Review of computer simulations of isotope effects on biochemical reactions: From the Bigeleisen equation to Feynman's path integral

Wong, Kin Yiu; Xu, Yuqing; Xu, Liang

doi:10.1016/j.bbapap.2015.04.021

Cited by 19 publications

(15 citation statements)

References 122 publications

(205 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Comparison of these values with those determined from computation for different mechanisms is frequently sufficient to establish the catalytic mechanism. Indeed, as computational methods have improved, experimentally determined kinetic isotope effects have come to provide necessary constraints on the structures of transition state structures derived from computation [3, 4]. …”

mentioning

confidence: 99%

13C kinetic isotope effects on the reaction of a flavin amine oxidase determined from whole molecule isotope effects

Tormos

Suarez

Fitzpatrick

2016

Archives of Biochemistry and Biophysics

View full text Add to dashboard Cite

A large number of flavoproteins catalyze the oxidation of amines. Because of the importance of these enzymes in metabolism, their mechanisms have previously been studied using deuterium, nitrogen, and solvent isotope effects. While these results have been valuable for computational studies to distinguish among proposed mechanisms, a measure of the change at the reacting carbon has been lacking. We describe here the measurement of a 13C kinetic isotope effect for a representative amine oxidase, polyamine oxidase. The isotope effect was determined by analysis of the isotopic composition of the unlabeled substrate, N, N'-dibenzyl-1,4-diaminopropane, to obtain a pH-independent value of 1.025. The availability of a 13C isotope effect for flavoproteincatalyzed amine oxidation provides the first measure of the change in bond order at the carbon involved in this carbon-hydrogen bond cleavage and will be of value to understanding the transition state structure for this class of enzymes.

show abstract

mentioning

confidence: 99%

13C kinetic isotope effects on the reaction of a flavin amine oxidase determined from whole molecule isotope effects

Tormos

Suarez

Fitzpatrick

2016

Archives of Biochemistry and Biophysics

View full text Add to dashboard Cite

show abstract

“…For instance, its normal kinetic-isotope-effect (KIE) value (which is always larger than unity in the classical world) agrees with the analytical results from the famous Bigeleisen equation (for computing quantum KIE) at the classical limit. [3,21,54,[94][95][96][97][98][99][100][101]…”

Section: Transition-state Theory (Tst) For a Many-body Systemmentioning

confidence: 99%

Pitfall in Free‐Energy Simulations on Simplest Systems

Wong

2017

ChemistrySelect

Self Cite

View full text Add to dashboard Cite

Free‐energy simulation (FES) is widely used in science and engineering. Unconstrained FES (UFES, e. g., umbrella sampling with histogram binning) and constrained FES (CFES, e. g., blue‐moon sampling with mean‐force/thermodynamic integration) are two different types of FES. People prefer UFES to CFES, e. g., people correct constrained free‐energy profile (CFEP) to unconstrained FEP (UFEP), not the other way around. But remarkably, herein we show for a 1D free body subject to zero force, from an UFEP we find an infinitely‐high energy barrier. By contrast, we find no energy barrier from any CFEP. Besides, by providing in‐depth comparisons between UFEP and CFEP from the perspective of Jacobian scale factor, this work may also partially address recent issues on FES: (1) UFEP is preferred, but why do three recent papers conclude we should use CFEP for the transition‐state theory and why are these three papers not fully consistent with one another? (2) For relating UFEP to CFEP, why are there two different versions of Fixman term associated with velocity and momentum constraints, respectively? (3) How to normalize CFEP, for which the equation seems to be even unavailable?

show abstract

“…The main source of KIEs in chemical reactions are the vibrational contributions and quantum tunneling effects (as mentioned above we restrict the review to KIEs related to hydrogen atom isotopes). Neglecting tunneling, the Bigeleisen equation has likely been the most widely used method to determine the KIE just using harmonic vibrational frequencies:

K I E = \frac{k_{l}}{k_{h}} = ((), \frac{υ_{l}^{*}}{υ_{h}^{*}}) ((), \prod_{i = 1}^{3 N ‐ 7} \frac{υ_{i, l}^{‡}}{υ_{i, h}^{‡}}) ((), \prod_{i = 1}^{3 N ‐ 6} \frac{υ_{i, h}}{υ_{i, l}}) ((), \prod_{i = 1}^{3 N ‐ 7} \frac{sinh (u_{i, h}^{‡})}{sinh (u_{i, l}^{‡})}) ((), \prod_{i = 1}^{3 N ‐ 6} \frac{sinh (u_{i, l})}{sinh (u_{i, h})})

where the subscripts l and h stand for the light and heavy isotopes, respectively, k l and k h are the respective rate constants,

\frac{υ_{l}^{*}}{υ_{h}^{*}}

is the ratio of the imaginary frequencies at the transition state structure, N is the number of atoms of the supermolecule, υ i is the i th normal mode frequency of the corresponding isotopolog ( l or h ), ‡ denote the transition state structure,

u_{i} = \frac{h υ_{i}}{2 k_{B} T}

, k B is Boltzmann's constant, T is temperature, and h is Planck's constant. Equation includes both the zero‐point energy contributions (which are usually the most important vibrational contributions) and the effect caused by the vibrational excited states.…”

Section: The Bigeleisen Equationmentioning

confidence: 99%

“…The Bigeleisen equation can be extended beyond the harmonic vibrational approximation and including quantum tunneling effects in the framework of Feynman path integrals:

KIE = \frac{k_{l}}{k_{h}} = ((), \frac{υ_{l}^{*}}{υ_{h}^{*}}) \frac{{normale}^{‐ \frac{([], W_{l}^{‡} ((), z_{l}^{‡}) - W_{h}^{‡} ((), z_{h}^{‡}))}{k_{B} T}}}{{normale}^{‐ \frac{([], W_{l}^{R} ((), z_{l}^{R}) - W_{h}^{R} ((), z_{h}^{R}))}{k_{B} T}}}

where W X ( z X ) is the centroid effective potential along the reaction coordinate z X calculated from the path integrals for isotopolog X , and

W_{X}^{‡} ((), z_{X}^{‡})

and

W_{X}^{R} ((), z_{X}^{R})

are its values at the transition state and reactant structures. Under the harmonic approximation and neglecting quantum tunneling effects, Eq.…”

Section: The Bigeleisen Equationmentioning

confidence: 99%

Kinetic isotope effects in chemical and biochemical reactions: physical basis and theoretical methods of calculation

González‐Lafont

Lluch

2016

WIREs Comput Mol Sci

View full text Add to dashboard Cite

Kinetic isotope effects (KIEs) are a valuable tool for the analysis of chemical and biochemical reaction mechanisms. Theoretical methods of calculation of those KIEs have been developed with the aim to better understand their experimental behavior. In this review, the physical basis as well as several of those computational approaches to calculate primary hydrogen KIEs is presented. Examples of interesting chemical reactions and relevant enzymatic processes are given to demonstrate how theory is used to interpret those complex kinetic magnitudes. In particular, KIE computations within generalized transition state theory formulations are shown here to explain the temperature dependence of chemical and biochemical KIEs caused by multidimensional quantum effects contributions, such as zero point vibrational energy and quantum tunneling. An unexpected large isotope effect on the phosphorescence emission of an organic reaction is analyzed by means of KIE calculations as a function of energy and including also tunneling corrections. More quantum-based methodologies such as the Multiconfiguration Time-Dependent Hartree method and Feynman path integral simulations are discussed within the context of KIE computations. The special kinetic treatment of proton-coupled electron transfer reactions is also analyzed.

show abstract

Review of computer simulations of isotope effects on biochemical reactions: From the Bigeleisen equation to Feynman's path integral

Cited by 19 publications

References 122 publications

13C kinetic isotope effects on the reaction of a flavin amine oxidase determined from whole molecule isotope effects

13C kinetic isotope effects on the reaction of a flavin amine oxidase determined from whole molecule isotope effects

Pitfall in Free‐Energy Simulations on Simplest Systems

Kinetic isotope effects in chemical and biochemical reactions: physical basis and theoretical methods of calculation

Contact Info

Product

Resources

About