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An investigation of basic assumption in enzyme kinetics using results of the geometric theory of differential equations

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Abstract

Up to the present time, the following property of the product component in the reversible one substrate-one intermediate-one product enzymic mechanism has been taken only as anassumption, viz., during the course of the reaction, the time-rate of change of product concentration is never negative and the product concentration never exceeds its equilibrium value. Applying the methods of the geometric theory of ordinary differential equations it is shown that this result follows as a direct deduction from the differential equations governing the mechanism together with the initial conditions. Further, the nature of the equilibrium point as a stable node is established.

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Literature

  • Hearon, J. Z., S. A. Bernhard, S. L. Friess, D. J. Botts and M. F. Morales. 1959. “Enzyme Kinetics.” InThe Enzymes, P. D. Boyer, H. Lardy and K. Myrbäck eds., Vol. 1, New York: Academic Press, 49–142.

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  • Lefschetz, S. 1963.Differential Equations: Geometric Theory, 2nd ed. New York: Interscience Publishers.

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  • Walter, C. F. and M. F. Morales. 1964. “An Analogal Computer Investigation of Certain Issues in Enzyme Kinetics.”J. Biol. Chem.,239, 1277–1283.

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Authors and Affiliations

  1. Department of Biochemistry, The University of New South Wales, Kensington, N.S.W., Australia

    I. G. Darvey & R. F. Matlak

  2. Department of Pure Mathematics, The University of New South Wales, Kensington, N.S.W., Australia

    I. G. Darvey & R. F. Matlak

Authors
  1. I. G. Darvey
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  2. R. F. Matlak
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Darvey, I.G., Matlak, R.F. An investigation of basic assumption in enzyme kinetics using results of the geometric theory of differential equations. Bulletin of Mathematical Biophysics 29, 335–341 (1967). https://doi.org/10.1007/BF02476904

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  • DOI: https://doi.org/10.1007/BF02476904

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