Temperature Dependence of Kinetic Isotope Effects for Enzymatic Carbon−Hydrogen Bond Cleavage

Abstract

An analysis is reported of the anomalously weak temperature dependence of large kinetic isotope effects (KIEs) observed for enzymes that catalyze carbon−hydrogen bond cleavage. After a critical examination of the experimental data, rate expressions for proton tunneling are used to derive a universal relationship between KIEs and their temperature dependence for a model in which the tunneling coordinate, represented by two crossing Morse potentials or a quartic double-minimum potential, is assisted by a harmonic promoting mode. Since the reactions involve electron transfer to a redox system as well as proton transfer from a CH to an OH bond, both adiabatic and nonadiabatic mechanisms are considered. Model calculations are reported, which show that the derived relationship is valid under a wide range of conditions and depends on a minimum number of model parameters, namely almost exclusively on the proton transfer distance and the tunneling-mode anharmonicity. The results are used to derive proton transfer distances and promoting-mode force constants from the available data on temperature-dependent isotope effects for several enzymatic reactions effecting CH cleavage, including the reactions of linoleic acid catalyzed by soybean lipoxygenase-1 (SLO1), of primary amines catalyzed by methylamine and aromatic amine dehydrogenase (MADH and AADH), and of a dicopper complex that models the active site of monooxygenases and lacks a protein environment. These distances are found to be shorter and the force constants to be larger than those implied by van der Waals radii, but with anharmonicities suitably adjusted, they resemble those encountered in systems with hydrogen bonding. It is proposed that the strong redox system, which is always present in these enzymes, acts so as to withdraw electron density from the C···H···O transfer system. This will tend to shrink the tunneling barrier to a size that allows effective passage of H but not necessarily of D, a condition that may lead to a large KIE. It will also increase the enzyme−substrate force constant, thus reducing the temperature dependence of the KIE. For the reaction catalyzed by SLO1, a transfer distance of 0.9−1.0 Å is found. Similar results are obtained for three artificial mutants from which it is concluded that parts of the protein located outside the reaction site have little influence on the proton transfer. For the reactions catalyzed by MADH and AADH, the corresponding values range from 0.5 to 1.0 Å; however, the values much below 1.0 Å may be unrealistic since they are based on data that show anomalies suggesting that an incomplete kinetic model was used in their derivation. The analysis also yields a transfer distance of about 0.9 Å for the dicopper complex, a value similar to that of SLO1, although no protein is present. Since results for three different systems cluster about the same transfer distance of 0.9−1.0 Å, it is concluded that the large KIEs and their weak temperature dependence are due to a redox-induced C···H···O hydrogen bond.