Transition state theory can be used in studies of enzyme catalysis: lessons from simulations of tunnelling and dynamical effects in lipoxygenase and other systems

The idea that enzyme catalysis involves special factors such as coherent fluctuations, quantum mechanical tunnelling and non-equilibrium solvation (NES) effects has gained popularity in recent years. It has also been suggested that transition state theory (TST) cannot be used in studies of enzyme catalysis. The present work uses reliable state of the art simulation approaches to examine the above ideas. We start by demonstrating that we are able to simulate any of the present catalytic proposals using the empirical valence bond (EVB) potential energy surfaces, the dispersed polaron model and the quantized classical path (QCP) approach, as well as the approximate vibronic method. These approaches do not treat the catalytic effects by phenomenological treatments and thus can be considered as first principles approaches (at least their ability to compare enzymatic reaction to the corresponding solution reactions). This work will consider the lipoxygenase reaction, and to lesser extent other enzymes, for specific demonstration. It will be pointed out that our study of the lipoxygenase reaction reproduces the very large observed isotope effect and the observed rate constant while obtaining no catalytic contribution from nuclear quantum mechanical (NQM) effects. Furthermore, it will be clarified that our studies established that the NQM effect decreases rather than increases when the donor-acceptor distance is compressed. The consequences of these findings in terms of the temperature dependence of the kinetic isotope effect and in terms of different catalytic proposals will be discussed. This paper will also consider briefly the dynamical effects and conclude that such effects do not contribute in a significant way to enzyme catalysis. Furthermore, it will be pointed out that, in contrast to recent suggestions, NES effects are not dynamical effects and should therefore be part of the activation free energy rather than the transmission factor. In view of findings of the present work and our earlier works, it seems that TST provides a quantitative tool for studies of enzyme catalysis and that the key open questions are related to the nature of the factors that lead to transition state stabilization.     

Computer simulation of primary kinetic isotope effects in the proposed rate-limiting step of the glyoxalase I catalyzed reaction

The proposed rate-limiting step of the glyoxalase I catalyzed reaction is the proton abstraction from the C1 carbon of the substrate by Glu(172). Here we examine primary kinetic isotope effects and the influence of quantum dynamics on this process by computer simulations. The calculations utilize the empirical valence bond method in combination with the molecular dynamics free energy perturbation technique and path integral simulations. For the enzyme-catalyzed reaction a H/D kinetic isotope effect of 5.0 +/- 1. 3 is predicted in reasonable agreement with the experimental result of about 3. Furthermore, the magnitude of quantum mechanical effects is found to be very similar for the enzyme reaction and the corresponding uncatalyzed process in solution, in agreement with other studies. The problems associated with attaining the required accuracy in order for the present approach to be useful as a diagnostic tool for the study of enzyme reactions are also discussed.     

Environmentally coupled hydrogen tunneling. Linking catalysis to dynamics.

Many biological C-H activation reactions exhibit nonclassical kinetic isotope effects (KIEs). These nonclassical KIEs are too large (kH/kD > 7) and/or exhibit unusual temperature dependence such that the Arrhenius prefactor KIEs (AH/AD) fall outside of the semiclassical range near unity. The focus of this minireview is to discuss such KIEs within the context of the environmentally coupled hydrogen tunneling model. Full tunneling models of hydrogen transfer assume that protein or solvent fluctuations generate a reactive configuration along the classical, heavy-atom coordinate, from which the hydrogen transfers via nuclear tunneling. Environmentally coupled tunneling also invokes an environmental vibration (gating) that modulates the tunneling barrier, leading to a temperature-dependent KIE. These properties directly link enzyme fluctuations to the reaction coordinate for hydrogen transfer, making a quantum view of hydrogen transfer necessarily a dynamic view of catalysis. The environmentally coupled hydrogen tunneling model leads to a range of magnitudes of KIEs, which reflect the tunneling barrier, and a range of AH/AD values, which reflect the extent to which gating modulates hydrogen transfer. Gating is the primary determinant of the temperature dependence of the KIE within this model, providing insight into the importance of this motion in modulating the reaction coordinate. The potential use of variable temperature KIEs as a direct probe of coupling between environmental dynamics and the reaction coordinate is described. The evolution from application of a tunneling correction to a full tunneling model in enzymatic H transfer reactions is discussed in the context of a thermophilic alcohol dehydrogenase and soybean lipoxygenase-1.     

H-tunneling in the multiple H-transfers of the catalytic cycle of morphinone reductase and in the reductive half-reaction of the homologous pentaerythritol tetranitrate reductase

The mechanism of flavin reduction in morphinone reductase (MR) and pentaerythritol tetranitrate (PETN) reductase, and flavin oxidation in MR, has been studied by stopped-flow and steady-state kinetic methods. The temperature dependence of the primary kinetic isotope effect for flavin reduction in MR and PETN reductase by nicotinamide coenzyme indicates that quantum mechanical tunneling plays a major role in hydride transfer. In PETN reductase, the kinetic isotope effect (KIE) is essentially independent of temperature in the experimentally accessible range, contrasting with strongly temperature-dependent reaction rates, consistent with a tunneling mechanism from the vibrational ground state of the reactive C-H/D bond. In MR, both the reaction rates and the KIE are dependent on temperature, and analysis using the Eyring equation suggests that hydride transfer has a major tunneling component, which, unlike PETN reductase, is gated by thermally induced vibrations in the protein. The oxidative half-reaction of MR is fully rate-limiting in steady-state turnover with the substrate 2-cyclohexenone and NADH at saturating concentrations. The KIE for hydride transfer from reduced flavin to the alpha/beta unsaturated bond of 2-cyclohexenone is independent of temperature, contrasting with strongly temperature-dependent reaction rates, again consistent with ground-state tunneling. A large solvent isotope effect (SIE) accompanies the oxidative half-reaction, which is also independent of temperature in the experimentally accessible range. Double isotope effects indicate that hydride transfer from the flavin N5 atom to 2-cyclohexenone, and the protonation of 2-cyclohexenone, are concerted and both the temperature-independent KIE and SIE suggest that this reaction also proceeds by ground-state quantum tunneling. Our results demonstrate the importance of quantum tunneling in the reduction of flavins by nicotinamide coenzymes. This is the first observation of (i) three H-nuclei in an enzymic reaction being transferred by tunneling and (ii) the utilization of both passive and active dynamics within the same native enzyme.     

Quantum catalysis in B12-dependent methylmalonyl-CoA mutase: experimental and computational insights

B12-dependent methylmalonyl-CoA mutase catalyses the interchange of a hydrogen atom and the carbonyl-CoA group on adjacent carbons of methylmalonyl-CoA to give the rearranged product, succinyl-CoA. The first step in this reaction involves the transient generation of cofactor radicals by homolytic rupture of the cobalt-carbon bond to generate the deoxyadenosyl radical and cob(II)alamin. This step exhibits a curious sensitivity to isotopic substitution in the substrate, methylmalonyl-CoA, which has been interpreted as evidence for kinetic coupling. The magnitude of the isotopic discrimination is large and a deuterium isotope effect ranging from 35.6 at 20 degrees C to 49.9 at 5 degrees C has been recorded. Arrhenius analysis of the temperature dependence of this isotope effect provides evidence for quantum tunnelling in this hydrogen transfer step. The mechanistic complexity of the observed rate constant for cobalt-carbon bond homolysis together with the spectroscopically silent nature of many of the component steps limits the insights that can be derived by experimental approaches alone. Computational studies using a newly developed geometry optimization scheme that allows determination of the transition state in the full quantum mechanical/molecular mechanical coordinate space have yielded novel insights into the strategy deployed for labilizing the cobalt-carbon bond and poising the resulting deoxyadenosyl radical for subsequent hydrogen atom abstraction.     

Vibrationally enhanced hydrogen tunneling in the Escherichia coli thymidylate synthase catalyzed reaction

The enzyme thymidylate synthase (TS) catalyzes a complex reaction that involves forming and breaking at least six covalent bonds. The physical nature of the hydride transfer step in this complex reaction cascade has been studied by means of isotope effects and their temperature dependence. Competitive kinetic isotope effects (KIEs) on the second-order rate constant (V/K) were measured over a temperature range of 5-45 degrees C. The observed H/T ((T)V/K(H)) and D/T ((T)V/K(D)) KIEs were used to calculate the intrinsic KIEs throughout the temperature range. The Swain-Schaad relationships between the H/T and D/T V/K KIEs revealed that the hydride transfer step is the rate-determining step at the physiological temperature of Escherichia coli (20-30 degrees C) but is only partly rate-determining at elevated and reduced temperatures. H/D KIE on the first-order rate constant k(cat) ((D)k = 3.72) has been previously reported [Spencer et al. (1997) Biochemistry 36, 4212-4222]. Additionally, the Swain-Schaad relationships between that (D)k and the V/K KIEs reported here suggested that at 20 degrees C the hydride transfer step is the rate-determining step for both rate constants. Intrinsic KIEs were calculated here and were found to be virtually temperature independent (DeltaE(a) = 0 within experimental error). The isotope effects on the preexponential Arrhenius factors for the intrinsic KIEs were A(H)/A(T) = 6.8 +/- 2.8 and A(D)/A(T) = 1.9 +/- 0.25. Both effects are significantly above the semiclassical (no-tunneling) predicted values and indicate a contribution of quantum mechanical tunneling to this hydride transfer reaction. Tunneling correction to transition state theory would predict that these isotope effects on activation parameters result from no energy of activation for all isotopes. Yet, initial velocity measurements over the same temperature range indicate cofactor inhibition and result in significant activation energy on k(cat) (4.0 +/- 0.1 kcal/mol). Taken together, the temperature-independent KIEs, the large isotope effects on the preexponential Arrhenius factors, and a significant energy of activation all suggest vibrationally enhanced hydride tunneling in the TS-catalyzed reaction.     

Hydrogen tunnelling in enzyme-catalysed H-transfer reactions: flavoprotein and quinoprotein systems

It is now widely accepted that enzyme-catalysed C-H bond breakage occurs by quantum mechanical tunnelling. This paradigm shift in the conceptual framework for these reactions away from semi-classical transition state theory (TST, i.e. including zero-point energy, but with no tunnelling correction) has been driven over the recent years by experimental studies of the temperature dependence of kinetic isotope effects (KIEs) for these reactions in a range of enzymes, including the tryptophan tryptophylquinone-dependent enzymes such as methylamine dehydrogenase and aromatic amine dehydrogenase, and the flavoenzymes such as morphinone reductase and pentaerythritol tetranitrate reductase, which produced observations that are also inconsistent with the simple Bell-correction model of tunnelling. However, these data-especially, the strong temperature dependence of reaction rates and the variable temperature dependence of KIEs-are consistent with other tunnelling models (termed full tunnelling models), in which protein and/or substrate fluctuations generate a configuration compatible with tunnelling. These models accommodate substrate/protein (environment) fluctuations required to attain a configuration with degenerate nuclear quantum states and, when necessary, motion required to increase the probability of tunnelling in these states. Furthermore, tunnelling mechanisms in enzymes are supported by atomistic computational studies performed within the framework of modern TST, which incorporates quantum nuclear effects.     

Hydrogen tunneling in quinoproteins

It is now widely accepted that substrate C-H bond breakage by quinoprotein enzymes occurs by quantum mechanical tunneling. This paradigm shift in the conceptual framework for these reactions away from semi-classical transition state theory (i.e., including zero-point energy but with no tunneling correction) has been driven over recent years by experimental studies of the temperature dependence of kinetic isotope effects for these reactions in the TTQ-dependent enzymes methylamine dehydrogenase and aromatic amine dehydrogenase, which produced observations also inconsistent with the simple Bell correction model of tunneling. However, these data-specifically, the strong temperature dependence of reaction rates and the variable temperature dependence of kinetic isotope effects-are consistent with other tunneling models (denoted full tunneling models) in which protein and/or substrate fluctuations generate a configuration compatible with tunneling. These models accommodate substrate/protein (environment) fluctuations required to attain a configuration with degenerate quantum states and, when necessary, motion required to increase the probability of tunneling in these states. Furthermore, tunneling mechanisms in quinoproteins are supported by computational studies employing variational transition state theory with multidimensional tunneling corrections; these studies are also discussed in this review. Potential pitfalls in analyzing the temperature dependence of kinetic isotope effects as probes of tunneling are also discussed with reference to PQQ-dependent methanol dehydrogenase.     

Nature of hydrogen transfer in soybean lipoxygenase 1: separation of primary and secondary isotope effects

Previous measurements of the kinetics of oxidation of linoleic acid by soybean lipoxygenase 1 have indicated very large deuterium isotope effects, but have not been able to distinguish the primary isotope effect from the alpha-secondary effect. To address this question, singly deuterated linoleic acid was prepared, and enantiomerically resolved using the enzyme itself. Noncompetitive measurements of the primary deuterium isotope effect give a value of ca. 40 which is temperature-independent. The enthalpy of activation is low and isotope-independent, and there is a large isotope effect on the Arrhenius prefactor. A very large apparent secondary isotope effect (ca. 2.1) is measured with deuterium in the primary position, but a greatly reduced value (1.1) is observed with protium in the primary position. Mutagenesis of the active site leads to a significant reduction in k(cat) and perturbed isotope effects, in particular, a secondary effect of 5.6 when deuterium is in the primary position. The anomalous secondary isotope effects are shown to arise from imperfect stereoselectivity of hydrogen abstraction which, for the mutant, is attributed to a combination of inverse substrate binding and increased flexibility at the reactive carbon. After correction, a very large primary (76-84) and small secondary (1.1-1.2) kinetic isotope effects are calculated for both mutant and wild-type enzymes. The weight of the evidence is taken to favor hydrogen tunneling as the primary mechanism of hydrogen transfer.     

The role of tunneling in enzyme catalysis of C-H activation

Recent data from studies of enzyme catalyzed hydrogen transfer reactions implicate a new theoretical context in which to understand C-H activation. This is much closer to the Marcus theory of electron transfer, in that environmental factors influence the probability of effective wave function overlap from donor to acceptor atoms. The larger size of hydrogen and the availability of three isotopes (H, D and T) introduce a dimension to the kinetic analysis that is not available for electron transfer. This concerns the role of gating between donor and acceptor atoms, in particular whether the system in question is able to tune distance between reactants to achieve maximal tunneling efficiency. Analysis of enzyme systems is providing increasing evidence of a role for active site residues in optimizing the inter-nuclear distance for nuclear tunneling. The ease with which this optimization can be perturbed, through site-specific mutagenesis or an alteration in reaction conditions, is also readily apparent from an analysis of the changes in the temperature dependence of hydrogen isotope effects.     

The role of tunneling in enzyme catalysis of C-H activation

Recent data from studies of enzyme catalyzed hydrogen transfer reactions implicate a new theoretical context in which to understand C-H activation. This is much closer to the Marcus theory of electron transfer, in that environmental factors influence the probability of effective wave function overlap from donor to acceptor atoms. The larger size of hydrogen and the availability of three isotopes (H, D and T) introduce a dimension to the kinetic analysis that is not available for electron transfer. This concerns the role of gating between donor and acceptor atoms, in particular whether the system in question is able to tune distance between reactants to achieve maximal tunneling efficiency. Analysis of enzyme systems is providing increasing evidence of a role for active site residues in optimizing the inter-nuclear distance for nuclear tunneling. The ease with which this optimization can be perturbed, through site-specific mutagenesis or an alteration in reaction conditions, is also readily apparent from an analysis of the changes in the temperature dependence of hydrogen isotope effects.     

Three applications of path integrals: equilibrium and kinetic isotope effects, and the temperature dependence of the rate constant of the [1,5] sigmatropic hydrogen shift in (Z)-1,3-pentadiene

Recent experiments have confirmed the importance of nuclear quantum effects even in large biomolecules at physiological temperature. Here we describe how the path integral formalism can be used to describe rigorously the nuclear quantum effects on equilibrium and kinetic properties of molecules. Specifically, we explain how path integrals can be employed to evaluate the equilibrium (EIE) and kinetic (KIE) isotope effects, and the temperature dependence of the rate constant. The methodology is applied to the [1,5] sigmatropic hydrogen shift in pentadiene. Both the KIE and the temperature dependence of the rate constant confirm the importance of tunneling and other nuclear quantum effects as well as of the anharmonicity of the potential energy surface. Moreover, previous results on the KIE were improved by using a combination of a high level electronic structure calculation within the harmonic approximation with a path integral anharmonicity correction using a lower level method.     

Incorporation of hydrostatic pressure into models of hydrogen tunneling highlights a role for pressure-modulated promoting vibrations

Hydrostatic pressure offers an alternative to temperature as an experimental probe of hydrogen-transfer reactions. H tunneling reactions have been shown to exhibit kinetic isotope effects (KIEs) that are sensitive to pressure, and environmentally coupled H tunneling reactions, those reactions in which H transfer is coupled to atomic fluctuations (a promoting vibration) along the reaction coordinate, often have quite temperature-dependent KIEs. We present here a theoretical treatment of the combined effect of temperature and pressure on environmentally coupled H tunneling reactions. We develop a generalized expression for the KIE, which can be used as a simple fitting function for combined experimental temperature- and pressure-dependent KIE data sets. With this expression, we are able to extract information about the pressure dependence of both the apparent tunneling distance and the frequency of the promoting vibration. The KIE expression is tested on two data sets {the reduction of chloranil by leuco crystal violet [Isaacs, N. S., Javaid, K., and Rannala, E. (1998) J. Chem. Soc., Perkin Trans. 2, 709-711] and the reduction of morphinone reductase by NADH [Hay, S., Sutcliffe, M. J., and Scrutton, N. S. (2007) Proc. Natl. Acad. Sci. U.S.A. 104, 507-512]} and suggests that hydrostatic pressure is a sensitive probe of nuclear quantum mechanical effects in H-transfer reactions.     

The action of soybean lipoxygenase-1 on 12-iodo-cis-9-octadecenoic acid: the importance of C11-H bond breaking

Previous work has demonstrated that the ferric form of soybean lipoxygenase-1 will catalyze an elimination reaction on 12-iodo-cis-9-octadecenoic acid (12-IODE) to produce 9, 11-octadecadienoic acid and iodide ion. Elimination is accompanied by irreversible inactivation of the enzyme on 1 out of 10 turnovers. In the present work, 11,11-dideuterio-12-IODE (D(2)-12-IODE) was synthesized and used to demonstrate that both the elimination reaction and inactivation of the enzyme exhibit very large kinetic isotope effects. The rates with the deuterated compound are so low that the isotope effects are difficult to quantify, but they appear to be comparable to the isotope effects previously observed for the normal reaction catalyzed by lipoxygenase and much larger than can be explained by zero-point energy considerations. ESR spectroscopy was used to demonstrate that 12-IODE can reduce ferric lipoxygenase to the ferrous form, and a large isotope effect on this process was observed with D(2)-12-IODE. It is proposed that the pathway leading to reduction and inactivation by 12-IODE is initiated by homolytic cleavage of the C(11)-H bond. Elimination could be initiated either by homolytic or by heterolytic cleavage of this bond. The results suggest that very large isotope effects may be a general feature of C-H bond cleavages catalyzed by this enzyme.     

An internal equilibrium preorganizes the enzyme-substrate complex for hydride tunneling in choline oxidase

The hydride transfer reaction catalyzed by choline oxidase under irreversible regime, i.e., at saturating oxygen, was shown in a recent study to occur quantum mechanically within a highly preorganized active site, with the reactive configuration for hydride tunneling being minimally affected by environmental vibrations of the reaction coordinate other than those affecting the distance between the alpha-carbon of the choline alkoxide substrate and the N(5) atom of the enzyme-bound flavin cofactor [Fan, F., and Gadda, G. (2005) J. Am. Chem. Soc. 127, 17954-17961]. In this study, we have determined the effects of pH and temperature on the substrate kinetic isotope effects with 1,2-[2H4]choline as substrate for choline oxidase at 0.2 mM oxygen to gain insights on the mechanism of hydride transfer under reversible catalytic regime. The data presented indicated that the kinetic complexity arising from the net flux through the reverse of the hydride transfer step changed with temperature, with the hydride transfer reaction becoming more reversible with increasing temperatures. After this kinetic complexity was accounted for, analyses of the kcat/Km and D(kcat/Km) values determined at 0.2 mM according to the Eyring and Arrhenius formalisms suggested that the quantum mechanical nature of the hydride transfer reaction is, not surprisingly, maintained during enzymatic catalysis under reversible regime. A comparison of the thermodynamic and kinetic parameters of the hydride transfer reaction under reversible and irreversible catalytic regimes showed that the enthalpies of activation (DeltaH++) were significantly larger in the reversible catalytic regime. This reflects the presence of an enthalpically unfavorable internal equilibrium of the enzyme-substrate Michaelis complex occurring prior to, and independently from, CH bond cleavage. Such an internal equilibrium is required to preorganize the enzyme-substrate complex for efficient quantum mechanical tunneling of the hydride ion from the substrate alpha-carbon to the flavin N(5) atom.     

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

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

Enzymatic H-transfer requires vibration-driven extreme tunneling

Enzymatic breakage of the substrate C-H bond by Methylophilus methyltrophus (sp. W3A1) methylamine dehydrogenase (MADH) has been studied by stopped-flow spectroscopy. The rate of reduction of the tryptophan tryptophylquinone (TTQ) cofactor has a large kinetic isotope effect (KIE = 16.8 +/- 0.5), and the KIE is independent of temperature. Analysis of the temperature dependence of C-H bond breakage revealed that extreme (ground state) quantum tunneling is responsible for the transfer of the hydrogen nucleus. Reaction rates are strongly dependent on temperature, indicating thermally induced, vibrational motion drives the H-transfer reaction. The data provide direct experimental evidence for enzymatic bond breakage by extreme tunneling driven by vibrational motion of the protein scaffold. The results demonstrate that classical transition state theory and its tunneling derivatives do not adequately describe this enzymatic reaction.     

Dual role of oxygen during lipoxygenase reactions

Studying the oxygenation kinetics of (19R/S,5Z,8Z,11Z,14Z)-19-hydroxyeicosa-5,8,11,14-tetraenoic acid (19-OH-AA) by rabbit 15-lipoxygenase-1 we observed a pronounced oxygen dependence of the reaction rate, which was not apparent with arachidonic acid as substrate. Moreover, we found that peroxide-dependent activation of the lipoxygenase depended strongly on the oxygen concentration. These data can be described with a kinetic model that extends previous schemes of the lipoxygenase reaction in three essential aspects: (a) the product of 19-OH-AA oxygenation is a less effective lipoxygenase activator than (13S,9Z,11E)-13-hydroperoxyoctadeca-9,11-dienoic acid; (b) molecular dioxygen serves not only as a lipoxygenase substrate, but also impacts peroxide-dependent enzyme activation; (c) there is a leakage of radical intermediates from the catalytic cycle, which leads to the formation of inactive ferrous lipoxygenase. This enzyme inactivation can be reversed by another round of peroxide-dependent activation. Taken together our data indicate that both peroxide activation and the oxygen affinity of lipoxygenases depend strongly on the chemistry of the lipid substrate. These findings are of biological relevance as variations of the reaction conditions may turn the lipoxygenase reaction into an efficient source of free radicals.     

Reaction-path energetics and kinetics of the hydride transfer reaction catalyzed by dihydrofolate reductase

We have studied the hydride transfer reaction catalyzed by the enzyme dihydrofolate reductase (DHFR) and the coenzyme nicotinamide adenine dinucleotide phosphate (NADPH); the substrate is 5-protonated 7,8-dihydrofolate, and the product is tetrahydrofolate. The potential energy surface is modeled by a combined quantum mechanical-molecular mechanical (QM/MM) method employing Austin model 1 (AM1) and a simple valence bond potential for 69 QM atoms and employing the CHARMM22 and TIP3P molecular mechanics force fields for the other 21 399 atoms; the QM and MM regions are joined by two boundary atoms treated by the generalized hybrid orbital (GHO) method. All simulations are carried out using periodic boundary conditions at neutral pH and 298 K. In stage 1, a reaction coordinate is defined as the difference between the breaking and forming bond distances to the hydride ion, and a quasithermodynamic free energy profile is calculated along this reaction coordinate. This calculation includes quantization effects on bound vibrations but not on the reaction coordinate, and it is used to locate the variational transition state that defines a transition state ensemble. Then, the key interactions at the reactant, variational transition state, and product are analyzed in terms of both bond distances and electrostatic energies. The results of both analyses support the conclusion derived from previous mutational studies that the M20 loop of DHFR makes an important contribution to the electrostatic stabilization of the hydride transfer transition state. Third, transmission coefficients (including recrossing factors and multidimensional tunneling) are calculated and averaged over the transition state ensemble. These averaged transmission coefficients, combined with the quasithermodynamic free energy profile determined in stage 1, allow us to calculate rate constants, phenomenological free energies of activation, and primary and secondary kinetic isotope effects. A primary kinetic isotope effect (KIE) of 2.8 has been obtained, in good agreement with the experimentally determined value of 3.0 and with the value 3.2 calculated previously. The primary KIE is mainly a consequence of the quantization of bound vibrations. In contrast, the secondary KIE, with a value of 1.13, is almost entirely due to dynamical effects on the reaction coordinate, especially tunneling.     

A quantum mechanics/molecular mechanics study of the catalytic mechanism of the thymidylate synthase

A theoretical study of the molecular mechanism of the thymidylate synthase-catalyzed reaction has been carried out using hybrid quantum mechanics/molecular mechanics methods. We have examined all of the stationary points (reactants, intermediates, transition structures, and products) on the multidimensional potential energy surfaces for the multistep enzymatic process. The characterization of these relevant structures facilitates the gaining of insight into the role of the different residues in the active site. Furthermore, analysis of the full energy profile has revealed that the step corresponding to the reduction of the exocyclic methylene intermediate by hydride transfer from the 6S position of 5,6,7,8-tetrahydrofolate (H4folate), forming dTMP and 7,8-dihydrofolate (H2folate), is the rate-limiting step, in accordance with the experimental data. In this step, the hydride transfer and the scission of an overall conserved active site cysteine residue (Cys146 in Escherichia coli) take place in a concerted but very asynchronous way. These findings have also been tested with primary and secondary deuterium, tritium, and sulfur kinetic isotope effects, and the calculations have been compared to experimental data. Finally, the incorporation of high-level quantum mechanical corrections to the semiempirical AM1 Hamiltonian into our hybrid scheme has allowed us to obtain reasonable values of the energy barrier for the rate-limiting step. The resulting picture of the complete multistep enzyme mechanism that is obtained reveals several new features of substantial mechanistic interest.