recap issues of notation δ vs. r vs. f vs. %f (last three are exact)
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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 - PowerPoint PPT PresentationTRANSCRIPT
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RecapIssues 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. εEquilibrium vs. kineticEquilibrium, closed: phase plots, mass balance equationsEquilibrium, open: Rayleigh equationsKinetic, closed: Rayleigh equationsKinetic, open (simple): mass flow equations
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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
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Open Systems at Steady State
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Open system approaching steady state
δ1 = 0From 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 = 1000lnR/P
R/P = (1000+ δR )/(1000+ δP)
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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
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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
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
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ISOTOPES IN LAND PLANTS
C3 vs. C4 vs. CAM
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Cool season grassmost trees and shrubs
Warm season grassArid adapted dicots
Cerling et al. 97Nature
δ13C
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C3 - C4 balance varies with climate
Tieszen et al.
Ecol. Appl. (1997) Tieszen et al. Oecologia (1979)
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δ13C varies with environment within C3 plants
C3 plants
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εt = 4.4‰εf = 27‰
φ1,δ1
φ3,δ3
δi, Ci
Int CO2
δf
3(CH2O)
φ2,δ2 ,εf
εt
δa, Ca
Atm CO2 Rubisco
Plus some logic that flows from how flux relates to concentration φ1 C∝ a φ3 C∝ i φ3/φ1 = Ci/Ca φ2/φ1 = 1 - Ci/Ca
Want our equation in terms of substances that can be measuredSome 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
One branch point for a mass balance
In = Out φ1 = φ2 + φ3
φ1δ1 = φ2δ2 + φ3δ3
δ1 = δ2φ2/φ1 + δ3φ3/φ1
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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.
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Ci, δi
Inside leafCa,δa
Ca,δa
Cf,δf
φ1,δ1,εt
φ3,δ3,εt
φ2,δ2,εf
-12.4‰
-35‰
-27‰
Plant δ13C
(if atm = -8‰)
εp = εt = +4.4‰
εp = εf = +27‰
εf
0 0.5 1.0
Fraction C leaked (φ3/φ1 C∝ i/Ca)
δi
δf
δ1
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(Relative to preceding slide, note that the Y axis is reversed, so that εp increases up the scale)
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G3P
Photo-respirationMajor source of leakageIncreasingly bad with rising T or O2/CO2 ratio
Why is C3 photosynthesis so inefficient?
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CO2 a
δa
φ1,δ1
φ3,δ3
δi CO2 i
(aq)
HCO3
δi-εd/b
“Equilibrium box”
C4
PEP pyruvate
CO2 xδx
Cf
δf
φ2,δ2 ,εf
φ4,δ4,εPEP
Leakageφ5,δ5,εtw
εta
εta = 4.4‰εtw = 0.7‰εPEP = 2.2‰εf = 27‰εd/b = -7.9‰ @ 25°C
δ1 = δa - εta δ2 = δx - εf
δ3 = δi - εta
δ4 = δi + 7.9 - εPEP
δ5 = δx - εtw
Two branch points: i and x• φ1δ1 + φ5δ5 = φ4δ4 + φ3δ3
i) 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)
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Ci/Ca
In C4, L is ~ 0.3, so εp is insensitive to Ci/Ca, typically with values less than
those for εta.
εp = εta+[εPEP-7.9+L(εf-εtw)-εta](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.
εp = 4.4+[-10.1+L(26.3)](Ci/Ca)