## 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 CO_{2} 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 CO_{2} supply and demand co-vary among leaves in real plant canopies.

### Similar content being viewed by others

## References

Barbour MM, Warren CR, Farquhar GD, Forrester G, Brown H (2010) Variability in mesophyll conductance between barley genotypes, and effects on transpiration efficiency and carbon isotope discrimination. Plant Cell Environ 33(7):1176–1185. doi:10.1111/j.1365-3040.2010.02138.x

Bögelein R, Hassdenteufel M, Thomas FM, Werner W (2012) Comparison of leaf gas exchange and stable isotope signature of water-soluble compounds along canopy gradients of co-occurring Douglas-fir and European beech. Plant Cell Environ 35(7):1245–1257. doi:10.1111/j.1365-3040.2012.02486.x

Buckley TN, Miller JM, Farquhar GD (2002) The mathematics of linked optimisation for nitrogen and water use in a canopy. Silva Fennica 36:639–669

Buckley TN, Cescatti A, Farquhar GD (2013) What does optimisation theory actually predict about crown profiles of photosynthetic capacity, when models incorporate greater realism? Plant Cell Environ. doi:10.1111/pce.12091

Cooper GJ, Boron WF (1998) Effect of PCMBS on CO

_{2}permeability of*Xenopus*oocytes expressing aquaporin 1 or its C189S mutant. Am J Physiol Cell Ph 275(6):C1481–C1486Cowan IR (1977) Stomatal behaviour and environment. Adv Bot Res 4:117–228

Cowan IR (1986) Economics of carbon fixation in higher plants. In: Givnish TJ (ed) On the economy of plant form and function. Cambridge University Press, Cambridge, pp 133–170

Douthe C, Dreyer E, Epron D, Warren CR (2011) Mesophyll conductance to CO

_{2}, assessed from online TDL-AS records of (CO_{2})–C-13 discrimination, displays small but significant short-term responses to CO_{2}and irradiance in*Eucalyptus*seedlings. J Exp Bot 62(15):5335–5346. doi:10.1093/Jxb/Err141Douthe C, Dreyer E, Brendel O, Warren CR (2012) Is mesophyll conductance to CO

_{2}in leaves of three*Eucalyptus*species sensitive to short-term changes of irradiance under ambient as well as low O_{2}? Funct Plant Biol 39(5):435–448. doi:10.1071/Fp11190Duan BL, Li Y, Zhang XL, Korpelainen H, Li CY (2009) Water deficit affects mesophyll limitation of leaves more strongly in sun than in shade in two contrasting

*Picea asperata*populations. Tree Physiol 29(12):1551–1561. doi:10.1093/treephys/tpp085Epron D, Godard D, Cornic G, Genty B (1995) Limitation of net CO

_{2}assimilation rate by internal resistances to CO_{2}transfer in the leaves of 2 tree species (*Fagus sylvatica*L and*Castanea sativa*Mill). Plant Cell Environ 18(1):43–51Evans JR (2009) Potential errors in electron transport rates calculated from chlorophyll fluorescence as revealed by a multilayer leaf model. Plant Cell Physiol 50(4):698–706. doi:10.1093/Pcp/Pcp041

Evans JR, von Caemmerer S, Setchell BA, Hudson GS (1994) The relationship between CO

_{2}transfer conductance and leaf anatomy in transgenic tobacco with a reduced content of Rubisco. Aust J Plant Physiol 21(4):475–495Evans JR, Kaldenhoff R, Genty B, Terashima I (2009) Resistances along the CO

_{2}diffusion pathway inside leaves. J Exp Bot 60(8):2235–2248. doi:10.1093/Jxb/Erp117Farquhar GD (1989) Models of integrated photosynthesis of cells and leaves. Philos Trans R Soc B 323:357–367

Farquhar GD, von Caemmerer S, Berry JA (1980) A biochemical model of photosynthetic CO

_{2}assimilation in leaves of C_{3}species. Planta 149:78–90Field C (1983) Allocating leaf nitrogen for the maximization of carbon gain: leaf age as a control on the allocation program. Oecologia 56:341–347

Flexas J, Diaz-Espejo A, Galmes J, Kaldenhoff R, Medrano H, Ribas-Carbo M (2007) Rapid variations of mesophyll conductance in response to changes in CO

_{2}concentration around leaves. Plant Cell Environ. doi:10.1111/j.1365-3040.2007.01700.xFlexas J, Ribas-Carbo M, Diaz-Espejo A, Galmes J, Medrano H (2008) Mesophyll conductance to CO

_{2}: current knowledge and future prospects. Plant Cell Environ 31(5):602–621. doi:10.1111/j.1365-3040.2007.01757.xFlexas J, Barbour MM, Brendel O, Cabrera HM, Carriqui M, Diaz-Espejo A, Douthe C, Dreyer E, Ferrio JP, Gago J, Galle A, Galmes J, Kodama N, Medrano H, Niinemets U, Peguero-Pina JJ, Pou A, Ribas-Carbo M, Tomas M, Tosens T, Warren CR (2012) Mesophyll diffusion conductance to CO

_{2}: an unappreciated central player in photosynthesis. Plant Sci 193:70–84. doi:10.1016/j.plantsci.2012.05.009Galmes J, Conesa MA, Ochogavia JM, Perdomo JA, Francis DM, Ribas-Carbo M, Save R, Flexas J, Medrano H, Cifre J (2011) Physiological and morphological adaptations in relation to water use efficiency in Mediterranean accessions of

*Solanum lycopersicum*. Plant Cell Environ 34(2):245–260. doi:10.1111/j.1365-3040.2010.02239.xHan QM (2011) Height-related decreases in mesophyll conductance, leaf photosynthesis and compensating adjustments associated with leaf nitrogen concentrations in

*Pinus densiflora*. Tree Physiol 31(9):976–984. doi:10.1093/treephys/tpr016Hanba YT, Miyazawa SI, Kogami H, Terashima I (2001) Effects of leaf age on internal CO

_{2}transfer conductance and photosynthesis in tree species having different types of shoot phenology. Aust J Plant Physiol 28(11):1075–1084Harley PC, Loreto F, Di Marco G, Sharkey TD (1992) Theoretical considerations when estimating the mesophyll conductance to CO

_{2}flux by analysis of the response of photosynthesis to CO_{2}. Plant Physiol 98(4):1429–1436Hassiotou F, Ludwig M, Renton M, Veneklaas EJ, Evans JR (2009) Influence of leaf dry mass per area, CO

_{2}, and irradiance on mesophyll conductance in sclerophylls. J Exp Bot 60(8):2303–2314. doi:10.1093/Jxb/Erp021Heckwolf M, Pater D, Hanson DT, Kaldenhoff R (2011) The

*Arabidopsis thaliana*aquaporin AtPIP1;2 is a physiologically relevant CO_{2}transport facilitator. Plant J 67(5):795–804. doi:10.1111/j.1365-313X.2011.04634.xHikosaka K, Terashima I (1995) A model of the acclimation of photosynthesis in the leaves of C3 plants to sun and shade with respect to nitrogen use. Plant Cell Environ 18:605–618

Laisk A, Oja V, Rahi M (1970) Diffusion resistance of leaves in connection with their anatomy. Fiziologiya Rastenii 47:40–48

Loreto F, Harley PC, Di Marco G, Sharkey TD (1992) Estimation of mesophyll conductance to CO

_{2}flux by 3 different methods. Plant Physiol 98(4):1437–1443Miyazawa SI, Terashima I (2001) Slow development of leaf photosynthesis in an evergreen broad-leaved tree,

*Castanopsis sieboldii*: relationships between leaf anatomical characteristics and photosynthetic rate. Plant Cell Environ 24(3):279–291Montpied P, Granier A, Dreyer E (2009) Seasonal time-course of gradients of photosynthetic capacity and mesophyll conductance to CO

_{2}across a beech (*Fagus sylvatica*L.) canopy. J Exp Bot 60(8):2407–2418. doi:10.1093/jxb/erp093Nakhoul NL, Davis BA, Romero MF, Boron WF (1998) Effect of expressing the water channel aquaporin-1 on the CO

_{2}permeability of*Xenopus*oocytes. Am J Physiol Cell Physiol 274(2):C543–C548Niinemets U (2012) Optimization of foliage photosynthetic capacity in tree canopies: towards identifying missing constraints. Tree Physiol 32(5):505–509. doi:10.1093/treephys/tps045

Niinemets U, Cescatti A, Rodeghiero M, Tosens T (2006) Complex adjustments of photosynthetic potentials and internal diffusion conductance to current and previous light availabilities and leaf age in Mediterranean evergreen species

*Quercus ilex*. Plant Cell Environ 29:1159–1178Niinemets U, Diaz-Espejo A, Flexas J, Galmes J, Warren CR (2009a) Importance of mesophyll diffusion conductance in estimation of plant photosynthesis in the field. J Exp Bot 60(8):2271–2282. doi:10.1093/Jxb/Erp063

Niinemets U, Diaz-Espejo A, Flexas J, Galmes J, Warren CR (2009b) Role of mesophyll diffusion conductance in constraining potential photosynthetic productivity in the field. J Exp Bot 60(8):2249–2270. doi:10.1093/Jxb/Erp036

Nobel PS (1977) Internal leaf area and cellular CO

_{2}resistance: photosynthetic implications of variations with growth conditions and plant species. Physiol Plant 40:137–144Nobel PS (1991) Physicochemical and environmental plant physiology. Academic Press, San Diego

Nobel PS, Zaragoza LJ, Smith WK (1975) Relation between mesophyll surface area, photosynthetic rate, and illumination level during development for leaves of

*Plectranthuis parviflorus*Henckel. Plant Physiol 55:1067–1070Parkhurst DF, Mott KA (1990) Intercellular diffusion limits to CO

_{2}uptake in leaves. Plant Physiol 94(3):1024–1032Peltoniemi MS, Duursma RA, Medlyn BE (2012) Co-optimal distribution of leaf nitrogen and hydraulic conductance in plant canopies. Tree Physiol 32(5):510–519. doi:10.1093/treephys/tps023

Pepin S, Livingston NJ, Whitehead D (2002) Responses of transpiration and photosynthesis to reversible changes in photosynthetic foliage area in western red cedar (

*Thuja plicata*) seedlings. Tree Physiol 22(6):363–371Piel C, Frak E, Le Roux X, Genty B (2002) Effect of local irradiance on CO

_{2}transfer conductance of mesophyll in walnut. J Exp Bot 53(379):2423–2430Pons TL, Welschen RAM (2003) Midday depression of net photosynthesis in the tropical rainforest tree

*Eperua grandiflora*: contributions of stomatal and internal conductances, respiration and Rubisco functioning. Tree Physiol 23(14):937–947Sands PJ (1995) Modelling canopy production. I. Optimal distribution of photosynthetic resources. Aust J Plant Physiol 22:593–601

Scafaro AP, Von Caemmerer S, Evans JR, Atwell BJ (2011) Temperature response of mesophyll conductance in cultivated and wild

*Oryza*species with contrasting mesophyll cell wall thickness. Plant Cell Environ 34(11):1999–2008. doi:10.1111/j.1365-3040.2011.02398.xSharkey TD, Bernacchi CJ, Farquhar GD, Singsaas EL (2007) Fitting photosynthetic carbon dioxide response curves for C3 leaves. Plant Cell Environ 30(9):1035–1040

Soolanayakanahally RY, Guy RD, Silim SN, Drewes EC, Schroeder WR (2009) Enhanced assimilation rate and water use efficiency with latitude through increased photosynthetic capacity and internal conductance in balsam poplar (

*Populus balsamifera*L.). Plant Cell Environ 32(12):1821–1832. doi:10.1111/j.1365-3040.2009.02042.xTerashima I, Hanba YT, Tholen D, Niinemets U (2011) Leaf functional anatomy in relation to photosynthesis. Plant Physiol 155(1):108–116. doi:10.1104/pp.110.165472

Tholen D, Ethier G, Genty B, Pepin S, Zhu X-G (2012) Variable mesophyll conductance revisited: theoretical background and experimental implications. Plant Cell Environ. doi:10.1111/j.1365-3040.2012.02538.x

Uehlein N, Otto B, Hanson DT, Fischer M, McDowell N, Kaldenhoff R (2008) Function of

*Nicotiana tabacum*aquaporins as chloroplast gas pores challenges the concept of membrane CO_{2}permeability. Plant Cell 20(3):648–657. doi:10.1105/tpc.107.054023von Caemmerer S, Evans JR (1991) Determination of the average partial-pressure of CO

_{2}in chloroplasts from leaves of several C_{3}plants. Aust J Plant Physiol 18(3):287–305Vrabl D, Vaskova M, Hronkova M, Flexas J, Santrucek J (2009) Mesophyll conductance to CO

_{2}transport estimated by two independent methods: effect of variable CO_{2}concentration and abscisic acid. J Exp Bot 60(8):2315–2323. doi:10.1093/Jxb/Erp115Warren CR (2006) Estimating the internal conductance to CO

_{2}movement. Funct Plant Biol 33(5):431–442Warren CR (2008a) Soil water deficits decrease the internal conductance to CO

_{2}transfer but atmospheric water deficits do not. J Exp Bot 59(2):327–334. doi:10.1093/Jxb/Erm314Warren CR (2008b) Stand aside stomata, another actor deserves centre stage: the forgotten role of the internal conductance to CO

_{2}transfer. J Exp Bot 59:1475–1487Warren CR, Adams MA (2006) Internal conductance does not scale with photosynthetic capacity: implications for carbon isotope discrimination and the economics of water and nitrogen use in photosynthesis. Plant Cell Environ 29(2):192–201. doi:10.1111/j.1365-3040.2005.01412.x

Warren CR, Dreyer E (2006) Temperature response of photosynthesis and internal conductance to CO

_{2}: results from two independent approaches. J Exp Bot 57:3057–3067. doi:10.1093/jxb/erl067Warren CR, Ethier GJ, Livingston NJ, Grant NJ, Turpin DH, Harrison DL, Black TA (2003) Transfer conductance in second growth Douglas-fir (

*Pseudotsuga menziesii*(Mirb.)Franco) canopies. Plant, Cell Environ 26(8):1215–1227Warren CR, Low M, Matyssek R, Tausz M (2007) Internal conductance to CO

_{2}transfer of adult*Fagus sylvatica*: variation between sun and shade leaves and due to free-air ozone fumigation. Environ Exp Bot 59(2):130–138Whitehead D, Barbour MM, Griffin KL, Turnbull MH, Tissue DT (2011) Effects of leaf age and tree size on stomatal and mesophyll limitations to photosynthesis in mountain beech (

*Nothofagus solandrii*var. cliffortiodes). Tree Physiol 31(9):985–996. doi:10.1093/treephys/tpr021Woodruff DR, Meinzer FC, Lachenbruch B, Johnson DM (2009) Coordination of leaf structure and gas exchange along a height gradient in a tall conifer. Tree Physiol 29(2):261–272. doi:10.1093/treephys/tpn024

Wullschleger SD (1993) Biochemical limitations to carbon assimilation in C

_{3}plants: a retrospective analysis of the A/c_{i}curves from 109 species. J Exp Bot 44:907–920Yamori W, Noguchi K, Hanba YT, Terashima I (2006) Effects of internal conductance on the temperature dependence of the photosynthetic rate in spinach leaves from contrasting growth temperatures. Plant Cell Physiol 47(8):1069–1080

## Author information

### Authors and Affiliations

### Corresponding author

## Appendix

### 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

where the partial derivative at right, ∂*A*/∂*N* at constant *c*
_{c}, is

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 CO_{2} 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}, ∂ln*V*
_{m}/∂*N*
_{v} = 1/*N*
_{v} and

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

where *g*
_{w} is total conductance to H_{2}O. 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, 1.6*g*/*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

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 CO_{2} 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,

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

This is readily solved for ∂*A*/∂*N*
_{m} to give

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

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

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

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

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

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 CO_{2} 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}):

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 CO_{2} 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 2.1*V*
_{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^{−}/h*ν*); 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 CO_{2} compensation point, *Γ*
_{*}, 37 μmol mol^{−1}; ambient CO_{2} mol fraction, *c*
_{a}, 385 μmol mol^{−1}; and respiration rate in the light, *R*
_{d}, 0.01*V*
_{m}. These values for *K*′ and *Γ*
_{*} are approximately equivalent to a temperature of 25 °C and normal atmospheric pO_{2} (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 CO_{2} 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).

## Rights and permissions

## About this article

### Cite this article

Buckley, T.N., Warren, C.R. The role of mesophyll conductance in the economics of nitrogen and water use in photosynthesis.
*Photosynth Res* **119**, 77–88 (2014). https://doi.org/10.1007/s11120-013-9825-2

Received:

Accepted:

Published:

Issue Date:

DOI: https://doi.org/10.1007/s11120-013-9825-2