Vibrational analysis of the chorismate rearrangement: relaxed force constants, isotope effects and activation entropies calculated for reaction in vacuum, water and the active site of chorismate mutase

We present results derived from vibrational Hessians calculated for the reactant complex, transition structure and product complex of the rearrangement of chorismate to prephenate under different conditions. The AM1 semiempirical MO and B3LYP/6–31G* density functional methods were employed for calculations in vacuum, whereas a hybrid QM/MM method AM1/CHARMM/TIP3P was used for calculations in water and within the active site of B. subtilis chorismate mutase. Kinetic and equilibrium isotope effects and entropies of activation and reaction were investigated as a function of the increasing size of the Hessian, as the system is expanded to include not only the atoms of chorismate/prephenate itself but also an increasing number of surrounding water molecules (up to 99) or active‐site residues (up to 225 atoms). Primary 13C and 18O isotope effects are not sensitive to the size of the Hessian, but secondary 3H–C5 and 3H2–C9 effects require the inclusion of at least those atoms directly involved in hydrogen bonds to the substrate or, better, a complete first solvation shell or cage of active‐site amino acid residues. Pauling bond orders for the breaking CO and making CC bonds are remarkably similar for the transition structures in all three media. Relaxed force constants for stretching of these bonds (which allow meaningful comparisons to be made along a reaction path) give a significantly different picture of the bonding changes in the transition structures. The ratio of logarithms of kinetic and equilibrium isotope effects does not agree with measures of transition‐state structure derived from Pauling bond orders or from relaxed force constants. There is no simple relationship between kinetic isotope effects and transition‐state structure for this Claisen rearrangement. The calculated vibrational entropy of activation for the enzymic reaction agrees well with an experimental value for E. coli chorismate mutase. Vibrational entropy reduces the free energy barrier for the catalysed reaction by about 1 kJ mol−1 at 333 K. Copyright © 2004 John Wiley & Sons, Ltd.