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

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: δ R = δ P f P + (1-f P )δ Q. Again, this should look familiar; it is identical to closed system, equilibrium behavior, with exactly the same equations: δ P = δ R + (1-f P )(δ P- δ Q ) = δ R + (1-f P )ε P/Q δ Q = δ R - f P ε P/Q

Open Systems at Steady State

Open system approaching steady state δ 1 = 0 From mass balance at steady state: δ 1 = δ 2 Yet δ 2 = δ B - ε 2 = δ B - 25, so δ B = +25‰ Note that for Hayes (and most biologists): δ R -δ P =ε R/P, so ε is a positive number for kinetic isotope effects. Above, δ P = δ R -ε R/P ε R/P = 1000ln  R/P  R/P = (1000+ δ R )/(1000+ δ P )

Nier-type mass Spectrometer Ion Source Gas molecules ionized to + ions by e - impact Accelerated towards flight tube with k.e.: 0.5mv 2 = 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 grass most trees and shrubs Warm season grass Arid adapted dicots Cerling et al. 97 Nature δ 13 C

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

δ 13 C varies with environment within C3 plants C3 plants

ε t = 4.4‰ ε f = 27‰ φ 1,δ 1 φ 3,δ 3 δ i, C i Int CO 2 δ f 3(CH 2 O) φ 2,δ 2,ε f εtεt δ a, C a Atm CO 2 Rubisco Plus some logic that flows from how flux relates to concentration φ 1 ∝ C a φ 3 ∝ C i φ 3 /φ 1 = C i /C a φ 2 /φ 1 = 1 - C i /C a Want our equation in terms of substances that can be measured Some key equations for substitutions δ 1 = δ a - ε t δ 2 = δ i - ε f δ 3 = δ i - ε t δ i = δ f + ε f δ a - ε t = (δ i - ε f )(1 - C i /C a ) + (δ i - ε t )C i /C a δ a - ε t = (δ f + ε f - ε f )(1 - C i /C a ) + (δ f + ε f - ε t )C i /C a δ a - ε t = δ f - δ f C i /C a + δ f C i /C a + (ε f - ε t )C i /C a ε P = δ a - δ f = ε t + (ε f - ε t )C i /C a One branch point for a mass balance In = Out φ 1 = φ 2 + φ 3 φ 1 δ 1 = φ 2 δ 2 + φ 3 δ 3 δ 1 = δ 2 φ 2 /φ 1 + δ 3 φ 3 /φ 1

ε p = δ a - δ f = ε t + (C i /C a )(ε f -ε t ) When C i ≈ C a (low rate of photosynthesis, open stomata), then ε p ≈ ε f. Large fractionation, low plant δ 13 C values. When C i << C a (high rate of photosynthesis, closed stomata), then ε p ≈ ε t. Small fractionation, high plant δ 13 C values.

C i, δ i Inside leaf C a,δ a C f,δ f φ 1,δ 1,ε t φ 3,δ 3,ε t φ 2,δ 2,ε f -12.4‰ -35‰ -27‰ Plant δ 13 C (if atm = -8‰) ε p = ε t = +4.4‰ ε p = ε f = +27‰ εfεf Fraction C leaked (φ 3 /φ 1 ∝ C i /C a ) δiδi δfδf δ1δ1

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

G3P Photo-respiration Major source of leakage Increasingly bad with rising T or O 2 /CO 2 ratio Why is C3 photosynthesis so inefficient?

CO 2 a δ a φ 1,δ 1 φ 3,δ 3 δ i CO 2 i (aq) HCO 3 δ i -ε d/b “Equilibrium box” C4 PEPpyruvate CO 2 x δ x CfδfCfδf φ 2,δ 2,ε f φ 4,δ 4,ε PEP Leakage φ 5,δ 5,ε tw ε ta ε ta = 4.4‰ ε tw = 0.7‰ ε PEP = 2.2‰ ε f = 27‰ ε d/b = 25°C δ 1 = δ a - ε ta δ 2 = δ x - ε f δ 3 = δ i - ε ta δ 4 = δ i ε PEP δ 5 = δ x - ε tw Two branch points: i and x i)φ 1 δ 1 + φ 5 δ 5 = φ 4 δ 4 + φ 3 δ 3 x)φ 4 δ 4 = φ 5 δ 5 + φ 2 δ 2 Leakiness: L = φ 5 /φ 4 After a whole pile of substitution ε p = δ a - δ f = ε ta + [ε PEP L(ε f - ε tw ) - ε ta ](C i /C a )

C i /C a In C4, L is ~ 0.3, so ε p is insensitive to C i /C a, typically with values less than those for ε ta. ε p = ε ta +[ε PEP -7.9+L(ε f -ε tw )-ε ta ](C i /C a ) Under arid conditions, succulent CAM plants use PEP to fix CO 2 to malate at night and then use RUBISCO for final C fixation during the daytime. The L value for this is typically higher than Under more humid conditions, they will directly fix CO 2 during the day using RUBISCO. As a consequence, they have higher, and more variable, ε p values. ε p = 4.4+[-10.1+L(26.3)](C i /C a )