Page 43 - Visions of the Future Chemistry and Life Science

32 M. J. SUTCLIFFE AND N. S. SCRUTTON

2.6 Transition state theory and corrections for hydrogen
tunnelling

Deviations from classical behaviour are usefully probed via the kinetic
isotope effect (Section 2.2). For non-enzymatic reactions, several factors –
in addition to inflated kinetic isotope effects (i.e. kinetic isotope effect 7)
– have been used to indicate quantum tunnelling of hydrogen. A particu-
larly striking indication of quantum tunnelling comes from studying the
temperature dependence of the reaction rate – this manifests itself as cur-
vature in the plot of ln (rate) vs. 1/T (the so-called ‘Arrhenius plot’; where
‘ln’ is the natural logarithm, log , and T is the temperature in kelvin, °C
e
273) over an extensive temperature range. Interestingly, this has been
observed in non-enzymatic radical reactions. However, curvature in
Arrhenius plots is not a useful indicator of quantum tunnelling because the
limited experimental temperature range available in studies using
enzymes make it impossible to detect any such curvature. An alternative
approach is to estimate, from the Arrhenius plot, the activation energy for
the reaction (from the slope) and the so-called ‘preexponential factors’
(from the intercept). Large differences in the activation energies for
1
protium and deuterium transfer ( 5.4kJmol ) and values deviating from
unity for the ratio of Arrhenius preexponential factors, can indicate non-
classical behaviour. In conjunction with inflated kinetic isotope effects,
these parameters have been used to demonstrate quantum tunnelling in
enzyme molecules.
Small deviations from classical behaviour have been reported for the
enzymes yeast alcohol dehydrogenase, bovine serum amine oxidase,
monoamine oxidase and glucose oxidase. More recently, the enzyme lipox-
ygenase has been shown to catalyse hydrogen transfer by a more extreme
quantum tunnelling process. In this case, the apparent activation energy
was found to be much smaller than for reactions catalysed by yeast alcohol
dehydrogenase, bovine serum amine oxidase, monoamine oxidase and
glucose oxidase, suggesting a correlation between apparent activation
energy and the extent of tunnelling. Use of a static (transition state theory-
like) barrier in the treatment of hydrogen tunnelling in enzymes has
allowed the construction of (hypothetical) relationships between the reac-
tion rate and temperature. These relationships are readily visualised in the
context of an Arrhenius plot and are observed in studies that employ
isotope (i.e. H, D and T) substitution within the reactive bond. The plot can