Dependence Of Kinetic Isotope Effect Research Articles

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.

Solvent Effects on the Temperature Dependence of Hydride Kinetic Isotope Effects: Correlation to the Donor-Acceptor Distances.

Protein structural effects on the temperature (T) dependence of kinetic isotope effects (KIEs) in H-tunneling reactions have recently been used to discuss about the role of enzyme thermal motions in catalysis. Frequently observed nearly T-independent KIEs in the wild-type enzymes and T-dependent KIEs in variants suggest that H-tunneling in the former is assisted by the naturally evolved protein constructive vibrations that help sample short donor-acceptor distances (DADs) needed. This explanation that correlates the T-dependence of KIEs with DAD sampling has been highly debated as simulations following other H-tunneling models sometimes gave alternative explanations. In this paper, solvent effects on the T-dependence of KIEs of two hydride tunneling reactions of NADH/NAD+ analogues (represented by ΔEa = EaD - EaH) were determined in attempts to replicate the observations in enzymes and test the protein vibration-assisted DAD sampling concept. Effects of selected aprotic solvents on the DADPRC's of the productive reactant complexes (PRCs) and the DADTRS's of the activated tunneling ready states (TRSs) were obtained through computations and analyses of the kinetic data, including 2° KIEs, respectively. A weaker T-dependence of KIEs (i.e., smaller ΔEa) was found in a more polar aprotic solvent in which the system has a shorter average DADPRC and DADTRS. Further results show that a charge-transfer (CT) complexation made of a stronger donor/acceptor gives rise to a smaller ΔEa. Overall, the shorter and less broadly distributed DADs resulting from the stronger CT complexation vibrations give rise to a smaller ΔEa. Our results appear to support the explanation that links the T-dependence of KIEs to the donor-acceptor rigidity in enzymes.

Direct Correlation between Donor-Acceptor Distance and Temperature Dependence of Kinetic Isotope Effects in Hydride-Tunneling Reactions of NADH/NAD+ Analogues.

Recent study of structural effects on primary kinetic isotope effects (1° KIEs) of H-transfer reactions in enzymes and solution revealed that a more rigid reaction system gave rise to a weaker temperature dependence of 1° KIEs, i.e., a smaller isotopic activation energy difference (ΔEa = EaD - EaH). This has been explained within the contemporary vibrationally assisted activated H-tunneling (VA-AHT) model in which rigidity is defined according to the density of donor-acceptor distance (DADTRS) populations at the tunneling ready state (TRS) sampled by heavy atom motions. To test the relationship between DADTRS and ΔEa in the model, we developed a computational method to obtain the TRS structures for H-transfer reactions. The method was applied to three hydride transfer reactions of NADH/NAD+ analogues for which the ΔEa's as well as secondary (2°) KIEs have been reported. The 2° KIEs computed from each TRS structure were fitted to the observed values to obtain the optimal TRSs/DADTRS's. It was found that a shorter DADTRS does correspond with a smaller ΔEa. This appears to support the VA-AHT model. Moreover, an analysis of hybridizations at the bent TRS structures shows that rehybridizations at the donor-acceptor centers are much more advanced than predicted from the classical mechanism. This implies that more orbital preparations are required for the nonclassical H-tunneling to take place.

Substituent Effects on Temperature Dependence of Kinetic Isotope Effects in Hydride-Transfer Reactions of NADH/NAD+ Analogues in Solution: Reaction Center Rigidity Is the Key

Substituent effects on the temperature dependence of primary kinetic isotope effects, characterized by ΔEa = EaD - EaH, for two series of the title reactions in acetonitrile were studied. The change from ΔEa ≈ 0 for a highly rigid system to ΔEa > 0 for systems with reduced rigidities was observed. The rigidities were controlled by the electronic and steric effects. This work replicates the observations in enzymes and opens a new research direction that studies structure-ΔEa relationship.

Oscillatory Active-site Motions Correlate with Kinetic Isotope Effects in Formate Dehydrogenase.

Thermal motions of enzymes have been invoked to explain the temperature dependence of kinetic isotope effects (KIE) in enzyme-catalyzed hydride transfers. Formate dehydrogenase (FDH) from Candida boidinii exhibits a temperature independent KIE that becomes temperature dependent upon mutation of hydrophobic residues in the active site. Ternary complexes of FDH that mimic the transition state structure allow investigation of how these mutations influence active-site dynamics. A combination of X-ray crystallography, two-dimensional infrared (2D IR) spectroscopy, and molecular dynamic simulations characterize the structure and dynamics of the active site. FDH exhibits oscillatory frequency fluctuations on the picosecond timescale, and the amplitude of these fluctuations correlates with the temperature dependence of the KIE. Both the kinetic and dynamic phenomena can be reproduced computationally. These results provide experimental evidence for a connection between the temperature dependence of KIEs and motions of the active site in an enzyme-catalyzed reaction consistent with activated tunneling models of the hydride transfer reaction.

Temperature dependence of dynamic, tunnelling and kinetic isotope effects in formate dehydrogenase.

The origin of the catalytic power of enzymes has been a question of debate for a long time. In this regard, the possible contribution of protein dynamics in enzymatic catalysis has become one of the most controversial topics. In the present work, the hydride transfer step in the formate dehydrogenase (FDH EC 1.2.1.2) enzyme is studied by means of molecular dynamic (MD) simulations with quantum mechanics/molecular mechanics (QM/MM) potentials in order to explore any correlation between dynamics, tunnelling effects and the rate constant. The temperature dependence of the kinetic isotope effects (KIEs), which is one of the few tests that can be studied by experiments and simulations to shed light on this debate, has been computed and the results have been compared with previous experimental data. The classical mechanical free energy barrier and the number of recrossing trajectories seem to be temperature-independent while the quantum vibrational corrections and the tunnelling effects are slightly temperature-dependent over the interval of 5-45 °C. The computed primary KIEs are in very good agreement with previous experimental data, being almost temperature-independent within the standard deviations. The modest dependence on the temperature is due to just the quantum vibrational correction contribution. These results, together with the analysis of the evolution of the collective variables such as the electrostatic potential or the electric field created by the protein on the key atoms involved in the reaction, confirm that while the protein is well preorganised, some changes take place along the reaction that favour the hydride transfer and the product release. Coordinates defining these movements are, in fact, part of the real reaction coordinate.

Effects of Isotopic Substitution in Enzyme and Co‐factor on Enzyme Catalyzed Hydride Transfer

Enzyme dynamics range from seconds to femtoseconds. Previous computational, theoretical, and experimental studies have shown an imperative role of slow enzyme dynamics in its function. It is equally important to unravel the origin of fast enzyme dynamics, which are more likely to play a role in catalyzing chemical bond cleavage. Isotopically labeled (heavy) enzymes and subsequently heavy cofactors were employed to experimentally study the role of fast dynamics. Here, we used nicotinamide adenine dinucleotide (NAD+) dependent formate dehydrogenase (FDH, EC 1.2.1.2) as the model system. Heavy enzyme studies were carried out with 13C; 15N and 13C; 15N; 2H labeled FDHs. Temperature dependence of kinetic isotope effects (KIE) were compared between light and heavy FDHs. The results showed that perturbation of fast enzyme dynamics by mass modulation, alters the chemical step at the tunneling ready state (TRS, a diffused transition state) of the catalyzed hydride transfer. Studies are underway to examine similar trend using heavy cofactor (NAD+). Temperature dependence of KIE would give insight to the extent of contribution of the ring motions in sampling the donor‐acceptor distances at the TRS.In addition to the kinetic measurements, vibrational spectroscopy will be used to test the effect of heavy protein and cofactor on dynamics at the enzyme's transition state. Azide ion, which is a transition state analog of the FDH catalyzed reaction, is a good IR chromophore. This enables the use of vibrational spectroscopic methods such as two dimensional IR (2D‐IR), to directly probe the femtosecond‐picosecond timescale motions in the enzyme active site. Together, these studies should shed light on the molecular origin of fast motions that enhance catalytic efficiency of enzymes.Support or Funding InformationNIH GM065368 and GM79368, NSF CHE‐1149023, BSF 2012340

Benchmarking Quantum Mechanics/Molecular Mechanics (QM/MM) Methods on the Thymidylate Synthase-Catalyzed Hydride Transfer.

Given the ubiquity of hydride-transfer reactions in enzyme-catalyzed processes, identifying the appropriate computational method for evaluating such biological reactions is crucial to perform theoretical studies of these processes. In this paper, the hydride-transfer step catalyzed by thymidylate synthase (TSase) is studied by examining hybrid quantum mechanics/molecular mechanics (QM/MM) potentials via multiple semiempirical methods and the M06-2X hybrid density functional. Calculations of protium and tritium transfer in these reactions across a range of temperatures allowed calculation of the temperature dependence of kinetic isotope effects (KIE). Dynamics and quantum-tunneling effects are revealed to have little effect on the reaction rate, but are significant in determining the KIEs and their temperature dependence. A good agreement with experiments is found, especially when computed for RM1/MM simulations. The small temperature dependence of quantum tunneling corrections and the quasiclassical contribution term cancel each other, while the recrossing transmission coefficient seems to be temperature-independent over the interval of 5-40 °C.

Donor-Acceptor Distance Sampling Enhances the Performance of "Better than Nature" Nicotinamide Coenzyme Biomimetics.

Understanding the mechanisms of enzymatic hydride transfer with nicotinamide coenzyme biomimetics (NCBs) is critical to enhancing the performance of nicotinamide coenzyme-dependent biocatalysts. Here the temperature dependence of kinetic isotope effects (KIEs) for hydride transfer between "better than nature" NCBs and several ene reductase biocatalysts is used to indicate transfer by quantum mechanical tunneling. A strong correlation between rate constants and temperature dependence of the KIE (ΔΔH(⧧)) for H/D transfer implies that faster reactions with NCBs are associated with enhanced donor-acceptor distance sampling. Our analysis provides the first mechanistic insight into how NCBs can outperform their natural counterparts and emphasizes the need to optimize donor-acceptor distance sampling to obtain high catalytic performance from H-transfer enzymes.

Enzymatic Kinetic Isotope Effects from Path-Integral Free Energy Perturbation Theory.

Path-integral free energy perturbation (PI-FEP) theory is presented to directly determine the ratio of quantum mechanical partition functions of different isotopologs in a single simulation. Furthermore, a double averaging strategy is used to carry out the practical simulation, separating the quantum mechanical path integral exactly into two separate calculations, one corresponding to a classical molecular dynamics simulation of the centroid coordinates, and another involving free-particle path-integral sampling over the classical, centroid positions. An integrated centroid path-integral free energy perturbation and umbrella sampling (PI-FEP/UM, or simply, PI-FEP) method along with bisection sampling was summarized, which provides an accurate and fast convergent method for computing kinetic isotope effects for chemical reactions in solution and in enzymes. The PI-FEP method is illustrated by a number of applications, to highlight the computational precision and accuracy, the rule of geometrical mean in kinetic isotope effects, enhanced nuclear quantum effects in enzyme catalysis, and protein dynamics on temperature dependence of kinetic isotope effects.

Change in heat capacity accurately predicts vibrational coupling in enzyme catalyzed reactions

The temperature dependence of kinetic isotope effects (KIEs) have been used to infer the vibrational coupling of the protein and or substrate to the reaction coordinate, particularly in enzyme-catalyzed hydrogen transfer reactions. We find that a new model for the temperature dependence of experimentally determined observed rate constants (macromolecular rate theory, MMRT) is able to accurately predict the occurrence of vibrational coupling, even where the temperature dependence of the KIE fails. This model, that incorporates the change in heat capacity for enzyme catalysis, demonstrates remarkable consistency with both experiment and theory and in many respects is more robust than models used at present.

Does the pressure dependence of kinetic isotope effects report usefully on dynamics in enzyme H-transfer reactions?

The temperature dependence of kinetic isotope effects (KIEs) has emerged as the main experimental probe of enzymatic H‐transfer by quantum tunnelling. Implicit in the interpretation is a presumed role for dynamic coupling of H‐transfer chemistry to the protein environment, the so‐called ‘promoting motions/vibrations hypothesis’. This idea remains contentious, and others have questioned the importance and/or existence of promoting motions/vibrations. New experimental methods of addressing this problem are emerging, including use of mass‐modulated enzymes and time‐resolved spectroscopy. The pressure dependence of KIEs has been considered as a potential probe of quantum tunnelling reactions, because semi‐classical KIEs, which are defined by differences in zero‐point vibrational energy, are relatively insensitive to kbar changes in pressure. Reported combined pressure and temperature (p‐T) dependence studies of H‐transfer reactions are, however, limited. Here, we extend and review the available p‐T studies that have utilized well‐defined experimental systems in which quantum mechanical tunnelling is established. These include flavoproteins, quinoproteins, light‐activated enzymes and chemical model systems. We show that there is no clear general trend between the p‐T dependencies of the KIEs in these systems. Given the complex nature of p‐T studies, we conclude that computational simulations using determined (e.g. X‐ray) structures are also needed alongside experimental measurements of reaction rates/KIEs to guide the interpretation of p‐T effects. In providing new insight into H‐transfer/environmental coupling, combined approaches that unite both atomistic understanding with experimental rate measurements will require careful evaluation on a case‐by‐case basis. Although individually informative, we conclude that p‐T studies do not provide the more generalized insight that has come from studies of the temperature dependence of KIEs.

Fast protein motions are coupled to enzyme H-transfer reactions.

Coupling of fast protein dynamics to enzyme chemistry is controversial and has ignited considerable debate, especially over the past 15 years in relation to enzyme-catalyzed H-transfer. H-transfer can occur by quantum tunneling, and the temperature dependence of kinetic isotope effects (KIEs) has emerged as the "gold standard" descriptor of these reactions. The anomalous temperature dependence of KIEs is often rationalized by invoking fast motions to facilitate H-transfer, yet crucially, direct evidence for coupled motions is lacking. The fast motions hypothesis underpinning the temperature dependence of KIEs is based on inference. Here, we have perturbed vibrational motions in pentaerythritol tetranitrate reductase (PETNR) by isotopic substitution where all non-exchangeable atoms were replaced with the corresponding heavy isotope ((13)C, (15)N, and (2)H). The KIE temperature dependence is perturbed by heavy isotope labeling, demonstrating a direct link between (promoting) vibrations in the protein and the observed KIE. Further we show that temperature-independent KIEs do not necessarily rule out a role for fast dynamics coupled to reaction chemistry. We show causality between fast motions and enzyme chemistry and demonstrate how this impacts on experimental KIEs for enzyme reactions.

Connecting Protein Conformational Dynamics with Catalytic Function As Illustrated in Dihydrofolate Reductase

Combined quantum mechanics/molecular mechanics molecular dynamics simulations reveal that the M20 loop conformational dynamics of dihydrofolate reductase (DHFR) is severely restricted at the transition state of the hydride transfer as a result of the M42W/G121V double mutation. Consequently, the double-mutant enzyme has a reduced entropy of activation, i.e., increased entropic barrier, and altered temperature dependence of kinetic isotope effects in comparison with those of wild-type DHFR. Interestingly, in both wild-type DHFR and the double mutant, the average donor-acceptor distances are essentially the same in the Michaelis complex state (~3.5 Å) and the transition state (2.7 Å). It was found that an additional hydrogen bond is formed to stabilize the M20 loop in the closed conformation in the M42W/G121V double mutant. The computational results reflect a similar aim designed to knock out precisely the dynamic flexibility of the M20 loop in a different double mutant, N23PP/S148A.

Quantum instanton calculation of rate constant for CH4 + OH → CH3 + H2O reaction: Torsional anharmonicity and kinetic isotope effect

Thermal rate constants for the title reaction are calculated by using the quantum instanton approximation within the full dimensional Cartesian coordinates. The results reveal that the quantum effect is remarkable for the reaction at both low and high temperatures, and the obtained rates are in good agreement with experimental measurements at high temperatures. Compared to the harmonic approximation, the torsional anharmonic effect of the internal rotation has a little influence on the rates at low temperatures, however, it enhances the rate by about 20% at 1000 K. In addition, the free energy barriers for the isotopic reactions and the temperature dependence of kinetic isotope effects are also investigated. Generally speaking, for the title reaction, the replacement of OH with OD will reduce the free energy barrier, while substituting D for H (connected to C) will increase the free energy barrier.

Evidence that a ‘dynamic knockout’ in Escherichia coli dihydrofolate reductase does not affect the chemical step of catalysis

The question of whether protein motions play a role in the chemical step of enzymatic catalysis has generated much controversy in recent years. Debate has recently reignited over possible dynamic contributions to catalysis in dihydrofolate reductase, following conflicting conclusions from studies of the N23PP/S148A variant of the Escherichia coli enzyme. By investigating the temperature dependence of kinetic isotope effects, we present evidence that the reduction in the hydride transfer rate constants in this variant is not a direct result of impairment of conformational fluctuations. Instead, the conformational state of the enzyme immediately before hydride transfer, which determines the electrostatic environment of the active site, affects the rate constant for the reaction. Although protein motions are clearly important for binding and release of substrates and products, there appears to be no detectable dynamic coupling of protein motions to the hydride transfer step itself.

Good vibrations in enzyme-catalysed reactions

Fast motions (femtosecond to picosecond) and their potential involvement during enzyme-catalysed reactions have ignited considerable interest in recent years. Their influence on reaction chemistry has been inferred indirectly from studies of the anomalous temperature dependence of kinetic isotope effects and computational simulations. But can such motion reduce the width and height of energy barriers along the reaction coordinate, and contribute to quantum mechanical and/or classical nuclear-transfer chemistry? Here we discuss contemporary ideas for enzymatic reactions invoking a role for fast 'promoting' (or 'compressive') motions that, in principle, can aid hydrogen-transfer reactions. Of key importance is the direct demonstration of a role for compressive motions and the ability to understand in atomic detail the structural origin of these fast motions, but so far this has not been achieved. Here we discuss both indirect experimental evidence that supports a role for compressive motion and the additional insight gained from computational simulations.

Temperature dependence of the kinetic isotope effects in thymidylate synthase. A theoretical study.

In recent years, the temperature dependence of primary kinetic isotope effects (KIE) has been used as indicator for the physical nature of enzyme-catalyzed H-transfer reactions. An interactive study where experimental data and calculations examine the same chemical transformation is a critical means to interpret more properly temperature dependence of KIEs. Here, the rate-limiting step of the thymidylate synthase-catalyzed reaction has been studied by means of hybrid quantum mechanics/molecular mechanics (QM/MM) simulations in the theoretical framework of the ensemble-averaged variational transition-state theory with multidimensional tunneling (EA-VTST/MT) combined with Grote-Hynes theory. The KIEs were calculated across the same temperature range examined experimentally, revealing a temperature independent behavior, in agreement with experimental findings. The calculations show that the H-transfer proceeds with ∼91% by tunneling in the case of protium and ∼80% when the transferred protium is replaced by tritium. Dynamic recrossing coefficients are almost invariant with temperature and in all cases far from unity, showing significant coupling between protein motions and the reaction coordinate. In particular, the relative movement of a conserved arginine (Arg166 in Escherichia coli ) promotes the departure of a conserved cysteine (Cys146 in E. coli ) from the dUMP by polarizing the thioether bond thus facilitating this bond breaking that takes place concomitantly with the hydride transfer. These promoting vibrations of the enzyme, which represent some of the dimensions of the real reaction coordinate, would limit the search through configurational space to efficiently find those decreasing both barrier height and width, thereby enhancing the probability of H-transfer by either tunneling (through barrier) or classical (over-the-barrier) mechanisms. In other words, the thermal fluctuations that are coupled to the reaction coordinate, together with transition-state geometries and tunneling, are the same in different bath temperatures (within the limited experimental range examined). All these terms contribute to the observed temperature independent KIEs in thymidylate synthase.

Quantum instanton calculation of rate constants for the C2H6 + H → C2H5 + H2 reaction: anharmonicity and kinetic isotope effects

Thermal rate constants and kinetic isotope effects for the title reaction are calculated by using the quantum instanton approximation within the full dimensional Cartesian coordinates. The obtained results are in good agreement with experimental measurements at high temperatures. The detailed investigation reveals that the anharmonicity of the hindered internal rotation motion does not influence the rate too much compared to its harmonic oscillator approximation. However, the motion of the nonreactive methyl group in C(2)H(6) significantly enhances the rates compared to its rigid case, which makes conventional reduced-dimensionality calculations a challenge. In addition, the temperature dependence of kinetic isotope effects is also revealed.

The role of quantum effects in proton transfer reactions in enzymes: quantum tunneling in a noisy environment?

We consider the role of quantum effects in the transfer of hydrogen-like species in enzyme-catalyzed reactions. This review is stimulated by claims that the observed magnitude and temperature dependence of kinetic isotope effects (KIEs) implies that quantum tunneling below the energy barrier associated with the transition state significantly enhances the reaction rate in many enzymes. We review the path integral approach and the Caldeira–Leggett model, which provides a general framework to describe and understand tunneling in a quantum system that interacts with a noisy environment at nonzero temperature. Here the quantum system is the active site of the enzyme, and the environment is the surrounding protein and water. Tunneling well below the barrier only occurs for temperatures less than a temperature T0, which is determined by the curvature of the potential energy surface near the top of the barrier. We argue that for most enzymes this temperature is less than room temperature. We review typical values for the parameters in the Caldeira–Leggett Hamiltonian, including the frequency-dependent friction and noise due to the environment. For physically reasonable parameters, we show that quantum transition state theory gives a quantitative description of the temperature dependence and magnitude of KIEs for two classes of enzymes that have been claimed to exhibit signatures of quantum tunneling. The only quantum effects are those associated with the transition state, both reflection at the barrier top and tunneling just below the barrier. We establish that the friction and noise due to the environment are weak and only slightly modify the reaction rate. Furthermore, at room temperature and for typical energy barriers environmental fluctuations with frequencies much less than 1000 cm−1 do not have a significant effect on quantum corrections to the reaction rate. This is essentially because the time scales associated with the dynamics of proton transfer are faster than much of the low-frequency noise associated with the protein and solvent.