Bulletin of Mathematical Biology

, Volume 50, Issue 6, pp 579–593 | Cite as

On the validity of the steady state assumption of enzyme kinetics

  • Lee A. Segel


By estimating relevant time scales, a simple new condition can be found that ensures the validity of the steady state assumption for a standard enzyme-substrate reaction. The generality of the approach is demonstrated by applying it to the determination of validity criteria for the steady state assumption applied to an enzyme-substrate-inhibitor system.


Slow Time Scale Steady State Approximation Singular Perturbation Theory Steady State Assumption Enzyme Kinetics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Fersht, A. 1985.Enzyme Structure and Mechanism, 2nd Edn. New York: W. F. Freeman.Google Scholar
  2. Frenzen, C. L. and P. K. Maini, Kinetics for a two step enzymic reaction with comparable initial enzyme substrate ratios. Submitted for publication.Google Scholar
  3. Heineken, F., Tsuchiya, H. and Aris, R. 1967. “On the Mathematical Status of the Pseudo-Steady State Hypothesis of Biochemical Kinetics.”Math. Biosci.,1, 95–113.CrossRefGoogle Scholar
  4. Lin, C. C. and L. A. Segel, 1974.Mathematics Applied to Deterministic Problems in the Natural Sciences. New York: MacMillan.Google Scholar
  5. Miller, H. K. and M. E. Balis 1969. Glutaminase Activity ofL-asparagine amidohydrolase.”Biochem. Pharmacol. 18, 2225–2232.CrossRefGoogle Scholar
  6. Murray, J. D. 1977.Lectures on Nonlinear Differential Equation Models in Biology. London: Clarendon Press.Google Scholar
  7. Odell, G. M. and L. A. Segel. 1987.BIOGRAPH. A Graphical Simulation Package With Exercises. To Accompany Lee A. Segel's “Modeling Dynamic Phenomenon in Molecular and Cellular Biology”. Cambridge: Cambridge University Press.Google Scholar
  8. Rubinow, S. I. 1975.Introduction to Mathematical Biology. New York: Wiley.Google Scholar
  9. — and J. L. Lebowitz. 1970. “Time-Dependent Michaelis-Menten Kinetics for an Enzyme-Substrate-Inhibitor System.”J. Am. Chem. Soc.,92, 3888–3893.CrossRefGoogle Scholar
  10. Segel, L. A. 1984.Modeling Dynamic Phenomena in Molecular and Cellular Biology. Cambridge: Cambridge University Press.Google Scholar
  11. Segel, L. A. and M. Slemrod. 1988. “The Quasi-Steady State Assumption: A Case Study in Perturbation.”SIAM Review. in press.Google Scholar
  12. Sols, A. and Marco, R. 1970. “Concentrations of Metabolites and Binding Sites. Implications in Metabolic Regulation.” InCurrent Topics in Cellular Regulation, Vol. 2. New York: Academic Press.Google Scholar
  13. Wong, J. T.-F. 1965. “On the Steady-State Method of Enzyme Kinetics.”J. Am. Chem. Soc.,87, 1788–1793.CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 1988

Authors and Affiliations

  • Lee A. Segel
    • 1
  1. 1.Department of Applied Mathematics and Computer ScienceThe Weizmann Institute of ScienceRehovotIsrael

Personalised recommendations