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Recap Issues of notation δ vs. R vs. F vs. %F (last three are exact)

Recap Issues of notation δ vs. R vs. F vs. %F (last three are exact) Isotope ecology is balance between fractionation & mixing Fractionation: δ vs. Δ vs. ε Equilibrium vs. kinetic Equilibrium, closed: phase plots, mass balance equations Equilibrium, open: Rayleigh equations

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Recap Issues of notation δ vs. R vs. F vs. %F (last three are exact)

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  1. Recap Issues of notation δ vs. R vs. F vs. %F (last three are exact) Isotope ecology is balance between fractionation & mixing Fractionation: δ vs. Δ vs. ε Equilibrium vs. kinetic Equilibrium, closed: phase plots, mass balance equations Equilibrium, open: Rayleigh equations Kinetic, closed: Rayleigh equations Kinetic, open (simple): mass flow equations

  2. Kinetic Fractionation, Open System Consider a system with 1 input and 2 outputs (i.e., a branching system). At steady state, the amount of R entering the system equals the amounts of products leaving: R = P + Q. A similar relationship holds for isotopes: δR = δPfP + (1-fP)δQ. Again, this should look familiar; it is identical to closed system, equilibrium behavior, with exactly the same equations: δP = δR + (1-fP)(δP-δQ) = δR + (1-fP)εP/Q δQ = δR - fPεP/Q

  3. Open Systems at Steady State

  4. Open system approaching steady state δ1 = 0 From mass balance at steady state: δ1 = δ2 Yet δ2 = δB - ε2 = δB - 25, so δB = +25‰ Note that for Hayes (and most biologists): δR-δP=εR/P, so ε is a positive number for kinetic isotope effects. Above, δP = δR-εR/P εR/P = 1000lnR/P R/P = (1000+ δR )/(1000+ δP)

  5. Nier-type mass Spectrometer Ion Source Gas molecules ionized to + ions by e- impact Accelerated towards flight tube with k.e.: 0.5mv2 = e+V where e+ is charge, m is mass, v is velocity, and V is voltage Magnetic analyzer Ions travel with radius: r = (1/H)*(2mV/e+)0.5 where H is the magnetic field higher mass > r Counting electronics

  6. Continuous Flow sample injected into He stream cleanup and separation by GC high pumping rate 1 to 100 nanomoles gas reference gas not regularly altered with samples loss of precision Dual Inlet sample and reference analyzed alternately 6 to 10 x viscous flow through capillary change-over valve 1 to 100 μmole of gas required highest precision

  7. ISOTOPES IN LAND PLANTS C3 vs. C4 vs. CAM

  8. Cerling et al. 97 Nature δ13C Warm season grass Arid adapted dicots Cool season grass most trees and shrubs

  9. C3 - C4 balance varies with climate Tieszen et al. Ecol. Appl. (1997) Tieszen et al. Oecologia (1979)

  10. δ13C varies with environment within C3 plants C3 plants

  11. One branch point for a mass balance In = Out φ1 = φ2 + φ3 φ1δ1 = φ2δ2 + φ3δ3 δ1 = δ2φ2/φ1 + δ3φ3/φ1 Want our equation in terms of substances that can be measured Some key equations for substitutions δ1 = δa - εt δ2 = δi - εf δ3 = δi - εt δi = δf + εf δa - εt = (δi - εf)(1 - Ci/Ca) + (δi - εt)Ci/Ca δa - εt = (δf + εf - εf)(1 - Ci/Ca) + (δf + εf - εt)Ci/Ca δa - εt = δf - δfCi/Ca + δfCi/Ca + (εf - εt)Ci/Ca εP = δa - δf = εt + (εf - εt)Ci/Ca φ2,δ2 ,εf φ1,δ1 δi, Ci Int CO2 εt = 4.4‰ εf = 27‰ δf 3(CH2O) δa, Ca Atm CO2 εt Rubisco φ3,δ3 Plus some logic that flows from how flux relates to concentration φ1 ∝ Ca φ3 ∝ Ci φ3/φ1 = Ci/Ca φ2/φ1 = 1 - Ci/Ca

  12. εp = δa - δf = εt + (Ci/Ca)(εf-εt) When Ci ≈ Ca (low rate of photosynthesis, open stomata), then εp ≈ εf. Large fractionation, low plant δ13C values. When Ci << Ca (high rate of photosynthesis, closed stomata), then εp ≈ εt. Small fractionation, high plant δ13C values.

  13. Plant δ13C (if atm = -8‰) δi εf εp = εt = +4.4‰ δ1 -12.4‰ δf -27‰ εp = εf = +27‰ -35‰ 0 0.5 1.0 Fraction C leaked (φ3/φ1 ∝ Ci/Ca) φ3,δ3,εt φ1,δ1,εt Ca,δa Ci, δi Inside leaf Ca,δa Cf,δf φ2,δ2,εf

  14. (Relative to preceding slide, note that the Y axis is reversed, so that εp increases up the scale)

  15. G3P Why is C3 photosynthesis so inefficient? Photo-respiration Major source of leakage Increasingly bad with rising T or O2/CO2 ratio

  16. “Equilibrium box” PEP pyruvate φ1,δ1 φ2,δ2 ,εf δi CO2 i (aq) HCO3 δi-εd/b CO2x δx Cf δf CO2 a δa C4 εta φ4,δ4,εPEP φ3,δ3 Leakage φ5,δ5,εtw δ1 = δa - εta δ2 = δx - εf δ3 = δi - εta δ4 = δi + 7.9 - εPEP δ5 = δx - εtw εta = 4.4‰ εtw = 0.7‰ εPEP = 2.2‰ εf = 27‰ εd/b = -7.9‰ @ 25°C Two branch points: i and x φ1δ1 + φ5δ5 = φ4δ4 + φ3δ3 φ4δ4 = φ5δ5 + φ2δ2 Leakiness: L = φ5/φ4 After a whole pile of substitution εp = δa - δf = εta + [εPEP - 7.9 + L(εf -εtw)- εta](Ci/Ca)

  17. εp = εta+[εPEP-7.9+L(εf-εtw)-εta](Ci/Ca) εp = 4.4+[-10.1+L(26.3)](Ci/Ca) Under arid conditions, succulent CAM plants use PEP to fix CO2 to malate at night and then use RUBISCO for final C fixation during the daytime. The L value for this is typically higher than 0.38. Under more humid conditions, they will directly fix CO2 during the day using RUBISCO. As a consequence, they have higher, and more variable, εp values. Ci/Ca In C4, L is ~ 0.3, so εp is insensitive to Ci/Ca, typically with values less than those for εta.

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