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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
Perspective

ABSTRACT

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.

KEY WORDS

biophase concentration receptor dissociation constant null method 

ABBREVIATIONS

A

drug concentration in bulk solution in absence of receptor blockade

A’

drug concentration in bulk solution in presence of receptor blockade

C

drug concentration in biophase

K

dissociation constant of ligand-receptor interaction

k1

forward rate constant of ligand-receptor interaction

k2

reverse rate constant of ligand-receptor interaction

PK

pharmacokinetics

PD

pharmacodynamics

Rt

total number of receptors

r

receptor concentration

x

bound drug concentration

ξ

unblocked fraction of receptors

Φ

constant relating bulk and biophase concentrations

Notes

ACKNOWLEDGMENTS & DISCLOSURES

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

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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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