Modeling Leaf Gas Exchange

  • Kouki Hikosaka
  • Ko Noguchi
  • Ichiro Terashima
Part of the Advances in Photosynthesis and Respiration book series (AIPH, volume 42)


Leaves are photosynthetic organs that absorb light and convert the photon energy of light to chemical energy for use in CO2 assimilation. Here we review how CO2 assimilation rates vary, depending on environmental factors and among leaves. Net CO2 assimilation is a balance between the carboxylation of ribulose 1,5-bisphosphate (RuBP) catalyzed by ribulose-1,5-bisphosphate carboxylase/oxygenase (Rubisco) and the release of CO2 by photorespiration and mitochondrial respiration. The steady-state biochemical model of CO2 assimilation considers photosynthetic metabolism as a composite of two processes, namely, RuBP carboxylation and regeneration. The former, modeled based on the Rubisco kinetics, is limited mainly by CO2 supply, whereas the latter is assumed to be limited by the rate of photon absorption at low light and by its use in electron transport at high light. CO2 concentration at the assimilation sites in chloroplasts depends on the stomatal and mesophyll conductances for CO2 diffusion. Both these conductances are sensitive to environmental variables, but no mechanistic models of environmental responses for these conductances are available. Various empirical models have been developed and combined with the biochemical photosynthesis model allowing for expression of CO2 assimilation rates as a function of environmental variables.


CO2 assimilation CO2 response Dark respiration Day respiration Interspecific variation Light response Mesophyll conductance Rubisco Stomatal conductance Temperature dependence 



Net CO2 assimilation rate


RuBP -saturated A


RuBP -limited A


Maximum A (photosynthetic capacity)


A limited by TP use


Abscisic acid


Cyanide-resistant alternative oxidase


Net anabolic NADH supply

CaCc, Cf and Ci

CO2 partial pressures at air, chloroplast , leaf surface and intercellular space respectively


Heat capacity of air


Cytochrome pathway


Leaf-to-air vapor pressure deficit


Fitted parameter for D in Eq. 3.29


Minimum ion diffusion rate in modeling stomatal conductance in Eq. 3.36


Evapotranspiration rate


Activation energy


Activation energy of the respiratory pathway


Activation energy at the reference temperature

fi and fref

Value of f at T = ∞ and the reference temperature


Fraction of photorespiratory NADH that remains in mitochondria


Maximum dark-adapted quantum yield for photosystem I I


Sensitivity of stomata to leaf water potential


Flavin adenine dinucleotide


Total diffusion conductance for CO2 from air to chloroplasts

g0 and g1

Fitted parameters for stomatal conductance

gbgm, and gs

Conductances for CO2 diffusion across boundary layer, mesophyll and stomata


Leaf boundary layer for heat conductance


Leaf CO2 conductance including stomatal and boundary layer conductance s


Leaf water vapor conductance including stomatal and boundary layer conductance s


Sensible heat flux


Energy of deactivation


Relative humidity at the leaf surface


High temperature


Photosynthetically active photon flux density (irradiance )


Electron transport rate


Maximum J

Kc and Ko

Michaelis–Menten constant s for carboxylation and oxygenation


Rubisco turnover rate (rate of CO2 fixation per Rubisco active site)


Hydraulic conductance for the whole plant


Leaf mass per area


Low temperature


Empirical constant in Eq. 3.32


Plant dry mass


Malate dehydrogenase


Fraction of photorespiratory NADH that remains in mitochondria


Type II NAD(P)H dehydrogenases


O2 partial pressure in chloroplasts


Oxaloacetic acid


Oxidative pentose phosphate pathway

Pg and Pe

Pressure potentials of the guard cells and the bulk epidermal cells


Export rate of triose phosphate


Pyruvate dehydrogenase complex


Phosphoenolpyruvate carboxylase






Photosystem I I


Ratio of the process rate at a reference temperature + 10 K to the rate at the reference temperature


Total resistance to CO2 diffusion from air to chloroplasts

rb, rm, and rs

Resistances to CO2 diffusion at boundary layer, mesophyll, and stomata

rwb and rws

Resistances to water vapor at boundary layer and stomata


Universal gas constant


Rate of non-photorespiratory CO2 release


Respiration rate in the light


Growth respiration coefficient


Maintenance respiration rate


Respiration rate in the dark


Net radiation


Rate of non-photorespiratory O2 consumption


Photorespiratory rate


Respiration rate at the reference temperature


Minimum R d


Relative growth rate


Ribulose-1,5-bisphosphate carboxylase/oxygenase


Ribulose 1,5-bisphosphate


Chloroplast surface area


Relative specificity of Rubisco (specificity factor)


Sensitivity parameter in Eq. 3.38

SA and SD

Starch-accumulating and deficient species



Tl and Ta

Leaf and air temperatures


Temperature in Kelvin


Optimal temperature


Reference temperature


Temperature of the sky


Uncoupling protein




Rate of carbon flow to CO2 as a by-product of flows into anabolic products


Rate of carboxylation


Rate of CO2 release due to catabolic substrate oxidation


Maximum V c


Rate of oxygenation


CO2 release rate from substrate oxidation via cytosolic OPPP


Maximum V o


CO2 release rate from substrate oxidation via chloroplastic OPPP


Photo-reductant export rate


Vapor pressure deficit

Wa and Wi

Water vapor pressure s in air and intercellular air space


Leaf absorptance

αS and αIR

Shortwave and infrared absorptance s


Empirical constant in Eq. 3.34

γ and ξ

Empirical constants in Eq. 3.36


Coefficient to describe dynamic response of E o to temperature


Thickness of mesophyll cell wall


Entropy term


Leaf long-wave emissivity


Ratio of RuBP oxygenation to carboxylation rates


Initial slopes of the light response curve


CO2 compensation point of CO2 assimilation


CO2 compensation point of CO2 assimilation in the absence of R d


Heat of vaporization


Marginal water cost of carbon gain


Osmotic potential of apoplastic water near the stomatal guard cells


Osmotic potential of epidermis cells


Osmotic potential in the guard cells


Curvature factors in Eqs. 3.11, 3.12 and 3.16


Shortwave reflectance of the surroundings


Stefan–Boltzmann constant


Scale R o to a daily rate


ATP concentration in the guard cells


Slope of light response of R d


Hydraulic conductance between the bulk epidermis and stomatal guard cells


Water potential of epidermis cell


Water potential of guard cell


Reference potential


Soil water potential


Bulk leaf water potential



We thank Ülo Niinemets for the valuable comments. This work was supported by Grants-in-Aid for Scientific Research on Innovative Areas (Nos. 21114001, 21114007, 21114009), by KAKENHI (Nos. 20677001, 25291095 and 25660113) and by CREST, JST, Japan.


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© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Graduate School of Life SciencesTohoku UniversitySendaiJapan
  2. 2.CRESTJSTTokyoJapan
  3. 3.School of Life SciencesTokyo University of Pharmacy and Life SciencesHachiojiJapan
  4. 4.School of ScienceThe University of TokyoTokyoJapan

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