Biomedical Engineering Reference
In-Depth Information
A theory of KIE for multistep enzymatic reactions was developed by Cleland and
Northrop (1999). It is obvious that when the barrier of the chemical reaction step is at
least several kcal/mole above all others, the step is essentially step- limiting. The isotope
in this step is fully expressed in the experimental ratio V/K , where V and K are the
reaction maximum rate and Michaelis constant, respectively. If the chemical step does
not have the highest barrier, the isotope effect can be partially or fully suppressed. For
the mechanism:
where is the isotope sensitive chemical step, the isotope effect on V/K at
the substitution of a light atom X for a heaver atom Y is given by
where and are combinations of rate constants of different steps (so called
commitments). The forward commitment
whereas the reverse commitment
When
and
are very small
and experimental KIE is directly
related to the limiting chemical step. If
is very large, the KIE will be completely
suppressed.
Analysis of experimental data on KIE indicate certain interesting conclusions about
the detail mechanism of rate-limiting chemical reaction step and TS structure. In general,
atoms that become vibrationally less constrained in the TS give normal KIE
> 1). Conversely, atoms more constrained at the TS course give inverse KIE. Fig. 1.12
summarized the primary and secondary T KIE's expected for different reaction
mechanisms. As is seen from the Figure, the pattern of these two KIF is sufficient to
distinguish the mechanisms. Analysis of the KIE magnitudes is capable of providing
quantitative information on broken bonds order in transition state for each type of
reaction.
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