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.

Figure 1.

The gas-phase PES scans as a function of dihedrals for the activated complexes of the reactants state (in blue color) and products state (in orange color) at DAD = 2.8 Å for the hydride-transfer reaction from DMPBIH to MA⁺ (top 3D plot). The dihedral φ is defined by N11-N12-C13-C17 in DMPBIH, and θ by C36-C39-C44-H60 in MA⁺. The lowest intersecting energy point of the two PES’s is taken as the TRS structure (circled point). It is the hybrid of the reactant state ([DMPBI-H MA]^≠, bottom left) and product state ([DMPBI H-MA]^≠, bottom right). This is one of the two TRS’s found with ${\mathrm{D}\mathrm{A}\mathrm{D}}_{\mathrm{T}\mathrm{R}\mathrm{S}}=2.8\mathrm{\AA }$ and it has the lower electronic energy. In [DMPBI-H MA]^≠, the transferring H16 is at C13; in [DMPBIH-MA]^≠, it is at C39. The ${\mathrm{D}\mathrm{A}\mathrm{D}}_{\mathrm{T}\mathrm{R}\mathrm{S}}$ refers to the C13-C39 distance.

Figure 2.

Schematic description of the ${\mathrm{D}\mathrm{A}\mathrm{D}}_{\mathrm{T}\mathrm{R}\mathrm{S}}$ sampling activation by heavy atom motions (thermal molecular vibrations) from PRCs in acetonitrile and chloroform. Both the weight averaged ${\mathrm{D}\mathrm{A}\mathrm{D}}_{\mathrm{P}\mathrm{R}\mathrm{C}}$ and the equilibrium ${\mathrm{D}\mathrm{A}\mathrm{D}}_{\mathrm{T}\mathrm{R}\mathrm{S}}$ are shorter in acetonitrile than in chloroform. The positively charged PRC and TRS are more stable in acetonitrile than in chloroform. It is well known that the most efficient ${\mathrm{D}\mathrm{A}\mathrm{D}}_{\mathrm{T}\mathrm{R}\mathrm{S}}$ for H-tunneling to occur is about 2.7–2.8 Å. The left figure is copied from the reference 47 (Copyright: American Chemical Society).