Journal of Mathematical Biology

, Volume 26, Issue 6, pp 689–703 | Cite as

Enzyme kinetics for a two-step enzymic reaction with comparable initial enzyme-substrate ratios

  • C. L. Frenzen
  • P. K. Maini


We extend the validity of the quasi-steady state assumption for a model double intermediate enzyme-substrate reaction to include the case where the ratio of initial enzyme to substrate concentration is not necessarily small. Simple analytical solutions are obtained when the reaction rates and the initial substrate concentration satisfy a certain condition. These analytical solutions compare favourably with numerical solutions of the full system of differential equations describing the reaction. Experimental methods are suggested which might permit the application of the quasi-steady state assumption to reactions where it may not have been obviously applicable before.

Key words

Michaelis Menten approximation Quasi-steady state assumption Scaling Singular perturbations Fast and slow timescales 


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Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • C. L. Frenzen
    • 1
  • P. K. Maini
    • 2
  1. 1.Department of MathematicsSouthern Methodist UniversityDallasUSA
  2. 2.Centre for Mathematical BiologyMathematical InstituteOxfordUK

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