Diffusion fronts in enzyme-catalysed reactions

In this paper the nature and validity of the mathematical formulation of Michaelis–Menten-type kinetics for enzyme-catalysed biochemical reactions is studied. Previous work has in the main concentrated on isolated, spatially uniform (well-mixed) reactions. The effects of substrate input and diffusion on this formulation, in particular, on the nature and validity of the quasi-steady-state-assumption for diffusion-driven fronts are investigated. It is shown that, provided the Michaelis–Menten constant K M is sufficiently large, an appropriate quasi-steady-state assumption is valid at all points in space and for all times other than in a region that closely tracks the front itself. Moreover, it is shown that this region shrinks with time.