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Enzymology takes a quantum leap forward  31



                                 occurs between two ‘centres’ (known as redox centres since one reduces
                                 the other, and in so doing is itself oxidised) – the ‘electron donor’ (which is
                                 thereby oxidised) supplies an electron to the ‘electron acceptor’ (which is
                                 thereby reduced). This can be modelled using quantum mechanics.
                                    It is well established that electron transfer in proteins is driven by dis-
                                 tortion in the nuclear (protein) geometry of the reactant state. This is facil-
                                 itated by the natural, thermally activated breathing of the protein
                                 molecule. Thermal activation of the reactant state leads to overlap with
                                 the potential energy curve for the product state – the point of overlap is the
                                 nuclear geometry that is compatible with electron tunnelling. At this
                                 intersection point, there is an energy barrier through which the electron
                                 must tunnel to arrive on the product side. The theory for protein-mediated
                                 electron transfer reactions illustrates an important role for protein dynam-
                                 ics in driving the tunnelling process. The importance of dynamic fluctua-
                                 tions in the protein can be appreciated by considering those reactions that
                                 have a nonzero change in overall energy for the electron transfer reaction.
                                 Since tunnelling is significant only between states of nearly equal energy,
                                 tunnelling is unlikely in such instances. However, dynamic fluctuations
                                 in the protein overcome this problem. These equalise the energy between
                                 the reactant and product at the intersection point of the R (reactant) and P
                                 (product) potential energy curves (i.e. their configurations are identical),
                                 thus enabling transfer by quantum tunnelling. The term ‘vibrationally
                                 assisted tunnelling’ is therefore appropriate for protein electron transfer
                                 reactions. As described below, our recent work has also demonstrated a
                                 similar role for dynamic fluctuations of the protein during enzyme-
                                 catalysed hydrogen tunnelling. Electron transfer theory therefore provides
                                 a useful framework for understanding enzymatic hydrogen tunnelling.
                                 Despite this, until very recently tunnelling derivatives of transition state
                                 theory – that do not take into account the fluctuating nature of the enzyme
                                 – have been used to account fully for enzymatic hydrogen tunnelling. As a
                                 backdrop to the very recent dynamic treatments of hydrogen tunnelling in
                                 enzymes, we describe below static barrier approaches – i.e. tunnelling cor-
                                 rection theories of transition state theory – that have been applied to some
                                 enzyme systems.
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