On the quasi-steady-state assumption applied to Michaelis-Menten and suicide substrate reactions with diffusion

We consider a recent extension to the validity of the quasi-steady-state assumption ( QSSA ) which includes the case where the ratio of the initial enzyme to substrate concentration is not necessarily small. We extend the analysis to include diffusion of substrate, in which case the initial enzyme to substrate ratio is spatially dependent and no longer constant. We show that the region in which the QSSA holds depends on the nature of the enzyme-substrate reaction: if the enzyme is inactivated by the substrate then the QSSA holds in a growing disc; if the enzyme is unchanged after reaction then the QSSA holds in a ring travelling through space.