  The Michaelis-Menten mechanism is probably the best known model for an
enzyme-catalyzed reaction. For spatially homogeneous concentrations, QSS
reductions are well known, but this is not the case when chemical species are
allowed to diffuse. We will discuss QSS reductions for both the irreversible
and reversible Michaelis-Menten reaction in the latter case, given small
initial enzyme concentration and slow diffusion. Our work is based on a
heuristic method to obtain an ordinary differential equation which admits
reduction by Tikhonov-Fenichel theory. We will not give convergence proofs but
we provide numerical results that support the accuracy of the reductions.
