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.     

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.     

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.     

Proton-coupled electron transfer in soybean lipoxygenase

The proton-coupled electron transfer reaction catalyzed by soybean lipoxygenase-1 is studied with a multistate continuum theory that represents the transferring hydrogen nucleus as a quantum mechanical wave function. The inner-sphere reorganization energy of the iron cofactor is calculated with density functional theory, and the outer-sphere reorganization energy of the protein is calculated with the frequency-resolved cavity model for conformations obtained with docking simulations. Both classical and quantum mechanical treatments of the proton donor-acceptor vibrational motion are presented. The temperature dependence of the calculated rates and kinetic isotope effects is in agreement with the experimental data. The weak temperature dependence of the rates is due to the relatively small free energy barrier arising from a balance between the reorganization energy and the reaction free energy. The unusually high deuterium kinetic isotope effect of 81 is due to the small overlap of the reactant and product proton vibrational wave functions and the dominance of the lowest energy reactant and product vibronic states in the tunneling process. The temperature dependence of the kinetic isotope effect is strongly influenced by the proton donor-acceptor distance with the dominant contribution to the overall rate. This dominant proton donor-acceptor distance is significantly smaller than the equilibrium donor-acceptor distance and is determined by a balance between the larger coupling and the smaller Boltzmann probability as the distance decreases. Thus, the proton donor-acceptor vibrational motion plays a vital role in decreasing the dominant donor-acceptor distance relative to its equilibrium value to facilitate the proton-coupled electron transfer reaction.     

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.     

Hydrogen tunneling in peptidylglycine alpha-hydroxylating monooxygenase

The temperature dependence of the primary and secondary intrinsic isotope effects for the C-H bond cleavage catalyzed by peptidylglycine alpha-hydroxylating monooxygenase has been determined. Analysis of the magnitude and Arrhenius behavior of the intrinsic isotope effects provides strong evidence for the use of tunneling as a primary catalytic strategy for this enzyme. Modeling of the isotope effect data allows for a comparison to the hydrogen transfer catalyzed by soybean lipoxygenase in terms of environmental reorganization energy and frequency of the protein vibration that controls the hydrogen transfer.     

Oxygen isotope effects on electron transfer to O2 probed using chemically modified flavins bound to glucose oxidase

Apo-glucose oxidase has been reconstituted with flavins modified in the 7 and 8 positions and characterized with regard to the catalytic rate of O(2) reduction and oxygen-18 isotope effects on this process. Kinetic studies as a function of driving force indicate a reorganization energy for electron transfer to O(2) of lambda = 28 kcal mol(-)(1) at optimal pH, which is similar to the value obtained earlier from temperature dependencies of rates (Roth, J. P.; Klinman, J. P. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 62-67). For the various enzyme-bound flavins, competitive oxygen-18 kinetic isotope effects fall within the narrow range of 1.0266(5) to 1.0279(6), apparently because of the dominant contribution of outer-sphere reorganization to the activation barrier; within the context of semiclassical and quantum mechanical electron transfer theories, the magnitude of the isotope effects reveals the importance of nuclear tunneling.     

Evidence for concerted electron proton transfer in charge recombination between FADH- and 306Trp• in Escherichia coli photolyase

Proton-coupled electron-transfer (PCET) is a mechanism of great importance in protein electron transfer and enzyme catalysis, and the involvement of aromatic amino acids in this process is of much interest. The DNA repair enzyme photolyase provides a natural system that allows for the study of PCET using a neutral radical tryptophan (Trp(?)). In Escherichia coli photolyase, photoreduction of the flavin adenine dinucleotide (FAD) cofactor in its neutral radical semiquinone form (FADH(?)) results in the formation of FADH(-) and (306)Trp(?). Charge recombination between these two intermediates requires the uptake of a proton by (306)Trp(?). The rate constant of charge recombination has been measured as a function of temperature in the pH range from 5.5 to 10.0, and the data are analyzed with both classical Marcus and semi-classical Hopfield electron transfer theory. The reorganization energy associated with the charge recombination process shows a pH dependence ranging from 2.3 eV at pH ≤ 7 and 1.2 eV at pH(D) 10.0. These findings indicate that at least two mechanisms are involved in the charge recombination reaction. Global analysis of the data supports the hypothesis that PCET during charge recombination can follow two different mechanisms with an apparent switch around pH 6.5. At lower pH, concerted electron proton transfer (CEPT) is the favorable mechanism with a reorganization energy of 2.1-2.3 eV. At higher pH, a sequential mechanism becomes dominant with rate-limiting electron-transfer followed by proton uptake which has a reorganization energy of 1.0-1.3 eV. The observed 'inverse' deuterium isotope effect at pH < 8 can be explained by a solvent isotope effect that affects the free energy change of the reaction and masks the normal, mass-related kinetic isotope effect that is expected for a CEPT mechanism. To the best of our knowledge, this is the first time that a switch in PCET mechanism has been observed in a protein.     

Free energies for biological electron transfer from QM/MM calculation: method, application and critical assessment

Computer simulations of biological electron transfer reactions are reviewed with a focus on the calculation of reaction free energy (driving force) and reorganization free energy. Then a mixed quantum mechanical/molecular mechanical (QM/MM) approach is described which is designed for computation of these quantities for pure electron transfer reactions with large donor-acceptor separation distances. The method is applied to intra-protein electron transfer in Ru(bpy)(2)(im)His33 cytochrome c and the results compared to experimental data. Several modeling aspects which are important for successful calculation of free energies with QM/MM are discussed in detail.     

Combined QM/MM and path integral simulations of kinetic isotope effects in the proton transfer reaction between nitroethane and acetate ion in water

An integrated Feynman path integral-free energy perturbation and umbrella sampling (PI-FEP/UM) method has been used to investigate the kinetic isotope effects (KIEs) in the proton transfer reaction between nitroethane and acetate ion in water. In the present study, both nuclear and electronic quantum effects are explicitly treated for the reacting system. The nuclear quantum effects are represented by bisection sampling centroid path integral simulations, while the potential energy surface is described by a combined quantum mechanical and molecular mechanical (QM/MM) potential. The accuracy essential for computing KIEs is achieved by a FEP technique that transforms the mass of a light isotope into a heavy one, which is equivalent to the perturbation of the coordinates for the path integral quasiparticle in the bisection sampling scheme. The PI-FEP/UM method is applied to the proton abstraction of nitroethane by acetate ion in water through molecular dynamics simulations. The rule of the geometric mean and the Swain-Schaad exponents for various isotopic substitutions at the primary and secondary sites have been examined. The computed total deuterium KIEs are in accord with experiments. It is found that the mixed isotopic Swain-Schaad exponents are very close to the semiclassical limits, suggesting that tunneling effects do not significantly affect this property for the reaction between nitroethane and acetate ion in aqueous solution.     

Protein's electronic polarization contributes significantly to its catalytic function

Ab initio quantum mechanical/molecular mechanical method is combined with the polarized protein-specific charge to study the chemical reactions catalyzed by protein enzymes. Significant improvement in the accuracy and efficiency of free-energy simulation is demonstrated by calculating the free-energy profile of the primary proton transfer reaction in triosephosphate isomerase. Quantitative agreement with experimental results is achieved. Our simulation results indicate that electronic polarization makes important contribution to enzyme catalysis by lowering the energy barrier by as much as 3 kcal/mol.     

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.     

Theoretical study of electron, proton, and proton-coupled electron transfer in iron bi-imidazoline complexes.

A comparative theoretical investigation of single electron transfer (ET), single proton transfer (PT), and proton-coupled electron transfer (PCET) reactions in iron bi-imidazoline complexes is presented. These calculations are motivated by experimental studies showing that the rates of ET and PCET are similar and are both slower than the rate of PT for these systems (Roth, J. P.; Lovel, S.; Mayer, J. M. J. Am. Chem. Soc. 2000, 122, 5486). The theoretical calculations are based on a multistate continuum theory, in which the solute is described by a multistate valence bond model, the transferring hydrogen nucleus is treated quantum mechanically, and the solvent is represented as a dielectric continuum. For electronically nonadiabatic electron transfer, the rate expressions for ET and PCET depend on the inner-sphere (solute) and outer-sphere (solvent) reorganization energies and on the electronic coupling, which is averaged over the reactant and product proton vibrational wave functions for PCET. The small overlap of the proton vibrational wave functions localized on opposite sides of the proton transfer interface decreases the coupling for PCET relative to ET. The theory accurately reproduces the experimentally measured rates and deuterium kinetic isotope effects for ET and PCET. The calculations indicate that the similarity of the rates for ET and PCET is due mainly to the compensation of the smaller outer-sphere solvent reorganization energy for PCET by the larger coupling for ET. The moderate kinetic isotope effect for PCET arises from the relatively short proton transfer distance. The PT reaction is found to be dominated by solute reorganization (with very small solvent reorganization energy) and to be electronically adiabatic, leading to a fundamentally different mechanism that accounts for the faster rate.     

Semiclassical study of quantum coherence and isotope effects in ultrafast electron transfer reactions coupled to a proton and a phonon bath

The linearized semiclassical initial value representation is employed to describe ultrafast electron transfer processes coupled to a phonon bath and weakly coupled to a proton mode. The goal of our theoretical investigation is to understand the influence of the proton on the electronic dynamics in various bath relaxation regimes. More specifically, we study the impact of the proton on coherences and analyze if the coupling to the proton is revealed in the form of an isotope effect. This will be important in distinguishing reactions in which the proton does not undergo significant rearrangement from those in which the electron transfer is accompanied by proton transfer. Unlike other methodologies widely employed to describe nonadiabatic electron transfer, this approach treats the electronic and nuclear degrees of freedom consistently. However, due to the linearized approximation, quantum interference effects are not captured accurately. Our study shows that at small phonon bath reorganization energies, coherent oscillations and isotope effect are observed in both slow and fast bath regimes. The coherences are more substantially damped by deuterium in comparison to the proton. Further, in contrast to the dynamics of the spin-boson model, the coherences are not long-lived. At large bath reorganization energies, the decay is incoherent in the slow and fast bath regimes. In this case, the extent of the isotope effect depends on the relative relaxation timescales of the proton mode and the phonon bath. The isotope effect is magnified for baths that relax on picosecond timescales in contrast to baths that relax in femtoseconds.     

H atom transfer of collinear OH…O system

A quantum mechanical calculation was performed to study the hydrogen atom transfer of collinear OH…O/OD…O system, for which Delves' coordinates and R- matrix propagation method were applied in a Melius-Blint potential energy surface. The calculation result showed that the state-state H atom transfer probability comported strong oscillation phenomena and collision delay time of the title system was in the fs-ps time scale. The kinetic isotope effect was calculated in this work too.     

Ab initio quantum mechanical/molecular mechanical molecular dynamics simulation of enzyme catalysis: the case of histone lysine methyltransferase SET7/9

To elucidate enzyme catalysis through computer simulation, a prerequisite is to reliably compute free energy barriers for both enzyme and solution reactions. By employing on-the-fly Born-Oppenheimer molecular dynamics simulations with the ab initio quantum mechanical/molecular mechanical approach and the umbrella sampling method, we have determined free energy profiles for the methyl-transfer reaction catalyzed by the histone lysine methyltransferase SET7/9 and its corresponding uncatalyzed reaction in aqueous solution, respectively. Our calculated activation free energy barrier for the enzyme catalyzed reaction is 22.5 kcal/mol, which agrees very well with the experimental value of 20.9 kcal/mol. The difference in potential of mean force between a corresponding prereaction state and the transition state for the solution reaction is computed to be 30.9 kcal/mol. Thus, our simulations indicate that the enzyme SET7/9 plays an essential catalytic role in significantly lowering the barrier for the methyl-transfer reaction step. For the reaction in solution, it is found that the hydrogen bond network near the reaction center undergoes a significant change, and there is a strong shift in electrostatic field from the prereaction state to the transition state, whereas for the enzyme reaction, such an effect is much smaller and the enzyme SET7/9 is found to provide a preorganized electrostatic environment to facilitate the methyl-transfer reaction. Meanwhile, we find that the transition state in the enzyme reaction is a little more dissociative than that in solution.     

Transmission coefficient calculation for proton transfer in triosephosphate isomerase based on the reaction path potential method

A global potential energy surface has been constructed through interpolation of our recently developed reaction path potential for chemical reactions in enzymes which is derived from combined ab initio quantum mechanical and molecular mechanical calculations. It has been implemented for the activated molecular dynamics simulations of the initial proton transfer reaction catalyzed by triosephosphate isomerase. To examine the dynamical effects on the rate constants of the enzymatic reaction, the classical transmission coefficient kappa(t) is evaluated to be 0.47 with the reactive flux approach, demonstrating considerable deviations from transition state theory. In addition, the fluctuations of protein environments have small effects on the barrier recrossing, and the transmission coefficient kappa(t) strongly depends on the fluctuations of atoms near the active site of the enzyme.     

Hydrogen atom tunneling in triplet o-methylbenzocycloalkanones: effects of structure on reaction geometry and excited state configuration

The rates of phosphorescence decay of 4,7-dimethylindanone (2), 6,9-dimethylbenzosuberone (3), and several related compounds have been analyzed between 4 and 100 K to determine the contributions of intramolecular hydrogen atom tunneling from the o-methyl group to the excited state carbonyl oxygen. Changes in the benzocycloalkanone ring size from five to seven not only affect the geometry at the reaction center, but they also affect the electronic configuration of the triplet excited state in a significant manner. While the triplet state of 5,8-dimethyltetralone (1) in nonpolar glasses can be clearly described as having a predominant n,pi configuration, compounds 2 and 3 have a significantly larger contribution of the less reactive pi,pi state. 4,7-Dimethylindanone (2) is stable under cryogenic conditions and in solution at ambient temperature. In contrast, triplet lifetimes and product analysis indicate that 6,9-dimethylbenzosuberone (3) reacts by quantum mechanical tunneling at temperatures as low as 4 K. A surprisingly small isotope effect k(H)/k(D) approximately 1.1 between 4 and 50 K increases steadily up to k(H)/k(D) approximately 5.1 at 100 K. This unusual observation is interpreted in terms of a vibrationally activated quantum mechanical tunneling process with hydrogen atom transfer at the lowest temperatures being mediated by zero-point-energy reaction-promoting skeletal motions. Results presented here indicate that the combined effects of increasing pi,pi character and unfavorable reaction geometry contribute to the diminished reactivity of o-methyl ketones 2 and 3 as compared to those of tetralone 1.     

The directive of the protein: how does cytochrome P450 select the mechanism of dopamine formation?

Dopamine can be generated from tyramine via arene hydroxylation catalyzed by a cytochrome P450 enzyme (CYP2D6). Our quantum mechanical/molecular mechanical (QM/MM) results reveal the decisive impact of the protein in selecting the 'best' reaction mechanism. Instead of the traditional Meisenheimer-complex mechanism, the study reveals a mechanism involving an initial hydrogen atom transfer from the phenolic hydroxyl group of the tyramine to the iron-oxo of the compound I (Cpd I), followed by a ring-π radical rebound that eventually leads to dopamine by keto-enol rearrangement. This mechanism is not viable in the gas phase since the O-H bond activation by Cpd I is endothermic and the process does not form a stable intermediate. By contrast, the in-protein reaction has a low barrier and is exothermic. It is shown that the local electric field of the protein environment serves as a template that stabilizes the intermediate of the H-abstraction step and thereby mediates the catalysis of dopamine formation at a lower energy cost. Furthermore, it is shown that external electric fields can either catalyze or inhibit the process depending on their directionality.