The contribution of proximity and orientation to catalytic reaction rates

Abstract We present calculations of the possible magnitude of propinquity which has been proposed to play an important role in enzymic catalysis. The effect has been evaluated as in the past by calculating the ratio of bimolecular to intramolecular reaction rates. The ratio is estimated for intramolecular catalysis in rigid systems as well as for systems with five and six rotatable bonds. Our method differs from others mainly in the way cyclization has been treated. The reaction rate (in all cases) is proportional to the probability that the reactive units have the appropriate spatial and orientational positioning for reaction. This probability is obtained by evaluating a distance distribution function within the spatial and angular intervals to which the units are constrained after reaction. For the bimolecular case we have made the usual assumption that the distribution function is uniform. For the intramolecular reaction, neither the spatial nor the angular part of the distribution function is uniform. The pertinent parameters in this case are the bond lengths and angles, and the statistical weight matrices describing torsional rotation. The difficulty in obtaining analytical expressions for the distribution function is circumvented by using Monte Carlo methods. It is argued that the spatial contribution to rate accelerations in rigid systems can be as high as 10 7 M , depending upon the size of the volume to which the reactive units are constrained after reaction. The limitation on the smallest physically reasonable volume is estimated from considerations of energy requirements and vibrational amplitudes. Accelerations by five‐ and six‐membered ring cyclizations were estimated at 10 3 M , the six‐membered ring exhibiting the smaller rate enhancement.