Implementing Receptor Theory in PK-PD Modeling
Meindert Danhof and Bart Ploeger
Leiden-Amsterdam Center for Drug Research and LAP&P Consultants BV, Leiden, the Netherlands
Mechanism-based pharmacokinetic-pharmacodynamic (PK-PD) models differ from conventional PK-PD models in that they quantitatively characterize specific processes on the causal path between drug administration and effect. This includes target site distribution, target binding and activation, pharmacodynamic interactions, transduction and homeostatic feedback mechanisms. Consequently, the effects on disease processes are considered. It has been demonstrated that, compared to traditional descriptive models, mechanism-based PK-PD models have improved properties for extrapolation and prediction. Hence, they constitute a scientific basis for rational drug discovery and development [1,2].
Mechanism-based PK-PD models utilize receptor theory concepts for characterization of target binding and target activation processes. In this respect, receptor theory constitutes the basis for 1) prediction of in vivo drug concentration-effect relationships and 2) characterization of target association-dissociation kinetics as determinants of hysteresis in the time course of the drug effect.
Prediction of in vivo concentration-effect relationships
In the traditional PK-PD modeling approach rather empirical models such as the Hill equation are used to describe in vivo drug concentration-effect relationships. However, the Hill equation does not provide insight into factors determining the shape and location (in terms of concentration) of the concentration-effect relationship.
In theory, the relationship between drug concentration and biological response depends on drug and biological system specific factors. Therefore, the prediction of in vivo drug concentration-effect relationships requires distinguishing ‘drug-specific' and ‘biological system-specific' parameters. Classical receptor theory can be applied for making this separation, since it describes drug action by 2 independent parts, which relate to drug-specific (i.e. the agonist-dependent part) and system specific properties (i.e. the tissue-dependent part). Hence, receptor theory constitutes a scientific basis for the prediction of in vivo concentration-effect relationships [3].
Receptor theory has been incorporated in pharmacodynamic modeling in semi-parametric and full-parametric approaches. Both approaches use a hyperbolic function for describing target binding and activation, but differ in the way they describe the system-specific transducer or stimulus-response function. In the semi-parametric approach no specific assumptions are made with regard to the transducer function, making this approach particularly suitable for exploratory data analysis [4], whereas the full parametric approach requires the shape of the transducer function to be known. Particularly in systems with a high receptor reserve a hyperbolic transducer function is commonly observed, which can be implemented using the ‘Operational Model of Agonism' [5,6].
Mechanism-based PK-PD models can be identified by simultaneously analysing concentration-effect relationships of a variety of compounds with different target affinity and intrinsic efficacy. In this manner the system-specific transducer function, describing the unique relation between target activation and effect, can be identified. In addition, for each of the compounds estimates of the in vivo operational affinity and intrinsic efficacy are obtained. In a series of investigations on drugs acting at G-protein coupled receptors (i.e. adenosine A1, µ-opioid and serotonin 5-HT1A receptors) and at the GABAA receptor complex, close correlations have been observed between estimated in vivo values and corresponding values derived from in vitro bioassays [6 - 9]. This shows the utility of receptor theory models for predicting in vivo concentration-effect relationships using in vitro bioassays data. This modeling approach has been successfully applied in the characterization of tissue-selectivity of drug effects [10], inter-species extrapolation of concentration-effect relationships [11] and analysis of inter-individual variability in pharmacodynamics resulting from ‘receptor down regulation' [12]. Most recently the application of receptor theory in PK-PD modeling has been extended to pharmacodynamic drug interactions [13].
Target association-dissociation kinetics as determinants of hysteresis
Target association-dissociation kinetics can be a significant determinant of hysteresis between plasma concentration and effect. Estimation of the rate constants of in vivo target association-dissociation is often complex as it may be confounded by the biophase distribution kinetics and the kinetics of transduction. However, a number of studies [14 - 19] have shown that measuring drug concentrations in the biophase and/or the availability of data from dedicated pharmacological experiments allows accurate and precise estimation of target binding kinetics. An investigation in rats has shown that advanced imaging technologies (e.g. positron emission tomography) enable direct estimation of the target association and dissociation kinetics by PK-PD modeling [14]. Alternatively, simultaneous fitting of a series of in vitro binding experiments allows estimating the receptor association and dissociation rate constants [15]. Biophase distribution and target association-dissociation kinetics of semi-synthetic opioids were simultaneously estimated using data on the time-course of their analgesic and respiratory depressant effect in rats [16,17] and in humans [18,19]. A crucial factor in these analyses was the availability of dense data on the time course of drug concentration and effects following administration of a wide dose range. These models have been successfully applied for extrapolation of the pharmacodynamics of buprenorphine from rats to humans [20] as well as the design of optimized dosing regimens for the antagonism of buprenorphine-induced respiratory depression with naloxone [21].
References
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[5] Black JW and Leff P (1983). Operational models of pharmacological agonism. Proc. R. Soc. London B 220: 141-162.
[6] Van der Graaf PH, Van Schaick EA, Mathôt RAA, IJzerman AP and Danhof M (1997). Mechanism-based pharmacokinetic-pharmacodynamic modeling of the effects of N6-Cyclopentyladenosine analogs on heart rate in rat: estimation of in vivo operational affinity and efficacy at adenosine A1 receptors. J. Pharmacol. Exp. Ther., 283: 809-816.
[7] Cox EH, Kerbusch T, Van der Graaf PH and Danhof M (1998). Pharmacokinetic- pharmacodynamic modelling of the electroencephalogram effect of synthetic opioids in the rat. Correlation with binding at the µ-opioid receptor.J. Pharmacol. Exp. Ther., 284: 1095-1103.
[8] Visser SAG, Wolters FL, Gubbens-Stibbe KM, Tukker E, Van Der Graaf PH, Peletier LA and Danhof M (2003). Mechanism-based pharmacokinetic-pharmacodynamic modeling of the electroencephalogram effects of GABAA receptor modulators: in vitro-in vivo correlations. J Pharmacol Exp Ther 304: 88-101.
[9] Zuideveld KP, Van der Graaf PH, Newgreen D, Thurlow R, Petty N, Jordan P, Peletier LA and Danhof M (2004). Mechanism-based pharmacokinetic-pharmacodynamic modeling of 5-HT1A receptor agonists: estimation of in vivo affinity and intrinsic efficacy on body temperature in rats. J. Pharmacol Exp Ther. 308: 1012-1020.
[10] Van der Graaf PH, Van Schaick EA, Visser SAG, De Greef HJMM, IJzerman AP, and Danhof M (1999): Mechanism-based pharmacokinetic-pharmacodynamic modelling of the anti-lipolytic effects of adenosine A1 receptor agonists in rats: prediction of tissue dependent efficacy in vivo. J. Pharmacol. Exp. Ther., 290: 702-709.
[11] Cox EH, Langemeijer MWE, Gubbens-Stibbe JM, Muir KT and Danhof M (1999). The comparative pharmacodynamics of remifentanil and its metabolite, GR90291, in a rat EEG model. Anesthesiology , 90: 535-544.
[12] Garrido M, Gubbens-Stibbe JM, Tukker E, Cox EH, Von Freitag Drabbe Künzel J, IJzerman AP, Danhof M and Van der Graaf PH (2000). Pharmacokinetic-pharmacodynamic analysis of the EEG effect of alfentanil in rats following funaltrexamine-induced opioid receptor "knockdown" in vivo. Pharm. Res. 17: (6) 653-659.
[13] Jonker DM, Visser SAG, Van der Graaf PH, Voskuyl RA, Danhof M (2005): Towards a mechanism-based analysis of pharmacodynamic drug-drug interactions in vivo. Pharmacol.Ther. 106: 1-18.
[14] Liefaard LC, Ploeger BA, Molthoff CF, Boellaard R, Lammertsma AA, Danhof M and Voskuyl RA (2005): Population pharmacokinetic analysis for simultaneous determination of Bmax and KD in vivo by positron emission tomography. Mol. Imaging Biol. 7: 411-421.
[15] Benson N, Snelder N, Ploeger B , Napier C, Sale H and van der Graaf P (2007) Utility of a mixed effects approach to defining target binding rate constants. PAGE 16 Abstr 1103 [www.page-meeting.org/?abstract=1103]
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[17] Yassen A, Kan J, Olofsen E, Suidgeest E, Dahan A, Danhof M (2006) Mechanism-based pharmacokinetic-pharmacodynamic modeling of the respiratory-depressant effect of buprenorphine and fentanyl in rats. J Pharmacol Exp Ther.;319: 682-692.
[18] Yassen A, Olofsen E, Romberg R, Sarton E, Danhof M, Dahan A.(2006) Mechanism-based pharmacokinetic-pharmacodynamic modeling of the antinociceptive effect of buprenorphine in healthy volunteers. Anesthesiology.;104:1232-1242.
[19] Yassen A, Olofsen E, Romberg R, Sarton E, Teppema L, Danhof M, Dahan A. (2007) Mechanism-based PK/PD modeling of the respiratory depressant effect of buprenorphine and fentanyl in healthy volunteers. Clin Pharmacol Ther. 81:50-58
[20] Yassen A, Olofsen E, Kan J, Dahan A, Danhof M. (2007) Animal-to-human extrapolation of the pharmacokinetic and pharmacodynamic properties of buprenorphine.Clin Pharmacokinet.;46:433-447
[21] Yassen A, Olofsen E, van Dorp E, Sarton E, Teppema L, Danhof M, Dahan A (2007) Mechanism-based pharmacokinetic-pharmacodynamic modelling of the reversal of buprenorphine-induced respiratory depression by naloxone : a study in healthy volunteers. Clin Pharmacokinet.;46:965-980.
