Abstract
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.
Original language | English |
---|---|
Pages (from-to) | 157 - 169 |
Number of pages | 12 |
Journal | Journal of Engineering Mathematics |
Volume | 59 |
Issue number | 2 |
DOIs | |
Publication status | Published - 31 Dec 2007 |
Keywords
- michealis-menten
- quasi-steady state
- open system