Enzyme reaction rates and the stochastic theory of kinetics

The kinetics of an elementary reaction step are discussed from the viewpoint of the stochastic theory of chemical kinetics. The general form of the rate constant found in the stochastic approach is described and compared with the expression from transition state theory. Whereas the stochastic theory predicts a rate enhancement in cases which are not adiabatic (in the quantum mechanical sense), transition state theory, which is essentially an adiabatic theory of reaction rates, does not permit inclusion of the effect. This effect can be expected to be of greater importance in cases of catalysis by structures, such as enzymes, containing large numbers of vibrational degrees of freedom (particularly low frequency ones) than in cases lacking such structures. The stochastic theory is more general than the transition state theory, the rate constant expression given by the latter being obtainable from the former when restrictive assumptions, including that of adiabaticity, are made. Interpretations of enzyme catalysis based on the transition state theory must thus be viewed as speculative.