Table D1. List of symbols
SymbolDefinition (and First Appearance in the Text)Unit
Embedded ImageIsotope fractionation factor during CO2 diffusion through the leaf boundary layer and the stomata (Eq. 12)
ach, ashIsotope fractionation factor during CO2 diffusion across the chloroplast (ach; C3 plant) or the bundle sheath cells (ash; C4 plant) (Eq. C4)
acbIsotope fractionation factor between CO2 and bicarbonate at equilibrium (i.e. acb = αcb − 1) (Eq. 7)
awIsotope fractionation factor during CO2 dissolution and diffusion from the substomatal cavity to the CA site (Eq. 1)
A, 18ANet total CO2 and C18OO flux (Eq. 1)mol m−2 s−1
b, bPEPCIsotope fractionation factor during Rubisco and PEPC carboxylation (Appendix C)
BDimensionless solubility of CO2 in water (i.e. 8.314KHT, where T is temperature) (Eq. B11)m3 m−3
Cc, BcCO2 and bicarbonate concentrations at the Rubisco site (chloroplast stroma in C3 plants, bundle sheath in C4 plants) (Fig. 1)mol mol−1
Cm, BmCO2 and bicarbonate concentrations in the cytoplasm of mesophyll cells (Fig. 1)mol mol−1
ETranspiration rate (Eq. 11)mol m−2 s−1
FrRatio of respiratory to net CO2 flux [i.e. (Vr + 0.5Vo)/A] (Eq. 6)Unitless
gbc, gsc, gtcBoundary layer, stomatal, and total conductance to CO2 (Eq. 11)mol m−2 s−1
gch, gshConductance to CO2 from the CA site to the Rubisco site (i.e. across the chloroplast [gch; C3 plant] or the bundle sheath cells [gsh; C4 plant])mol m−2 s−1
gmMesophyll conductance to CO2 from the intercellular air space to the CA site (Fig. 1)mol m−2 s−1
kCALeaf CA activity rate (Eqs. 7 and 9)mol m−2 s−1 Pa−1
kCA,origLeaf CA activity rate, before applying the pH correction (Eq. 10)mol m−2 s−1 Pa−1
kcat,assay, kuncat,assayCA-catalyzed and uncatalyzed CO2 hydration rates under CA assay conditions (Eq. 9)s−1
18kd, 16kdH2C18OO2 and H2C16O3 dehydration rates (Eq. B1)s−1
KHSolubility of CO2 in water (Eq. 9)mol m−3 Pa−1
kh, 16kh, 18kh, 18khCO2 hydration rate (introduction, after Eq. 5) and CO2-H2O, C18OO-H2O, and CO2-H218O reaction rates (Eq. B1)s−1
18khm, 18khcC18OO-H2O reaction rate in the mesophyll and the chloroplast, respectively (Eqs. C4 and C6)s−1
kisoCO2-H2O isotopic exchange rate (Eq. 4)s−1
kuncat,invivoUncatalyzed CO2 hydration rate under in vivo conditions (Eq. 9)s−1
PAtmospheric pressure (Fig. 1)Pa
pa, pi, pCACO2 partial pressure in outside air, intercellular air space, and at the CA site (Fig. 1)Pa
pHassay, pHinvivopH of the assay solution and of the leaf CA-containing compartment (Eq. 10)Unitless
RAIsotope ratio of net CO2 flux (=0.518A/A)Unitless
RiIsotope ratio of CO2 in intercellular air space when ternary effects are neglected (Eq. A1)Unitless
Ra, Ri, RCAIsotope ratio of CO2 in outside air, intercellular air space, and at the CA site (Fig. 1)Unitless
RbIsotope ratio of bicarbonate (Eq. B5)Unitless
Rb,eqIsotope ratio of bicarbonate in equilibrium with water (Eq. B5)Unitless
Rc, RcIsotope ratio of CO2 and bicarbonate at the Rubisco site (Fig. 1)Unitless
RcIsotope ratio of CO2 (Eq. B5)Unitless
Rc,eqIsotope ratio of CO2 in equilibrium with water (i.e. Rwαwc) (Eq. B4)Unitless
ReqIsotope ratio of CO2 in equilibrium with water at the evaporation site (i.e. Resαwc) (Eq. 6)Unitless
ReqIsotope ratio of CO2 in equilibrium with water in bundle sheath cells (i.e. Rxαwc) (Eq. 6)Unitless
ResIsotope ratio of water at the evaporation site (Eq. 2)Unitless
Ri0, RCA0, Rc0Ri, RCA, and Rc in the absence of CA activity (Eqs. 8 and C26)Unitless
Rm, RmIsotope ratio of CO2 and bicarbonate in the cytoplasm of mesophyll cells (Fig. 1)Unitless
Rmi, RmiIsotope ratio of CO2 produced in mitochondria of mesophyll and bundle sheath cells (Fig. 1)Unitless
RpIsotope ratio of CO2 released from C4 acids in bundle sheath cells (Eq. C6)Unitless
RtransIsotope ratio of transpired water vapor (Appendix C)Unitless
RxIsotope ratio of water in bundle sheath cells (Eq. 6)Unitless
RwIsotope ratio of water (Eq. B4)Unitless
STotal bicarbonate species (i.e. [H2CO3] + [HCO3] + [CO32−]) (Eq. B8)mol m−3
SGSurface area of the gas-liquid interface (Eq. B11)m2
SleafLeaf area used for the CA assay (Eq. 9)m2
tTime (Eq. 4)s
tTernary correction factor (Eq. 11)Unitless
taTernary correction factor for CO2 isotopes (Eq. 13)Unitless
VassayVolume of the CA assay solution (Eq. 9)m3
VcRubisco carboxylase activity rate in the chloroplast stroma of C3 plants or bundle sheath cells of C4 plants (Fig. 1)mol m−2 s−1
VG, VLVolumes of the gas and liquid phases (Eq. B11)m3
Vhc, VdcCO2 hydration and dehydration rates in the chloroplast stroma of C3 plants (Fig. 1)mol m−2 s−1
Vhm, VdmCO2 hydration and dehydration rates in the cytoplasm of mesophyll cells (Fig. 1)mol m−2 s−1
Vo, VrPhotorespiration and mitochondrial respiration rates (Fig. 1)mol m−2 s−1
VpPEPC activity rates in the cytoplasm of C4 mesophyll cells (and CO2 release rate from C4 acid in bundle sheath cells) (Fig. 1)mol m−2 s−1
Embedded ImagecwIsotope fractionation between CO2 and water at equilibrium (i.e. Rc,eq/Rw) (Eqs. 2 and B4)Unitless
Embedded Image, αcbIsotope fractionation between CO2 and bicarbonate at equilibrium (i.e. Rc,eq/Rb,eq) (Eq. B6)Unitless
Γ*CO2 compensation point in the absence of mitochondrial respiration (Appendix C)mol mol−1
APhotosynthetic C18OO discrimination (i.e. Ra/RA − 1) (Eq. 12)
ciIsotope ratio of CO2 at the CA site, expressed relative to that in the intercellular air space (i.e. RCA/Ri − 1) (Eq. 1)
ci0ci in the absence of CA activity (Eq. 3)
eaIsotope ratio of CO2 in equilibrium with the evaporation site, expressed relative to that in air (i.e. Req/Ra − 1) (Eq. 11)
eiIsotope ratio of CO2 in equilibrium with the evaporation site, expressed relative to that in the intercellular air space (i.e. Req/Ri − 1) (Eq. 2)
eqIsotope ratio of the evaporation site, expressed relative to that of bundle sheath cell water (i.e. Res/Rx − 1) (Eq. 7)
iPhotosynthetic C18OO discrimination, expressed relative to the isotope ratio of CO2 in the intercellular air space (i.e. Ri/RA − 1) (Eq. 1)
iaIsotope ratio of CO2 in the intercellular air space, expressed relative to that in the outside air (i.e. Ri/Ra − 1) (Eq. A4)
∆′iaia without ternary corrections (Eq. 11)
mcIsotope fractionation factor between respired CO2 and CO2 at the Rubisco carboxylation site (i.e. Rmi/Rc − 1) (Appendix C)
εcipCA/(pipCA) (Eq. 1)Unitless
εiapi/(papi) (Eq. 11)Unitless
θDegree of isotopic equilibration (Eq. 3)Unitless
πtTransfer coefficient between the gas and liquid phases (Eq. B11)m s−1
ρRatio of net CO2 flux to CA activity [i.e. A/(kCApCA)] (Eq. 7)Unitless
ρiRatio of net CO2 flux to kCApi (Eq. 7)Unitless
τTime scale of CO2-H2O isotopic exchange dynamics (Eq. B8)s
τ′Decay rate of 18O in the CO2 atom fraction (Eq. B11)s
τ1, τ2C18O2 decay rates before and after leaf extract addition during the CA assay (Appendix B)s
τresResidence time of CO2 inside the leaf mesophyll (Eq. 5)s
ϕrFraction of respired CO2 not recycled by the chloroplast stroma (C3 plant) or not produced in the bundle sheath (C4 plant) (Fig. 1)Unitless