000 µmol quanta m-2 s-1 and a leaf temperature of 25°C. Lines show Rubisco-limited rates of CO2 assimilation (see legend to Figure 2).The reduction in Rubisco in transgenic tobacco was achieved with an antisense gene directed against the mRNA of the Rubisco small subunit (Hudson et al. 1992). Arrows indicate the points obtained at an external CO2 partial pressure of 350 µbar .


Both Rubisco and electron transport components are expensive in terms of leaf nitrogen. For example, Rubisco represents up to 25% of a leaf’s protein nitrogen, with energy transduction components a further 25%. At a ci where the transition from a Rubisco limitation to RuBP regeneration limitation occurs, both capacities are used efficiently and colimit net CO2 assimilation. That is, assimilation can only be increased if both sets of component processes are increased. Where then should the balance lie if a plant is to use nitrogen-based resources to best effect? The transition obviously varies with irradiance and temperature so that an optimal balance will vary with habitat. However, surprisingly little variation has been observed and plants appear unable to shift this point of balance. As an example, important in the context of rising atmospheric CO2 concentrations, plants grown in a high CO2 environment should manage with less Rubisco and thus put more nitrogen into the capacity of RuBP regeneration. Surprisingly, such adjustments have not been observed experimentally, but given prospects of global change, our need for understanding gains urgency.


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