Page 46 - Visions of the Future Chemistry and Life Science

Enzymology takes a quantum leap forward 35

and P curves intersect (Figure 2.6). At the intersection point (X) of the two
curves, the hydrogen tunnels – the average tunnelling probability is
decreased when heavier isotopes (e.g. deuterium) are transferred, thus
giving rise to a kinetic isotope effect 1. At the intersection point, tunnel-
ling is from the vibrational ground state – since vibrational energy differ-
ences are comparable to barrier height, and therefore vibrational excitation
would lead to a classical ‘over-the-barrier’ transfer.
Clearly protein dynamics is hypothesised to have a major role in
driving hydrogen tunnelling in enzymes. However, like all hypotheses, this
requires experimental verification. The activation energy of the reaction is
associated with distortion of the protein molecule. Following the tunnel-
ling event, rapid movement away from the intersection point along the P
curve prevents coherent oscillations of the hydrogen between the R and P
curves. As such, the reaction is modelled in much the same way as elec-
tron transfer in proteins (i.e. Fermi’s Golden Rule applies and the non-adi-
abatic regime operates). A key prediction of this theory is that hydrogen
tunnelling can occur even when the value of the kinetic isotope effect
7,
thus suggesting that (contrary to current dogma) kinetic isotope effects
may be poor indicators of quantum tunnelling in enzymes. This is an
important point, since static barrier models of hydrogen tunnelling suggest
that hydrogen tunnelling does not occur when kinetic isotope effect
7.
This indicates that detailed temperature dependence studies are required
to demonstrate unequivocally that tunnelling is a feature of an enzyme cat-
alysed reaction.
The fluctuating enzyme model of hydrogen tunnelling can be divided
into two reaction components: (i) a thermally activated nuclear reorganisa-
tion step, and (ii) the hydrogen tunnelling event at the intersection point
of the potential energy curves. This leads to three possible rate-limiting
regimes in which either (i) nuclear reorganisation is rate-limiting, (ii)
quantum tunnelling is rate-limiting, or (iii) both factors contribute to the
observed rate. The value of the kinetic isotope effect is affected directly by
these steps. When nuclear reorganisation is rate limiting, the kinetic
isotope effect is unity (since this is independent of isotope) and reaction
rates are dependent on solvent viscosity (i.e. the ease with which the
protein structure can reorganise). In the quantum tunnelling limiting
regime, the kinetic isotope effect is not dependent on solvent viscosity and
is not unity (since tunnelling rate is a function of isotope). However, when
both nuclear reorganisation and quantum tunnelling contribute to the