ABSTRACT:This paper provides an overview of a new method developed to include quantum mechanical effects and free energy sampling in calculations of reaction rates in enzymes. The paper includes an overview of variational transition state theory with optimized multidimensional tunneling for simple gas-phase reactions and then shows how this is extended to incorporate free energy effects and to include protein motions in the reaction coordinate by ensemble averaging. Finally we summarize recent comparisons to experiment for primary and secondary kinetic isotope effects for proton and hydride transfer reactions catalyzed by enzymes.

We have applied molecular dynamics umbrella-sampling simulations and ensemble-averaged variational transition state theory with multidimensional tunneling (EA-VTST/MT) to explore the free energy surface, reaction paths, and dideuterium kinetic isotope effect (KIE) of the β-oxidation of butyryl-coenzyme A by short-chain acyl-CoA dehydrogenase. The potential energy surface is obtained by combined quantum mechanics-molecular mechanics (QM/MM) with specific reaction parameters and a simple valence bond term. The calculations include determination of the potential of mean force (PMF) in both two dimensions (2D) and one dimension (1D) by using the weighted histogram analysis method. The 2D PMF indicates that the hydride transfer is the rate-limiting step of the mechanism, and the 1D PMFs are used to calculate rate constants. We include full molecular dynamics of a 7824-atom reaction zone with stochastic boundary conditions in a first approximation of the quasiclassical rate constant. This first approximation is then corrected by transmission coefficients that account for dynamical recrossing and tunneling. For the calculation of transmission coefficients, the system is divided into a 43-atom primary zone, consisting of atoms directly involved in the enzyme reaction, and a 23 234-atom secondary zone, called the bath. In both approximations considered, the primary zone atoms are allowed to have kinetic energy in all steps. For calculation of the transmission coefficient in the static-secondary-zone (SSZ) approximation, the bath is frozen for each member of an ensemble of transition state configurations and associated reaction paths, which are then averaged, whereas in the equilibrium-secondary-zone (ESZ) approximation 7781 atoms of the bath are fully relaxed (with stochastic boundary conditions) along each reaction path. We found that the SSZ simulations underestimate the KIE, whereas the ESZ simulations overestimate the KIE.

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Several substituted difuranonaphthalenes have been identified as being viable sensitizers for the production of singlet molecular oxygen (a 1 ∆ g ) upon two-photon nonlinear excitation with a focused laser beam. The two-photon absorption cross sections of these molecules are comparatively large and depend significantly on the functional groups attached to the chromophore. To facilitate the further development of such sensitizers, computational tools have been employed to model the two-photon absorption cross sections of some difuranonaphthalenes as well as distyryl benzenes that likewise can be viable singlet oxygen precursors. Ab initio calculations using response theory yield cross sections that reproduce experimental data well. Specifically, for these comparatively large molecules, the calculations not only model relative substituent-dependent changes well but also yield reasonably accurate cross sections. Thus, ab initio computational methods can indeed be used as a predictive tool in the design of potentially useful, two-photon singlet oxygen sensitizers.