Free energy relationship analysis for temperature dependence of hydride kinetic isotope effects of NADH/NAD+ model reactions: implication for barrier compression by enzyme dynamics

Abstract

The observed shift from temperature (T)-independence of hydrogen kinetic isotope effects (KIEs) in wild-type enzymes to T-dependence of KIEs in enzyme mutants has been explained as evidence for the role of protein dynamics in compressing donor (Don)–acceptor (Acc) distances (DADs) for catalysis. To test this explanation, correlation analysis of free energy changes (ΔG° = −44.3 to 6.7 kcal mol⁻¹) that simulate system rigidities and T-dependence of KIEs (represented by ΔE_a = E_aD − E_aH) was carried out for 34 hydride-tunneling reactions of NADH/NAD⁺ models in acetonitrile. For exergonic reactions, ΔE_a increases as ΔG° approaches zero, with the linear trend appearing to reverse for endergonic reactions. Both ΔE_a and KIEs reach their maximum near thermoneutral reactions, where the charge-transfer (CT) complexation vibration is the weakest and DAD is the longest. A small portion of the free energy change drives the CT complexation vibrations and thus the DAD sampling that correlates with KIEs and their T-dependences. The results support the role of protein dynamics in barrier compression for catalysis. The new physical-organic linear ΔE_a–ΔG° relationship will contribute to the development of future H-tunneling models as well as updated theories for enzyme catalysis.