The mechanistic basis of internal conductance: a theoretical analysis of mesophyll cell photosynthesis and CO2 diffusion

Abstract

Photosynthesis is limited by the conductance of carbon dioxide (CO(2)) from intercellular spaces to the sites of carboxylation. Although the concept of internal conductance (g(i)) has been known for over 50 years, shortcomings in the theoretical description of this process may have resulted in a limited understanding of the underlying mechanisms. To tackle this issue, we developed a three-dimensional reaction-diffusion model of photosynthesis in a typical C(3) mesophyll cell that includes all major components of the CO(2) diffusion pathway and associated reactions. Using this novel systems model, we systematically and quantitatively examined the mechanisms underlying g(i). Our results identify the resistances of the cell wall and chloroplast envelope as the most significant limitations to photosynthesis. In addition, the concentration of carbonic anhydrase in the stroma may also be limiting for the photosynthetic rate. Our analysis demonstrated that higher levels of photorespiration increase the apparent resistance to CO(2) diffusion, an effect that has thus far been ignored when determining g(i). Finally, we show that outward bicarbonate leakage through the chloroplast envelope could contribute to the observed decrease in g(i) under elevated CO(2). Our analysis suggests that physiological and anatomical features associated with g(i) have been evolutionarily fine-tuned to benefit CO(2) diffusion and photosynthesis. The model presented here provides a novel theoretical framework to further analyze the mechanisms underlying diffusion processes in the mesophyll.

Figure 1.

A, The 3D structure of a mesophyll cell with a diameter of 20 μm and containing 96 chloroplasts and 96 mitochondria. The structure was further defined by the following parameters: a, chloroplast-wall distance (variable, 0.1 μm by default); b, maximum chloroplast thickness (2 μm); c, chloroplast-mitochondria distance (0.2 μm); d, diameter of the mitochondria (1.4 μm); e, chloroplast-vacuole distance (1.1 μm); and f, wall-vacuole distance (3.1 μm). B, Schematic representation of the reactions and fluxes in the model. CO₂ enters through the cell wall into the cytosol (A), where it is partially converted into HCO₃⁻ (h_C,1). Both CO₂ and HCO₃⁻ diffuse toward the chloroplast (with diffusivities d_C,1 and d_B,1), but only CO₂ can easily enter the chloroplast stroma (with diffusivity d_C,2). This results in dehydration (h_C,2) close to the chloroplast envelope, in order to maintain the equilibrium between CO₂ and HCO₃⁻. Although the chloroplast membrane is relatively impermeable to HCO₃⁻some leakage (d_B,2) may occur, because the high chloroplast pH results in a much larger [HCO₃⁻] in the stroma compared with that in the cytosol. Rapid dehydration of HCO₃⁻ in the center of the chloroplast stroma prevents a large decrease in [CO₂], even although CO₂ is fixed by the Rubisco enzyme (f). An additional source of CO₂ is the respiration (r_d) and photorespiration (r_p) in the mitochondria.

Figure 2.

An example of a typical CO₂ response curve (continuous line) as predicted by the C₃ biochemical model (Farquhar et al., 1980). The 3D reaction-diffusion model is an extension of this biochemical model that adds a description of the diffusion pathway through the mesophyll. Using the default parameters of the model (Table I), the reaction-diffusion model predicts somewhat lower rates of photosynthesis (dotted line). The dashed line gives an example of the expected rates of photosynthesis when the resistance of the cell wall is 10 times higher than the default value. Vertical lines indicate three different CO₂ concentrations at which the sensitivity of the model to different parameters was tested.

Figure 3.

The relative rates of photosynthesis (A) and internal conductance (B) as affected by the cell wall (and plasmalemma) conductance. The model was run at three different intercellular CO₂ levels. The gray areas indicate wall conductances outside the biologically relevant range as given in Table I. Vertical lines indicate default values used in the model. The effects of a change in the structure on photosynthesis (C) and internal conductance (D) were examined by increasing the distance (d) between the cell wall and the chloroplast envelope. Eight different model structures (indicated by the points) were analyzed.

Figure 4.

The effects of chloroplast envelope permeability to CO₂ (A and B) and HCO₃⁻ (C and D) on photosynthesis (A and C) and internal conductance (B and D). The gray areas indicate permeabilities outside the biologically relevant range as given in Table I. The dashed vertical lines indicate default values used in the model.

Figure 5.

The effects of the stromal CA concentration on photosynthesis (A) and internal conductance (B). The gray areas indicate concentrations that are thought to be outside the biologically relevant range (Table I). The dashed lines indicate the default values used in the model.

Figure 6.

A and B, The modeled and measured dependency of the net photosynthesis and of internal conductance on the oxygen partial pressure at three different CO₂ levels. For the measured data, Γ* was determined at 10, 21, and 40 kPa oxygen and was 1.7, 3.8, and 7.6 Pa. C and D, The measured responses of photosynthesis and internal conductance as a function of CO₂ partial pressure. E and F, The modeled results, calculated at three different membrane HCO₃⁻ permeabilities to estimate the effect of HCO₃⁻ leakage. For all measurements, average values of four Arabidopsis plants are shown ± se.