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

A Foundational Shift in Models for Enzyme Function

This Perspective addresses the unresolved, and still hotly contested, question of how enzymes transition from stable enzyme-substrate (ES) complexes to successful, femtosecond barrier crossings. By extending Marcus theory to enzyme-catalyzed reactions, we argue that environmental reorganization of the protein scaffold, together with associated water molecules, achieves the intersection of reactant and product potential energy surfaces. After discussing the experimentally demonstrated importance of reduced activation enthalpy in enzyme-catalyzed transformations, we describe new methodologies that measure the temperature dependence of (i) time-averaged hydrogen/deuterium exchange into backbone amides and (ii) time-dependent Stokes shifts to longer emission wavelengths in appended chromophores at the protein/water interface. These methods not only identify specific pathways for the transfer of thermal energy from solvent to the reacting bonds of bound substrates but also suggest that collective thermally activated protein restructuring must occur very rapidly (on the ns-ps time scale) over long distances. Based on these findings, we introduce a comprehensive model for how barrier crossing takes place from the ES complex. This exploits the structural preorganization inherent in protein folding and subsequent conformational sampling, which optimally positions essential catalytic components within ES ground states and correctly places reactive bonds in the substrate(s) relative to embedded energy transfer networks connecting the protein surface to the active site. The existence of these anisotropic energy distribution pathways introduces a new dimension into the ongoing quest for improved de novo enzyme design.

Structural Effects on the Hydride-Tunneling Kinetic Isotope Effects of NADH/NAD+ Model Reactions: Relating to the Donor-Acceptor Distances

Contemporary H-tunneling theories predict that a longer donor-acceptor distance (DAD) corresponds to a larger kinetic isotope effect (KIE). Herein, hydride-tunneling reactions of NADH/NAD+ analogues in acetonitrile were used to examine the KIE-DAD relationship. Reaction pairs of similar tunneling-ready conformations were selected, so that additional factors influencing KIEs would be relatively fixed. Positive results were obtained, with some reaction pairs displaying a reversal of the traditional KIE-ΔG° relationship in favor of the KIE-DAD relationship, lending strong support to the latter.

Secondary Amine Catalysis in Enzyme Design: Broadening Protein Template Diversity through Genetic Code Expansion

Secondary amines, due to their reactivity, can transform protein templates into catalytically active entities, accelerating the development of artificial enzymes. However, existing methods, predominantly reliant on modified ligands or N-terminal prolines, impose significant limitations on template selection. In this study, genetic code expansion was used to break this boundary, enabling secondary amines to be incorporated into alternative proteins and positions of choice. Pyrrolysine analogues carrying different secondary amines could be incorporated into superfolder green fluorescent protein (sfGFP), multidrug-binding LmrR and nucleotide-binding dihydrofolate reductase (DHFR). Notably, the analogue containing a D-proline moiety demonstrated both proteolytic stability and catalytic activity, conferring LmrR and DHFR with the desired transfer hydrogenation activity. While the LmrR variants were confined to the biomimetic 1-benzyl-1,4-dihydronicotinamide (BNAH) as the hydride source, the optimal DHFR variant favorably used the pro-R hydride from NADPH for stereoselective reactions (e.r. up to 92 : 8), highlighting that a switch of protein template could broaden the nucleophile option for catalysis. Owing to the cofactor compatibility, the DHFR-based secondary amine catalysis could be integrated into an enzymatic recycling scheme. This established method shows substantial potential in enzyme design, applicable from studies on enzyme evolution to the development of new biocatalysts.

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.

Anisotropic dynamics of an interfacial enzyme active site observed using tethered substrate analogs and ultrafast 2D IR spectroscopy

Enzymes accelerate the rates of biomolecular reactions by many orders of magnitude compared to bulk solution, and it is widely understood that this catalytic effect arises from a combination of polar pre-organization and electrostatic transition state stabilization. A number of recent reports have also implicated ultrafast (femtosecond-picosecond) timescale motions in enzymatic activity. However, complications arising from spatially-distributed disorder, the occurrence of multiple substrate binding modes, and the influence of hydration dynamics on solvent-exposed active sites still confound many experimental studies. Here we use ultrafast two-dimensional infrared (2D IR) spectroscopy and covalently-tethered substrate analogs to examine dynamical properties of the promiscuous Pyrococcus horikoshii ene-reductase (PhENR) active site in two binding configurations mimicking proposed "inactive" and "reactive" Michaelis complexes. Spectral diffusion measurements of aryl-nitrile substrate analogs reveal an end-to-end tradeoff between fast (sub-ps) and slow (>5 ps) motions. Fermi resonant aryl-azide analogs that sense interactions of coupled oscillators are described. Lineshape and quantum beat analyses of these probes reveal characteristics that correlate with aryl-nitrile frequency fluctuation correlation functions parameters, demonstrating that this anisotropy is an intrinsic property of the water-exposed active site, where countervailing gradients of fast dynamics and disorder in the reactant ground state are maintained near the hydration interface. Our results suggest several plausible factors leading to state-selective rate enhancement and promiscuity in PhENR. This study also highlights a strategy to detect perturbations to vibrational modes outside the transparent window of the mid-IR spectrum, which may be extended to other macromolecular systems.

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.

Employing deuterium kinetic isotope effects to uncover the mechanism of (R)-3-hydroxybutyrate dehydrogenase

Short-chain dehydrogenases/reductases (SDR) form a large enzyme superfamily playing important roles in health and disease. Furthermore, they are useful tools in biocatalysis. Unveiling the nature of the transition state for hydride transfer is a crucial undertaking toward defining the physicochemical underpinnings of catalysis by SDR enzymes, including possible contributions from quantum mechanical tunneling. Primary deuterium kinetic isotope effects can uncover the contribution from chemistry to the rate-limiting step and potentially provide detailed information on the hydride-transfer transition state in SDR-catalyzed reactions. For the latter, however, one needs to determine the intrinsic isotope effect: that which would be measured if hydride transfer were rate determining. Alas, as is the case for many other enzymatic reactions, those catalyzed by SDRs are often limited by the rate of isotope-insensitive steps, such as product release and conformational changes, which masks the expression of the intrinsic isotope effect. This can be overcome by the powerful yet underexplored method of Palfey and Fagan via which intrinsic kinetic isotope effects can be extracted from pre-steady-state kinetics data. SDRs are ideal systems to which this method can be applied. We have employed this approach to elucidate the transition states for hydride transfer catalyzed by NADH-dependent cold- and warm-adapted (R)-3-hydroxybutyrate dehydrogenase. Experimental conditions which simplify the analysis are discussed.

Robust total X-ray scattering workflow to study correlated motion of proteins in crystals

The breathing motions of proteins are thought to play a critical role in function. However, current techniques to study key collective motions are limited to spectroscopy and computation. We present a high-resolution experimental approach based on the total scattering from protein crystals at room temperature (TS/RT-MX) that captures both structure and collective motions. To reveal the scattering signal from protein motions, we present a general workflow that enables robust subtraction of lattice disorder. The workflow introduces two methods: GOODVIBES, a detailed and refinable lattice disorder model based on the rigid-body vibrations of a crystalline elastic network; and DISCOBALL, an independent method of validation that estimates the displacement covariance between proteins in the lattice in real space. Here, we demonstrate the robustness of this workflow and further demonstrate how it can be interfaced with MD simulations towards obtaining high-resolution insight into functionally important protein motions.

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.

Hydride Transfer Mechanism of Enzymatic Sugar Nucleotide C2 Epimerization Probed with a Loose-Fit CDP-Glucose Substrate

Transient oxidation–reduction through hydride transfer with tightly bound NAD coenzyme is used by a large class of sugar nucleotide epimerases to promote configurational inversion of carbon stereocenters in carbohydrate substrates. A requirement for the epimerases to coordinate hydride abstraction and re-addition with substrate rotation in the binding pocket poses a challenge for dynamical protein conformational selection linked to enzyme catalysis. Here, we studied the thermophilic C2 epimerase from Thermodesulfatator atlanticus (TaCPa2E) in combination with a slow CDP-glucose substrate (k_cat ≈ 1.0 min^–1; 60 °C) to explore the sensitivity of the enzymatic hydride transfer toward environmental fluctuations affected by temperature (20–80 °C). We determined noncompetitive primary kinetic isotope effects (KIE) due to ²H at the glucose C2 and showed that a normal KIE on the k_cat (^Dk_cat) reflects isotope sensitivity of the hydrogen abstraction to enzyme-NAD⁺ in a rate-limiting transient oxidation. The ^Dk_cat peaked at 40 °C was 6.1 and decreased to 2.1 at low (20 °C) and 3.3 at high temperature (80 °C). The temperature profiles for k_cat with the ¹H and ²H substrate showed a decrease in the rate below a dynamically important breakpoint (∼40 °C), suggesting an equilibrium shift to an impaired conformational landscape relevant for catalysis in the low-temperature region. Full Marcus-like model fits of the rate and KIE profiles provided evidence for a high-temperature reaction via low-frequency conformational sampling associated with a broad distribution of hydride donor–acceptor distances (long-distance population centered at 3.31 ± 0.02 Å), only poorly suitable for quantum mechanical tunneling. Collectively, dynamical characteristics of TaCPa2E-catalyzed hydride transfer during transient oxidation of CDP-glucose reveal important analogies to mechanistically simpler enzymes such as alcohol dehydrogenase and dihydrofolate reductase. A loose-fit substrate (in TaCPa2E) resembles structural variants of these enzymes by extensive dynamical sampling to balance conformational flexibility and catalytic efficiency.

Pairing structural reconstruction with catalytic competence to evaluate the mechanisms of key enzymes in the folate-mediated one-carbon pathway

Mammalian metabolism comprises a series of interlinking pathways that include two major cycles: the folate and methionine cycles. The folate-mediated metabolic cycle uses several oxidation states of tetrahydrofolate to carry activated one-carbon units to be readily used and interconverted within the cell. They are required for nucleotide synthesis, methylation and metabolism, and particularly for proliferation of cancer cells. Based on the latest progress in genome-wide CRISPR loss-of-function viability screening of 789 cell lines, we focus on the most cancer-dependent enzymes in this pathway, especially those that are hyperactivated in cancer, to provide new insight into the chemical basis for cancer drug development. Since the complete 3D structure of several of these enzymes of the one-carbon pathway in their active form are not available, we used homology modelling integrated with the interpretation of the reaction mechanism. In addition, have reconstructed the most likely scenario for the reactions taking place paired with their catalytic competence that provides a testable framework for this pathway.

Single-Molecule Sampling of Dihydrofolate Reductase Shows Kinetic Pauses and an Endosteric Effect Linked to Catalysis

The ability to sample multiple reactions on the same single enzyme is important to link rare intermediates with catalysis and to unravel the role of conformational changes. Despite decades of efforts, however, the single-molecule characterization of nonfluorogenic enzymes during multiple catalytic turnovers has been elusive. Here, we show that nanopore currents allow sampling the dynamic exchange between five structural intermediates during E. coli dihydrofolate reductase (DHFR) catalysis. We found that an endosteric effect promotes the binding of the substrate to the enzyme with a specific hierarchy. The chemical step then switched the enzyme from the closed to the occluded conformation, which in turn promotes the release of the reduced cofactor NADP⁺. Unexpectedly, only a few reactive complexes lead to catalysis. Furthermore, second-long catalytic pauses were observed, possibly reflecting an off-path conformation generated during the reaction. Finally, the free energy from multiple cofactor binding events were required to release the product and switch DHFR back to the reactive conformer. This catalytic fueled concerted mechanism is likely to have evolved to improve the catalytic efficiency of DHFR under the high concentrations of NADP⁺ in E. coli and might be a general feature for complex enzymatic reactions where the binding and release of the products must be tightly controlled.

Evolution of Optimized Hydride Transfer Reaction and Overall Enzyme Turnover in Human Dihydrofolate Reductase

Evolution of dihydrofolate reductase (DHFR) has been studied using the enzyme from Escherichia coli DHFR (ecDHFR) as a model, but less studies have used the enzyme from Homo sapiens DHFR (hsDHFR). Each enzyme maintains a short and narrow distribution of hydride donor-acceptor distances (DAD) at the tunneling ready state (TRS). Evolution of the enzyme was previously studied in ecDHFR where three key sites were identified as important to the catalyzed reaction. The corresponding sites in hsDHFR are F28, 62-PEKN, and 26-PPLR. Each of these sites was studied here through the creation of mutant variants of the enzyme and measurements of the temperature dependence of the intrinsic kinetic isotope effects (KIEs) on the reaction. F28 is mutated first to M (F28M) and then to the L of the bacterial enzyme (F28L). The KIEs of the F28M variant are larger and more temperature-dependent than wild-type (WT), suggesting a broader and longer average DAD at the TRS. To more fully mimic ecDHFR, we also study a triple mutant of the human enzyme (F32L-PP26N-PEKN62G). Remarkably, the intrinsic KIEs, while larger in magnitude, are temperature-independent like the WT enzymes. We also construct deletion mutations of hsDHFR removing both the 62-PEKN and 26-PPLR sequences. The results mirror those described previously for insertion mutants of ecDHFR. Taken together, these results suggest a balancing act during DHFR evolution between achieving an optimal TRS for hydride transfer and preventing product inhibition arising from the different intercellular pools of NADPH and NADP⁺ in prokaryotic and eukaryotic cells.

Temperature-Dependent Low-Frequency Modes in the Active Site of Bovine Carbonic Anhydrase II Probed by 2D-IR Spectroscopy

Enzyme catalysis achieves tremendous rate accelerations. Enzyme reaction centers provide a constraint geometry that preferentially binds an activated form of the substrate and thus lowers the energy barrier. However, this transition state picture neglects the flexibility of proteins and its role in enzymatic catalysis. Especially for proton transfer reactions, it has been suggested that motions of the protein modulate the donor-acceptor distance and prepare a tunneling-ready state. We report the detection of frequency fluctuations of an azide anion (N₃^-) bound in the active site of the protein carbonic anhydrase II, where a low-frequency mode of the protein has been proposed to facilitate proton transfer over two water molecules during the catalyzed reaction. 2D-IR spectroscopy resolves an underdamped low-frequency mode at about 1 THz (30 cm^-1). We find its frequency to be viscosity- and temperature-dependent and to decrease by 6 cm^-1 between 230 and 320 K, reporting the softening of the mode's potential.

Correlated Motions in Structural Biology

Correlated motions in proteins arising from the collective movements of residues have long been proposed to be fundamentally important to key properties of proteins, from allostery and catalysis to evolvability. Recent breakthroughs in structural biology have made it possible to capture proteins undergoing complex conformational changes, yet intrinsic correlated motions within a conformation remain one of the least understood facets of protein structure. For many decades, the analysis of total X-ray scattering held the promise of animating crystal structures with correlated motions. With recent advances in both X-ray detectors and data interpretation methods, this long-held promise can now be met. In this Perspective, we will introduce how correlated motions are captured in total scattering and provide guidelines for the collection, interpretation, and validation of data. As structural biology continues to push the boundaries, we see an opportunity to gain atomistic insight into correlated motions using total scattering as a bridge between theory and experiment.

Cryo-kinetics Reveal Dynamic Effects on the Chemistry of Human Dihydrofolate Reductase

Effects of isotopic substitution on the rate constants of human dihydrofolate reductase (HsDHFR), an important target for anti-cancer drugs, have not previously been characterized due to its complex fast kinetics. Here, we report the results of cryo-measurements of the kinetics of the HsDHFR catalyzed reaction and the effects of protein motion on catalysis. Isotopic enzyme labeling revealed an enzyme KIE (kHLE /kHHE ) close to unity above 0 °C; however, the enzyme KIE was increased to 1.72±0.15 at -20 °C, indicating that the coupling of protein motions to the chemical step is minimized under optimal conditions but enhanced at non-physiological temperatures. The presented cryogenic approach provides an opportunity to probe the kinetics of mammalian DHFRs, thereby laying the foundation for characterizing their transition state structure.

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.

Capturing the Catalytic Proton of Dihydrofolate Reductase: Implications for General Acid-Base Catalysis

Acid–base catalysis, which involves one or more proton transfer reactions, is a chemical mechanism commonly employed by many enzymes. The molecular basis for catalysis is often derived from structures determined at the optimal pH for enzyme activity. However, direct observation of protons from experimental structures is quite difficult; thus, a complete mechanistic description for most enzymes remains lacking. Dihydrofolate reductase (DHFR) exemplifies general acid–base catalysis, requiring hydride transfer and protonation of its substrate, DHF, to form the product, tetrahydrofolate (THF). Previous X-ray and neutron crystal structures coupled with theoretical calculations have proposed that solvent mediates the protonation step. However, visualization of a proton transfer has been elusive. Based on a 2.1 Å resolution neutron structure of a pseudo-Michaelis complex of E. coli DHFR determined at acidic pH, we report the direct observation of the catalytic proton and its parent solvent molecule. Comparison of X-ray and neutron structures elucidated at acidic and neutral pH reveals dampened dynamics at acidic pH, even for the regulatory Met20 loop. Guided by the structures and calculations, we propose a mechanism where dynamics are crucial for solvent entry and protonation of substrate. This mechanism invokes the release of a sole proton from a hydronium (H₃O⁺) ion, its pathway through a narrow channel that sterically hinders the passage of water, and the ultimate protonation of DHF at the N5 atom.

Identification of Thermal Conduits That Link the Protein-Water Interface to the Active Site Loop and Catalytic Base in Enolase

We report here on the salient role of protein mobility in accessing conformational landscapes that enable efficient enzyme catalysis. We are focused on yeast enolase, a highly conserved lyase with a TIM barrel domain and catalytic loop, as part of a larger study of the relationship of site selective protein motions to chemical reactivity within superfamilies. Enthalpically hindered variants were developed by replacement of a conserved hydrophobic side chain (Leu 343) with smaller side chains. Leu343 is proximal to the active site base in enolase, and comparative pH rate profiles for the valine and alanine variants indicate a role for side chain hydrophobicity in tuning the pK_a of the catalytic base. However, the magnitude of a substrate deuterium isotope effect is almost identical for wild-type (WT) and Leu343Ala, supporting an unchanged rate-determining proton abstraction step. The introduced hydrophobic side chains at position 343 lead to a discontinuous break in both activity and activation energy as a function of side chain volume. Hydrogen-deuterium exchange mass spectrometry (HDX-MS) experiments were performed as a function of time and temperature for WT and Leu343Ala, and provide a spatially resolved map of changes in protein flexibility following mutation. Impacts on protein flexibility are localized to specific networks that arise at the protein-solvent interface and terminate in a loop that has been shown by X-ray crystallography to close over the active site. These interrelated effects are discussed in the context of long-range, solvent-accessible and thermally activated networks that play key roles in tuning the precise distances and interactions among reactants.

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.

The Soybean Lipoxygenase-Substrate Complex: Correlation between the Properties of Tunneling-Ready States and ENDOR-Detected Structures of Ground States

Hydrogen tunneling in enzymatic C-H activation requires a dynamical sampling among ground-state enzyme-substrate (E-S) conformations, which transiently generates a tunneling-ready state (TRS). The TRS is characterized by a hydrogen donor-acceptor distance (DAD) of 2.7 Å, ∼0.5 Å shorter than the dominant DAD of optimized ground states. Recently, a high-resolution, 13C electron-nuclear double-resonance (ENDOR) approach was developed to characterize the ground-state structure of the complex of the linoleic acid (LA) substrate with soybean lipoxygenase (SLO). The resulting enzyme-substrate model revealed two ground-state conformers with different distances between the target C11 of LA and the catalytically active cofactor [Fe(III)-OH]: the active conformer "a", with a van der Waals DAD of 3.1 Å between C11 and metal-bound hydroxide, and an inactive conformer "b", with a distance that is almost 1 Å longer. Herein, the structure of the E-S complex is examined for a series of six variants in which subtle structural modifications of SLO have been introduced either at a hydrophobic side chain near the bound substrate or at a remote residue within a protein network whose flexibility influences hydrogen transfer. A remarkable correlation is found between the ENDOR-derived population of the active ground-state conformer a and the kinetically derived differential enthalpic barrier for D versus H transfer, ΔEa, with the latter increasing as the fraction of conformer a decreases. As proposed, ΔEa provides a "ruler" for the DAD within the TRS. ENDOR measurements further corroborate the previous identification of a dynamical network coupling the buried active site of SLO to the surface. This study shows that subtle imperfections within the initial ground-state structures of E-S complexes are accompanied by compromised geometries at the TRS.

Engineering an alcohol dehydrogenase with enhanced activity and stereoselectivity toward diaryl ketones: reduction of steric hindrance and change of the stereocontrol element

Engineering an alcohol dehydrogenase with enhanced activity and stereoselectivity toward diaryl ketones: reduction of steric hindrance and change of the stereocontrol element.

What are the signatures of tunnelling in enzyme-catalysed reactions?

Computed tunnelling contributions and correlations between apparent activation enthalpy and entropy are explored for the interpretation of enzyme-catalysed H-transfer reactions.

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.

Isotopic Labeling of Formate Dehydrogenase Perturbs the Protein Dynamics

Isotope substitution of enzymes has become a means of addressing the participation of protein motions in enzyme-catalyzed reactions. The idea is that only the enzyme mass will be altered and not the electrostatics, so that the protein dynamics are essentially the same but at lower frequencies because of the mass change. In this study, we variably label all carbon atoms in formate dehydrogenase (FDH) with ¹³C, all nitrogen atoms with ¹⁵N, and all nonexchangeable hydrogen atoms with deuterium and investigate the impact that isotopic substitution has on the dynamics at the active site by two-dimensional infrared spectroscopy and compare with the measurements of the temperature dependence of the intrinsic kinetic isotope effects (KIEs). We show that ¹⁵N labeling of FDH has the largest effect and makes the active site more heterogeneous, whereas the addition of nonexchangeable deuterium appears to have the opposite effect of ¹⁵N on active-site dynamics, resulting in a behavior similar to that of native FDH. Nevertheless, the temperature dependence of the KIEs shows a monotonic trend with protein mass that does not correspond with the changes in dynamics. These results suggest that isotope labeling has more than just a mass effect on enzyme dynamics and may influence electrostatics in ways that complicate the interpretation of the protein isotope effect.

Evolution Conserves the Network of Coupled Residues in Dihydrofolate Reductase

Understanding protein motions and their role in enzymatic reactions is an important and timely topic in enzymology. Protein motions that are involved in the chemical step of catalysis are particularly intriguing but difficult to identify. A global network of coupled residues in Escherichia coli dihydrofolate reductase (E. coli DHFR), which assists in catalyzing the chemical step, has previously been demonstrated through quantum mechanical/molecular mechanical and molecular dynamics simulations as well as bioinformatic analyses. A few specific residues (M42, G121, F125, and I14) were shown to function synergistically with measurements of single-turnover rates and the temperature dependence of intrinsic kinetic isotope effects (KIEsint) of site-directed mutants. This study hypothesizes that the global network of residues involved in the chemical step is evolutionarily conserved and probes homologous residues of the potential global network in human DHFR through measurements of the temperature dependence of KIEsint and computer simulations based on the empirical valence bond method. We study mutants M53W and S145V. Both of these remote residues are homologous to network residues in E. coli DHFR. Non-additive isotope effects on activation energy are observed between M53 and S145, indicating their synergistic effect on the chemical step in human DHFR, which suggests that both of these residues are part of a network affecting the chemical step in enzyme catalysis. This finding supports the hypothesis that human and E. coli DHFR share similar networks, consistent with evolutionary preservation of such networks.

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.

The crystal structure of a tetrahydrofolate-bound dihydrofolate reductase reveals the origin of slow product release

Dihydrofolate reductase (DHFR) catalyzes the stereospecific reduction of 7,8-dihydrofolate (FH2) to (6s)-5,6,7,8-tetrahydrofolate (FH4) via hydride transfer from NADPH. The consensus Escherichia coli DHFR mechanism involves conformational changes between closed and occluded states occurring during the rate-limiting product release step. Although the Protein Data Bank (PDB) contains over 250 DHFR structures, the FH4 complex structure responsible for rate-limiting product release is unknown. We report to our knowledge the first crystal structure of an E. coli. DHFR:FH4 complex at 1.03 Å resolution showing distinct stabilizing interactions absent in FH2 or related (6R)-5,10-dideaza-FH4 complexes. We discover the time course of decay of the co-purified endogenous FH4 during crystal growth, with conversion from FH4 to FH2 occurring in 2–3 days. We also determine another occluded complex structure of E. coli DHFR with a slow-onset nanomolar inhibitor that contrasts with the methotrexate complex, suggesting a plausible strategy for designing DHFR antibiotics by targeting FH4 product conformations.

Hongnan Cao et al. present the X-ray crystal structure of E. coli dihydrofolate reductase (DHFR) in complex with its reduced substrate, (6s)-5,6,7,8-tetrahydrofolate (FH4). This structure provides the first glimpse of the rate-limiting product release step of the DHFR mechanism and suggests a strategy for designing DHFR-targeting antibiotics.

Nonequivalence of Second Sphere "Noncatalytic" Residues in Pentaerythritol Tetranitrate Reductase in Relation to Local Dynamics Linked to H-Transfer in Reactions with NADH and NADPH Coenzymes

Many enzymes that catalyze hydride transfer reactions work via a mechanism dominated by quantum mechanical tunneling. The involvement of fast vibrational modes of the reactive complex is often inferred in these reactions, as in the case of the NAD(P)H-dependent pentaerythritol tetranitrate reductase (PETNR). Herein, we interrogated the H-transfer mechanism in PETNR by designing conservative (L25I and I107L) and side chain shortening (L25A and I107A) PETNR variants and using a combination of experimental approaches (stopped-flow rapid kinetics, X-ray crystallography, isotope/temperature dependence studies of H-transfer and NMR spectroscopy). X-ray data show subtle changes in the local environment of the targeted side chains but no major structural perturbation caused by mutagenesis of these two second sphere active site residues. However, temperature dependence studies of H-transfer revealed a coenzyme-specific and complex thermodynamic equilibrium between different reactive configurations in PETNR–coenzyme complexes. We find that mutagenesis of these second sphere “noncatalytic” residues affects differently the reactivity of PETNR with NADPH and NADH coenzymes. We attribute this to subtle, dynamic structural changes in the PETNR active site, the effects of which impact differently in the nonequivalent reactive geometries of PETNR−NADH and PETNR−NADPH complexes. This inference is confirmed through changes observed in the NMR chemical shift data for PETNR complexes with unreactive 1,4,5,6-tetrahydro-NAD(P) analogues. We show that H-transfer rates can (to some extent) be buffered through entropy–enthalpy compensation, but that use of integrated experimental tools reveals hidden complexities that implicate a role for dynamics in this relatively simple H-transfer reaction. Similar approaches are likely to be informative in other enzymes to understand the relative importance of (distal) hydrophobic side chains and dynamics in controlling the rates of enzymatic H-transfer.

Effect of Asp122 Mutation on the Hydride Transfer in E. coli DHFR Demonstrates the Goldilocks of Enzyme Flexibility

Dihydrofolate reductase (DHFR) catalyzes the reduction of dihydrofolate (DHF) to tetrahydrofolate (THF) in the presence of NADPH. The key hydride transfer step in the reaction is facilitated by a combination of enzyme active site preorganization and correlated protein motions in the Michaelis-Menten (E:NADPH:DHF) complex. The present theoretical study employs mutagenesis to examine the relation between structural and functional properties of the enzyme. We mutate Asp122 in Escherichia coli DHFR, which is a conserved amino acid in the DHFR family. The consequent effect of the mutation on enzyme catalysis is examined from an energetic, structural and short-time dynamic perspective. Our investigations suggest that the structural and short-time dynamic perturbations caused by Asp122X mutations (X = Asn, Ser, Ala) are along the reaction coordinate and lower the rate of hydride transfer. Importantly, analysis of the correlated and principle component motions in the enzyme suggest that the mutation alters the coupled motions that are present in the wild-type enzyme. In the case of D122N and D122S, the mutations inhibit coupled motion, whereas in the case of D122A, the mutation enhances coupled motion, although all mutations result in similar rate reduction. These results emphasize a Goldilocks principle of enzyme flexibility, that is, enzymes should neither be too rigid nor too flexible.

Primary Deuterium Kinetic Isotope Effects: A Probe for the Origin of the Rate Acceleration for Hydride Transfer Catalyzed by Glycerol-3-Phosphate Dehydrogenase

Large primary deuterium kinetic isotope effects (1° DKIEs) on enzyme-catalyzed hydride transfer may be observed when the transferred hydride tunnels through the energy barrier. The following 1° DKIEs on k_cat/K_m and relative reaction driving force are reported for wild-type and mutant glycerol-3-phosphate dehydrogenase (GPDH)-catalyzed reactions of NADL (L = H, D): wild-type GPDH, ΔΔG^⧧ = 0 kcal/mol, 1° DKIE = 1.5; N270A, 5.6 kcal/mol, 3.1; R269A, 9.1 kcal/mol, 2.8; R269A + 1.0 M guanidine, 2.4 kcal/mol, 2.7; R269A/N270A, 11.5 kcal/mol, 2.4. Similar 1° DKIEs were observed on k_cat. The narrow range of 1° DKIEs (2.4–3.1) observed for a 9.1 kcal/mol change in reaction driving force provides strong evidence that these are intrinsic 1° DKIEs on rate-determining hydride transfer. Evidence is presented that the intrinsic DKIE on wild-type GPDH-catalyzed reduction of DHAP lies in this range. A similar range of 1° DKIEs (2.4–2.9) on (k_cat/K_GA, M^–1 s^–1) was reported for dianion-activated hydride transfer from NADL to glycolaldehyde (GA) [Reyes, A. C.; Amyes, T. L.; Richard, J. P. J. Am. Chem. Soc.2016, 138, 14526–14529]. These 1° DKIEs are much smaller than those observed for enzyme-catalyzed hydrogen transfer that occurs mainly by quantum mechanical tunneling. These results support the conclusion that the rate acceleration for GPDH-catalyzed reactions is due to the stabilization of the transition state for hydride transfer by interactions with the protein catalyst. The small 1° DKIEs reported for mutant GPDH-catalyzed and for wild-type dianion-activated reactions are inconsistent with a model where the dianion binding energy is utilized in the stabilization of a tunneling ready state.

Engineered control of enzyme structural dynamics and function

Enzymes undergo a range of internal motions from local, active site fluctuations to large-scale, global conformational changes. These motions are often important for enzyme function, including in ligand binding and dissociation and even preparing the active site for chemical catalysis. Protein engineering efforts have been directed towards manipulating enzyme structural dynamics and conformational changes, including targeting specific amino acid interactions and creation of chimeric enzymes with new regulatory functions. Post-translational covalent modification can provide an additional level of enzyme control. These studies have not only provided insights into the functional role of protein motions, but they offer opportunities to create stimulus-responsive enzymes. These enzymes can be engineered to respond to a number of external stimuli, including light, pH, and the presence of novel allosteric modulators. Altogether, the ability to engineer and control enzyme structural dynamics can provide new tools for biotechnology and medicine.

Contribution of buried distal amino acid residues in horse liver alcohol dehydrogenase to structure and catalysis

The dynamics of enzyme catalysis range from the slow time scale (∼ms) for substrate binding and conformational changes to the fast time (∼ps) scale for reorganization of substrates in the chemical step. The contribution of global dynamics to catalysis by alcohol dehydrogenase was tested by substituting five different, conserved amino acid residues that are distal from the active site and located in the hinge region for the conformational change or in hydrophobic clusters. X-ray crystallography shows that the structures for the G173A, V197I, I220 (V, L, or F), V222I, and F322L enzymes complexed with NAD⁺ and an analogue of benzyl alcohol are almost identical, except for small perturbations at the sites of substitution. The enzymes have very similar kinetic constants for the oxidation of benzyl alcohol and reduction of benzaldehyde as compared to the wild-type enzyme, and the rates of conformational changes are not altered. Less conservative substitutions of these amino acid residues, such as G173(V, E, K, or R), V197(G, S, or T), I220(G, S, T, or N), and V222(G, S, or T) produced unstable or poorly expressed proteins, indicating that the residues are critical for global stability. The enzyme scaffold accommodates conservative substitutions of distal residues, and there is no evidence that fast, global dynamics significantly affect the rate constants for hydride transfers. In contrast, other studies show that proximal residues significantly participate in catalysis.

Protein Mass Effects on Formate Dehydrogenase

Isotopically labeled enzymes (denoted as "heavy" or "Born-Oppenheimer" enzymes) have been used to test the role of protein dynamics in catalysis. The original idea was that the protein's higher mass would reduce the frequency of its normal-modes without altering its electrostatics. Heavy enzymes have been used to test if the vibrations in the native enzyme are coupled to the chemistry it catalyzes, and different studies have resulted in ambiguous findings. Here the temperature-dependence of intrinsic kinetic isotope effects of the enzyme formate dehydrogenase is used to examine the distribution of H-donor to H-acceptor distance as a function of the protein's mass. The protein dynamics are altered in the heavy enzyme to diminish motions that determine the transition state sampling in the native enzyme, in accordance with a Born-Oppenheimer-like effect on bond activation. Findings of this work suggest components related to fast frequencies that can be explained by Born-Oppenheimer enzyme hypothesis (vibrational) and also slower time scale events that are non-Born-Oppenheimer in nature (electrostatic), based on evaluations of protein mass dependence of donor-acceptor distance and forward commitment to catalysis along with steady state and single turnover measurements. Together, the findings suggest that the mass modulation affected both local, fast, protein vibrations associated with the catalyzed chemistry and the protein's macromolecular electrostatics at slower time scales; that is, both Born-Oppenheimer and non-Born-Oppenheimer effects are observed. Comparison to previous studies leads to the conclusion that isotopic labeling of the protein may have different effects on different systems, however, making heavy enzyme studies a very exciting technique for exploring the dynamics link to catalysis in proteins.

Evidence for proton tunneling and a transient covalent flavin-substrate adduct in choline oxidase S101A

The effect of temperature on the reaction of alcohol oxidation catalyzed by choline oxidase was investigated with the S101A variant of choline oxidase. Anaerobic enzyme reduction in a stopped-flow spectrophotometer was biphasic using either choline or 1,2-[²H₄]-choline as a substrate. The limiting rate constants k_lim1 and k_lim2 at saturating substrate were well separated (k_lim1/k_lim2>9), and were >15-fold slower than for wild-type choline oxidase. Solvent deuterium kinetic isotope effects (KIEs) ~4 established that k_lim1 probes the proton transfer from the substrate hydroxyl to a catalytic base. Primary substrate deuterium KIEs ≥7 demonstrated that k_lim2 reports on hydride transfer from the choline alkoxide to the flavin. Between 15°C and 39°C the k_lim1 and k_lim2 values increased with increasing temperature, allowing for the analyses of H⁺ and H^- transfers using Eyring and Arrhenius formalisms. Temperature-independent KIE on the k_lim1 value (^H2Ok_lim1/^D2Ok_lim1) suggests that proton transfer occurs within a highly reorganized tunneling-ready-state with a narrow distribution of donor-acceptor distances. Eyring analysis of the k_lim2 value gave lines with the slope_(choline)>slope_(D-choline), suggesting kinetic complexity. Spectral evidence for the transient occurrence of a covalent flavin-substrate adduct during the first phase of the anaerobic reaction of S101A CHO with choline is presented, supporting the notion that an important role of amino acid residues in the active site of flavin-dependent enzymes is to eliminate alternative reactions of the versatile enzyme-bound flavin for the reaction that needs to be catalyzed.

The role of the Met20 loop in the hydride transfer in Escherichia coli dihydrofolate reductase

A key question concerning the catalytic cycle of Escherichia coli dihydrofolate reductase (ecDHFR) is whether the Met²⁰ loop is dynamically coupled to the chemical step during catalysis. A more basic, yet unanswered question is whether the Met²⁰ loop adopts a closed conformation during the chemical hydride transfer step. To examine the most likely conformation of the Met²⁰ loop during the chemical step, we studied the hydride transfer in wild type (WT) ecDHFR using hybrid quantum mechanics-molecular mechanics free energy simulations with the Met²⁰ loop in a closed and disordered conformation. Additionally, we investigated three mutant forms (I14X; X = Val, Ala, Gly) of the enzyme that have increased active site flexibility and donor-acceptor distance dynamics in closed and disordered Met²⁰ loop states. We found that the conformation of the Met²⁰ loop has a dramatic effect on the ordering of active site hydration, although the Met²⁰ loop conformation only has a moderate effect on the hydride transfer rate and donor-acceptor distance dynamics. Finally, we evaluated the pK_a of the substrate N5 position in closed and disordered Met²⁰ loop states and found a strong correlation between N5 basicity and the conformation of the Met²⁰ loop.

Enhanced Rigidification within a Double Mutant of Soybean Lipoxygenase Provides Experimental Support for Vibronically Nonadiabatic Proton-Coupled Electron Transfer Models

Soybean lipoxygenase (SLO) is a prototype for nonadiabatic hydrogen tunneling reactions and, as such, has served as the subject of numerous theoretical studies. In this work, we report a nearly temperature-independent kinetic isotope effect (KIE) with an average KIE value of 661 ± 27 for a double mutant (DM) of SLO at six temperatures. The data are well-reproduced within a vibronically nonadiabatic proton-coupled electron transfer model in which the active site has become rigidified compared to wild-type enzyme and single-site mutants. A combined temperature-pressure perturbation further shows that temperature-dependent global motions within DM-SLO are more resistant to perturbation by elevated pressure. These findings provide strong experimental support for the model of hydrogen tunneling in SLO, where optimization of both local protein and ligand motions and distal conformational rearrangements is a prerequisite for effective proton vibrational wave function overlap between the substrate and the active-site iron cofactor.

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.

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.

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.

Oscillatory Enzyme Dynamics Revealed by Two-Dimensional Infrared Spectroscopy

Enzymes move on a variety of length and time scales. While much is known about large structural fluctuations that impact binding of the substrates and release of products, little is known about faster motions of enzymes and how these motions may influence enzyme-catalyzed reactions. This Letter reports frequency fluctuations of the azide anion bound to the active site of formate dehydrogenase measured via 2D IR spectroscopy. These measurements reveal an underdamped oscillatory component to the frequency-frequency correlation function when the azide is bound to the NAD(+) ternary complex. This oscillation disappears when the reduced cofactor is added, indicating that the oscillating contributions most likely come from the charged nicotinamide ring. These oscillatory motions may be relevant to donor-acceptor distance sampling of the catalyzed hydride transfer and therefore may give future insights into the dynamic behavior involved in enzyme catalysis.

Structural and Kinetic Studies of Formate Dehydrogenase from Candida boidinii

The structure of formate dehydrogenase from Candida boidinii (CbFDH) is of both academic and practical interests. First, this enzyme represents a unique model system for studies on the role of protein dynamics in catalysis, but so far these studies have been limited by the availability of structural information. Second, CbFDH and its mutants can be used in various industrial applications (e.g., CO2 fixation or nicotinamide recycling systems), and the lack of structural information has been a limiting factor in commercial development. Here, we report the crystallization and structural determination of both holo- and apo-CbFDH. The free-energy barrier for the catalyzed reaction was computed and indicates that this structure indeed represents a catalytically competent form of the enzyme. Complementing kinetic examinations demonstrate that the recombinant CbFDH has a well-organized reactive state. Finally, a fortuitous observation has been made: the apoenzyme crystal was obtained under cocrystallization conditions with a saturating concentration of both the cofactor (NAD(+)) and inhibitor (azide), which has a nanomolar dissociation constant. It was found that the fraction of the apoenzyme present in the solution is less than 1.7 × 10(-7) (i.e., the solution is 99.9999% holoenzyme). This is an extreme case where the crystal structure represents an insignificant fraction of the enzyme in solution, and a mechanism rationalizing this phenomenon is presented.

Minimization of dynamic effects in the evolution of dihydrofolate reductase

Protein isotope labeling is a powerful technique to probe functionally important motions in enzyme catalysis and can be applied to investigate the conformational dynamics of proteins. Previous investigations have indicated that dynamic coupling is detrimental to catalysis by dihydrofolate reductase (DHFR) from the mesophile Escherichia coli (EcDHFR). Comparison of DHFRs from organisms adapted to survive at a wide range of temperatures suggests that dynamic coupling in DHFR catalysis has been minimized during evolution; it arises from reorganizational motions needed to facilitate charge transfer events. Contrary to the behaviour observed for the DHFR from the moderate thermophile Geobacillus stearothermophilus (BsDHFR), the chemical transformation catalyzed by the cold-adapted bacterium Moritella profunda (MpDHFR) is only weakly affected by protein isotope substitutions at low temperatures, but the isotopically substituted enzyme is a substantially inferior catalyst at higher, non-physiological temperatures. QM/MM studies revealed that this behaviour is caused by the enzyme's structural sensitivity to temperature changes, which enhances unfavorable dynamic coupling at higher temperatures by promoting additional recrossing trajectories on the transition state dividing surface. We postulate that these motions are minimized by fine-tuning DHFR flexibility through optimization of the free energy surface of the reaction, such that a nearly static reaction-ready configuration with optimal electrostatic properties is maintained under physiological conditions.