Temperature response of parameters of a biochemically based model of photosynthesis. II. A review of experimental data


Belinda E. Medlyn, School of Biological, Earth and Environmental Science, University of New South Wales, UNSW Sydney 2052, Australia. Fax: + 61 (0)29385 1558; e-mail: B.Medlyn@unsw.edu.au


The temperature dependence of C3 photosynthesis is known to vary with growth environment and with species. In an attempt to quantify this variability, a commonly used biochemically based photosynthesis model was parameterized from 19 gas exchange studies on tree and crop species. The parameter values obtained described the shape and amplitude of the temperature responses of the maximum rate of Rubisco activity (Vcmax) and the potential rate of electron transport (Jmax). Original data sets were used for this review, as it is shown that derived values of Vcmax and its temperature response depend strongly on assumptions made in derivation. Values of Jmax and Vcmax at 25 °C varied considerably among species but were strongly correlated, with an average Jmax : Vcmax ratio of 1·67. Two species grown in cold climates, however, had lower ratios. In all studies, the Jmax : Vcmax ratio declined strongly with measurement temperature. The relative temperature responses of Jmax and Vcmax were relatively constant among tree species. Activation energies averaged 50 kJ mol−1 for Jmax and 65 kJ mol−1 for Vcmax, and for most species temperature optima averaged 33 °C for Jmax and 40 °C for Vcmax. However, the cold climate tree species had low temperature optima for both Jmax(19 °C) and Vcmax (29 °C), suggesting acclimation of both processes to growth temperature. Crop species had somewhat different temperature responses, with higher activation energies for both Jmax and Vcmax, implying narrower peaks in the temperature response for these species. The results thus suggest that both growth environment and plant type can influence the photosynthetic response to temperature. Based on these results, several suggestions are made to improve modelling of temperature responses.


Many of the models used to study effects of global change on plant function and growth incorporate the Farquhar, von Caemmerer & Berry (1980) model of C3 photosynthesis (e.g. Cramer et al. 2001). This model is particularly useful in this context because it represents mechanistically the effects of elevated atmospheric [CO2], a major factor in global change, on photosynthesis. The model has two major parameters, the potential rate of electron transport (Jmax) and the maximum rate of ribulose-1,5-bisphosphate carboxylase-oxygenase (Rubisco) activity (Vcmax). There is now a large database of values of Jmax and Vcmax (Wullschleger 1993) and the effects of elevated [CO2] on these parameters (Medlyn et al. 1999). The model also has the potential to accurately represent the effects of elevated temperature, a second major factor in global change that directly affects plant growth. However, as many modellers are aware, there is a dearth of information regarding the temperature responses of Jmax and Vcmax (Leuning 1997).

We know that these temperature responses are likely to vary, because the temperature response of photosynthesis itself varies with genotype and environmental conditions, and may acclimate to changes in growth temperature (Slatyer & Morrow 1977; Berry & Björkman 1980). To date, however, there has been a fairly limited number of studies examining temperature responses in the context of the Farquhar model (Leuning 1997). The limited amount of information available can result in possibly inappropriate parameter choices. The database of temperature responses of model parameters has the potential to expand in the near future, given recent improvements in temperature control in commercially available gas exchange systems. However, there is a second obstacle to identifying variation in these responses between species, which is that parameter values obtained from data can differ according to the method used to derive them, as is shown below. Direct comparison of parameter values between different studies can therefore be misleading. Wullschleger (1993) solved this problem when compiling a database of Jmax and Vcmax by deriving all parameter values himself directly from ACi curves, thus ensuring consistency between parameters.

The aim of this study was to improve modelling of photosynthetic temperature responses by compiling and comparing existing information on the temperature response of the parameters of the Farquhar et al. (1980) model of photosynthesis. Few studies have compared variation of these parameters among species, so a broad understanding of temperature responses and their relationship to species characteristics and growth environment is lacking. We adopted the approach of Wullschleger (1993), using consistent methods to derive model parameters from the original data sets. Some 19 data sets were obtained. In order to draw some generalizations from these data sets, we attempted to link variation in the parameters between data sets to ecological factors such as functional type and growth environment.



Estimates of the parameters Jmax and Vcmax may be obtained in several ways including gas exchange (Kirschbaum & Farquhar 1984; Harley, Tenhunen & Lange 1986), in vitro methods (Badger & Collatz 1977; Armond, Schreiber & Björkman 1978) or chlorophyll fluorescence (Niinemets, Oja & Kull 1999). In order to ensure that responses were comparable, we chose only to include gas exchange data. In this method, values of Jmax and Vcmax are obtained from the response of photosynthesis under high light (A) to intercellular CO2 (Ci). A family of ACi curves at different temperatures will thus give the temperature response of the two parameters Jmax and Vcmax. Obtaining such a family of curves is very time-consuming and hence several authors have attempted to estimate the temperature responses of Jmax and Vcmax using reduced data sets (e.g. Hikosaka, Murakami & Hirose 1999; Wohlfahrt et al. 1999). We attempted to include some of these studies here, but we found that such shortcuts considerably reduced the accuracy of the parameter values, and therefore decided against their inclusion.

We required the original ACi curves from each study, for reasons illustrated below. However, in two cases the original data were no longer available (Kirschbaum & Farquhar 1984; Harley et al. 1992). Temperature responses from these two studies have been extensively used in modelling, so we thought it important to include them in the comparison. Therefore, in these two cases, typical ACi curves were reconstructed from reported parameter values and the model was re-fitted to these curves. Statistical information on parameters obtained in this way is necessarily missing. Details of all data sets used are given in Table 1.

Table 1.  Details of experimental data sets used
SpeciesCommon nameAuthorMeasurement TPlantsPointsGrowth TGrowth conditionsAge of plantsNotes
  1. Points is the total number of data points used. Growth T is the mean temperature in the month preceding the measurements. Growth conditions: GH, greenhouse; GH – T, temperature-controlled greenhouse; N, nursery; OTC, open-top chamber (control treatment); ME, mini-ecosystem (control treatment); FACE, free-air CO2 exchange (control ring).

Glycine maxSoybeanHarley, Weber & Gates
20,25,30,35,4034825GH – TseedlingsO2 varied also
Gossypium hirsutumCottonHarley et al. (1992)18,26,29,352 29GH – TseedlingsRaw data
Deciduous trees
Acer pseudoplatanusSycamoreDreyer et al. (2001)10,18,25,32,36,4052816N (France)seedlings 
Betula pendulaSilver birchWang (unpub.)5,10,22,26,3242014OTC (Finland)seedlings 
Betula pendulaSilver birchDreyer et al. (2001)10,18,25,32,4052517N (France)seedlings 
Fagus sylvaticaCommon beechDreyer et al. (2001)10,18,25,32,4052517N (France)seedlings 
Fagus sylvaticaCommon beechStrassemeyer & Forstreuter
19,23,26,30,3572820ME (Germany)seedlings 
Fraxinus excelsiorAshDreyer et al. (2001)10,18,25,32,36,4053016N (France)seedlings 
Juglans regiaWalnutDreyer et al. (2001)10,18,25,32,4052517N (France)seedlings 
Prunus persicaPeachWalcroft et al. (2002)10,20,25,32,3751919GH (France)2 year 
Quercus petraeaSessile oakDreyer et al. (2001)10,18,25,32,36,4052516N (France)seedlings 
Quercus roburEnglish oakDreyer et al. (2001)10,18,25,32,36,4053016N (France)seedlings 
Quercus roburEnglish oakStrassemeyer & Forstreuter
15,21,26,30,3682920ME (Germany)seedlings 
Evergreen trees
Abies albaSilver firRobakowski et al. (2002)10,18,26,32,36,4052825N (France)seedlings 
Eucalyptus paucifloraSnowgumKirschbaum & Farquhar
15–351 20GH – TseedlingsRaw data
Pinus pinasterMaritime pineMedlyn et al. (2002)15,20,25,30,3562724field (France)30 yearLocal provenance,
Pinus radiataRadiata pineWalcroft et al. (1997)8,15,20,25,3031424GH (NZ)seedlingsTwo fertilization
Pinus sylvestrisScots pineWang, Kellomaki &Laitinen
6,11,21,26,3141814OTC (Finland)20–25 year 
Pinus taedaLoblolly pineEllsworth & Klimas
15,28,3551424FACE (N. Carolina)12 yearJune and August

In most cases, temperature responses were obtained by applying temperature control to leaves for the duration of the gas exchange measurements. In contrast, in the experiments carried out by Dreyer et al. (2001) and Robakowski, Montpied & Dreyer (2002) (Table 1), temperature changes were applied to the whole seedlings for the night preceding the measurements. This procedure could potentially have modified the temperature response, as there is evidence that the thermal properties of photosystem II (PSII) and of electron transport may begin to acclimate after even a few hours at a given temperature (e.g. Havaux 1993). The results presented below, however, do not appear to indicate any difference between the experiments carried out by this group and other experiments.


Overview of the Farquhar et al. (1980) model of photosynthesis

Farquhar et al. (1980) proposed that net leaf photosynthesis, An, could be modelled as the minimum of two limiting rates:


Ac is the rate of photosynthesis when Rubisco activity is limiting and Aj the rate when ribulose-1,5-bisphosphate (RuBP)-regeneration is limiting. Rd is the rate of mitochondrial respiration. Rubisco-limited photosynthesis is given by:


where Vcmax is the maximum rate of Rubisco activity, Ci and Oi are the intercellular concentrations of CO2 and O2, respectively, Kc and Ko are the Michaelis–Menten coefficients of Rubisco activity for CO2 and O2, respectively, and Γ* is the CO2 compensation point in the absence of mitochondrial respiration. This formulation of the model assumes that the cell-wall conductance, the conductance between the intercellular space and the site of carboxylation, is negligible. Some authors have argued that this conductance is significant and may vary with leaf temperature (e.g. Makino, Nakano & Mae 1994). For most species considered here, we did not have access to appropriate data to evaluate the cell-wall conductance and hence were obliged to use the form of the model given above.

The rate of photosynthesis when RuBP regeneration is limiting is given by:


where J is the rate of electron transport. J is related to incident photosynthetically active photon flux density, Q, by:


where Jmax is the potential rate of electron transport, θ is the curvature of the light response curve and α is the quantum yield of electron transport. The value of α was fixed at 0·3 mol electrons mol−1 photon, based on an average C3 photosynthetic quantum yield of 0·093 and a leaf absorptance of 0·8 (Long, Postl & Bolharnordenkampf 1993). The value of θ was taken to be 0·90. These parameter values have only a slight effect on the estimated value of Jmax.

The key parameters of the model, which vary among species, are Jmax and Vcmax. It is the temperature dependences of these parameters that we set out to examine. In addition, it is known that the parameters Kc, Ko and Γ* vary with temperature. These parameters, by contrast, are thought to be intrinsic properties of the Rubisco enzyme and are generally assumed constant among species, thereby minimizing the number of parameters to be fitted (Harley et al. 1986).

T-dependence of Kc, Ko, andΓ*

The in-vivo temperature dependence of the Michaelis–Menten coefficients of Rubisco, Kc (mmol mol-1) and Ko (mmol mol-1), was recently measured in transgenic tobacco over the temperature range 10–40 °C (Bernacchi et al. 2001) and the following relationships obtained:


Tk denotes leaf temperature in K and R is the universal gas constant (8·314 J mol-1 K-1). Previous parameterizations of the photosynthesis model have been based on in vitro determinations of these functions, carried out by Badger & Collatz (1977) and Jordan & Ogren (1984), which are given here for comparison. Badger & Collatz (1977) determined carboxylase and oxygenase activities over the temperature range 5–35 °C of Rubisco purified from leaves of Atriplex glabriscula. They obtained the following relations (as given in Farquhar et al. 1980):


Jordan & Ogren (1984), working with Rubisco purified from spinach over the temperature range 5–40 °C, obtained the following relationships (equations derived by Harley & Baldocchi 1995):


Figure 1a illustrates the temperature dependence of the effective Michaelis–Menten coefficient for CO2, Km = Kc(1 + Oi/Ko), at an intercellular O2 concentration of 210 mmol mol−1, using each of these three sets of equations.

Figure 1.

(a) Alternative forms for the response of Km = Kc(1 + Oi/Ko) to leaf temperature. (b) Alternative forms for the response of Γ* to leaf temperature. (c) Response of Vcmax to leaf temperature obtained by fitting a sample data set using alternative forms for Km. (d) Response of ratio Jmax : Vcmax to leaf temperature obtained by fitting a sample data set using alternative forms for Km. Key: Solid line: data from Badger & Collatz (1977). Dotted line: data from Jordan & Ogren (1984). Dashed line: data from Bernacchi et al. (2001).

Similarly, the temperature dependence of the CO2 compensation point, Γ* (mmol mol-1), was estimated by Bernacchi et al. (2001) to be:


Alternative expressions of the temperature dependence of the CO2 compensation point, Γ*, are generally based on the work of either Badger and colleagues (Badger & Andrews 1974, Badger & Collatz 1977), Jordan & Ogren (1984) or Brooks & Farquhar (1985). These three alternative temperature dependences are illustrated in Fig. 1b. The CO2 compensation point is related to Kc and Ko and to the maximum oxygenation activity of Rubisco, Vomax(Farquhar et al. 1980):


Badger & Andrews (1974) observed that the ratio Vomax/Vcmax = 0·21, independent of temperature, allowing the temperature dependence of Γ* to be determined from that of Kc and Ko. Jordan & Ogren (1984) studied the CO2 specificity factor τ = KcVomax/(KoVcmax) of Rubisco purified from spinach and obtained (equation derived by Harley et al. 1992):


Brooks & Farquhar (1985) estimated the CO2 compensation point of spinach in vivo using a gas-exchange technique and obtained the following relation, valid over the range 15–30 °C:


They report that this relationship closely resembles that obtained by Jordan & Ogren (1984).

We explored the significance of the differences between these alternative formulations when fitting the parameters Jmax and Vcmax. We found that the parameter Jmax was only very slightly sensitive to the formulation of either Km or Γ* (not shown). However, the parameter Vcmax was highly sensitive to the formulation of Km chosen (Fig. 1c). The ratio of Jmax: Vcmax was thus also highly sensitive to Km (Fig. 1d). This sensitivity is the reason why we considered it necessary to use a consistent method to derive all parameters in a consistent fashion from original ACi curves before comparing the temperature responses.

In the current work, we chose to use the temperature functions obtained by Bernacchi et al. (2001), because these functions were measured in vivo, without disturbance of the leaf, and are hence more likely to reflect accurately activity within the leaf. When using the temperature dependences of Jmax and Vcmax presented below, it is important to also use the Bernacchi et al. (2001) temperature dependences for Kc, Ko and Γ*, because of the sensitivity of the model to these functions illustrated in Fig. 1.

T-dependence of Jmaxand Vcmax

On reviewing the literature, it is daunting to observe the number of alternative functions that have been used to model the temperature dependences of Jmax and Vcmax (compare, for example, Harley et al. 1986; Long 1991; Harley et al. 1992; Harley & Baldocchi 1995; Lloyd et al. 1995). However, all these equations are actually just alternative expressions of two basic functions. The first is the Arrhenius function:


which has parameters k25 (the value at 25 °C) and Ea (the exponential rate of rise of the function). The second is a peaked function (Johnson, Eyring & Williams 1942), which is essentially the Arrhenius equation (Eqn 16) modified by a term that describes how conformational changes in the enzyme at higher temperatures start to negate the on-going benefits that would otherwise come from further increasing temperature. This equation can be written in two equivalent forms:


The first form has parameters k25, Ha, Hd and ΔS, whereas the second form has parameters kopt, Ha, Hd and Topt. Ha and Hd are the same between the two forms, whereas ΔS and Topt are related by:


The parameters can be interpreted as follows: k25 and kopt are the values of Jmax or Vcmax at temperatures 25 °C and Topt, respectively; Ha gives the rate of exponential increase of the function below the optimum (and is analogous to parameter Ea in the Arrhenius function); Hd describes the rate of decrease of the function above the optimum; and Topt is the optimum temperature. ΔS is known as an entropy factor but is not readily interpreted.

Model fitting

The first step in fitting the model was to obtain a value of Jmax and Vcmax for each individual ACi curve. This step was carried out by fitting Eqns 1, 2, 3 and 4 to each curve using the non-linear regression routine with Gaussian algorithm in SAS (SAS Institute Inc., Cary, NC, USA). The parameter Rd was also fitted but was not used further, because this parameter was found to be poorly estimated by the model.

Temperature response parameters were then obtained by fitting Eqns 16, 17 and 18 to response curves of Jmax and Vcmax to leaf temperature, using SigmaPlot (SPSS Inc. Chicago, IL, USA). It was assumed that Jmax and Vcmax at a given temperature could vary between leaves (according to factors such as leaf nitrogen per unit area) but that relative temperature responses of the parameters would be constant. This assumption was incorporated in the model by introducing dummy variables li to represent each leaf and putting:


in Eqns 16, 17 and 18 (Kleinbaum et al. 1998). Here, li = 1 for leaf i and 0 otherwise, and ki is the value of k25 or kopt for leaf i. Reported values of the parameters k25 and kopt are mean and standard deviation of values of ki.

The Arrhenius model is a subset of the peaked model (compare Eqns 16 and 17). Therefore, an F-test was used to determine whether the peaked model gave a significantly better fit to data than the Arrhenius model (Kleinbaum et al. 1998). As others have found, the four-parameter peaked model was often over-parameterized, i.e. there was insufficient data to determine all parameters (Harley et al. 1992; Dreyer et al. 2001). Hence, this model was also fitted under the assumption that Hd = 200 kJ mol−1, and an F-test used to determine whether Hd was significantly different from this value.

Implied temperature response of photosynthesis

We wanted to identify the implications for photosynthesis of differences in the temperature responses of model parameters. To do so, Eqns 1, 2, 3 and 4 were used to calculate a typical temperature response of net photosynthesis from the derived parameter values. This calculation was made by assuming standard ambient environmental conditions for light-saturated photosynthesis: an atmospheric [CO2] concentration of 350 µmol mol−1, a constant Ci : Ca ratio of 0·7, and a value for J of 0·9Jmax. Leaf respiration was modelled for all species using a base rate of 0·01 Vcmax and a Q10 of 2.


Temperature response of Vcmax

Fitted parameters of the temperature response of Vcmax are given in Table 2. In most cases, the peaked function (Eqn 17) with Hd fixed at 200 kJ mol−1 gave a significantly better fit to the data than the Arrhenius function (Eqn 16). In no case, however, did relaxing the constraint on Hd significantly improve the fit to the data. Species for which no peak in the temperature response of Vcmax was discernible were Fraxinus excelsior, Prunus persica, Pinus taeda and Pinus radiata. Note, however, that measurements on P. radiata did not go above 30 °C (Table 1), and that peak values close to 40 °C (maximal measurement temperature) are statistically difficult to estimate (e.g. for F. excelsior); in all cases a peak may well occur above the highest measurement temperature.

Table 2.  Parameters of the temperature response of Vcmax
SpeciesArrhenius modelPeaked model
k25 (µmol m−2 s−1)Ea(kJ mol−1)r2k25 (µmol m−2 s−1)kopt (µmol m−2 s−1)Ha(kJ mol−1)Hd(kJ mol−1)Topt(°C)r2P
  1. Values of k25 and kopt are expressed on a one-sided leaf area basis. Standard deviations of k25 and kopt, and standard errors of other parameters, are given in parentheses. P, probability that the peaked model is not a significantly better fit to the data than the Arrhenius model. OTC, open top chamber experiment; GH, greenhouse experiment; ME, mini-ecosystem experiment.

Glycine max97·76 (9·15)54·08 (3·86)0·8793·89 (8·34)277·50 (24·66) 69·50 (24·37)200·0041·89 (9·92)0·880·05
Gossypium hirsutum91·4893·59 (4·50)1·0090·22399·26116·38200·0040·601·00 
Deciduous trees
Acer pseudoplatanus72·96 (8·66)33·92 (7·19)0·6678·16 (11·01)136·28 (19·20) 75·88 (23·93)200·0034·95 (1·21)0·860·00
Betula pendula OTC85·07 (3·65)37·19 (4·98)0·87101·90 (3·85)114·82 (4·34) 63·75 (11·44)200·0029·28 (0·59)0·970·00
Betula pendula GH68·85 (14·19)50·60 (3·86)0·9469·09 (14·72)177·31 (37·78) 77·02 (18·76)200·0039·20 (3·76)0·970·00
Fagus sylvatica GH60·95 (5·48)41·38 (4·31)0·8963·83 (5·17)133·13 (10·78) 72·36 (15·34)200·0037·36 (0·87)0·970·00
Fagus sylvatica ME27·21 (3·41)46·81 (3·53)0·9227·51 (2·93) 49·25 (5·24) 65·40 (19·48)200·0036·16 (3·63)0·950·00
Fraxinus excelsior77·97 (9·65)50·61 (3·60)0·9378·43 (9·60)235·89 (28·88) 54·58 (13·11)200·0045·52 (36·87)0·930·47
Juglans regia62·10 (10·24)43·98 (6·21)0·8363·98 (10·62)146·39 (24·30)104·58 (23·56)200·0036·05 (0·45)0·970·00
Prunus persica65·50 (3·88)73·74 (3·28)0·9966·16 (3·91)464·59 (27·49) 75·14 (23·38)200·0050·86 (396·99)0·991·00
Quercus petraea79·50 (8·55)56·28 (2·79)0·9879·11 (8·10)244·53 (25·04) 67·72 (9·40)200·0042·77 (6·96)0·990·01
Quercus robur GH89·99 (11·98)55·50 (3·45)0·9689·71 (11·92)295·01 (39·19) 61·77 (13·57)200·0044·87 (25·44)0·960·26
Quercus robur ME40·83 (12·28)46·26 (3·11)0·9742·32 (13·42) 84·97 (26·94) 57·59 (12·22)200·0038·76 (10·69)0·970·06
Evergreen trees
Abies alba41·64 (5·15)35·16 (3·97)0·8643·50 (5·33) 78·11 (9·56) 60·02 (9·88)200·0036·81 (0·65)0·950·00
Eucalyptus pauciflora87·7351·56 (2·09)0·9990·42175·81 60·79 (4·93)200·0037·83 (3·54)1·00 
Pinus pinaster89·98 (5·01)62·22 (2·76)0·9992·42 (4·65)213·30 (10·77) 74·16 (11·17)200·0038·34 (7·36)0·990·01
Pinus radiata fert.97·01 (4·46)49·07 (3·73)0·9699·15 (4·71)174·33 (8·33) 51·32 (19·21)200·0037·74 (152·04)0·960·77
Pinus radiata unfert.83·57 (17·5)61·31 (3·71)0·9885·86 (17·7)171·59 (35·81) 64·78 (21·32)200·0037·68 (125·99)0·980·69
Pinus sylvestris53·99 (7·22)35·53 (5·93)0·8167·33 (9·72) 70·75 (10·21) 69·83 (12·56)200·0027·56 (0·61)0·960·00
Pinus taeda57·05 (9·33)60·88 (3·68)0·9857·66 (9·43)340·45 (55·63) 61·21 (304·11)200·0053·30 (47033)0·981·00

Values of k25, the maximum rate of Rubisco activity at 25 °C, varied across data sets by a factor of three. Some of this variation is probably caused by variations in leaf nitrogen content between data sets. Values were highest for crop species, but were comparable for coniferous and deciduous species. Note that all rates are expressed on a one-sided leaf area basis.

The activation energy Ha was generally in the range 60–80 kJ mol−1, implying a similarity in the temperature responses of Vcmax across data sets. Two data sets had values of Ha slightly below this range (F. excelsior and fertilized P. radiata) whereas another two had values of Ha considerably above this range (Gossypium hirsutum and Juglans regia).

The optimum temperature for Vcmax, Topt, was undetermined for those experiments where the peaked function was not a significantly better fit than the Arrhenius function. Among the other experiments, Topt was generally in the range 35–41 °C, with no clear pattern in the variation, with two exceptions. Betula pendula and Pinus sylvestris, grown in Finland, experienced the lowest growing temperatures and showed significantly lower values of Topt (27–29 °C).

The variability in the temperature response of Vcmax is illustrated in Fig. 2a, which shows the temperature responses normalized to 1 at 25 °C. Most of the temperature responses lie between the two curves shown for Juglans regia and Acer pseudoplatanus. The exceptions are cotton, Gossypium hirsutum, which has a much steeper Vcmax–T response owing to its high value of Ha, and the Finnish plants, B. pendula and P. sylvestris, which have a much lower optimal temperature for Vcmax.

Figure 2.

Sample responses of (a) Vcmax and (b) Jmax to leaf temperature. Values are normalized to 1 at 25 °C.

Temperature response of Jmax

The peaked function (Eqn 17) described the temperature response of Jmax significantly better than the Arrhenius function (Eqn 16) for all experiments other than P. radiata and P. taeda. Parameters for the peaked function are given in Table 3.

Table 3.  Parameters of the temperature response of Jmax
Speciesk25 (µmol m−2 s−1)kopt (µmol m−2 s−1)Ha (kJ mol−1)Hd (kJ mol−1)Topt (°C)r2
  1. Values of k25 and kopt are expressed on a one-sided leaf area basis. Standard deviations of k25 and kopt, and standard errors of other parameters, are given in parentheses. OTC, open top chamber experiment; GH, greenhouse experiment; ME, mini-ecosystem experiment.

Glycine max217·88 (2·89)328·57 (4·35) 88·82 (36·57)113·77 (10·78)38·17 (2·33)0·89
Gossypium hirsutum131·82221·57 77·1720034·441·00
Deciduous trees
Acer pseudoplatanus142·23 (12·37)173·90 (15·12) 44·14 (10·02)20031·96 (1·16)0·82
Betula pendula OTC111·89 (1·48)128·45 (1·70)108·45 (18·29)156·84 (12·60)19·20 (0·70)0·96
Betula pendula GH116·33 (13·21)169·66 (19·27) 42·83 (4·09)20035·77 (0·41)0·98
Fagus sylvatica GH 97·91 (12·31)173·18 (18·20) 48·09 (7·86)20035·24 (0·78)0·95
Fagus sylvatica ME 44·83 (7·50) 51·89 (8·68) 43·36 (12·37)20030·78 (0·65)0·94
Fraxinus excelsior147·03 (18·51)170·10 (21·42) 91·20 (15·20)131·89 (7·58)31·38 (0·62)0·95
Juglans regia103·81 (16·75)165·86 (26·76) 56·30 (8·59)20035·53 (0·60)0·97
Prunus persica106·27 (7·83)154·81 (11·41) 42·04 (8·73)20035·87 (1·56)0·95
Quercus petraea144·01 (12·02)220·75 (18·43) 42·14 (2·99)20036·89 (0·34)0·99
Quercus robur GH139·59 (23·98)212·90 (36·57) 36·92 (7·19)20037·91 (1·29)0·92
Quercus robur ME 66·03 (20·18) 80·75 (24·68) 35·87 (13·52)20032·86 (1·19)0·89
Evergreen trees
Abies alba 95·49 (5·73)128·15 (7·69) 50·82 (8·20)20033·20 (0·78)0·90
Eucalyptus pauciflora141·94175·13 43·7920032·19 
Pinus pinaster154·74 (10·80)220·91 (15·40) 34·83 (9·24)20036·87 (9·34)0·97
Pinus radiata fert.175·43 (14·29)189·66 (15·46) 43·18 (12·41)20029·01 (2·76)0·95
Pinus radiata unfert.136·57 (17·66)145·99 (18·85) 44·14 (16·60)20028·63 (3·21)0·92
Pinus sylvestris 70·77 (2·65)78·36 (2·93)100·28 (17·76)147·92 (10·28)19·89 (0·73)0·96
Pinus taeda 98·54 (14·09)155·76 (22·26) 37·87 (394·31)20038·48 (1213)0·95

Values of the activation energy Ha were in general highest for crop species (80–90 kJ mol−1), intermediate for deciduous species (40–60 kJ mol−1) and lowest for coniferous species (30–40 kJ mol−1). The major exceptions to this pattern were again the cold-climate trees from Finland, B. pendula and P. sylvestris, which both had high values of Ha, and F. excelsior. Values of Hd were significantly less than 200 kJ mol−1 for these three species and for soybean.

The optimal temperature for Jmax is generally in the range 30–38 °C, with no clear pattern among species, with the exception again of the Finnish plants. Betula pendula and P. sylvestris had much lower optimal temperatures for Jmax of about 20 °C.

The variability in the temperature response of Jmax is illustrated in Fig. 2b. The two Finnish species have similar responses, with low optimal temperatures. The other conifers have responses resembling that of P. pinaster, with a relatively low slope owing to low values of Ha. Deciduous tree responses generally lie between those of F. excelsior and F. sylvatica. Crop species responses are steeper again, as illustrated by the G. hirsutum response.

Ratio of Jmax : Vcmax

Figure 3 shows the relationship between values of Jmax and Vcmax at 25 °C. Most of the data points fall close to a straight line with a slope of 1·67. The major exceptions to this pattern are soybean, with a ratio of 2·4, and the two Finnish plants, which both have ratios of about 1. For each experiment, a linear function was fitted to the relationship between the Jmax : Vcmax ratio and leaf temperature. There was a significant negative slope in all cases, ranging from −0·045 to −0·08, highlighting the difference in activation energies for Jmax and Vcmax.

Figure 3.

Relationship between Jmax and Vcmax at 25 °C. Filled symbols: crop species; open symbols: broadleaf species; crosses: coniferous species. Fitted regression line has slope of 1·67.

Implications for the temperature response of light-saturated photosynthesis

The temperature response of photosynthesis was modelled for each data set, under the assumption of a constant Ci : Ca ratio. From the resulting curves, the optimal temperature for photosynthesis and its rate of increase over the range 15–30 °C were calculated, and these are plotted in Figs 4 and 5 against growth temperature. Figure 4 illustrates that for the majority of broadleaf and coniferous trees, the optimal temperature for photosynthesis varies between 23 and 30 °C and is largely unrelated to growth temperature. However, the trees grown in cold conditions in Finland had considerably lower optimal temperatures. The optimal temperatures for the two crop species, which were grown in warm conditions, were comparable to the highest optimal temperatures obtained for the tree species. The rate of increase of photosynthesis between 15 and 30 °C was also similar for most plants in the survey, ranging from 1·2 to 1·6 (Fig. 5). The exceptions were the Finnish trees, again, for which photosynthesis actually decreased over this temperature range, and walnut (J. regia) and cotton (G. hirsutum), which had particularly high rates of increase. From Figs 4 and 5 we can identify three broad classes of implied photosynthetic temperature response (Fig. 6). Most plants had fairly similar responses, falling between those of A. pseudoplatanus and Q. petraea. The two Finnish trees, B. pendula and P. sylvestris, had distinctly different responses, with much lower optimal temperatures. Finally, cotton (and to a lesser extent J. regia) differed in having a much steeper response curve.

Figure 4.

Modelled optimal temperature of light-saturated net photosynthesis plotted against mean temperature in month prior to measurements. Filled symbols: crop species; open symbols: broadleaf species; crosses: coniferous species.

Figure 5.

Modelled ratio of light-saturated net photosynthesis at 30 °C to that at 15 °C, plotted against mean temperature in month prior to measurements. Filled symbols: crop species; open symbols: broadleaf species; crosses: coniferous species.

Figure 6.

Sample responses of modelled leaf photosynthesis to leaf temperature. Values are normalized to 1 at 25 °C.


The aim of this review was to investigate variability in the temperature responses of the model parameters Jmax and Vcmax, with a view to improving parameter choice when modelling photosynthetic processes. The major factors thought to affect these responses are growth temperature and genotype or species (Berry & Björkman 1980). It has also been suggested that nutrition (Martindale & Leegood 1997) and light availability (Niinemets et al. 1999) may play a role.

We found that the temperature responses of Jmax and Vcmax obtained in gas exchange experiments were quite similar across many of the species included in the review (Tables 2 and 3), a promising finding as it potentially simplifies parameter choice. Parameter values obtained by alternative means (in vitro, chlorophyll fluorescence) are included for comparison in Table 4, and generally fall within the range of values reported in Tables 2 and 3. Responses of coniferous and broadleaf trees were broadly similar, with only a slight trend for lower Ha of Jmax in conifers. However, the responses of the two crop species, particularly cotton, differed from tree species in several aspects including activation energies of both Jmax and Vcmax and the ratio of Jmax : Vcmax at 25 °C, suggesting that alternative parameter sets are required for modelling these two plant types. This result needs to be clarified by expansion of the database on herbaceous species and crops, however.

Table 4.  Comparable parameter values obtained by other methods
  • 1

    in vitro;

  • 2

    in vivo measurements with transgenic low-Rubisco plants;

  • 3

    3 chlorophyll fluorescence.

58·52  Atriplex glabriscula,
 purified Rubisco
Badger & Collatz (1977)1
65·33  transgenic Nicotiana tabacumBernacchi et al. (2001)2
65·01179·233·7Populus tremula, intact leavesNiinemets et al. (1999)3
54·97325·540·3Tilia cordata, intact leavesNiinemets et al. (1999)3
3722031barley chloroplastsNolan & Smillie (1976)1

It is not possible to draw inferences about acclimation of photosynthesis to growing conditions from such a diverse set of studies, because several alternative explanations are possible for any observed differences, such as differences in experimental protocol or genotypic differences. Nevertheless some interesting comparisons can be made which can serve as a preliminary basis for generalizations about temperature responses in different environments.

For example, we can compare studies on the same species growing in different environmental conditions. Both Fagus sylvatica and Quercus robur were the subject of two different studies, one with seedlings growing individually in pots and one with seedlings growing densely in mini-ecosystems. Low foliar nitrogen in the mini-ecosystem studies led to low values of k25 for both Jmax and Vcmax. The relative temperature response of Vcmax was unchanged, but Topt of Jmax was lower in the mini-ecosystem experiment. This result parallels that of Niinemets et al. (1999) who found that the temperature optimum of Jmax was positively correlated with light availability and suggested that the correlation was a result of photosynthetic acclimation to microclimate.

There was generally a poor relationship between parameter values and growth temperature, with the clear exception of the lowest-temperature-grown plants, B. pendula and P. sylvestris, which had distinctly different temperature responses compared to plants of the same genus grown in temperate climates. The low-temperature-grown plants had low optimal temperatures for both Jmax and Vcmax, and low Jmax : Vcmax ratios. Although not completely comparable, a study on alpine grasses growing in low temperature environments (Wohlfahrt et al. 1999) does not show such dramatic differences in the temperature optima of Jmax and Vcmax. Further research is required to clearly establish the effects of growth in a cold climate on the temperature responses of Jmax and Vcmax. No data were available for tropical species; it would be interesting to see how optimal temperatures for such species compare with those reported here.

Another key requirement for future research highlighted by this study is the need for more information on the temperature dependence of Kc and Ko, the Michaelis–Menten coefficients for Rubisco activity. We have illustrated the fact that values of Vcmax derived from gas exchange data depend strongly on the assumed values of Kc and Ko and hence are not readily comparable between studies. In the absence of a clear resolution of the temperature dependence of these parameters, it is important, particularly when modelling, to ensure that parameter sets are consistent (Medlyn et al. 1999).

It should be noted that photosynthetic rates are determined not only by biochemical processes, but also by stomatal conductance to CO2. In this study we have omitted to consider the effects on photosynthesis of possible acclimation of stomatal conductance to temperature. (Figs 4–6 were constructed assuming a constant Ci : Ca ratio.) In the companion paper (Medlyn, Loustau & Delzon 2002), we showed that changes in stomatal conductance could contribute considerably to photosynthetic temperature acclimation. A similar result was found by Ferrar, Slatyer & Vranjic (1989) for Eucalyptus species and Ellsworth (2000) for Pinus taeda. Berry & Björkman (1980) suggested stomatal acclimation to temperature was uncommon but also noted that information on this topic was scarce. Even without acclimation, photosynthetic rates at ambient CO2 concentration at optimum temperature, and the temperature of optimum photosynthesis itself, can be strongly affected by stomatal responses to temperature and water vapour pressure deficits (Kirschbaum & Farquhar 1984). Hence, even with identical photosynthetic parameters, leaves can have different photosynthetic rates under ambient conditions due to different stomatal conductances caused by internal (e.g. water stress) or external (e.g. water vapour pressure deficits) factors. It has also been suggested that changes in the temperature response of cell-wall conductance may be a factor in temperature acclimation (Makino et al. 1994). We were unable to evaluate this possibility owing to lack of data.


The primary aim of this review of the temperature responses of model parameters Jmax and Vcmax was to highlight variability in these responses among species and growth environments in order to improve parameter choice when modelling temperature effects on photosynthesis and growth. In general, it was found that parameters for crop species, temperate trees, and boreal trees, fell into three distinct groups (see Tables 2 and 3), suggesting that modellers should use a set of parameters from the appropriate group. The limited data analysed here also revealed differences in photosynthetic temperature response parameters among growth environments, suggesting that equations should be chosen, where possible, to be appropriate for given radiation and temperature conditions. However, to better model temperature responses, a greater understanding of the functional significance of differences among broad plant types and growth environments is needed, which will require more careful experimental comparisons of within- versus among-species variation in temperature response parameters.


B.M. acknowledges financial support from the French Institut National de la Recherche Agronomique and the Australian Research Council. D.E. was supported by funds from the US Department of Energy, Office of Biological and Environmental Research under the Forest-Atmosphere Carbon Transfer and Storage (FACTS) project. We thank Georg Wohlfahrt for helpful discussion and Michael Battaglia for insightful comments on the manuscript.