References

384 E.A. Hobbie
2
Natural Abundance Measurements
Most chemical and biochemical processes favor the initial incorporation
of the lighter isotope in the product, leaving the remaining substrate enriched
in the heavy isotope. Such kinetic isotope effects can be contrasted
with equilibrium isotope effects, or the isotopic partitioning of elements
between components at equilibrium. Equilibrium isotope effects generally
result in the heavy isotope accumulating in the compound with the stronger
chemical bonds (Bigeleisen 1965). The partitioning of isotopes in reactions
is termed “isotopic fractionation”; the magnitude of isotopic fractionation
depends on the elements involved and the specific reaction mechanism.
Isotopically fractionating processes, therefore, result in variation in the
isotopic ratios between the substrate and the product. These ratios depend
on the isotopic ratio of the substrate, the proportion of substrate
transformed to product, and whether the system is open or closed (Fig. 1).
Natural abundance studies use small isotopic differences among different
ecosystem pools and compounds to understand the sources and fluxes
of many of the most biologically important elements. Because differences
in isotopic ratios are small, they are measured using the “δ” notation, in
deviations in parts per mille (‰) from a standard ratio, according to (18.1).
δ n X(‰) = (Rsample/Rstandard −1)× 1000 (18.1)
In (18.1), n equals the atomic mass of the heavy isotope, X is the symbol for
the element of interest, and R equals the molar abundance of the heavy isotope
divided by the light isotope (e.g., 13 C/ 12 C). The isotopic standard for
carbon is Vienna PeeDee Belemnite ( 13 C/ 12 C = 0. 0112372), for nitrogen,
Fig. 1. Isotopic composition of substrate and product in an open system depends on the
fraction (f ) of substrate transformed to the product and the isotopic fractionation (∆) of
the reaction. For discussion of the somewhat more complicated case of a closed system, see
Hayes (2002)