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A simple model for barrier frequencies for enzymatic reactions.

We present a simple model to rationalize the effects of environment on the reaction barrier frequencies derived from free energy profiles. These frequencies are relevant in deviations of a rate constant from its transition state theory value and in determining which environmental dynamics participate in the reaction. In particular, this simple model can be used to understand the changes in the reaction barrier frequencies of an enzymatic catalyzed reaction and the corresponding uncatalyzed process in aqueous solution, a change which has implications for dynamical environmental effects on the enzymatic reaction. Two possible cases are analyzed, in which the polarity (charge separation/localization) of the reacting system increases or decreases as the reaction advances. A simple modeling of the environment's effects allows the explanation of an unusual "inverse" effect on the reaction frequencies, that is, a free energy barrier lowering accompanied by an increase of the reaction frequency, a behavior observed in some enzymes. The model predictions are successfully compared with results from full simulations for four different enzyme reactions.