The role of mesophyll conductance in the economics of nitrogen and water use in photosynthesis

Abstract

A recent resurgence of interest in formal optimisation theory has begun to improve our understanding of how variations in stomatal conductance and photosynthetic capacity control the response of whole plant photosynthesis and growth to the environment. However, mesophyll conductance exhibits similar variation and has similar impact on photosynthesis as stomatal conductance; yet, the role of mesophyll conductance in the economics of photosynthetic resource use has not been thoroughly explored. In this article, we first briefly summarise the knowledge of how mesophyll conductance varies in relation to environmental factors that also affect stomatal conductance and photosynthetic capacity, and then we use a simple analytical approach to begin to explore how these important controls on photosynthesis should mutually co-vary in a plant canopy in the optimum. Our analysis predicts that when either stomatal or mesophyll conductance is limited by fundamental biophysical constraints in some areas of a canopy, e.g. reduced stomatal conductance in upper canopy leaves due to reduced water potential, the other of the two conductances should increase in those leaves, while photosynthetic capacity should decrease. Our analysis also predicts that if mesophyll conductance depends on nitrogen investment in one or more proteins, then nitrogen investment should shift away from Rubisco and towards mesophyll conductance if hydraulic or other constraints cause chloroplastic CO₂ concentration to decline. Thorough exploration of these issues awaits better knowledge of whether and how mesophyll conductance is itself limited by nitrogen investment, and about how these determinants of photosynthetic CO₂ supply and demand co-vary among leaves in real plant canopies.

Appendix

Analytical expressions for marginal carbon products of N and water use

The marginal carbon product of photosynthetic N, ∂A/∂N, was given by Buckley et al. (2002) as

$$ \frac{\partial A}{\partial N} = \left( {\frac{\partial A}{\partial N}} \right)_{{c_{\text{c}} }} \left( {\frac{g}{g + k}} \right) $$

(A1)

where the partial derivative at right, ∂A/∂N at constant c _c, is

$$ \left( {\frac{\partial A}{\partial N}} \right)_{{c_{\text{c}} }} = \left( {A + R_{\text{d}} } \right)\frac{\partial \ln W}{\partial N} - \frac{{R_{\text{d}} }}{N} $$

(A2)

In A2, W represents the maximum RuBP carboxylation velocity, V _m, when photosynthesis is carboxylation limited, or the potential electron transport rate, J, when photosynthesis is RuBP regeneration limited; and R _d is non-photorespiratory CO₂ release concurrent with photosynthesis. These derivatives apply to components of N as well, including Rubisco N (N _v), so N can be replaced with N _v in Eq. A2. Then, if V _m = χ _v N _v, ∂lnV _m/∂N _v = 1/N _v and

$$ \frac{\partial A}{{\partial N_{\text{v}} }} = \frac{A}{{N_{\text{v}} }}\left( {\frac{g}{g + k}} \right) $$

(A3)

Equation 2 in the main text is obtained by dividing through by k in the term in parentheses in Eq. A3. The marginal C product of water use, ∂A/∂E, under well-coupled conditions (negligible boundary layer resistance and constant temperature) is found by applying Eqs. A6, A18 and A23 to Eq. A40 in Buckley et al. (2002) to give

$$ \frac{\partial A}{\partial E} = \frac{A}{E}\left( {\frac{k}{k + g}} \right)\frac{1.6g}{{g_{\text{w}} }} $$

(A4)

where g _w is total conductance to H₂O. Under well-coupled conditions g = g _s ·g _m/(g _s + g _m) = g _s ·γ/(γ + 1) (where γ = g _m/g _s) and g _w = 1.6 g _s. Then, 1.6g/g _w = γ/(γ + 1). Equation 4 in the main text arises by applying this result to A4 and dividing through by g in the term in parentheses.

Analytical expression for marginal C product of mesophyll conductance N

If we hypothesise that mesophyll conductance increases monotonically in relation to the size of some N pool, N _m, then the marginal C product of N _m, ∂A/∂N _m, is

$$ \frac{\partial A}{{\partial N_{\text{m}} }} = \frac{\partial A}{{\partial c_{\text{c}} }}\frac{{\partial c_{\text{c}} }}{{\partial r_{\text{m}} }}\frac{{\partial r_{\text{m}} }}{{\partial g_{\text{m}} }}\frac{{\partial g_{\text{m}} }}{{\partial N_{\text{m}} }} $$

(A5)

where r _m = 1/g _m. The first partial on the right-hand side, ∂A/∂c _c, is the slope of the demand curve, k, at the operating point, and the third is −1/g ²_m . The second, ∂c _c /∂r _m, is found by differentiating the equation of CO₂ diffusion with respect to c _c. Ignoring boundary layer resistance as above and writing r _s = 1/g _s, the diffusion equation is A = (c _a–c _c)/(r _s + r _m), which rearranges to c _c = c _a − r _m A − r _s A. Then,

$$ \frac{{\partial c_{c} }}{{\partial r_{\text{m}} }} = - A - \left( {r_{\text{m}} + r_{\text{s}} } \right)\frac{\partial A}{{\partial r_{\text{m}} }} = - A - \frac{1}{g}\frac{\partial A}{{\partial r_{\text{m}} }} $$

(A6)

Noting that ∂A/∂r _m = (∂A/∂N _m)/[(∂r _m/∂g _m)(∂g _m/∂N _m)] and applying this and Eq. A6 to A5, we have

$$ \frac{\partial A}{{\partial N_{\text{m}} }} = k\left( { - A\frac{{\partial r_{\text{m}} }}{{\partial g_{\text{m}} }}\frac{{\partial g_{\text{m}} }}{{\partial N_{\text{m}} }} - \frac{1}{g}\frac{\partial A}{{\partial N_{\text{m}} }}} \right) = \frac{{\partial g_{\text{m}} }}{{\partial N_{\text{m}} }}\frac{k}{{g_{\text{m}}^{2} }}A - \frac{k}{g}\frac{\partial A}{{\partial N_{\text{m}} }} $$

(A7)

This is readily solved for ∂A/∂N _m to give

$$ \frac{\partial A}{{\partial N_{\text{m}} }} = \frac{{\partial g_{\text{m}} }}{{\partial N_{\text{m}} }}\frac{k}{{g_{\text{m}}^{2} }}A\left( {\frac{g}{g + k}} \right) $$

(A8)

From Eq. A25 in Buckley et al. (2002), k under Rubisco-limited conditions is

$$ k = V_{\text{m}} \frac{{\left( {\Upgamma_{*} + K^{\prime}} \right)}}{{\left( {c_{\text{c}} + K^{\prime}} \right)^{2} }} $$

(A9)

Expanding V _m as χ _v N _v, applying A9 to A8 and rearranging gives the ratio of g _m to V _m in the optimum as

$$ \frac{{g_{\text{m}} }}{{V_{\text{m}} }} = \sqrt {\frac{1}{{\chi_{\text{v}} }}\frac{{\partial g_{\text{m}} }}{{\partial N_{\text{m}} }}\frac{{\left( {\Upgamma_{*} + K^{\prime}} \right)}}{{\left( {c_{\text{c}} + K^{\prime}} \right)^{2} }}} $$

(A10)

If we assume g _m is directly proportional to N _m, say g _m = χ _m N _m, then ∂g _m/∂N _m = χ _m, so

$$ \frac{{g_{\text{m}} }}{{V_{\text{m}} }} = \sqrt {\frac{{\chi_{\text{m}} }}{{\chi_{\text{v}} }}\frac{{\left( {\Upgamma_{*} + K^{\prime}} \right)}}{{\left( {c_{\text{c}} + K^{\prime}} \right)^{2} }}} $$

(A11)

or equivalently, in terms of the ratio of N pools,

$$ \frac{{N_{\text{m}} }}{{N_{\text{v}} }} = \sqrt {\frac{{\chi_{\text{v}} }}{{\chi_{\text{m}} }}\frac{{\left( {\Upgamma_{*} + K^{\prime}} \right)}}{{\left( {c_{\text{c}} + K^{\prime}} \right)^{2} }}} $$

(A12)

which is Eq. 3 in the main text. If instead g _m represents two diffusion pathways in series, one of which scales with N _m and the other of which scales with N _v (with proportionality constant χ _mv), then

$$ g_{\text{m}} = \frac{{\left( {\chi_{\text{m}} N_{\text{m}} } \right)\left( {\chi_{\text{nv}} N_{\text{v}} } \right)}}{{\chi_{\text{m}} N_{\text{m}} + \chi_{\text{nv}} N_{\text{v}} }} $$

(A13)

and ∂g _m/∂N _m is g ²_m /(χ _m N ²_m ). Applying this to A8 and rearranging leads to the same expression as given in A12. Therefore, A12 applies whether g _m is given by χ _m N _m or by Eq. A13.

Numerical calculations for Figs. 1 and 2

We calculated ∂A/∂N and ∂A/∂E from the photosynthesis model of Farquhar et al. (1980) as described by Buckley et al. (2002), assuming zero boundary layer resistance. Net CO₂ assimilation rate was calculated from two rates, one applying in RuBP carboxylation limited conditions (A _v), and the other in RuBP regeneration limited conditions (A _j):

$$ A_{\text{v}} = \frac{{V_{\text{m}} \left( {c_{\text{c}} - \Upgamma_{*} } \right)}}{{c_{\text{c}} + K^{\prime}}} - R_{\text{d}} $$

(A14)

$$ A_{\text{j}} = \tfrac{1}{4}\frac{{J\left( {c_{\text{c}} - \Upgamma_{ *} } \right)}}{{c_{\text{c}} + 2\Upgamma_{*} }} - R_{\text{d}} $$

(A15)

and A was taken as the smaller root of θ _A A ² − A(A _v + A _j) + A _v A _j = 0 where θ _A is a dimensionless curvature parameter (0.99). The intersection of this solution with an expression for CO₂ diffusion to the sites of carboxylation, A = g(c _a − c _c), leads to a quartic expression for c _c, which is then substituted into the diffusion equation to calculate A. The potential electron transport rate J was taken as the smaller root of θ _A J ² − J(J _m + ϕI) + J _m ϕI = 0, where J _m is maximum potential electron transport rate (taken as 2.1V _m, Wullschleger 1993); I is incident irradiance (500 μmol m⁻² s⁻¹); ϕ is effective maximum quantum yield of electrons from incident irradiance (0.25 e⁻/hν); and θ _j is a dimensionless curvature parameter (0.86). Other parameters were as follows: effective Michaelis constant for RuBP carboxylation, K’, 617 μmol mol⁻¹; photorespiratory CO₂ compensation point, Γ _*, 37 μmol mol⁻¹; ambient CO₂ mol fraction, c _a, 385 μmol mol⁻¹; and respiration rate in the light, R _d, 0.01V _m. These values for K′ and Γ _* are approximately equivalent to a temperature of 25 °C and normal atmospheric pO₂ (Sharkey et al. 2007).

V _m was taken as 4.5·N _v; this proportionality arises from 6,290 mol N per mol of Rubisco (Hikosaka and Terashima 1995), a turnover time of 3.53 s⁻¹ (von Caemmerer and Evans 1991), and eight active sites per Rubisco molecule. Default values for N _v, g _s and γ (g _m/g _s) were 25 mmol m⁻², 0.12 mol m⁻² s⁻¹ and 1.45, respectively. The value for γ is the grand mean of (c _a − c _i)/(c _i − c _c), the ratio of the CO₂ drawdowns from the ambient air to the intercellular air spaces and from the intercellular spaces to the sites of carboxylation, given in Table 2. The default values for N _v and g _s were chosen arbitrarily to give realistic values of c _i and c _c. Calculation of ∂A/∂E also requires a value for leaf to air water vapour mole fraction gradient, which we took as 20 mmol mol⁻¹. The response curves in Figs 1 and 2 were generated by varying these quantities about these default values (the latter are represented by the dashed line in Fig. 1 and by solid symbols in Fig. 2).