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

Abstract

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 (V_cmax) and the potential rate of electron transport (J_max). Original data sets were used for this review, as it is shown that derived values of V_cmax and its temperature response depend strongly on assumptions made in derivation. Values of J_max and V_cmax at 25 °C varied considerably among species but were strongly correlated, with an average J_max : V_cmax ratio of 1·67. Two species grown in cold climates, however, had lower ratios. In all studies, the J_max : V_cmax ratio declined strongly with measurement temperature. The relative temperature responses of J_max and V_cmax were relatively constant among tree species. Activation energies averaged 50 kJ mol⁻¹ for J_max and 65 kJ mol⁻¹ for V_cmax, and for most species temperature optima averaged 33 °C for J_max and 40 °C for V_cmax. However, the cold climate tree species had low temperature optima for both J_max(19 °C) and V_cmax (29 °C), suggesting acclimation of both processes to growth temperature. Crop species had somewhat different temperature responses, with higher activation energies for both J_max and V_cmax, 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.

Introduction

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 (J_max) and the maximum rate of ribulose‐1,5‐bisphosphate carboxylase‐oxygenase (Rubisco) activity (V_cmax). There is now a large database of values of J_max and V_cmax (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 J_max and V_cmax (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 J_max and V_cmax by deriving all parameter values himself directly from A–C_i 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.

Methods

Data

Estimates of the parameters J_max and V_cmax 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 J_max and V_cmax are obtained from the response of photosynthesis under high light (A) to intercellular CO₂ (C_i). A family of A–C_i curves at different temperatures will thus give the temperature response of the two parameters J_max and V_cmax. Obtaining such a family of curves is very time‐consuming and hence several authors have attempted to estimate the temperature responses of J_max and V_cmax 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 A–C_i 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 A–C_i 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

Species	Common name	Author	Measurement T	Plants	Points	Growth T	Growth conditions	Age of plants	Notes
Crops
Glycine max	Soybean	Harley, Weber & Gates  (1985)	20,25,30,35,40	3	48	25	GH – T	seedlings	O2 varied also
Gossypium hirsutum	Cotton	Harley et al. (1992)	18,26,29,35	2		29	GH – T	seedlings	Raw data  unavailable
Deciduous trees
Acer pseudoplatanus	Sycamore	Dreyer et al. (2001)	10,18,25,32,36,40	5	28	16	N (France)	seedlings
Betula pendula	Silver birch	Wang (unpub.)	5,10,22,26,32	4	20	14	OTC (Finland)	seedlings
Betula pendula	Silver birch	Dreyer et al. (2001)	10,18,25,32,40	5	25	17	N (France)	seedlings
Fagus sylvatica	Common beech	Dreyer et al. (2001)	10,18,25,32,40	5	25	17	N (France)	seedlings
Fagus sylvatica	Common beech	Strassemeyer & Forstreuter  (1997)	19,23,26,30,35	7	28	20	ME (Germany)	seedlings
Fraxinus excelsior	Ash	Dreyer et al. (2001)	10,18,25,32,36,40	5	30	16	N (France)	seedlings
Juglans regia	Walnut	Dreyer et al. (2001)	10,18,25,32,40	5	25	17	N (France)	seedlings
Prunus persica	Peach	Walcroft et al. (2002)	10,20,25,32,37	5	19	19	GH (France)	2 year
Quercus petraea	Sessile oak	Dreyer et al. (2001)	10,18,25,32,36,40	5	25	16	N (France)	seedlings
Quercus robur	English oak	Dreyer et al. (2001)	10,18,25,32,36,40	5	30	16	N (France)	seedlings
Quercus robur	English oak	Strassemeyer & Forstreuter  (unpub.)	15,21,26,30,36	8	29	20	ME (Germany)	seedlings
Evergreen trees
Abies alba	Silver fir	Robakowski et al. (2002)	10,18,26,32,36,40	5	28	25	N (France)	seedlings
Eucalyptus pauciflora	Snowgum	Kirschbaum & Farquhar  (1984)	15–35	1		20	GH – T	seedlings	Raw data  unavailable
Pinus pinaster	Maritime pine	Medlyn et al. (2002)	15,20,25,30,35	6	27	24	field (France)	30 year	Local provenance,  August
Pinus radiata	Radiata pine	Walcroft et al. (1997)	8,15,20,25,30	3	14	24	GH (NZ)	seedlings	Two fertilization  treatments
Pinus sylvestris	Scots pine	Wang, Kellomaki &Laitinen  (1996)	6,11,21,26,31	4	18	14	OTC (Finland)	20–25 year
Pinus taeda	Loblolly pine	Ellsworth & Klimas  (submitted)	15,28,35	5	14	24	FACE (N. Carolina)	12 year	June and August  combined

• 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).

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.

Model

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

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

(1)

A _c is the rate of photosynthesis when Rubisco activity is limiting and A_j the rate when ribulose‐1,5‐bisphosphate (RuBP)‐regeneration is limiting. R_d is the rate of mitochondrial respiration. Rubisco‐limited photosynthesis is given by:

(2)

where V_cmax is the maximum rate of Rubisco activity, C_i and O_i are the intercellular concentrations of CO₂ and O₂, respectively, K_c and K_o 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:

(3)

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

(4)

where J_max 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 J_max.

The key parameters of the model, which vary among species, are J_max and V_cmax. It is the temperature dependences of these parameters that we set out to examine. In addition, it is known that the parameters K_c, K_o 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 K_c, K_o, andΓ*

The in‐vivo temperature dependence of the Michaelis–Menten coefficients of Rubisco, K_c (mmol mol^‐1) and K_o (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:

(5)

(6)

T _k 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):

(7)

(8)

(9)

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):

(10)

(11)

Figure 1a illustrates the temperature dependence of the effective Michaelis–Menten coefficient for CO₂, K_m = K_c(1 + O_i/K_o), 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 K_m = K_c(1 + O_i/K_o) to leaf temperature. (b) Alternative forms for the response of Γ* to leaf temperature. (c) Response of V_cmax to leaf temperature obtained by fitting a sample data set using alternative forms for K_m. (d) Response of ratio J_max : V_cmax to leaf temperature obtained by fitting a sample data set using alternative forms for K_m. 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:

(12)

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 K_c and K_o and to the maximum oxygenation activity of Rubisco, V_omax(Farquhar et al. 1980):

(13)

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

(14)

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:

(15)

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 J_max and V_cmax. We found that the parameter J_max was only very slightly sensitive to the formulation of either K_m or Γ* (not shown). However, the parameter V_cmax was highly sensitive to the formulation of K_m chosen (Fig. 1c). The ratio of J_max: V_cmax was thus also highly sensitive to K_m (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 A–C_i 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 J_max and V_cmax presented below, it is important to also use the Bernacchi et al. (2001) temperature dependences for K_c, K_o and Γ*, because of the sensitivity of the model to these functions illustrated in Fig. 1.

T‐dependence of J_maxand V_cmax

On reviewing the literature, it is daunting to observe the number of alternative functions that have been used to model the temperature dependences of J_max and V_cmax (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:

(16)

which has parameters k₂₅ (the value at 25 °C) and E_a (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:

(17)

(18)

The first form has parameters k₂₅, H_a, H_d and ΔS, whereas the second form has parameters k_opt, H_a, H_d and T_opt. H_a and H_d are the same between the two forms, whereas ΔS and T_opt are related by:

(19)

The parameters can be interpreted as follows: k₂₅ and k_opt are the values of J_max or V_cmax at temperatures 25 °C and T_opt, respectively; H_a gives the rate of exponential increase of the function below the optimum (and is analogous to parameter E_a in the Arrhenius function); H_d describes the rate of decrease of the function above the optimum; and T_opt 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 J_max and V_cmax for each individual A–C_i 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 R_d 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 J_max and V_cmax to leaf temperature, using SigmaPlot (SPSS Inc. Chicago, IL, USA). It was assumed that J_max and V_cmax 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 l_i to represent each leaf and putting:

(20)

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

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 H_d = 200 kJ mol⁻¹, and an F‐test used to determine whether H_d 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 C_i : C_a ratio of 0·7, and a value for J of 0·9J_max. Leaf respiration was modelled for all species using a base rate of 0·01 V_cmax and a Q₁₀ of 2.

Results

Temperature response of V_cmax

Fitted parameters of the temperature response of V_cmax are given in Table 2. In most cases, the peaked function (Eqn 17) with H_d 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 H_d significantly improve the fit to the data. Species for which no peak in the temperature response of V_cmax 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 V_cmax

Species	Arrhenius model			Peaked model
	k 25 (µmol m^−2 s^−1)	E a (kJ mol^−1)	r ^2	k 25 (µmol m^−2 s^−1)	k opt (µmol m^−2 s^−1)	H a (kJ mol^−1)	H d (kJ mol^−1)	T opt (°C)	r ^2	P
Crops
Glycine max	97·76 (9·15)	54·08 (3·86)	0·87	93·89 (8·34)	277·50 (24·66)	69·50 (24·37)	200·00	41·89 (9·92)	0·88	0·05
Gossypium hirsutum	91·48	93·59 (4·50)	1·00	90·22	399·26	116·38	200·00	40·60	1·00
Deciduous trees
Acer pseudoplatanus	72·96 (8·66)	33·92 (7·19)	0·66	78·16 (11·01)	136·28 (19·20)	75·88 (23·93)	200·00	34·95 (1·21)	0·86	0·00
Betula pendula OTC	85·07 (3·65)	37·19 (4·98)	0·87	101·90 (3·85)	114·82 (4·34)	63·75 (11·44)	200·00	29·28 (0·59)	0·97	0·00
Betula pendula GH	68·85 (14·19)	50·60 (3·86)	0·94	69·09 (14·72)	177·31 (37·78)	77·02 (18·76)	200·00	39·20 (3·76)	0·97	0·00
Fagus sylvatica GH	60·95 (5·48)	41·38 (4·31)	0·89	63·83 (5·17)	133·13 (10·78)	72·36 (15·34)	200·00	37·36 (0·87)	0·97	0·00
Fagus sylvatica ME	27·21 (3·41)	46·81 (3·53)	0·92	27·51 (2·93)	49·25 (5·24)	65·40 (19·48)	200·00	36·16 (3·63)	0·95	0·00
Fraxinus excelsior	77·97 (9·65)	50·61 (3·60)	0·93	78·43 (9·60)	235·89 (28·88)	54·58 (13·11)	200·00	45·52 (36·87)	0·93	0·47
Juglans regia	62·10 (10·24)	43·98 (6·21)	0·83	63·98 (10·62)	146·39 (24·30)	104·58 (23·56)	200·00	36·05 (0·45)	0·97	0·00
Prunus persica	65·50 (3·88)	73·74 (3·28)	0·99	66·16 (3·91)	464·59 (27·49)	75·14 (23·38)	200·00	50·86 (396·99)	0·99	1·00
Quercus petraea	79·50 (8·55)	56·28 (2·79)	0·98	79·11 (8·10)	244·53 (25·04)	67·72 (9·40)	200·00	42·77 (6·96)	0·99	0·01
Quercus robur GH	89·99 (11·98)	55·50 (3·45)	0·96	89·71 (11·92)	295·01 (39·19)	61·77 (13·57)	200·00	44·87 (25·44)	0·96	0·26
Quercus robur ME	40·83 (12·28)	46·26 (3·11)	0·97	42·32 (13·42)	84·97 (26·94)	57·59 (12·22)	200·00	38·76 (10·69)	0·97	0·06
Evergreen trees
Abies alba	41·64 (5·15)	35·16 (3·97)	0·86	43·50 (5·33)	78·11 (9·56)	60·02 (9·88)	200·00	36·81 (0·65)	0·95	0·00
Eucalyptus pauciflora	87·73	51·56 (2·09)	0·99	90·42	175·81	60·79 (4·93)	200·00	37·83 (3·54)	1·00
Pinus pinaster	89·98 (5·01)	62·22 (2·76)	0·99	92·42 (4·65)	213·30 (10·77)	74·16 (11·17)	200·00	38·34 (7·36)	0·99	0·01
Pinus radiata fert.	97·01 (4·46)	49·07 (3·73)	0·96	99·15 (4·71)	174·33 (8·33)	51·32 (19·21)	200·00	37·74 (152·04)	0·96	0·77
Pinus radiata unfert.	83·57 (17·5)	61·31 (3·71)	0·98	85·86 (17·7)	171·59 (35·81)	64·78 (21·32)	200·00	37·68 (125·99)	0·98	0·69
Pinus sylvestris	53·99 (7·22)	35·53 (5·93)	0·81	67·33 (9·72)	70·75 (10·21)	69·83 (12·56)	200·00	27·56 (0·61)	0·96	0·00
Pinus taeda	57·05 (9·33)	60·88 (3·68)	0·98	57·66 (9·43)	340·45 (55·63)	61·21 (304·11)	200·00	53·30 (47033)	0·98	1·00

• Values of k₂₅ and k_opt are expressed on a one‐sided leaf area basis. Standard deviations of k₂₅ and k_opt, 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.

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

The optimum temperature for V_cmax, T_opt, was undetermined for those experiments where the peaked function was not a significantly better fit than the Arrhenius function. Among the other experiments, T_opt 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 T_opt (27–29 °C).

The variability in the temperature response of V_cmax 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 V_cmax–T response owing to its high value of H_a, and the Finnish plants, B. pendula and P. sylvestris, which have a much lower optimal temperature for V_cmax.

Figure 2

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

Temperature response of J_max

The peaked function (Eqn 17) described the temperature response of J_max 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 J_max

Species	k 25 (µmol m^−2 s^−1)	k opt (µmol m^−2 s^−1)	H a (kJ mol^−1)	H d (kJ mol^−1)	T opt (°C)	r^2
Crops
Glycine max	217·88 (2·89)	328·57 (4·35)	88·82 (36·57)	113·77 (10·78)	38·17 (2·33)	0·89
Gossypium hirsutum	131·82	221·57	77·17	200	34·44	1·00
Deciduous trees
Acer pseudoplatanus	142·23 (12·37)	173·90 (15·12)	44·14 (10·02)	200	31·96 (1·16)	0·82
Betula pendula OTC	111·89 (1·48)	128·45 (1·70)	108·45 (18·29)	156·84 (12·60)	19·20 (0·70)	0·96
Betula pendula GH	116·33 (13·21)	169·66 (19·27)	42·83 (4·09)	200	35·77 (0·41)	0·98
Fagus sylvatica GH	97·91 (12·31)	173·18 (18·20)	48·09 (7·86)	200	35·24 (0·78)	0·95
Fagus sylvatica ME	44·83 (7·50)	51·89 (8·68)	43·36 (12·37)	200	30·78 (0·65)	0·94
Fraxinus excelsior	147·03 (18·51)	170·10 (21·42)	91·20 (15·20)	131·89 (7·58)	31·38 (0·62)	0·95
Juglans regia	103·81 (16·75)	165·86 (26·76)	56·30 (8·59)	200	35·53 (0·60)	0·97
Prunus persica	106·27 (7·83)	154·81 (11·41)	42·04 (8·73)	200	35·87 (1·56)	0·95
Quercus petraea	144·01 (12·02)	220·75 (18·43)	42·14 (2·99)	200	36·89 (0·34)	0·99
Quercus robur GH	139·59 (23·98)	212·90 (36·57)	36·92 (7·19)	200	37·91 (1·29)	0·92
Quercus robur ME	66·03 (20·18)	80·75 (24·68)	35·87 (13·52)	200	32·86 (1·19)	0·89
Evergreen trees
Abies alba	95·49 (5·73)	128·15 (7·69)	50·82 (8·20)	200	33·20 (0·78)	0·90
Eucalyptus pauciflora	141·94	175·13	43·79	200	32·19
Pinus pinaster	154·74 (10·80)	220·91 (15·40)	34·83 (9·24)	200	36·87 (9·34)	0·97
Pinus radiata fert.	175·43 (14·29)	189·66 (15·46)	43·18 (12·41)	200	29·01 (2·76)	0·95
Pinus radiata unfert.	136·57 (17·66)	145·99 (18·85)	44·14 (16·60)	200	28·63 (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)	200	38·48 (1213)	0·95

• Values of k₂₅ and k_opt are expressed on a one‐sided leaf area basis. Standard deviations of k₂₅ and k_opt, and standard errors of other parameters, are given in parentheses. OTC, open top chamber experiment; GH, greenhouse experiment; ME, mini‐ecosystem experiment.

Values of the activation energy H_a 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 H_a, and F. excelsior. Values of H_d were significantly less than 200 kJ mol⁻¹ for these three species and for soybean.

The optimal temperature for J_max 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 J_max of about 20 °C.

The variability in the temperature response of J_max 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 H_a. 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 J_max : V_cmax

Figure 3 shows the relationship between values of J_max and V_cmax 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 J_max : V_cmax 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 J_max and V_cmax.

Figure 3

Relationship between J_max and V_cmax 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 C_i : C_a 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.

Discussion

The aim of this review was to investigate variability in the temperature responses of the model parameters J_max and V_cmax, 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 J_max and V_cmax 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 H_a of J_max in conifers. However, the responses of the two crop species, particularly cotton, differed from tree species in several aspects including activation energies of both J_max and V_cmax and the ratio of J_max : V_cmax 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

Parameter values			Material	Authors
V cmax
E a
58·52			Atriplex glabriscula,  purified Rubisco	Badger & Collatz (1977)^1
65·33			transgenic Nicotiana tabacum	Bernacchi et al. (2001)^2
J max
H a	H d	T opt
65·01	179·2	33·7	Populus tremula, intact leaves	Niinemets et al. (1999)^3
54·97	325·5	40·3	Tilia cordata, intact leaves	Niinemets et al. (1999)^3
37	220	31	barley chloroplasts	Nolan & Smillie (1976)^1

• ¹ in vitro;
• ² in vivo measurements with transgenic low‐Rubisco plants;
• 3 ³ chlorophyll fluorescence.

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 J_max and V_cmax. The relative temperature response of V_cmax was unchanged, but T_opt of J_max was lower in the mini‐ecosystem experiment. This result parallels that of Niinemets et al. (1999) who found that the temperature optimum of J_max 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 J_max and V_cmax, and low J_max : V_cmax 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 J_max and V_cmax. Further research is required to clearly establish the effects of growth in a cold climate on the temperature responses of J_max and V_cmax. 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 K_c and K_o, the Michaelis–Menten coefficients for Rubisco activity. We have illustrated the fact that values of V_cmax derived from gas exchange data depend strongly on the assumed values of K_c and K_o 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 C_i : C_a 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.

Conclusion

The primary aim of this review of the temperature responses of model parameters J_max and V_cmax 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.

Acknowledgments

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.