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

  • John G. Wagner
Article

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.

Key words

Michaelis-Menten kinetics dose-dependent kinetics elimination half-life areas under blood level curves urinary excretion of metabolites 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L. Michaelis and M. L. Menten. Die Kinetik der Invertinwirkung.Biochem. Z.,49, 333–369 (1913).Google Scholar
  2. 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.Google Scholar
  3. 3.
    V. Henri. Theórie générale de l'action de quelques diastases.Compt. Rend. Hebd. Séanc. Acad. Sci. (Paris),135, 916–919 (1902).Google Scholar
  4. 4.
    A. Rescigno and G. Segre.Drug and Tracer Kinetics. Blaisdell, Waltham, Mass., 1966,p. 14.Google Scholar
  5. 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. 6.
    R. L. Dedrick and K. B. Bischoff. Pharmacokinetics in application of the artificial kidney.Chem. Engr. Prog. Symp. ser.,64, 32–44 (1968).Google Scholar
  7. 7.
    K. B. Bischoff and R. L. Dedrick. Thiopental pharmacokinetics.J. Pharm. Sci.,57, 1346–1357 (1968).PubMedCrossRefGoogle Scholar
  8. 8.
    K. B. Bischoff, R. L. Dedrick, and D. S. Zaharko. Preliminary model for methotrexate pharmacokinetics.J. Pharm. Sci. 59, 149–154 (1970).PubMedCrossRefGoogle Scholar
  9. 9.
    F. Lundquist and H. Wolthers. The kinetics of alcohol elimination in man.Acta Pharmacol. Toxicol.,14, 265–289 (1958).CrossRefGoogle Scholar
  10. 10.
    E. Krüger-Thiemer. Nonlinear dose-concentration relationships.Farmaco (Pavia) Ed. Sci.,23, 717–756 (1968).Google Scholar
  11. 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. 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).Google Scholar
  13. 13.
    A. Goldstein. Saturation of alcohol dehydrogenase by ethanol.New. Engl. J. Med.,283, 875 (1970).PubMedGoogle Scholar
  14. 14.
    G. Levy. Pharmacokinetics of salicylate elimination in man.J. Pharm. Sci.,54, 959–967 (1965).PubMedCrossRefGoogle Scholar
  15. 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).Google Scholar
  16. 16.
    N. Gerber and K. Arnold. Studies on the metabolism of diphenylhydantoin in mice.J. Pharmacol. Exptl. Therap.,167, 77–89 (1969).Google Scholar
  17. 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).Google Scholar
  18. 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).Google Scholar
  19. 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).Google Scholar
  20. 20.
    M. R. Morgan. Approximations of the integrated rate equation for enzyme reactions: The Veibel equation.Enzymologia,42, 219–233 (1972).Google Scholar

Copyright information

© Plenum Publishing Corporation 1973

Authors and Affiliations

  • John G. Wagner
    • 1
  1. 1.College of Pharmacy and Upjohn Center for Clinical PharmacologyThe University of MichiganAnn Arbor

Personalised recommendations