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

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 a role of protein dynamics in compressing donor(Don)-acceptor(Acc) distances (DADs) for catalysis. To test this explanation, correlation analysis between free energy changes (ΔG° = -44.3 to 6.7 kcal/mol) 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 KIE reach their maximum near thermoneutral reactions, where the charge-transfer (CT) complexation vibration is weakest and DAD is longest. A small portion of the free energy change drives the CT complexation vibrations and thus the DAD sampling that correlates to KIEs and their T-dependences. 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.