Computational Geosciences

, Volume 17, Issue 3, pp 599–608 | Cite as

Dynamics of target-mediated drug disposition: how a drug reaches its target

  • L. A. Peletier
  • J. Gabrielsson
Original Paper


We study the dynamics of drug–target interaction and the way it impacts the shape of drug versus time graphs through the derivation of accurate closed-form approximations, which reveal explicitly the relevance of rate constants in the system and can be used to compute such critical quantities as the area under the ligand (drug) curve, the clearance and the terminal slope λ z . We also use these approximations to verify the validity of well-known approximate models, in particular the rapid binding model (Mager and Krzyzanski, Pharm Res 22:1589–1596, 2005) and the quasi-steady state model (Gibiansky et al., J Pharmacokinet Pharmacodyn 35:573–591, 2008).


Pharmacokinetics Receptor-binding Michaelis–Menten Singular perturbations 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aston, P.J., Derks, G., Raji, A., Agoram, B.M., van der Graaf, P.H.: Mathematical analysis of the pharmacokinetic-pharmacodynamic (PKPD) behaviour of monoclonal antibodies: predicting in vivo potency. J. Theor. Biol. 281, 113–121 (2011)CrossRefGoogle Scholar
  2. 2.
    Dayneka, N.L., Garg, V., Jusko W.J.: Comparison of four basic models of indirect pharmacodynamic responses. J. Pharmacokinet. Biopharm. 21, 457–478 (1993)CrossRefGoogle Scholar
  3. 3.
    Gabrielsson, J., Weiner, D.: Pharmacokinetic Pharmacodynamic Data Analysis, Concepts and Applications, 4th edn. Swedish Pharmaceutical, Stockholm (2010)Google Scholar
  4. 4.
    Gibiansky, L., Gibiansky, E., Kakkar, T., Ma, P.: Approximations of the target-mediated drug disposition model and identifying of model parameters. J. Pharmacokin. Pharmacodyn. 35, 573–591 (2008)CrossRefGoogle Scholar
  5. 5.
    Krzyzanski, W., Wyska, E.: Pharmacokinetics and pharmacodynamics of erythropoietin receptor in healthy volunteers. Naunyn-Schmiedeberg’s Arch. Pharmacol. 377, 637–645 (2008)CrossRefGoogle Scholar
  6. 6.
    Levy G.: Pharmacologic target mediated drug disposition. Clin. Pharmacol. Ther. 56, 248–252 (1994)CrossRefGoogle Scholar
  7. 7.
    Lobo, E., Hansen, R.J., Balthasar, J.R.: Antibody pharmacokinetics and pharmacodynamics. J. Pharm. Sci. 93, 2645–2667 (2004)CrossRefGoogle Scholar
  8. 8.
    Ma, P.: Theoretical considerations of target-mediated drug disposition models: simplifications and approximations. Pharm. Res. 29, 866–882 (2012)CrossRefGoogle Scholar
  9. 9.
    Mager, D., Jusko, W.J.: General pharmacokinetic model for drugs exhibiting target-mediated drug disposition. J. Pharmacokin. Pharmacodyn. 28, 507–532 (2001)CrossRefGoogle Scholar
  10. 10.
    Mager, D., Krzyzanski, W.: Quasi-equilibrium pharmacokinetic model for drugs exhibiting target-mediated drug disposition. Pharm. Res. 22, 1589–1596 (2005)CrossRefGoogle Scholar
  11. 11.
    Mager, D.: Target-mediated drug disposition and dynamics. Biochem. Pharmacol. 72, 1–10 (2006)CrossRefGoogle Scholar
  12. 12.
    Michaelis, L., Menten, M.L.: Die kinetik der invertinwirkung. Biochem. Z. 49, 333–369 (1913)Google Scholar
  13. 13.
    Peletier, L.A., Gabrielsson, J., Haag, J.: A dynamical systems analysis of the indirect response model with special emphasis on time to peak response. J. Pharmacokin. Pharmacodyn. 32, 607–654 (2005)CrossRefGoogle Scholar
  14. 14.
    Peletier, L.A., Gabrielsson, J.: Dynamics of target-mediated drug disposition. Eur. J. Pharm. Sci. 38, 445–464 (2009)CrossRefGoogle Scholar
  15. 15.
    Peletier, L.A., Benson, N., van der Graaf, P.H.: Impact of plasma-protein binding on receptor occupancy: an analytical description. J. Theor. Biol. 256, 253–62 (2009)CrossRefGoogle Scholar
  16. 16.
    Segel, L.A.: The validity of the steady state assumption of enzyme kinetics. Bull. Math. Biol. 50, 579–593 (1988)Google Scholar
  17. 17.
    Segel, L.A., Slemrod, M.: The quasi-steady state assumption: a case study in perturbation. SIAM Rev. 31, 446–477 (1989)CrossRefGoogle Scholar
  18. 18.
    Sugiyama, Y., Hanano, M.: Receptor-mediated transport of peptide hormones and its importance in the overall hormone disposition in the body. Pharm. Res. 6, 192–202 (1989)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Mathematical InstituteLeiden UniversityRA LeidenThe Netherlands
  2. 2.Department of Biomedical Sciences and Veterinary Public Health, Division of Pharmacology and ToxicologySwedish University of Agricultural SciencesUppsalaSweden

Personalised recommendations