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

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

Open Systems at Steady State

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)

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

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

ISOTOPES IN LAND PLANTS

C3 vs. C4 vs. CAM

Cool season grassmost trees and shrubs

Warm season grassArid adapted dicots

Cerling et al. 97Nature

δ13C

C3 - C4 balance varies with climate

Tieszen et al.

Ecol. Appl. (1997) Tieszen et al. Oecologia (1979)

δ13C varies with environment within C3 plants

C3 plants

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

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.

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

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

G3P

Photo-respirationMajor source of leakageIncreasingly bad with rising T or O2/CO2 ratio

Why is C3 photosynthesis so inefficient?

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)

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)