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. We investigate 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. It is shown that provided the Michaelis-Menten constant K_M is sufficiently large, then an appropriate quasi-steady state assumption is valid at all points in space and for all times other than in a region which closely tracks the front itself. Moreover, it is shown that this region of shrinks with time.