The quantitative relations between diffusion-controlled reaction rate and characteristic parameters in enzyme-substrate reaction systems. I. Neutral substrates.

With the development of techniques for studying fast reactions, we are confronted with some experimental observations which, according to the classical diffusion-controlled reaction theory based on the assumption of pherical symmetry, will lead to paradoxical consequences. Recently, some investigators have attempted to present a theory of non-spherically symmetric diffusion-controlled reaction. Owing to the difficulty in mathematics, only the formal discussion has been given, and the numerical results have not yet been reported. The combination between enzyme and substrate is not only non-spherically symmetric, but also related to the force field existing between the reacting molecules. In the previous article we introduced the spatial factor and the force field factor and derived a general equation for these reaction systems. We present in this article a general method for finding the numerical solution of the above equation. With the numerical results obtained by this method we may interpret the experimental facts which can not be explained from the viewpoint of the classical diffusion-controlled reaction theory. In order to examine more closely the kinetic behaviour of enzyme-substrate reaction systems, we defined several characteristic parameters. The quantitative relation between these parameters and the rate of diffusion-controlled reaction has been discussed.