A kinetic isotope effect (KIE) is a measurement of how much a reaction
rate changes upon isotopically labeling the reactant. It is the ratio of reaction rate constants for reactant
molecules containing the light and heavy isotopes:
KIE = lightk/heavyk
Primary KIEs are where the labeled atom is directly involved in the bond making and bond breaking steps.
Secondary KIEs involve isotopic labels remote from the where the chemistry is occurring.
Both types of KIE are used to determine TS structures.
For example, in dAMP hydrolysis, the primary 9-15N KIE reports on the extent of C-N bond breakage at the
TS, while the secondary 2'-3H KIE gives the conformation of the ribose ring.
Measuring KIEs
We use both stable (e.g., 2H, 13C) and radioactive (e.g., 3H, 14C) labels
to measure KIEs.
We have developed mass spectrometric and NMR methods to measure KIEs, in addition to the more traditional methods using
scintillation counting of radioactive labels.
What KIEs Tell Us
KIEs tell us about the change in "vibrational environment" of an isotopically labeled atom between the reactant and the TS.
By "vibrational environment" we mean the strengths of the bonds (i.e., the stretching and bending force constants) between atoms
in a molecule.
When discussing KIEs, we think of molecules as spheres connected together with springs. The strength of each spring reflects the
strength of the bond. We treat each spring as a "harmonic oscillator", which means that is vibrates with a frequency
that depends on the spring strength and the mass of the sphere (i.e., the isotopic label).
KIEs depend (mostly) on zero point energies (ZPEs). ZPE is the vibrational energy in a bond at 0 K. Atoms cannot be at rest, even
at absolute zero, because this would violate the Heisenberg Uncertainty Principle. The ZPE is a function of vibrational frequency,
which is in turn a function of the strength of a bond, and the mass of the vibrating atoms.
Strong bonds, light atoms -> high ZPE
Weak bonds, heavy atoms -> low ZPE
If a bond becomes weaker in the transition state, its ZPE decreases more for the light isotope than the heavy isotope. This means that
the activation energy for the light isotope is less than for the heavy isotope and therefore it reacts faster - a KIE.
Using computational techniques, we can analyze KIEs to interpret what they tell us about atoms' vibrational environments; and we can
determine the TS structure with sub-Angstrom accuracy. |
dAMP molecule showing the sites of the 9-15N (blue) and
2'(S)-2H (red) isotopic labels, as well as the other isotopically labeled
sites (green) we have investigated.
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