Enzyme diffusion and action on soluble and insoluble substrate biopolymers

The action of enzymes on soluble and insoluble substrate biopolymers is discussed, taking into account enzyme diffusion along the biopolymer “surface” and interaction with interspersed ligand groups that may be modified by the action of the enzyme. It is shown that movement of the enzyme under trhe combined effect of these two processes can be described as a diffusion process characterized by an apparent diffusion coefficient that generally depends on both time and position. Equations describing the system are formulated and some specific examples analyzed in terms of analytical or numerical solutions. The concentration distributions of both the enzyme and the substrate (or product ) were obtained for different systems for which the apparent diffusion coefficient is a function of time only, as well as of both time and position. The relevance of the formulation, as developed, to systems in which reduction in dimensionality leads to enhanced enzyme efficiency is discussed, and possible uses of the theory in studies of biopolymer structure and enzyme‐biopolymer interactions are suggested.