Recap

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Recap Issues of notation d vs. R vs. F vs. F
(last three are exact) Isotope ecology is
balance between fractionation
mixing Fractionation d vs. ? vs. e Equilibrium
vs. kinetic Equilibrium, closed phase plots,
mass balance equations Equilibrium, open
Rayleigh equations Kinetic, closed Rayleigh
equations Kinetic, 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 dR
dPfP (1-fP)dQ. Again, this should look
familiar it is identical to closed system,
equilibrium behavior, with exactly the same
equations dP dR (1-fP)(dP-dQ) dR
(1-fP)eP/Q dQ dR - fPeP/Q
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Open Systems at Steady State
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Open system approaching steady state
d1 0 From mass balance at steady state d1
d2 Yet d2 dB - e2 dB - 25, so dB 25
Note that for Hayes (and most biologists) dR-dPe
R/P, so e is a positive number for kinetic
isotope effects. Above, dP dR-eR/P eR/P
1000ln?R/P ?R/P (1000 dR )/(1000 dP)
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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 eV 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 gt
r Counting electronics
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ISOTOPES IN LAND PLANTS C3 vs. C4 vs. CAM
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Cerling et al. 97 Nature
d13C
Warm season grass Arid adapted dicots
Cool season grass most trees and shrubs
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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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d13C varies with environment within C3 plants
C3 plants
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f2,d2 ,ef
f1,d1
et 4.4 ef 27
di, Ci Int CO2
df 3(CH2O)
da, Ca Atm CO2
et
Rubisco
f3,d3
Plus some logic that flows from how flux relates
to concentration f1 ? Ca f3 ? Ci
f3/f1 Ci/Ca f2/f1 1 - Ci/Ca
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ep da - df et (Ci/Ca)(ef-et)
When Ci Ca (low rate of photosynthesis, open
stomata), then ep ef. Large fractionation, low
plant d13C values. When Ci ltlt Ca (high rate of
photosynthesis, closed stomata), then ep et.
Small fractionation, high plant d13C values.
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Plant d13C (if atm -8)
di
ef
ep et 4.4
-12.4
d1
df
-27
ep ef 27
-35
0
0.5
1.0
Fraction C leaked (f3/f1 ? Ci/Ca)
f3,d3,et
Ca,da
f1,d1,et
Ci, di Inside leaf
Ca,da
Cf,df
f2,d2,ef
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(Relative to preceding slide, note that the Y
axis is reversed, so that ep increases up the
scale)
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Why is C3 photosynthesis so inefficient?
Photo-respiration Major source of
leakage Increasingly bad with rising T or O2/CO2
ratio
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Equilibrium box
PEP
pyruvate
f1,d1
f2,d2 ,ef
di CO2 i (aq)
HCO3 di-ed/b
CO2 x dx
Cf df
CO2 a da
C4
eta
f4,d4,ePEP
f3,d3
Leakage f5,d5,etw
d1 da - eta d2 dx - ef d3 di - eta d4 di
7.9 - ePEP d5 dx - etw
eta 4.4 etw 0.7 ePEP 2.2 ef 27 ed/b
-7.9 _at_ 25C

• Two branch points i and x
• f1d1 f5d5 f4d4 f3d3
• f4d4 f5d5 f2d2
• Leakiness L f5/f4

After a whole pile of substitution
ep da - df eta ePEP - 7.9 L(ef - etw) -
eta(Ci/Ca)
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ep etaePEP-7.9L(ef-etw)-eta(Ci/Ca)
ep 4.4-10.1L(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, ep values.
Ci/Ca
In C4, L is 0.3, so ep is insensitive to Ci/Ca,
typically with values less than those for eta.