Journal of Experimental Botany, Vol. 51, No. 90001, pp. 399-406,
February 2000
© 2000 Oxford University Press
Modelling the role of Rubisco activase in limiting non-steady-state photosynthesis
1 Biology Department, Utah State University, Logan, UT 843225305, USA
2 School of Botany, The Unversity of Melbourne, Parkville, Victoria 3052, Australia
Received 2 June 1999; Accepted 27 September 1999
| Abstract |
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The roles of ribulose-1,5-bisphosphate carboxylase/oxygenase (Rubisco) and Rubisco activase in limiting the approach of photosynthesis to steady-state following a step increase from a low to a saturating value of photon flux density (PFD) are reviewed. This information, along with the effect of Rubisco on steady-state photosynthetic rate and the effect of Rubisco activase on maximum Rubisco activation state, is then used to construct a model to predict the optimum allocation of protein between Rubisco and Rubisco activase for plants exposed to different light environments. The model predicts that the distribution of protein that produces the maximum steady-state rate of photosynthesis does not produce the maximum activation rate for Rubisco or the maximum steady-state activation state. The latter conclusion may explain why Rubisco is rarely found to be fully activated in leaves, even at saturating PFD values. The former suggests that plants exposed to fluctuating PFD should allocate more protein to Rubisco activase than plants exposed to constant PFD. This aspect of the model is explored in more detail for lightflecks of differing duration.
Key words: Rubisco, Rubisco activase, photosynthesis, model, light, photon flux density.
| Introduction |
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The catalytic activity of ribulose-1,5-bisphosphate carboxylase/oxygenase (Rubisco) in leaves decreases under conditions of low PFD and increases with high PFD. These changes in activity, termed deactivation and activation, occur over a period of minutes and have been shown to be caused by the reversible addition of CO2 and Mg2+ to the active site of the enzyme. A portion of the activation reaction is catalysed by another enzyme, Rubisco activase (Portis, 1995), and in most leaves the amount of activated enzyme in the steady-state is regulated such that it closely parallels the PFD-driven rate of electron transport and, therefore, the prevailing photosynthetic rate (Portis, 1992; Woodrow and Berry, 1988).
The benefits of deactivation under low PFD remain largely speculative, but it seems likely that it preserves the balance between the PFD-dependent rate of RuBP regeneration and the maximum rate of carboxylation. This allows metabolite pools in the PCR cycle to remain roughly constant despite widely differing fluxes through the cycle, and may have important consequences for regulation of triose phosphate transport out of the chloroplast (Woodrow and Berry, 1988). There is, however, at least one apparent disadvantage to changes in the activation state of Rubisco. The rate at which the catalytic activity of Rubisco is restored upon a return to high PFD is relatively slow and can limit the rate at which photosynthesis can respond to an increase in PFD (Pearcy et al., 1994). Several factors have been identified that can affect the rate of Rubisco activation and hence the approach of photosynthesis to steady state; among these is the activity of Rubisco activase (Hammond et al., 1998; Mott et al., 1997).
In this paper (1) the role of Rubisco activation rate in limiting the approach of photosynthesis to steady-state following an increase in PFD and (2) the role of Rubisco activase in determining the rate of Rubisco activation and the maximum activation state of Rubisco are briefly reviewed. A simple model is then presented to investigate the distribution of protein nitrogen between Rubisco and Rubisco activase that produces the maximum photosynthetic CO2 uptake under different light conditions.
| Role of Rubisco activation in limiting non-steady-state photosynthesis |
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When the PFD incident on a leaf is increased suddenly after a period of many minutes in low PFD or darkness, photosynthesis increases over a period of several minutes to a new steady-state rate commensurate with the higher PFD. If the stomatal contribution to this process is factored out (Woodrow and Mott, 1989), then the time-course for the approach of photosynthesis to steady-state is determined by two processes, both of which respond to PFD, but with very different time constants (Fig. 1a
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In many plants Rubisco activation proceeds with approximately exponential kinetics, and the portion of the photosynthetic time-course that is limited by Rubisco activation rate can be linearized using a semi-logarithmic plot (Fig. 1b). In this type of plot the natural logarithm of the approach of photosynthesis rate (A) to its maximum value (Af) is plotted against time. The portion of the time-course that is limited by the activation rate of Rubisco is visible as a linear portion of the data that begins sometime within the first minute after the increase in PFD. The relaxation time (
) for this phase is usually between 1 and 5 min depending on the species and the prevailing intercellular CO2 concentration during induction (Mott and Woodrow, 1993). Extrapolation of this slow exponential phase to time zero gives an estimate of the photosynthesis rate that would have occurred if the fast (RuBP regeneration) phase had responded instantly to the increase in PFD (Fig. 1). This photosynthethic rate is denoted Ai, and it is proportional to the Rubisco activation state that existed at time zero. By varying the length of time that a leaf is kept in low PFD or darkness, it is possible to vary initial activation state and the value of Ai, and to deduce the kinetics of Rubisco deactivation.
Evidence that the slow exponential phase of photosynthetic induction is limited by Rubisco activation is several-fold. First, RuBP concentrations are high and presumably saturating during this portion of photosynthetic induction (Seemann et al., 1988; Woodrow and Mott, 1989). Second, the relaxation time (
) for this phase corresponds to the
for Rubisco activation measured biochemically (Woodrow and Mott, 1989), even in plants with varying rates of Rubisco activation due to varying amounts of Rubisco activase (Hammond et al., 1998). Third, the sensitivity of photosynthesis to [O2] suggests a control coefficient for Rubisco of approximately 1.0 for most of this phase of photosynthetic induction (Mott and Woodrow, 1993). Fourth, the kinetics of deactivation in low PFD or darkness as determined from this phase match those of deactivation determined biochemically (Woodrow and Mott, 1989).
| The role of Rubisco activase |
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When Rubisco is in the decarbamylated (inactivated) state, a number of ligands, including RuBP, bind tightly to it and block the addition of CO2 and Mg2+. Under these conditions, carbamylation can proceed no faster than RuBP or other ligands can dissociate from the active site. Moreover, the equilibrium for the activation reaction favours the decarbamylated form of Rubisco. Rubisco activase has been shown to accelerate the rate at which ligands dissociate from the decarbamylated form of Rubisco, and it therefore shifts the equilibrium towards the carbamylated (activated) form (see Portis, 1995, for a review). This process is accompanied by ATP hydrolysis, and it has been proposed that Rubisco activase facilitates the removal of ligands from the inactive site utilizing the free energy available in ATP hydrolysis (Wang and Portis, 1992; Portis, 1995).
The dependence of maximum Rubisco activation state and, therefore, maximum light-saturated photosynthesis rate on Rubisco activase activity has been investigated several times with antisense techniques. In all cases there is very little effect on maximum Rubisco activation state or light-saturated photosynthesis rate unless the amount of Rubisco activase is reduced well below that of the wild-type (Mate et al., 1993; Jiang et al., 1994). However, the scatter in these data prevents an accurate assessment of the form of the relationship between activase content and Rubisco activation state. A mechanistic model for the effect of the activase amount on maximum Rubisco activation state has been developed (Mate et al., 1996). This model predicts a hyperbolic relationship between these two parameters, and the experimental data cited above are consistent with such a relationship.
Experiments with antisense plants containing reduced amounts of Rubisco activase also show an effect of activase amount on the rate of Rubisco activation following an increase in PFD (Mott et al., 1997; Hammond et al., 1998). In contrast with the steady-state activation state, the initial rate of Rubisco activation was found to be linearly related to the amount of activase over the entire range of activase amounts up to and including that of the wild type.
| Modelling protein allocation to Rubisco and Rubisco activase |
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Knowing the role of activase in regulating Rubisco activity and the role of Rubisco in determining the rate of photosynthesis, it is now possible to assess optimum resource allocation between the two proteins and how these may change under different PFD conditions. It is reasonable to assume that, in view of the abundance of Rubisco and activase (they are probably the most abundant stromal proteins in most plants), natural selection has favoured resource allocation to the two proteins such that net CO2 assimilation is maximized. For example, under conditions of rapidly changing PFD, a relatively high amount of activase may be advantageous because of the need to activate Rubisco as rapidly as possible. However, because nitrogen is generally in short supply in most ecosystems (Mooney and Field, 1986), any change in the amount of activase will probably come at the expense of other proteins, especially Rubisco. Gains in the non-steady-state may, therefore, be offset by losses in the steady-state. To understand this trade-off, the focus has been narrowed to consider the effect on photosynthesis of the allocation of a fixed amount of protein (and thus nitrogen, as both proteins are approximately 14% nitrogen) between Rubisco and activase. This simplification is similar to that made by Cowan in his appraisal of nitrogen allocation to Rubisco and carbonic anhydrase (Cowan, 1986).
Structure of the model
The resource allocation model contains five equations, which were solved simultaneously to calculate total photosynthesis over varying periods of time. The first equation makes use of the data of Hammond et al. who measured amounts of Rubisco and activase in fully expanded leaves of wild-type plants of about 1650 mg m-2 and 80 mg m-2, respectively (Hammond et al., 1998). These values have been used to constrain variations in the amount of the two proteins according to the following equation:
![]() | (1) |
The next equation describes the dependence of net CO2 assimilation rate on the amount of Rubisco activase. This dependence was assumed to be hyperbolic (Mate et al., 1996) and it is described with the following equation:
![]() | (2) |
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The next part of the modelling involved quantifying the effect of activase on non-steady-state photosynthesis following an instantaneous rise in PFD from a low value to one saturating for photosynthesis. The absolute PFD values are not required for the model, but it has been assumed that the low PFD value corresponds to a steady-state Rubisco activation state of 35%; i.e. Ai=0.35Af (Hammond et al., 1998). The interpretation of Ai is discussed in a previous section of this paper. Two important assumptions underlie this part of the model. First, it is assumed that the relaxation time for Rubisco activation (
) is constant when Ai is the only variable. While results supporting this assumption were found in a study of spinach (Woodrow and Mott, 1989), other studies have indicated that small variations in
may occur when Ai approaches Af (Woodrow et al., 1996). Second, the relaxation time for Rubisco activation is inversely proportional to the amount of activase. This assumption has recently been supported by the results of studies of transgenic plants with reduced amounts of activase (Hammond et al., 1998; Mott et al., 1997). Both studies showed a more or less linear relationship between the initial rate of Rubisco activation (vi) following a rise in PFD, and activase amount. This initial rate is related to the relaxation time according to the following equation:
![]() | (3) |
Ea is the increase in activated Rubisco sites following the rise in PFD, which is proportional to Af-Ai. In both studies, Af-Ai varied relatively little with activase amount, so for convenience and simplicity, a linear relationship between the amout of activase and the inverse of the relaxation time has been assumed (Fig. 3
![]() | (4) |
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Estimation of the relaxation time for Rubisco activation, together with estimates of Af and Ai, allows modelling of the change in photosynthetic rate with time according to the following equation:
![]() | (5) |
) occurring during a lightfleck of length t when the RuBP concentration is saturating:
![]() | (6) |
During very short lightflecks, the processes limiting the build-up of RuBP to saturation are undoubtedly as important, if not more important, than Rubisco activation in affecting photosynthesis. However, this process is relatively poorly understood mechanistically, and there is not enough information in the literature to model it accurately for a range of conditions. In addition, for sunflecks longer than about 2 min, the effect of the fast phase on the difference between the integrated photosynthesis rates of two leaves that differ only in the
for Rubisco activation is negligible (Fig. 1). Therefore, in this model the contribution of the fast phase was considered to be constant and negligible for sunflecks greater than about 2 min, and the approach of photosynthesis to steady-state was assumed to be controlled only by Rubisco activation.
The five equations discussed above were used to estimate the combinations of Rubisco and activase that maximize (optimize) photosynthesis during lightflecks of varying length and preceded by low light periods of different length. As noted above, the latter affects the activation process by changing Ai.
Predictions of the model
The first part of the modelling involved examining how changes in the amounts of Rubisco and Rubisco activase affect the time-course for Rubisco activation (Fig. 4
). For example, for a leaf containing 124 mg m-2 activase, Rubisco activation proceeds exponentially with a relaxation time of 105 s. In the steady-state, about 91% of the Rubisco pool is in the active (carbamylated) state. When the activase amount was increased to 248 mg m-2, however, Rubisco activated considerably faster (
=68.6 s) and reached a slightly higher steady-state activation state, but the final steady-state rate of photosynthesis (Af) was lower. This result occurred because the negative effect on photosynthesis caused by reallocating protein nitrogen from Rubisco to Rubisco activase was larger than the positive effect caused by the concurrent increase in Rubisco activation state. In the third example shown in Fig. 4, the activase amount was lowered to 62 mg m-2. In this case, not only did activation proceed relatively slowly, but Af was also the lowest of the three cases. The latter result occurred because, in this case, the effect of the low amount of activase on the Rubisco activation state had a larger effect on photosynthesis rate than did the increase in the amount of Rubisco caused by reallocation of nitrogen from Rubisco activase.
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These three examples illustrate that depending on the duration of illumination at high PFD, some Rubisco : activase ratios are more advantageous, in terms of maximizing photosynthesis, than others. Clearly, for a 300 s lightfleck, the larger activase amount would be an advantage over the other two cases. On the other hand, for constant PFD or for very long or infrequent sunflecks, the leaf with 124 mg m-2 activase would assimilate more CO2.
These interacting factors were considered further by calculating the activase and Rubisco amounts that maximize the total amount of photosynthesis during lightflecks of varying duration. The most extreme case considered was a lightfleck lasting 12 h; i.e. PFD is increased first thing in the morning and is not decreased until the end of the day. In this case, the optimal amount of activase was 124 mg m-2,
was 105 s, and the activation state of Rubisco was 90.1% (Fig. 5
). As the lightfleck duration was lowered, however, the optimal amount of activase rose marginally to about 150 mg m-2 for a 30 min lightfleck, but for shorter lightflecks the optimal amount of activase rose quite steeply. These data also show how an increase in the amount of activase increases Rubisco activation state (Fig. 5c), but causes a decline in Af (Fig. 5b) because of the decrease in the amount of Rubisco (equation 1).
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The model contains a number of parameters that have been estimated empirically. The most uncertain of these is the relationship between the amount of activase and the maximum steady-state Rubisco activation state (equation 2; Fig. 2). Clearly, a larger number of plants need to be examined before a curve can be fitted that has a high degree of correlation with the data. Because of this potential weakness in the accuracy of the model, the sensitivity of the model to variations in Kactivase (equation 2) was examined. The analysis showed that all of the models predictions are sensitive to this parameter to varying degrees. For example, halving the estimated Kactivase value from about 12 to 6 mg m-2, caused a 25% reduction in the optimal amount of activase and a 35% rise in
(Fig. 6
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The final part of the modelling involved examining how the duration of preceding low light periods affects the optimal amount of activase. Rubisco inactivation following a high to low PFD transition can be relatively slow (Woodrow and Mott, 1989; Jackson et al., 1991), so if the light is raised again before full inactivation has occurred, then the activation speed may be of less importance in the subsequent lightfleck. This effect was examined by calculating the optimal amount of activase for different Ai : Af ratios at the onset of a lightfleck (Fig. 7
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| Conclusions |
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Because of the interrelated roles of Rubisco and Rubisco activase in limiting both steady-state and non-steady-state photosynthesis, the optimal allocation of protein between these two enzymes depends on the prevailing light environment. In an environment with more or less constant light, the distribution of protein that produces the highest steady-state rate of photosynthesis will be the optimal. Interestingly, the amounts of Rubisco and Rubisco activase that produce the maximum steady-state rate of photosynthesis do not produce the maximum Rubisco activation rate or the maximum Rubisco activation state. While the former conclusion is not surprising, the latter is certainly not intuitive. It arises because the effect of Rubisco activase amount on Rubisco activation is hyperbolic. Therefore for high amounts of Rubisco activase, the increase in photosynthesis caused by allocating more protein towards activase is less than the increase that could be achieved by using the same amount of protein to make more Rubisco, even though that Rubisco will not be fully activated. This simple trade-off between the amount of Rubisco and its maximum activation state as controlled by Rubisco activase may explain why Rubisco is rarely found to be 100% activated even under saturating PFD.
Under conditions of fluctuating light, the situation is slightly more complex, and the optimal allocation of nitrogen between Rubisco and Rubisco activase depends on the duration of the sunfleck and the duration of the preceding low PFD period. The shorter the sunfleck the higher the optimal amount of activase, and the shorter the period at low PFD the lower the optimal amount of activase. Thus, environments characterized by short sunflecks separated by relatively long periods of time should have the greatest allocation of nitrogen to Rubisco activase. In contrast, environments with constant light or long sunflecks with short intervals in between should have the lowest amounts of activase.
Although the quantitative predictions of the model concerning the optimal amounts of Rubisco and Rubisco activase depend on the parameters used, the qualitative predictions depend only on the general form of the relationships between variables. Thus, the prediction that the maximum steady-state photosynthesis rate occurs at less than 100% activation of Rubisco depends only on the hyperbolic relationship between the amount of Rubisco activase and Rubisco activation state and the linear relationship between the amount of Rubisco and photosynthesis. The parameters used in these relationships affect the amounts of Rubisco and Rubisco activase, as well as the Rubisco activation state and photosynthesis rate, at which this maximum occurs. Similarly, relationships between Rubisco activase amount, Rubisco activation rate, and maximum Rubisco activation state define the existence of an optimal amount of activase that maximizes CO2 uptake under conditions of fluctuating PFD. They also define the general trends for how the optimal amount of activase depends on sunfleck duration. The parameters of the relationships affect only the amount of activase that produces maximum photosynthesis under a particular set of conditions.
Empirical validation of this model awaits data for amounts of activase and Rubisco in plants grown under a range of PFD conditions. It seems possible that the type of optimization predicted by this model would rarely occur in a single species, but may be more generally observed by comparing species that are adapted for different PFD environments. Supporting this are understorey plants growing in the rainforests near Cairns, Australia, as the ratio of activase to Rubisco was found to be approximately five times greater than for tobacco plants (Hammond et al., 1998; Kelly, 1998).
| Footnotes |
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3 To whom correspondence should be addressed. Fax: +1 435 797 1575. E-mail:kmott{at}biology.usu.edu
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