Abstract
A systematic perturbative procedure (the method of singular perturbation) is developed to follow the time evolution of an enzyme catalyzed reaction with one intermediate product over the entire time domain of interest. The perturbation parameter is the ratio of the enzyme concentration to the Michaelis-Menten constant. The treatment leads to a meaningful definition of the so-called quasisteady state often invoked in the description of enzyme catalyzed reactions. The legitimacy and the domain of validity of this assumption are examined in the context of both the reversible and irreversible Michaelis-Menten kinetics.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Glick, N., Landman, A. D., Roufogalis, B. D.: Correcting Lineweaver-Burk calculations of V and K m . TIBS 4, 82–83 (1979)
Hommes, F. A.: The integrated Michaelis-Menten equation. Arch. Biochem. Biophys. 96, 28–31 (1962a)
Hommes, F. A.: Analog computer studies of a simple enzyme-catalyzed reaction. Arch. Biochem. Biophys. 96, 32–36 (1962b)
Reich, J. G., Sel'kov, E. E.: Mathematical analysis of metabolic networks. FEBS Lett. 40, 119–127 (1974)
Schauer, M., Heinrich, R.: Analysis of the quasi-steady-state approximation for an enzymatic one-substrate reaction. J. Theor. Biol. 79, 425–442 (1979)
Stayton, M. M., Fromm, H. J.: A computer analysis of the validity of integrated Michaelis-Menten equation. J. Theor. Biol. 78, 309–323 (1979)
Van Dyke, M.: Perturbation methods in fluid mechanics. Stanford: Parabolic Press 1975
Walter, C. F., Morales, M. F.: An analogue computer investigation of certain issues in enzyme kinetics. J. Biol. Chem. 239, 1277–1283 (1964)
Walter, C.: The practicality of the use of the steady-state assumption and the inflection point method in enzyme kinetics. J. Theor. Biol. 15, 1–33 (1966)
Walter, C.: The validity of using a quasi-steady state approximation for the reversible Michaelis-Menten mechanism of enzyme action. J. Theor. Biol. 44, 1–5 (1974)
Wong, J.: On the steady-state method of enzyme kinetics. J. Am. Chem. Soc. 87, 1788–1793 (1965)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Seshadri, M.S., Fritzsch, G. Analytical solutions of a simple enzyme kinetic problem by a perturbative procedure. Biophys. Struct. Mechanism 6, 111–123 (1980). https://doi.org/10.1007/BF00535748
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00535748