Free-energy perturbation calculations of binding and transition-state energies: hydrolysis of phenyl esters by β-cyclodextrin

The use of free-energy perturbation simulations for calculating binding and transition-state energies is examined. Reactions of three phenyl esters with β-cyclodextrin are considered. The binding free energies are calculated using conventional mutation of the substrate force field from one chemical structure to another (two-state problem) in water and in the neutral inclusion complex. For calculation of activation free-energy differences between two substrates the transition states are represented by linear combinations of reactant (anionic inclusion complexes) and product (tetrahedral intermediate) force fields (four-state problem). The coefficients of this linear combination are obtained from empirical valence bond simulations of a reference substrate. The calculated relative binding and activation energies are in a good agreement with experimental data. The approximations underlying this procedure are discussed.