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. 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.
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Boswell, G.P., Davidson, F.A. Diffusion fronts in enzyme-catalysed reactions. J Eng Math 59, 157–169 (2007). https://doi.org/10.1007/s10665-007-9142-x
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DOI: https://doi.org/10.1007/s10665-007-9142-x