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24 M. J. SUTCLIFFE AND N. S. SCRUTTON
Figure 2.2. Illustration of the wave-like property of matter by analogy with the
vibrations on a violin string. The solid and dashed lines illustrate the extremities
of the vibration. Although there is a node (a position where the string is
stationary) in the centre of the string, the vibration is transmitted through this
node – this is analogous to passing through a region of zero probability as in
quantum tunnelling.
products. Thus, quantum tunnelling may play an important role in driving
enzyme-catalysed reactions, especially for the transfer of small nuclei such
as hydrogen.
Indeed, quantum tunnelling is the established mechanism for enzyme-
mediated transfer of the much smaller electron. Proteins are electrical
insulators; nevertheless, electrons can travel large distances on the atomic
scale (up to around 3 10 9 m) through them. This apparent paradox – of
an electron passing through an electrical insulator – can be understood in
terms of the wave-like properties of the electron. Thus, the electron can
pass via quantum tunnelling through regions from which it would be
excluded by its particle-like nature.
In contrast to electron transfer via quantum tunnelling, evidence for
hydrogen tunnelling in enzyme molecules is extremely limited. This arises
conceptually because the mass of the hydrogen is approximately 1840
times greater than that of the electron. The probability of tunnelling
decreases with increasing mass, which reduces significantly the probabil-
ity of hydrogen versus electron tunnelling. Nevertheless, for those
enzyme-catalysed reactions with a large activation energy – requiring a