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



                               catalysing the breakage of C–H bonds – a direct result of the type of poten-
                               tial energy barrier that is used. Temperature-independent tunnelling is a
                               direct result of invoking a static (Eyring-like) potential energy barrier.
                               However, an alternative approach comes from invoking a fluctuating
                               (Kramers-like) potential energy barrier. This is conceptually more realistic
                               as it takes into account the dynamic motion of the protein. These dynamic
                               effects will give rise to more complex temperature dependencies for rates
                               of hydrogen transfer than those illustrated in Figure 2.5. The role of protein
                               dynamics in driving enzymatic hydrogen tunnelling is discussed below.


                               2.7 Hydrogen tunnelling driven by protein dynamics

                               In recent years, attempts have been made to model theoretically enzymatic
                               hydrogen tunnelling by incorporating thermal vibrations. However, and
                               importantly, none of these approaches have been verified experimentally.
                               Recently, the kinetic data for bovine serum amine oxidase have been re-
                               evaluated for thermally activated substrate vibrations, but with the protein
                               molecule treated as rigid. Computational molecular dynamics simulation
                               studies have also suggested a dynamic role for the protein molecule in
                               enzymatic hydrogen tunnelling. Indeed, some theoretical treatments have
                               recognised the role of thermal motion in the protein in hydrogen tunnel-
                               ling, but fail to predict the experimentally observed kinetic isotope effect
                               – and again experimental verification of these theories is lacking.
                                  The only (to the best of our knowledge) theoretical treatment of hydro-
                               gen transfer by tunnelling to explicitly recognise the role of protein dynam-
                               ics, and relate this in turn to the observed kinetic isotope effect, was
                               described by Bruno and Bialek. This approach has been termed ‘vibration-
                               ally enhanced ground state tunnelling theory’. A key feature of this theory
                               – and one that sets it apart from many other theoretical approaches – is that
                               tunnelling occurs from the ground state vibrational energy levels of the
                               substrate, i.e. there is no thermal activation of the substrate. The temper-
                               ature dependence of the reaction is therefore attributed to the natural ther-
                               mally induced breathing of the enzyme molecule, thus shortening the
                               distance the hydrogen must tunnel. Thus, the natural breathing of the
                               enzyme molecule can be visualised in the context of the familiar R (reac-
                               tant) and P (product) potential energy curve depiction encountered in dis-
                               cussions of electron transfer in proteins (Section 2.5). Hydrogen tunnelling
                               does not occur until the geometry of the protein is distorted so that the R
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