induction, while lower NPQ does not
4.4 Model validation
To test the predictive power of the model, measurements of CO2 assimilation under
fluctuating conditions (i.e., lightflecks) by Kaiser et al. (2016) were used. The measurements were performed on the same plants used for parameter estimation (Section 4.3), but were statistically independent and explored a different dynamic behaviour of the system. In these measurements, irradiance was varied as a square wave in order to produce symmetrical, periodical lightflecks (Figure 4.33). A square wave is a function of time that consists of a periodic repetition of cycles. Each cycle consists of two half-cycles of equal length. The total length of a cycle is called “period”. During each half- cycle, irradiance was kept constant. For each cycle, the irradiance of the first half-cycle was always higher than in the second half-cycle. The difference between the irradiance of the first and second half-cycle is called “amplitude”. The average of the irradiances of the first and second half-cycle was always 300 μmol m–2 s–1, but three amplitudes of 100, 200 and 500 μmol m–2 s–1 were used. Each amplitude was combined with three periods
(120, 60 and 10 s). This resulted in nine amplitude × period combinations that were used for measurements on biological replicates of each genotype (same replicates and genotypes as in Section 4.3). The measurements were averaged across replicates for each combination of genotype, period and amplitude, and compared to simulations with the model, choosing the inputs to emulate the measurement protocols.
There was good agreement between the predictions of the model and measurements of average CO2 assimilation in the lightfleck experiment (Figure 4.34A). The fraction of
variance explained by the model across genotypes varied between 96% and 99%, whereas the RMSE varied from 0.16 μmol m−2 s−1 to 0.31 μmol m−2 s−1. The linear
regression between simulated and measured CO2 assimilation did not have a significant
intercept whereas the slope was 0.88 (Figure 4.34A). This indicates that the predictions of the model were, on average, not biased and that the model captured the general trend of variation across genotype, lightfleck period and amplitude.
Figure 4.32: Example of measured time series of apparent CO2 assimilation (>"TT, black lines) and
irradiance (I, red lines) in the lightfleck experiment by Kaiser et al. (2016).
However, predictions underestimated the measurements on Col-0 (on average, by 0.90 μmol m−2 s−1) which explains the slope of 0.88. To identify the origin of this deviation,
measurements and simulations were normalized by the steady-state values at the beginning of each lightfleck series (Figure 4.34B). The agreement between simulations and measurements increased slightly and, more importantly, there was no significant bias in the predictions with respect to each individual genotype. This indicates that the model captured accurately the relative effect of fluctuating irradiance on average CO2
assimilation, but the absolute values may have varied due to factors not considered in the model, such as leaf age or time of the day at which the measurements took place. To further test the model, an analysis of variance of the measurements that included all main effects and interactions among genotype, lightfleck period and amplitude was performed on the measurements and simulations. This analysis revealed that 65% of the variation in the experimental data was explained by the amplitude, 28% by the genotype, whereas the period only explained 2% of the variation (interactions among factors explained small fractions of the total variance). In the simulations, the amplitude, genotype and period explained 65%, 29% and 1.7% of the total variation. The similar results for both ANOVAs performed on the measurements and simulations provides further evidence that the model captured the influence of fluctuating irradiance on CO2
assimilation correctly.
4.5 Factors limiting dynamic CO
2assimilation at the leaf level
To gain insights into the role of the different physiological processes that may limit photosynthesis, a series of in silico experiments were performed, where virtual leaves adapted to low irradiance (50 μmol m−2 s−1) were exposed to high irradiance (1000
μmol m−2 s−1) for 40 minutes and then returned to 50 μmol m−2 s−1 for 40 minutes. Other
environmental conditions were: air temperature of 20 °C, air [CO2] of 400 μmol mol−1,
vapour pressure of the air of 2×103 Pa and a wind velocity of 20.5 m s−1 (required for
boundary layer conductance of 9.2 mol m−2 s−1). Unlike in Sections 4.3 and 4.4, the
simulations in this section did not include the corrections for the time response of the measurement instrument.
The virtual experiment was repeated for a series of virtual mutants in which each process was either knocked-out or assumed to respond instantaneously to changes in irradiance. These mutants were achieved by modifying the values of specific parameters (Table 4.9), and do not correspond to any real mutant and may not even be feasible to achieve due to physical and chemical constraints. Instead, they represent the (theoretical) situation where a process no longer limits CO2 assimilation. The differences in predicted CO2 assimilation with respect to the original parameterization was used to calculate the limitation imposed by the process being modified in each virtual mutant. Several virtual mutants were constructed to quantify the limitations associated to CO2 diffusion by assuming instantaneous changes in stomatal conductance, or non-limiting stomatal and/or mesophyll conductance (Figure 4.35A). The values for the parameters were chosen manually by increasing the rate constant of changes in stomatal conductance (Kî&) until changes in predicted assimilation were negligible (i.e., below 0.1%), which was achieved with a Kî& that was 104 higher than the original value (Tables
conductance were not limiting, resulting in values that were 106 higher than the original
values (Tables 4.7 and 4.9).
The simulations indicated that the kinetics of stomatal opening reduced CO2 assimilation
throughout the first half of the experiment (i.e., increasing irradiance), and that the maximum level of limitation (more than 10% reduction) occurred during the first 10 minutes (Figure 4.35A). Assuming non-limiting stomatal conductance resulted in a similar pattern, although the maximum reduction was 25% and this maximum occurred at a later stage of induction. The effect of removing the limitation imposed by a finite mesophyll conductance differed significantly, as the limitation increased progressively during the induction up to a maximum of 25% (Figure 4.35A). Finally, when all the conductances were assumed to be non-limiting, the total diffusional limitation reached a maximum of 37%, its temporal evolution resembled that of stomatal limitation and its values were smaller than the sum of limitations imposed separately by stomatal and mesophyll conductances.
In the second half of the virtual experiment where irradiance was decreased, the kinetics of stomatal closure had a small positive effect on assimilation, though this was always below 2%, and the effect rapidly decreased towards the end of the transition (Figure 4.35A). The limitation due to a finite mesophyll conductance was also small (2%). The limitation due to a finite stomatal conductance was, however, larger (20%) and total diffusional limitation remained lower than in the first half of the experiment.
Figure 4.33: Simulated and measured average apparent CO2 assimilation, corrected for the time
response of the measurement instrument (>"TT) during the lightfleck measurements (A) and the
same values normalized by the simulated and measured steady-state values of >"TT at the
beginning of each lightfleck sequence (B). Each value corresponds to a combination of genotype, lightfleck period and amplitude. The solid line represents the 1:1 line in both panels whereas the
dashed line represents the linear regression between simulated and measured >"TT (A) and
relative >"TT (B). Measurements from Kaiser et al. (2016). Parameters for wildtype (Col-0) as in
Table 4.7. Mutants have the same parameter values as the wildtype except for the parameters indicated in Table 4.8.
In order to quantify the limitations imposed by metabolism, three virtual mutants were constructed where CO2 assimilation was not limited by (i) kinetics of Rubisco activation,
(ii) kinetics of activation of enzymes in the regeneration phase of the Calvin cycle, and (iii) delays in CO2 release from photorespiration. As with the previous virtual mutants,
the values of the relevant parameters (Table 4.9) were increased until differences in simulated CO2 assimilation for the virtual experiment were negligible. This was achieved
in all cases by increasing the relevant rate constants by three orders of magnitude. The limitation imposed by activation of enzymes in the regeneration phase of the Calvin cycle was small (< 10%, Figure 4.35B) and limited to the first minute after an increase in irradiance (no effect after a decrease in irradiance). A larger reduction by the kinetics of Rubisco activation was observed, with a maximum value of 60% at the start of the virtual experiment and a decrease to negligible values after 10 minutes of exposure to high irradiance. As the rate constant of Rubisco deactivation was not modified, no effect was observed after a decrease in irradiance for this mutant (Figure 4.35B). Finally, the delay in the release of CO2 due to photorespiration had a positive effect on assimilation
during the first 5 minutes of the virtual experiment, as well as the first two minutes after the decrease in irradiance (Figure 4.35B), though maximum relative changes were always lower than 5%. In addition, effects after increasing and decreasing irradiance compensated each other, such that time-integrated CO2 assimilation was not affected.
To quantify effects of the regulation of the electron transport chain on CO2 assimilation
under fluctuating light conditions, six virtual mutants were created. The first three consisted of virtual mutants for which the rate constants of qE induction and relaxation, chloroplast movement, and the quantum yield of photoinhibition and rate constant of PSII repair were increased until they were no longer kinetically limiting (Table 4.9), while maintaining the steady-state values of qE, relative absorptance changes due to chloroplast movement and fraction of photoinhibited PSII reaction centres. The other three virtual mutants were constructed such that they lacked qE, photoinhibition or chloroplast movement, by setting the relevant parameter values to zero (Table 4.9). Assuming instantaneous changes in qE did not affect CO2 assimilation during the first
half of the experiment, but it limited assimilation up to 40% after the decrease in irradiance (Figure 4.35C). However, this limitation only lasted for the first 5 minutes, given the high rate of qE relaxation. These predictions are in agreement with experimental results by Armbruster et al. (2014) and Kromdijk et al. (2016), where a faster qE relaxation resulted in increases of CO2 assimilation.
The slow rate of chloroplast movement had a small positive effect during the first half of the experiment, which disappeared after 25 minutes of exposure to high irradiance. On the other hand, after the decrease in irradiance, the rate at which the chloroplasts returned to its original position resulted in a strong reduction in assimilation that lasted until the end of the simulation (Figure 4.35C). The larger effect of chloroplast movement at low irradiances can be explained by the fact that, at ambient temperature and [CO2],
CO2 assimilation was proportional to absorbed irradiance below 100 μmol m−2 s−1, but it
was less sensitive at high irradiance. Instantaneous changes in the fractions of photoinhibited PSII reaction centres had a very small effect on CO2 assimilation in the
first half of the experiment and a small but sustained effect in CO2 assimilation after the
decrease in irradiance, due to the slow rate of PSII repair (Table 4.7).
Table 4.9: Virtual mutants designed to quantify limitations by different processes on dynamic CO2
assimilation. Simulations for all virtual mutants were calculated with the parameter values in Table 4.7, except for those listed below.
Scenario Modified parameters
Non-limiting stomatal kinetics Kî& = 10 s–1 Non-limiting stomatal conductance $&'J = 106 mol m–2 s–1
Non-limiting mesophyll conductance $(J,NZ = $',NZ = 106 mol m–2 s–1
Non-limiting stomatal and mesophyll
conductance (no diffusional limitation) $&'J = $(J,NZ = $',NZ= 106 mol m–2 s–1 No photoinhibition Iëxíê = 0 m2 mol–1 No limitation due to kinetics of photoinhibition Këxíê = 0.21×106 m2 mol–1 and K w†T,NZ = 102 s−1 No qE Pö4 = 0
No limitation due to kinetics of qE Këö4 = 2.53×102 s−1 and Kuö4 = 1.37×102 s−1
No chloroplast movement ìw"( = 0 and ìw"ù = 0 No limitation due to kinetics of
chloroplast movement Këú,NZ = 1.49×102 s−1 and Kuú,NZ= 1.85×102 s−1 Non-limiting activation of enzyme responsible for regeneration of RuBP Kë* = 10 s–1 Non-limiting kinetics of Rubisco activation K*#X = 10 m2 mg–2 s–1 No delay in CO2 release by photorespiration K2* = 102 s–1
The analysis of the simulations with mutants that lacked qE, photoinhibition or chloroplast movement yielded similar results compared to the mutants that affected the kinetics of these processes. The lack of qE did not affect CO2 assimilation in the first half
of the experiment (Figure 4.35D) and it resulted in an increase of assimilation in the first minutes after a decrease in irradiance. However, it also resulted in a decrease in CO2
assimilation for most of the second half of the experiment (Figure 4.35D), due to enhanced photoinhibition caused by the decrease in photoprotection. The lack of chloroplast movement resulted in a small increase in CO2 assimilation in the first half of the experiment, whereas, after a decrease in irradiance, there was a strong enhancement of CO2 assimilation during the first 20 minutes and a decrease afterwards, as the steady-state absorptance at low irradiance is higher than at dark-adapted levels due to the chloroplast accumulation response. These results indicate that the reduction of photoinhibition due to chloroplast avoidance movement at high irradiance does not offset the direct effects on CO2 assimilation by reduced absorptance. This may explain why sun-adapted leaves generally display very little (if any) changes in absorptance due to chloroplast movement (Davis et al., 2011), as the losses outweighs the benefits. Because the plants used to parameterize chloroplast movement were grown at continuous, low irradiance (Section 4.3.1), the movement of chloroplasts at high irradiance did not represent a limitation to their growth and it may be advantageous if leaves are exposed to short sunflecks on a low irradiance background.
Figure 4.34: Simulated relative changes in CO2 assimilation as a function of time after an increase
in irradiance from 50 μmol m−2 s−1 to 1000 μmol m−2 s−1, followed by a second transient back to 50
μmol m−2 s−1, for different virtual mutants. The system was in steady-state at the beginning of the
simulation. The dashed vertical line at Time = 40 min, indicates the transition between irradiances. Parameter values as in Table 4.7, with changes for each virtual mutant as described in Table 4.9.
The mutant “Kgs” assumes stomatal conductance to be in quasi-steady state, whereas “gm”, “gs”, and
“gt” are mutants with non-limiting mesophyll conductance, non-limiting stomatal conductance and
the combination of these two mutations, respectively. The mutants “kRCA”, and “kfR” are
characterized by non-limiting kinetics of activation of Rubisco and enzymes that regenerate RuBP,
respectively. The mutant “kPR” assumes no delays in the release of CO2 by photorespiration. The
mutants “qE”, “qI”, and “qM” assume that qE, photoinhibition and chloroplast movement are in quasi-steady state. “No qI” is a mutant without photoinhibition, “No qM” lacks chloroplast movement, and “No qE” does not have qE.