Diffusion-controlled reactions of enzymes. An approximate analytic solution of Chou's model

Based on Chou's model, a criterion was derived, by which one can judge whether or not the physical picture of the critical spherical shell described by Chou for an enzyme-substrate fast reaction system can emerge. Furthermore, for those reaction systems with such a physical picture, an approximate analytical solution was presented, which can be easily handled to calculate the upper limit of the diffusion-controlled reaction and the corresponding concentration distribution of substrate molecules on the surface of the major protein outside the active site. The results thus obtained are in good agreement with those computed by Chou et al. through the approach of numerical solution. Furthermore, the physical significance of the criterion and its relation to the critical spherical shell are substantiated during the process of derivation, which is very helpful for gaining an insight into this kind of biomolecular system with surprisingly high reaction rates.