Page 39 - Visions of the Future Chemistry and Life Science

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

reactions. Solvent dynamics and the natural ‘breathing’ of the enzyme
molecule need to be included for a more complete picture of enzymatic
reactions. Kramers put forward a theory that explicitly recognises the role
of solvent dynamics in catalysis. For the reaction Reactants→Products,
Kramers suggested that this proceeds by a process of diffusion over a poten-
tial energy barrier. The driving force for the reaction is derived from
random thermally induced structural fluctuations in the protein, and these
‘energise’ the motion of the substrate. This kinetic motion in the substrate
is subsequently dissipated because of friction with the surroundings and
enables the substrate to reach a degree of strain that is consistent with it
progressing to the corresponding products (along the reaction pathway) –
the so-called ‘transient strain’ model of enzyme catalysis. By acknowledg-
ing the dynamic nature of protein molecules, Kramers’ theory (but not
transition state theory) for classical transfers provides us with a platform
from which to develop new theories of quantum tunnelling in enzyme
molecules.

2.4 Wave–particle duality and the concept of tunnelling

Tunnelling is a phenomenon that arises as a result of the wave-properties
of matter. Quantum tunnelling is the penetration of a particle into a region
that is excluded in classical mechanics (due to it having insufficient energy
to overcome the potential energy barrier). An important feature of
quantum mechanics is that details of a particle’s location and motion are
defined by a wavefunction. The wavefunction is a quantity which, when
squared, gives the probability of finding a particle in a given region of space.
Thus, a nonzero wavefunction for a given region means that there is a finite
probability of the particle being found there. A nonzero wavefunction on
one side of the barrier will decay inside the barrier where its kinetic energy,
E, is less than the potential energy of the barrier, V (i.e. E
V; if E V, it can
pass over the barrier). On emerging at the other side of the barrier, the wav-
efunction amplitude is nonzero, and there is a finite probability that the
particle is found on the other side of the barrier – i.e. the particle has tun-
nelled (Figure 2.3).
Quantum tunnelling in chemical reactions can be visualised in terms
of a reaction coordinate diagram (Figure 2.4). As we have seen, classical
transitions are achieved by thermal activation – nuclear (i.e. atomic posi-
tion) displacement along the R curve distorts the geometry so that the