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An improved theory for calculating leaf gas exchange more precisely accounting for small fluxes

Nature Plants volume 7, pages 317–326 (2021)Cite this article

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An Author Correction to this article was published on 19 April 2021

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Abstract

The widely used theory for gas exchange proposed by von Caemmerer and Farquhar (vCF) integrates molar fluxes, mole fraction gradients and ternary effects but does not account for cuticular fluxes, for separation of the leaf surface conditions or for ternary effects within the boundary layer. The magnitude of cuticular conductance to water (gcw) is a key factor for determining plant survival in drought but is difficult to measure and often neglected in routine gas exchange studies. The vCF ternary effect is applied to the total flux without the recognition of different pathways that are affected by it. These simplifications lead to errors in estimations of stomatal conductance, intercellular carbon dioxide concentration (Ci) and other gas exchange parameters. The theory presented here is a more precise physical approach to the electrical resistance analogy for gas exchange, resulting in a more accurate calculation of gas exchange parameters. Additionally, we extend our theory, using physiological concepts, to create a model that allows us to calculate cuticular conductance to water.

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Fig. 1: Typical configuration of a gas exchange device and diagrams of the gas exchange of amphi- and hypostomatous leaves.
Fig. 2: Cuticular conductance calculated for single leaf surfaces for four leaves of the same C. annuum plant.
Fig. 3: Average cuticular conductance calculated for a single leaf surface for leaves of different plants (κ = 1).
Fig. 4: Gas exchange parameters calculated using equations (9)–(15) and the vCF theory for experiments changing ASD and stomatal aperture from dark to light (opening) on C. annuum plants.
Fig. 5: Comparison of Ci calculation using vCF, Gas-Mix vCF and equation (14) calculations.

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Data availability

All generated and analysed data from this study are included in the published article, its Supplementary Information and in the GitHub repository (https://github.com/PlantPhysiologist/When_small_fluxes_matter-calculating-leaf-gas-exchange). Source data are provided with this paper.

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Acknowledgements

We thank CONICYT Doctorado, Becas Chile/2015 Folio 72160160 and the Australian Research Council Centre of Excellence for Translational Photosynthesis for funding part of the research. We also thank P. Groeneveld for technical support and building the LI-6800 connector; S. Chin Wong for providing extra minimum conductance data and technical support; and Australian National University Plant Services for taking care of the plant material.

Author information

Authors and Affiliations

  1. Research School of Biology, The Australian National University, Canberra, Australian Capital Territory, Australia

    Diego A. Márquez, Hilary Stuart-Williams & Graham D. Farquhar

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  1. Diego A. Márquez
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  2. Hilary Stuart-Williams
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  3. Graham D. Farquhar
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Contributions

D.M.A., H.S-W. and G.D.F. conceived the study. D.M.A. undertook the experimental work and data analysis. D.M.A. and G.D.F. carried out the modelling. D.M.A. wrote the manuscript with help from all authors.

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Correspondence to Graham D. Farquhar.

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The authors declare no competing interests.

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Peer review information Nature Plants thanks David Hanson, Thomas Sharkey and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Effect of κ on cuticular conductance calculations.

Variation of gcw calculation if the [CO2] at the evaporative sites of the adaxial and abaxial surfaces of the leaf differ (Variation = gcw(κ) - gcw(1)). Differences in [CO2] in the evaporative site of the adaxial and abaxial surfaces impact gas exchange measurements and calculations to different degrees depending on the external measured values. For the purposes of our study, the impact on the gcw calculation was tested by keeping measurements of external gas exchange parameters constant and changing κ.

Extended Data Fig. 2 Average gcw for a C. annuum leaf under different atmospheric conditions (assuming κ = 1).

a, gcw measured under different atmospheric CO2 concentrations (Ca) over 30 minutes after achieving stable conditions (blue dots) and an average of 24 hours under light at constant [CO2] following a diurnal cycle of atmospheric conditions (red dot); and (b) at different temperatures of the leaf and varying relative humidity (RH) also expressed as atmospheric saturation deficits (ASD) for the black dots. In panel (a), each blue point gives the average and standard deviation of 8 to 16 measurements (n); the red point gives the average and standard deviation of 239 measurements (n), one measurement being taken every 4 minutes. In panel (b), each red and blue dot gives the average and standard deviation of 16 to 31 measurements (n), one measurement taken every 2 minutes; black dots are single measurements under stable gas exchange conditions for at least 25 minutes. The measurements were made from low to high ASD and later from high to low ASD. Graphs (a) and (b) are different leaves. Cuticular conductance (gcw) is expressed as the value for one surface and therefore needs to be doubled for the whole leaf (γ = 1).

Source data

Extended Data Fig. 3 Effect of possible differences in abaxial and adaxial leaf cuticular conductance.

Impact of unequal adaxial and abaxial gcw in (a) the total cuticular conductance (gcw-T = gcw-ad+gcw-ab) calculated for a leaf and in (b) the Ci calculation, depending on the proportion of abaxial over adaxial cuticular conductance (γ) using as a reference gcw-T calculated with γ=1. A single measurement under stable gas exchange conditions was selected for calculating the variation of each species using κ = 1. The dots show the values using our dark measurements to estimate γ for each species. Zhang et al.40 measured weight loss via cuticle of detached leaves and they concluded that astomatous surfaces have about 30% lower evaporation than the cuticle of the surfaces with stomata. It is difficult to extrapolate these evaporation values to gcw values in growing leaves because the boundary layer conductance and leaf temperature were not provided, and the leaves had already been detached for one hour. Bearing this in mind, we used dark measurements to estimate inequalities between the adaxial and abaxial cuticular conductance, which can be used to quantify a possible gcw difference between the adaxial and adaxial surfaces. Then, assuming equal stomatal closure on the adaxial and abaxial surface, in G. biloba only 6% of the difference in glw was not explained by the stomatal density differences, 8% for G. hirsutum and 15% for C. annuum; the abaxial and adaxial glw of H. annuus were practically the same in the dark. Using equation (18), it was found that significant variations in γ can have a big impact on the calculated total cuticular conductance (gcw-T=gcw-ad+gcw-ab). The magnitude of this impact depends on how much γ affects the wi -ws gradient.

Extended Data Fig. 4 Diagram of the connection of two LI-6800.

Part A: Flanges on the lower cuvette and the second LI-6800. Part B: Lid of the upper cuvette, the lid of the lower cuvette includes two cavities to insert two thermocouples. Part C: Flange to block the flow of gases from and to the lower cuvette.

Supplementary information

Source data

Source Data Fig. 2

C. annuum cuticular conductance in four leaves.

Source Data Fig. 3

Cuticular conductance for four species.

Source Data Fig. 4

Gas exchange under water stress and stomatal opening.

Source Data Fig. 5

Comparison between Ci calculations.

Source Data Extended Data Fig. 2

Gas exchange at different atmospheric conditions.

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Márquez, D.A., Stuart-Williams, H. & Farquhar, G.D. An improved theory for calculating leaf gas exchange more precisely accounting for small fluxes. Nat. Plants 7, 317–326 (2021). https://doi.org/10.1038/s41477-021-00861-w

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