Drug Metab. Pharmacokinet. 24 (1): 3–15 (2009). Review Incorporating Theory in Mechanism-Based Pharmacokinetic-Pharmacodynamic (PK-PD) Modeling

Bart A. PLOEGER1,3,*,PietH.vanderGRAAF2 and Meindert DANHOF1,3 1LAP&P Consultants BV, Leiden, The Netherlands 2Pfizer, Department of Pharmacokinetics, Dynamics, and Metabolism (PDM), Sandwich, United Kingdom 3Leiden-Amsterdam Center for Drug Research, Division of Pharmacology, University of Leiden, Leiden, The Netherlands

Full text of this paper is available at http://www.jstage.jst.go.jp/browse/dmpk

Summary: Pharmacokinetic-Pharmacodynamic (PK-PD) modeling helps to better understand drug efficacy and safety and has, therefore, become a powerful tool in the learning-confirming cycles of drug-development. In translational drug research, mechanism-based PK-PD modeling has been recognized as a tool for bringing forward early insights in drug efficacy and safety into the clinical development. These models differ from descriptive PK-PD models in that they quantitatively characterize specific processes in the causal chain be- tween drug administration and effect. This includes target site distribution, binding and activation, phar- macodynamic interactions, transduction and homeostatic feedback mechanisms. Compared to descriptive models mechanism-based PK-PD models that utilize receptor theory concepts for characterization of target binding and target activation processes have improved properties for extrapolation and prediction. In this respect, receptor theory constitutes the basis for 1) prediction of in vivo drug concentration-effect relation- ships and 2) characterization of target association-dissociation kinetics as determinants of hysteresis in the time course of the drug effect. This approach intrinsically distinguishes drug- and system specific parameters explicitly, allowing accurate extrapolation from in vitro to in vivo and across species. This review provides an overview of recent developments in incorporating receptor theory in PK-PD modeling with a specific focus on the identifiability of these models.

Keywords: receptor theory; mechanism-based Pharmacokinetic-Pharmacodynamic modeling; kinetics of drug action; Operational Model of Agonism, target site distribution

bringing forward early (discovery and preclinical) insights Introduction in drug efficacy and safety into the clinical development Pharmacokinetic-Pharmacodynamic modeling (PK-PD) stage.12) Mechanism-based PK-PD models differ from em- and simulation has been recognized as a key factor to im- pirical PK-PD models in that they quantitatively charac- prove the efficiency of the drug-development process, terize specific processes in the causal chain between drug which is facing high attrition rates. Over the years, the administration and effect.6) However, for their part, useofPK-PDmodelingtobetterunderstanddrugeffica- mechanism-based PK-PD models differ from full cy and safety, thereby improving the quality of decision mechanistic or systems biology models. In mechanism- making in drug-development, has been advocated by based PK-PD modeling one follows a data driven, top- pharmaceutical companies,1–5) academia6,7) and regulato- down approach starting at a parsimonious descriptive lev- ry agencies.7–9) When these insights are obtained in early el and subsequently add more complexity to better un- development they can be used in a translational approach derstand the system. Hence, the parameters in these to better predict efficacy and safety in the later stages of models are composites of the actual (patho)-physiological clinical development.6,10) This will reduce the attrition and pharmacological processes. On the other hand, sys- risk during clinical development due to lack of efficacy tems biology models are inherently complete and fully or safety.11) In translational drug-research, mechanism- mechanistic and follows a bottom-up approach, starting based PK-PD modeling has evolved as an essential tool for from the level of molecular pathways.13) Using the ter-

Received; October 31, 2008, Accepted; December 18, 2008 *To whom correspondence should be addressed: Bart PLOEGER, LAP&P Consultants BV, Archimedesweg 31, 2333 CM Leiden, The Netherlands. Tel. ＋31715243005, fax. ＋31715243001, E-mail: b.ploeger＠lapp.nl

3 4 Bart A. PLOEGER, et al.

Fig. 1. Processes in the causal chain between drug administration and the change in response over time, including the phar- macokinetics of a drug (process A), target site distribution and receptor (target) binding kinetics (process B), receptor activation (process C) and transduction (process D) These processes are characterized by receptor theory models incorporated in mechanism-based PK-PD models. These models explicitly distinguish drug and system specific properties, which are shown in the solid white and shaded area's respectively.

Cl, clearance; V, volume of distribution; Ka, absorption rate constant; Ke0, biophase distribution constant; kon, association rate constant; koff, dissociation rate constant; KA, receptor affinity; e, intrinsic efficacy; KAR, receptor occupancy resulting in 50% stimulus; Em, maximum effect; nE slope of stimulus-response relationship; KE, stimulus resulting in 50% effect.

minology of Weiss et al., who distinguished parsimonious chain include target site distribution, target binding and and heuristic models at the extremes of the modeling activation, pharmacodynamic interactions, transduction philosophy spectrum,14) empirical PK-PD models are the and homeostatic feedback mechanisms. Consequently, parsimonious and systems biology models the heuristic changes in these processes due to disease progress can be models in the PK-PD modeling spectrum. The complexity considered.15,16) These mechanism-based PK-PD models of the empirical models is limited by the identifiability of utilize receptor theory concepts for characterization of the parameters, whereas systems biology models are not target binding and target activation processes.6) In this limited in terms of complexity. Mechanism-based PK-PD respect, receptor theory constitutes the basis for 1) modeling can be found somewhere in the middle of this prediction of in vivo drug concentration-effect relation- spectrum, i.e. trying to be as mechanistic as possible ships and 2) characterization of target association-dissoci- while still considering the identifiability of the ation kinetics as determinants of hysteresis in the time parameters. course of the drug effect. As this approach intrinsically As illustrated in Figure 1 the processes on the causal distinguishes drug- and biological-system specific Receptor Theory in Mechanism-Based PK-PD Modeling 5

parameters it allows accurate extrapolation from in vitro response relationships under equilibrium conditions is to in vivo and from one species to another, which are the well established, its intrinsically descriptive nature limits key processes in translational drug research. its use for extrapolation. For instance, the Hill equation The principles of receptor theory date back to the for the concentration-effect relationship cannot be readi- pivotal work of Clark and Gaddum in the 1930s, based ly used to predict this relationship in another tissue with on earlier work of Hill,17) providing the basics of Black a different receptor density or another stimulus-response and Leff's operational model of agonism18) and it's princi- relationship. This would require a mechanism-based ples and applications have been extensively reviewed by model that separates drug from system-specific others.6,19) However, recognition of mechanism-based parameters. Classical receptor theory can be applied for PK-PD modeling as a valuable tool in translational drug making this separation, since it describes drug action by research has led to new developments in incorporating 2 independent parts, which relate to drug-specific (i.e. receptor theory in this emerging science. In this review the -dependent part) and system specific proper- we will discuss these developments with a specific focus ties (i.e. the tissue-dependent part). Hence, receptor the- on how to predict in vivo drug concentration-effect ory constitutes a scientific basis for the prediction of in relationships under equilibrium (steady state) conditions. vivo concentration-effect relationships.6) Moreover, we will discuss the application of receptor The system specific part is determined by the receptor theory to describe the kinetics of drug action (i.e. drug ef- concentration, which determines the receptor binding fects under non equilibrium conditions) by characteriz- capacity and the nature of the stimulus response relation- ing target site distribution and receptor association and ship or transducer function (process D in Fig. 1). Recep- dissociation. However, this review primarily focuses on tor binding and activation determine the drug-specific mechanism-based PK-PD modeling and does not include component (process C in Fig. 1). In all approaches to in- a discussion on alternative approaches in the PK-PD corporate receptor theory in PK-PD modeling the recep- modeling spectrum, such as systems biology modeling. tor or target binding component is described with a For a discussion on systems biology modeling in drug de- hyperbolic function, typically the Hill-Langmuir equation velopment we refer to the review of Butcher et al.13) (i.e. the Hill equation with a Hill factor fixed to 1). On the other hand, the stimulus-response relationship has Equilibrium in vivo been incorporated in different ways, which can be sepa- concentration-effect relationships rated in semi-parametric and full parametric approaches. In the traditional PK-PD modeling approach rather Semi-parametric approach: As mechanism-based empirical models such as the Hill equation are used to PK-PD models are typically defined by more parameters describe the typical hyperbolic shape of in vivo drug con- compared to descriptive models, parameter estimation centration-effect relationships. The Hill equation is de- requires combining data from multiple experiments in fined by 3 parameters: the maximum effect, the concen- order to distinguish drug and system specific parameters. tration resulting in 50% of the maximum effect and a Hill For instance, Tuk et al. used separate experiments for es- coefficient representing the steepness of the concentra- timating receptor binding and activation and the stimulus tion effect-relationship (see Danhof et al.6) for the equa- response relationship respectively for benzodiazepines.20) tion). The Hill equation combines all intermediate steps Fixing the system specific parameters of the stimulus between receptor association and the associated receptor response relationship to the values obtained from one ex- activation (stimulus) response relationship in one equa- periment allowed estimation of the drug specific tion. Hence, the Hill equation does not allow to explicitly parameters intrinsic efficacy and receptor affinity in distinguish drug specific (i.e. receptor affinity and the another experiment. Whereas other descriptive ap- ability to activate the receptors (intrinsic activity)) from proaches failed, this approach allowed a description of system specific parameters, which relate to receptor den- the pharmacodynamic interaction between midazolam sity and the relationship (transducer function) between and its active metabolite a-OH-midazolam using the elec- receptor activation and pharmacological effect. For ex- troencephalogram (EEG) as pharmacodynamic endpoint ample, the concentration-effect relationship for a drug in rats. Tuk et al. used an unknown, but monotonically with a high affinity for a receptor, but with a low efficacy increasing stimulus-response function to link receptor (i.e. the ability to evoke an effect after binding to the binding to the resulting effect.20) This is a semi-paramet- receptor) can be described with the same set of ric approach, since it used a parametric function to parameters compared to a drug with low affinity but high describe the receptor binding and activation process in efficacy.19) In addition, the Hill equation assumes combination with a nonparametric function to describe equilibrium conditions of the system. This important as- transduction.6) This relationship could be estimated using sumption might be valid in some cases, but definitely not data from at least 2 other benzodiazepines including one by definition as will be discussed later on. Although the that reaches the maximum product of intrinsic efficacy use of the Hill equation for describing concentration- (i.e. receptor activation relative to receptor density) and 6 Bart A. PLOEGER, et al.

receptor density of 1. relationship (n), where Em and n are defined by the in- Full parametric approach (Operational Model of trinsic efficacy and slope of the Hill equation of the full Agonism): In contrast with the semi-parametric ap- agonist, respectively.23) As a result, relative estimates of proach, the full-parametric approach requires the shape the in vivo operational affinity and intrinsic efficacy are of the transducer function to be known, since both the obtained for the partial . However, the explicit receptor binding and activation process and transduction assumption in this approach that all partial agonists oper- process are described with a parametric function. The ate trough the same receptor system might not be gener- `Operational Model of Agonism' (OMA) is a full-paramet- ally applicable, for instance, if some of the compounds ric approach, in which the receptor binding and activa- bind to other receptors or subtypes also. This might tion is linked to a hyperbolic stimulus-response relation- result in biased parameter estimates, since the operation- ship,18) although, in principle, the stimulus-response al affinity and intrinsic efficacy are, in that case, a compo- relationship can be of any shape21) (see Danhof et al.6) for site of different receptor occupancy curves. the OMA equation). The OMA can be applied for es- (2) Inactivation method timating receptor affinity of both agonists and antagonists Alternatively, partial agonism can be induced by addition to the intrinsic efficacy of partial agonists. reducing the total number of receptors by (irreversible) Identifiability: As with the semi-parametric ap- receptor inactivation (inactivation method23)). This yields proach, the OMA is also defined by many parameters. As information on the effect of a full (without receptor inac- these parameters refer to different interrelated processes tivation) and partial (with receptor inactivation) agonist, in the causal chain between drug administration and ef- which share the same system specific parameters for Em fect (Fig. 1), they cannot be estimated simultaneously us- and n. Hence, the inactivation method is the only ing data from a single exposure response relationship.22) method that allows estimating the target affinity and in- This would result in biased parameter estimates showing trinsic efficacy of a full agonist. Nevertheless, Van der high uncertainty due to statistical correlations. Over the Graaf et al. showed that high statistical correlations are years, several methods have been proposed that allow expected between affinity and efficacy.24,25) This is incon- adequate estimation of the OMA. Reviewing the litera- sistent with the inherent feature of receptor theory ture learned that 4 different methods can be distin- models to distinguish between system and drug specific guished: the comparative, inactivation, interaction and parameters. Their finding is independent of the design of the prior method. References to studies that used one of the study. The multiple curve design, in which usually these methods are summarized in Table 1. two curves (for the full and partial agonist) are derived (1) Comparative method using the same tissue, does not perform better compared The comparative method uses concentration-effect to the single curve design studying only one curve per tis- data from a variety of compounds with different target af- sue.25) Garrido et al. reported similar issues in estimating finity and intrinsic efficacy.23) This method assumes that the parameters of the operational model when applied to the compounds share the same system specific alfentanil concentration-effect curves with and without parameters for the maximum effect (Em) and the irreversible blockade of the m-receptor with b-funaltrexa- parameter for the steepness of the stimulus response mine in rats.26) Although these curves could be adequate- ly described with a Hill equation, fitting the curves with the OMA did not result in unique estimates for affinity Table 1. Examples of applications of the four methods for es- and efficacy.26) The inability of the irreversible antagonist timating in vivo receptor affinity and efficacy to relevantly reduce maximum response and eliminate Method Mechanism of action Reference the receptor reserve of the system was argued as the main cause for this finding.26) Comparative Adenosine A1 receptor agonists Van der Graaf et al.,(25) (3) Interaction method GABA receptor modulators Visser et al., (32) A The interaction method uses concentration-effect data 5HT1 receptor agonists Zuideveld et al., (35) A from a full agonist alone and in the presence of a partial Inactivation m Opioid receptor agonists Garrido et al., (26) agonist to estimate the receptor affinity and relative ef- m Opioid receptor agonists Zernig et al., (38,80) ficacy of the partial agonist.27) In contrast with the com- et al. 5HT1A receptor agonists Koek , (81) parative method the interaction method actually con- Adenosine A1 receptor agonists Van Muilwijk-Koezen et al.,(82) firms the assumption that the full and partial agonist bind 27) Interaction — No published examples to the same receptor. Although successfully applied to in vitro 27,28) Prior m Opioid receptor agonists Cox et al., (29) data, we are not aware of studies that applied this method for estimating in vivo parameters. GABA receptor modulators Cleton et al., (83) A (4) Prior method hERG channel blockade Jonker et al., (40) Using independently derived prior information on one b Adrenoceptor antagonists Van Steeg et al.,(33) or more model parameters, some of the model Receptor Theory in Mechanism-Based PK-PD Modeling 7

parameters can be fixed resulting in higher statistical heart rate in rats.31) A significant correlation between the power to estimate the remaining unknown parameters. in vitro and in vivo affinity constants was found. In addi- For instance, the in vivo receptor affinity could be fixed tion, a similar correlation was reported for the estimated to values derived from in vitro receptor binding studies. in vivo intrinsic efficacy parameter and the GTP shift (the This prior method has been successfully applied to the ratio between Ki in the presence and absence of GTP), synthetic m-opioids alfentanil, sufentanil and fentanyl, which is a measure of the in vitro efficacy of adenosine A1 showing that their in vivo concentration-effect relation- agonists.31) The same authors applied their receptor theo- ships using EEG recordings as pharmacodynamic en- ry model to evaluate tissue specificity of adenosine A1 dpoint in rats could be well predicted using in vitro der- receptor agonists in vivo.25) The receptor density and/or 29) ived parameters for affinity and intrinsic efficacy. The receptor activation of adenosine A1 receptors mediating preclinical estimates for affinity and efficacy appeared to antilipolytic effects is much higher compared to the closely resemble the human values, showing the receptors mediating heart rate effects. This would pro- applicability of receptor theory models for inter-species vide the opportunity to design A1 receptor agonists extrapolation.30) The high in vitro and in vivo correlation preventing lipolysis, but without raising cardiovascular 25) of the receptor affinity for adenosine A1 receptor related safety issues. 31) 32) agonists and GABAA modulators indicate that the The utility of receptor theory models for predicting in prior approach would be applicable to these compounds vivo concentration-effect relationships using in vitro bioas- also. Another example of the prior method is a recent says was also shown for GABAA modulators. The esti- study estimating the in vivo affinity of atenolol for the b1- mated in vivo affinity and intrinsic efficacy of series adrenoreceptor, using a model based on the OMA to GABAA modulators (benzodiazepines) on basis of their describe the effect of atenolol on isoprenaline induced EEG effects closely resembled the in vitro affinity and the 33) tachycardia. The operational model was extended with ratio between the in vitro IC50 without and with GABA a term for the competition of isoprenaline and atenolol (GABA-shift) as the in vitro efficacy.32) Earlier attempts to for the b1-adrenoreceptor in addition to the displace- predict the concentration-effect relationship of benzodia- ment of the endogenous agonist adrenaline. Using this zepines using the operational model had been unsuccess- pharmacodynamic interaction, model the in vivo affinity ful, since none of the evaluated benzodiazepines reached constant of atenolol could be estimated, while fixing the maximum effect.20) However, neuroactive steroids, such in vivo receptor affinity of the full agonist isoprenaline to as alphaxalone, show 2–3 times higher EEG effects com- the in vitro affinity constant Ki.Thisresultedinin vivo pared to the benzodiazapines confirming that the maxi- values being close to the in vitro affinity constant from mumsystemicresponsecouldnotbereachedusingben- functional bioassays.33) Van Steeg et al. aimed at estimat- zodiazepines.21) A biphasic response is observed for these ing the in vivo affinity of an antagonist, but, in principle, neuroactive steroids: at low concentrations the EEG theirmodelcouldalsobeusedtoestimatetheaffinity response increases to a maximum, but further increase of and intrinsic efficacy of different full and partial agonists. the concentration results in a decrease of the effect. In fact, this approach would be comparable to the recep- Visser et al. described this biphasic response with a para- tor inactivation method with the difference that a com- bolic equation, which depends on the drug-receptor petitive antagonist is used rather than an irreversible an- stimulus.21) As this model clearly allows distinguishing tagonist to reduce the number of available receptors. It drug from system specific parameters, this model could would be interesting to see if taking the competitive dy- also successfully describe the concentration-effect namic interaction between agonists and antagonist ex- relationship of benzodiazepines, which behave as partial plicitly into account allows estimating affinity and effica- agonist relative to neuroactive steroids.32) cy parameters that are not confounded with system For 5-HT1A receptor agonists Zuideveld et al. showed specific parameters. The combination of response sur- that the operational model can also be applied when the face analysis, looking at the drug effect as function of two pharmacological effect is influenced by homeostatic feed- 35) drug concentrations, and receptor theory, as recently back. 5-HT1A receptor agonists lower the body temper- proposed by Jonker et al.34) could be a valuable tool in ature in rats and the change of their hypothermic effect this attempt, since this approach can be applied to any over time shows a consistent oscillatory behavior. Their type of interaction (synergistic or antagonistic). effect on body temperature is due to a change in the set- Application of the operational model of point for maintaining body temperature. This thermostat- agonism: like regulation of body temperature was described using (1) Comparative method a model in which the body temperature is continuously Van der Graaf et al. used the comparative method in compared to a reference temperature or setpoint. When addition to nonlinear mixed effect modeling for estimat- this setpoint is lowered by 5-HT1A receptor agonists the ing receptor affinity and intrinsic efficacy of a series of thermostat will perceive a temperature that is too high, adenosine A1 receptor agonists for their in vivo effect on which will result in lowering the temperature by chang- 8 Bart A. PLOEGER, et al.

ing the thermostat signal. As body temperature and the possible in vivo safety issues using parameters derived setpoint are interdependent, changing the thermostat sig- from in vitro bioassays. For example, prolongation of the nal will result in oscillatory behavior. The estimated in QT interval poses a potential safety issue, because it vivo and derived in vitro intrinsic efficacy correlated could result in ventricular arrhythmias leading to life closely, whereas a rather poor correlation was found be- threatening Torsades des Pointes.39) The in vitro hERG as- tween the in vitro and in vivo binding affinity.35) Poor cor- say is widely applied to test drugs for their potential to in- relation was especially observed for flesinoxan. As this hibit potassium channels in cardiac cells.39) In a recent compound is transported actively to the brain36) the publication, Jonker et al. used a receptor theory model to flesinoxan plasma concentration is presumably not a predict QT prolongation of an anti-arrhythmic drug in good predictor for the in vivo drug effect. This shows the humans using data from the in vitro hERG assay.40) In importance of considering target site distribution in principle, their model could be used to predict the poten- receptor theory models particularly for drugs that are tial of QT interval prolongation of other drugs that selec- transported actively by specific transporters to their site tively block hERG channels. However, caution should be of action.6) After allometric scaling of the system specific taken in the extrapolation of this model to other drugs, parameterswhileleavingthedrugspecificparameterun- since hERG channel blockade is not always a reliable changed the receptor theory model could predict the ex- predictor for QT prolongation.40) tent and time course of the temperature change reasona- Recently, Jacqmin et al. took notice of the similarity bly well in humans.37) Leaving the drug specific between the cascade of viral replication (e.g. binding of parameters unchanged is consistent with receptor theo- virus to CD4 and CCR5 receptors resulting in the ry, since 5-HT1A receptor binding and activation are ex- production of new virus via reverse transcription of the pected to be similar between rat and human.37) Interest- DNA, replication of viral RNA and protein synthesis) and ingly, the characteristic oscillatory behavior in the the receptor-binding-activation and stimulus response change in body temperature in rats is not predicted in cascade.41) On the basis of this interesting idea, they de- humans, which completely concurs the observations.37) cided to incorporate the operational model into an exist- On the basis of their experience with 5-HT1A receptor ing model for the dynamics of viral replication. In this agonist the authors suggest that allometric scaling of drug concept, the virus is considered an agonist, of which the effects could in particular be applied to physiological sys- effect (viral replication) can be inhibited by an antagonist tems which are conserved from an evolutionary perspec- that binds to the CD4 or CCR5 receptor. A reduction in tive.37) the number of free receptors will result in a reduction of (2) Inactivation method the infection rate. Previous simulations showed an appar- Zernig et al. used the inactivation method for estimat- ent discrepancy between the ex vivo ing the in vivo receptor affinity and intrinsic efficacy of of maraviroc, a CCR5 antagonist, and the in vivo IC50, four opioids after irreversible inactivation of the m-recep- since the reduction in viral load was clearly over-predict- tor with the antagonist clocinnamox in mice.38) The an- ed on basis of the dissociation constant as if the actual tinociceptive response was measured using the tail CCR5 receptor occupancy was over-predicted. However, withdrawal test. Correlation close to unity was found be- the receptor theory model learned that this discrepancy tween the in vivo and in vitro affinity constants of all four could be explained with the assumption of activated tar- agonists. However, since the PK of the compounds was get cells expressing more receptors than needed, since not taken into consideration by using dose rather than activation of only 1.2% of the receptors results in 50% of concentration data, the estimated in vivo affinity con- the maximum infection rate.41) These spare receptors stants were consistently higher compared to the in vitro need to be blocked first by the antagonist before the in- values, which were expressed as concentrations. On the fection rate can be reduced.41) This work is an excellent other hand, comparable values for the in vitro and in vivo example of the application of receptor theory in PK-PD affinity constants are found as discussed previously for modeling to learn about the mechanism of drug action. adenosine A receptor agonists31) and GABA modula- 1 A Kinetics of drug action tors.32) Furthermore, similar affinity constants for syn- thetic m-opioids in rats and humans were shown based on Receptor theory models for predicting the in vivo con- concentration-effect data.30) Hence, concentration-effect centration-effect relationship, as discussed above, use the data offer more possibilities for extrapolation from in steady state concentration in plasma to estimate the size vitro to in vivo and from one species to another compared of the effect. However, as the site of action of most drugs to dose response data. is outside the plasma and/or it will take time for receptor (3) Prior method binding to reach equilibrium, it will take some time to Also in safety pharmacology the ability of receptor the- observe an effect after administration of a drug. Hence, ory PK-PD models to distinguish system from drug specif- the change in the effect will lag behind the change in the ic properties show its merits, since it allows predicting plasma concentration, a process that is commonly Receptor Theory in Mechanism-Based PK-PD Modeling 9 referred to as hysteresis. As the primary objective of PK- rocuronium-induced NMB. A model that explicitly dis- PD modeling is the prediction of the time course of drug tinguishes biophase distribution from receptor binding action42) the kinetics of drug action need to be consi- (process B in Fig. 1) could have addressed this issue. dered to describe this hysteresis. Most PK-PD models in- However, attempts to estimate this model were unsuc- clude an effect compartment model for describing target cessful, since the data did not allow estimating all model site distribution delays43) or, if in addition to target-site parameter simultaneously. Apparently, specific informa- distribution slow transduction processes are involved, in- tion on one or both processes by sampling in the clude turn-over or indirect response models.44) As these biophase and/or estimating receptor association and dis- models have been extensively reviewed by others6,45,46) we sociation kinetics is required to separate target site distri- believe that a discussion on these models is beyond the bution from receptor binding kinetics. The authors sug- scope of this review. Although effect compartment gest that data from a wider rocuronium dose range might models and turn-over models describe the time-course of allow estimating the receptor kinetics of rocuronium.48) the effect as function of the plasma concentration ade- Recent studies show that dense data on the time quately in most cases, these models inherently combine course of drug concentration and effects following ad- processes in the causal chain between drug administra- ministration of a wide dose range allows distinguishing tion and effect (Fig. 1). Therefore, they are not truly biophase distribution from receptor binding kinetics. mechanistic, which might limit their application to These studies characterized the time course of the effect predict the kinetics of drug action in different circum- of a potassium competitive acid blocker in dogs49) and the stances. For instance, Visser et al. used concentration de- analgesic and respiratory depressant effect of semi-syn- pendent target site distribution to describe the hysteresis thetic opioids in rats50–52) and in humans53,54) respectively. in the effect of alphaxolone, which is probably due to The time course of the potassium competitive acid block- changes in target site perfusion due to an effect of this er showed hysteresis between the change in plasma con- drug on heart rate and aortic pressure and/or capacity centration and effect. In addition, the half-life of the ef- limitation in specific transport into the brain.21) Specific fect was considerably longer than the PK half-life and the information of the target site distribution could have time to the peak of the effect decreased with dose.49) In helped addressing these issues. Also, the kinetics of drug principle, the hysteresis in the effect could be adequately action of drugs acting in the CNS are expected to be in- described with an effect compartment model, but this fluenced by their target site distribution due to involve- model would predict the time to maximum effect to be ment of specific transporters.19,47) independent of the dose. Therefore, a receptor binding Recently, Ploeger et al. proposed a PK-PD model for model was included, which accounted for both the delay reversal of neuromuscular blockade by sugammadex, a in the effect and the dose dependency in the time to max- cyclodextrin that specifically binds the steroidal neu- imum effect. Nevertheless, these observations could also romuscular blocking drugs rocuronium and vecuroni- be described using a turn-over or indirect response um.48) Since the seminal paper of Sheiner et al. the hyste- model. As the pharmacological effect is thought to be di- resis in the effect of neuromuscular blocking drugs are rectlyrelatedtotheenzymeinhibitionandnosubse- typically described using an effect compartment model.43) quent transduction processes are involved after enzyme Under the assumption that sugammadex also distributes blockade, a receptor binding model is mechanistically to the effect compartment and will form a complex with more plausible.49) Although not explicitly stated, the rocuronium or vecuronium, reversal of neuromuscular authors also assumed that the drug can inhibit the en- blockade results from a decrease in the free drug concen- zyme activity completely, resulting in complete inhibi- tration. Hence, the distribution of sugammadex to the tion of acid secretion. Consequently, the maximum effect neuromuscular junction determines the time course of or total enzyme binding capacity does not need to be esti- the reversal. This assumption results in an adequate mated resulting in a higher statistical power for estimat- prediction of rocuronium and vecuronium induced ing the other parameters. Simultaneous modeling of the reversal by sugammadex in different populations and cir- PK-PD data of the parent and metabolite under the as- cumstances. However, the reversal time for lower sumption that parent and metabolite compete for the sugammadex doses equal to or below 2 mg/kg was under same enzyme showed that the metabolite has a lower af- predicted. It was hypothesized that this might arise from finity for the enzyme, but results in higher systemic ex- not considering rate limiting receptor dissociation in the posure with a longer half-life compared to the parent. model. Observations for vecuonium, which dissociates Hence, the relative contribution of the metabolite to the more slowly from the nicotinic receptor compared to effect will increase with time resulting in a longer dura- rocuronium, seem to support this hypothesis. Not taking tion of the effect than expected on the basis of the PK of into account the rate of receptor dissociation affects the the parent.49) prediction of the reversal of vecuronium-induced NMB Also for the semi-synthetic opioid buprenorphine, a to a greater extent than prediction of the reversal of considerable delay between the change in plasma con- 10 Bart A. PLOEGER, et al. centration and the antinociceptive and respiratory tion is needed to distinguish receptor occupancy from depressive effects was observed in both rats51,55) and hu- the stimulus response relationship, as we previously dis- man. A receptor binding model in combination with an cussed for estimating the in vivo steady state exposure- effect compartment to describe the biophase distribution response relationship. In principle, all 4 methods would was developed to describe this hysteresis. As a result, the be applicable (Table 1). antinociceptive and respiratory depressant effect in hu- Target site distribution: Sampling drug concen- mans could be predicted using rat data following (allo- trations at the site of action is quite complex and suffers metric) inter-species extrapolation of the biophase from methodological and practical limitations.57,58) Using equilibrium rate constant (Ke0; Fig. 1), while assuming biopsy sampling drug concentrations in specific tissues the same parameters for the receptor kinetics in both and organs can be measured. However, this is a burden- species.56) Using this model, they optimized the dosing some procedure to subjects, which will limit the number scheme for the reversal of buprenorphine-induced of samples.59) Non-invasive techniques, like positron respiratory depression by naloxone, showing that due to emission tomography (PET) and the invasive technique the slow receptor kinetics of buprenorphine and the microdialysis, suffer less from practical and ethical draw- rapid elimination of naloxone a continuous infusion backs and are therefore promising techniques for sam- scenario is most efficient.56) pling in the biophase.58) With both approaches a detailed In contrast with the effect of the potassium competi- concentration versus time profile can be obtained. tive acid blocker49) these effects are not directly related to PET scanning has been widely applied to obtain recep- receptor occupancy, since a receptor-stimulus response tor information, such as the maximum binding capacity relationship is required for predicting the change in these (Bmax) and the steady state binding constant KD for the 51,53–55) 60) effects over time, making the PK-PD model more GABAA receptor. However, Liefaard et al. recently complex. Hence, the informativeness of the data showed that target site distribution in addition to recep- becomes more crucial, since more parameters need to be tor properties could be estimated by simultaneously fit- estimated. Therefore, Yassen et al. studied the time ting of plasma and by PET scanning derived brain con- course of the antinociceptive and respiratory depressive centration-time curves of the GABAA receptor agonist effects for a wide dose range and infusion scenario's. flumazenil in rats.61) Their model containing compart- Nevertheless, this study required making assumptions in ments for free and capacity limited GABAA bound con- order to simplify their model. The fractional receptor centration of flumazenil in the brain allowed estimating binding was modeled rather than the concentration of the distribution of free flumazenil over the blood-brain the drug-receptor complex, since the total receptor con- barrier. In an animal model for epilepsy, the same centration could not be derived from the data. As a authors showed that both the flumazenil transport into result, the total receptor concentration had to be set to the brain and the GABAA receptor density are different in unity. Despite the wide dose range that was tested in epileptic rats, resulting in an net decrease in the both species, no maximum antinociceptive effect for fen- flumazenil brain concentration compared to control tanyl and buprenorphine could be observed. This is most rats.62) This finding corresponds well to the observed likely the reason for not being able to estimate the total reduction in the EEG effect of midazolam in the same receptor concentration. Interestingly, a ceiling effect in animal model, showing that using receptor theory princi- the respiratory depression could be observed for fentanyl ples information can be derived about patho-physiologi- in both rats and human. However, the hysteresis in the cal changes in the disease. Specifically, for epilepsy this respiratory depressant effect of fentanyl can be complete- information can be used to better understand the ly attributed to biophase distribution, since the receptor decrease in the effectiveness of antiepileptic drugs (phar- association and dissociation of fentanyl is very fast. macoresistance), which leads to poorly controlled sei- Hence, the PK-PD model for fentanyl could be reduced zures in 20–30% of all epileptic patients.62) to an Emax model linked to the biophase concentration. As most infections are located in the extracellular fluid For buprenorphine no maximum respiratory depressant and the extracellular fluid can be easily accessed by effectcouldbeobservedinbothspeciesandassumptions microdialysis, this technique has been widely applied to similar to the antinociceptive PK-PD model had to be measure the concentrations of antibiotics and to lesser made in order to estimate all parameters independently. extent antivirals.57) These measurements have been suc- It would be interesting to see if administration of higher cessfully applied to link the PK of antibiotics to the doses, resulting in saturation of the effect would provide change in bacterial kill/growth over time, providing infor- information to estimate the total receptor concentration. mation for rational dosing of antibiotics.63) However, this ceiling effect could, in principle, also be Another application of microdialysis is the measure- attributed to the intrinsic efficacy, since in case of recep- ment of drug concentrations in the brain by intercerebral tor reserve full receptor occupation is not required to ob- micodialysis.19) Distribution to the brain is limited by the serve the maximum effect. Hence, additional informa- blood-brain barrier, which has important implications for Receptor Theory in Mechanism-Based PK-PD Modeling 11

target site distribution and thereby the kinetics of drug and effect.6) In addition, the duration of the pharmaco- action of CNS active drugs. For instance, Geldof et al. logical effect is related to the residence time (i.e. the measured the free concentrations of the serotonin reup- reciprocal of the dissociation rate constant) of the drug- take inhibitor fluvoxamine in the frontal cortex of rats target complex.69) Hence, target binding kinetics may be using microdialysis and found a disproportional increase a useful criterion to select drug candidates in drug-dis- in brain concentrations with dose.64) This non-linearity in covery.70) Similar to the pharmacological effect the dura- the brain distribution could be adequately predicted un- tion of toxic effects are also related to the association and der the assumption that fluvoxamine diffuses passively to dissociation kinetics of complexes between drug and tox- a shallow brain compartment and subsequently diffuses icity related macromolecules. Therefore, data on the passively to a deep brain compartment. The source for binding kinetics of a drug to its pharmacological and tox- the non-linearity was the capacity limited efflux of icological targets would provide a better understanding fluvoxamine from this deep brain compartment, suggest- of the tissue selectively and safety profile of a drug.70) In ing that fluvoxamine is a PgP substrate. There are indica- their review, Tummino et al. discuss the relevance of tions that this is indeed the case for fluvoxamine, slow receptor dissociation kinetics for the development although data are found to be conflicting.64) The same of multidrug resistance in HIV, which appears to be a authors found that the observed ex-vivo 5-HT transporter greater issue for protease inhibitors with a shorter resi- occupancy of fluvoxamine in rats could be better predict- dence time compared to the recently developed drug ed on the basis of the fluvoxamine concentration in the darunavir showing slow dissociation kinetics.70) Other ex- brainthantoplasmaconcentrations.65) This shows the amples of drugs, such as the 5a-reductase inhibitor importance of using target site concentration rather than finasteride and the angiotensin II the plasma concentration for prediction of the time candesartan, with long dissociation half-lives (i.e. long course of drug action in PK-PD modeling when target site residence times) showing sustained clinical duration of distribution is complex. action compared to competitors with shorter dissociation For morphine, it has been found that distribution into half-lives are discussed by Copeland et al.69) the brain is determined by slow passive diffusion, show- Asdrugsarelikelytobindtoothermacromolecules ing capacity limited uptake and active efflux, mediated by also in addition to their target receptor, such as plasma PgP, which results in non-linear distribution of morphine proteins, understanding the influence of plasma protein to and from the brain.66) Interestingly, PgP mediated ef- binding on receptor binding and subsequently drug effect flux could only partly be inhibited by a PgP blocker, sug- seems relevant, but is not well understood. In a theoreti- gesting that also other transporters are involved in the cal approach, Peletier et al. evaluated the impact of plas- transport of morphine from the brain.66) In another rat ma-protein binding on receptor occupancy.71) In one of study, a simpler (linear) model was applied to describe the possible applications of the model they evaluated the the brain distribution of a lower dose of morphine and impact of displacement of a drug from plasma protein by another opioid oxycodone.67) By comparing the brain dis- another compound, which could potentially result in tribution of both compounds it was found that the un- safety concerns by increased exposure. However, only bound concentration of oxycodone is approximately 6 for compounds with low intrinsic clearance and moder- fold higher compared to morphine. The change in the ob- ate plasma protein binding replacement from plasma pro- served pharmacodynamic response (tail flick latency) teins will result in increased exposure. When compounds couldbelinkeddirectlytothepredictedunboundbrain are highly protein bound, show a high intrinsic clearance concentrations of both drugs.67) In contrast, Groenendaal or both, exposure, changes only minimally after displace- et al. were not able to find a direct link between predict- ment of the drug resulting in higher receptor occupancy. ed brain concentration and EEG effects, but needed a This is also the case for compounds with low intrinsic biophase distribution model to describe the hysteresis.68) clearance and low plasma protein binding. Although The predicted concentration versus time profile in the receptor binding is high for these compounds, the in- biophase appeared to be different from the PK of mor- crease in exposure is again limited after displacement. phine in the extracellular fluid of the brain, which led to Estimation of the rate constants of in vivo target as- theconclusionthatdistributionintothebrainandeffect sociation-dissociation is often complex as it may be con- site are distinctly different.68) This discrepancy could be founded by the kinetics of target site distribution and attributed to other process involved in the causal chain transduction. However, measuring drug concentrations between drug administration and effect other than target in the biophase and/or the availability of data from dedi- site distribution, such as the kinetics of receptor associa- cated pharmacological experiments should allow ac- tion and dissociation (Fig. 1). curate and precise estimation of target binding kinetics. Target association-dissociation kinetics: Target As described earlier, an investigation in rats has shown association-dissociation kinetics can be a significant de- that PET scanning enables direct estimation of the target terminant of hysteresis between plasma concentration association and dissociation kinetics by PK-PD model- 12 Bart A. PLOEGER, et al.

ing.61) Also, microdialysis can be applied for measuring Conclusion binding kinetics, as was recently shown to estimate the rapid association and dissociation of ketoprofen binding Mechanism-based PK-PD modeling aims at describing to human serum albumin.72) Nevertheless, the most com- the processes in the causal chain between drug adminis- mon approach for measuring receptor association and tration and effect such as target site distribution, recep- dissociation rate constants are in vitro competitive bind- tor binding kinetics and the dynamics of receptor activa- ing experiments, in which most often a radiolabeled tion and transduction. Receptor theory plays an im- tracer competes with a test compound for a receptor.73) portant role in this approach, since it forms the basis for Typically, these experiments involve studying the recep- predicting the in vivo drug concentration-effect relation- tor-tracer binding under equilibrium conditions, follow- ships and receptor binding kinetics as determinants of ing the association and dissociation of the tracer to and hysteresis in the time course of the drug effect. The main from the receptor over time and a competition experi- challenge in mechanism-based PK-PD modeling in gener- ment, in which different concentrations of the test com- al and specifically receptor theory models is how to dis- pound replace the tracer from the receptor.73) Simultane- tinguish the estimation of parameters of the processes in ously fitting of a mathematical model for receptor bind- the causal chain. Estimating parameters with adequate ing kinetics to all data from these experiments with or accuracy and precision requires collecting data from in without test compound results in more accurate and vitro and in vivo experiments that are specially designed to precise parameter estimates compared to fitting each ex- estimate parameters independently and subsequently periment separately.74) A mixed-effect modeling ap- combining these data from different sources in one com- proach further improves the quality of the parameter esti- prehensive PK-PD model. This approach fully exploits the mates.75) The improved statistical power for parameter pertinent feature of mechanism-based PK-PD modeling estimation allows for significant reductions in ex- to distinguish system from drug specific parameters. For perimental efforts without compromising the quality of instance, prior information on receptor binding kinetics the parameter estimates.75) However, receptor activation from in vitro studies in addition to information on target as a result of binding of an agonist to a receptor will most site distribution would provide independent information likely cause some conformational changes.76) Hence, the to distinguish the causal steps in the kinetics of drug ac- actual receptor dissociation constant in the inactivated tion. In this approach mechanism-based PK-PD modeling (ground) state of the receptor might deviate from the ex- would be essential for combining all sources of informa- perimentally determined dissociation constant, since this tion. In addition, it can be used to indirectly derive infor- measurement is the sum of the actual dissociation con- mation about unknown process involved in the kinetics stant and some aspects of receptor activation. For ion- of drug action. As such, mechanism-based PK-PD models linked receptors the actual and observed dissociation constitute a scientific basis for learning about drug effica- constants differ considerably. However, for G protein- cy and safety. It is expected that better understanding of coupled receptors one can reasonably assume that the drug efficacy and safety will lead to improved efficiency observed dissociation constant is a good estimate of ac- in the drug development process and less attrition. tual dissociation constant since experiments with mutat- ed receptors, preventing or reducing receptor activation Acknowledgements: The authors would like to thank and G-coupling, show that for most G protein-coupled Henk-Jan Drenth, Jean Smeets, Nelleke Snelder, Eline receptors the observed dissociation constant is very close van Maanen and Tamara van Steeg (LAP&P Consultants to the actual constant.76) BV, Leiden, The Netherlands) for their contribution to Incorporating kinetics of drug action in PK-PD this review. modelling: There are many examples of incorporating References receptor binding kinetics in PK-PD modeling; for in- stance to predict receptor-mediated disposition and acti- 1) Chien, J. Y., Friedrich, S., Heathman, M. A., de Alwis, D. P. and vation of erythropoietic stimulation by human recom- Sinha, V.: Pharmacokinetics/Pharmacodynamics and the stages binant erythropoietin77) or other small and large molec- of drug development: role of modeling and simulation. Aaps J., ules,78) such as monoclonal antibodies.10) Nevertheless, 7: E544–559 (2005). we are not aware of studies that incorporate in vitro 2) Zhang, L., Sinha, V., Forgue, S. T., Callies, S., Ni, L., Peck, R. receptor binding kinetic parameters for predicting the ki- and Allerheiligen, S. R.: Model-based drug development: the road to quantitative pharmacology. J. Pharmacokinet Phar- netics of in vivo receptor occupancy and/or effect. macodyn, 33: 369–393. Epub 2006 Jun 13 (2006). Although, Shimada et al. showed that the estimated slow 3) Dingemanse, J. and Appel-Dingemanse, S.: Integrated phar- receptor association-dissociation kinetics, describing the macokinetics and pharmacodynamics in drug development. time course of the antihypertensive effect of eight calci- Clin. Pharmacokinet., 46: 713–737 (2007). um channel blockers, correlated well with data from in 4) Lalonde,R.L.,Kowalski,K.G.,Hutmacher,M.M.,Ewy,W., vitro binding studies.79) Nichols, D. J., Milligan, P. A., Corrigan, B. W., Lockwood, P. A., Receptor Theory in Mechanism-Based PK-PD Modeling 13

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