Pressure effects on enzyme-catalyzed quantum tunneling events arise from protein-specific structural and dynamic changes

The rate and kinetic isotope effect (KIE) on proton transfer during the aromatic amine dehydrogenase-catalyzed reaction with phenylethylamine shows complex pressure and temperature dependences. We are able to rationalize these effects within an environmentally coupled tunneling model based on constant pressure molecular dynamics (MD) simulations. As pressure appears to act anisotropically on the enzyme, perturbation of the reaction coordinate (donor-acceptor compression) is, in this case, marginal. Therefore, while we have previously demonstrated that pressure and temperature dependences can be used to infer H-tunneling and the involvement of promoting vibrations, these effects should not be used in the absence of atomistic insight, as they can vary greatly for different enzymes. We show that a pressure-dependent KIE is not a definitive hallmark of quantum mechanical H-tunneling during an enzyme-catalyzed reaction and that pressure-independent KIEs cannot be used to exclude tunneling contributions or a role for promoting vibrations in the enzyme-catalyzed reaction. We conclude that coupling of MD calculations with experimental rate and KIE studies is required to provide atomistic understanding of pressure effects in enzyme-catalyzed reactions.     

Analysis of classical and quantum paths for deprotonation of methylamine by methylamine dehydrogenase.

The hydrogen-transfer reaction catalysed by methylamine dehydrogenase (MADH) with methylamine (MA) as substrate is a good model system for studies of proton tunnelling in enzyme reactions--an area of great current interest--for which atomistic simulations will be vital. Here, we present a detailed analysis of the key deprotonation step of the MADH/MA reaction and compare the results with experimental observations. Moreover, we compare this reaction with the related aromatic amine dehydrogenase (AADH) reaction with tryptamine, recently studied by us, and identify possible causes for the differences observed in the measured kinetic isotope effects (KIEs) of the two systems. We have used combined quantum mechanics/molecular mechanics (QM/MM) techniques in molecular dynamics simulations and variational transition state theory with multidimensional tunnelling calculations averaged over an ensemble of paths. The results reveal important mechanistic complexity. We calculate activation barriers and KIEs for the two possible proton transfers identified-to either of the carboxylate oxygen atoms of the catalytic base (Asp428beta)-and analyse the contributions of quantum effects. The activation barriers and tunnelling contributions for the two possible proton transfers are similar and lead to a phenomenological activation free energy of 16.5+/-0.9 kcal mol(-1) for transfer to either oxygen (PM3-CHARMM calculations applying PM3-SRP specific reaction parameters), in good agreement with the experimental value of 14.4 kcal mol(-1). In contrast, for the AADH system, transfer to the equivalent OD1 was found to be preferred. The structures of the enzyme complexes during reaction are analysed in detail. The hydrogen bond of Thr474beta(MADH)/Thr172beta(AADH) to the catalytic carboxylate group and the nonconserved active site residue Tyr471beta(MADH)/Phe169beta(AADH) are identified as important factors in determining the preferred oxygen acceptor. The protein environment has a significant effect on the reaction energetics and hence on tunnelling contributions and KIEs. These environmental effects, and the related clearly different preferences for the two carboxylate oxygen atoms (with different KIEs) in MADH/MA and AADH/tryptamine, are possible causes of the differences observed in the KIEs between these two important enzyme reactions.     

Interpretation of the gas-phase solvent deuterium kinetic isotope effects in the S(N)2 reaction mechanism: Comparison of theoretical and experimental results in the reaction of microsolvated fluoride ions with methyl halides

We carried out a comprehensive ab initio calculation and transition-state theory analysis of the solvent and secondary deuterium kinetic isotope effects in the SN2 reactions of microsolvated fluoride ions with methyl halides. Water, methanol, and hydrogen fluoride were used as solvents, and the results are compared with recent experiments. Kinetic isotope effects were dissected into contributions from translations, rotations, and different vibration modes, and the validity of such analysis is also discussed. Excellent agreement was found for some reactions, whereas the agreement was poor for other reactions. We showed that the deviation between theory and experiments is related to the reaction kinetics; a faster reaction produced a kinetic isotope effect that was systematically larger (less inverse) than the calculated value. In addition, we also found that the magnitude of the deviation is proportional to the reaction efficiency. We rationalize the disagreement as a failure of the transition-state theory to model barrierless reactions, and we propose a very simple scheme to interpret these findings and predict the deviation between experimental and theoretical values in those reactions.     

Quantum effects in ab-initio calculations of rate constants for chemical reactions occuring in the condensed phase

An overview of recent advances in the development of methods designed to calculate rate constants for chemical reactions obeying mass action kinetic equations in condensed phases is presented. A general framework addressing mixed quantum-classical systems is elaborated that enables quantum features such as tunneling effects, zero-point vibrations, dynamic quantum coherence, and non-adiabatic effects to be calculated. An efficient Monte Carlo sampling method for performing ab-initio calculations of rate constants and isotope effects in chemical processes in condensed phases is outlined, and the connection of isotope effects to reaction mechanism is explored     

A computational study of the intramolecular deprotonation of a carbon acid in aqueous solution

Proton transfer reactions are the rate-limiting steps in many biological and synthetic chemical processes, often requiring complex cofactors or catalysts to overcome the generally unfavourable thermodynamic process of carbanion intermediate formation. It has been suggested that quantum tunnelling processes enhance the kinetics of some of these reactions, which when coupled to protein motions may be an important consideration for enzyme catalysis. To obtain a better fundamental and quantitative understanding of these proton transfer mechanisms, a computational analysis of the intramolecular proton transfer from a carbon acid in the small molecule, 4-nitropentanoic acid, in aqueous solution is presented. Potential-energy surfaces from gas-phase, implicit and QM/MM (quantum mechanical/molecular mechanical) explicit solvation quantum chemistry models are compared, and the potential of mean force, for the full reaction coordinate, using umbrella-sampling molecular dynamics is analysed. Semi-classical multidimensional tunnelling corrections are also used to estimate the quantum tunnelling contributions and to understand the origin of the primary deuterium kinetic isotope effects (KIEs). The computational results are found to be in excellent agreement with the KIEs and the energetics obtained experimentally.     

Simulations of the large kinetic isotope effect and the temperature dependence of the hydrogen atom transfer in lipoxygenase

Elucidating the role of nuclear quantum mechanical (NQM) effects in enzyme catalysis is a topic of significant current interest. Despite the great experimental progress in this field it is important to have theoretical approaches capable of evaluating and analyzing nuclear quantum mechanical contributions to catalysis. In this study, we use the catalytic reaction of lipoxygenase, which is characterized by an extremely large kinetic isotope effect, as a challenging test case for our simulation approach. This is done by applying the quantum classical path (QCP) method with an empirical valence bond potential energy surface. Our computational strategy evaluates the relevant NQM corrections and reproduces the large observed kinetic isotope effect and the temperature dependence of the H atom transfer reaction while being less successful with the D atom transfer reaction. However, the main point of our study is not so much to explore the temperature dependence of the isotope effect but rather to develop and validate an approach for calculations of nuclear quantum mechanical contributions to activation free energies. Here, we find that the deviation between the calculated and observed activation free energies is small for both H and D at all investigated temperatures. The present study also explores the nature of the reorganization energy in the enzyme and solution reactions. It is found that the outer-sphere reorganization energy is extremely small. This reflects the fact that the considered reaction involves a very small charge transfer. The implication of this finding is discussed in the framework of the qualitative vibronic model. The main point of the present study is, however, that the rigorous QCP approach provides a reliable computational tool for evaluating NQM contributions to catalysis even when the given reaction includes large tunneling contributions. Interestingly, our results indicate that the NQM effects in the lipoxygenase reaction are similar in the enzyme and in the reference solution reactions, and thus do not contribute to catalysis. We also reached similar conclusions in studies of other enzymes.     

Solvent effects on environmentally coupled hydrogen tunnelling during catalysis by dihydrofolate reductase from Thermotoga maritima

Protein motions may be perturbed by altering the properties of the reaction medium. Here we show that dielectric constant, but not viscosity, affects the rate of the hydride-transfer reaction catalysed by dihydrofolate reductase from Thermotoga maritima (TmDHFR), in which quantum-mechanical tunnelling has previously been shown to be driven by protein motions. Neither dielectric constant nor viscosity directly alters the kinetic isotope effect of the reaction or the mechanism of coupling of protein motions to tunnelling. Glycerol and sucrose cause a significant increase in the rate of hydride transfer, but lead to a reduction in the magnitude of the kinetic isotope effect as well as an extension of the temperature range over which "passive" protein dynamics (rather than "active" gating motions) dominate the reaction. Our results are in agreement with the proposal that non-equilibrium dynamical processes (promoting motions) drive the hydride-transfer reaction in TmDHFR.     

Dependence of transition state structure on substrate: the intrinsic C-13 kinetic isotope effect is different for physiological and slow substrates of the ornithine decarboxylase reaction because of different hydrogen bonding structures

Ornithine decarboxylase is the first and the rate-controlling enzyme in polyamine biosynthesis; it decarboxylates l-ornithine to form the diamine putrescine. We present calculations performed using a combined quantum mechanical and molecular mechanical (QM/MM) method with the AM1 semiempirical Hamiltonian for the wild-type ornithine decarboxylase reaction with ornithine (the physiological substrate) and lysine (a "slow" substrate) and for mutant E274A with ornithine substrate. The dynamical method is variational transition state theory with quantized vibrations. We employ a single reaction coordinate equal to the carbon-carbon distance of the dissociating bond, and we find a large difference between the intrinsic kinetic isotope effect for the physiological substrate, which equals 1.04, and that for the slow substrate, which equals 1.06. This shows that, contrary to a commonly accepted assumption, kinetic isotope effects on slow substrates are not always good models of intrinsic kinetic isotope effects on physiological substrates. Furthermore, analysis of free-energy-based samples of transition state structures shows that the differences in kinetic isotope effects may be traced to different numbers of hydrogen bonds at the different transition states of the different reactions.     

Isotope effects and medium effects on sulfuryl transfer reactions

Kinetic isotope effects and medium effects have been measured for sulfuryl-transfer reactions of the sulfate ester p-nitrophenyl sulfate (pNPS). The results are compared to those from previous studies of phosphoryl transfer, a reaction with mechanistic similarities. The N-15 and the bridge O-18 isotope effects for the reaction of the pNPS anion are very similar to those of the p-nitrophenyl phosphate (pNPP) dianion. This indicates that in the transition states for both reactions the leaving group bears nearly a full negative charge resulting from a large degree of bond cleavage to the leaving group. The nonbridge O-18 isotope effects support the notion that the sulfuryl group resembles SO(3) in the transition state. The reaction of the neutral pNPS species in acid solution is mechanistically similar to the reaction of the pNPP monoanion. In both cases proton transfer from a nonbridge oxygen atom to the leaving group is largely complete in the transition state. Despite their mechanistic similarities, the phosphoryl- and sulfuryl-transfer reactions differ markedly in their response to medium effects. Increasing proportions of the aprotic solvent DMSO to aqueous solutions of pNPP cause dramatic rate accelerations of up to 6 orders of magnitude, but only a 50-fold rate increase is observed for pNPS. Similarly, phosphoryl transfer from the pNPP dianion to tert-amyl alcohol is 9000-fold faster than the aqueous reaction, while the sulfuryl transfer from the pNPS anion is some 40-fold slower. The enthalpic and entropic contributions to these differing medium effects have been measured and compared.     

Mechanistic study of the Soai autocatalytic reaction informed by kinetic analysis

Detailed kinetic studies of the Soai reaction affirm the basic mechanistic picture previously developed in kinetic, spectroscopic and molecular modelling studies, and also suggest that refinements to the proposed elementary reaction steps must be considered. The alkanol reaction product is driven strongly and without bias towards the formation of homochiral and heterochiral dimers. The reaction is catalyzed by only the homochiral dimers. Consideration of the kinetic profiles from reactions carried out with different initial dialkylzinc concentrations support a proposal for a tetrameric transition state, but further experimental work is required to delineate the nature of this species. The power of reaction calorimetry as a kinetic tool for discerning subtle effects of the shape of the kinetic profile is highlighted. The importance of combining kinetic evidence with spectroscopic and other characterization tools is emphasized.     

Kinetic isotope effect in hydrogen transfer arising from the effects of rotational excitation and occurrence of hydrogen tunneling in molecular systems

Hydrogen kinetic isotope effect with values of alpha identical with ln(kH/kT)/ln(kD/kT)>3.3 which are generally ascribed to quantum tunneling of hydrogen are shown to arise in O+HCl(DCl,TCl) reactions due to the effects of rotational excitation on the distribution of encounters with the critical dividing surface. At higher rotational excitations these distributions are shifted towards the regions of the critical dividing surface with low barrier energies which can lead to a large enhancement of the barrier crossing. This effect depends strongly on the hydrogen isotope involved in the reaction and, at some temperatures, gives rise to alpha much larger than 3.3. It can be readily seen that the effect should arise also in condensed molecular systems, due to internal rotations or other vibrations "perpendicular" to the reaction coordinate.     

Transition states for glucopyranose interconversion

Glucose is a central molecule in biology and chemistry, and the anomerization reaction has been studied for more than 150 years. Transition-state structure is the last impediment to an in-depth understanding of its solution chemistry. We have measured kinetic isotope effects on the rate constants for approach of alpha-glucopyranose to its equilibrium with beta-glucopyranose, and these were converted into unidirectional kinetic isotope effects using equilibrium isotope effects. Saturation transfer 13C NMR spectroscopy has yielded the relative free energies of the transition states for the ring-opening and ring-closing reactions, and both transition states contribute to the experimental kinetic isotope effects. Both transition states of the anomerization process have been modeled with high-level computational theory with constraints from the primary, secondary, and solvent kinetic isotope effects. We have found the transition states for anomerization, and we have also concluded that it is forbidden for the water molecule to form a hydrogen bond bridge to both OH1 and O5 of glucose simultaneously in either transition state.     

Transition structures, energetics, and secondary kinetic isotope effects for cope rearrangements of cis-1,2-divinylcyclobutane and cis-1,2-divinylcyclopropane: a DFT study

The minimum energy reaction paths and secondary kinetic isotope effects (KIE) for the Cope rearrangements of cis-1,2-divinylcyclobutane and cis-1,2-divinylcyclopropane obtained by (U)B3LYP calculations are reported. Both reactions proceed through endo-boatlike reaction paths, and have aromatic transition states. The predicted activation energies are in agreement with the experimental data. The reaction paths of the rearrangements are intervened by enantiomerization saddle points of the products (and the reactant in the case of divinylcyclobutane). The calculated KIEs are similar in the two systems, and consistent with the geometries of the transition structures. There is computational evidence that the isotope effect associated with the conversion of a pure sp(2) C-H bond into a pure sp(3) one might be the same in all molecules. The predicted KIEs agree with experiment for divinylcyclopropane, but not for divinylcyclobutane.     

A review of proton transfer reactions between various carbon-acids and amine bases in aprotic solvents

The subject of proton transfer between carbon acids and nitrogen bases in aprotic solvents is reviewed. Equilibrium and rate constants that characterize such reactions are most often determined utilizing UV-visible spectrophotometry. At ambient temperature reaction rates are sufficiently rapid that fast reaction methods, for example, the stopped-flow and temperature-jump techniques are required in many cases. Variation of the properties of the donor and acceptor reaction pairs enables electronic and steric effects upon thermodynamic and kinetic parameters of proton transfer to be assessed. Determination of the kinetic isotope effect (KIE), i.e. k(protium)/k(deuterium) led to the conclusion that, under certain circumstances and when the KIE is greater than seven, the proton undergoes reaction with a significant degree of quantum mechanical tunneling, consistent with a theoretical prediction advanced several decades earlier. In fact this aspect may be one of the most significant outgrowths of these studies. Many reactions have been characterized (by tunneling) but rarely are the reacting systems experimentally amenable to obtaining all the experimental criteria that support tunneling. Controversy that has arisen regarding treatment of experimental data and resulting conclusions from them is visited in this review. The structural nature of the product state of reaction is formulated based on spectroscopic evidence, in favorable cases, and probable structures of the transition state can be inferred.     

Deuterium kinetic isotope effects in microsolvated gas-phase E2 reactions

This work describes the first experimental studies of deuterium kinetic isotope effects (KIEs) for the gas-phase E2 reactions of microsolvated systems. The reactions of F(-)(H(2)O)(n) and OH(-)(H(2)O)(n), where n = 0, 1, with (CH(3))(3)CX (X = Cl, Br), as well as the deuterated analogs of the ionic and neutral reactants, were studied utilizing the flowing afterglow-selected ion flow tube technique. The E2 reactivity is found to decrease with solvation. Small, normal kinetic isotope effects are observed for the deuteration of the alkyl halide, while moderately inverse kinetic isotope effects are observed for the deuteration of the solvent. Minimal clustering of the product ions is observed, but there are intriguing differences in the nature and extent of the clustering process. Electronic structure calculations of the transition states provide qualitative insight into these microsolvated E2 reactions.     

Diels-Alder and ene reactions of singlet oxygen,nitroso compounds and triazolinediones: transition states and mechanisms from contemporary theory

Singlet oxygen, nitroso compounds and triazolinediones have similar electronic structures: they share a low lying LUMO, making them powerful electrophiles, and a high lying HOMO, orthogonal to the LUMO and consisting of an antibonding combination of lone paris. This bestows some nucleophilic character on these species. We describe a number of studies employing the best levels of theory currently available for systems of this size and demonstrate that the Diels-Alder and ene reactions of these three species are calculated to show subtle changes in mechanism. The calculations have been calibrated, wherever possible, by comparison to experimental observations including measured activation and reaction energies, regio- and stereo-selectivities, intermediates observed either spectroscopically or by trapping, and kinetic isotope effects.     

Rate-promoting vibrations and coupled hydrogen-electron transfer reactions in the condensed phase: a model for enzymatic catalysis

A model is presented for coupled hydrogen-electron transfer reactions in condensed phase in the presence of a rate promoting vibration. Large kinetic isotope effects (KIEs) are found when the hydrogen is substituted with deuterium. While these KIEs are essentially temperature independent, reaction rates do exhibit temperature dependence. These findings agree with recent experimental data for various enzyme-catalyzed reactions, such as the amine dehydrogenases and soybean lipoxygenase. Consistent with earlier results, turning off the promoting vibration results in an increased KIE. Increasing the barrier height increases the KIE, while increasing the rate of electron transfer decreases it. These results are discussed in light of other views of vibrationally enhanced tunneling in enzymes.     

Correction of pre-steady-state KIEs for isotopic impurities and the consequences of kinetic isotope fractionation

We show, both experimentally and by kinetic modeling, that enzymatic single-turnover (pre-steady-state) H-transfer reactions can be significantly complicated by kinetic isotope fractionation. This fractionation results in the formation of more protiated than deuterated product and is a unique problem for pre-steady-state reactions. When observed rate constants are measured using rapid-mixing (e.g., stopped flow) methodologies, kinetic isotope fractionation can lead to a large underestimation of both the magnitude and temperature dependence of kinetic isotope effects (KIEs). This fractionation is related to the isotopic purity of the substrates used and highlights a major problem with experimental studies which measure KIEs with substrates that are not isotopically pure. As it is not always possible to prepare isotopically pure substrates, we describe two general methods for the correction, for known isotope impurities, of KIEs calculated from pre-steady-state measurements.     

Solvent as a Probe of Active Site Motion and Chemistry during the Hydrogen Tunnelling Reaction in Morphinone Reductase

The reductive half‐reaction of morphinone reductase involves a hydride transfer from enzyme‐bound β‐nicotinamide adenine dinucleotide (NADH) to a flavin mononucleotide (FMN). We have previously demonstrated that this step proceeds via a quantum mechanical tunnelling mechanism. Herein, we probe the effect of the solvent on the active site chemistry. The pK_a of the reduced FMN N1 is 7.4±0.7, based on the pH‐dependence of the FMN midpoint potential. We rule out that protonation of the reduced FMN N1 is coupled to the preceding H‐transfer as both the rate and temperature‐dependence of the reaction are insensitive to changes in solution pH above and below this pK_a. Further, the solvent kinetic isotope effect is ～1.0 and both the 1° and 2° KIEs are insensitive to solution pH. The effect of the solvent’s dielectric constant is investigated and the rate of H‐transfer is found to be unaffected by changes in the dielectric constant between ～60 and 80. We suggest that, while there is crystallographic evidence for some water in the active site, the putative promoting motion involved in the H‐tunnelling reaction is insensitive to such changes.     

Dependance conformationnelle de l'effet isotopique dans les reactions d'addition nucleophiles : Influence du sens d'attaque sur la variation du terme hyperconjugatif

The secondary kinetic deuterium isotope effects measured in addition reactions of sulfite and borohydride ions has confirmed the importance of the hyperconjugative factor. Semi-quantitative evaluation of this stabilizing factor by calculating the orbital overlap evolution during reaction shows that the hyperconjugative contribution to the isotope effect is much more important during equatorial attack than during axial attack. This explains why isotope effects are similar for the additions, though their directions of attack are opposite and their transition states located differently along the reaction coordinate.