Diffusion-controlled effects in reversible enzymatic fast reaction systems--critical spherical shell and proximity rate constant

In this paper the diffusion-controlled effects in reversible enzyme fast reaction systems have been discussed. The main results are as follows: 1) An expression for the relation between the proximity second-order rate constant and the usual experimental second-order rate constant has been presented. From this expression we can see that the two kinds of rate constants are generally not equal unless the reaction proceeds very slowly (in comparison with the corresponding diffusion limit). 2) A new joint relation has been given between the theoretical calculated results and the experimentally measured ones for the activation energy. It has been pointed out that, for the reaction systems discussed here, it would no longer be valid to adopt the absolute reaction rate theory to calculate the activation energy as done commonly. 3) A formula has been given to calculate the upper limit obtainable possibly by experiments for the second-order rate constants in the reversible enzymatic fast reaction system. According to this formula, the value of such an upper limit is related not only to the diffusion coefficients of reacting molecules, the size of active surface, and the like, but also to the ratio of the concentration of product molecules to that of the substrate molecules at the equilibrium of the reaction system. Furthermore, the reversible enzymatic fast reaction system with multi-substrate and multi-product has been discussed, and a general equation for calculating the degree of reaction flow derived as well.