Kinetic isotope effects of L-Dopa decarboxylase

A mixed centroid path integral and free energy perturbation method (PI-FEP/UM) has been used to investigate the primary carbon and secondary hydrogen kinetic isotope effects (KIEs) in the amino acid decarboxylation of L-Dopa catalyzed by the enzyme L-Dopa decarboxylase (DDC) along with the corresponding uncatalyzed reaction in water. DDC is a pyridoxal 5'-phosphate (PLP) dependent enzyme. The cofactor undergoes an internal proton transfer between the zwitterionic protonated Schiff base configuration and the neutral hydroxyimine tautomer. It was found that the cofactor PLP makes significant contributions to lowering the decarboxylation barrier, while the enzyme active site provides further stabilization of the transition state. Interestingly, the O-protonated configuration is preferred both in the Michaelis complex and at the decarboxylation transition state. The computed kinetic isotope effects (KIE) on the carboxylate C-13 are consistent with that observed on decarboxylation reactions of other PLP-dependent enzymes, whereas the KIEs on the α carbon and secondary proton, which can easily be validated experimentally, may be used as a possible identification for the active form of the PLP tautomer in the active site of DDC.     

The normal range for secondary Swain-Schaad exponents without tunneling or kinetic complexity

An analysis is presented of the range of secondary Swain-Schaad exponents to be expected at 25 degrees C in the absence of tunneling or kinetic complexity. From 15 996 sets of exact harmonic semiclassical equilibrium isotope effects for simple C-H/D/T exchange reactions and 954 sets of exact harmonic semiclassical secondary H/D/T kinetic isotope effects for C-H positions in simple organic reactions, the distribution of Swain-Schaad exponents versus magnitude of the isotope effect is determined. This distribution defines when a secondary Swain-Schaad exponent may be considered to implicate nonsemiclassical behavior, revises the expected Swain-Schaad exponent for extrapolation of secondary isotope effects, and serves as a guide to the uncertainty in such extrapolations.     

Origin of the temperature dependence of isotope effects in enzymatic reactions: the case of dihydrofolate reductase

The origin of the temperature dependence of kinetic isotope effects (KIEs) in enzyme reactions is a problem of general interest and a major challenge for computational chemistry. The present work simulates the nuclear quantum mechanical (NQM) effects and the corresponding KIE in dihydrofolate reductase (DHFR) and two of its mutants by using the empirical valence bond (EVB) and the quantum classical path (QCP) centroid path integral approach. Our simulations reproduce the overall observed trend while using a fully microscopic rather than a phenomenological picture and provide an interesting insight. It appears that the KIE increases when the distance between the donor and acceptor increases, in a somewhat counter intuitive way. The temperature dependence of the KIE appears to reflect mainly the temperature dependence of the distance between the donor and acceptor. This trend is also obtained from a simplified vibronic treatment, but as demonstrated here, the vibronic treatment is not valid at short and medium distances, where it is essential to use the path integral or other approaches capable of moving seamlessly from the adiabatic to the diabatic limits. It is pointed out that although the NQM effects do not contribute to catalysis in DHFR, the observed temperature dependence can be used to refine the potential of mean force for the donor and acceptor distance and its change due to distanced mutations.     

Path-integral calculations of heavy atom kinetic isotope effects in condensed phase reactions using higher-order Trotter factorizations

A convenient approach to compute kinetic isotope effects (KIEs) in condensed phase chemical reactions is via path integrals (PIs). Usually, the primitive approximation is used in PI simulations, although such quantum simulations are computationally demanding. The efficiency of PI simulations may be greatly improved, if higher-order Trotter factorizations of the density matrix operator are used. In this study, we use a higher-order PI method, in conjunction with mass-perturbation, to compute heavy-atom KIE in the decarboxylation of orotic acid in explicit sulfolane solvent. The results are in good agreement with experiment and show that the mass-perturbation higher-order Trotter factorization provides a practical approach for computing condensed phase heavy-atom KIE.     

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.     

Nuclear quantum and H/D isotope effects on three-centered bonding diborane: Path integral molecular dynamics simulations

Nuclear quantum and H/D isotope effects of bridging and terminal hydrogen atoms of diborane (B₂H₆) molecules were systematically studied by classical ab initio molecular dynamics (CLMD) and ab initio path integral molecular dynamics (PIMD) simulations with BHandHLYP/6-31++G** level of theory at room temperature (298.15 K). Calculated results clearly show that H/D isotope effect appears in the distribution of hydrogen (deuterium) of B₂H₆ (B₂D₆). Geometry of B₂H₆ also plays a significant role in the nuclear quantum effect proved by PIMD simulations, but slightly deviated from its equilibrium structure when simulated via CLMD simulation. The bond lengths between boron atoms R (B1 … B2) and the bridging hydrogen atoms R_HH (H_B1 … H_B2) of the B₂H₆ molecule obtained from PIMD simulations are slightly longer than those of the deuterated form of the diborane (B₂D₆) molecule. The principal component analysis (PCA) was also employed to distinguish the important modes of bridging hydrogen as related to the nuclear quantum and H/D isotope effects. The highest level of contribution obtained from PCA of PIMD simulations is bending, while various mixed vibrations with less contribution were also found. Therefore, the nuclear quantum and H/D isotope effects need to be taken into account for a better understanding of diborane geometry.     

Nuclear quantum effects on an enzyme-catalyzed reaction with reaction path potential: proton transfer in triosephosphate isomerase

Nuclear quantum mechanical effects have been examined for the proton transfer reaction catalyzed by triosephosphate isomerase, with the normal mode centroid path integral molecular dynamics based on the potential energy surface from the recently developed reaction path potential method. In the simulation, the primary and secondary hydrogens and the C and O atoms involving bond forming and bond breaking were treated quantum mechanically, while all other atoms were dealt classical mechanically. The quantum mechanical activation free energy and the primary kinetic isotope effects were examined. Because of the quantum mechanical effects in the proton transfer, the activation free energy was reduced by 2.3 kcal/mol in comparison with the classical one, which accelerates the rate of proton transfer by a factor of 47.5. The primary kinetic isotope effects of kH/kD and kH/kT were estimated to be 4.65 and 9.97, respectively, which are in agreement with the experimental value of 4+/-0.3 and 9. The corresponding Swain-Schadd exponent was predicted to be 3.01, less than the semiclassical limit value of 3.34, indicating that the quantum mechanical effects mainly arise from quantum vibrational motion rather than tunneling. The reaction path potential, in conjunction with the normal mode centroid molecular dynamics, is shown to be an efficient computational tool for investigating the quantum effects on enzymatic reactions involving proton transfer.     

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.     

Theoretical study on isotope and temperature effect in hydronium ion using ab initio path integral simulation

We have applied the ab initio path integral molecular dynamics simulation to study hydronium ion and its isotopes, which are the simplest systems for hydrated proton and deuteron. In this simulation, all the rotational and vibrational degrees of freedom are treated fully quantum mechanically, while the potential energies of the respective atomic configurations are calculated "on the fly" using ab initio quantum chemical approach. With the careful treatment of the ab initio electronic structure calculation by relevant choices in electron correlation level and basis set, this scheme is theoretically quite rigorous except for Born-Oppenheimer approximation. This accurate calculation allows a close insight into the structural shifts for the isotopes of hydronium ion by taking account of both quantum mechanical and thermal effects. In fact, the calculation is shown to be successful to quantitatively extract the geometrical isotope effect with respect to the Walden inversion. It is also shown that this leads to the isotope effect on the electronic structure as well as the thermochemical properties.     

A combined quantum mechanical and molecular mechanical study of the reaction mechanism and alpha-amino acidity in alanine racemase

Combined quantum mechanical/molecular mechanical simulations have been carried out to investigate the origin of the carbon acidity enhancement in the alanine racemization reaction catalyzed by alanine racemase (AlaR). The present study shows that the enhancement of carbon acidity of alpha-amino acids by the cofactor pyridoxal 5'-phosphate (PLP) with an unusual, unprotonated pyridine is mainly due to solvation effects, in contrast to the intrinsic electron-withdrawing stabilization by the pyridinium ion to form a quinonoid intermediate. Alanine racemase further lowers the alpha-proton acidity and provides an overall 14-17 kcal/mol transition-state stabilization. The second key finding of this study is that the mechanism of racemization of an alanine zwitterion in water is altered from an essentially concerted process to a stepwise reaction by formation of an external aldimine adduct with the PLP cofactor. Finally, we have used a centroid path integral method to determine the intrinsic kinetic isotope effects for the two proton abstraction reactions, which are somewhat greater than the experimental estimates.     

Kinetic isotope effects for concerted multiple proton transfer: a direct dynamics study of an active-site model of carbonic anhydrase II

The rate constant of the reaction catalyzed by the enzyme carbonic anhydrase II, which removes carbon dioxide from body fluids, is calculated for a model of the active site. The rate-determining step is proton transfer from a zinc-bound water molecule to a histidine residue via a bridge of two or more water molecules. The structure of the active site is known from X-ray studies except for the number and location of the water molecules. Model calculations are reported for a system of 58 atoms including a four-coordinated zinc ion connected to a methylimidazole molecule by a chain of two waters, constrained to reproduce the size of the active site. The structure and vibrational force field are calculated by an approximate density functional treatment of the proton-transfer step at the Self-Consistent-Charge Density Functional Tight Binding (SCC-DFTB) level. A single transition state is found indicating concerted triple proton transfer. Direct-dynamics calculations for proton and deuteron transfer and combinations thereof, based on the Approximate Instanton Method and on Variational Transition State Theory with Tunneling Corrections, are in fair agreement and yield rates that are considerably higher and kinetic isotope effects (KIEs) that are somewhat higher than experiment. Classical rate constants obtained from Transition State Theory are smaller than the quantum values but the corresponding KIEs are five times larger. For multiple proton transfer along water bridges classical KIEs are shown to be generally larger than quantum KIEs, which invalidates the standard method to distinguish tunneling and over-barrier transfer. In the present case, a three-way comparison of classical and quantum results with the observed data is necessary to conclude that proton transfer along the bridge proceeds by tunneling. The results suggest that the two-water bridge is present in low concentrations but makes a substantial contribution to proton transport because of its high efficiency. Bridging structures containing more water molecules may have lower energies but are expected to be less efficient. The observed exponential dependence of the KIEs on the deuterium concentration in H(2)O/D(2)O mixtures implies concerted transfer and thus rules out substantial contributions from structures that lead to stepwise transfer via solvated hydronium ions, which presumably dominate proton transfer in less efficient carbonic anhydrase isozymes.     

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.     

A quantum generalization of intrinsic reaction coordinate using path integral centroid coordinates

We propose a generalization of the intrinsic reaction coordinate (IRC) for quantum many-body systems described in terms of the mass-weighted ring polymer centroids in the imaginary-time path integral theory. This novel kind of reaction coordinate, which may be called the "centroid IRC," corresponds to the minimum free energy path connecting reactant and product states with a least amount of reversible work applied to the center of masses of the quantum nuclei, i.e., the centroids. We provide a numerical procedure to obtain the centroid IRC based on first principles by combining ab initio path integral simulation with the string method. This approach is applied to NH(3) molecule and N(2)H(5) (-) ion as well as their deuterated isotopomers to study the importance of nuclear quantum effects in the intramolecular and intermolecular proton transfer reactions. We find that, in the intramolecular proton transfer (inversion) of NH(3), the free energy barrier for the centroid variables decreases with an amount of about 20% compared to the classical one at the room temperature. In the intermolecular proton transfer of N(2)H(5) (-), the centroid IRC is largely deviated from the "classical" IRC, and the free energy barrier is reduced by the quantum effects even more drastically.     

The mechanism of base-promoted HF elimination from 4-fluoro-4-(4'-nitrophenyl)butan-2-one: a multiple isotope effect study including the leaving group (18)F/(19)F KIE.

Leaving-group fluorine as well as the primary and secondary deuterium kinetic isotope effects (KIEs) have been determined for the base-promoted elimination of hydrogen fluoride from 4-fluoro-4-(4'-nitrophenyl)butan-2-one in aqueous solution. The elimination was studied for formate, acetate, and imidazole as the catalyzing base. The fluorine KIEs were determined using the accelerator-produced short-lived radionuclide (18)F in combination with natural (19)F. The (19)F substrate was labeled with (14)C in a remote position to enable radioactivity measurement of both isotopic substrates. The elimination reaction exhibits large primary deuterium KIEs: 3.2, 3.7, and 7.5 for formate, acetate, and imidazole, respectively, thus excluding the E1 mechanism. The corresponding C(4)-secondary deuterium KIEs are 1.038, 1.050 and 1.014 and the leaving group fluorine KIEs are 1.0037, 1.0047 and 1.0013, respectively. The size of the fluorine KIEs corresponds to 5-15% of the estimated maximum of 1.03 for complete C-F bond breakage. No H/D exchange is observed during the reaction. The size and trends of the KIEs for the different bases are consistent with an E1cB-like E2 or an E1cB(ip) mechanism.     

Simulation of tunneling in enzyme catalysis by combining a biased propagation approach and the quantum classical path method: application to lipoxygenase

The ability of using wave function propagation approaches to simulate isotope effects in enzymes is explored, focusing on the large H/D kinetic isotope effect of soybean lipoxygenase-1 (SLO-1). The H/D kinetic isotope effect (KIE) is calculated as the ratio of the rate constants for hydrogen and deuterium transfer. The rate constants are calculated from the time course of the H and D nuclear wave functions. The propagations are done using one-dimensional proton potentials generated as sections from the full multidimensional surface of the reacting system in the protein. The sections are obtained during a classical empirical valence bond (EVB) molecular dynamics simulation of SLO-1. Since the propagations require an extremely long time for treating realistic activation barriers, it is essential to use an effective biasing approach. Thus, we develop here an approach that uses the classical quantum path (QCP) method to evaluate the quantum free energy change associated with the biasing potential. This approach provides an interesting alternative to full QCP simulations and to other current approaches for simulating isotope effects in proteins. In particular, this approach can be used to evaluate the quantum mechanical transmission factor or other dynamical effects, while still obtaining reliable quantized activation free energies due to the QCP correction.     

Geometrical H/D isotope effect on hydrogen bonds in charged water clusters

To investigate the proton/deuteron geometrical isotope effect of positively and negatively charged water complexes, H5O2+ and H3O2-, we have carried out accurate ab initio path integral simulations considering the electron correlation effect. It has been found that the isotope effect on the hydrogen bond is different between these two species in that the oxygen separation becomes shorter in H5O2+ while longer in H3O2- by deuteron substitution. This behavior is ascribed to the change in the quantum effect of hydrogen bonds whether the shared hydrogen is on a single or double well potential surface.     

Hydride transfer catalyzed by xylose isomerase: mechanism and quantum effects

We have applied molecular dynamics umbrella-sampling simulation and ensemble-averaged variational transition state theory with multidimensional tunneling (EA-VTST/MT) to calculate the reaction rate of xylose-to- xylulose isomerization catalyzed by xylose isomerase in the presence of two Mg2+ ions. The calculations include determination of the free energy of activation profile and ensemble averaging in the transmission coefficient. The potential energy function is approximated by a combined QM/MM/SVB method involving PM3 for the quantum mechanical (QM) subsystem, CHARMM22 and TIP3P for the molecular mechanical (MM) environment, and a simple valence bond (SVB) local function of two bond distances for the hydride transfer reaction. The simulation confirms the essential features of a mechanism postulated on the basis of kinetics and X-ray data by Whitlow et al. (Whitlow, M.; Howard, A. J.; Finzel, B. C.; Poulos, T. L.; Winborne, E.; Gilliland, G. L. Proteins 1991, 9, 153) and Ringe, Petsko, and coworkers (Labie, A.; Allen, K.-N.; Petsko, G. A.; Ringe, D. Biochemistry 1994, 33, 5469). This mechanism involves a rate-determining 1,2-hydride shift with prior and post proton transfers. Inclusion of quantum mechanical vibrational energy is important for computing the free energy of activation, and quantum mechanical tunneling effects are essential for computing kinetic isotope effects (KIEs). It is found that 85% of the reaction proceeds by tunneling and 15% by overbarrier events. The computed KIE for the ratio of hydride to deuteride transfer is in good agreement with the experimental results. The molecular dynamics simulations reveal that proton and hydride transfer reactions are assisted by breathing motions of the mobile Mg2+ ion in the active site, providing evidence for concerted motion of Mg2+ during the hydride transfer step.     

Effects of Quantum Nuclear Delocalisation on NMR Parameters from Path Integral Molecular Dynamics

The influence of nuclear delocalisation on NMR chemical shifts in molecular organic solids is explored using path integral molecular dynamics (PIMD) and density functional theory calculations of shielding tensors. Nuclear quantum effects are shown to explain previously observed systematic deviations in correlations between calculated and experimental chemical shifts, with particularly large PIMD‐induced changes (up to 23 ppm) observed for carbon atoms in methyl groups. The PIMD approach also enables isotope substitution effects on chemical shifts and J couplings to be predicted in excellent agreement with experiment for both isolated molecules and molecular crystals. An approach based on convoluting calculated shielding or coupling surfaces with probability distributions of selected bond distances and valence angles obtained from PIMD simulations is used to calculate isotope effects.     

Proton-coupled electron transfer in soybean lipoxygenase: dynamical behavior and temperature dependence of kinetic isotope effects

The dynamical behavior and the temperature dependence of the kinetic isotope effects (KIEs) are examined for the proton-coupled electron transfer reaction catalyzed by the enzyme soybean lipoxygenase. The calculations are based on a vibronically nonadiabatic formulation that includes the quantum mechanical effects of the active electrons and the transferring proton, as well as the motions of all atoms in the complete solvated enzyme system. The rate constant is represented by the time integral of a probability flux correlation function that depends on the vibronic coupling and on time correlation functions of the energy gap and the proton donor-acceptor mode, which can be calculated from classical molecular dynamics simulations of the entire system. The dynamical behavior of the probability flux correlation function is dominated by the equilibrium protein and solvent motions and is not significantly influenced by the proton donor-acceptor motion. The magnitude of the overall rate is strongly influenced by the proton donor-acceptor frequency, the vibronic coupling, and the protein/solvent reorganization energy. The calculations reproduce the experimentally observed magnitude and temperature dependence of the KIE for the soybean lipoxygenase reaction without fitting any parameters directly to the experimental kinetic data. The temperature dependence of the KIE is determined predominantly by the proton donor-acceptor frequency and the distance dependence of the vibronic couplings for hydrogen and deuterium. The ratio of the overlaps of the hydrogen and deuterium vibrational wavefunctions strongly impacts the magnitude of the KIE but does not significantly influence its temperature dependence. For this enzyme reaction, the large magnitude of the KIE arises mainly from the dominance of tunneling between the ground vibronic states and the relatively large ratio of the overlaps between the corresponding hydrogen and deuterium vibrational wavefunctions. The weak temperature dependence of the KIE is due in part to the dominance of the local component of the proton donor-acceptor motion.     

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.