Diffusion fronts in enzyme-catalysed reactions

Graeme P. Boswell; Fordyce A. Davidson

doi:10.1007/s10665-007-9142-x

Diffusion fronts in enzyme-catalysed reactions

Graeme P. Boswell
, Fordyce A. Davidson

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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.

Original language	English
Pages (from-to)	157-169
Number of pages	13
Journal	Journal of Engineering Mathematics
Volume	59
Issue number	2
DOIs	https://doi.org/10.1007/s10665-007-9142-x
Publication status	Published - 2007

Keywords

Diffusible substrate
Michaelis-Menten
Open system
Quasi-steady state

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10.1007/s10665-007-9142-x

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title = "Diffusion fronts in enzyme-catalysed reactions",

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.",

keywords = "Diffusible substrate, Michaelis-Menten, Open system, Quasi-steady state",

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T1 - Diffusion fronts in enzyme-catalysed reactions

AU - Boswell, Graeme P.

AU - Davidson, Fordyce A.

N1 - dc.publisher: Springer-Verlag

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

KW - Diffusible substrate

KW - Michaelis-Menten

KW - Open system

KW - Quasi-steady state

U2 - 10.1007/s10665-007-9142-x

DO - 10.1007/s10665-007-9142-x

M3 - Article

SN - 0022-0833

VL - 59

SP - 157

EP - 169

JO - Journal of Engineering Mathematics

JF - Journal of Engineering Mathematics

IS - 2

ER -

Diffusion fronts in enzyme-catalysed reactions

Abstract

Keywords

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