Free energy relationship analysis for temperature dependence of hydride kinetic isotope effects of NADH/NAD⁺ model...

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.