Analysis of Kinetic Isotope Effects in Enzymatic Carbon–Hydrogen Cleavage Reactions

The instanton approach, as previously applied to proton tunneling in molecular systems, is adapted to carbon-hydrogen bond cleavage catalyzed by enzymes. To compensate for the complexity of enzymatic reactions, simplifications are introduced based on the observation in numerous X-ray measurements that enzymes tend to form compact structures, which is assumed to have led toward optimization of specific parameters that govern the tunneling rate in the instanton formalism. On this basis, semiempirical equations are derived that link observed kinetic data directly to these parameters. These equations provide an analytical relation between the kinetic isotope effect and its temperature dependence for each hydrogen isotope, from which mechanistic and structural information can be extracted, including the nature of the hydrogen acceptor, the magnitude of the hydrogen transfer distance, the presence of endothermicity, and the contribution and frequency of skeletal vibrations that assist the tunneling. The method is used to analyze kinetic data reported for eight enzymatic CH-cleavage reactions; the enzymes or models thereof studied include methylmalonyl-coenzyme A mutase (coenzyme B(12)), galactose oxidase, lipoxygenase-1 with six mutants, methylamine dehydrogenase, an oxoiron(IV)porphyrin radical cation, phenylalanine hydroxylase, a bis(μ-oxo)dicopper complex, and rice α-oxygenase.