Simulations of the electrochromic shift (ecs) were tested with experimental results reported on A. thaliana. The following types of steady-state measurements were used:
1. Total ecs (ecst) as a function of irradiance and CO2.
2. Inverse ecs (ecsi) as a function of irradiance and CO2.
3. ATPase conductance (gH) as a function of irradiance and CO2.
Throughout the simulations, it was assumed that ecs is proportional to ΔΨ. However, the relationship is leaf-specific and therefore ecst and ecsi are expressed in arbitrary units
(Cruz et al., 2001). This means that neither ecst nor ecsi provide absolute estimations of
pmf and its components, but they can capture the relative changes with irradiance and CO2. ecst is calculated as the difference between ecs in the light and the minimum ecs
achieved in the darkness, whereas ecsi is calculated as the difference between the steady-
state level in the darkness and the minimum in the darkness (Figure 5.12). Minimum ecs was achieved around 200 – 300 ms after the transition to darkness and a steady-state value in the darkness was reached at around 10 s after the transition.
Simulations of steady-state values of ecst and ecsi as a function of irradiance and for air
[CO2] of 372 μmol mol−1 and 50 μmol mol−1 were compared to measurements by Takizawa
et al. (2007). A scaling factor of 11.76 V−1 was used to compare the simulations of ΔΨ with
measurements of ecst and ecsi. The model predicted correctly the increase of ecst and ecsi
with irradiance and decrease with CO2 (Figure 5.13). Under low Ci, both ecst and ecsi
saturated at low irradiance in the measurements and simulations, indicative of limitations due to lower metabolic capacity that increased pmf. Analysis of the simulations in Figure 5.13 indicated that pmf and ecst were linearly correlated, as well as ecsi and ΔpH (Figure
5.14, in both cases R2 > 0.99), in agreement with the model used by Cruz et al. (2001) to
interpret ecst and ecsi measurements.
An Ohmic model of ATP synthesis has been proposed (Cruz et al., 2001), whereby the flux of H) through the ATPase (0
&) is assumed proportional to the pmf. This allows defining a conductivity to H), which is simply the ratio 0
&/pmf. That model predicts that the initial relative rate of decrease of ΔΨ (denote as %&) during a dark interval (Figure 5.12) is proportional to 0&/pmf (Kanazawa and Kramer, 2002; Avenson et al., 2005). Simulations of %& with our model for different irradiances and CO2 were compared (Figure 5.15A)
with the measurements reported by Avenson et al. (2005). There was poor agreement between the simulations and the measurements. In particular, the absolute values obtained from the simulations at low irradiance were an order of magnitude lower than the measured values. Although similar values were obtained for irradiance > 200 μmol m−2 s−1, the experiment by Avenson et al. (2005) did not include such conditions. Prior
measurements in other species (Kanazawa and Kramer, 2002) suggest that the values of %& would not change much for irradiances between 100 μmol m−2 s−1 and 2000 μmol m−2
s−1, whereas the model predicted an increase with irradiance, especially under ambient
CO2 conditions. Furthermore, the simulations indicated that %& and 0&/pmf were not
proportional to each other across different irradiances (Figure 5.15B), except at low irradiances. Although the dynamics of z{ were simulated correctly at the scale of seconds (Figure 5.12), the assumption of first-order kinetics for counter-ion transport may result in incorrect simulations of z{ at the scale of milliseconds, and this would affect calculations of %& from simulated data.
Figure 5.12: Simulation of the electrical field across the thylakoid membrane (z{) as function of time for a light-adapted virtual leaf that is exposed to darkness at time = 1 s. Arrows indicate the changes in z{ that are proportional to total electrochromic shift (ecst) and inverse electrochromic shift (ecsi). Figure 5.13: Simulated (lines) and measured (symbols) total electrochromic shift (A) and inverse electrochromic shift (B). Simulations were scaled by dividing changes in z{ by 0.085 V in order to obtain a similar scale to the measurements. Measurements from Takizawa et al. (2007).
If scaled values of 0&/pmf are compared with measurements of %&, the observed patterns are still not captured by the model (Figure 5.15A), as 0&/pmf increased with irradiance, especially at ambient [CO2]. If the concentrations of substrates for ATP synthesis are kept
constant, 0& increases in a sigmoidal fashion with pmf (Figure 5.16A), which means that, in the pmf range 100−200 mV, 0&/pmf would vary with pmf (Figure 5.16B).
If %& is proportional to 0&/pmf in vivo, a lack of %& increase with irradiance would require regulation of ATPase activity (Kanazawa and Kramer, 2002). The model suggested that a decrease in the concentration of ADP (and/or an increase in ATP) would decrease
Figure 5.14: Comparison between simulated total electrochromic shift and pmf (A), and between simulated inverse electrochromic shift and ΔpH (B). Symbols correspond to simulations for the conditions of the experiment by Takizawa et al. (2007) as shown in Figure 5.13. Lines represent fitted linear models.
0&/pmf, in accordance with the experimental results by Pänke and Rumberg (1996). Indeed, the small decrease in simulated 0&/pmf at [CO2] = 50 μmol mol−1 and irradiance
> 100 μmol m−2 s−1, which paralleled changes in measured %
& (Figure 5.15A), was possible because simulated ADP concentrations were as low as 0.1 mol m−3 (ADP/ATP = 0.1,
ATP/ADP/Pi = 3900 M−1), whereas at ambient CO2, ADP remained higher than 0.2 mol m−3
(ADP/ATP > 0.35, ATP/ADP/Pi < 500 M−1). Reported values of ADP/ATP in chloroplasts, across different irradiance and [CO2] levels are always higher than 0.35 (Hampp et al., 1982; Dietz and Heber, 1984; Prinsley et al., 1986a; Siebke et al., 1990; Heineke et al., 1991), whereas ATP/ADP/Pi remained lower than 1000 M−1 (Giersch et al., 1980; Siebke et al., 1990), so regulation of ATPase activity by low ADP concentrations may not occur in vivo (Kanazawa and Kramer, 2002). The underestimation of ADP/ATP by the model may be the result of the parameter values chosen for regulation of Rubisco activase (Section 5.2.7.1) or consumption by the Calvin cycle in the regeneration of RuBP (Section 5.2.7.2).
Experimental evidence shows that reduction in Pi downregulates ATPase activity in vivo (Takizawa et al., 2008). In the simulations used for Figure 5.15, Pi decreased with irradiance in the range 7.3 − 5.3 mol m−3 ([CO2] = 372 μmol mol−1) and 7.3 − 2.5 mol m−3
([CO2] = 50 μmol mol−1). These values are in agreement with some estimations of free Pi
in the stroma (Hampp et al., 1982; Sharkey and Vanderveer, 1989; Siebke et al., 1990), although other estimations result in values an order of magnitude higher (Dietz and Heber, 1984; Prinsley et al., 1986a).
5.3.4 P
700reduction
In the absence of kinetic limitations on the acceptor side of P700, its redox state is a
measure of the quantum yield of PSI (Harbinson et al., 1989), due to the high quantum yield of PSIac and the strong quenching by long-lived P“77) (see Section 5.2.3 for details).
the kinetics of PQH2 oxidation by the cytochrome b6f complex (Harbinson and Hedley,
1989a) and thus gives an indication of electron transport regulation in vivo.
To test the model, measurements of steady-state P“77) and the rate constant of P “77) reduction (eñ“77) by Hald et al. (2008) were used. Whereas the redox state of P700 is an
output of the model, the rate constant of P“77) reduction was fitted to simulations of P
700
after rapid transition to darkness following the experimental protocol described by Hald et al. (2008). The measurements by Hald et al. (2008) consisted of an irradiance response curve at an air [CO2] of 2000 μmol mol−1, ambient O2 and a CO2 response curve at an
irradiance of 1500 μmol m−2 s−1 and ambient O2.
The model reproduced the measurements accurately (Figure 5.17), with a small overestimation of the rate constant of P“77) reduction at high irradiance and [CO
2]. The
response of the rate constant of P“77) reduction to irradiance and CO
2 was dependent on
the amount of PQH2 before the transition to darkness and the rate constant of PQH2
oxidation by cytochrome b6f. Indeed, the relationship between the simulated variables
could be well described as eñ“77 = egÃ^/2 GLZ+ GL + GLZ+ , where egÃ^ is the rate constant of PQH2 oxidation by the cytochrome b6f complex. In the steady-state response
to irradiance (Figure 5.17C), the changes in eñ“77 were dominated by changes in GLZ+ as egÃ^ remained relatively constant due to moderate pH in the lumen (pH > 6.9). However, in the CO2 response curve (Figure 5.17D), the changes in eñ“77 were dominated by
changes egÃ^ due to increasing acidification of the lumen at low [CO2].
Figure 5.15: Panel A: Simulated (lines) and measured (symbols) steady-state response of ATPase
conductance (gH) as a function of irradiance at air [CO2] of 372 μmol mol−1 (black solid line and
circles) and 50 μmol mol−1 (red dashed line and triangles). In addition, simulated flux of Z) (0
&) over
pmf multiplied by a conversion factor (cf) of 30 μmol−1 m2 mV at [CO2] of 372 μmol mol−1 (dotted line)
and 50 μmol mol−1 (red, dash-dotted line). Measurements from Avenson et al. (2005). Panel B:
Relationship between simulated 0&/pmf and simulated gH, for the same conditions as in Panel A.
Figure 5.16: Relationship between the flux of Z) through the ATPase (0
&) and the proton motive
force (pmf) based on measurements of ATPase activity by Junesch and Gräber (1987), scaled
assuming 0.5 μmol m−2 of ATP synthase and 14 Z) per rotation (symbols in Panel A), and the ratio
between 0& and pmf as a function of pmf (symbols in Panel B). A Hill equation was fitted to the
measurements of 0& (line in Panel A), and 0&/pmf derived from it (line in Panel B).