Enzymatic H-transfer requires vibration-driven extreme tunneling

Study of the Effects of Remote Heavy Group Vibrations on the Temperature Dependence of Hydride Kinetic Isotope Effects of the NADH/NAD+ Model Reactions

It has recently been observed that the temperature(T)-dependence of KIEs in H-tunneling reactions, characterized by isotopic activation energy difference (ΔEa = EaD - EaH), is correlated to the rigidity of the tunneling ready states (TRSs) in enzymes. A more rigid system with narrowly distributed H-donor-acceptor distances (DADs) at the TRSs gives rise to a weaker T-dependence of KIEs (i.e., a smaller ΔEa). Theoreticians have attempted to develop new H-tunneling models to explain this, but none has been universally accepted. In order to further understand the observations in enzymes and provide useful data to build new theoretical models, we have studied the electronic and solvent effects on ΔEa's for the hydride-tunneling reactions of NADH/NAD+ analogues. We found that a tighter charge-transfer (CT) complex system gives rises to a smaller ΔEa, consistent with the enzyme observations. In this paper, we use the remote heavy group (R) vibrational effects to mediate the system rigidity to study the rigidity-ΔEa relationship. The specific hypothesis is that slower vibrations of a heavier remote group would broaden the DAD distributions and increase the ΔEa value. Four NADH/NAD+ systems were studied in acetonitrile but most of such heavy group vibrations do not appear to significantly increase the ΔEa. The remote heavy group vibrations in these systems may have not affected the CT complexation rigidity to a degree that can significantly increase the DADs, and further, the ΔEa values.

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.

Effect of solvent viscosity on the activation barrier of hydrogen tunneling in the lipoxygenase reaction

Hydrogen tunneling in enzyme reactions has played an important role in linking protein thermal motions to the chemical steps of catalysis. Lipoxygenases (LOXs) have served as model systems for such reactions, showcasing deep hydrogen tunneling mechanisms associated with enzymatic C-H bond cleavage from polyunsaturated fatty acids. Here, we examined the effect of solvent viscosity on the protein thermal motions associated with LOX catalysis using trehalose and glucose as viscogens. Kinetic analysis of the reaction of the paradigm plant orthologue, soybean lipoxygenase (SLO), with linoleic acid revealed no effect on the first-order rate constants, kcat, or activation energy, Ea. Further studies of SLO active site mutants displaying varying Eas, which have been used to probe catalytically relevant motions, likewise provided no evidence for viscogen-dependent motions. Kinetic analyses were extended to a representative fungal LOX from M. oryzae, MoLOX, and a human LOX, 15-LOX-2. While MoLOX behaved similarly to SLO, we show that viscogens inhibit 15-LOX-2 activity. The latter implicates viscogen sensitive, conformational motions in animal LOX reactions. The data provide insight into the role of water hydration layers in facilitating hydrogen (quantum) tunneling in LOX.

Nonadiabatic Nuclear-Electron Dynamics: A Quantum Computing Approach

Coupled quantum electron-nuclear dynamics is often associated with the Born-Huang expansion of the molecular wave function and the appearance of nonadiabatic effects as a perturbation. On the other hand, native multicomponent representations of electrons and nuclei also exist, which do not rely on any a priori approximation. However, their implementation is hampered by prohibitive scaling. Consequently, quantum computers offer a unique opportunity for extending their use to larger systems. Here, we propose a quantum algorithm for simulating the time-evolution of molecular systems and apply it to proton transfer dynamics in malonaldehyde, described as a rigid scaffold. The proposed quantum algorithm can be easily generalized to include the explicit dynamics of the classically described molecular scaffold. We show how entanglement between electronic and nuclear degrees of freedom can persist over long times if electrons do not follow the nuclear displacement adiabatically. The proposed quantum algorithm may become a valid candidate for the study of such phenomena when sufficiently powerful quantum computers become available.

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.

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 ΔE_a = E_aD - E_aH) 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 DAD_PRC's of the productive reactant complexes (PRCs) and the DAD_TRS'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 ΔE_a) was found in a more polar aprotic solvent in which the system has a shorter average DAD_PRC and DAD_TRS. Further results show that a charge-transfer (CT) complexation made of a stronger donor/acceptor gives rise to a smaller ΔE_a. Overall, the shorter and less broadly distributed DADs resulting from the stronger CT complexation vibrations give rise to a smaller ΔE_a. 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 (ΔE_a = E_aD - E_aH). 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 (DAD_TRS) populations at the tunneling ready state (TRS) sampled by heavy atom motions. To test the relationship between DAD_TRS and ΔE_a 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 ΔE_a'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/DAD_TRS's. It was found that a shorter DAD_TRS does correspond with a smaller ΔE_a. 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 ΔE_a = E_aD - E_aH, for two series of the title reactions in acetonitrile were studied. The change from ΔE_a ≈ 0 for a highly rigid system to ΔE_a > 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-ΔE_a relationship.

Temperature, Dynamics, and Enzyme-Catalyzed Reaction Rates

We review the adaptations of enzyme activity to different temperatures. Psychrophilic (cold-adapted) enzymes show significantly different activation parameters (lower activation enthalpies and entropies) from their mesophilic counterparts. Furthermore, there is increasing evidence that the temperature dependence of many enzyme-catalyzed reactions is more complex than is widely believed. Many enzymes show curvature in plots of activity versus temperature that is not accounted for by denaturation or unfolding. This is explained by macromolecular rate theory: A negative activation heat capacity for the rate-limiting chemical step leads directly to predictions of temperature optima; both entropy and enthalpy are temperature dependent. Fluctuations in the transition state ensemble are reduced compared to the ground state. We show how investigations combining experiment with molecular simulation are revealing fundamental details of enzyme thermoadaptation that are relevant for understanding aspects of enzyme evolution. Simulations can calculate relevant thermodynamic properties (such as activation enthalpies, entropies, and heat capacities) and reveal the molecular mechanisms underlying experimentally observed behavior.

The Hydride Transfer Process in NADP-dependent Methylene-tetrahydromethanopterin Dehydrogenase

NADP-dependent methylene-tetrahydromethanopterin (methylene-H₄MPT) dehydrogenase (MtdA) catalyzes the reversible dehydrogenation of methylene-H₄MPT to form methenyl-H₄MPT⁺ by using NADP⁺ as a hydride acceptor. This hydride transfer reaction is involved in the oxidative metabolism from formaldehyde to CO₂ in methylotrophic and methanotrophic bacteria. Here, we report on the crystal structures of the ternary MtdA-substrate complexes from Methylorubrum extorquens AM1 obtained in open and closed forms. Their conversion is accomplished by opening/closing the active site cleft via a 15° rotation of the NADP, relative to the pterin domain. The 1.08 Å structure of the closed and active enzyme-NADP-methylene-H₄MPT complex allows a detailed geometric analysis of the bulky substrates and a precise prediction of the hydride trajectory. Upon domain closure, the bulky substrate rings become compressed resulting in a tilt of the imidazolidine group of methylene-H₄MPT that optimizes the geometry for hydride transfer. An additional 1.5 Å structure of MtdA in complex with the nonreactive NADP⁺ and methenyl-H₄MPT⁺ revealed an extremely short distance between nicotinamide-C4 and imidazoline-C14a of 2.5 Å, which demonstrates the strong pressure imposed. The pterin-imidazolidine-phenyl butterfly angle of methylene-H₄MPT bound to MtdA is smaller than that in the enzyme-free state but is similar to that in H₂- and F₄₂₀-dependent methylene-H₄MPT dehydrogenases. The concept of compression-driven hydride transfer including quantum mechanical hydrogen tunneling effects, which are established for flavin- and NADP-dependent enzymes, can be expanded to hydride-transferring H₄MPT-dependent enzymes.

Temperature-Independent Kinetic Isotope Effects as Evidence for a Marcus-like Model of Hydride Tunneling in Phosphite Dehydrogenase

Phosphite dehydrogenase catalyzes the transfer of a hydride from phosphite to NAD⁺, producing phosphate and NADH. We have evaluated the role of hydride tunneling in a thermostable variant of this enzyme (17X-PTDH) by measuring the temperature dependence of the primary ²H kinetic isotope effects (KIEs) between 5 and 45 °C. Pre-steady-state kinetic measurements were used to demonstrate that the hydride transfer is rate-determining across this temperature range and that the observed KIEs are equal to the intrinsic isotope effect on the chemical step. The KIEs on the pre-exponential factor (A_H/A_D) and the activation energy (ΔE_a) were 1.6 ± 0.1 and 0.21 ± 0.05 kcal/mol, respectively, suggesting that 17X-PTDH facilitates extensive tunneling of both isotopes via a Marcus-like model. Site-directed mutagenesis was used to evaluate the role of an active site threonine (Thr104) found on the back face of the nicotinamide in promoting the close packing of the substrates. In mutants with reduced steric bulk at this position, values of A_H/A_D and ΔE_a fall within the range describing semiclassical "over the barrier" reactivity, suggesting that Thr104 acts as a steric backstop to promote tunneling in 17X-PTDH. Whereas hydrogen tunneling is now a widely appreciated feature of C-H activating enzymes, these observations with a P-H activating system are consistent with the proposal that tunneling is likely to be a common feature on all enzymes that catalyze hydrogen transfers.

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.

Universality of fold-encoded localized vibrations in enzymes

Enzymes speed up biochemical reactions at the core of life by as much as 15 orders of magnitude. Yet, despite considerable advances, the fine dynamical determinants at the microscopic level of their catalytic proficiency are still elusive. In this work, we use a powerful mathematical approach to show that rate-promoting vibrations in the picosecond range, specifically encoded in the 3D protein structure, are localized vibrations optimally coupled to the chemical reaction coordinates at the active site. Remarkably, our theory also exposes an hithertho unknown deep connection between the unique localization fingerprint and a distinct partition of the 3D fold into independent, foldspanning subdomains that govern long-range communication. The universality of these features is demonstrated on a pool of more than 900 enzyme structures, comprising a total of more than 10,000 experimentally annotated catalytic sites. Our theory provides a unified microscopic rationale for the subtle structure-dynamics-function link in proteins.

Kinetic Isotope Effects as Probes for Hydrogen Tunneling, Coupled Motion and Dynamics Contributions to Enzyme Catalysis

Since the early days of enzymology attempts have been made to deconvolute the various contributions of physical phenomena to enzyme catalysis. Here we present experimental and theoretical studies that examine the possible role of hydrogen tunneling, coupled motion, and enzyme dynamics in catalysis. In this review, we first introduce basic concepts of enzyme catalysis from a physical chemistry point of view. Then, we present several recent developments in the application of experimental tools that can probe tunneling, coupled motion, dynamic effects and other possible physical phenomena that may contribute to catalysis. These tools include kinetic isotope effects (KIEs), their temperature dependency and H/D/T mutual relations (the Swain–Schaad relationship). Several theories and models that assist in understanding those phenomena are also described. The possibility that these models invoke a direct role for the enzyme's dynamics (environmental fluctuations and rearrangements) is discussed. Finally, the need to compare the enzymatic reaction to the uncatalyzed one while investigating contributions to catalysis is emphasised.

Biophysical Characterization of a Disabled Double Mutant of Soybean Lipoxygenase: The "Undoing" of Precise Substrate Positioning Relative to Metal Cofactor and an Identified Dynamical Network

Soybean lipoxygenase (SLO) has served as a prototype for understanding the molecular origin of enzymatic rate accelerations. The double mutant (DM) L546A/L754A is considered a dramatic outlier, due to the unprecedented size and near temperature-independence of its primary kinetic isotope effect, low catalytic efficiency, and elevated enthalpy of activation. To uncover the physical basis of these features, we herein apply three structural probes: hydrogen-deuterium exchange mass spectrometry, room-temperature X-ray crystallography and EPR spectroscopy on four SLO variants (wild-type (WT) enzyme, DM, and the two parental single mutants, L546A and L754A). DM is found to incorporate features of each parent, with the perturbation at position 546 predominantly influencing thermally activated motions that connect the active site to a protein-solvent interface, while mutation at position 754 disrupts the ligand field and solvation near the cofactor iron. However, the expanded active site in DM leads to more active site water molecules and their associated hydrogen bond network, and the individual features from L546A and L754A alone cannot explain the aggregate kinetic properties for DM. Using recently published QM/MM-derived ground-state SLO-substrate complexes for WT and DM, together with the thorough structural analyses presented herein, we propose that the impairment of DM is the combined result of a repositioning of the reactive carbon of linoleic acid substrate with regard to both the iron cofactor and a catalytically linked dynamic region of protein.

Proton tunnelling in hydrogen bonds and its implications in an induced-fit model of enzyme catalysis

The role of proton tunnelling in biological catalysis is investigated here within the frameworks of quantum information theory and thermodynamics. We consider the quantum correlations generated through two hydrogen bonds between a substrate and a prototypical enzyme that first catalyses the tautomerization of the substrate to move on to a subsequent catalysis, and discuss how the enzyme can derive its catalytic potency from these correlations. In particular, we show that classical changes induced in the binding site of the enzyme spreads the quantum correlations among all of the four hydrogen-bonded atoms thanks to the directionality of hydrogen bonds. If the enzyme rapidly returns to its initial state after the binding stage, the substrate ends in a new transition state corresponding to a quantum superposition. Open quantum system dynamics can then naturally drive the reaction in the forward direction from the major tautomeric form to the minor tautomeric form without needing any additional catalytic activity. We find that in this scenario the enzyme lowers the activation energy so much that there is no energy barrier left in the tautomerization, even if the quantum correlations quickly decay.

Promoting Vibrations and the Function of Enzymes. Emerging Theoretical and Experimental Convergence

A complete understanding of enzyme catalysis requires knowledge of both transition state features and the detailed motions of atoms that cause reactant molecules to form and traverse the transition state. The seeming intractability of the problem arises from the femtosecond lifetime of chemical transition states, preventing most experimental access. Computational chemistry is admirably suited to short time scale analysis but can be misled by inappropriate starting points or by biased assumptions. Kinetic isotope effects provide an experimental approach to transition state structure and a method for obtaining transition state analogues but, alone, do not inform how that transition state is reached. Enzyme structures with transition state analogues provide computational starting points near the transition state geometry. These well-conditioned starting points, combined with the unbiased computational method of transition path sampling, provide realistic atomistic motions involved in transition state formation and passage. In many, but not all, enzymatic systems, femtosecond local protein motions near the catalytic site are linked to transition state formation. These motions are not inherently revealed by most approaches of transition state theory, because transition state theory replaces dynamics with the statistics of the transition state. Experimental and theoretical convergence of the link between local catalytic site vibrational modes and catalysis comes from heavy atom ("Born-Oppenheimer") enzymes. Fully labeled and catalytic site local heavy atom labels perturb the probability of finding enzymatic transition states in ways that can be analyzed and predicted by transition path sampling. Recent applications of these experimental and computational approaches reveal how subpicosecond local catalytic site protein modes play important roles in creating the transition state.

Insights on the Origin of Catalysis on Glycine N-Methyltransferase from Computational Modeling

The origin of enzyme catalysis remains a question of debate despite much intense study. We report a QM/MM theoretical study of the SN2 methyl transfer reaction catalyzed by a glycine N-methyltransferase (GNMT) and three mutants to test whether recent experimental observations of rate-constant reductions and variations in inverse secondary α-3H kinetic isotope effects (KIEs) should be attributed to changes in the methyl donor-acceptor distance (DAD): Is catalysis due to a compression effect? Semiempirical (AM1) and DFT (M06-2X) methods were used to describe the QM subset of atoms, while OPLS-AA and TIP3P classical force fields were used for the protein and water molecules, respectively. The computed activation free energies and KIEs are in good agreement with experimental data, but the mutations do not meaningfully affect the DAD: Compression cannot explain the experimental variations on KIEs. On the contrary, electrostatic properties in the active site correlate with the catalytic activity of wild type and mutants. The plasticity of the enzyme moderates the effects of the mutations, explaining the rather small degree of variation in KIEs and reactivities.

Origins of Enzyme Catalysis: Experimental Findings for C-H Activation, New Models, and Their Relevance to Prevailing Theoretical Constructs

The physical basis for enzymatic rate accelerations is a subject of great fundamental interest and of direct relevance to areas that include the de novo design of green catalysts and the pursuit of new drug regimens. Extensive investigations of C-H activating systems have provided considerable insight into the relationship between an enzyme's overall structure and the catalytic chemistry at its active site. This Perspective highlights recent experimental data for two members of distinct, yet iconic C-H activation enzyme classes, lipoxygenases and prokaryotic alcohol dehydrogenases. The data necessitate a reformulation of the dominant textbook definition of biological catalysis. A multidimensional model emerges that incorporates a range of protein motions that can be parsed into a combination of global stochastic conformational thermal fluctuations and local donor-acceptor distance sampling. These motions are needed to achieve a high degree of precision with regard to internuclear distances, geometries, and charges within the active site. The available model also suggests a physical framework for understanding the empirical enthalpic barrier in enzyme-catalyzed processes. We conclude by addressing the often conflicting interface between computational and experimental chemists, emphasizing the need for computation to predict experimental results in advance of their measurement.

Step-Economical Photoassisted Diversity-Oriented Synthesis: Sustaining Cascade Photoreactions in Oxalyl Anilides to Access Complex Polyheterocyclic Molecular Architectures

Atom- and step-economy in photoassisted diversity-oriented synthesis (DOS) is achieved with a versatile oxalyl linker offering rapid access to complex alkaloid mimics in very few experimentally simple steps: (i) it allows for fast tethering of the photoactive core to the unsaturated pendants, especially important in the case of (hetero)aromatic amines-essentially a one-pot reaction with no isolation of intermediates; (ii) the α-dicarbonyl tether acts as a chromophore enhancer, extending the conjugation chain and facilitating the "harvest" of the lower energy photons for the primary and secondary photoreactions; (iii) it enhances the quantum yield of intersystem crossing (ISC), i.e., it is capable of sensitizing secondary photochemical processes in the cascade; and (iv) the tether forms an additional heterocyclic moiety, imidazolidine-4,5-dione, a known pharmacophore. The overall photoassisted cascade is an efficient complexity-building process as quantified by computed step-normalized complexity indices, leading to extended polyheterocyclic molecular architectures comparable in complexity to natural products such as paclitaxel while requiring only 2-4 simple synthetic steps from readily available chemical feedstock.

Ab Initio QM/MM Modeling of the Rate-Limiting Proton Transfer Step in the Deamination of Tryptamine by Aromatic Amine Dehydrogenase

Aromatic amine dehydrogenase (AADH) and related enzymes are at the heart of debates on the roles of quantum tunneling and protein dynamics in catalysis. The reaction of tryptamine in AADH involves significant quantum tunneling in the rate-limiting proton transfer step, shown by large H/D primary kinetic isotope effects (KIEs), with unusual temperature dependence. We apply correlated ab initio combined quantum mechanics/molecular mechanics (QM/MM) methods, at levels up to local coupled cluster theory (LCCSD(T)/(aug)-cc-pVTZ), to calculate accurate potential energy surfaces for this reaction, which are necessary for quantitative analysis of tunneling contributions and reaction dynamics. Different levels of QM/MM treatment are tested. Multiple pathways are calculated with fully flexible transition state optimization by the climbing-image nudged elastic band method at the density functional QM/MM level. The average LCCSD(T) potential energy barriers to proton transfer are 16.7 and 14.0 kcal/mol for proton transfer to the two carboxylate atoms of the catalytic base, Asp128β. The results show that two similar, but distinct pathways are energetically accessible. These two pathways have different barriers, exothermicity and curvature, and should be considered in analyses of the temperature dependence of reaction and KIEs in AADH and other enzymes. These results provide a benchmark for this prototypical enzyme reaction and will be useful for developing empirical models, and analyzing experimental data, to distinguish between different conceptual models of enzyme catalysis.

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.

Perspective: Defining and quantifying the role of dynamics in enzyme catalysis

Enzymes control chemical reactions that are key to life processes, and allow them to take place on the time scale needed for synchronization between the relevant reaction cycles. In addition to general interest in their biological roles, these proteins present a fundamental scientific puzzle, since the origin of their tremendous catalytic power is still unclear. While many different hypotheses have been put forward to rationalize this, one of the proposals that has become particularly popular in recent years is the idea that dynamical effects contribute to catalysis. Here, we present a critical review of the dynamical idea, considering all reasonable definitions of what does and does not qualify as a dynamical effect. We demonstrate that no dynamical effect (according to these definitions) has ever been experimentally shown to contribute to catalysis. Furthermore, the existence of non-negligible dynamical contributions to catalysis is not supported by consistent theoretical studies. Our review is aimed, in part, at readers with a background in chemical physics and biophysics, and illustrates that despite a substantial body of experimental effort, there has not yet been any study that consistently established a connection between an enzyme's conformational dynamics and a significant increase in the catalytic contribution of the chemical step. We also make the point that the dynamical proposal is not a semantic issue but a well-defined scientific hypothesis with well-defined conclusions.

Untangling Heavy Protein and Cofactor Isotope Effects on Enzyme-Catalyzed Hydride Transfer

"Heavy" (isotopically labeled) enzyme isotope effects offer a direct experimental probe of the role of protein vibrations on enzyme-catalyzed reactions. Here we have developed a strategy to generate isotopologues of the flavoenzyme pentaerythritol tetranitrate reductase (PETNR) where the protein and/or intrinsic flavin mononucleotide (FMN) cofactor are isotopically labeled with ²H, ¹⁵N, and ¹³C. Both the protein and cofactor contribute to the enzyme isotope effect on the reductive hydride transfer reaction, but their contributions are not additive and may partially cancel each other out. However, the isotope effect specifically arising from the FMN suggests that vibrations local to the active site play a role in the hydride transfer chemistry, while the protein-only "heavy enzyme" effect demonstrates that protein vibrations contribute to catalysis in PETNR. In all cases, enthalpy-entropy compensation plays a major role in minimizing the magnitude of "heavy enzyme" isotope effects. Fluorescence lifetime measurements of the intrinsic flavin mononucleotide show marked differences between "light" and "heavy" enzymes on the nanosecond-picosecond time scale, suggesting relevant time scale(s) for those vibrations implicated in the "heavy enzyme" isotope effect on the PETNR reaction.

Protein motions and dynamic effects in enzyme catalysis

The role of protein motions in promoting the chemical step of enzyme catalysed reactions remains a subject of considerable debate. Here, a unified view of the role of protein dynamics in dihydrofolate reductase catalysis is described. Recently the role of such motions has been investigated by characterising the biophysical properties of isotopically substituted enzymes through a combination of experimental and computational analyses. Together with previous work, these results suggest that dynamic coupling to the chemical coordinate is detrimental to catalysis and may have been selected against during DHFR evolution. The full catalytic power of Nature's catalysts appears to depend on finely tuning protein motions in each step of the catalytic cycle.

Path Integral Simulations of Proton Transfer Reactions in Aqueous Solution Using Combined QM/MM Potentials

A bisection sampling method was implemented in path integral simulations of chemical reactions in solution in the framework of the quantized classical path approach. In the present study, we employ a combined quantum mechanical and molecular mechanical (QM/MM) potential to describe the potential energy surface and the path integral method to incorporate nuclear quantum effects. We examine the convergence of the bisection method for two proton-transfer reactions in aqueous solution at room temperature. The first reaction involves the symmetrical proton transfer between an ammonium ion and an ammonia molecule. The second reaction is the ionization of nitroethane by an acetate ion. To account for nuclear quantum mechanical corrections, it is sufficient to quantize the transferring light atom in the ammonium ion-ammonia reaction, while it is necessary to also quantize the donor and acceptor atoms in the nitroethane-acetate ion reaction. Kinetic isotope effects have been computed for isotopic substitution of the transferring proton by a deuteron in the nitroethane-acetate reaction. In all computations, it is important to employ a sufficient number of polymer beads along with a large number of configurations to achieve convergence in these simulations.

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.

Chemical Ligation and Isotope Labeling to Locate Dynamic Effects during Catalysis by Dihydrofolate Reductase

Chemical ligation has been used to alter motions in specific regions of dihydrofolate reductase from E. coli and to investigate the effects of localized motional changes on enzyme catalysis. Two isotopic hybrids were prepared; one with the mobile N-terminal segment containing heavy isotopes ((2) H, (13) C, (15) N) and the remainder of the protein with natural isotopic abundance, and the other one with only the C-terminal segment isotopically labeled. Kinetic investigations indicated that isotopic substitution of the N-terminal segment affected only a physical step of catalysis, whereas the enzyme chemistry was affected by protein motions from the C-terminal segment. QM/MM studies support the idea that dynamic effects on catalysis mostly originate from the C-terminal segment. The use of isotope hybrids provides insights into the microscopic mechanism of dynamic coupling, which is difficult to obtain with other studies, and helps define the dynamic networks of intramolecular interactions central to enzyme catalysis.

The importance of ensemble averaging in enzyme kinetics

The active site of an enzyme is surrounded by a fluctuating environment of protein and solvent conformational states, and a realistic calculation of chemical reaction rates and kinetic isotope effects of enzyme-catalyzed reactions must take account of this environmental diversity. Ensemble-averaged variational transition state theory with multidimensional tunneling (EA-VTST/MT) was developed as a way to carry out such calculations. This theory incorporates ensemble averaging, quantized vibrational energies, energy, tunneling, and recrossing of transition state dividing surfaces in a systematic way. It has been applied successfully to a number of hydrogen-, proton-, and hydride-transfer reactions. The theory also exposes the set of effects that should be considered in reliable rate constants calculations.

We first review the basic theory and the steps in the calculation. A key role is played by the generalized free energy of activation profile, which is obtained by quantizing the classical potential of mean force as a function of a reaction coordinate because the one-way flux through the transition state dividing surface can be written in terms of the generalized free energy of activation. A recrossing transmission coefficient accounts for the difference between the one-way flux through the chosen transition state dividing surface and the net flux, and a tunneling transmission coefficient converts classical motion along the reaction coordinate to quantum mechanical motion. The tunneling calculation is multidimensional, accounting for the change in vibrational frequencies along the tunneling path and shortening of the tunneling path with respect to the minimum energy path (MEP), as promoted by reaction-path curvature. The generalized free energy of activation and the transmission coefficients both involve averaging over an ensemble of reaction paths and conformations, and this includes the coupling of protein motions to the rearrangement of chemical bonds in a statistical mechanically correct way. The standard deviations of the transmissions coefficients provide information on the diversity of the distribution of reaction paths, barriers, and protein conformations along the members of an ensemble of reaction paths passing through the transition state.

We first illustrate the theory by discussing the application to both wild-type and mutant Escherichia coli dihydrofolate reductase and hyperthermophilic Thermotoga maritima dihydrofolate reductase (DHFR); DHFR is of special interest because the protein conformational changes have been widely studied. Then we present shorter discussions of several other applications of EA-VTST/MT to transfer of protons, hydrogen atoms, and hydride ions and their deuterated analogs. Systems discussed include hydride transfer in alcohol dehydrogenase, xylose isomerase, and thymidylate synthase, proton transfer in methylamine dehydrogenase, hydrogen atom transfer in methylmalonyl-CoA mutase, and nucleophilic substitution in haloalkane dehalogenase and two-dimensional potentials of mean force for potentially coupled proton and hydride transfer in the β-oxidation of butyryl-coenzyme A catalyzed by short-chain acyl-CoA dehydrogenase and in the pyruvate to lactate transformation catalyzed by lactate dehydrogenase.

Nuclear quantum tunnelling in enzymatic reactions – an enzymologist's perspective

The roles of nuclear quantum tunnelling and dynamics in enzyme reactions are discussed in this perspective on H-transfer reactions.

Stress Test for Quantum Dynamics Approximations: Deep Tunneling in the Muonium Exchange Reaction D + HMu → DMu + H

Quantum effects play a crucial role in chemical reactions involving light atoms at low temperatures, especially when a light particle is exchanged between two heavier partners. Different theoretical methodologies have been developed in the last decades attempting to describe zero-point energy and tunneling effects without abandoning a classical or semiclassical framework. In this work, we have chosen the D + HMu → DMu + H reaction as a stress test system for three well-established methods: two representative versions of transition state theory (TST), canonical variational theory and semiclassical instanton, and ring polymer molecular dynamics (RPMD). These calculations will be compared with accurate quantum mechanical results. Despite its apparent simplicity, the exchange of the extremely light muonium atom (0.114 u) becomes a most challenging reaction for conventional methods. The main result of this work is that RPMD provides an overall better performance than TST-based methods for such a demanding reaction. RPMD might well turn out to be a useful tool beyond TST applicability.

Protein isotope effects in dihydrofolate reductase from Geobacillus stearothermophilus show entropic-enthalpic compensatory effects on the rate constant

Catalysis by dihydrofolate reductase from the moderately thermophilic bacterium Geobacillus stearothermophilus (BsDHFR) was investigated by isotope substitution of the enzyme. The enzyme kinetic isotope effect for hydride transfer was close to unity at physiological temperatures but increased with decreasing temperatures to a value of 1.65 at 5 °C. This behavior is opposite to that observed for DHFR from Escherichia coli (EcDHFR), where the enzyme kinetic isotope effect increased slightly with increasing temperature. These experimental results were reproduced in the framework of variational transition-state theory that includes a dynamical recrossing coefficient that varies with the mass of the protein. Our simulations indicate that BsDHFR has greater flexibility than EcDHFR on the ps-ns time scale, which affects the coupling of the environmental motions of the protein to the chemical coordinate and consequently to the recrossing trajectories on the reaction barrier. The intensity of the dynamic coupling in DHFRs is influenced by compensatory temperature-dependent factors, namely the enthalpic barrier needed to achieve an ideal transition-state configuration with minimal nonproductive trajectories and the protein disorder that disrupts the electrostatic preorganization required to stabilize the transition state. Together with our previous studies of other DHFRs, the results presented here provide a general explanation why protein dynamic effects vary between enzymes. Our theoretical treatment demonstrates that these effects can be satisfactorily reproduced by including a transmission coefficient in the rate constant calculation, whose dependence on temperature is affected by the protein flexibility.

Computational replication of the abnormal secondary kinetic isotope effects in a hydride transfer reaction in solution with a motion assisted H-tunneling model

We recently reported abnormal secondary deuterium kinetic isotope effects (2° KIEs) for hydride transfer reactions from alcohols to carbocations in acetonitrile (Chem. Comm. 2012, 48, 11337). Experimental 2° KIE values were found to be inflated on the 9-C position in the xanthylium cation but deflated on the β-C position in 2-propanol with respect to the values predicted by the semi-classical transition-state theory. No primary (1°) isotope effect on 2° KIEs was observed. Herein, the KIEs were replicated by the Marcus-like H-tunneling model that requires a longer donor–acceptor distance (DAD) in a lighter isotope transfer process. The 2° KIEs for a range of potential tunneling-ready-states (TRSs) of different DADs were calculated and fitted to the experiments to find the TRS structure. The observed no effect of 1° isotope on 2° KIEs is explained in terms of the less sterically hindered TRS structure so that the change in DAD due to the change in 1° isotope does not significantly affect the reorganization of the 2° isotope and hence the 2° KIE. The effect of 1° isotope on 2° KIEs may be expected to be more pronounced and thus observable in reactions occurring in restrictive environments such as the crowded and relatively rigid active site of enzymes.

Effects of cavities at the nicotinamide binding site of liver alcohol dehydrogenase on structure, dynamics and catalysis

A role for protein dynamics in enzymatic catalysis of hydrogen transfer has received substantial scientific support, but the connections between protein structure and catalysis remain to be established. Valine residues 203 and 207 are at the binding site for the nicotinamide ring of the coenzyme in liver alcohol dehydrogenase and have been suggested to facilitate catalysis with “protein-promoting vibrations” (PPV). We find that the V207A substitution has small effects on steady-state kinetic constants and the rate of hydrogen transfer; the introduced cavity is empty and is tolerated with minimal effects on structure (determined at 1.2 Å for the complex with NAD⁺ and 2,3,4,5,6-pentafluorobenzyl alcohol). Thus, no evidence is found to support a role for Val-207 in the dynamics of catalysis. The protein structures and ligand geometries (including donor–acceptor distances) in the V203A enzyme complexed with NAD⁺ and 2,3,4,5,6-pentafluorobenzyl alcohol or 2,2,2-trifluoroethanol (determined at 1.1 Å) are very similar to those for the wild-type enzyme, except that the introduced cavity accommodates a new water molecule that contacts the nicotinamide ring. The structures of the V203A enzyme complexes suggest, in contrast to previous studies, that the diminished tunneling and decreased rate of hydride transfer (16-fold, relative to that of the wild-type enzyme) are not due to differences in ground-state ligand geometries. The V203A substitution may alter the PPV and the reorganization energy for hydrogen transfer, but the protein scaffold and equilibrium thermal motions within the Michaelis complex may be more significant for enzyme catalysis.

The power of integrating kinetic isotope effects into the formalism of the Michaelis-Menten equation

The final arbiter of enzyme mechanism is the ability to establish and test a kinetic mechanism. Isotope effects play a major role in expanding the scope and insight derived from the Michaelis-Menten equation. The integration of isotope effects into the formalism of the Michaelis-Menten equation began in the 1970s and has continued until the present. This review discusses a family of eukaryotic copper proteins, including dopamine β-monooxygenase, tyramine β-monooxygenase and peptidylglycine α-amidating enzyme, which are responsible for the synthesis of neuroactive compounds, norepinephrine, octopamine and C-terminally carboxamidated peptides, respectively. The review highlights the results of studies showing how combining kinetic isotope effects with initial rate parameters permits the evaluation of: (a) the order of substrate binding to multisubstrate enzymes; (b) the magnitude of individual rate constants in complex, multistep reactions; (c) the identification of chemical intermediates; and (d) the role of nonclassical (tunnelling) behaviour in C-H activation.

Hydrogen tunneling links protein dynamics to enzyme catalysis

The relationship between protein dynamics and function is a subject of considerable contemporary interest. Although protein motions are frequently observed during ligand binding and release steps, the contribution of protein motions to the catalysis of bond making/breaking processes is more difficult to probe and verify. Here, we show how the quantum mechanical hydrogen tunneling associated with enzymatic C-H bond cleavage provides a unique window into the necessity of protein dynamics for achieving optimal catalysis. Experimental findings support a hierarchy of thermodynamically equilibrated motions that control the H-donor and -acceptor distance and active-site electrostatics, creating an ensemble of conformations suitable for H-tunneling. A possible extension of this view to methyl transfer and other catalyzed reactions is also presented. The impact of understanding these dynamics on the conceptual framework for enzyme activity, inhibitor/drug design, and biomimetic catalyst design is likely to be substantial.

Protein dynamics and enzyme catalysis: the ghost in the machine?

One of the most controversial questions in enzymology today is whether protein dynamics are significant in enzyme catalysis. A particular issue in these debates is the unusual temperature-dependence of some kinetic isotope effects for enzyme-catalysed reactions. In the present paper, we review our recent model [Glowacki, Harvey and Mulholland (2012) Nat. Chem. 4, 169-176] that is capable of reproducing intriguing temperature-dependences of enzyme reactions involving significant quantum tunnelling. This model relies on treating multiple conformations of the enzyme-substrate complex. The results show that direct 'driving' motions of proteins are not necessary to explain experimental observations, and show that enzyme reactivity can be understood and accounted for in the framework of transition state theory.

A model reaction assesses contribution of H-tunneling and coupled motions to enzyme catalysis

To assess the contribution of physical features to enzyme catalysis, the enzymatic reaction has to be compared to a relevant uncatalyzed reaction. While such comparisons have been conducted for some hydrolytic and radical reactions, it is most challenging for biological hydride transfer and redox reactions in general. Here, the same experimental tools used to study the H-tunneling and coupled motions for enzymatic hydride transfer between two carbons were used in the study of an uncatalyzed model reaction. The enzymatic oxidations of benzyl alcohol and its substituted analogues mediated by alcohol dehydrogenases were compared to the oxidations by 9-phenylxanthylium cation (PhXn(+)). The PhXn(+) serves as an NAD(+) model, while the solvent, acetonitrile, models the protein environment. Experimental comparisons included linear free energy relations with Hammett reaction constant (ρ) of zero versus -2.7; temperature-independent versus temperature-dependent primary KIEs; deflated secondary KIEs with deuteride transfer (i.e., primary-secondary coupled motion) versus no coupling between secondary KIEs and H- or D-transfer; and large versus small secondary KIEs for the enzymatic versus uncatalyzed alcohol oxidation. Some of the differences may come from differences in the order of microscopic steps between the catalyzed versus uncatalyzed reactions. However, several of these comparative experiments indicate that in contrast to the uncatalyzed reaction the transition state of the enzymatic reaction is better reorganized for H-tunneling and its H-donor is better rehybridized prior to the C-H→C transfer. These findings suggest an important role for these physical features in enzyme catalysis.

Deuterium kinetic isotope effects in heterotetrameric sarcosine oxidase from Corynebacterium sp. U-96: the anionic form of the substrate in the enzyme-substrate complex is a reactive species

Heterotetrameric sarcosine oxidase is a flavoprotein that catalyses the oxidative demethylation of sarcosine. It is thought that the dehydrogenated substrate is the anionic form of sarcosine. To verify this assumption, the rate of flavin-adenine dinucleotide (FAD) reduction (k(red)) was analysed using protiated and deuterated sarcosine (N-methyl-d(3)-Gly) at various pH values using stopped-flow method. By increasing the pH from 6.2 to 9.8, k(red) increased for both substrates and reached a plateau, but the pK(a) value (reflecting the ionization of the enzyme-substrate complex) was 6.8 and 7.1 for protiated and deuterated sarcosine, respectively, and the kinetic isotope effect of k(red) decreased from approximately 19 to 8, indicating deprotonation of the bound sarcosine. The k(red)/K(d) (K(d), sarcosine dissociation constant) increased with increasing pH and reached a plateau. The pK (reflecting the ionization of free enzyme or free sarcosine) was 7.0 for both substrates, suggesting deprotonation of the βLys358 residue, which has a pK(a) of 6.7, as the pK(a) of the free sarcosine amine proton was determined to be approximately 10.1. These results indicate that the amine proton of sarcosine is transferred to the unprotonated Lys residue in the enzyme-substrate complex.

Taking Ockham's razor to enzyme dynamics and catalysis

The role of protein dynamics in enzyme catalysis is a matter of intense current debate. Enzyme-catalysed reactions that involve significant quantum tunnelling can give rise to experimental kinetic isotope effects with complex temperature dependences, and it has been suggested that standard statistical rate theories, such as transition-state theory, are inadequate for their explanation. Here we introduce aspects of transition-state theory relevant to the study of enzyme reactivity, taking cues from chemical kinetics and dynamics studies of small molecules in the gas phase and in solution--where breakdowns of statistical theories have received significant attention and their origins are relatively better understood. We discuss recent theoretical approaches to understanding enzyme activity and then show how experimental observations for a number of enzymes may be reproduced using a transition-state-theory framework with physically reasonable parameters. Essential to this simple model is the inclusion of multiple conformations with different reactivity.