Multidimensional Tunneling, Recrossing, and the Transmission Coefficient for Enzymatic Reactions

Pu, Jingzhi; Gao, Jiali; Truhlar, Donald G.

doi:10.1021/cr050308e

Cited by 334 publications

(517 citation statements)

References 468 publications

(1,299 reference statements)

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“…[37][38][39][40] It is also useful to rewrite eq. (3) as follows (6) where the path integral centroid free energy of activation is defined by (7) and (8) corresponds to the free energy of the system in the reactant (R) state region relative to the lowest point, which may be interpreted as the entropic contributions or motions correlating with the progress coordinate z. λ eff is the de Broglie thermal wavelength of the centroid reaction coordinate with an effective mass M eff at the dividing surface, which is determined in the centroid path transition state ensemble.…”

Section: Theoretical Background Path Integral Quantum Mechanical Ratementioning

confidence: 99%

“…These results are close to the semiclassical limit, suggesting that tunneling contributions are not significant for this reaction in aqueous solution. To assess the tunneling contributions, we have used the multidimensional tunneling (MT) algorithm developed by Truhlar and coworkers, 9 extended to enzyme applications in the EA-VTST method, 5,6 to determine the average tunneling transmission factor, yielding a value of 〈κ〉 = 1.3 using the present potential. 30 This suggests that tunneling only makes minor contributions in the present case for the aqueous reaction.…”

Section: Swain-schaad Exponentsmentioning

confidence: 99%

“…3,4 Quantum mechanics is essential for computing KIEs of reactions in solutions and in enzymes. 5,6 First, electronic structural theory is required to adequately describe the potential energy surface for bond forming and breaking processes. Secondly, nuclear quantum effects including both quantized vibration and tunneling are needed to obtain accurate rate constants.…”

Section: Introductionmentioning

confidence: 99%

“…9 In principle, these techniques can be directly extended to condensed phase systems; however, the size and complexity of these systems often make it intractable computationally. One method that has been successfully introduced to the study of enzyme reaction rates is the ensemble-averaged variational transition state theory with QM/MM sampling (EA-VTST-QM/ MM), 5,6 which has been applied to a number of enzyme systems. This technique includes multidimensional tunneling.…”

Section: Introductionmentioning

confidence: 99%

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

2007

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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.

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Section: Theoretical Background Path Integral Quantum Mechanical Ratementioning

confidence: 99%

Section: Swain-schaad Exponentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

2007

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“…One method that has been successfully introduced to computational enzymology is the ensembleaveraged variational transition-state theory with QM/MM sampling (EA-VTST-QM/MM), which has been applied to a number of enzyme systems. 2,3,[9][10][11][12][13] Both primary and secondary KIEs can be computed using the EA-VTST-QM/ MM method, and the method includes contributions of multidimensional tunneling. In another work, a grid-based hybrid approach was used to model quantum effects in hydrogen transfer reactions by numerically solving the vibrational wavefunction of the transferring hydrogen nucleus.…”

Section: Introductionmentioning

confidence: 99%

An Integrated Path Integral and Free-Energy Perturbation−Umbrella Sampling Method for Computing Kinetic Isotope Effects of Chemical Reactions in Solution and in Enzymes

Major

Gao

2007

J. Chem. Theory Comput.

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234

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An integrated centroid path integral and free-energy perturbation-umbrella sampling (PI-FEP/UM) method for computing kinetic isotope effects (KIEs) for chemical reactions in solution and in enzymes is presented. The method is based on the bisection quantized classical path sampling in centroid path integral simulations to include nuclear quantum corrections in the classical potential of mean force. The required accuracy for computing kinetic isotope effects is achieved by coupled free-energy perturbation and umbrella sampling for reactions involving different isotopes. The use of FEP results in relatively small statistical uncertainties, whereas if kinetic isotope effects are computed directly by the difference in free energies obtained from the quantum mechanical potentials of mean force for different isotopes, the statistical errors are significantly greater. The PI-FEP/UM method is illustrated in two applications. The first reaction is the decarboxylation of N-methyl picolinate in water, and the primary 13 C and secondary 15 N KIEs have been determined. The second reaction is the proton-transfer reaction between nitroethane and acetate ions in water, and the total kinetic isotope effects were obtained. In both cases, the computational results are in accord with experimental results, and the findings provide further insight into the mechanism of these reactions in water.

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Kinetic Isotope Effects in Enzymes

Kohen

Roston

Stojković

et al. 2010

Encyclopedia of Analytical Chemistry

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Kinetic isotope effects (KIEs) have progressed to become one of the most useful analytical techniques to study enzymatic reactions and can answer a variety of questions ranging from the basic mechanism of a reaction to the structure of a transition state (TS) and the role of quantum mechanical tunneling. Here, we briefly discuss the development of the theory behind KIEs with an emphasis on how it guides the interpretation of experimental data. We then present some of the instrumentation and techniques commonly used for KIE experiments, followed by a number of different examples from the enzymology literature wherein KIEs have been used to probe chemical transformations, with an emphasis on the effects of quantum mechanical tunneling on KIEs.

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Multidimensional Tunneling, Recrossing, and the Transmission Coefficient for Enzymatic Reactions

Cited by 334 publications

References 468 publications

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

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 Path Integral and Free-Energy Perturbation−Umbrella Sampling Method for Computing Kinetic Isotope Effects of Chemical Reactions in Solution and in Enzymes

Kinetic Isotope Effects in Enzymes

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