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Properties of the Michaelis-Menten equation and its integrated form which are useful in pharmacokinetics

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An Erratum to this article was published on 01 August 1973

Abstract

Some old equations are reviewed and some new equations have been derived which indicate certain properties of the Michaelis-Menten equation and its integrated forms. Simulated data which obey Michaelis-Menten kinetics have been plotted in various ways to illustrate special relationships. An equation is derived which accurately estimates the slope of the apparently linear decline (ko)of concentrations from the values of Co, Km,and Vm.This indicates the hybrid nature of ko.It is pointed out that if a metabolite is formed by Michaelis-Menten kinetics, then (a)one would not expect linear plots of cumulative amount of metabolite excreted in the urine vs. time, and (b)the plasma clearance of the drug will change with dose, and the plasma clearance of the drug would be expected to be different following administration of the same dose in a rapidly available and a slowly available dosage form. The distortion in parameter values when data arising from Michaelis-Menten kinetics are evaluated by classical linear pharmacokinetics is indicated.

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References

  1. L. Michaelis and M. L. Menten. Die Kinetik der Invertinwirkung.Biochem. Z.,49, 333–369 (1913).

    CAS  Google Scholar 

  2. A. F. Bartholomay. Stochastic models in medicine and biology. In Proceedings of a Symposium, Mathematics Research Center, U.S. Army, University of Wisconsin, June 12–14, (1963), pp. 105–112.

  3. V. Henri. Theórie générale de l'action de quelques diastases.Compt. Rend. Hebd. Séanc. Acad. Sci. (Paris),135, 916–919 (1902).

    CAS  Google Scholar 

  4. A. Rescigno and G. Segre.Drug and Tracer Kinetics. Blaisdell, Waltham, Mass., 1966,p. 14.

    Google Scholar 

  5. J. G. Wagner. A new generalized nonlinear pharmacokinetic model and its implications. InBiopharmaceutics and Relevant Pharmacokinetics, Drug Intelligence Publications, Hamilton Press, Hamilton, Ill. (1971), pp. 302–317.

    Google Scholar 

  6. R. L. Dedrick and K. B. Bischoff. Pharmacokinetics in application of the artificial kidney.Chem. Engr. Prog. Symp. ser.,64, 32–44 (1968).

    CAS  Google Scholar 

  7. K. B. Bischoff and R. L. Dedrick. Thiopental pharmacokinetics.J. Pharm. Sci.,57, 1346–1357 (1968).

    Article  CAS  PubMed  Google Scholar 

  8. K. B. Bischoff, R. L. Dedrick, and D. S. Zaharko. Preliminary model for methotrexate pharmacokinetics.J. Pharm. Sci. 59, 149–154 (1970).

    Article  CAS  PubMed  Google Scholar 

  9. F. Lundquist and H. Wolthers. The kinetics of alcohol elimination in man.Acta Pharmacol. Toxicol.,14, 265–289 (1958).

    Article  CAS  Google Scholar 

  10. E. Krüger-Thiemer. Nonlinear dose-concentration relationships.Farmaco (Pavia) Ed. Sci.,23, 717–756 (1968).

    Google Scholar 

  11. E. Krüger-Thiemer and R. R. Levine. The solution of pharmacological problems with computers. Part 8. Non first-order models of drug metabolism.Arzneim.-Forsch.,18, 1575–1579 (1968).

    Google Scholar 

  12. E. S. Vesell, J. G. Page, and G. T. Passonanti. Genetic and environmental factors affecting ethanol metabolism in man.Clin. Pharmacol. Therap.,12, 192–201 (1971).

    CAS  Google Scholar 

  13. A. Goldstein. Saturation of alcohol dehydrogenase by ethanol.New. Engl. J. Med.,283, 875 (1970).

    CAS  PubMed  Google Scholar 

  14. G. Levy. Pharmacokinetics of salicylate elimination in man.J. Pharm. Sci.,54, 959–967 (1965).

    Article  CAS  PubMed  Google Scholar 

  15. G. Levy, T. Tsuchuja, and L. P. Amsel. Limited capacity for salicyl phenolic glucuronide formation and its effect on the kinetics of salicylate elimination in man.Clin. Pharmacol. Therap.,13, 258–268 (1972).

    CAS  Google Scholar 

  16. N. Gerber and K. Arnold. Studies on the metabolism of diphenylhydantoin in mice.J. Pharmacol. Exptl. Therap.,167, 77–89 (1969).

    CAS  Google Scholar 

  17. N. Gerber and J. G. Wagner. Explanation of dose-dependent decline of diphenylhydantoin plasma levels by fitting to the integrated form of the Michaelis-Menten equation.Res. Commun. Chem. Pathol. Pharm.,3, 455–466 (1972).

    CAS  Google Scholar 

  18. J. G. Wagner and J. A. Patel. Variations in absorption and elimination rates of ethyl alcohol in a single subject.Res. Commun. Chem. Pathol. Pharm. 4:61–76 (1972).

    CAS  Google Scholar 

  19. C. S. Lieber and L. M. DeCarli. The role of the hepatic microsomal ethanol oxidizing system (MEOS) for ethanol metabolismin vivo.J. Pharmacol. Exptl. Therap.,181, 279–287 (1972).

    CAS  Google Scholar 

  20. M. R. Morgan. Approximations of the integrated rate equation for enzyme reactions: The Veibel equation.Enzymologia,42, 219–233 (1972).

    CAS  Google Scholar 

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Authors and Affiliations

  1. College of Pharmacy and Upjohn Center for Clinical Pharmacology, The University of Michigan, 48104, Ann Arbor, Michigan

    John G. Wagner

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  1. John G. Wagner
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An erratum to this article is available at http://dx.doi.org/10.1007/BF01060041.

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Wagner, J.G. Properties of the Michaelis-Menten equation and its integrated form which are useful in pharmacokinetics. Journal of Pharmacokinetics and Biopharmaceutics 1, 103–121 (1973). https://doi.org/10.1007/BF01059625

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  • DOI: https://doi.org/10.1007/BF01059625

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