The hydrogen transfer reaction catalysed by soybean lipoxygenase (SLO) has been the focus of intense study following observations of a high kinetic isotope effect (KIE). Today high KIEs are generally thought to indicate departure from classical rate theory and are seen as a strong signature of tunnelling of the transferring particle, hydrogen or one of its isotopes, through the reaction energy barrier. In this paper, we build a qualitative quantum rate model with few free parameters that describes the dynamics of the transferring particle when it is exposed to energetic potentials exerted by the donor and the acceptor. The enzyme’s impact on the dynamics is modelled by an additional energetic term, an oscillatory contribution known as “gating.” By varying two key parameters, the gating frequency and the mean donor-acceptor separation, the model is able to reproduce well the KIE data for SLO wild-type and a variety of SLO mutants over the experimentally accessible temperature range. While SLO-specific constants have been considered here, it is possible to adapt these for other enzymes.
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The WKB approximation provides a good estimate of the tunnelling probability through a barrier when . In this case the tunnelling probability is . The action is for a one-dimensional potential V(x) that has a barrier in the range , and the incident particle has energy E and mass m. For the purposes of an order estimation, let us assume the barrier is rectangular, i.e. V(x) = V for and zero otherwise. Then . Typical parameters for the transfer distance Å and for the activation energy kcal/mol J (from SLO data in Ref. 13). Hence indicating that the WKB regime is not a very good approximation.
