Correlation of temperature dependence of hydride kinetic isotope effects with donor–acceptor distances in two solvents of different polarities

Abstract

Recently observed nearly temperature (T)-independent kinetic isotope effects (KIEs) in wild-type enzymes and T-dependent KIEs in variants were used to suggest that H-tunneling in enzymes is assisted by the fast protein vibrations that help sample short donor–acceptor distances (DADs). This supports the recently proposed role of protein vibrations in DAD sampling catalysis. However, use of T-dependence of KIEs to suggest DAD sampling associated with protein vibrations is debated. We have formulated a hypothesis regarding the correlation and designed experiments in solution to investigate it. The hypothesis is, a more rigid system with shorter DAD_TRS's at the tunneling ready states (TRSs) gives rise to a weaker T-dependence of KIEs, i.e., a smaller ΔE_a (= E_aD − E_aH). In a former work, the solvent effects of acetonitrile versus chloroform on the ΔE_a of NADH/NAD⁺ model reactions were determined, and the DAD_PRC's of the productive reactant complexes (PRCs) were computed to substitute the DAD_TRS for the DAD_TRS–ΔE_a correlation study. A smaller ΔE_a was found in the more polar acetonitrile where the positively charged PRC is better solvated and has a shorter DAD_PRC, indirectly supporting the hypothesis. In this work, the TRS structures of different DAD_TRS's for the hydride tunneling reaction from 1,3-dimethyl-2-phenylimidazoline to 10-methylacridinium were computed. The N-CH₃/CD₃ secondary KIEs on both reactants were calculated and fitted to the observed values to find the DAD_TRS order in both solutions. It was found that the equilibrium DAD_TRS is shorter in acetonitrile than in chloroform. Results directly support the DAD_TRS–ΔE_a correlation hypothesis as well as the explanation that links T-dependence of KIEs to DAD sampling catalysis in enzymes.