Structural Effects on the Temperature Dependence of Hydride Kinetic Isotope Effects of the NADH/NAD+ Model Reactions in Acetonitrile: Charge-Transfer Complex Tightness Is a Key

It has recently frequently been found that the kinetic isotope effect (KIE) is independent of temperature (T) in H-tunneling reactions in enzymes but becomes dependent on T in their mutants. Many enzymologists found that the trend is related to different donor-acceptor distances (DADs) at tunneling-ready states (TRSs), which could be sampled by protein dynamics. That is, a more rigid system of densely populated short DADs gives rise to a weaker T dependence of KIEs. Theoreticians have attempted to develop H-tunneling theories to explain the observations, but none have been universally accepted. It is reasonable to assume that the DAD sampling concept, if it exists, applies to the H-transfer reactions in solution, as well. In this work, we designed NADH/NAD+ model reactions to investigate their structural effects on the T dependence of hydride KIEs in acetonitrile. Hammett correlations together with N-CH3/CD3 secondary KIEs were used to provide the electronic structure of the TRSs and thus the rigidity of their charge-transfer complexation vibrations. In all three pairs of reactions, a weaker T dependence of KIEs always corresponds to a steeper Hammett slope on the substituted hydride acceptors. It was found that a tighter/rigid charge-transfer complexation system corresponds with a weaker T dependence of KIEs, consistent with the observations in enzymes.

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

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 DADTRS's at the tunneling ready states (TRSs) gives rise to a weaker T-dependence of KIEs, i.e., a smaller ΔEa (= EaD - EaH). In a former work, the solvent effects of acetonitrile versus chloroform on the ΔEa of NADH/NAD+ model reactions were determined, and the DADPRC's of the productive reactant complexes (PRCs) were computed to substitute the DADTRS for the DADTRS-ΔEa correlation study. A smaller ΔEa was found in the more polar acetonitrile where the positively charged PRC is better solvated and has a shorter DADPRC, indirectly supporting the hypothesis. In this work, the TRS structures of different DADTRS'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 DADTRS order in both solutions. It was found that the equilibrium DADTRS is shorter in acetonitrile than in chloroform. Results directly support the DADTRS-ΔEa correlation hypothesis as well as the explanation that links T-dependence of KIEs to DAD sampling catalysis in enzymes.

Replication of the Enzymatic Temperature Dependency of the Primary Hydride Kinetic Isotope Effects in Solution: Caused by the Protein-Controlled Rigidity of the Donor-Acceptor Centers?

The change from the temperature independence of the primary (1°) H/D kinetic isotope effects (KIEs) in wild-type enzyme-catalyzed H-transfer reactions (ΔE_a = E_aD - E_aH ∼ 0) to a strong temperature dependence with the mutated enzymes (ΔE_a ≫ 0) has recently been frequently observed. This has prompted some enzymologists to develop new H-tunneling models to correlate ΔE_a with the donor-acceptor distance (DAD) at the tunneling-ready state (TRS) as well as the protein thermal motions/dynamics that sample the short DAD_TRS's for H-tunneling to occur. While extensive evidence supporting or disproving the thermally activated DAD sampling concept has emerged, a comparable study of the simpler bimolecular H-tunneling reactions in solution has not been carried out. In particular, small ΔE_a's (∼0) have not been found. In this paper, we report a study of the hydride-transfer reactions from four NADH models to the same hydride acceptor in acetonitrile. The ΔE_a's were determined: 0.37 (small), 0.60, 0.99, and 1.53 kcal/mol (large). The α-secondary (2°) KIEs on the acceptor that serve as a ruler for the rigidity of reaction centers were previously reported or determined. All possible productive reactant complex (PRC) configurations were computed to provide insight into the structures of the TRS's. Relationships among structures, 2° KIEs, DAD_PRC's, and ΔE_a's were discussed. The more rigid system with more suppressed 2° C-H vibrations at the TRS and more narrowly distributed DAD_PRC's in PRCs gave a smaller ΔE_a. The results replicated the trend observed in enzymes versus mutated enzymes and appeared to support the concepts of different thermally activated DAD_TRS sampling processes in response to the rigid versus flexible donor-acceptor centers.

Role of dynamics in enzyme catalysis: substantial versus semantic controversies

The role of the enzyme’s dynamic motions in catalysis is at the center of heated contemporary debates among both theoreticians and experimentalists. Resolving these apparent disputes is of both intellectual and practical importance: incorporation of enzyme dynamics could be critical for any calculation of enzymatic function and may have profound implications for structure-based drug design and the design of biomimetic catalysts.

Analysis of the literature suggests that while part of the dispute may reflect substantial differences between theoretical approaches, much of the debate is semantic. For example, the term “protein dynamics” is often used by some researchers when addressing motions that are in thermal equilibrium with their environment, while other researchers only use this term for nonequilibrium events. The last cases are those in which thermal energy is “stored” in a specific protein mode and “used” for catalysis before it can dissipate to its environment (i.e., “nonstatistical dynamics”). This terminology issue aside, a debate has arisen among theoreticians around the roles of nonstatistical vs statistical dynamics in catalysis. However, the author knows of no experimental findings available today that examined this question in enzyme catalyzed reactions.

Another source of perhaps nonsubstantial argument might stem from the varying time scales of enzymatic motions, which range from seconds to femtoseconds. Motions at different time scales play different roles in the many events along the catalytic cascade (reactant binding, reprotonation of reactants, structural rearrangement toward the transition state, product release, etc.). In several cases, when various experimental tools have been used to probe catalytic events at differing time scales, illusory contradictions seem to have emerged. In this Account, recent attempts to sort the merits of those questions are discussed along with possible future directions.

A possible summary of current studies could be that enzyme, substrate, and solvent dynamics contribute to enzyme catalyzed reactions in several ways: first via mutual “induced-fit” shifting of their conformational ensemble upon binding; then via thermal search of the conformational space toward the reaction’s transition-state (TS) and the rare event of the barrier crossing toward products, which is likely to be on faster time scales then the first and following events; and finally via the dynamics associated with products release, which are rate-limiting for many enzymatic reactions. From a chemical perspective, close to the TS, enzymatic systems seem to stiffen, restricting motions orthogonal to the chemical coordinate and enabling dynamics along the reaction coordinate to occur selectively. Studies of how enzymes evolved to support those efficient dynamics at various time scales are still in their infancy, and further experiments and calculations are needed to reveal these phenomena in both enzymes and uncatalyzed reactions.

Escherichia coli dihydrofolate reductase catalyzed proton and hydride transfers: temporal order and the roles of Asp27 and Tyr100

The reaction catalyzed by Escherichia coli dihydrofolate reductase (ecDHFR) has become a model for understanding enzyme catalysis, and yet several details of its mechanism are still unresolved. Specifically, the mechanism of the chemical step, the hydride transfer reaction, is not fully resolved. We found, unexpectedly, the presence of two reactive ternary complexes [enzyme:NADPH:7,8-dihydrofolate (E:NADPH:DHF)] separated by one ionization event. Furthermore, multiple kinetic isotope effect (KIE) studies revealed a stepwise mechanism in which protonation of the DHF precedes the hydride transfer from the nicotinamide cofactor (NADPH) for both reactive ternary complexes of the WT enzyme. This mechanism was supported by the pH- and temperature-independent intrinsic KIEs for the C-H→C hydride transfer between NADPH and the preprotonated DHF. Moreover, we showed that active site residues D27 and Y100 play a synergistic role in facilitating both the proton transfer and subsequent hydride transfer steps. Although D27 appears to have a greater effect on the overall rate of conversion of DHF to tetrahydrofolate, Y100 plays an important electrostatic role in modulating the pKa of the N5 of DHF to enable the preprotonation of DHF by an active site water molecule.

Stereospecific multiple isotopic labeling of benzyl alcohol

Isotopically labeled enzymatic substrates and biological metabolites are useful for many mechanistic analyses, particularly the study of kinetic and equilibrium isotope effects, determining the stereospecificity of enzymes, and resolving metabolic pathways. Here, we present the one-pot synthesis, purification, and kinetic analysis of 7R-[(2) H]-phenyl-[(14) C]-benzyl alcohol. The procedure involves a chemoenzymatic synthesis that couples formate dehydrogenase to alcohol dehydrogenase with a catalytic amount of nicotinamide cofactor. The reaction goes to completion overnight, and the measurement of a competitive kinetic isotope effect on the enzymatic oxidation of the purified product identified no (1) H contamination. This measurement is very sensitive to such isotopic contamination and verified the high level of isotopic and enantiomeric purity yielded by the new synthetic procedure.

A critical test of the "tunneling and coupled motion" concept in enzymatic alcohol oxidation

The physical mechanism of C-H bond activation by enzymes is the subject of intense study, and we have tested the predictions of two competing models for C-H activation in the context of alcohol dehydrogenase. The kinetic isotope effects (KIEs) in this enzyme have previously suggested a model of quantum mechanical tunneling and coupled motion of primary (1°) and secondary (2°) hydrogens. Here we measure the 2° H/T KIEs with both H and D at the 1° position and find that the 2° KIE is significantly deflated with D-transfer, consistent with the predictions of recent Marcus-like models of H-transfer. The results suggest that the fast dynamics of H-tunneling result in a 1° isotope effect on the structure of the tunneling ready state: the trajectory of D-transfer goes through a shorter donor-acceptor distance than that of H-transfer.

Hydrogen donor-acceptor fluctuations from kinetic isotope effects: a phenomenological model

Kinetic isotope effects (KIEs) and their temperature dependence can probe the structural and dynamic nature of enzyme-catalyzed proton or hydride transfers. The molecular interpretation of their temperature dependence requires expensive and specialized quantum mechanics/molecular mechanics (QM/MM) calculations to provide a quantitative molecular understanding. Currently available phenomenological models use a nonadiabatic assumption that is not appropriate for most hydride and proton-transfer reactions, while others require more parameters than the experimental data justify. Here we propose a phenomenological interpretation of KIEs based on a simple method to quantitatively link the size and temperature dependence of KIEs to a conformational distribution of the catalyzed reaction. This model assumes adiabatic hydrogen tunneling, and by fitting experimental KIE data, the model yields a population distribution for fluctuations of the distance between donor and acceptor atoms. Fits to data from a variety of proton and hydride transfers catalyzed by enzymes and their mutants, as well as nonenzymatic reactions, reveal that steeply temperature-dependent KIEs indicate the presence of at least two distinct conformational populations, each with different kinetic behaviors. We present the results of these calculations for several published cases and discuss how the predictions of the calculations might be experimentally tested. This analysis does not replace molecular QM/MM investigations, but it provides a fast and accessible way to quantitatively interpret KIEs in the context of a Marcus-like model.

Effects of the donor-acceptor distance and dynamics on hydride tunneling in the dihydrofolate reductase catalyzed reaction

A significant contemporary question in enzymology involves the role of protein dynamics and hydrogen tunneling in enhancing enzyme catalyzed reactions. Here, we report a correlation between the donor-acceptor distance (DAD) distribution and intrinsic kinetic isotope effects (KIEs) for the dihydrofolate reductase (DHFR) catalyzed reaction. This study compares the nature of the hydride-transfer step for a series of active-site mutants, where the size of a side chain that modulates the DAD (I14 in E. coli DHFR) is systematically reduced (I14V, I14A, and I14G). The contributions of the DAD and its dynamics to the hydride-transfer step were examined by the temperature dependence of intrinsic KIEs, hydride-transfer rates, activation parameters, and classical molecular dynamics (MD) simulations. Results are interpreted within the framework of the Marcus-like model where the increase in the temperature dependence of KIEs arises as a direct consequence of the deviation of the DAD from its distribution in the wild type enzyme. Classical MD simulations suggest new populations with larger average DADs, as well as broader distributions, and a reduction in the population of the reactive conformers correlated with the decrease in the size of the hydrophobic residue. The more flexible active site in the mutants required more substantial thermally activated motions for effective H-tunneling, consistent with the hypothesis that the role of the hydrophobic side chain of I14 is to restrict the distribution and dynamics of the DAD and thus assist the hydride-transfer. These studies establish relationships between the distribution of DADs, the hydride-transfer rates, and the DAD's rearrangement toward tunneling-ready states. This structure-function correlation shall assist in the interpretation of the temperature dependence of KIEs caused by mutants far from the active site in this and other enzymes, and may apply generally to C-H→C transfer reactions.

H-transfers in Photosystem II: what can we learn from recent lessons in the enzyme community?

Over the last 10 years, studies of enzyme systems have demonstrated that, in many cases, H-transfers occur by a quantum mechanical tunneling mechanism analogous to long-range electron transfer. H-transfer reactions can be described by an extension of Marcus theory and, by substituting hydrogen with deuterium (or even tritium), it is possible to explore this theory in new ways by employing kinetic isotope effects. Because hydrogen has a relatively short deBroglie wavelength, H-transfers are controlled by the width of the reaction barrier. By coupling protein dynamics to the reaction coordinate, enzymes have the potential ability to facilitate more efficient H-tunneling by modulating barrier properties. In this review, we describe recent advances in both experimental and theoretical studies of enzymatic H-transfer, in particular the role of protein dynamics or promoting motions. We then discuss possible consequences with regard to tyrosine oxidation/reduction kinetics in Photosystem II.