Impact of plant type and growth environment on individually fitted parameters
An impact of plant type on individually fitted parameters was only apparent in case of the base rates Vcmax25 and Jmax25, as the average values of broadleaved and coniferous plants were about half the average of herbaceous plants (Fig. 2a,b), and for the activation energy, Ha, of Vcmax. In the latter case, two herbaceous outliers to high values could be observed (Fig. 2c). An impact of controlled versus natural growth environment was not observed.
Figure 2. Parameter values of individually fitted functions to characterize the temperature dependence of Vcmax (a,c,e,g) and Jmax (b,d,f,h) in relation to plant growth temperature: (a,b) standard values at 25 °C; (c,d) activation energy (Ha); (e,f) entropy term (ΔS); (g,h) optimum temperature (Topt). Open symbols: plants grown in glasshouses with controlled temperature; closed symbols: plants grown at naturally variable temperature regimes. Linear regressions are shown in dashed lines and are based on all points except when pretreated (rectangles) and those shown in grey [(a,c,e,g): points excluded with optimum temperature above 50 °C; (b,d,h): points excluded with optimum temperature below 20 °C].
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Impact of plant growth temperature on individually fitted parameters
The individually fitted values for Vcmax25 and Jmax25 varied by a factor of five to six, but did not show any impact of plant growth temperature. The slopes of their temperature acclimation functions (Eqn 4) were slightly positive, but not significantly, as the slope's 95% confidence interval (twice SE) included zero (Fig. 2a,b, Table 3).
Table 3. Results of linear regression of the form y = a + bx of parameter values (y-value) against growth temperature, (x-value, tgrowth) and mean values of parameters [‘mean(y)’]
|tgrowth||Vcmax25||11.0||29.0||44|| || ||48.48||29.1||2.78||1.53||0.072|
|tgrowth||Jmax25||11.0||35.0||31|| || ||105.77||22.6||0.29||1.18||0.011|
|tgrowth||Ha(Vcmax)||11.0||29.0||38||71 513||3347||82 992||11 360||−632||598||0.030|
|tgrowth||Ha(Jmax)||11.0||35.0||24||49 884||2448||53 032||7509||−190||390.2||0.010|
The activation energy, Ha, of Vcmax varied from 45 to 90 kJ mol−1 with three outliers above 100 kJ mol−1, and an average of 72 ± 3.3 kJ mol−1 (SE, with an SD of 21 kJ mol−1, see Fig. 2c). The activation energy of Jmax varied between 35 and 108 kJ mol−1, an average of 50 ± 2.4 kJ mol−1 and an SD of 15 kJ mol−1 (Fig. 2d). The slopes of the temperature acclimation functions were slightly negative, but this was again not significant (Table 3). This result was independent of the choice of data, either including or excluding outliers or pretreatment.
The temperature acclimation functions of the entropy terms, ΔS, had negative slopes, −1.07 ± 0.19 J mol−1 K−2 for Vcmax and −0.75 ± 0.21 J mol−1 K−2 for Jmax, with an intercept of 668 ± 3.6 and 660 ± 4.1 J mol−1 K−1, respectively (Fig. 2e,f; Table 3). Plants exposed to pretreatment consistently showed a lower ΔS than the respective average without pretreatment (Fig. 2e,f). Assuming a growth temperature of 40 °C, however, which was the temperature during pretreatment which was followed by measurement at 40 °C, would bring them into much better agreement with the other data. The two outliers to lower ΔS in Fig. 2e are related to the data sets with Topt above 50 °C, which had been excluded from the regression analysis of temperature acclimation.
The optimum temperature, Topt, increased by 0.44 ± 0.08 °C for Vcmax and 0.33 ± 0.09 °C for Jmax per 1 °C increase of growth temperature with an intercept of 24.9 ± 1.6 and 26.2 ± 1.7 °C, respectively (Fig. 2g,h; Table 3). As already stated, cases with Topt higher than 50 °C (Pinus taeda, Prunus persica) or Topt less than 20 °C (Betula pendula OTC, Pinus sylvestris) were excluded from the regression analysis of temperature acclimation. Including those data would have amplified the observed degree of acclimation of Topt to growth temperature. The impact of growth temperature on Topt in our analysis was caused solely by its effect on ΔS, because Hd was fixed and growth temperature had no significant impact on the activation energy Ha. The Topt of all pretreated plants was above the respective average of plants without pretreatment. Again, assuming a growth temperature of 40 °C, the temperature during pretreatment before measurement at 40 °C would bring those data into much better agreement with the other data.
The optimum temperatures of Vcmax and Jmax were positively correlated, with an r2 of 0.26 (Fig. 3b). Including the data with pretreatment would increase r2 to 0.49. This confirms a close coregulation of RuBP carboxylation-limited photosynthesis and RuBP regeneration-limited photosynthesis, even for pretreated plants.
Figure 3. (a) Individually fitted values of the ratio Jmax/Vcmax at standard leaf temperature of 25 °C (Jmax25/Vcmax25 = rJ,V) against growth temperature. (b) Individually fitted optimum temperature of Jmax against Vcmax. (c) Jmax against Vcmax at 25 °C leaf temperature but individual growth temperature. (d) Jmax against Vcmax at 25 °C leaf temperature extrapolated to 25 °C growth temperature using the linear regression shown in (a). Open symbols: plant growth temperature > 18 °C; closed symbols: plant growth temperature < 18 °C. Linear regressions are shown in dashed lines and are based on all points except when pretreated (rectangles) and those shown in grey [(b): points excluded with optimum temperature above 50 °C; (a–d): points excluded with optimum temperature below 20 °C].
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The ratio of Jmax25 to Vcmax25, rJ,V, depended on plant growth temperature with an intercept of 2.59 ± 0.17 and a slope of −0.035 ± 0.009 K−1 (Fig. 3a; Table 3). Without correction for different growth temperatures, Jmax25 and Vcmax25 were correlated with r2 = 0.81, and an average ratio of 1.97 ± 0.07 (Table 2; Fig. 3c). After correction to a common growth temperature of 25 °C, r2 increased to 0.88, while the average ratio decreased to 1.71 ± 0.05 (Fig. 3d). The rJ,V values of pretreated plants are all well below the regression line (Fig. 3a): these plants had grown at 16 °C and 17 °C respectively but they had been pretreated for 1 d at 25 °C before measurement at 25 °C was conducted and may already have acclimated to that temperature, at least to some extent. Assuming a growth temperature of 25 °C, however, would again bring them mostly in line with the other data, in analogy to what was observed for the acclimation of ΔS and Topt. Two data sets showed an exceptionally low value of rJ,V: B. pendula OTC (1.05) and P. sylvestris (1.10) (Fig. 3a). This was caused by their extremely low optimum temperature of Jmax below 25 °C, while the optimum temperature of Vcmax was within the average range and above 25 °C (Fig. 3b). In all other cases, the optimum temperatures of both Vcmax and Jmax were above 25 °C. Therefore, the relationship of Jmax25 to Vcmax25 seemed to be ‘decoupled’ in these two cases, and they were hence excluded from the regression analysis of temperature acclimation.
Proposed models with and without acclimation to plant growth temperature
The proposed general model without temperature acclimation is given by Eqn 1 using the following parameter values with uncertainties (averages of the compilation and one SE): 1.97 ± 0.07 for rJ,V, 72 ± 3.3 kJ mol−1 for Ha and 649 ± 1.43 J mol−1 K−1 for ΔS of Vcmax, 50 ± 2.4 kJ mol−1 for Ha and 646 ± 1.66 J mol−1 K−1 for ΔS of Jmax (Table 3).
For the general model with temperature acclimation, we propose to include a temperature acclimation of ΔS for Vcmax and Jmax and a temperature acclimation of rJ,V, resulting in the following equations:
The base rate, Vcmax25, still needs to be specified according to species and nutrition, while the activation energy, Ha, is derived as the average from the compilation and is the same as for the model with and without temperature acclimation (72 ± 3.3 kJ mol−1 for Vcmax and 50 ± 2.4 kJ mol−1 for Jmax). The values, a and b, of the temperature regression parameters can be found in Table 3, and the deactivation energy, Hd, is fixed at 200 kJ mol−1.
To evaluate the derived general models with and without temperature acclimation, we compare them against the individually fitted functions, using the RMSE (RMSEV and RMSEJ) as described by Eqns 6 and 8. The individually fitted functions describing Vcmax, fi(Tl), show small relative variations below 25 °C and high relative variations above 25 °C (Fig. 4a). Therefore, RMSEV against the general normalized temperature function without acclimation is small below 25 °C and large above 25 °C (Fig. 4c). Including the temperature acclimation of ΔS (Table 3; Eqn 9) had almost no impact on the temperature dependence of Vcmax below 25 °C, but the optimum of Vcmax was shifted to higher temperatures and higher values with increasing plant growth temperatures (Fig. 4e). Accordingly, the temperature acclimation of ΔS did not affect the RMSEV range below 25 °C, but reduced RMSEV by up to 25% at temperatures above 25 °C, depending on leaf temperature (Fig. 4g).
Figure 4. Temperature functions of Vcmax (a,c,e) and Jmax (b,d,f), and root mean square error (RMSE) of general temperature functions against the individually fitted functions (g,h). All curves have been normalized by dividing by the value of Vcmax at 25 °C, such that Vcmax at 25 °C appears as 1 and Jmax at 25 °C appears as the ratio of Jmax25/Vcmax25. (a) Individually fitted temperature functions for Vcmax for those data sets which had been used to derive the average models (solid lines). Temperature functions of Prunus persica (dashed) and Pinus taeda (dotted) with Topt > 50 °C. (b) Same for Jmax (solid lines), with results for Betula pendula OTC (dashed) and Pinus sylvestris (dotted) with Topt < 20 °C. (c) General normalized temperature function without temperature acclimation for Vcmax ± RMSE against the individually fitted functions. (d) The same for Jmax. (e) General normalized temperature functions with temperature acclimation for Vcmax for plant growth temperatures of 10, 15, 20, 25, 30 °C. (f) Same for Jmax. (g) RMSE for general normalized temperature function with and without temperature acclimation of Vcmax against individual fits. (h) Same for Jmax.
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For Jmax, we show the temperature function rJ,Vg(Tl), which assumes the value of Jmax25/Vcmax25 at 25 °C. This ratio varies among the different temperature functions fitted to the individual data sets. As a consequence, the variability between individually fitted functions is relatively high for the whole range of leaf temperatures (Fig. 4b), and RMSEJ against the general normalized temperature function without acclimation is relatively constant (Fig. 4d). Jmax normalized to 1 at 25 °C would show a variability similar to Vcmax. If the general model includes the temperature acclimation of ΔS and rJ,V (Table 3; Eqn 10), the optimum of Jmax is shifted to higher temperatures with increasing plant growth temperature, but almost constant optimum values (Fig. 4f). Including the temperature acclimation generally reduces the RMSEJ compared to no acclimation for a wide range of leaf temperatures (Fig. 4h).
Impact of temperature acclimation on modelled photosynthesis
Figure 5 presents the impact of the temperature acclimation of Vcmax and Jmax on modelled light-saturated RuBP carboxylation-limited photosynthesis (AC) and RuBP regeneration-limited photosynthesis (AJ), using the general model with temperature acclimation. Increasing plant growth temperature from 10 to 25 °C shifts the optimum temperature of AC from about 23 to 29 °C, and the optimum temperature of AJ from about 29 to 33 °C. These results are in good agreement with the optimum temperatures of photosynthesis published by Medlyn et al. (2002a). Maximum values of AC increase, while maximum values of AJ decrease. Both AC and AJ at low leaf temperatures are higher for plants grown at 10 °C compared to those grown at 25 °C. For growth temperatures of 10 °C, photosynthesis at light saturation would be limited by AC at all leaf temperatures, while for a growth temperature of 25 °C, AJ would limit light-saturated photosynthesis at leaf temperatures below 25 °C.
Figure 5. Impact of temperature acclimation on modelled photosynthesis. (a) Light-saturated ribulose-1,5-bisphosphate (RuBP) carboxylation (AC) and RuBP regeneration (AJ) at intercellular CO2 concentration (Ci) of 315 ppm (photosynthetically active irradiance = 1500 µmol m−2 s−1, Vcmax25 = 60 µmol m−2 s−1). (b) Same as (a) but for Ci of 500 ppm. (c) The ratio of modelled photosynthesis of plants grown at 10 and 25 °C to plants grown at 17 °C for Ci = 315 µmol mol−1.
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The overall effect of acclimation on gross photosynthesis is summarized in Fig. 5c: plants grown at 10 °C would profit by about 10% at leaf temperatures below 25 °C compared to plants grown at 17 °C, while above 25 °C, modelled photosynthesis would become less effective. Plants grown at 25 °C would have less effective photosynthesis below 25 °C compared to plants grown at 17 °C, but above 25 °C photosynthesis would be strongly enhanced, up to as much as 100% at 40 °C. Figure 5b shows the combined impact of temperature acclimation and elevated CO2 on modelled photosynthesis, disregarding the possibility of some CO2 acclimation happening: AJ would become more limiting, especially for plants grown at high temperatures.
We find that within the relevant ranges of leaf temperature, light-saturated photosynthesis was mostly limited by AC. The observed temperature acclimation shifted the rates of AC at optimum temperature to higher values, but interestingly the rates of AJ at optimum temperature decreased. This is caused by the decrease of rJ,V with increasing growth temperature. An additional temperature acclimation of Vcmax25 to higher values at lower growth temperatures would decrease the effect on AC at Topt, but would further intensify the relative decrease of AJ at Topt with rising growth temperature.