Symbol | Definition (and First Appearance in the Text) | Unit |
---|---|---|

Isotope fractionation factor during CO_{2} diffusion through the leaf boundary layer and the stomata (Eq. 12) | ‰ | |

a_{ch}, a_{sh} | Isotope fractionation factor during CO_{2} diffusion across the chloroplast (a_{ch}; C_{3} plant) or the bundle sheath cells (a_{sh}; C_{4} plant) (Eq. C4) | ‰ |

a_{cb} | Isotope fractionation factor between CO_{2} and bicarbonate at equilibrium (i.e. a_{cb} = α_{cb} − 1) (Eq. 7) | ‰ |

a_{w} | Isotope fractionation factor during CO_{2} dissolution and diffusion from the substomatal cavity to the CA site (Eq. 1) | ‰ |

A, ^{18}A | Net total CO_{2} and C^{18}OO flux (Eq. 1) | mol m^{−2} s^{−1} |

b, b_{PEPC} | Isotope fractionation factor during Rubisco and PEPC carboxylation (Appendix C) | ‰ |

B | Dimensionless solubility of CO_{2} in water (i.e. 8.314K_{H}T, where T is temperature) (Eq. B11) | m^{3} m^{−3} |

C_{c}, B_{c} | CO_{2} and bicarbonate concentrations at the Rubisco site (chloroplast stroma in C_{3} plants, bundle sheath in C_{4} plants) (Fig. 1) | mol mol^{−1} |

C_{m}, B_{m} | CO_{2} and bicarbonate concentrations in the cytoplasm of mesophyll cells (Fig. 1) | mol mol^{−1} |

E | Transpiration rate (Eq. 11) | mol m^{−2} s^{−1} |

F_{r} | Ratio of respiratory to net CO_{2} flux [i.e. (V_{r} + 0.5V_{o})/A] (Eq. 6) | Unitless |

g_{bc}, g_{sc}, g_{tc} | Boundary layer, stomatal, and total conductance to CO_{2} (Eq. 11) | mol m^{−2} s^{−1} |

g_{ch}, g_{sh} | Conductance to CO_{2} from the CA site to the Rubisco site (i.e. across the chloroplast [g_{ch}; C_{3} plant] or the bundle sheath cells [g_{sh}; C_{4} plant]) | mol m^{−2} s^{−1} |

g_{m} | Mesophyll conductance to CO_{2} from the intercellular air space to the CA site (Fig. 1) | mol m^{−2} s^{−1} |

k_{CA} | Leaf CA activity rate (Eqs. 7 and 9) | mol m^{−2} s^{−1} Pa^{−1} |

k_{CA,orig} | Leaf CA activity rate, before applying the pH correction (Eq. 10) | mol m^{−2} s^{−1} Pa^{−1} |

k_{cat,assay}, k_{uncat,assay} | CA-catalyzed and uncatalyzed CO_{2} hydration rates under CA assay conditions (Eq. 9) | s^{−1} |

^{18}k_{d}, ^{16}k_{d} | H_{2}C^{18}OO_{2} and H_{2}C^{16}O_{3} dehydration rates (Eq. B1) | s^{−1} |

K_{H} | Solubility of CO_{2} in water (Eq. 9) | mol m^{−3} Pa^{−1} |

k_{h}, ^{16}k_{h}, ^{18}k_{h}, ^{18}k′_{h} | CO_{2} hydration rate (introduction, after Eq. 5) and CO_{2}-H_{2}O, C^{18}OO-H_{2}O, and CO_{2}-H_{2}^{18}O reaction rates (Eq. B1) | s^{−1} |

^{18}k_{hm}, ^{18}k_{hc} | C^{18}OO-H_{2}O reaction rate in the mesophyll and the chloroplast, respectively (Eqs. C4 and C6) | s^{−1} |

k_{iso} | CO_{2}-H_{2}O isotopic exchange rate (Eq. 4) | s^{−1} |

k_{uncat,invivo} | Uncatalyzed CO_{2} hydration rate under in vivo conditions (Eq. 9) | s^{−1} |

P | Atmospheric pressure (Fig. 1) | Pa |

p_{a}, p_{i}, p_{CA} | CO_{2} partial pressure in outside air, intercellular air space, and at the CA site (Fig. 1) | Pa |

pH_{assay}, pH_{invivo} | pH of the assay solution and of the leaf CA-containing compartment (Eq. 10) | Unitless |

R_{A} | Isotope ratio of net CO_{2} flux (=0.5^{18}A/A) | Unitless |

R′_{i} | Isotope ratio of CO_{2} in intercellular air space when ternary effects are neglected (Eq. A1) | Unitless |

R_{a}, R_{i}, R_{CA} | Isotope ratio of CO_{2} in outside air, intercellular air space, and at the CA site (Fig. 1) | Unitless |

R_{b} | Isotope ratio of bicarbonate (Eq. B5) | Unitless |

R_{b,eq} | Isotope ratio of bicarbonate in equilibrium with water (Eq. B5) | Unitless |

R_{c}, R′_{c} | Isotope ratio of CO_{2} and bicarbonate at the Rubisco site (Fig. 1) | Unitless |

R_{c} | Isotope ratio of CO_{2} (Eq. B5) | Unitless |

R_{c,eq} | Isotope ratio of CO_{2} in equilibrium with water (i.e. R_{w}α_{wc}) (Eq. B4) | Unitless |

R_{eq} | Isotope ratio of CO_{2} in equilibrium with water at the evaporation site (i.e. R_{es}α_{wc}) (Eq. 6) | Unitless |

R′_{eq} | Isotope ratio of CO_{2} in equilibrium with water in bundle sheath cells (i.e. R_{x}α_{wc}) (Eq. 6) | Unitless |

R_{es} | Isotope ratio of water at the evaporation site (Eq. 2) | Unitless |

R_{i0}, R_{CA0}, R_{c0} | R_{i}, R_{CA}, and R_{c} in the absence of CA activity (Eqs. 8 and C26) | Unitless |

R_{m}, R′_{m} | Isotope ratio of CO_{2} and bicarbonate in the cytoplasm of mesophyll cells (Fig. 1) | Unitless |

R_{mi}, R′_{mi} | Isotope ratio of CO_{2} produced in mitochondria of mesophyll and bundle sheath cells (Fig. 1) | Unitless |

R_{p} | Isotope ratio of CO_{2} released from C_{4} acids in bundle sheath cells (Eq. C6) | Unitless |

R_{trans} | Isotope ratio of transpired water vapor (Appendix C) | Unitless |

R_{x} | Isotope ratio of water in bundle sheath cells (Eq. 6) | Unitless |

R_{w} | Isotope ratio of water (Eq. B4) | Unitless |

S | Total bicarbonate species (i.e. [H_{2}CO_{3}] + [HCO_{3}^{−}] + [CO_{3}^{2−}]) (Eq. B8) | mol m^{−3} |

S_{G} | Surface area of the gas-liquid interface (Eq. B11) | m^{2} |

S_{leaf} | Leaf area used for the CA assay (Eq. 9) | m^{2} |

t | Time (Eq. 4) | s |

t′ | Ternary correction factor (Eq. 11) | Unitless |

t_{a} | Ternary correction factor for CO_{2} isotopes (Eq. 13) | Unitless |

V_{assay} | Volume of the CA assay solution (Eq. 9) | m^{3} |

V_{c} | Rubisco carboxylase activity rate in the chloroplast stroma of C_{3} plants or bundle sheath cells of C_{4} plants (Fig. 1) | mol m^{−2} s^{−1} |

V_{G}, V_{L} | Volumes of the gas and liquid phases (Eq. B11) | m^{3} |

V_{hc}, V_{dc} | CO_{2} hydration and dehydration rates in the chloroplast stroma of C_{3} plants (Fig. 1) | mol m^{−2} s^{−1} |

V_{hm}, V_{dm} | CO_{2} hydration and dehydration rates in the cytoplasm of mesophyll cells (Fig. 1) | mol m^{−2} s^{−1} |

V_{o}, V_{r} | Photorespiration and mitochondrial respiration rates (Fig. 1) | mol m^{−2} s^{−1} |

V_{p} | PEPC activity rates in the cytoplasm of C_{4} mesophyll cells (and CO_{2} release rate from C_{4} acid in bundle sheath cells) (Fig. 1) | mol m^{−2} s^{−1} |

,α_{cw} | Isotope fractionation between CO_{2} and water at equilibrium (i.e. R_{c,eq}/R_{w}) (Eqs. 2 and B4) | Unitless |

, α_{cb} | Isotope fractionation between CO_{2} and bicarbonate at equilibrium (i.e. R_{c,eq}/R_{b,eq}) (Eq. B6) | Unitless |

Γ* | CO_{2} compensation point in the absence of mitochondrial respiration (Appendix C) | mol mol^{−1} |

∆_{A} | Photosynthetic C^{18}OO discrimination (i.e. R_{a}/R_{A} − 1) (Eq. 12) | ‰ |

∆_{ci} | Isotope ratio of CO_{2} at the CA site, expressed relative to that in the intercellular air space (i.e. R_{CA}/R_{i} − 1) (Eq. 1) | ‰ |

∆_{ci0} | ∆_{ci} in the absence of CA activity (Eq. 3) | ‰ |

∆_{ea} | Isotope ratio of CO_{2} in equilibrium with the evaporation site, expressed relative to that in air (i.e. R_{eq}/R_{a} − 1) (Eq. 11) | ‰ |

∆_{ei} | Isotope ratio of CO_{2} in equilibrium with the evaporation site, expressed relative to that in the intercellular air space (i.e. R_{eq}/R_{i} − 1) (Eq. 2) | ‰ |

∆_{eq} | Isotope ratio of the evaporation site, expressed relative to that of bundle sheath cell water (i.e. R_{es}/R_{x} − 1) (Eq. 7) | ‰ |

∆_{i} | Photosynthetic C^{18}OO discrimination, expressed relative to the isotope ratio of CO_{2} in the intercellular air space (i.e. R_{i}/R_{A} − 1) (Eq. 1) | ‰ |

∆_{ia} | Isotope ratio of CO_{2} in the intercellular air space, expressed relative to that in the outside air (i.e. R_{i}/R_{a} − 1) (Eq. A4) | ‰ |

∆′_{ia} | ∆_{ia} without ternary corrections (Eq. 11) | ‰ |

∆_{mc} | Isotope fractionation factor between respired CO_{2} and CO_{2} at the Rubisco carboxylation site (i.e. R_{mi}/R_{c} − 1) (Appendix C) | ‰ |

ε_{ci} | p_{CA}/(p_{i} – p_{CA}) (Eq. 1) | Unitless |

ε_{ia} | p_{i}/(p_{a} – p_{i}) (Eq. 11) | Unitless |

θ | Degree of isotopic equilibration (Eq. 3) | Unitless |

π_{t} | Transfer coefficient between the gas and liquid phases (Eq. B11) | m s^{−1} |

ρ | Ratio of net CO_{2} flux to CA activity [i.e. A/(k_{CA}p_{CA})] (Eq. 7) | Unitless |

ρ_{i} | Ratio of net CO_{2} flux to k_{CA}p_{i} (Eq. 7) | Unitless |

τ | Time scale of CO_{2}-H_{2}O isotopic exchange dynamics (Eq. B8) | s |

τ′ | Decay rate of ^{18}O in the CO_{2} atom fraction (Eq. B11) | s |

τ_{1}, τ_{2} | C^{18}O_{2} decay rates before and after leaf extract addition during the CA assay (Appendix B) | s |

τ_{res} | Residence time of CO_{2} inside the leaf mesophyll (Eq. 5) | s |

ϕ_{r} | Fraction of respired CO_{2} not recycled by the chloroplast stroma (C_{3} plant) or not produced in the bundle sheath (C_{4} plant) (Fig. 1) | Unitless |