A dynamic model of Rubisco turnover in cereal leaves


  • Louis John Irving,

    1. School of Biological Sciences, University of Aberdeen, Cruickshank Building, St Machar Drive, Aberdeen AB24 3UU, UK; Present address: Institute of Natural Resources, Massey University, Palmerston North, Private Bag 11222, New Zealand
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  • David Robinson

    1. School of Biological Sciences, University of Aberdeen, Cruickshank Building, St Machar Drive, Aberdeen AB24 3UU, UK; Present address: Institute of Natural Resources, Massey University, Palmerston North, Private Bag 11222, New Zealand
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Author for correspondence: Louis Irving Tel: +64 6 3569099 Fax: +64 6 3565679 Email: L.J.Irving@massey.ac.nz


  • • A simple, improved model of Rubisco synthesis and degradation in cereal leaves is developed using data obtained over the leaf lifespan to return maximum likelihood values for Rubisco proteolysis and biosynthesis. It assumes that the time course of leaf Rubisco content can be described using a log-normal curve, and degradation of the Rubisco pool occurs exponentially.
  • • Curve parameters give an insight into how Rubisco dynamics differ among treatments or genotypes; also, statistical analyses can be performed more easily, requiring fewer data and allowing more flexibility in sampling than previous studies.
  • • Predicted patterns of synthesis correlate well with independent rbc gene transcript data. Rubisco degradation is a first-order decay process, and biosynthesis correlates with leaf elongation rates.
  • • As Rubisco degradation takes place according to first-order kinetics, control of leaf Rubisco concentration must be exerted by adjustment of biosynthetic, rather than proteolytic, rates.


Rubisco (ribulose-1,5-bisphosphate carboxylase/oxygenase, EC is the Calvin cycle enzyme responsible for the catalytic addition of CO2 to ribulose-1,5-bisphosphate, although recent evidence suggests that Rubisco can also act independently of the Calvin cycle (Schwender et al., 2004). Because Rubisco is catalytically inefficient, a large proportion of leaf nitrogen is invested in it. In rice (Oryza sativa), Rubisco accounts for 25–32% of leaf N, approx. 56% of total soluble protein (Mae et al., 1983), and is a potential N-storage protein in many species (Huffaker & Peterson, 1974; Millard, 1988). This dual role, both as the enzyme responsible for current carbon fixation and as an N store for future growth and C assimilation, makes quantifying changes in Rubisco pool size, and determining the mechanisms by which these changes are effected, a desirable goal in many studies.

Leaf Rubisco content has been the subject of a number of studies, both of leaves under ambient (Mae et al., 1983; Makino et al., 1984b; Suzuki et al., 2001; Yamauchi et al., 2002) and stressed conditions (Ferreira & Davies, 1989; Ferreira & Teixeira, 1992; Pell et al., 1992; Bose et al., 1999; Simova-Stoilova et al., 2002; Takeuchi et al., 2002). Changes in Rubisco content can result from a change in the rate of synthesis, degradation, or both, and although many of the above studies show net changes in Rubisco content between treatments, few are able definitively to ascribe those changes to differences in either synthesis or degradation.

Rubisco is a decahexamer, comprising eight large chloroplast-encoded subunits (LSU) and eight small nuclear-encoded subunits (SSU). Synthesis of these two subunits is well coordinated and apparently closely regulated; the presence of the SSU protein in the chloroplast upregulates the translation of rbcL RNA, causing LSU production. The LSU protein has feedback repression of its own translation; thus when LSU is in excess it downregulates the LSU production (Rodermel, 1999). As the production of LSU is mediated by SSU availability, it seems likely that control of Rubisco production is mediated by controlling either the transcription or translation of the SSU. Suzuki et al. (2001) showed a correlation between rbc transcript abundance and protein synthesis and, as rbc transcript abundance is correlated with N availability (Crafts-Brandner et al., 1998), this indicates that the regulation of transcription may be the main determinant of Rubisco biosynthetic rates.

While the control of Rubisco synthesis is relatively well understood, this cannot be said of the factors controlling Rubisco degradation, although these can be split broadly into degradation within, and outside, the chloroplast.

A recent paper presented apparent evidence for the downregulation of Rubisco degradation in rbc antisense mutants with decreased Rubisco content (Ishizuka et al., 2004). Large errors were associated with the measurements of rbc transcript, used to estimate synthesis and convince the reader that any differences in the profiles of Rubisco content through time were caused by differential degradation. The errors involved, however, rendered the study inconclusive. Conversely, and not discussed in the paper, if Rubisco protein were better protected from degradation because of its low concentration, this would also result in decreased rates of protein degradation. Rubisco is protected from proteolysis when in an active state, or when bound to CA-1-P (Khan et al., 1999). rbc antisense mutants with decreased Rubisco content would have a relatively greater capacity to protect the remaining Rubisco from degradation compared with wild-type plants, as the agents responsible for both Rubisco activation (Rubisco activase, RuBP, CO2, Mg2+) and Rubisco protection (CA-1-P) would be relatively more abundant. Furthermore, if we were to accept that rates of Rubisco synthesis and degradation can be tightly controlled, this presents a paradox: in many plants the balance between carboxylation capacity and Rubisco content is not good (Theobald et al., 1998). Furthermore, the generic protease trypsin can degrade catalytically inactive Rubisco in vivo, suggesting that degradation may be actioned by generic proteases (Khan et al., 1999), further degrading the ‘proteolytic regulation’ hypothesis. Proteases are necessary throughout the lifespan of any cell (or organelle), fulfilling many roles including catalysing the turnover of proteins with post-transcriptional errors, allowing the rapid re-use of amino acids (Xiang-Qin & Jagendorf, 1984). There is little evidence to suggest that the action of these proteases changes throughout the leaf lifespan.

The second chloroplast method of Rubisco degradation is by active oxygen species which oxidatively modify specific cysteine residues within the Rubisco complex (Garcia-Ferris & Moreno, 1994; Moreno & Spreitzer, 1999). The mechanism of this cleavage is not fully understood; however, it seems likely that oxidation modifies the proteolytic susceptibility of the affected cysteine residue, or amino acids associated with it, as there is evidence that active oxygen species are not sufficient in themselves to cause proteolysis (Desimone et al., 1996). The primary degradation product of oxidative modification is a 36-kDa fragment, which appears to represent a bottleneck in the degradation process as these fragments can accumulate to the concentrations required for electrophoretic detection (Ishida et al., 1998). Oxidative damage may occur at higher rates in senescent leaves as the chloroplast becomes a more oxidizing environment because of superoxide production, which is not counteracted by enzymatic radical scavenging (McRae & Thompson, 1983; Mehta et al., 1992). Rubisco fragments have an increased affinity to bind to the chloroplast envelope, which presumably increases the transport of these fragments from the chloroplast (Desimone et al., 1996); this may be important in the degradation process if the majority of degradation takes place outside the chloroplast.

There are two mechanisms by which extra-chloroplastidic Rubisco degradation may occur: vesicular transport from the chloroplast to the cytoplasm/vacuole (Chiba et al., 2003); and chloroplast lysis. Chloroplast lysis can be assumed to be of minor importance until the advanced stages of senescence, as little appreciable loss of chloroplasts/gerontoplasts occurs until late in the leaf lifespan (Mae et al., 1984; Ono et al., 1995; Hörtensteiner & Feller, 2002). It is unknown if oxidative modification of Rubisco is required for vesicular transport; however, the increased binding of Rubisco to the chloroplast envelope presumably increases the probability of transport. Once outside the chloroplast, either cytosolic or vacuolar proteases may cause Rubisco degradation, especially in the low-pH environment of the vacuole. Rubisco degradation products have been isolated from plant vacuoles (Huffaker, 1990), although this in itself is not evidence that this was the degradation site (Hortensteiner & Feller, 2002).

Several studies have investigated the dynamics of Rubisco content in rice (Mae et al., 1983; Makino et al., 1984a, 1984b; Suzuki et al., 2001; Takeuchi et al., 2002), using loss of 15N from a labelled Rubisco pool to estimate turnover rates. The mathematics used in this technique were devised by Mae et al. (1983), and have not been revised or verified subsequently. These studies, and the mathematics used, make several implicit assumptions. First, the leaf Rubisco pool is homogeneously labelled with 15N. Second, no reincorporation into new Rubisco of 15N-labelled amino acids derived from the proteolytic breakdown of Rubisco occurs. Third, no degradation of Rubisco occurs when the total quantity of 15N-labelled Rubisco does not decrease.

Cells exhibit different biosynthetic and proteolytic rates according to their physical position within a leaf. Therefore non-uniform 15N labelling of the Rubisco pool can over- or underestimate the rate of proteolysis when scaled up to the whole-leaf level. This might occur, for instance, if the label was primarily incorporated into the oldest (most distal) tissue in a leaf. As the protein in this section is degraded, 15N will be exported; however, the N exported will have a higher atom percentage than the leaf average, which will lead to an overestimation of leaf N export (as this is calculated from the amount of lost 15N), and a subsequent overestimation of new biosynthesis. Second, the equations used to determine Rubisco degradation assume that Rubisco proteolysis can be estimated from the loss of 15N from the Rubisco pool. If 15N-labelled amino acids are reincorporated into new Rubisco, this will lead to an underestimate of proteolysis, which again will lead to an underestimation of biosynthesis. Finally, the assumption that no Rubisco degradation occurs during leaf expansion could be too simplistic; for example, Rubisco degradation has been measured in ozone- or dark-treated Solanum tuberosum during leaf expansion (Eckardt & Pell, 1994), indicating that the capacity exists for protein degradation.

There are also theoretical problems with the application of the standard model. The equations of Mae et al. (1983) require estimation of the size and enrichment of a 15N-labelled Rubisco pool at two time points. Typically, a small number of replicates are used to estimate these parameters, yielding means with associated errors. The means are used to estimate the quantity of 15N label in the pool at each time point. Any change of 15N content, expressed as a percentage of the initial pool, is multiplied by the initial size of that pool to estimate the total loss of Rubisco. The difference between the derived loss and the Rubisco pool size change can be used to infer new Rubisco synthesis. Errors are not taken into account in these calculations, which are codependent, causing errors to be compounded and making the resulting predictions error-prone and highly variable.

A rationalization of these calculations is necessary to allow much of this variability to be removed, which will clarify patterns of synthesis and degradation, yielding information on the mechanisms of Rubisco regulation and allowing effective statistical comparisons between treatments, genotypes, species, etc. This paper proposes a model that develops the approach first used by Mae et al. (1983). We will set out the revised calculations, using several data sets from rice, wheat and barley to verify the model assumptions, and then use the model to derive the synthesis and degradation for the Mae et al. (1983) data set. Finally, the model will be used to re-analyse data from a number of studies, demonstrating the superior applicability of this model compared with previous models.

Materials and Methods

Leaf Rubisco content and 15N atom percentage data are required to calibrate the model, although Rubisco concentration can also be used. An appropriate method of 15N-labelling and its subsequent determination is described by Suzuki et al. (2001) and briefly reviewed at the end of this section. Previous studies indicate that leaf Rubisco content increases rapidly during leaf expansion, reaching a maximum around full leaf expansion and decreasing thereafter in a roughly exponential fashion through to leaf death (Fig. 1; Table 1). Leaf Rubisco content over time is assumed in this model to be described by a log-normal curve (Equation 1; Casella & Berger, 2002):

Figure 1.

(a) Rubisco content of the 12th leaf of rice from emergence through to death. Each point represents a single plant. Data from Mae et al. (1983). (b) Rubisco content of the primary leaf of wheat from emergence through to senescence. Data from Mae et al. (1989). (c) Rubisco content of the first leaf of barley from emergence through to senescence. Each data point represents the mean of three replicates. Data from Friedrich & Huffaker (1980). Solid lines represent a parameterized log-normal curve (Equation 1); statistics in Table 1. Dashed lines, 95% confidence limits of the regression line; dotted lines, 95% confidence limits of the population.

Table 1. Curve-fitting statistics for the model using data from Mae et al. (1983, 1989) and Friedrich & Huffaker (1980) (Fig. 1a–c)
Plot d f g df r 2
  1. Least-squares regression was used in sigmaplot (ver. 9) to estimate these parameters. d, maximum Rubisco content (see Fig. 1 for units) at time g; f, measure of log-normal curve width. P is always < 0.001.

a0.71 (0.02)0.85 (0.04)14.4 (0.5)250.950
b0.43 (0.02)0.38 (0.03) 8.8 (0.2) 80.990
c2.57 (0.09)0.42 (0.03)10.2 (0.3) 80.993
image(Eqn 1)

where NRt is the Rubisco content, measured in terms of Rubisco-N per leaf, at time t; d is the maximum Rubisco content; g is the time (in days) that d occurs; and f is a measure of curve width. While this model is not mechanistic in the sense that the curve parameters represent actual biological processes, the curve parameters are biologically relevant. The log-normal distribution represents the balance between the biosynthetic and degradative activities of the leaf, where synthesis is mainly restricted to the period during leaf expansion, after which the rates of proteolysis are higher than the rates of biosynthesis causing a net decrease in Rubisco concentration. In this way the model parameters give information on the underlying processes, for example, an increase in d may be elicited by either decreased proteolysis, an increase in biosynthesis, or both. Likewise, changes in f represent differences in either the duration of Rubisco biosynthesis or a change in the rate of proteolysis. Equation 1 can be simplified as:

image(Eqn 2)

where Q=−1/2{[ln(t/g)]/f}2 at time t.

Experiments (Mae et al., 1983) show that following 15N pulse-labelling, the 15N atom percentage of the Rubisco pool is initially high before decreasing towards zero with time. This time course is typical of pulse-labelling experiments, and is usually described mathematically using an exponential model (Phillips & Fahey, 2005). The postlabelling decline in Rubisco 15N is assumed to reflect Rubisco degradation (subject to assumption 3 above, that no degradation of Rubisco occurs when the total quantity of 15N-labelled Rubisco does not decrease): the faster the decline, the greater the degradation. Expressing the postlabelling 15N content of Rubisco as an exponential decay curve gives:

image(Eqn 3)

where 15NR is the percentage atom excess of Rubisco at time t; a is the (theoretical) value of 15NR when t equals zero; and b is the rate constant. The initial measurement(s) after the termination of 15N labelling may not be suitable for defining the exponential curve, as the leaf may still be producing Rubisco, leading to decreases in 15N concentration caused by dilution by new 14N-Rubisco, which has little to do with the underlying physical processes of proteolysis. This can decrease the validity of the exponential fit used to determine Rubisco degradation. A suitable statistical package, such as sigmaplot (ver. 9) used here, should be used to determine the values of a, b, d, f and g by least-squares regressions of an exponential decay function for 15N atom percentage on time and a three-parameter log-normal function for Rubisco content on time.

Equations 4–6 are equivalent to equations 1–3 of Suzuki et al. (2001), which use the Mae et al. (1983) formulae.

image(Eqn 4)
image(Eqn 5)
image(Eqn 6)

where 15NRt is the 15N content, expressed as Rubisco-15N per leaf blade, of the Rubisco pool at time t; 15NR is the 15N atom percentage of the Rubisco pool at time t; and 15NF is the 15N atom percentage of the label applied to the plant. inline image(Rdeg in Suzuki et al., 2001) is the flux of N to or from
the leaf Rubisco pool between times t0 and t1. Rsynth is the quantity of Rubisco-N incorporated between times t0 and t1.

Given the assumption that Equations 2 and 3 above describe Rubisco concentration and 15N concentration over time, all the parameters for Equation 4 can be determined from those equations. As Equations 5 and 6 can be determined from Equation 4, we can therefore combine Equations 2 and 3 with Equation 4, and Equation 4 with Equation 5 and 6, to give Equations 7 and 8. Equation 9 is derived from combining Equations 2 and 6.

image(Eqn 7)
image(Eqn 8)
image(Eqn 9)

Mathematically, Rflux will, over an infinite timespan, tend towards zero, as both the log-normal and exponential curves used to derive it also tend towards zero. However, over a physiologically relevant timescale Rflux will approach a steady-state value during senescence, which represents the true rate of proteolysis. Therefore an arbitrary time point, or the average of several time points, is used to estimate the rate of degradation, denoted as inline image. Assuming that this steady-state represents the actual rate of proteolysis (as a percentage of total Rubisco content), and that the rate does not change over time, the derived degradation rate can be extrapolated backwards through time to estimate the rate of proteolysis during leaf expansion, covering times not amenable to direct measurement, and unable to be estimated by previous methods. Equation 9 is then used to calculate synthesis.

The model requires several parameters that can be measured using, for example, the method of Suzuki et al. (2001). In this method, plants are grown up to the required age in hydroponic culture. During leaf expansion they are briefly labelled with 15N-ammonium sulphate (normally c. 3 d). After labelling, the plants are re-immersed in 14N solution and sampled destructively over time. Labelled leaves are excised at the leaf node, and the lamina immediately immersed in water to prevent desiccation. After weighing, the leaves are ground in a pH-buffered solution. To an aliquot of the homogenate, lithium dodecyl sulphate and triton X-100 (25%) is added to dissociate protein subunits from each other and from the chloroplast membranes, respectively. These samples are boiled to prevent catalytic degradation, and quantified against purified Rubisco standards using SDS–PAGE. Rubisco 15N atom percentage is determined by running the remaining homogenate on a native PAGE gel, eluting the (visible) Rubisco protein band, and using trichloroactetic acid to condense the protein. 15N atom percentage of the Rubisco fraction can then be determined using isotope ratio mass spectrometry or emission spectrometry (Yamamuro, 1981).


Comparison of model with experimental data

The model was compared with data obtained in six studies including rice, wheat and barley (Friedrich & Huffaker, 1980; Mae et al., 1983; Makino et al., 1984b; Mae et al., 1989; Suzuki et al., 2001; Takeuchi et al., 2002). The model assumption that Rubisco content can be described by a log-normal curve was tested in rice against data from Mae et al. (1983, Fig. 1a); in wheat against data from Mae et al. (1989, Fig. 1b); and in primary leaves of barley using data from Friedrich & Huffaker (1980, Fig. 1c). In all three studies Rubisco content increases initially, reaching a maximum around the time of full leaf expansion followed by a degradation phase; this pattern was also evident in the data reported later in the studies by Makino et al. (1984b) and Takeuchi et al. (2002). During the senescence phase Rubisco content initially decreased rapidly, although progressively less rapidly over time. Up to 50 d after leaf emergence the log-normal curve provided a good fit to the data, with all or most of the measurements falling within the 95% confidence limits for the regression.

In the Mae et al. (1983) data set, there is a significant lack of fit between the log-normal curve and the experimental data in leaves older than 50 d (Fig. 1a). These points represent the very old leaves that may have made the transition from senescence to necrosis. During senescence the leaf is still alive, and although senescence is defined as the process leading to death, it must still retain protein and other macromolecules. Immediately before death the leaf cells increase proteolytic rates by, for instance, chloroplast and/or vacuole lysis (Ono et al., 1995; Obara et al., 2001). This allows more effective reincorporation of leaf nutrients and causes a sharp decrease in Rubisco content.

The second assumption, that 15N loss from the labelled Rubisco pool occurs exponentially, is tested against two data sets (Fig. 2a,b; Table 2). Older studies, such as Mae et al. (1983, Fig. 2a), exhibit a dog-leg in the data set followed by an almost constant rate of 15N loss from the Rubisco pool. The dog-leg is caused not by the rapid loss of 15N from the pool, but rather by a rapid increase in 14N Rubisco after the end of the labelling period, diluting the 15N-labelled protein. This can easily be seen in Fig. 2a where the 15N concentration decreases rapidly for the first two time points, although the 15N content actually increases indicating synthesis, rather than degradation, of 15N Rubisco. Postlabelling synthesis probably represents the plant using any remaining 15N amino acids, completing the incorporation. More recent studies, such as Suzuki et al. (2001, Fig. 2b), more clearly exhibit an exponential decrease in 15N atom percentage excess over time. Although the early studies appear to exhibit a linear decrease in 15N concentration after the dog-leg, the best fit is provided by using an exponential decay model.

Figure 2.

(a) 15N concentration (open circles) and content (closed circles) of Rubisco in the 12th leaf of rice. Plants were 15N-labelled in 10.3 atom percentage ammonium sulphate for 3 d following leaf emergence. The initial two measurements were not used to fit the exponential curve (Table 2). While 15N concentration initially dropped rapidly, 15N content did not; the rapid decrease in Rubisco 15N concentration is caused by the leaf synthesizing 14N Rubisco rather than the degradation of 15N Rubisco. Data from Mae et al. (1983). (b) 15N atom percentage excess of Rubisco in the eighth leaf of rice. Plants were labelled with 30.3 atom percentage ammonium sulphate for 3 d following leaf emergence. Each point represents the mean of three replicates. Data from Suzuki et al. (2001).

Table 2. Regression statistics for exponential decay curves fitted to the 15N concentration of the Rubisco pool of rice leaves in two studies (Fig. 2)
InvestigationParameterEstimate (SE) r 2
  1. P is always < 0.001.

Mae et al. (1983) a 2.73 (0.08)0.999
b 0.004 (0.001) 
Suzuki et al. (2001) a 9.96 (0.30)0.999
b 0.025 (0.002) 

The flux of N to or from the Rubisco pool, Rflux, determined using Equation 8, was initially approx. 100% (Fig. 3), which suggests that immediately after the end of 15N labelling, Rubisco is still being produced and there is no net export of 15N. Over time Rflux decreased, reaching zero around day 16 then becoming negative, and stabilizing at approx. −3% d−1. Despite the fact that protein degradation cannot be measured experimentally during leaf expansion, and bearing in mind it is known to occur in expanding leaves (Xiang-Qin & Jagendorf, 1984), the most parsimonious argument is that there is no change in the rate of Rubisco degradation through emergence, maturation and senescent life phases. The value of −3% was therefore assumed to be the steady-state rate of Rubisco proteolysis over the leaf lifespan. Using this rate of proteolysis, defined as a percentage of Rubisco content degraded per day, we can derive the rate of Rubisco synthesis. Derived rates of synthesis, degradation and quantity are shown in Fig. 4. Whereas synthesis ends c. day 30, degradation continues into the period of leaf senescence, through to leaf death. Mae et al. (1983) stated that ‘around 90% of Rubisco synthesis occurs between leaf emergence and 1 week after full leaf expansion’. Our model predicts approx. 87% of Rubisco synthesis as occurring between leaf emergence and maximum Rubisco content, which is roughly synonymous with full leaf expansion, and 98% of Rubisco synthesis occurring within the first 20 d after leaf emergence. Table 1 in Mae et al. (1983) suggests that small amounts of Rubisco synthesis continue throughout the leaf lifespan. This assertion is not supported by our model, nor is it corroborated by Figure 4 in the same paper. It is possible that the analytical techniques used were not sufficiently accurate to detect this synthesis in the main Mae et al. (1983) data set, or that reincorporation of 15N amino acids liberated by the proteolysis of 15N Rubisco leads us to underestimate both degradation and synthesis of Rubisco in both our and the previous models. This may explain this apparent paradox; however, there is insufficient evidence to confirm this explanation and, without further evidence, we feel it is not necessary to address this point.

Figure 3.

Flux of nitrogen to or from the leaf Rubisco pool in the 12th leaf blade of rice, determined using Equation 7. The flux of 15N is approx. −3.5% d−1 after the model stabilizes. Data from Mae et al. (1983).

Figure 4.

Model-derived synthesis, degradation and quantity for the 12th leaf blade of rice grown hydroponically. Synthesis ends c. day 30; degradation reaches a maximum c. day 21 and continues until leaf senescence. Data from Mae et al. (1983).

As an independent verification of the model, predicted Rubisco synthesis was compared against rbcS and rbcL transcript abundance data. Suzuki et al. (2001) estimated relative rbcS and rbcL transcript abundances over the lifespan of the eighth leaf in rice, along with the quantities of Rubisco synthesized and degraded using the Mae et al. (1983) model. They concluded that, as both Rubisco synthesis and transcript abundance apparently decreased to approx. 10% of their maximum levels after full leaf expansion, there was a good correlation between these factors, although no statistics were presented to support this. Suzuki et al. (2001) measured synthesis as the amount of Rubisco synthesized between successive time points, while transcript abundance was measured at discrete time points; this is an unfair comparison. To equate these measurements properly, transcript abundances between time points must be inferred as shown in Fig. 5. The revised estimates of rbcS and rbcL transcript were plotted against Rubisco synthesis as determined by Suzuki et al. (2001), and as derived from the model defined here (Fig. 6). The correlation between transcript abundance and Rubisco synthesis derived by our model was stronger than that suggested by Suzuki et al.'s estimates of synthesis (Table 3). We suggest, therefore, that our model provides an improved description of Rubisco synthesis compared with the original model.

Figure 5.

(a) rbcS and (b) rbcL transcript abundance in the eighth leaf blade of rice plants (cv. Notohikari). Areas under curves have been broken down into geometric shapes to allow determination of area. Data from Suzuki et al. (2001)

Figure 6.

rbcS and rbcL relative transcript abundance plotted against Rubisco synthesized in the eighth leaf blade of rice (cv. Notohikari) determined by (a) Suzuki et al. (2001); (b) the model; statistics in Table 3. Data from Suzuki et al. (2001). Open circles, rbcS transcript; closed circles, rbcL transcript. Solid and dashed lines represent linear regressions for rbcS and L, respectively.

Table 3. Linear regression statistics, derived using sigmaplot (ver. 9), for the relationship between rbc transcript abundance and Rubisco synthesis as determined by Suzuki et al. (2001) and the model (Fig. 6)
GeneParameterValueSE P df r 2
Model-determined values
rbcLGradient 5.460.41< 0.00170.989
y-intercept−0.110.73  0.890  
rbcSGradient 4.800.21< 0.00170.996
y-intercept 0.310.41  0.488  
Suzuki-determined values
rbcLGradient 4.640.77  0.00270.935
y-intercept−1.411.37  0.349  
rbcSGradient 3.890.84  0.00670.898
y-intercept−0.771.64  0.661  

Applications of the model

A stated aim in developing the model was to allow the statistical analysis of Rubisco dynamics. During least-squares regression d, f and g values are returned with standard errors (or another measure of variance). From these, the variance is determined, and a z-test used to test for statistical difference among treatments, genotypes, etc. Here some examples of how the model can be applied in practice are described.

Takeuchi et al. (2002) grew two rice genotypes, Sasanishiki and Norin-1, in hydroponics; half of the replicate plants of each genotype were grown with supplemental UV-B as a stressor. Statistical tests using our model show no differences in maximum Rubisco content (d) between Sasanishiki and Norin-1 grown under control conditions (Fig. 7; Table 4). Using model-derived parameters, Norin-1, the UV-B-sensitive genotype, had a smaller d value when grown under supplemental UV-B than did either Norin-1 control plants or Sasanishiki grown under UV-B (P  0.001 and 0.044, respectively, z-test). There was no statistical difference in d between Sasanishiki grown under UV-B or control conditions. The difference in curve widths (f) of the two sets of control plants approached significance (P = 0.104), and the time (g) at which Norin-1 grown under UV-B conditions reached its maximum Rubisco content was 2.5 d earlier than that of the control plants (P = 0.013); the time of maximum Rubisco content in Sasanishiki, however, was unaffected by UV-B. This example illustrates (a) statistically distinct genotypic differences in Rubisco dynamics; and (b) a statistically significant effect of an abiotic stress (UV-B) on some, but not all, the determinants of those dynamics, a subtle effect that would have been difficult, if not impossible, to detect without our model.

Figure 7.

Rubisco concentration from emergence through to senescence for two genotypes of rice grown under control conditions either with or without supplementary UV-B as an abiotic stressor. Circles, Sasanishiki; squares, Norin-1; open symbols, control plants; closed symbols, UV-B-stressed plants. Solid curve is a log-normal regression to control Sasanishiki plants; long dashes, UV-B-stressed Sasanishiki plants. Short dashed line, log-normal regression of Norin-1 control plants; dotted line, UV-B-stressed Norin-1 plants; statistics in Table 4. Data from Takeuchi et al. (2002).

Table 4. Curve-fitting statistics for two rice genotypes grown under control conditions or with supplemental UV-B (Fig. 7)
GenotypeTreatment d f g r 2
  1. d, Maximum Rubisco concentration (µmol g−1 f. wt); g, time of d. Standard errors in parentheses. P is always < 0.001.

SasanishikiControl0.35 (0.01)0.91 (0.04)9.5 (0.3)0.998
UV-B0.31 (0.02)0.89 (0.08)8.1 (0.5)0.992
Norin-1Control0.39 (0.01)0.73 (0.03)8.7 (0.2)0.997
UV-B0.22 (0.01)0.85 (0.06)6.2 (0.3)0.994

Makino et al. (1984b) grew rice plants hydroponically with three different N availabilities, low, intermediate and high, and measured Rubisco synthesis and degradation rates in these plants (Fig. 8; Table 5). A positive correlation between N applied and Rubisco content was reported, but differences between the three N treatments were not tested statistically in the original paper. Time g occurred c. day 12 in the low-N plants, and day 14 in the intermediate and high-N plants, although these were not statistically different. After full leaf expansion, Rubisco content decreased in all treatments. In the low-N treatment, Rubisco was undetectable by day 61. Table 5 reports curve statistics for the three treatments. No significant difference was noted between the treatments for f or g, however, d was significantly higher (P = 0.011) in the high-N than in the low-N plants. There were no significant differences in d between the low- and intermediate, and the intermediate and high-N treatments. This is probably because of the high variance in experimental measurements around the curve maximums.

Figure 8.

Leaf Rubisco content from emergence through to senescence in rice plants grown under high-, intermediate and low-N supplies. Circles, high-N plants; open squares, plants grown with intermediate N; triangles, plants grown under low-N conditions. Each point represents a single plant. Solid line, log-normal regression for high-N plants; dashed line, regression for plants grown under intermediate N; dotted line, log-normal regression for the low-N plants; statistics in Table 5. Data from Makino et al. (1984b).

Table 5. Curve-fitting statistics for rice plants grown hydroponically under high-, intermediate and low-N conditions (Fig. 8)
Treatment d f g r 2
  1. d, Maximum Rubisco-N concentration (mm Rubisco-N g−1 f. wt); g, time at which d occurs (d after leaf emergence). P < 0.001 in all cases.

High N0.21 (< 0.01)0.87 (0.02)14.6 (0.4)0.995
Intermediate0.16 (< 0.01)0.84 (0.05)14.2 (0.7)0.984
Low N0.13 (< 0.01)0.80 (0.06)12.8 (0.8)0.981


The model's assumptions provide realistic and useful descriptions of Rubisco dynamics in expanding, mature and partly senescent leaves. Leaf Rubisco content is well described by Equation 1 (P < 0.001 in every case and r2 consistently > 0.95). Similarly, Equation 3 provides a good description of the time course of 15N loss from Rubisco (P < 0.002 and r2 = 0.999 in both examples shown). The main caveat to this is that the model's assumptions can apply only to living leaves. Effectively dead leaves obviously cannot meet the model's assumptions, and so it is not surprising that the model does not describe well the behaviour of the small Rubisco pools in dead and dying leaves.

Rubisco degradation occurs exponentially in accordance with first-order kinetic principles, which normally indicates a simple process that is not tightly regulated. Enzymatic degradation of proteins is either active, requiring suitable energy sources, and in general is highly regulated; or passive, following simple (normally first-order) kinetics. The specific mechanisms of Rubisco degradation have not yet been elucidated, and it is unclear whether degradation takes place enzymatically or nonenzymatically within the chloroplast, or whether the patterns shown here are better explained by transport of Rubisco from the chloroplast to the cytoplasm (Chiba et al., 2003) and its subsequent degradation. Our model could equally support one, some or all of these mechanisms; however, based on our data, complex regulation of Rubisco degradation is unlikely to be important in cereal leaves.

Physiological studies on ryegrass leaf expansion suggest that Rubisco biosynthesis takes place within the leaf at a given location c. 5–8 cm distal from the cell-division zone (Skinner & Nelson, 1995), and is essentially complete by 110 mm distal from the ligule (Gastal & Nelson, 1994). As leaf length increases as a sigmoidal curve, the time course of leaf elongation rate is described by a normal curve (Fournier et al., 2005). It follows, therefore, that the rate of Rubisco biosynthesis should likewise occur with an approximately normal distribution though time, albeit with a delay compared with the time course for lamina production corresponding to the time taken to produce the 50–80 mm of tissue between the cell-division zone and the physical location of Rubisco biosynthesis. The exponential decrease of synthesis after the termination of leaf expansion that is predicted by the model represents the second half of this normal curve, and correlates with published data that show an exponential decrease in rbc transcript abundances over this period (Crafts-Brandner et al., 1998; Suzuki et al., 2001; Ishizuka et al., 2004). This close integration of leaf growth and Rubisco biosynthesis suggests a common signalling pathway which both controls leaf development and triggers rbc gene expression.

The data set of Makino et al. (1984b) exhibits a lack of difference in f and g values between treatments, suggesting that, within genotypes, the mechanisms and profiles of Rubisco synthesis and degradation in the leaf are not affected by N availability, but only the absolute fluxes and d are controlled by the quantity of N available. This suggests that either leaf Rubisco concentration or leaf size is moderated by the availability of N. If Rubisco concentration, rather than leaf size, is controlled by N availability, this would suggest that synthesis is upregulated under high-N conditions, as degradation rate is directly controlled by Rubisco concentration. Conversely, if leaf size is regulated and Rubisco concentration is constant under varying N availability, this suggests that N concentration-dependent triggers exist within the plant that control leaf growth and, presumably, primordia initiation. Leaf emergence rates have been shown to be plastic in barley and wheat plants, and controlled by a number of factors including temperature (Kirby, 1995) and N availability (Longnecker et al., 1993). Fournier et al. (2005) show convincing data that while leaf growth rate and the final size of the leaf may change, the shape of the growth curve does not change, suggesting strongly conserved patterns of leaf development. In this way it is possible to tie in the process of Rubisco biosynthesis with other processes occurring in the developing leaf at the same time.

To date we have applied the model only to annual C3 graminoid plants; however there are good reasons to believe that the patterns identified may be common to other members of the Poaceae (such as biennial and perennial grasses). The Poaceae exhibit a characteristic basal meristem, allowing the production of leaves in a typically linear fashion which allows the patterns of leaf growth and development described above. It is possible that C4 plants may also exhibit patterns of leaf development different from those shown here. C4 represents an adaptation of the photosynthetic machinery to water stress. Rubisco is physically restricted to the bundle sheath cells of the leaf, and high carboxylation efficiency may be achieved as CO2 is concentrated in these cells by the action of phosphoenolpyruvate carboxylase in the mesophyll cells. C4 plants typically have lower leaf N and Rubisco concentrations, related to the increased efficiency of the enzyme in the elevated CO2 environment in C4 mesophyll cells. It appears that less of the enzyme is actually required. It seems plausible that mechanisms exist within these plants to regulate Rubisco concentration closely, and invest that N better in new growth. It is unlikely that nongraminoid plants exhibit the same regulation of Rubisco content as graminoid plants, mainly because nongraminoid plants exhibit leaf expansion in two planes, increasing width and length simultaneously. However, data to test these assumptions, or to derive a new model for these plants, are lacking.


The proposed model has several benefits over previous methods of determining Rubisco content and turnover. First, the model can be fitted to a limited number of data points, distributed (relatively) arbitrarily throughout the leaf's lifespan. It can be used to estimate leaf Rubisco content, synthesis and degradation at any point in the leaf's lifespan, and for any duration. Statistical analyses can also be computed from the fitted curve. As it is the curve that is analysed, rather than the raw data, different treatments can be compared statistically, even if sample harvests for the treatments did not take place on the same day, or if replication was too low to allow conventional statistical tests. The model describes the relationship between rbc transcript abundance and calculated Rubisco synthesis better than previous models, and therefore provides an improved description of these processes.

Rubisco degradation is a first-order kinetic process, and it is therefore unlikely that regulation of Rubisco content is mediated by regulation of proteolysis. Synthesis, however, correlates well with rbc transcript abundance, and it seems likely that some form of reduced N promotes transcription and leaf growth, as well as being a substrate for Rubisco biosynthesis. The exponential decrease in Rubisco synthesis during leaf senescence might represent a decrease in the availability of reduced N to that leaf as new sinks open up, decreasing the relative sink strength of the study leaf. This reduction of available N would decrease both leaf growth rates and the production of rbc transcript, limiting the substrate available for translation, and therefore the synthesis of new Rubisco molecules.


This work was kindly supported by BBSRC as a Research Studentship to L.J.I. We would like to thank Professor T. Mae, Dr A. Makino and Dr C. Matthew for their comments on the manuscript, Mr T. Marthews for his assistance in the model derivation, and Mr H. Mansoor for his assistance in the final editing.