Improved temperature response functions for models of Rubisco-limited photosynthesis


  • *Current address: University of Michigan Biological Station, 9008 Biological Road, Pellston, MI 49769, USA.

  • †Permanent address: Departamento de Fitotecnia, Universidade Federal Rural do Rio de Janeiro, Seropedica, 23851–970 Brazil.

Correspondence: Stephen P. Long. Fax: +1 217 244 7563; e-mail:


Predicting the environmental responses of leaf photosynthesis is central to many models of changes in the future global carbon cycle and terrestrial biosphere. The steady-state biochemical model of C3 photosynthesis of Farquhar et al. (Planta 149, 78–90, 1980) provides a basis for these larger scale predictions; but a weakness in the application of the model as currently parameterized is the inability to accurately predict carbon assimilation at the range of temperatures over which significant photosynthesis occurs in the natural environment. The temperature functions used in this model have been based on in vitro measurements made over a limited temperature range and require several assumptions of in vivo conditions. Since photosynthetic rates are often Rubisco-limited (ribulose, 1-5 bisphosphate carboxylase/oxygenase) under natural steady-state conditions, inaccuracies in the functions predicting Rubisco kinetic properties at different temperatures may cause significant error. In this study, transgenic tobacco containing only 10% normal levels of Rubisco were used to measure Rubisco-limited photosynthesis over a large range of CO2 concentrations. From the responses of the rate of CO2 assimilation at a wide range of temperatures, and CO2 and O2 concentrations, the temperature functions of Rubisco kinetic properties were estimated in vivo. These differed substantially from previously published functions. These new functions were then used to predict photosynthesis in lemon and found to faithfully mimic the observed pattern of temperature response. There was also a close correspondence with published C3 photosynthesis temperature responses. The results represent an improved ability to model leaf photosynthesis over a wide range of temperatures (10–40 °C) necessary for predicting carbon uptake by terrestrial C3 systems.




Predicting the responses of leaf photosynthesis to elevated atmospheric [CO2] and increased temperature is fundamental to projecting the impact of global change on the biosphere (Long 1991). Describing temperature effects at the leaf level is equally critical to predicting community gas exchange as leaf temperature varies diurnally and seasonally (Harley & Baldocchi 1995). Farquhar, von Caemmerer & Berry (1980) presented a steady-state mechanistic model of C3 leaf photosynthetic carbon assimilation (A), modified by Harley & Sharkey (1991). This model reasons that A, under any given set of conditions, will be limited by the slower of three processes: (1) the maximum rate of Rubisco-catalyzed carboxylation (Rubisco-limited) (ribulose 1-5 bisphosphate carboxylase/oxygenase); (2) the regeneration of RuBP controlled by electron transport rate (RuBP-limited); or (3) the regeneration of RuBP controlled by the rate of triose-phosphate utilization (TPU-limited). This approach has been widely validated and has provided the basis for scaling carbon uptake to canopies (Wang & Jarvis 1990; Amthor 1995; Lloyd & Farquhar 1996; dePury & Farquhar 1997), ecosystems (Field & Avissar 1998) and landscapes (Sellers et al. 1996; Sellers et al. 1997).

The original model of Farquhar et al. (1980) was parameterized for a leaf temperature of 25 °C. Although effective at this temperature the accuracy of the model appears to decrease at higher and lower temperatures. Although other temperature functions have been proposed (McMurtrie & Wang 1993; Harley & Baldocchi 1995) these also produce modelled values for A that deviate strongly from observed measurements as temperatures deviate from 25 °C. The error associated with these temperature functions most likely results from their derivation from in vitro measurements made over a narrow temperature range. Use of these temperature functions requires assumptions about in vivo conditions, such as pH and CO2 diffusion to the site of carboxylation.

Better predictions of Rubisco-limited photosynthesis are necessary because photosynthesis is commonly Rubisco-limited under natural conditions (Rogers & Humphries 2000). The difficulties associated with the in vitro estimations of kinetics might be overcome through in vivo measurements using antisense Rubisco small subunit (antirbcS) tobacco plants, which express low Rubisco concentrations. Such plants were developed and used to study Rubisco kinetics at 25 °C (von Caemmerer et al. 1994), Rubisco activation (Mate et al. 1996) and CO2 transfer conductance (Evans et al. 1994). The photosynthetic rates of the antirbcS plants are Rubisco-limited over a large range of Ci in contrast to wild-types. This provides a more accurate basis for estimating Rubisco kinetic properties (von Caemmerer et al. 1994; Andrews et al. 1995; von Caemmerer 2000).

The objective of this study was to determine in vivo temperature dependencies of Rubisco kinetic parameters through the use of CO2 gas exchange over a range of biologically significant temperatures. Because the properties of Rubisco enzyme kinetics are conserved among higher plants (von Caemmerer 2000), the in vivo temperature functions developed with this research should provide increased accuracy of leaf, canopy, and global vegetation models. This expectation was tested using the new temperature functions derived from transgenic tobacco to predict the temperature response of Rubisco-limited photosynthesis in a contrasting species, lemon.


Both CO2 and O2 compete for the Rubisco binding site in the processes known as carboxylation and oxygenation, respectively (Farquhar et al. 1980). To account for the competitive inhibition between CO2 and O2, A is mathematically expressed as


where vc and vo are the rates of carboxylation and oxygenation, respectively, and Rd is mitochondrial respiration in the light (Farquhar et al. 1980).

When A is Rubisco limited the velocity of carboxylation can be expressed as


where Vc,max is the maximum rate of carboxylation, O is the oxygen concentration, and Kc and Ko are the Michaelis–Menten constants for CO2 and O2, respectively (Farquhar et al. 1980). The oxygenation of RuBP is analogously expressed as


where Vo,max is the maximum rate of oxygenation (Farquhar et al. 1980).

Incorporating Rubisco-limited photosynthesis into Eqn (1) yields:


where the term (1 –Γ*/Ci) is used to account for CO2 released through photorespiration (Harley & Tenhunen 1991; von Caemmerer 2000). The term Γ* is expressed as


where τ, the Rubisco specificity factor, is derived from Rubisco kinetics as


(Harley & Tenhunen 1991).

For the equations described above, the following parameters are required for predicting Rubisco-limited photosynthesis: Vc,max, Kc, Ko, Γ* and Rd. Values for Vo,max can be derived by substituting Eqn 5 into Eqn 6 and rearranging:


Values for Γ* are determined by in vivo measurements (Laisk 1977; Brooks & Farquhar 1985).

Temperature functions

The generic temperature responses of the six parameters Vc,max, Vo,max, Γ*, Ko, Kc and Rd are fit using the equation:


where R is the molar gas constant and Tk is the leaf temperature (Tenhunen et al. 1976; Harley & Tenhunen 1991). The terms c and ΔHa represent a scaling constant and activation energy, respectively. Use of this equation assumes that, regardless of the amount of enzyme present or the activation state of the enzyme, the activity will continue to increase exponentially as temperature increases. The terms c and ΔHa are fit to the values for each of the six parameters measured at a range of temperatures.


Plant material

Plants were germinated and grown in environmentally controlled greenhouses located at the University of Illlinois, Urbana, IL, USA. A transformed line of tobacco (Nicotiana tabacum, L. cv W38) described by Rodermel, Abbott & Bogoras (1988) was used. Seeds were sown in 0·9 L plastic containers and were individually transplanted into 1·5 L square pots approximately 2 weeks after emergence. Sowings were staggered to allow a continuous supply of plants at a similar developmental stage. Plants were grown in a soil-less growth medium (Sunshine Mix No.1; SunGro Horticulture, Inc., Bellevue, WA, USA) and were watered regularly. Nutrient additions were given weekly in the form of 300 μL L−1 of NPK 15 : 5 : 15 (Peters Excel; The Scotts Co., Marysville. OH, USA) to pot saturation. Greenhouse temperature levels were set at 25 °C for the 16 h photoperiod and 18 °C for night. Low photosynthetic capacity made these plants vulnerable to photo-inhibition. This was avoided by maintaining leaves at a photosynthetically active photon flux density (PPFD) of approximately 200 μmol m−2 s−1 using shade cloth and artificial light sources as needed.

Gas exchange

Leaf gas exchange rates were measured using an open gas exchange system with independent [CO2] control using a 6 cm2 clamp-on leaf cuvette (LI 6400; LI-COR, Inc., Lincoln, NE, USA) on the two newest fully expanded leaves of each plant. The gas exchange system was zeroed daily using CO2-free air. The chamber was modified by replacing the Peltier external heat sink with a metal block containing water channels, which in turn were connected to a heating/cooling circulating water bath (Endocal RTE-100; Neslab Instruments, Inc., Newington, NH, USA). This allowed maintenance of leaf temperature at any preset value between 10 and 40 °C. Leaf temperature was measured using a chromel–constanten thermocouple appressed to the lower leaf surface. The temperatures reported by this particular thermocouple were cross-checked against standard mercury-in-glass thermometers in a controlled temperature chamber and found to be within ± 0·4 °C. The oxygen levels were controlled using a gas mixing system (Series 850 Ga Blender; Signal, Camberley, UK) and measured using a gas phase oxygen sensor (S102 Oxygen sensor; Qubit Systems Inc., Ontario Canada). The oxygen sensor was calibrated with pure N2 and pure O2 only, as the response of this sensor to O2 is linear (Loggr Pro; Vernier Software, Beaverton, OR, USA).

Photosynthesis was measured at PPFD of 300 μmol m−2 s−1 to prevent photo-inhibition from occurring. This PPFD was light-saturating for the genotype. PPFD was controlled using a red–blue led light source built into the leaf cuvette calibrated against an internal photodiode (LI-6400–03; LiCor, Inc.). The vapour pressure deficit in the cuvette was maintained between 0·5 and 2·0 kPa to prevent stomatal closure. This was accomplished by passing the air entering the cuvette through either anhydrous calcium carbonate (Drierite; W.A. Hammond Drierite Company, Ltd, Xenia, OH, USA) at lower temperatures when humidity was high or by bubbling the air through water for the higher temperatures. Diffusion of CO2 into and out of the empty chamber was determined for each [CO2]. These values were used to correct measured leaf fluxes. Values for A and Ci were calculated using the equations of von Caemmerer & Farquhar (1981).

Model parameterization

Three replicate individuals were measured at 5 °C intervals between 10 and 40 °C to determine Rd and Γ*, three to determine Vc,max and Kc, and a final three to determine Ko. Two sets of data were discarded when signs of irreversible leaf damage became apparent (i.e. Kc at 35 °C and Ko at 40 °C). The temperature responses of Rd and Γ* were determined from measurements made following the procedure of Laisk (1977) which takes advantage of changes in photorespiration at different PPFD. Unlike Rd, rates of photorespiration are highly dependent on PPFD. Therefore, if measurements of A are taken at a range of Ca below 100 μmol mol−1 and at a range of PPFD, the point at which A versus Ci for all three PPFDs intersect represents Γ* when extrapolated to Ci and the level of Rd when extrapolated to A (Laisk 1977; Brooks & Farquhar 1985).

We used gas exchange measurements at differing Ci and O2 concentrations to solve for the six parameters. Measurements of A/Ci curves in 2% O2, to minimize photorespiration, were used to estimate Vc,max and Kc. The equation describing the Michaelis–Menten function approximating the response of A to Ci in the absence of O2 was fit to these data by maximum-likelihood regression (SigmaPlot 5·0; SPSS, Inc., Chicago, IL, USA). Measurements of A over a range of [O2] were used to determine Ko using Eqn 4 with values of Kc and Vc,max taken from the A/Ci curves above. Values for Ko were then used to solve again for Kc and Vc,max, this time accounting for photorespiration. This was repeated until values for Ko, Kc and Vc,max were constant. Values of Kc, Ko and Vc,max and Γ* were then used to solve for Vo,max using equation [7].

Upon completion of these measurements the temperature responses of Γ*, Rd, Vc,max, Vo,max, Kc and Ko were determined using Eqn 8. The temperature responses of Vc,max and Rd were standardized to a value of 1·0 at 25 °C. This allows for a temperature response curve to be extrapolated from any absolute values of Vc,max and Rd obtained at 25 °C.

Jurik, Webber & Gates (1988) provide temperature responses (10 °C–40 °C) of A at ambient concentrations of CO2 for sugar maple (Acer saccharum), a major component of deciduous and mixed forest. These observed temperature responses were compared with those predicted in earlier studies (Farquhar et al. 1980; McMurtrie & Wang 1993; Harley & Baldocchi 1995). Values of A were normalized to unity at 25 °C for each set of temperature responses The modelled values were expressed as percentage deviation from the observed values.

A further test of the temperature functions derived in this study were tested against measurements of lemon (Citrus limon L.). The values of Vc,max and Rd were estimated for lemon at 25 °C and then Rubisco-limited assimilation was predicted from the temperature functions for Vc,max, Kc, Ko, Γ* and Rd. The modelled values were then compared to measured values over the same temperature range. Three lemon trees were grown in a controlled-environment greenhouse with 16 h photoperiods and daily maximum PPFDs of between 600 and 1200 μmol m−2 s−1. Nutrients were applied weekly and the trees were watered as needed. Photosynthesis was measured using an open gas exchange system as outlined above for tobacco using a constant Ci of 100 μmol mol−1 at temperatures from 10 to 40 °C. Preliminary A/Ci curves showed that a Ci of 100 μmol mol−1 would ensure Rubisco-limited photosynthesis at all temperatures. Three measurements were made at each temperature and A/Ci curves were made on the plants at 25 °C to determine Vc,max and Rd for use in the model. Measured rates of Rubisco-limited photosynthesis for lemon and modelled values using the temperature responses determined from the transgenic tobacco were compared at each temperature.


The derived functions (Eqn 8) for the six parameters that describe the temperature response for CO2 uptake during Rubisco-limited photosynthesis are given in Table 1. The regression coefficients were significant at P < 0·0001 for all parameters.

Table 1.  The values for c and ΔHa describing the temperature responses of the six parameters used to predict CO2 uptake by leaves during Rubisco-limited photosynthesis [Parameter = exp(c–ΔHa/RTk)]. Parameters were determined from leaf gas-exchange measured on a Rubisco-antisense line of tobacco (Nicotiana tabacum L. cv. W38). Parameters that vary between plants, Rd, Vc,max and Vo,max, were normalized to unity at 25 °C
at 25 °C
(kJ mol−1)
  1. Ko (mmol mol−1)

  2. 278·4

  3. 20·30

  4. 36·38

Rd (μmol m−2 s−1)118·7246·39
Vc,max (μmol m−2 s−1)126·3565·33
Vo,max (μmol m−2 s−1)122·9860·11
Γ* (μmol mol−1) 42·7519·0237·83
Kc (μmol mol−11)404·938·0579·43

Constants associated with the kinetic properties of Rubisco (i.e. Ko, Kc, Γ*) are generally conserved for most higher terrestrial plants utilizing the C3 photosynthesis pathway (von Caemmerer 2000). Therefore, once these parameters are established, they may be incorporated into generic leaf, canopy and ecosystem photosynthesis models. Parameters that depend on enzyme concentration (Vc,max, Vo,max and Rd) are not conserved even within an individual. On the other hand, relative changes in these parameters with temperature should be conserved since they depend on enzyme structure and not on the concentration. The temperature response of these parameters is expected to remain proportional for all species and can thus be normalized to 25 °C (Farquhar et al. 1980; McMurtrie & Wang 1993; Harley & Baldocchi 1995).

Parameters Γ*and Rd

The responses of Γ* and Rd increased exponentially with temperature (Fig. 1a & b). The temperature response of Γ* is similar to values determined by previous studies at lower temperatures. However, the temperature dependence is not linear, as evident from the data at higher temperatures (Laisk 1977; Brooks & Farquhar 1985; von Caemmerer 2000). A possible explanation for the inconsistency with previous studies is that there are a limited number of replicate measurements made at higher temperatures. For example, Brooks & Farquhar (1985) determined only one value of Γ* above 30 °C. The temperature function of Rd was normalized to 25 °C to provide a relative temperature function.

Figure 1.

Temperature responses of the six parameters describing Rubisco-limited photosynthesis determined from gas exchange measurements on Rubisco-antisense tobacco (Nicotiana tabacum L. cv. W38) plants. (a) The temperature response of Γ* (filled circles) compared with the temperature response from Brooks & Farquhar (1985) (broken line). (b) The temperature response of Rd normalized to 25 °C. (c) The responses of Vc,max (filled circles) and Vo,max (open circles) to temperature. (d) The ratio of Vc,max and Vo,max versus temperature for data obtained in this study (filled circles) compared with previously published results (broken line) of Badger & Collatz (1977). (e and f) The temperature responses the Michaelis constants for carboxylation (Kc) and oxygenation (Ko), respectively. Each point is the mean of three replicate plants (± 1 SE).

Parameters Vc,max and Vo,max

The temperature responses of Vc,max and Vo,max are shown in Fig. 1c. At a given temperature, Vc,max is expected to differ between species and among individuals of a species based on enzyme content and activation state. The pattern and magnitude of variation in Rubisco-limited CO2 assimilation with temperature should be conserved as it is a property of enzyme kinetics that should remain constant for all species and growth conditions (von Caemmerer 2000). The activation energy of Vc,max obtained in the present study was 65·3 kJ mol−1 and is similar to the 64·9 kJ mol−1 obtained above 15 °C in a previous study (Badger & Collatz 1977). Previous studies have incorporated a de-activation function for parameters whose values depend on the amount of active enzyme (e.g. Harley & Tenhunen 1991). There was no de-activation apparent for any of the six parameters at higher temperatures. Thus, addition of a de-activation term was unnecessary at temperatures ≤ 40 °C and avoids the additional error that a further term would impose. However, above 40 °C the additional term used by Harley & Tenhunen (1991) may well be essential.

The temperature dependence of Vo,max has been assumed to be a constant proportion of Vc,max over a range of temperature at 0·21 ×Vc,max (Farquhar et al. 1980; Farquhar & von Caemmerer 1982) though numerous values ranging from 0·19 to 0·77 ×Vc,max have been determined (Badger & Andrews 1974; Badger & Collatz 1977; Jordon & Ogren 1981, 1984; Makino, Mae & Ohira 1988; Whitney et al. 1999;von Caemmerer 2000). Although numerous studies report values for the ratio of Vo,max/Vc,max at 25 °C, very few studies have determined the temperature response of this ratio. One study provides temperature responses from in vitro measurements of Vc,max and Vo,max (Badger & Collatz 1977). The temperature response of Vo,max was derived from measured in vivo values of Vc,max, Ko, Kc and Γ* using Eqn (9). The ratio, Vo,max/Vc,max, decreases with temperature (Fig. 1d) as observed previously (Badger & Collatz 1977). However, our ratio was considerably higher (Fig. 1d). The differences between these data and those presented by Badger & Collatz (1977) might be attributable to in vivo versus in vitro measurements. Although it was not measured in this study, the temperature response of mesophyll conductance would allow us to verify if this difference is attributed to intracellular diffusion of CO2.

Parameters Kc and Ko

The temperature responses of Kc and Ko are shown in Fig. 1e & f. Reported values for Kc and Ko vary considerably at a given temperature (Badger & Collatz 1977; Jordan & Ogren 1984; Harley, Weber & Gates 1985), even though the values for these parameters are expected to remain similar among higher plants (von Caemmerer et al. 1994). One possible explanation for the variety of values for Kc and Ko at 25 °C might again be in vitro conditions. The values determined in this study can only be compared with those of von Caemmerer et al. (1994) who provide in vivo values for Kc and Ko. Results from this study and those reported by von Caemmerer et al. (1994) are within 1% of each other at 25 °C for Kc and within 10% for Ko (Fig. 1e), even though the two studies used different transgenic strains of tobacco.

Testing the tobacco temperature functions

The ability of these temperature functions derived from tobacco to predict temperature dependence of Rubisco-limited photosynthesis was compared, along with previously published temperature functions, to experimental data (Fig. 2; experimental data from Jurik et al. 1988). The temperature response of Rubisco-limited photosynthesis modelled using the data from this study shows stronger correspondence with the experimental data than previous temperature functions. In addition to the comparison of temperature responses, the ability of the temperature response functions to accurately predict photosynthesis at any temperature between 10 and 40 °C was tested against data collected from lemon (Fig. 3). These comparisons suggest the temperature responses of the in vivo enzyme kinetics improves the ability to predict the rate of Rubisco-limited photosynthesis over the temperature range at which most carbon assimilation will occur in the terrestrial biosphere.

Figure 2.

Percentage deviation of assimilation predicted by four different sets of temperature functions from the previously published temperature response of photosynthetic CO2 uptake in sugar maple (Acer saccharum) of Jurik et al. (1988). Each set of temperature functions was normalized to unity at 25 °C.

Figure 3.

Measured photosynthetic rates (A) for lemon (Citrus limon) leaves at a Ci of 100 μmol mol−1 and compared to the response predicted with the temperature functions derived from transgenic tobacco. Each point is the mean of three replicate plants (± 1 SE)

Mesophyll conductance

Exact determination of Kc requires a knowledge of the mesophyll diffusive conductance (gm), as this determines the CO2 concentration at the site of Rubisco which will be lower than Ci used here. In effect we are reporting the temperature response of an apparent, rather than actual, Kc. However, gm varies significantly with species and its temperature function is unknown. Scaling to canopies and landscapes would require knowledge of both and the probably impractical separation of the contribution made by different species and leaf classes. We therefore contend that an apparent Kc represents a practical approach for scaling the temperature responses to higher scales. What error might omission of gm represent? Citrus spp. have previously been shown to have an exceptionally low gm in contrast to tobacco (von Caemmerer & Evans 1991; Loreto et al. 1992;). Any error introduced by the unknown values for gm appear small since the temperature functions derived here from tobacco appear very effective in predicting the temperature response of leaf photosynthesis in lemon (Fig. 3) as well as other C3 tree species (Fig. 2).


The biochemical model of leaf photosynthesis presented by Farquhar et al. (1980) has been used to scale photosynthesis from the leaf level to canopies, ecosystems, and landscapes. The temperature functions currently used for predicting photosynthesis are based on in vitro data that do not provide accurate modelled temperature responses of Rubisco-limited A (Fig. 2). Implementing the temperature functions developed in this study into the model of leaf photosynthesis greatly improves predictions of Rubisco-limited A over the temperature range of 10–40 °C (Figs 2 & 3). By improving the temperature response of leaf photosynthesis models, these data will improve ability to predict how photosynthetic carbon uptake by vegetation will respond to variation in temperature from diurnal cycles to future global change.


The authors thank Dr Phil Davey, Dr Shawna Naidu, Hyungshim Yoo, Xinguang Zhu, Kevin Young and Lisa Ainsworth for helpful comments on the manuscript. The authors also thank Steve Rodermel for supplying us with the antirbcS tobacco and Suzanne von Caemmerer for suggesting this approach to estimating Rubisco kinetics. This research was funded by the Integrative Photosynthesis Research training grant to CJB (NSF DBI96–02240).