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A relationship between the preexponent of the rate constant and thedistribution over activation barrier energies for enzymatic/protein reactionsis revealed. We consider an enzyme solution as an ensemble of individualmolecules with different values of the activation barrier energy described bythe distribution. From the solvent viscosity effect on the preexponent wederive the integral equation for the distribution and find its approximatesolution. Our approach enables us to attain a twofold purpose. On the one handit yields a simple interpretation of the solvent viscosity dependence forenzymatic/protein reactions that requires neither a modification of theKramers' theory nor that of the Stokes law. On the other hand our approachenables us to deduce the form of the distribution over activation barrierenergies. The obtained function has a familiar bell-shaped form and is inqualitative agreement with the results of single enzyme kinetics measurements.General formalism is exemplified by the analysis of literature experimentaldata.

Relationship between preexponent and distribution over activation barrier energies for enzymatic reactions