Pharmaceutical Research

, Volume 29, Issue 3, pp 637–642 | Cite as

‘Null Method’ Determination of Drug Biophase Concentration

  • Ronald J. Tallarida
  • Neil Lamarre
  • Robert B. Raffa


PK/PD modeling is enhanced by improvements in the accuracy of its metrics. For PK/PD modeling of drugs and biologics that interact with enzymes or receptors, the equilibrium constant of the interaction can provide critical insight. Methodologies such as radioliogand binding and isolated tissue preparations can provide estimates of the equilibrium constants (as the dissociation constant, K value) for drugs and endogenous ligands that interact with specific enzymes and receptors. However, an impediment to further precision for PK/PD modeling is that it remains a problem to convert the concentration of drug in bulk solution (A) into an estimate of receptor occupation, since A is not necessarily the concentration (C) of drug in the biophase that yields fractional binding from the law of mass action, viz., C/(C + K). In most experimental studies A is much larger than K, so the use of administered instead of biophase concentration gives fractional occupancies very close to unity. We here provide a simple way to obtain an estimate of the factor that converts the total drug concentration into the biophase concentration in isolated tissue preparation. Our approach is an extension of the now classic ‘null method’ introduced and applied by Furchgott to determination of drug-receptor dissociation constants.


biophase concentration receptor dissociation constant null method 



drug concentration in bulk solution in absence of receptor blockade


drug concentration in bulk solution in presence of receptor blockade


drug concentration in biophase


dissociation constant of ligand-receptor interaction


forward rate constant of ligand-receptor interaction


reverse rate constant of ligand-receptor interaction






total number of receptors


receptor concentration


bound drug concentration


unblocked fraction of receptors


constant relating bulk and biophase concentrations



R.J.T. was supported by NIH/NIDA grant DA013429 and N.L. was supported by NIH/NIDA training-grant DA07237-17.


  1. 1.
    Raffa RB, Tallarida RJ. Affinity: Historical development in chemistry and pharmacology. Bull Hist Chem. 2010;35:7–16.Google Scholar
  2. 2.
    Maehle AH. Receptive substances: John Newport Langley (1852–1925) and his path to a receptor theory of drug action. Med Hist. 2004;48:153–74.PubMedCrossRefGoogle Scholar
  3. 3.
    Parascandola J, Jasensky R. Origins of the receptor theory of drug action. Bull Hist Med. 1974;48:199–220.PubMedGoogle Scholar
  4. 4.
    Kenakin TP. Pharmacologic analysis of drug-receptor interaction, ed 3. Lippincott Williams and Wilkins: Philadelphia; 1997.Google Scholar
  5. 5.
    Tallarida RJ, Raffa RB, McGonigle P. Principles in general pharmacology. Springer-Verlag: New York; 1988.CrossRefGoogle Scholar
  6. 6.
    Tallarida RJ. Pharmacologic methods for identification of receptors. Life Sci. 1988;43:2169–76.PubMedCrossRefGoogle Scholar
  7. 7.
    Pries AR, Secomb TW: Blood flow in microvascular networks: Comprehensive Physiology, 2011, pp 3–36.Google Scholar
  8. 8.
    Furchgott RF. The use of β-haloalkylamines in the differentiation of receptors and in the determination of dissociation constants or receptor-agonist complexes. Adv Drug Res. 1966;3:21–55.Google Scholar
  9. 9.
    Furchgott RF, Bursztyn P. Comparison of dissociation constants and of relative efficacies of selected agonists acting on parasympathetic receptors. Ann NY Acad Sci. 1967;144:882–99.CrossRefGoogle Scholar
  10. 10.
    Tallarida RJ, Jacob LS. Dose-response relation in pharmacology. Springer: New York; 1979.Google Scholar
  11. 11.
    Limbird LE. Cell surface receptors: A short course on theory and methods. Springer: New York; 1986.Google Scholar
  12. 12.
    Strecker RB, Hubbard WC, Michelakis AM. Dissociation constant of the norepinephrine-receptor complex in normotensive and hypertensive rats. Circ Res. 1975;37:658–63.PubMedGoogle Scholar
  13. 13.
    Schroder W, Tzschentke TM, Terlinden R, De Vry J, Jahnel U, Christoph T, et al. Synergistic interaction between the two mechanisms of action of tapentadol in analgesia. J Pharmacol Exp Ther. 2011;337:312–20.PubMedCrossRefGoogle Scholar
  14. 14.
    van Steeg TJ, Freijer J, Danhof M, de Lange EC. Mechanism-based pharmacodynamic modeling of s(−)-atenolol: Estimation of in vivo affinity for the beta1-adrenoceptor with an agonist-antagonist interaction model. J Pharmacol Exp Ther. 2008;324:1234–42.PubMedCrossRefGoogle Scholar
  15. 15.
    van Steeg TJ, Boralli VB, Krekels EH, Slijkerman P, Freijer J, Danhof M, et al. Influence of plasma protein binding on pharmacodynamics: Estimation of in vivo receptor affinities of beta blockers using a new mechanism-based pk-pd modelling approach. J Pharm Sci. 2009;98:3816–28.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Ronald J. Tallarida
    • 1
  • Neil Lamarre
    • 1
  • Robert B. Raffa
    • 2
  1. 1.Department of Pharmacology & Center for Substance Abuse ResearchTemple University School of MedicinePhiladelphiaUSA
  2. 2.Department of Pharmaceutical Sciences, School of PharmacyTemple UniversityPhiladelphiaUSA

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