Journal of Experimental Botany, Vol. 51, GMP Special Issue,
pp. 399–406, February 2000
Modelling the role of Rubisco activase in limiting
non-steady-state photosynthesis
Keith A. Mott1,3 and Ian E. Woodrow2
1 Biology Department, Utah State University, Logan, UT 84322–5305, USA
2 School of Botany, The Unversity of Melbourne, Parkville, Victoria 3052, Australia
Received 2 June 1999; Accepted 27 September 1999
Abstract
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
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
CO and Mg2+ to the active site of the enzyme. A portion
2
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 CO uptake under different light conditions.
2
3 To whom correspondence should be addressed. Fax: +1 435 797 1575. E-mail: [email protected]
© Oxford University Press 2000
400 Mott and Woodrow
Role of Rubisco activation in limiting
non-steady-state photosynthesis
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 timecourse 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).
The first of these processes is the rate of RuBP regeneration by the photosynthetic carbon reduction (PCR) cycle.
This process responds relatively rapidly to PFD and
Fig. 1. Schematic representation of the roles of RuBP regeneration rate
and Rubisco activity in limiting the approach of photosynthesis to
steady-state following a step increase from a low to a saturating PFD
value. The solid line in (a) shows the response of RuBP regeneration
rate, and the dotted lines show the response of Rubisco activity for
high and low values of t and for two different initial Rubisco activation
states. A and A ∞ are the rates of photosynthesis that would have
i
i
occurred if RuBP regeneration rate responded instantly for a low and
high initial Rubisco activation state, respectively. A is the final steadyf
state rate of photosynthesis. The observed photosynthetic time-course
is the minimum of the RuBP regeneration curve and the appropriate
Rubisco activity curve. The solid lines in (b) show the semi-log plots
of the observed photosynthetic time-courses. The linear portion
corresponds to the portion of the time-course that is limited by Rubisco
activity, and the dashed lines show the extrapolation of this phase back
to time zero.
typically limits photosynthetic induction for the first
minute or less after the increase in PFD (Sassenrath-Cole
and Pearcy, 1992; Pearcy et al., 1994). The second process
is the increase in carboxylation capacity of Rubisco
caused by the conversion of Rubisco to the catalytically
active form.
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 (A ) is plotted against time. The portion of the
f
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 (t) for this phase is usually
between 1 and 5 min depending on the species and the
prevailing intercellular CO concentration during induc2
tion (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 A , and it
i
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 A , and to deduce the
i
kinetics of Rubisco deactivation.
Evidence that the slow exponential phase of photosynthetic induction is limited by Rubisco activation is severalfold. 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 (t) for this phase corresponds
to the t 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 [O ] suggests a control
2
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
When Rubisco is in the decarbamylated (inactivated )
state, a number of ligands, including RuBP, bind tightly
to it and block the addition of CO and Mg2+. Under
2
these conditions, carbamylation can proceed no faster
than RuBP or other ligands can dissociate from the active
Non-steady-state photosynthesis 401
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
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 CO assimilation is maximized. For example,
2
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:
[Rubisco]+[activase]=1730 mg m−2
(1)
The second equation describes the effect of the amount
of Rubisco (assuming 100% activation and saturation
with RuBP) on the maximum steady-state, light-saturated
rate of photosynthesis (A ). Both the equation and the
sat
constants are described elsewhere ( Woodrow and Berry,
1988).
The next equation describes the dependence of net CO
2
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:
A [activase]
sat
A=
+c
f K
+[activase]
activase
(2)
where A is the maximum steady-state, light-saturated
f
rate of photosynthesis at the Rubisco activation state
allowed by the prevailing amount of Rubisco activase,
K
is a constant, characteristic of the shape of the
activase
hyperbola, and c is the y-intercept of the hyperbola,
which would equal the respiration rate. When this equation was applied to the data of Hammond et al. (1998)
using non-linear regression analysis (Fig. 2), K
and
activase
c were determined to be 12.3 mg m−2 and −0.25 mmol
m−2 s−1, respectively. Interestingly, this analysis predicts
that wild-type plants, which contain some 80 mg m−2
activase, could increase their A values by about 15% if
f
activase were saturating for carbamylation and the
amount of Rubisco were held constant. In other words,
80 mg m−2 is sufficient to activate only 85% of the
Rubisco pool.
402 Mott and Woodrow
Fig. 2. Effect of activase amount on the steady-state, light-saturated rate of photosynthesis (A) of tobacco leaves (redrawn from Hammond et al.,
1998). Each point reflects a measurement on a separate plant. Wild-type plants had amounts of activase in excess of 60 mg m−2, whereas all antiactivase plants had amounts below this value. The line was fitted to the data using equation (2) and non-linear regression analysis; the maximum
predicted value of A is 20.02 mmol m−2 s−1, and the value of K
is 12.3 mg m−2.
activase
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 steadystate Rubisco activation state of 35%; i.e. A =0.35A
i
f
(Hammond et al., 1998). The interpretation of A is
i
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
(t) is constant when A is the only variable. While results
i
supporting this assumption were found in a study of
spinach ( Woodrow and Mott, 1989), other studies have
indicated that small variations in t may occur when A
i
approaches A ( Woodrow et al., 1996). Second, the
f
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 (v ) following a rise in
i
PFD, and activase amount. This initial rate is related to
the relaxation time according to the following equation:
DE
n= a
i
t
(3)
where DE is the increase in activated Rubisco sites
a
following the rise in PFD, which is proportional to
A −A . In both studies, A −A varied relatively little with
f
i
f
i
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).
From these data (modified from Hammond et al., 1998),
Fig. 3. Effect of the amount of activase on the apparent rate constant
(1/t) for Rubisco activation. The data are from experiments by
Hammond et al. who altered activase amounts using an antisense
approach (Hammond et al., 1998). Each point reflects a measurement
on a separate plant. Wild-type plants had amounts of activase in excess
of 60 mg m−2, whereas all anti-activase plants had less than this.
the next equation of the model, which describes the
relaxation time for Rubisco activation, can be formulated:
k
t=
[activase]
(4)
where k is a constant, which equals 216.9 min mg m−2.
Estimation of the relaxation time for Rubisco activation, together with estimates of A and A , allows modelf
i
ling of the change in photosynthetic rate with time
according to the following equation:
A=A −(A −A )e−t/t
(5)
f
f
i
where t is the time after the rise in PFD. Integration of
this equation allows estimation of the amount of photo-
Non-steady-state photosynthesis 403
synthesis (A
9 ) occurring during a lightfleck of length t
when the RuBP concentration is saturating:
A
(6)
9 =A t−(A −A )t+(A −A )te−t/t
f
f
i
f
i
This is the final equation of the model.
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 t 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 A .
i
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 (t=68.6 s)
and reached a slightly higher steady-state activation state,
Fig. 4. Modelled relationship between photosynthesis rate (A) and time
for different amounts of activase.
but the final steady-state rate of photosynthesis (A ) was
f
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 A was also the lowest of the three cases. The
f
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.
These three examples illustrate that depending on the
duration of illumination at high PFD, some Rubisco5
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 CO .
2
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, t 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 A
f
( Fig. 5b) because of the decrease in the amount of
Rubisco (equation 1).
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 K
(equation
activase
2) was examined. The analysis showed that all of the
model’s predictions are sensitive to this parameter to
varying degrees. For example, halving the estimated
K
value from about 12 to 6 mg m−2, caused a 25%
activase
reduction in the optimal amount of activase and a 35%
rise in t (Fig. 6). However, it is important to note that
404 Mott and Woodrow
optimum point is sensitive to the average sunfleck
duration.
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 A 5A ratios at the onset of a lightfleck ( Fig. 7).
i f
As this ratio increases, the optimal amount of activase
decreases for lightflecks of any duration (3 and 10 min
are shown in Fig. 7) until when A =A (i.e. no inactivai
f
tion occurs at all ), the optimal amount of activase is
approximately equal to 124 mg m−2. Activase is needed
under this condition simply to maintain Rubisco in the
active state.
Conclusions
Fig. 5. Modelled effect of lightfleck duration on (a) the optimum
amount of activase, (b) the steady-state, light saturated rate of
photosynthesis, and (c) the percentage of active (carbamylated) Rubisco.
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,
Fig. 6. Modelled effect changing K
on the relaxation time (t) for
activase
Rubisco activation and optimum amount of activase. The dotted line
shows the value of K
used in all other model runs.
activase
although this value affects the quantitative predictions of
the model, it does not affect the qualitative predictions
of the model, i.e. there is still an optimal allocation of
nitrogen between Rubisco and Rubisco activase, and this
Fig. 7. Effect of changing the initial activation state of Rubisco (as
reflected by A /A ) at the onset of a lightfleck. Data for 10 min and
f i
3 min lightflecks are shown.
Non-steady-state photosynthesis 405
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 CO uptake under conditions of fluctuating
2
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).
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