Bulletin of Mathematical Biology

, Volume 62, Issue 3, pp 483–499

Enzyme kinetics at high enzyme concentration


DOI: 10.1006/bulm.1999.0163

Cite this article as:
Schnell, S. & Maini, P.K. Bull. Math. Biol. (2000) 62: 483. doi:10.1006/bulm.1999.0163


We re-visit previous analyses of the classical Michaelis-Menten substrate-enzyme reaction and, with the aid of the reverse quasi-steady-state assumption, we challenge the approximation d[C]/dt ≈ 0 for the basic enzyme reaction at high enzyme concentration. For the first time, an approximate solution for the concentrations of the reactants uniformly valid in time is reported. Numerical simulations are presented to verify this solution. We show that an analytical approximation can be found for the reactants for each initial condition using the appropriate quasi-steady-state assumption. An advantage of the present formalism is that it provides a new procedure for fitting experimental data to determine reaction constants. Finally, a new necessary criterion is found that ensures the validity of the reverse quasi-steady-state assumption. This is verified numerically.

Copyright information

© Society for Mathematical Biology 2000

Authors and Affiliations

  1. 1.Centre for Mathematical BiologyMathematical InstituteOxfordUK