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. 2014 Feb 18;164(4):2247–2261. doi: 10.1104/pp.113.232611

Can the Cyanobacterial Carbon-Concentrating Mechanism Increase Photosynthesis in Crop Species? A Theoretical Analysis1,[W],[OPEN]

Justin M McGrath 1, Stephen P Long 1,*
PMCID: PMC3982776  PMID: 24550242

A model incorporating the full cyanobacterial carbon-concentrating mechanism into C3 plants indicates that CO2 uptake rate could be increased by 60%, thus increasing yield during a time when yield growth has stagnated.

Abstract

Experimental elevation of [CO2] around C3 crops in the field has been shown to increase yields by suppressing the Rubisco oxygenase reaction and, in turn, photorespiration. Bioengineering a cyanobacterial carbon-concentrating mechanism (CCM) into C3 crop species provides a potential means of elevating [CO2] at Rubisco, thereby decreasing photorespiration and increasing photosynthetic efficiency and yield. The cyanobacterial CCM is an attractive alternative relative to other CCMs, because its features do not require anatomical changes to leaf tissue. However, the potential benefits of engineering the entire CCM into a C3 leaf are unexamined. Here, a CO2 and HCO3− diffusion-reaction model is developed to examine how components of the cyanobacterial CCM affect leaf light-saturated CO2 uptake (Asat) and to determine whether a different Rubisco isoform would perform better in a leaf with a cyanobacterial CCM. The results show that the addition of carboxysomes without other CCM components substantially decreases Asat and that the best first step is the addition of HCO3− transporters, as a single HCO3− transporter increased modeled Asat by 9%. Addition of all major CCM components increased Asat from 24 to 38 µmol m−2 s−1. Several Rubisco isoforms were compared in the model, and increasing ribulose bisphosphate regeneration rate will allow for further improvements by using a Rubisco isoform adapted to high [CO2]. Results from field studies that artificially raise [CO2] suggest that this 60% increase in Asat could result in a 36% to 60% increase in yield.

C3 species include the major grain crops rice (Oryza sativa) and wheat (Triticum aestivum) and overall accounted for approximately 75% of all primary foodstuff production in 2012 (FAOSTAT, 2013). The yield of many crop species has been substantially improved through breeding and agronomy, but advancement in yield has substantially slowed in many of the major C3 crops in the last decade, suggesting that limits on yield improvement using these techniques are being reached and that other approaches are needed (Long and Ort, 2010; Ray et al., 2012).

One largely unexploited approach would be to improve the efficiency of photosynthesis in these species (Zhu et al., 2010). The photosynthetic enzyme Rubisco catalyzes the reaction of CO2 with ribulose bisphosphate (RuBP), which eventually forms carbohydrates. However, Rubisco will also react with oxygen as the first step in photorespiration. This reaction is considered wasteful, since energy is consumed to recover RuBP and CO2 is lost in the process. In C3 plants at 25°C and current atmospheric [CO2], photorespiration results in an approximately 30% decrease in net carbon assimilation (Zhu et al., 2010). Thus, it is a large inefficiency in carbon uptake and a target for improvement.

Since CO2 and oxygen act competitively at Rubisco, photorespiration can be decreased by increasing [CO2] around Rubisco. That this will increase yield is demonstrated by the many studies that have artificially increased atmospheric [CO2] around C3 crops growing in the field (Kimball et al., 2002; Long et al., 2006b). Other photosynthetic organisms have evolved mechanisms to internally elevate [CO2] at Rubisco to decrease or eliminate photorespiration. Such carbon-concentrating mechanisms (CCMs) include C4 photosynthesis, as in maize (Zea mays), and the carboxysome and pyrenoid CCMs of single-celled cyanobacteria and algae. The C4 pathway requires the addition of the photosynthetic C4 dicarboxylate cycle and inner photosynthetic cells (i.e. bundle sheath), where Rubisco is localized. Converting a C3 crop to a C4 crop will require a coordination of changes in photosynthetic tissue differentiation and enzyme and transporter localization. In contrast, cyanobacteria achieve the same effect in a single cell by localizing Rubisco to specialized subcellular compartments called carboxysomes, so in theory they would require fewer changes. Carboxysomes are polyhedral bodies with a protein shell that encloses carbonic anhydrase (CA) and Rubisco packed in an ordered or semiordered array (Long et al., 2007; Yeates et al., 2011). Bicarbonate is actively transported from the environment into the cytosol of the cyanobacteria, and CO2 in the cytosol is actively hydrated to HCO3− using NADH. CO2 is also hydrated to HCO3−, which serves to increase the [CO2] gradient between the medium and cytosol, increasing CO2 flux, and also serves to refix CO2 that leaks from the carboxysome. Since the cytosol lacks CA and the plasma membrane has low permeability to HCO3−, a high cytosolic [HCO3−] far from equilibrium with [CO2] is achieved. Bicarbonate diffuses through the protein shell of the carboxysome, and since CA is localized to the inner side of the shell, it is rapidly converted to CO2, given the disequilibrium. The resulting high [CO2] around Rubisco inside the carboxysome accelerates carboxylation and competitively inhibits the oxygenation reaction (for review, see Price et al., 2008, 2011, 2013; Espie and Kimber, 2011).

The C4 pathway has been well characterized, and several projects are attempting to engineer it into C3 plants with some success (Slewinski, 2013). However, a primary obstacle has been achieving the necessary two tissue types with the correct localization of the key enzymes (Covshoff and Hibberd, 2012). In this regard, cyanobacterial CCM may provide an attractive parallel approach to eliminating photorespiration in C3 plants for two reasons. First, the biochemical, structural, and genetic components of the CCM are well understood, in that all of the necessary proteins and their genes have been identified. Second, chloroplasts of higher plants evolved from a common ancestor with modern cyanobacteria (Raven and Allen, 2003) and, therefore, are structurally similar. Thus, engineering carboxysomes into the chloroplast could involve introducing an operon containing the genes associated with the cyanobacterial CCM into the chloroplast genome.

There are, however, multiple proteins in the cyanobacterial CCM, and simultaneously transforming all of the required genes into an organism may be particularly challenging. Furthermore, some of the proteins appear to have a similar function, and others may be deleterious if introduced without the full apparatus. A random sequence of gene stacking would likely be inefficient, while the addition of some genes may simply be unnecessary. However, the biophysical reactions involved are well understood, and there are some measurements of the kinetics of the enzymatic reactions and transporters. With this information, a mathematical model can be created to simulate the CCM. Such a model will allow deduction of the minimal component set necessary for an improvement of leaf photosynthetic efficiency and identify a logical sequence of gene additions to deliver progressive improvements and avoid any lethal effects. This model will also be used to determine which aspects of the CCM exert the most control over the overall process of photosynthetic CO2 assimilation, information that can then be used to optimize the CCM, help identify the ideal set of components, or identify parameters that need to be more accurately measured in order to improve the effectiveness of the CCM model. Similar kinetic models have been applied to propose systems optimization of the Calvin cycle when plants are grown in elevated [CO2] (Zhu et al., 2007), of the whole C3 photosynthetic system (Zhu et al., 2013), C4 photosynthesis (Yu et al., 2014), and to determine the mechanistic basis of mesophyll conductance (Tholen and Zhu, 2011).

This paper develops a kinetic model to determine the potential of the cyanobacterial CCM engineered into C3 crops for improving photosynthesis by determining the necessary components and estimating the potential improvement of CO2 assimilation rate and efficiency. There are four distinct features to the cyanobacterial CCM: (1) a carboxysome with internally localized Rubisco and CA; (2) active transport of HCO3− from the medium into the cyanobacterial cytosol (the equivalent compartment in higher plants is the stroma of the chloroplast); (3) active hydration of CO2 to HCO3− within the cytosol; and (4) the absence of CA in the cyanobacterial cytosol, in contrast to the higher plant stroma, which contains high activities of CA. Cyanobacteria have three HCO3− transporters and two CO2 hydration enzymes that have different kinetics and are induced under different conditions (Price et al., 2011). All of these enzymes were examined, giving a total of seven individual components (listed in Fig. 1A) to the full cyanobacterial CCM model. Because of the common ancestry between cyanobacteria and higher plant chloroplasts, the two have homologous membranes and compartments. Proteins were modeled within a C3 leaf using locations equivalent to those in cyanobacteria. That is, bicarbonate transporters were localized to the inner chloroplast membrane, and carboxysomes were localized to the stroma. The CO2 hydration enzymes are bound to the thylakoid and plasma membranes in cyanobacteria, but the reaction for both occurs within the cyanobacterial cytosol; therefore, in this model, hydration of CO2 by these enzymes was localized to the stroma. This model was used to determine the necessity of each of the features noted above, potential improvements in light-saturated CO2 uptake (Asat; irradiance of 1,800 µmol photons m−2 s−1) that would be achieved on incorporation of each feature in turn, a possible sequence of gene additions that would give an incremental improvement, and the key components of the CCM. The model was also used to test the value of using higher plant isoforms of Rubisco versus prokaryotic isoforms adapted to incorporation within the carboxysome. Sources of uncertainty in the model are also defined.

Figure 1.

Figure 1.

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Asat of leaf models with sequential addition of components of the cyanobacterial CCM. Each point represents a leaf that contains the component listed for that column and all of the components in the columns to the left of it. The columns represent the sequence of transformations that produce the fastest increase in Asat assuming that it is not possible to simultaneously add carboxysomes and remove stromal CA and that it is not desirable to add CO2 hydration enzymes before removal of stromal CA (A) and assuming that it is possible to simultaneously add carboxysomes and remove stromal CA (B).

RESULTS

Incorporating the four key features (composed of seven individual components) of a cyanobacterial CCM into a C3 leaf increased Asat from 23.8 to 38 µmol m−2 s−1 in this model (Fig. 1). The majority of changes that involved the addition of only a single feature decreased Asat, sometimes to levels that would greatly reduce plant growth and probably require rescue in high [CO2] (a list of all possible combinations of features and their effects on Asat is given in Supplemental Table S1). However, addition of any one of the HCO3− transporters, bicarbonate uptake A (BicA), bicarbonate transporter1 (BCT1), or sodium-bicarbonate transporter A (SbtA) alone, improved Asat. The addition of carboxysomes without removal of stromal CA or vice versa was detrimental to Asat regardless of the inclusion of other features. Thus, unless it is possible to simultaneously add carboxysomes and remove stromal CA, there is no series of transformations that provides increased Asat at each stage. Without the ability to make those changes simultaneously, the results here indicate that the best pathway of improvement is to first add the HCO3− transporters, add carboxysomes, remove stromal CA, and then add the NADH-driven CO2 hydration enzymes (Fig. 1A). If it is possible to add carboxysomes and remove stromal CA simultaneously, then a slightly different pathway provides faster initial improvement, as follows: adding (1) BicA, (2) carboxysomes with simultaneous removal of CA, (3) BCT1, (4) NAD(P)H dehydrogenase complex (NDH1,3), (5) NDH1,4, and (6) SbtA (Fig. 1B). The final result is the same regardless of which sequence of transformations is used (last columns in Fig. 1).

At minimum, in order for the carboxysome to be effective requires the removal of stromal CA and the addition of BicA, BCT1, or NDH1,3 (Supplemental Table S1). Individually, neither SbtA nor NDH1,4 increase the stromal [HCO3−] enough for the carboxysome to be effective. Although at the enzyme concentrations modeled, the HCO3− transporters are more effective than CO2 hydration enzymes at increasing Asat, since the CO2 hydration and HCO3− transport enzymes use different forms of energy, it may be desirable to include one of each type of enzyme so that the system is more flexible. If only one HCO3− transporter and one NDH isoform can be incorporated with a carboxysome, the pair that gives the highest Asat is BicA with NDH1,3 (Supplemental Table S1).

In the absence of a CCM, replacement of the C3 crop Rubisco with a cyanobacterial or algal isoform of Rubisco resulted in a 5% to 50% decrease in Asat (Fig. 2). However, when the addition of the CCM is simulated and Rubisco is assumed to be confined to the carboxysome, this disadvantage is eliminated for most of the cyanobacterial, bacterial, and algal isoforms, where, in the high [CO2] of the carboxysome, rates were often similar to, but did not exceed, those of the higher plant isoforms (Fig. 2).

Figure 2.

Figure 2.

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Asat of leaf models without (black symbols) and with (gray symbols) a cyanobacterial CCM using different isoforms of Rubisco. Species from which the Rubisco isoform parameters were used are listed on the vertical axis. Parameters for the isoforms are given in Supplemental Table S2. Symbols represent the class of species: closed circles, C3; closed squares, C4; closed triangles, cyanobacteria; open triangles, nongreen algae form I; and open circles, nongreen algae form II (where form I and form II are as defined by Gibson and Tabita [1977]).

In order to determine how limitations to photosynthesis are changed in a leaf with a CCM, the sensitivity of Asat to several parameters in the model was compared between an untransformed leaf and a leaf with all seven of the changes listed in Figure 1A. In the transformed leaf, Asat was very sensitive to the maximum rate of electron transport (Jmax), with slight sensitivity to stomatal conductance and cytosolic [H+] (Fig. 3). Following Farquhar et al. (1980), we use the term Jmax. During the development of that model, it was assumed that RuBP regeneration was limited solely by electron transport, but it is now known that enzyme activity in the Calvin cycle also limits RuBP regeneration (Lefebvre et al., 2005). Thus, when we refer to J (for rate of RuBP regeneration) and Jmax, this actually represents RuBP regeneration with the understanding that it may be limited by Calvin cycle activity or electron transport rate. Because assimilation is saturated at high [CO2], Asat in the transformed leaf will be insensitive to the many factors that limit CO2 transfer and [CO2] at Rubisco in the untransformed leaf. Therefore, the sensitivity of [CO2] within the carboxysome was also determined to assess which parameters most influence the CCM (Fig. 4). In this case, the carboxysomal [CO2] in the transformed leaf was similarly most sensitive to Jmax, but several other parameters exerted strong influence, in particular the carboxysome shell permeability to CO2 and HCO3−, the carboxysomal and cytosolic pH, the Km of BicA, and the Vmax of BicA, BCT1, and NDH1,3 (Fig. 4).

Figure 3.

Figure 3.

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Sensitivity of the predicted Asat to model parameters for leaf C3 photosynthesis without (black circles) or with (gray circles) the addition of the cyanobacterial CCM. Rd, Mitochondrial respiration in the light.

Figure 4.

Figure 4.

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Sensitivity of carboxysomal [CO2] to variation in model parameters for leaf C3 photosynthesis with the simulated addition of the cyanobacterial CCM. Rd, Mitochondrial respiration in the light.

To determine how the permeability of the protein shell to CO2 affects the effectiveness of the CCM, the coefficient of permeability was varied across a range of plausible values. Although low permeability to CO2 is a key characteristic of the protein shell (Dou et al., 2008; Cai et al., 2009), the actual permeability to CO2 has never been quantitatively measured directly or indirectly, and in this model it could only be assumed that is was similar to thin films of other proteins, in this case, whey protein isolate (Perez-gago and Krochta, 2001). Since there is such uncertainty in this parameter, it is desirable to know whether it could realistically have a value at which the cyanobacterial CCM would not be effective if introduced into a C3 leaf. The lower limit is zero permeability, and a reasonable upper limit is the same permeability to CO2 as lipid bilayer membranes, which are relatively permeable to small, uncharged molecules such as CO2 compared with protein layers (Pp,CO2 compared with Pcsome,CO2 in Table I). A modeled leaf with a CCM had higher values of Asat compared with a modeled leaf without a CCM regardless of the assumed permeability of the shell to CO2 (Fig. 5). The CCM becomes more effective as shell CO2 permeability decreases, while Asat shows high sensitivity to CO2 permeability around the best estimate value for this parameter (Fig. 5).

Table I. Parameters, values, and their sources.

Name Symbol Value Units References
Temperature T 298.15 K 25°C
Pressure pressure 101,325 Pa Atmospheric pressure
Gas constant R 8.31446 J mol−1 K−1 Universal gas constant
Atmospheric [CO2] Ca 390 × 10−6 mol mol−1 Approximate atmospheric [CO2] in 2012
Oxygen partial pressure O pressure × 0.208 Pa 21% oxygen
Solubility of CO2 Inline graphicHCO2 2,994.012 m3 Pa−1 mol−1 von Caemmerer (2000)
Solubility of oxygen Inline graphic 79,365.1 m3 Pa−1 mol−1 von Caemmerer (2000)
CO2 diffusivity in water Inline graphic 1.7 × 10−9 m2 s−1 Terashima et al. (2011)
HCO3− diffusivity in water Inline graphic Inline graphic m2 s−1 Evans et al. (2009)
Molarity of air nair 40.87 mol m−3 Calculated from T, R, and pressure using the ideal gas law.
Boundary thickness lb 0.0005 m Nobel (1983); 10-cm leaf at about 1 m s−1 wind speed
Cell wall thickness lw 0.32 × 10−6 m Pritchard et al. (1986)
Chloroplast-to-plasmalemma distance lthin cytosol 0.1 × 10−6 m Evans et al. (2009)
Boundary layer conductance gb 1.53 mol m−2 s−1 Calculated from lb
Stomatal conductance gs 0.4375 mol m−2 s−1 Bernacchi et al. (2006)
Mesophyll surface area fraction Sm 15 m2 m−2 (exposed mesophyll surface area per one-sided leaf area) Slaton and Smith (2002)
Carboxysome surface area fraction Scsome 72.75 m2 m−2 (surface area per one-sided leaf area) Long et al. (2007)a
CO2 transfer coefficient ktr Inline graphic m s−1 Assumed that CO2 dissolution into the cell wall only occurs in the one-tenth of the wall adjacent to the airspace
Cell wall porosity ϕapo 0.2 Dimensionless Evans et al. (2009)
Cell wall tortuosity τapo 1 Dimensionless Evans et al. (2009)
Plasmalemma permeability to CO2 Inline graphic 0.0035 m s−1 Gutknecht et al. (1977)
Plasmalemma permeability to HCO3− Inline graphic 0.5 × 10−6 m s−1 Tholen and Zhu (2011)
Chloroplast envelope permeability to CO2 Inline graphic Inline graphic m s−1 Calculated using two membrane layers of the envelope
Chloroplast envelope permeability to HCO3− Inline graphic Inline graphic m s−1 Calculated using two membrane layers of the envelope
Mitochondrial membrane permeability to CO2 Inline graphic Inline graphic m s−1 Calculated using two membrane layers of the mitochondrion
Mitochondrial membrane permeability to HCO3− Inline graphic Inline graphic m s−1 Calculated using two membrane layers of the mitochondrion
Carboxysome shell permeability to CO2 Inline graphic Inline graphic m s−1 Assumed
Carboxysome shell permeability to oxygen Inline graphic Inline graphic m s−1 Assumed
Carboxysome shell permeability to HCO3− Inline graphic Inline graphic m s−1 Assumed
Gluten film oxygen diffusivity Inline graphic 0.0914 × 10−12 m2 s−1 Perez-gago and Krochta (2001)
Carboxysome shell thickness lshell 0.03 × 10−6 m Long et al. (2007)
Chloroplast surface area fraction Schl 0.75 m2 m−2 (surface area appressed to the plasmalemma per mesophyll surface area) Tomás et al. (2013)
Mitochondria surface area fraction Smito 0.12 m2 m−2 (surface area appressed to the plasmalemma per mesophyll surface area) Tholen and Zhu (2011)
Cytosol viscosity Inline graphic 2 Dimensionless (relative to water) Tholen and Zhu (2011); compare with Scalettar et al. (1991) and Köhler et al. (2000)
Stroma viscosity Inline graphic 10 Dimensionless (relative to water) Tholen and Zhu (2011); compare with Köhler et al. (2000)
Carboxysome viscosity Inline graphic Inline graphic Dimensionless (relative to water) Assumed
CA keq ([HCO3−] × [H+]/[CO2]) keq 0.56 × 10−6 mol m−3 Pocker and Miksch (1978)
CA kcat kh,cat 0.3 × 106 s−1 Larsson et al. (1997)
CA Km,CO2 Kh,c 1.5 mol m−3 Pocker and Ng (1973)
CA Km,HCO3 Kh,b 34 mol m−3 Pocker and Miksch (1978)
Rubisco maximum rate of carboxylation Vc,max 7.6 mol m−3 s−1 Bernacchi et al. (2005)b
Rubisco carboxylation rate constant kc,cat 2.87 site−1 s−1 von Caemmerer (2000)
Rubisco Michaelis-Menten constant for CO2 Kc 0.0086 mol m−3 von Caemmerer (2000)c
Rubisco Michaelis-Menten constant for oxygen Ko 0.215 mol m−3 von Caemmerer (2000)c
CO2 photocompensation point Γ* 1.29 × 103 mol m−3 von Caemmerer (2000)c
Maximum rate of RuBP regeneration Jmax 13.7 mol m−3 s−1 Bernacchi et al. (2002) at 25°Cb,d
SbtA Michaelis-Menten constant for Na KNa 1.048 mol m−3 Shibata et al. (2002)e
SbtA Michaelis-Menten constant for HCO3− Inline graphic 0.019 mol m−3 Shibata et al. (2002)e
SbtA maximum rate of HCO3− transport Vmax,sbta 22.48 × 10−6 mol m−2 s−1 Shibata et al. (2002)e,f
BicA Michaelis-Menten constant for HCO3− Km,bica 0.217 mol m−3 Price et al. (2004)
BicA maximum rate of HCO3− transport Vmax,bica 185 × 10−6 mol m−2 s−1 Price et al. (2004)f
BCT1 Michaelis-Menten constant for HCO3− Km,bct1 0.015 mol m−3 Omata et al. (2002)
BCT1 maximum rate of HCO3− transport Vmax,bct1 55 × 10−6 mol m−2 s−1 Omata et al. (1999)f
NDH1,3 Michaelis-Menten constant for CO2 Km,ndh13 0.012 mol m−3 Price et al. (2011)
NDH1,3 maximum rate of CO2 hydration Vmax,ndh13 0.075 mol m−2 s−1 Berner (1993)g; David et al. (2002)
NDH1,4 Michaelis-Menten constant for CO2 Km,ndh14 0.002 mol m−3 Price et al. (2011)
NDH1,4 maximum rate of CO2 hydration Vmax,ndh14 Vmax,ndh13 mol m−2 s−1 Berner (1993)g; David et al. (2002)
Mitochondrial respiration in the light Rd 1.98 mol m−3 s−1 Bernacchi et al. (2002) at 25°C
Stromal CA concentration [CA]stroma 0.27 mol m−3 Tholen and Zhu (2011); compare with Gillon and Yakir (2000)
Mitochondrial CA concentration [CA]mito [CA]stroma mol m−3 Assumed
Cytosolic CA concentration [CA]cyto [CA]stroma/2 mol m−3 Tholen and Zhu (2011)
Apoplastic CA concentration [CA]apo [CA]stroma/2 mol m−3 Assumed
Stroma mesophyll volume fraction fstroma 0.147 m3 m−3 (volume per mesophyll cell volume) Winter et al. (1994)
Cytosol mesophyll volume fraction fcytosol 0.054 m3 m−3 (volume per mesophyll cell volume) Winter et al. (1994)
Airspace volume fraction None 0.5 m3 m−3 (volume per bulk volume of leaf) Byott (1976)
Stroma volume fraction None 0.87 × 10−6 m3 m−2 (volume per mesophyll surface area) Tholen and Zhu (2011)
Mitochondria volume fraction None 0.027 × 10−6 m3 m−2 (volume per mesophyll surface area) Tholen and Zhu (2011)
Leaf chlorophyll None 0.5 g m−2 Daughtry et al. (2000)
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a

The number of carboxysomes was chosen so that the concentration of Rubisco as mol m−2 was the same as a leaf without carboxysomes.  bConverted to a volumetric basis from a leaf-area basis using values of 100 and 180 µmol m−2 s−1 for Vc,max and Jmax.  cCalculated from Table 1.3 of von Caemmerer (2000) using solubilities of 0.0034 and 0.00126 mol L−1 bar−1 for CO2 and oxygen, respectively.  dWhen the model of Farquhar et al. (1980) was developed, the rate of RuBP regeneration was assumed to be entirely limited by the rate of electron transport. Thus, the symbol Jmax was used. It is now known that processes other than electron transport can limit RuBP regeneration. Here, we use the same symbol for continuity, but with the understanding that it represents RuBP regeneration, potentially being limited by several factors.  eValues were determined from Shibata et al. (2002) by fitting data to a two-substrate sequential enzyme reaction model.  fAssuming the same amount of protein per chlorophyll in cyanobacteria and leaf chlorophyll concentration from Daughtry et al. (2000).  gValues for protein concentration in cyanobacteria for these enzymes were obtained through personal communication with G. Dean Price. Values were calculated assuming that higher plants would have the same protein concentration per area of thylakoid membrane as in cyanobacteria. There were multiple estimates of Vmax and thylakoid surface area. To represent a typical value, the mean of the highest and lowest estimates was used.

Figure 5.

Figure 5.

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Predicted Asat for a C3 leaf with the simulated addition of the cyanobacterial CCM plotted against varying assumed permeabilities of the carboxysome protein shell to CO2. The range of permeabilities was chosen so that it would encompass all plausible values. The lower limit is zero permeability, and a reasonable upper limit is the same permeability to CO2 as lipid bilayer membranes, which are quite permeable to small, uncharged molecules such as CO2. The vertical dotted line is the best estimate for permeability, which was used in all other predictions (Figs. 1–5 and 7). The horizontal dashed line is the modeled assimilation rate of a C3 leaf without a CCM.

Even though Asat is not improved by using a cyanobacterial Rubisco isoform due to RuBP-regeneration limitation, carboxysomal [CO2] is nearly high enough to take advantage of the higher kcat of that isoform if the RuBP regeneration rate can be increased (Fig. 6). In saturating light, a modeled leaf with a cyanobacterial CCM was more efficient than a modeled C3 leaf in terms of ATP use per net CO2 fixation by Rubisco at internal airspace [CO2] (Ci) below about 300 µmol mol−1 (Fig. 7), whereas in light-limited conditions, the CCM was more ATP efficient at Ci below about 150 µmol mol−1 (Fig. 7).

Figure 6.

Figure 6.

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Predicted Asat versus carboxysome [CO2] for C3 (black lines) and cyanobacterial (gray lines) isoforms of Rubisco. Solid lines are modeled Asat. Dashed lines are the net carboxylation rate of Rubisco if RuBP regeneration were not limiting. Dotted-dashed lines are the supply function from the atmosphere to the carboxysome. The [CO2] at the x intercept is atmospheric [CO2], where the supply function intercept assimilation rate is the [CO2] in the carboxysome and Asat in atmospheric [CO2] (390 µmol mol−1).

Figure 7.

Figure 7.

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ATP use per net carboxylation by Rubisco (vc,net = vc – vo/2) versus intercellular airspace [CO2] in light-saturated (solid lines; 1,800 µmol photosynthetically active radiation m−2 s−1) and light-limited (dashed lines; 180 µmol photosynthetically active radiation m−2 s−1) conditions for a modeled C3 leaf without (black lines) or with (gray lines) a cyanobacterial CCM.

DISCUSSION

Potential Improvement to Asat

The increase in Asat from 23.8 to 38 µmol m−2 s−1 shown here from theory due to engineering a cyanobacterial CCM into C3 species could have remarkable benefits for crop production, including increased yield, nitrogen use efficiency, and water use efficiency. Increasing leaf photosynthesis by 25% through artificial elevation of [CO2] under open-air conditions in the field increased the yield of soybean (Glycine max) by 15% and water use efficiency by 20% to 40% (Long et al., 2006b; Bernacchi et al., 2007). In our simulation here, the 60% increase in Asat that is predicted would by analogy allow a 36% increase in yield. The smaller increase in yield than in photosynthesis for crops grown in the field under elevated [CO2] is suggested to result from sink limitation (i.e. the ability of the crop to make full use of the available additional photoassimilate; Ainsworth et al., 2004; Long et al., 2006a). Identifying germplasm with sufficient capacity to form grain or seed is considered less challenging than the generation of more resource to fill those grains or seed (Sheehy et al., 2001). Therefore, it might be expected that provision of an increase in photosynthetic efficiency of 60% could, with some breeding, be matched by an equal yield increase.

The prediction here is for Asat (i.e. light-saturated photosynthesis). Typically, about half of crop carbon gain is from light-limited photosynthesis (Baker et al., 1988). Here, though, an increase in photosynthesis would also be expected, since the maximum efficiency of carbon assimilation under light-limiting conditions is determined by the ratio of carboxylations to oxygenations at Rubisco. The model results indicate that the CCM was more ATP use efficient in light-limited conditions for Ci below about 150 µmol mol−1 (Fig. 7). The difference between light conditions occurs because in RuBP regeneration-limited photosynthesis, CO2 uptake saturates at a lower Ci than HCO3− transport. Therefore, as Ci increases, HCO3− transport increases more than CO2 uptake and ATP/CO2 increases. In low light, photosynthesis is limited by RuBP regeneration at a lower Ci, making this effect apparent at approximately 50 µmol mol−1 CO2 (Fig. 7). Although initially this suggests that the CCM is not as beneficial in light-limited conditions, if HCO3− transport were regulated to be proportional to light levels or inversely proportional to stromal [HCO3−], the efficiency in light-limited conditions would be higher than presented here. Regulation of these transporters has not been thoroughly studied, but some are inducible (Price et al., 2013), and it is reasonable to assume that they are disabled in the dark in the cyanobacterial system or that there would be futile cycling of CO2 in the dark. That suggests that their activity could also be proportional to light intensity. Therefore, the concentration of CO2 at Rubisco would be expected to increase not just light-saturated photosynthesis but also canopy photosynthesis to a similar degree.

Cyanobacterial and algal Rubisco isoforms performed very poorly under conditions assumed to operate in the normal C3 plastid (i.e. without a CCM; Fig. 2). This is to be expected, given that they presumably reflect millions of years of evolution to operate in a high [CO2] environment, with their low specificity resulting in high oxygenation rates in the low [CO2] of the C3 leaf chloroplast. Although the performance of these isoforms of Rubisco was increased greatly by the addition of the cyanobacterial CCM, none of these isoforms substantially outperformed the higher plant isoforms, despite their higher turnover number (kcat) per active site. This resulted because in the modeled system, the rate of RuBP regeneration and not the rate of carboxylation was limiting, preventing a stronger response in Asat and explaining the high sensitivity of the system to J (Figs. 3 and 4). Thus, at elevated [CO2], most Rubisco isoforms support a similar Asat, as simulated (Fig. 2). However, replacing the C3 crop Rubisco with a cyanobacterial isoform could still be of value. First, cyanobacterial Rubisco can assemble in a lattice form, and the carboxysome shell can enclose this. It is not known whether this is possible with higher plant or any eukaryotic Rubisco, so introducing the cyanobacterial Rubisco along with the carboxysome shell structure into the chloroplast would remove this uncertainty. Second, model results show that this CCM is capable of increasing carboxysomal [CO2] to levels high enough to take advantage of the higher kcat of the cyanobacterial Rubisco isoform (Fig. 6), which could be utilized in two ways: increasing Asat by increasing the capacity for RuBP regeneration or decreasing Rubisco concentration while maintaining the same Asat. Recent theoretical and practical evidence suggests that reoptimization of investment within the Calvin cycle could increase the rate of RuBP regeneration (Lefebvre et al., 2005; Zhu et al., 2007). RuBP regeneration might also be increased by increasing the maximum rate of whole-chain electron transport, which is suggested to be limited by the amount of cytochrome b6/f complex (Price et al., 1998; Ruuska et al., 2000). However, even with RuBP regeneration limiting photosynthesis, at high carboxysomal [CO2], a Rubisco isoform with a high kcat would allow for lower Rubisco concentrations than with a higher plant C3 isoform but still maintain the same photosynthetic rate, improving nitrogen use efficiency (Long et al., 2004).

The cyanobacterial Rubisco isoforms saturate at much higher [CO2] than C3 isoforms (Km,CO2 of 180 compared with 10 mmol m−3; Fig. 6). The results here show that they are not saturated even at the simulated high [CO2] of 1,700 µmol mol−1 achieved with the CCM here. Therefore, further increases in [CO2] would still be beneficial. The sensitivity of carboxysomal [CO2] to different system features indicates that the primary targets increase [CO2] further. Here, parameters with sensitivity coefficients greater than 0.1 were considered important (i.e. a 1% change in the parameter resulted in a greater than 0.1% change in carboxysomal [CO2]). Carboxysomal [CO2] is sensitive to the Vmax of BicA, BCT1, NDH1,3, and NDH1,4, suggesting that improving effectiveness may be as simple as increasing the activities of these enzymes (Fig. 4). In addition, the model is also sensitive to pH in both the carboxysome and cytosol (Fig. 4). The pH in the carboxysome will most likely be the same as in the stroma, since protons can readily cross the carboxysome shell (Menon, 2010), so altering carboxysomal pH would require changing stromal pH as well. However, it is not known how the diffusion of protons within the lattice of Rubisco will affect pH in the carboxysome. Since pH in both the cytosol and stroma is regulated, there are limits to altering pH in those compartments, but because sensitivity to these parameters is so high, even small changes should have a substantial effect. In addition to these factors, there are numerous anatomical features that are likely not optimized for a CCM, such as average cell volume, the exposed surface area of mesophyll cells, and cell wall thickness. Although altering these traits offers another route to improve the effectiveness of the CCM, examining all of them was beyond the scope of this study, whose primary aim was to assess the benefit of engineering the cyanobacterial CCM into the C3 crop chloroplast.

Necessary Components and an Optimal Gene-Stacking Sequence

The CCM involves many components, some of which may prove more difficult to introduce than others. For example, two of the HCO3− pumps, BicA and SbtA, require single transformations targeted at the plastid envelope and should be relatively easy transformations (Burnell, 2011). The carboxysome shell, by contrast, is encoded by up to nine genes, one with multiple products, that must be expressed in correct proportions, and it requires the assembly of the shell around Rubisco and CA (Price et al., 1993; Ludwig et al., 2000; Long et al., 2007, 2010; Yeates et al., 2008; Kinney et al., 2011; Rae et al., 2012). It may also be difficult to attach effective transit peptides to each component, making plastid transformation a better option. However, plastid transformation has succeeded so far in only a few species and, as yet, in none of the major grain and seed crops (Maliga, 2004; Meyers et al., 2010). Of the four key features of the cyanobacterial CCM, the HCO3− transporters improve photosynthesis independently of other features (Fig. 1; Supplemental Table S1). In contrast, carboxysomes and removal of stromal CA are mutually dependent, and both have a strongly detrimental effect on simulated Asat in the absence of the HCO3− transporters. This work suggests that while stacking all four major features of the cyanobacterial CCM would give by far the greatest benefit, an increase of 9% could be achieved by simply introducing the BicA transporter and an increase of 16% could be achieved by introducing BicA, BCT1, and SbtA together (Fig. 1A). This work also shows that this would be a valuable first step, since introducing the carboxysome and knocking out the stromal CA would be ineffective without HCO3− transporters. The total Vmax for transport of HCO3− across the membrane is the sum of the Vmax of each transporter. Thus, adding multiple transporters is more effective than adding a single transporter because it increases the Vmax of total transport. In that respect, it could be equally as effective to simply express more of a single transporter than to introduce multiple transporters. However, the different affinities (Table I) suggest that the transporters allow for uptake at a wide range of [HCO3−], allowing the CCM to be effective across a wider range of Ci. This would be particularly useful if the inducibility of the transporters seen in cyanobacteria (Price et al., 2013) is preserved in the C3 leaf, since that would allow for specific transporters to be inactivated at [HCO3−] where they are ineffective.

Key Model Parameters

The sensitivity of modeled C3 and CCMs suggests that transformation of the complete cyanobacterial CCM into the chloroplast would result in the control of Asat by stomatal conductance, the maximum rate of carboxylation by Rubisco (Vc,max), and the CO2 permeabilities of the chloroplast envelope and plasma membranes would shift to J, which here refers to RuBP regeneration that can be limited by electron transport or the activity of enzymes in the Calvin cycle. As discussed earlier, increasing the amount of cytochrome b6/f complex may be one approach to increase Jmax (Price et al., 1998; Ruuska et al., 2000). Increasing Jmax in C3 species certainly seems possible, since C4 species tend to have higher values of Jmax than C3 species (Wullschleger, 1993; Massad et al., 2007). There is also evidence that, in addition to electron transport, RuBP regeneration is colimited by enzyme activity in the Calvin cycle, specifically the amount of sedoheptulose-1,7-bisphosphatase (SBPase; Harrison et al., 2001), and increasing the concentration of SBPase has been shown to increase carbon assimilation and biomass in current atmospheric [CO2] (Lefebvre et al., 2005). Moreover, the increase in biomass in an SBPase-overexpressing line compared with the wild type was larger in elevated [CO2] compared with control [CO2] (Rosenthal et al., 2011), which would be expected since in saturating light, rising [CO2] shifts control from Rubisco to the rate of RuBP regeneration (Long et al., 2004). This would make SBPase overexpression a target to add to a plant containing a successful cyanobacterial CCM.

Assessment of the sensitivity of predicted carboxysome [CO2] to variation in parameters in the model (Fig. 4) had two purposes: (1) identifying the most effective components of the CCM and (2) identifying parameters in the model in most need of improved constraint, to focus effort to better understand the potential value of inclusion of the cyanobacterial CCM. The high sensitivity of the system to the kinetic properties of BicA and BCT1 underline the finding that the simulated inclusion of these HCO3− transporters alone will apparently increase Asat, making them primary first targets for transformation. The complete CCM was also sensitive to the kinetic properties of the CO2-hydrating enzyme NDH1,3, although this will depend on the diffusivity of CO2 across the carboxysome shell. These enzymes serve the purpose of greatly steepening the CO2 gradient between the atmosphere and stroma, thus accelerating CO2 uptake into the chloroplast. In theory, the effect of this steepened gradient should be far more effective in the leaf than in a cyanobacterium, given that diffusivity is orders of magnitude greater in air than in water. There are few estimates of kinetic parameters for these transporters, though, so there is substantial uncertainty regarding their true kinetic properties and even amounts. This highlights a key need moving forward in assessing the real value of pursuing the addition of these proteins to crop plant plastids.

Equally, the system proved very sensitive to the assumed permeability of the protein shell (Figs. 4 and 5). The CCM is beneficial in terms of increasing Asat across the plausible range of permeabilities (Fig. 5), indicating that, although there is little certainty in this value, the CCM provides a benefit regardless of the true permeability of the shell. Nonetheless, predictions of Asat vary strongly depending on the value used and are very sensitive to shell CO2 permeability at the value used in this model (Figs. 4 and 5). Thus, better constraint of this parameter will be crucial to a more accurate quantification of the benefit of adding carboxysomes and the potential value of engineering the shell to decrease CO2 permeability. The same argument can be made for the movement of HCO3− through the shell, particularly understanding whether this is a gated transfer (Klein et al., 2009). In contrast, the model is completely insensitive to permeability of the protein shell to oxygen. This is because oxygen in the atmosphere is very high at 21% and diffuses rapidly in air, so regardless of the permeability, large amounts of oxygen would diffuse into the carboxysome. Therefore, despite the fact that the true permeability to oxygen is also highly uncertain, obtaining better estimates will do little to improve the accuracy of model predictions.

CONCLUSION

This simulation of the addition of the cyanobacterial CCM to a C3 crop leaf suggests that a nearly 60% improvement in net leaf CO2 uptake could be achieved without any modification of leaf anatomy. By analogy to the artificial elevation of [CO2] in crop fields driving increased leaf CO2 uptake, this could lead to a 36% to 60% increase in C3 crop yield. The simulations suggest that the addition of the single BicA transporter would alone increase photosynthesis by 9% or 16% if all transporters are added. Beyond this, there is no benefit to introducing other components of the cyanobacterial CCM unless the complete CCM is added. Addition of carboxysomes and localization of Rubisco within this microcompartment would itself significantly depress leaf CO2 uptake; their benefit is only achieved by minimally adding a plastid envelope HCO3− transporter such as BicA or a stromal CO2 hydration enzyme such as NDH1,3 and complete removal of CA activity from the stroma. Introducing BicA and other transporters could be achieved by nuclear transformation and the inclusion of chloroplast envelope-targeting sequences. Achieving the full benefit of the cyanobacterial CCM will be considerably more challenging and most probably will depend on plastid transformation for expression of the shell proteins and an isoform of Rubisco adapted to packaging within the carboxysome.

MATERIALS AND METHODS

Carboxylation by Rubisco was simulated using the steady-state biochemical model of leaf photosynthesis of Farquhar et al. (1980):

graphic file with name pp_232611_E1.jpg (1)

where vc is the rate of carboxylation by Rubisco, Vc,max (mol m−3 s−1) and [CO2] (mol m−3) are as defined above, [O2] (mol m−3) is the oxygen concentration, Kc (mol m−3) and Ko (mol m−3) are the affinities of Rubisco for CO2 and oxygen, J (mol m−3 s−1) is as defined above, assumed to be limited by electron transport, and Γ* (mol m−3) is the CO2 photocompensation point. Values for all parameters, and their sources, are given in Table I.

Oxygenation by Rubisco was calculated as by von Caemmerer (2000):

graphic file with name pp_232611_E2.jpg (2)

where vo is the rate of oxygenation by Rubisco. CO2 was released in the mitochondria at a rate of vo/2.

J was calculated as a function of the amount of light absorbed by PSII (I2), Jmax, and a curvature factor (θ), using a nonrectangular hyperbolic relationship of J to I2:

graphic file with name pp_232611_E3.jpg (3)

The amount of light absorbed by PSII (I2) was calculated using an irradiance (I) of 1,800 µmol m−2 s−1, leaf absorptance (α), and a light quality correction factor (f):

graphic file with name pp_232611_E4.jpg (4)

Reversible conversion between HCO3− and CO2 by CA was modeled using Michaelis-Menten kinetics:

graphic file with name pp_232611_E5.jpg (5)

where kh,cat (s−1) is the hydration rate constant, the concentrations ([CA], [HCO3−], and [H+]) are measured in mol m−3, and Kh,c (mol m−3) and Kh,b (mol m−3) are the affinities of CA for CO2 and HCO3−.

Bicarbonate transport across the chloroplast envelope by BCT1 and BicA was calculated using one-substrate Michaelis-Menten kinetics as:

graphic file with name pp_232611_E6.jpg (6)

where Vmax is the maximum rate of transport for BCT1 or BicA and Km is the Michaelis-Menten constant of BCT1 or BicA for HCO3−.

Bicarbonate transport across the chloroplast envelope by SbtA was calculated using the two-substrate, sequential reaction Michaelis-Menten kinetics as from Alberty (1953):

graphic file with name pp_232611_E7.jpg (7)

where Vmax is the maximum rate of transport for SbtA and KHCO3- and KNa are the Michaelis-Menten constants for HCO3− and Na+, respectively. Parameters for this enzyme were determined by fitting this model to data from Shibata et al. (2002).

Diffusion of CO2 and HCO3− was modeled using various forms of Fick’s law depending on the compartment. For diffusion across the boundary layer and intercellular space, a conductance was used:

graphic file with name pp_232611_E8.jpg (8)

For diffusion across a membrane, a permeability was used:

graphic file with name pp_232611_E9.jpg (9)

And for diffusion within a gas or aqueous solution, a diffusivity was used:

graphic file with name pp_232611_E10.jpg (10)

where x1 and x2 are concentrations of CO2 or HCO3− in adjacent compartments, g (mol m−2 s−1) is conductance of CO2 across the stomata or boundary layer, P (m s−1) is permeability of the membrane through which either CO2 or HCO3− is diffusing, S (m2) is the surface area of this membrane, D (m2 s−1) is diffusivity of HCO3− through liquid or CO2 through liquid or air depending on the compartment, v (dimensionless) is the relative viscosity of the solution compared with water, and l (m) is the length of the diffusive path. Parameters were obtained by a literature search, and for anatomical characteristics, values for soybean (Glycine max) or similar species were used when available.

Diffusion was modeled from the atmosphere to the site of Rubisco via a potential nine compartments, as illustrated in Figure 8. The apoplast, thin cytosol, stroma, and carboxysome were each further divided into six subcompartments (for a total of 29 distinct compartments) in order to correctly estimate nonlinear reaction rates as described below. Since the majority of CO2 in the cytosol diffuses via a short path to the chloroplast (Terashima et al., 2011), the cytosol was modeled as two compartments: the thin portion of cytosol (labeled “thin cytosol” in Fig. 8) between the plasmalemma and chloroplast envelope and the bulk cytosol comprising the rest of the cytosol.

Figure 8.

Figure 8.

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Compartments with the fluxes between pools in each compartment. The nine biological compartments of the model are labeled in boldface italic letters. The apoplast, thin cytosol, chloroplast stroma, and carboxysome compartments were each divided into size subcompartments to allow for nonlinear reactions of Rubisco and CA with their substrates. Pools are given in roman letters. Fluxes are labeled in italics, and rate equations for each flux are given in Supplemental Appendix S1.

For the model, the carboxysome was assumed to approximate a sphere, with a layer of CA on the immediate inside of the shell and then concentric layers of Rubisco filling the remainder of the space. The permeability of the protein shell to CO2 and oxygen has not been determined quantitatively. In the absence of these measurements, it was assumed to be similar to a protein thin film, in this case whey protein isolate (Perez-gago and Krochta, 2001), corrected for the known thickness of the carboxysome protein shell (Long et al., 2007). Similarly, the permeability of the shell to HCO3− is unknown. Although HCO3− does not permeate lipid membranes easily, it is thought that the hexamers of the carboxysome shell form gated pores that allow selective permeation by HCO3− (Kerfeld et al., 2005; Klein et al., 2009). As a basis of comparison, it was reasoned that the shell should be as permeable to HCO3− as lipid membranes are to dissolved gases, so it was assumed that the permeability of the shell to HCO3− was similar to the permeability of CO2 through a lipid bilayer. The consequence of uncertainty in these parameters was evaluated using a sensitivity analysis (Figs. 3–5). The number of carboxysomes was chosen so that they would contain the same number of Rubisco molecules in the C3 leaf stroma, assuming 3,351 Rubisco molecules per carboxysome (Long et al., 2007), giving 2,700 carboxysomes per chloroplast. Carboxysomes are small compared with chloroplasts, and this number of carboxysomes accounts for only about 15% of the stromal volume.

Conversion between CO2 and HCO3− via CA was modeled in all aqueous compartments except in model runs that explicitly remove CA. Since the reaction rates of CA and Rubisco are nonlinear with respect to substrate concentration, the mean concentration of substrate in the compartment cannot be used to calculate reaction rate, because substrate concentration decreases along the path of net diffusion. To allow for this nonlinear activity, the apoplast, chloroplast, thin cytosol, and carboxysome were each divided into six subcompartments. The limit of the reaction rate as the number of subcompartments increases infinitely is the actual reaction rate, but there was little change in the estimated reaction rate past six subcompartments, so that number of subcompartments was deemed sufficient.

The system of differential equations (Supplemental Appendix S1) was solved by numerical integration using the lsodes algorithm from the deSolve package (Soetaert et al., 2010; version 1.10-4) in the R statistical computing language (R Development Core Team, 2012; version 2.15.2). This algorithm is part of the ODEPACK collection of differential equation solvers and was chosen for its ability to solve stiff sets of equations (Hindmarsh, 1983; Radhakrishnan and Hindmarsh, 1993). The simulation time was 20 s, which was long enough for the system to reach steady state. The maximum time step size was set to 0.02 s, and the relative error tolerance was set to 1 × 10−7. Source codes to run the model are provided in the supplemental material (Supplemental Data S1 and S2).

Sensitivity was calculated as Inline graphic, where x is the value of the parameter. Although the true sensitivity should be calculated using the derivative Inline graphic, this is not possible here because the equations were solved numerically. Therefore, to estimate the derivative, for each parameter, the model was run three times using the literature value of the parameter (Table I), a value 10% lower than the literature value, and a value 10% higher than the literature value, producing three estimates of Asat. For each parameter, a linear regression was fit to the three resulting points, with the value of the parameter as the dependent variable and Asat as the independent variable. The slope of that fit was used as Inline graphic. For all parameters, a 10% change from the value used in the model was small enough that the response of Asat versus x was linear. Thus,Inline graphic provided a good estimate of Inline graphic. A similar procedure was used to determine the sensitivity of carboxysomal [CO2] to parameters in the model using carboxysomal [CO2] as the independent variable instead of Asat.

To examine the performance of different Rubisco isoforms, kinetics for different isoforms (Supplemental Table S2) were used in a model of a normal C3 leaf, again with the same leaf but with the complete cyanobacterial CCM added, and with the Rubisco confined to the carboxysome.

To determine the ATP use per net carboxylation, stoichiometries for ATP per HCO3− of 1, 0.5, and 0.25 were used for BCT1, SbtA, and BicA, respectively (Price et al., 2011). Net carboxylation by Rubisco was calculated as:

graphic file with name pp_232611_E11.jpg (11)

Supplemental Data

The following materials are available in the online version of this article.

Supplementary Material

Supplemental Data
supp_164_4_2247__index.html (1.6KB, html)

Acknowledgments

We thank G. Dean Price for providing data for protein concentrations for NDH1,3 and NDH1,4. The visual table of contents icon was derived from an image created by Todd Yeates.

Glossary

RuBP

ribulose bisphosphate

CCM

carbon-concentrating mechanism

CA

carbonic anhydrase

Asat

light-saturated CO2 uptake

Jmax

maximum rate of electron transport

J

rate of ribulose bisphosphate regeneration

Vc,max

maximum rate of carboxylation by Rubisco

Footnotes

1

This work was supported by the National Science Foundation (grant no. EF–1105584) and the Bill and Melinda Gates Foundation.

[W]

The online version of this article contains Web-only data.

[OPEN]

Articles can be viewed online without a subscription.

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Associated Data

This section collects any data citations, data availability statements, or supplementary materials included in this article.

Supplementary Materials

Supplemental Data
supp_164_4_2247__index.html (1.6KB, html)
supp_pp.113.232611_232611cyanobacterial_CCM_in_leaf_model.zip (33.4KB, zip)
supp_pp.113.232611_232611odemodel.zip (18.2KB, zip)
supp_pp.113.232611_232611Table_S2._rubisco_isoforms.txt (4.1KB, txt)
supp_pp.113.232611_232611Appendix_A._Model_equations.docx (28.7KB, docx)
supp_pp.113.232611_232611Table_S1._all_flux_combinations.csv (9KB, csv)

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