Ensemble-averaged Variational Transition State Theory

Ensemble-averaged Variational Transition State Theory 

The calculations described in the previous paragraph yield, for each ensemble member , a free energy of activation profile AG (T, s) and a transmission coefficient K( T), where = 1,2. , and L is the number of MEPs computed. The standard EA-VTST/MT result, called the static-secondary-zone result, is then given by 

ENSEMBLE-AVERAGED VARIATIONAL TRANSITION STATE THEORY 

The concept of reaction coordinate plays an important role in VEST. In fact, there is more than one reaction coordinate. Globally the reaction coordinate is defined as the distance s along the reaction path, and this coordinate plays a critical role in tunneling calculations. Locally the reaction coordinate is the degree of freedom (sometimes called z, but often also called s) that is missing in the generalized transition state. 

When applying EA-VTST to enzyme reactions, another kind of system/ environment separation is made. Here the reactive system is considered to be the substrate and perhaps part of the enzyme or coenzyme (and perhaps including one or two closely coupled water molecules), and the environment is the rest of the substrate-coenzyme-enzyme complex plus the (rest of the) surrounding water. In what follows we will sometimes call the reactive system the primary subsystem and the environment as the secondary subsystem. For the treatment of reactions in liquids that was presented earlier, the solvent was replaced by a homogeneous dielectric medium, which greatly simplifies the calculation. For enzyme-catalyzed reactions, we treat the environment explicitly at the atomic level of detail. 

For enzyme-catalyzed reactions, we consider the unimolecular rate constant for the chemical step, which is the reaction of the Michaelis complex. The EA-VTST/OMT method involves a two-stage or three-stage procedure, where the third stage is optional. In stage one, a user-defined, physically meaningful reaction coordinate is used to calculate a one-dimensional potential of mean force. This provides a classical mechanical free energy of activation along that coordinate that is used to identify a transition state ensemble. In 

In the first step of stage 1, all atoms (5000-25000 atoms for a typical application to an enzyme-catalyzed reaction) are treated on the same footing. In this step, one calculates a one-dimensional potential of mean force (PMF) as a function of the distinguished reaction coordinate 2 by a classical molecular dynamics simulation. Any method for calculating classical mechanical PMFs could be used for example, one can use the CHARMM program to carry out this step by employing molecular dynamics simulation with umbrella sampling. As discussed below, this provides an approximation to the free 

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The SES, ESP, and NES methods are particularly well suited for use with continuum solvation models, but NES is not the only way to include nonequilibrium solvation. A method that has been very useful for enzyme kinetics with explicit solvent representations is ensemble-averaged variational transition state theory [26,27,87] (EA-VTST). In this method one divides the system into a primary subsystem and a secondary one. For an ensemble of configurations of the secondary subsystem, one calculates the MEP of the primary subsystem. Thus the reaction coordinate determined by the MEP depends on the coordinates of the secondary subsystem, and in this way the secondary subsystem participates in the reaction coordinate. 

Ensemble-averaged Variational Transition State Theory... 

T. D. (2004) Ensemble-averaged variational transition state theory with optimized multidimensional tunneling for enzyme kinetics and other condensed-phase reactions,... 

The AG value deduced from the PMF is corrected by replacing classical vibrational partition functions by their quantum homolog. Recrossing, tunnelling and non-classical reflection effects can be included in the transmission coefficient by various procedures. This ensemble-average variational transition state theory with multidimensional tunnelling (EA-VTST/MT) method was applied to proton and hydride transfers in various enzymes such as yeast enolase, liver alcohol dehydrogenase and triosephosphate isomerase. For a review, see ref. 3 and the chapter by J. Gao in this book. 

EA-VTST Ensemble-averaged variational transition state theory... 

Tmhlar DG, Gao JL, Garcia-Viloca M, Alhambra C, Corchado J, Sanchez ML, Poulsen TD (2004) Ensemble-averaged variational transition state theory with optimized multidimensional tunneling for enzyme kinetics and other condensed-phase reactions, hit J Quantum Chem 100(6) 1136-1152... 

ENSEMBLE-AVERAGED VARIATIONAL TRANSITION STATE THEORY... 

Ensemble-Averaged Variational Transition State Theory 207... 

Poulsen, Int. J. Quantum Chem., 100, 1136 (2004). Ensemble-Averaged Variational Transition State Theory with Optimized Multidimensional Tunneling for Enzyme Kinetics and Other Condensed-Phase Reactions. 

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