Would transformation of C3 crop plants with foreign Rubisco increase productivity? A computational analysis extrapolating from kinetic properties to canopy photosynthesis


  • X.-G. ZHU,

    1. Physiological and Molecular Plant Biology,
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  • A. R. PORTIS JR,

    1. Physiological and Molecular Plant Biology,
    2. Department of Plant Biology and
    3. Department of Crop Sciences, University of Illinois, Urbana, IL 61801, USA and
    4. Photosynthesis Research Unit, Agricultural Research Service, United States Department of Agriculture, Urbana, IL 61801, USA
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  • S. P. LONG

    Corresponding author
    1. Physiological and Molecular Plant Biology,
    2. Department of Plant Biology and
    3. Department of Crop Sciences, University of Illinois, Urbana, IL 61801, USA and
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Dr Stephen P. Long, Department of Crop Sciences, 190 ERML, 1201 W. Gregory Dr, Urbana, IL 61801, USA. Fax: +1 217 244 7563; e-mail: stevel@life.uiuc.edu


Genetic modification of Rubisco to increase the specificity for CO2 relative to O2 (τ) would decrease photorespiration and in principle should increase crop productivity. When the kinetic properties of Rubisco from different photosynthetic organisms are compared, it appears that forms with high τ have low maximum catalytic rates of carboxylation per active site (kcc). If it is assumed that an inverse relationship between kcc and τ exists, as implied from measurements, and that an increased concentration of Rubisco per unit leaf area is not possible, will increasing τ result in increased leaf and canopy photosynthesis? A steady-state biochemical model for leaf photosynthesis was coupled to a canopy biophysical microclimate model and used to explore this question. C3 photosynthetic CO2 uptake rate (A) is either limited by the maximum rate of Rubisco activity (Vcmax) or by the rate of regeneration of ribulose-1,5-bisphosphate, in turn determined by the rate of whole chain electron transport (J). Thus, if J is limiting, an increase in τ will increase net CO2 uptake because more products of the electron transport chain will be partitioned away from photorespiration into photosynthesis. The effect of an increase in τ on Rubisco-limited photosynthesis depends on both kcc and the concentration of CO2 ([CO2]). Assuming a strict inverse relationship between kcc and τ, the simulations showed that a decrease, not an increase, in τ increases Rubisco-limited photosynthesis at the current atmospheric [CO2], but the increase is observed only in high light. In crop canopies, significant amounts of both light-limited and light-saturated photosynthesis contribute to total crop carbon gain. For canopies, the present average τ found in C3 terrestrial plants is supra-optimal for the present atmospheric [CO2] of 370 µmol mol−1, but would be optimal for a CO2 concentration of around 200 µmol mol−1, a value close to the average of the last 400 000 years. Replacing the average Rubisco of terrestrial C3 plants with one having a lower and optimal τ would increase canopy carbon gain by 3%. Because there are significant deviations from the strict inverse relationship between kcc and τ, the canopy model was also used to compare the rates of canopy photosynthesis for several Rubiscos with well-defined kinetic constants. These simulations suggest that very substantial increases (> 25%) in crop carbon gain could result if specific Rubiscos having either a higher τ or higher kcc were successfully expressed in C3 plants.


Ribulose bisphosphate carboxylase/oxygenase (Rubisco; EC is a bifunctional enzyme. It catalyses the addition of CO2 to ribulose-1,5-bisphosphate (RuBP) through the photosynthetic carbon reduction cycle (PCRC) to produce two molecules of 3-photosphoglycerate (3-PGA), which are then metabolized to triose phosphate. It also catalyses the addition of O2 to RuBP to produce one molecule of 3-PGA and one molecule of 2-phosphoglycolate. The 2-phosphoglycolate is metabolized through the photosynthetic carbon oxidation pathway (PCOP) releasing one CO2 for every two oxygenations. PCOP serves to recycle 75% of the carbon entering 2-phosphoglycolate through RuBP oxygenation. CO2 and O2 compete for the same active sites of Rubisco. Although PCOP provides precursors for various metabolic pathways, these are dispensable since plants can be grown successfully at saturating CO2 concentrations ([CO2]), where little or no photorespiration occurs (Spreitzer 1999). Photorespiration in C3 crops is estimated to decrease productivity by over 30% at the current atmospheric [CO2] (Ogren 1984; Long 1998). Although the benefit of decreasing photorespiration as a means to increase crop yields was once questioned (Evans 1993), many experiments that have grown C3 field crops under elevated CO2 provide clear evidence that very substantial gains in yield may be achieved by inhibiting photorespiration (Kimball 1983; Long 1998). Competitive inhibition of carboxylation by O2, the release of CO2 by the PCOP pathway and the energetic cost of recycling the carbon diverted to this pathway all contribute to the reduction in C3 crop productivity (e.g. Long 1991). Theoretically, the inhibition of PCOP reactions downstream of Rubisco, but before the glycine decarboxylase, will decrease photorespiratory CO2 release. However, any restriction here will prevent recycling of carbon back to the PCRC. Decreasing the activity of glycine decarboxylase also proved to be an inappropriate solution for decreasing photorespiratory CO2 release. Photosynthesis in Arabidopsis with deficient glycine decarboxylase activity was irreversibly inhibited in normal air (Somerville & Ogren 1982; Somerville & Somerville 1983). Similarly the host-selective toxin victorin, which severely inhibits glycine decarboxylase activity, causes symptoms typical of Victoria blight disease on susceptible plants (Douce & Heldt 2000). Therefore, the only feasible means to eliminate photorespiration and increase net photosynthesis for field-grown crops is via modification of Rubisco to prevent the initial reaction of the pathway, RuBP oxygenation. Decreasing photorespiratory CO2 loss by increasing the specificity of Rubisco for CO2 relative to O2 is an obvious target.

The specificity of Rubisco for CO2 relative to O2 (τ), was first defined by Jordan & Ogren (1981) as:


where kcc and koc are the numbers of carboxylations and oxygenations, respectively, that one active site of Rubisco may catalyse per second. kcm and K°m are the Michaelis–Menten constants of Rubisco for CO2 and O2, respectively. Although Rubisco is a highly conserved protein within C3 terrestrial plants, τ shows great variation when all groups of photosynthetic organisms are considered (Jordan & Ogren 1981; Tabita 1999). When measured at 25 °C, terrestrial C3 plants show an average τ of about 92.5; cyanobacteria and green algae generally have a lower τ of about 50–60; whereas a few marine red algae may have a τ above 100 (Tabita 1999). The existence of different τ in Rubisco from different organisms, especially the existence of high τ in marine non-green algae, raises the possibility of transforming C3 crop plants to express these forms of Rubisco with a higher τ and to decrease photorespiration. So far, efforts to increase Rubisco-limited photosynthetic rate by increasing τ via directed mutagenesis have had little success (Chene, Day & Fersht 1992; Romanova, Cheng & Mcfadden 1997; Madgwick, Parmar & Parry 1998; Ramage, Read & Tabita 1998). Most mutants exhibit a lower τ than the wild type from which they were obtained (Bainbridge et al. 1995; Parry et al. 2003). Comparison of the kinetic properties of Rubisco from different photosynthetic bacteria, green algae and land plants suggests an inverse relationship between τ and kcc (Bainbridge et al. 1995; Spreitzer & Salvucci 2002). This correlation suggests τ might only be increased via genetic engineering of the protein at the expense of a decrease in kcc and vice versa; namely higher specificity is at the cost of slower catalysis. Slower catalysis could be overcome by expressing more Rubisco in the photosynthetic cell; however, Rubisco already represents about 50% of leaf soluble protein in C3 crop leaves, and calculations of volumes suggest there may not be physical capacity to add more (Pyke & Leech 1987). What is the implication for photosynthesis at the leaf and canopy level if we assume that τ can be increased only at the expense of kcc? It has been pointed out that τ, by itself, does not necessarily confer higher Rubisco-limited photosynthesis if kcc is too low or kcm is too high (Whitney et al. 2001; Spreitzer & Salvucci 2002). Furthermore, extrapolating conclusions based on leaf photosynthesis models to the crop canopy level is complicated by the fact that net carbon uptake in a canopy will be the result of a combination of RuBP- and Rubisco-limited photosynthesis. These two respond differently to changes in kcc and τ. Can we assess the impact of these opposite effects at the canopy level?

The widely validated C3 biochemical model of Farquhar, von Caemmerer & Berry (1980) predicts the steady-state rate of leaf photosynthetic CO2 uptake (A) for given conditions of light, temperature and [CO2]. It assumes that for any given set of conditions A is limited by either the maximum activity of Rubisco (Vcmax) or the rate of regeneration of RuBP, which is in turn limited by the rate of whole chain electron transport (J). Changes in τ and kcc affect RuBP-limited photosynthesis and Rubisco-limited photosynthesis differently. An increase in τ will increase RuBP-limited photosynthesis because a lower oxygenase activity diverts less of the limiting flow of electrons to PCOP. Rubisco-limited photosynthesis however, depends on changes in both kcc and τ. Increasing τ without a change in kcc will increase Rubisco-limited photosynthesis because there is less inhibition of carboxylation by oxygen and less CO2 released by the PCOP cycle. An increase in τ together with a decrease in kcc following the inverse relationship will influence Rubisco-limited photosynthesis in a complex manner depending on the relative changes in kcc and τ. At low light, A is limited by J, but at high light, it is more likely to be limited by Vcmax. For a crop canopy with multiple layers of leaves, total CO2 uptake results from a combination of both RuBP-limited and Rubisco-limited photosynthesis. Because photorespiratory loss decreases with rising CO2, the benefit of increasing τ at the expense of kcc also depends on the atmospheric [CO2]. By integrating a steady-state biochemical model of leaf photosynthesis (Farquhar et al. 1980) into a canopy microclimate model (Norman 1980; Forseth & Norman 1993), these combined effects were assessed. The objectives of this study were to determine how increasing τ affects crop photosynthesis for current and past [CO2], assuming that τ and kcc have a fixed inverse relationship and that Rubisco content per unit leaf area cannot be increased beyond the level found in sun leaves of non-stressed mature C3 crops. Because some naturally occurring Rubiscos appear to deviate substantially from the inverse relationship between τ and kcc, we also assessed the hypothetical value to C3 crop canopy photosynthesis of substituting the average form of Rubisco found in terrestrial C3 plants with forms from other photosynthetic organisms.


Dependence of kcc on τ

To quantify the apparent inter-relationship between τ and kcc, literature estimates for these values at 25 °C from different photosynthetic organisms (Jordan & Ogren 1981, 1984; Jordan & Chollet 1985; Parry, Keys & Gutteridge 1989; Read & Tabita 1994; Bainbridge et al. 1995; Horken & Tabita 1999) were compiled (Fig. 1). Where values were obtained at temperatures other than 25 °C, estimates were corrected to 25 °C following Bernacchi et al. (2001). Ignoring mutant forms of Rubisco, the least-square best-fit inverse relationship of τ and kcc was determined (Fig. 1). This relationship was assumed in the subsequent simulations unless otherwise noted.

Figure 1.

The specificity (τ) versus catalytic rate per active site (kcc) for Rubisco from different photosynthetic organisms. Values are for wild type (closed symbols) and mutated forms (open symbols) from Jordan & Ogren (1981, 1984), Jordan & Chollet (1985), Parry et al. (1989), Read & Tabita (1994), Bainbridge et al. (1995), Horken & Tabita (1999) (▪, C3 plants; d, C4 plants; ▴, green algae; ▾, non-green algae; r, prokaryotes; diamond with white spot, mutant). The least-square, best-fit inverse relationship (——) between τ and kcc for the wild-type forms of Rubiscos was an exponential: inline image. The arrows point to the τ (92.5) and kcc (2.5) of a hypothetical ‘average’ C3 crop Rubisco, used for the subsequent simulations.

Leaf photosynthesis

Prediction of the leaf-level photosynthetic rate was based on the mechanistic steady-state biochemical model of Farquhar et al. (1980); which has been widely used and validated across a large range of terrestrial C3 plants (von Caemmerer & Farquhar 1981; Long 1985; Harley 1992). The equations (see Appendix I) are from the models of Farquhar et al. (1980) and as modified by von Caemmerer (2000). Equations 3–6 were used to predict the leaf photosynthetic rate of CO2 uptake. The value of intercellular [CO2] (Ci) is assumed to be 70% of ambient [CO2] (Ca) (Eqn 7). The value of intercellular [O2] is assumed to be the same as ambient [O2] (Eqn 8). Equations 9 and 10 were used to predict the potential rate of electron transport governing the RuBP-limited rate of photosynthesis (Evans & Farquhar 1991). The reference point for these simulations were the amounts and properties of Rubisco reported for non-stressed mature C3 crop leaves. The kinetic constants (K°m and kcm) were those of Bernacchi et al. (2001). τ and kcc for the average C3 leaf were set to 92.5 and 2.5, respectively, which was obtained by calculating the τ corresponding to the average kcc of terrestrial C3 plants following the inverse relationship shown in Fig. 1 (Farquhar et al. 1980; Jordan & Ogren 1981; Bainbridge et al. 1995). Variation in τ around this C3 crop average was simulated by changing K°m and Kcm simultaneously with each contributing to half of the change in τ. If there is m% increase in τ, the following equations were used to obtain the changes in Kcm and K°m.


The value of kcc was predicted from τ as defined in Fig. 1. Variation in kcc was simulated via Vcmax as

Vcmax = Mkcc

where M is the concentration of Rubisco active sites per unit leaf area (assumed to be: 26 µmol m−2), calculated from the average Vcmax for 109 studies of C3 plants species) (Wullschleger 1993). A fixed ratio of koc to kcc of 0.3 was assumed at 25 °C (Bernacchi et al. 2001). Leaf temperature was kept constant at 25 °C throughout the simulations except for data presented in Fig. 4d.

Figure 4.

As for Fig. 2, but showing the τ that results in the greatest daily total canopy carbon gain (Ac′) at any given [CO2]. The prediction uses sun–earth geometry to determine solar angles and incident photon flux, to predict light at different points within the canopy. The control is for the 200th day of the year, and assumes a day with clear sky, a constant leaf temperature of 25 °C, a maximum rate of electron transport supporting ribulose-1:5 bisphosphate regeneration (Jmax) of 250 µmol m−2 s−1, a leaf area index 3 and a random inclination of foliage. As in Fig. 2, the atmospheric CO2 concentration (C1) at which the average specificity of C3 crops (τ1) would be optimal for maximizing Ac′ and the specificity (τ2) that would be optimal for maximizing Ac′ in the current atmosphere (C2) are also indicated in (a). For each individual simulation, control parameters were used except for the tested parameters that were varied. The six parameters varied in the simulations are: (a), LAI; (b), the ratio of horizontal : vertical projected leaf area (χ); (c), atmospheric transmittance (α); (d), canopy temperature; (e), the ratio of [Ci]/[Ca]; (f ), Jmax. In (c), the values of τ at different temperatures were all converted to τ at 25 °C for easy comparison. The percentage increase of canopy carbon uptake by decreasing τ from τ1 to τ2 at C2 is 3.1% in (a).

Canopy photosynthesis

We used the sunlit–shaded model in wimovac, a model that integrates the widely used biochemical model of Farquhar et al. (1980) and the biophysical model of canopy microclimate of Norman (1980), as described in detail previously (Humphries & Long 1995). In summary, the sunlit-shaded model treats the leaves of the canopy as two dynamic populations, namely those sunlit and those shaded, following Forseth & Norman (1993). This division of leaves into sunlit and shaded classes was shown to provide a substantial improvement in prediction over models which simply assumed an exponential decline in light through homogeneously lit canopy layers (Norman 1980). The method for calculating canopy photosynthesis was as described previously by Long (1991) except the leaf and canopy temperatures were maintained at a constant 25 °C (Eqns 11–23). The simulation was for the 200th day of the year at 44° N, since this would correspond to the middle of reproductive growth for many temperate C3 annual crops. The canopy was assumed to have a leaf area index of three (LAI = 3) and random angles of orientation and inclination, namely a ratio of the horizontal : vertical projected leaf area of unity, which are good approximations to many C3 crop canopies (Forseth & Norman 1993). The values of K°m, Kcm and Vcmax were as given in the leaf photosynthesis model. The Rubisco content of the leaves was assumed to be constant throughout the simulations.

Sensitivity analysis

A sensitivity analysis was conducted by sequentially varying six major parameters affecting canopy photosynthesis: LAI, the maximal rate of electron transport (Jmax); the ratio of the horizontal : vertical projected leaf area of canopy (χ), atmospheric transmittance (α), the ratio of [Ci]/[Ca], and leaf temperature (Tl). The response of K°m, Kcm, kc, ko to Tl follows Bernacchi et al. (2001). The response of Jmax to Tl follows Bernacchi, Pimental & Long (2003).


Leaf photosynthesis

Figure 1 shows the inverse interrelationship between kcc and τ which was most effectively described by Eqn 1 (Appendix I). For each τ, the corresponding kcc was calculated based on this inverse relationship. Asat is the light-saturated rate of CO2 uptake under each [CO2]. At each [CO2], Asat was calculated for a range of τ (from 40 to 160). The optimal τ for any given [CO2] was assumed to be that at which Asat was a maximum. Figure 2 shows that the optimal τ for Asat declines exponentially with [CO2]. The τ of 92.5, which is the average τ for terrestrial C3 plants, would be optimal, with respect to Asat, for a [CO2] of about 150 µmol mol−1 and supra-optimal at the current atmospheric [CO2] of 370 µmol mol−1 (Fig. 2). Furthermore, simulations showed that at the current [CO2], a decrease in τ from the current 92.5 (kcc = 2.5) to 65 (kcc = 4.1) would increase Asat by 12%.

Figure 2.

Assuming a fixed number of active sites per unit leaf area and the dependence of kcc on τ described in Fig. 1, the line shows, for any given atmospheric CO2 concentration, the τ that will give the highest light-saturated rate of leaf photosynthetic CO2 uptake (Asat). The average τ for terrestrial C3 crop plants (92.5) is indicated (τ1) together with the interpolated atmospheric [CO2] at which it would yield the maximum Asat (C1). Point τ2 is the specificity that would yield the highest Asat at the current [CO2] of the atmosphere (C2). At C2, decrease in τ from current average (τ1) to the optimum for current CO2 concentration (τ2) can increase light-saturated leaf photosynthetic carbon uptake by 12%.

Canopy photosynthesis

Photosynthesis of leaves in real canopies can be either light saturated or light limited. Light-limited photosynthesis is RuBP-limited whereas light-saturated photosynthesis is commonly Rubisco-limited, particularly at lower [CO2]. The effect of varying τ at different light levels on single leaves is shown in Fig. 3. Leaves with a simulated 10% higher τ exhibited higher light-limited photosynthesis and lower light-saturated photosynthesis compared with those with unaltered τ. Similarly, leaves containing a Rubisco with 10% lower τ (and therefore higher kcc according to Fig. 1) exhibited higher light-saturated photosynthesis and lower light-limited photosynthesis compared with the control (Fig. 3).

Figure 3.

The relative effects of a 10% increase and of a 10% decrease in τ on net photosynthetic CO2 uptake as a function of photon flux. Calculations assume the dependence of kcc on τ described in Fig. 1. The control was the average τ (92.5) and average kcc (2.5 CO2 per active site per second) for terrestrial C3 vascular plants. ——, control; ········, 10% higher τ; – − –, 10% lower τ.

The opposing effects of increasing τ on light-saturated and light-limited photosynthesis and the fact that variation in [CO2] does not affect these two kinds of photosynthesis equally resulted in a different optimal τ for canopy photosynthesis at each [CO2]. Assuming Jmax as 250 µmol m−2 s−1, simulations showed that for a canopy of LAI = 3 at 44° N latitude on the 200th day of the year, the current τ is higher than that which would be optimal for achieving maximal canopy photosynthesis at the current atmospheric [CO2] (Fig. 4a). The optimal τ (τ2, 78; in Fig. 4a) for maximizing the daily integral of canopy CO2 uptake (Ac′) for current [CO2] (Point C2 in Fig. 4a), fell significantly below the current average of 92.5 (τ1). The τ of 92.5 would be optimal for an atmospheric [CO2] of about 220 µmol mol−1 (Fig. 4a). The LAI of canopies constantly change during growth and development of crop canopies. Since LAI influences the light conditions inside the canopy (Eqns 12, 13 and 19 in Appendix I), canopies with different LAI will have different optimal τ under each [CO2]. To test the validity of the conclusions obtained using an LAI of 3, we used an LAI of 2 to represent a canopy at the early stage of development and an LAI of 6 to represent a closed canopy. Simulations showed that alteration of LAI does not change the trend, namely optimal τ decreases with [CO2] (Fig. 4a).

Similar to LAI, the ratio of the horizontal : vertical projected leaf area (χ) also influences light conditions inside the canopy (Eqn 14 in Appendix I). Sensitivity analysis was conducted using χ-values of 2, 1 and 0.5. Canopies with χ of 2 have low inclination angles (the angle between leaf axis and horizontal plane); canopies with χ of 0.5 have high inclination angles; whereas canopies with χ of 1 represent canopies with leaves with an equal distribution between all angles of inclination. Figure 4b shows that χ has little effect on optimal τ and its decrease with [CO2].

Atmospheric transmittance (α) influences the photon flux density above the canopy and the ratio of diffuse to direct light, and therefore affects the light conditions at the canopy surface and below (Eqn 17). Decreasing α decreases light incident on all leaves. The α of 0.5 corresponds to a cloudy day; while α of 0.95 corresponds to a clear sky. Nevertheless, the general trend in optimal τ with [CO2] is unchanged (Fig. 4c).

Temperature influences RuBP-limited photosynthesis and Rubisco-limited photosynthesis differently (Bernacchi et al. 2001, 2003). Therefore, the optimal τ for a given [CO2] differs with temperature. Crop canopies in temperate zones often experience temperatures between 20 to 35 °C. Over this range, the pattern of decline in optimal τ with [CO2] shows little variation (Fig. 4d).

For a given ambient [CO2], variation in the ratio of [Ci]/[Ca] will alter [Ci] and therefore affects proportions of Rubisco-limited photosynthesis and RuBP-limited photosynthesis. Therefore, optimal τ under a given [CO2] differs with the ratio of [Ci]/[Ca]. The ratio of [Ci]/[Ca] varies within 20% of its ‘typical’ value. Within this range, the pattern of the decline in optimal τ with [CO2] shows little variation (Fig. 4e).

Leaves and species can differ with respect to their capacity for RuBP regeneration. Jmax of 250 and 180 µmol m−2 s−1 both show that optimal τ decreases with [CO2] (Fig. 4f). If Jmax was assumed as 150 µmol m−2 s−1, the optimal τ first decreases, but then increases in contrast to the trend of continuous decrease of optimal τ under higher Jmax with increase in [CO2] (Fig. 4f). Therefore, the general trend revealed throughout Fig. 4a–e was altered for low Jmax.

Compared with the optimal τ of 78 for current [CO2] with a Jmax of 250 µmol m−2 s−1, the optimal τ for current [CO2] with Jmax = 180 µmol m−2 s−1 is slightly higher at 83 (kcc = 2.9) (Fig. 4f and Table 1). The gain in canopy photosynthesis that would be achieved by using a Rubisco with an optimal τ for this Jmax in the canopy is also smaller (Table 1, Fig. 4f). This difference is explained by the fact that at the higher Jmax (Jmax = 250 µmol m−2 s−1), 61% of Ac′ is attributed to Rubisco-limited photosynthesis, but only 52% for the lower Jmax (Table 1).

Table 1.  Specificity (τ) found to be optimal for a canopy of LAI = 3 and random inclination of foliage elements on a clear summer day at latitude 44°N assuming two different capacities for whole chain electron transport (Jmax)
 Jmax (µmol m−2 s−1)
  1. The increases in the daily integral of canopy photosynthesis that would result from substituting such an optimal Rubisco into the canopy, relative to the current average form (τ= 92.5). The proportion of the daily integral of canopy carbon gain (A′) that would be obtained under Rubisco-limited conditions is also given. The atmospheric [CO2] at which the current Rubisco would yield the highest Ac′ for the two values of Jmax is also calculated.

Predicted optimal τ for current atmospheric [CO2] 83 78
Predicted percent increase in Ac′ that would be achieved by substituting the optimal τ under current [CO2]  1.7%  3.1%
Predicted increase in Ac′ with the optimal τ under current [CO2]15 mmol m−2 d−130 mmol m−2 d−1
The percentage of Ac′ that is Rubisco-limited for the corresponding optimal Rubisco 52% 61%
The predicted optimal atmospheric [CO2] (µmol mol−1) for current τ200220

Figure 1 indicates that for a few species, there is considerable deviation from the strict inverse relationship between τ and kcc assumed in the simulations presented above. Other potentially important observations with respect to the potential for increasing crop photosynthesis are that (a) among higher plants, kcc and kcm vary far more than τ, especially in comparisons of C3 and C4 species (Yeoh, Badger & Watson 1981; Seeman, Badger & Berry 1984) and (b) non-green algal Rubiscos possess very high τ that may not be compromised by a very low kcc (Whitney et al. 2001). Table 2 shows the predicted effects of hypothetically substituting the ‘average’ C3 terrestrial Rubisco with Rubiscos from other species. Compared with the average C3 crop Rubisco used in the previous simulations, the tobacco parameters result in an 11.4% increase in Ac′. Thus, the lower than average τ (82) is more than compensated for by the higher kcc of the tobacco (3.4) Rubisco. Of the two C4 Rubiscos examined, Rubisco from Amaranthus edulis substantially increased Ac′ compared to crop C3 Rubisco forms due to its high kcc, with maintenance of a sufficiently low Kcm. Rubisco from a non-green algae, Griffithsia monilis, which has a higher τ but maintains a similar kcc and kcm to tobacco (Whitney et al. 2001), would increase Ac′ by 27% (Table 2).

Table 2.  Estimates of the daily canopy carbon gain (Ac′), as in Table 1 and Fig. 4, assuming the hypothetical replacement of the ‘average’ form of Rubisco from C3 crop species with Rubiscos from other species.
(mmol m−2 d−1)
(µmol m−2 s−1)
  1. Reported values for kcc and Kcm of these species (Jordan & Ogren 1984; Seeman et al. 1984; Whitney et al. 2001) were used to calculate K°m using Eqn 2a (Appendix I) and assuming a fixed ratio of koc to kcc of 0.3 at 25 °C (Bernacchi et al. 2001). The Farquhar et al. (1980) model uses intercellular [CO2]in vivo. Since Kcm was reported as the [CO2] around Rubisco in solution, mesophyll conductance was used to adjust this reported value to Kcm expressed as intercellular CO2 concentration. Percentage*represents the percentage of Ac′ attributed to Rubisco-limited photosynthesis.

Current ‘average’ C3 crop (kcc = 2.5, τ = 92.5)104010014.959.2
Tobacco (kcc = 3.4, τ = 82)1170111.419.154.8
Zea mays (kcc = 5.6, τ = 78)1180111.919.841.9
Amaranthus edulis (kcc = 7.3, τ = 82)1250117.128.3 0
Griffithsia monilis (kcc = 2.6, τ = 167)143012721.561.6
Phaeodactylum tricornutum (kcc = 3.4, τ = 113) 965 92.312.560.9


Within the strict assumptions made, decreasing τ to the apparent optimum would increase leaf photosynthesis by 12% and canopy photosynthesis by considerably less. The increase in canopy photosynthesis is less than in leaf photosynthesis because a significant portion of canopy photosynthesis is RuBP-limited and therefore unaffected by an increase in kcc. Importantly, increasing specificity would result in less, not more, net photosynthesis at both the leaf and canopy level at current [CO2]. These conclusions rest on several critical assumptions; namely that τ and kcc are inversely related (Eqn 1, Fig. 1) and that the parameters chosen to describe leaf, canopy and environmental conditions are representative. Several surveys have shown a clear trend in which τ appears inversely related to kcc (Bainbridge et al. 1995; Spreitzer & Salvucci 2002) (Fig. 1) as assumed here. As noted earlier, mutagenesis has so far either decreased τ and kcc at the same time, or increased τ at the expense of kcc, and vice versa (Fig. 1). The repeated evolution of C4 photosynthesis from C3 despite the complexities of Kranz structure and partitioning of enzymes and transporters to avoid photorespiration suggest that land plants may have met an evolutionary barrier, that is, the ‘best’ achievable structure of higher plant Rubisco for high CO2 affinity with an adequate kcc might have already been obtained (Long 1998). The rationale is that if it were possible to significantly increase τ without decreasing kcc, evolution would have already found a route, rather than evolving the complex Kranz structure and using the C4 pathway for concentrating CO2. If we assume that the relationship described by Fig. 1 is generally invariable, improved crop photosynthesis could still be achieved by determining the optimal τ for the given canopy structure, and replacing the current Rubisco with a form that lies close to the predicted optimum for current atmospheric [CO2].

The simulations assume 26 µmol Rubisco active sites per square metre leaf area. This value was held constant in all the simulations. Rubisco content varies between species, leaves within a canopy, and even mature leaves transferred from low to high grown irradiances (Sims & Pearcy 1992; Frak et al. 2001; Oguchi, Hikosaka & Hirose 2003). However, less Rubisco in shaded leaves may reflect the fact that photosynthesis will be RuBP-limited in low light. Theoretically, decreasing kcc with increasing τ could be compensated for by simply increasing the amount of Rubisco. A survey across 109 studies of C3 species gave a mean Vcmax of 64 µmol m−2 s−1 (Wullschleger 1993), which would give, assuming a mean kcc of 2.5, a Rubisco concentration of 26 µmol m−2 as used here. As noted earlier Rubisco typically accounts for about 50% of leaf soluble protein, and calculations of chloroplast and photosynthetic cell volumes suggest there may be little or no physical capacity to add more (Pyke & Leech 1987). At such a high concentration, Rubisco is already expensive in terms of the amount of nitrogen and energy it represents. Increasing Rubisco to compensate for a lower kcc may result in a proportional decrease in efficiency of nitrogen use, an undesirable trait in crop plants.

The lower the Jmax/Vcmax, the lower the proportion of Rubisco-limited photosynthesis to RuBP-limited photosynthesis. The lower the Jmax/Vcmax in a leaf or canopy, the less important kcc is, since a smaller proportion of plant carbon is fixed by Rubisco-limited photosynthesis. Jmax at 250 µmol m−2 s−1 used in these simulations is high, but in line with values reported for C3 crops grown under high nitrogen and high light (Farage, McKee & Long 1998; Bunce 2000). Decreasing Jmax by 28% (from 250 to 180 µmol m−2 s−1) roughly halved the advantage of selecting a Rubisco optimized for canopy carbon gain (Table 1). The benefit of replacing current Rubisco with a form with a higher kcc and lower τ will in part depend on the amount of Rubisco relative to the capacity for regeneration of RuBP. Although a close positive correlation between these two capacities is apparent in surveys of C3 species (Wullschleger 1993), over two-fold variation in the ratio of these two capacities is found within crops (Bunce 2000) and linkage can also be varied by altering rbcS expression (Harrison et al. 2001).

It is remarkable that even with the large changes in LAI, χ, α, temperature and the ratio of [Ci]/[Ca], the trend that optimal τ for maximum canopy carbon uptake decreases with [CO2] does not change (Fig. 4a–e). This pattern only broke down when Jmax was lowered by 40% to 150 µmol m−2 s−1. Here the optimal τ for canopy carbon uptake first decreases then increases with [CO2] (Fig. 4f). This is because a higher proportion of canopy photosynthesis is RuBP-limited photosynthesis under lower Jmax, and the gain due to high τ outweighs the loss due to lower kcc. However, as noted earlier for well fertilized C3 crops a Jmax of 150 µmol m−2 s−1 would be low.

If Rubisco was modified to the τ that would maximize Ac′, then the increase in Ac′ is greater in canopies with properties favouring Rubisco-limited photosynthesis (e.g. higher Jmax, lower Vcmax, lower LAI, lower χ, higher atmospheric transmittance, and lower ratio of [Ci]/[Ca]) compared with those favouring RuBP-limited photosynthesis. Modifying τ to its optimum would be particularly beneficial to plants in semi-arid regions. These plants generally show low stomata conductance (Gomes, Meilke & de Almeida 2002) and low LAI. Low stomata conductance leads to a low [Ci] and low LAI leads to a high-light microclimate in plant canopies. As a consequence of these two factors, a high proportion of canopy photosynthesis would be Rubisco-limited photosynthesis in semi-arid regions. Improved ability to assimilate CO2 at low [Ci] would allow increased efficiency of water use, which can be a competitive advantage in these regions. Optimizing τ and kcc can increase Ac′ by up to 12% when all leaves are light-saturated and Rubisco-limited, for example, during early crop growth prior to canopy closure, lowering to 3% at canopy closure.

Accepting the inverse relationship between kcc and τ and assuming the parameters describing canopy and environment used in this study are representative, our simulations revealed that a decrease, not an increase in τ will increase Ac′ at current [CO2]. However naturally occurring forms of Rubisco might not strictly follow this assumed inverse relationship. For example, Rubiscos from some non-green algae have been reported with a significantly greater τ than that of C3 crops, yet with a similar or higher kcc (Whitney et al. 2001) and C4 forms of Rubisco generally appear to have adapted to the high CO2 environment by increasing kcc at the expense of Kcm with little change in τ (Sage 2002). If it were possible to substitute some of these forms into C3 crops, much larger increases in canopy photosynthesis could be achieved for the same quantity of Rubisco (Table 2).

So far transferring sequences coding for the non-green algal forms of Rubisco to the higher-plant plastome has not succeeded in providing a functional Rubisco (Whitney et al. 2001) because of problems in either folding or assembly of these quite evolutionarily diverse forms. However, successful folding and assembly of Rubisco transferred from other higher plants has been achieved (Kanevski et al. 1999; Whitney & Andrews 2001). Our results suggest that replacing the average Rubisco of C3 crops or the Rubisco found in tobacco with the Rubisco of C4 plants, such as Amaranthus edulis, could result in a substantial increase in canopy photosynthesis for the same amount of Rubisco. If forms from non-green algae are successfully expressed in crop leaves, even larger increases become possible. Whitney et al. (2001) has already shown through modelling that the Rubisco from Griffithsia could increase leaf photosynthesis by 4%. Here we extend this by showing that it would increase Ac′ by 22 and 27% compared to tobacco Rubisco and the hypothetical average C3 Rubisco, respectively (Table 2). The potential increase in canopy photosynthesis for other C3 plant replacements will depend on the relative kinetic parameters of the Rubiscos being considered, but can now be readily ascertained by the modelling procedures we have followed.

Our simulation suggests that Rubisco of current C3 plants would be optimal for an atmospheric [CO2] of about 200 µmol mol−1 (Table 1, Fig. 4a–f). This falls in the range of atmospheric [CO2] over the last 450 thousand years, which fluctuated between 180 and 290 µmol mol−1 as detected from the Vostok ice core (Barnola et al. 1999). Rubisco appeared early in the history of life more than three billion years ago when [CO2] was orders of magnitude higher than current [CO2] and when [O2] was low. In that environment, RuBP oxygenation would have been a rare event (Sage 1999) and not a selective factor in the evolution of Rubisco. The increase in photorespiratory potential triggered by the increase in the atmospheric [O2] : [CO2] over the past 50 million years created high evolutionary pressure for dealing with these disadvantages (Ehleringer et al. 1991). The current Rubisco found in C3 crops might be a result of evolutionary optimization to the low [CO2] and high [O2] over the past 450 thousand years after millions of years of evolution or selection. From the simulations made here, the current Rubisco is not operating at its optimal τ and kcc, which is possibly due to the unprecedented rapid increase in [CO2] since the Industrial Revolution, which may have far exceeded the speed of Rubisco evolution.

In conclusion, this study examined the rationale of current efforts to increase photosynthetic rate by increasing τ using genetic modification of existing land-plant Rubisco and/or replacing them with other naturally occurring Rubisco with significantly different kinetic parameters. If increasing τ can only be achieved at the expense of a decrease in kcc, a decrease, not an increase in τ will increase both leaf photosynthesis and daily canopy carbon gain for the current atmospheric [CO2] if the leaf or canopy has a sufficiently high Jmax. In shade environments or leaves with a low Jmax/Vcmax, increasing τ can increase the total canopy carbon gain for current [CO2]. The optimal τ reflects a balance between the Rubisco-limited photosynthesis and RuBP-limited photosynthesis. These simulations show that even if engineering a Rubisco with improved τ without loss of kcc is elusive, crop carbon gain could be increased substantially by substituting the existing average C3 crop Rubisco with those from other photosynthetic organisms. Specifically, substituting the average existing C3 crop Rubisco with the Griffithsia monilis Rubisco (a non-green algae) could increase carbon gain by more than 25% without any increase in the amount of Rubisco per unit leaf area. Substituting with the Rubisco from Amaranthus edulis could increase carbon gain by 17%. It is hard to conceive of other genetic transformations that could result in a greater increase in potential C3 crop yields.


Equations used to simulate leaf and canopy net photosynthetic carbon uptake


Vcmax  =  kccM (2b)


inline image, where m/100 represents the percentage change in τ(2d)


Ci = 0.7 Ca(7)

Oi = Oa(8)

J = {I2 + Jmax − [(I2 + Jmax)2 − 4ΘI2Jmax]0.5}/2Θ(9)

I2 = I0(1 − s)(1 − r)/2 (10)

Ac = ƒ[Isun, Tl, Ci, Oi].Fsun + ƒ[Ishade, Tl, Ci, Oi].Fshade(11)

where ƒ indicates A as a function of these variables as described in Eqns 1–9.

Fsun = [1 − e( − kF/cosθ)]cosθ/k(12)

Fshade = F − Fsun(13)


cos θ = sin Ω sin δ + cos Ω cos δ cos(15[t − tsn]) (15)

δ = − 23.5 cos[360(Dj + 10)/365](16)


Iscat = 0.07Idir(1.1 − 0.1F)e−cosθ(20)

Isun = Idir cos λ/cos θ + Ishade(21)

λ = cos −1k(22)



Definition of symbols. Values in parenthesis are those used in simulations, unless stated otherwise

Aµmol m−2 s−1Photosynthetic CO2 uptake rate
Acµmol m−2 s−1Canopy carbon uptake per metre square ground area per second
Acmmol m−2 d−1Ac integrated over the course of one day
Asatµmol m−2 s−1Light saturated rate of leaf photosynthetic rate under certain [CO2]
Caµmol mol−1Atmospheric CO2 concentration
Ciµmol mol−1Intercellular CO2 concentration
Djday of yearThe ith day in a year (200)
Fm2 m−2Total leaf area index, i.e. the ratio of leaf area per unit ground area (3)
Fshadem2 m−2F that is shaded at any point in time
Fsunm2 m−2F that is sunlit at any point in time
gsmmol mol−1Stomatal conductance
Iµmol m−2 s−1Photon flux density
Ioµmol m−2 s−1Incident photon flux density
Idiffµmol m−2 s−1Photon flux density of diffuse radiation
Idirµmol m−2 s−1Photon flux density of direct radiation
Is mol m−2 s−1Solar constant, i.e. the photon flux density in a plane perpendicular to the solar beam above the atmosphere (2600)
Iscatµmol m−2 s−1Photon flux density of scattered radiation within the canopy
Ishadeµmol m−2 s−1Mean I for shaded leaves within a canopy
Isunµmol m−2 s−1Mean I for sunlit leaves within a canopy
I2µmol m−2 s−1Photon flux density absorbed by PSII
Jµmol m−2 s−1Potential rate of whole chain electron transport through PSII for a given I2
Jmaxµmol m−2 s−1Light saturated J (250 or 180)
kdimensionlessFoliar absorption coefficient
kccs−1Maximum rate of carboxylation per active site of Rubisco (2.5 for the control)
kocs−1Maximum rate of oxygenation per active site of Rubisco.
Kcmµmol mol−1Rubisco Michaelis–Menten constant for CO2 (460 for the control)
K°mmmol mol−1Rubisco Michaelis–Menten constant for O2 (330 for the control)
Mmol m−2The concentration of Rubisco active sites on a leaf area basis (26)
Oammol mol−1Atmospheric O2 concentration (210)
Oimmol mol−1Intercellular O2 concentration (210)
PkPaAtmospheric pressure
PokPaStandard atmospheric pressure at sea level (101.324)
rdimensionlessPercentage of light that is reflected and transmitted (23%)
Rdµmol m−2 s−1Dark respiration rate (0)
sdimensionlessSpectral imbalance (0.25), indicating the percentage of light energy that can not be used in photochemistry
thourTime of day
tsnhourTime of solar noon (12)
Tl°CLeaf temperature (25)
Vcmaxµmol m−2 s−1Maximum rate of carboxylation at RuBP and CO2 saturation
Wcµmol m−2 s−1Rubisco-limited rate of carboxylation
Wjµmol m−2 s−1RubP-limited rate of carboxylation
xdimensionlessThe ratio of horizontal : vertical projected area of a canopy (1)
Γ*µmol mol−1CO2 compensation point in the absence of dark respiration
τdimensionlessThe specificity of Rubisco for CO2 relative to O2 (92.5 for the control)
αdimensionlessAtmospheric transmittance (0.85)
ΘdimensionlessConvexity factor for the nonrectangular hyperbolic response of electron transport through photosystem II to photon flux (0.7)
δdegreeSolar declination
Ω°Latitude (44°N)
θ°Solar zenith angle
λ°Angle between leaf surface and the direct beam solar radiation