Model for solvent viscosity effect on enzymatic reactions

The solvent viscosity dependence for enzymatic reactions is discussed. We suggest the interpretation of the phenomenon that requires neither a modification of the Kramers' theory nor that of the Stokes law. We assume that an enzyme solution is an ensemble of samples with different values of the viscosity for the movement of the system along the reaction coordinate. We quantify the extent of this difference by some parameter, introduce heterogeneity in our system with the help of a distribution over this parameter and find the solution of the integral equation for the function of the distribution. All parameters of the model are related to experimentally observable values. The meaning of fractional exponents appears to be the characteristic for the behavior of the distribution. Our approach yields the existence of the limit value for the fractional power exponent with the decrease of cosolvent molecular weight in agreement with known experimental data.