Translational Modeling in Schizophrenia: Predicting Human Dopamine D₂ Receptor Occupancy

Abstract

Objectives

To assess the ability of a previously developed hybrid physiology-based pharmacokinetic-pharmacodynamic (PBPKPD) model in rats to predict the dopamine D₂ receptor occupancy (D₂RO) in human striatum following administration of antipsychotic drugs.

Methods

A hybrid PBPKPD model, previously developed using information on plasma concentrations, brain exposure and D₂RO in rats, was used as the basis for the prediction of D₂RO in human. The rat pharmacokinetic and brain physiology parameters were substituted with human population pharmacokinetic parameters and human physiological information. To predict the passive transport across the human blood–brain barrier, apparent permeability values were scaled based on rat and human brain endothelial surface area. Active efflux clearance in brain was scaled from rat to human using both human brain endothelial surface area and MDR1 expression. Binding constants at the D₂ receptor were scaled based on the differences between in vitro and in vivo systems of the same species. The predictive power of this physiology-based approach was determined by comparing the D₂RO predictions with the observed human D₂RO of six antipsychotics at clinically relevant doses.

Results

Predicted human D₂RO was in good agreement with clinically observed D₂RO for five antipsychotics. Models using in vitro information predicted human D₂RO well for most of the compounds evaluated in this analysis. However, human D₂RO was under-predicted for haloperidol.

Conclusions

The rat hybrid PBPKPD model structure, integrated with in vitro information and human pharmacokinetic and physiological information, constitutes a scientific basis to predict the time course of D₂RO in man.

Introduction

In schizophrenia drug therapy and research, dopamine D₂ receptor occupancy (D₂RO) is often used as a target biomarker to quantify the relationship between efficacy and side effects (1). Several studies suggest that blockade of 65 to 80% of D₂ receptors is the key to antipsychotic efficacy for both conventional neuroleptics and novel antipsychotics (2–4). D₂RO higher than 80% increases the risk of adverse effects such as extra pyramidal symptoms (5). Thus, D₂RO has a central role in antipsychotic drug discovery, drug development and therapy. Target occupancy is important both in early drug discovery, where accurate knowledge of the degree of occupancy could help to determine the suitability of a drug candidate for further development, and later in the drug development process, when target site occupancy measurements can guide dose selection (6). D₂RO is clinically measured using positron emission tomography (PET) or single-photon emission computed tomography (SPECT) methodology, which are both expensive and time-consuming. Tools to predict clinical D₂RO in preclinical drug discovery phases are therefore valuable. It is well known that current antipsychotics also activate or antagonize other targets in the central nervous system. For example, risperidone has a higher affinity for serotonin (5-HT_2A) receptors than for D₂ receptors (5). Extensions of this tool to other receptors would therefore increase the value of the current translation framework.

Recently, we have reported physiology-based pharmacokinetic-pharmacodynamic (PBPKPD) models to characterize the time course of D₂RO and 5-HT_2A receptor occupancy (5-HT_2ARO) in rats (7,8). The mechanistic and physiological basis of these models should potentially allow the prediction of human PKPD properties using physiological parameters and prior information from in vitro and in vivo preclinical studies (9). The present investigation aimed to determine how these models can be used for translating receptor occupancy from rat to humans.

Development of a translation tool to predict human D₂RO (based on PKPD models) involves scaling information from rat to human. This involves accounting for drug distribution to the brain and the drug’s ability to bind to striatal D₂ receptors. Drug distribution to the brain is not only characterized by passive diffusion but also by active efflux transporters present at the luminal surface of the blood–brain barrier (BBB). Similarities in the in vitro permeability values determined by various types of experiments provide a basis to integrate and scale information on passive drug transport to the brain from in vitro to in vivo or from one species to the other (10). However, differential expression and limited homology of drug transporters involved in active drug transport across the BBB leads to challenges when scaling active transport related information from one species to another (11). Notwithstanding divergent reports on the species independence of drug-specific parameters, integration of in vitro parameters with physiologically based PKPD modeling would increase the potential of successfully translating effects from preclinical species to humans (12).

Hence, the objective of this work was to explore different approaches to predict human striatal D₂RO using a generic translational PBPKPD model structure, which allows integration and scaling of information from preclinical in vitro or in vivo data to the human situation. Different approaches were compared to determine the minimal amount of information required for this translational work. A previously developed extended model structure (8) was also used to predict human 5-HT_2ARO based on these approaches.

Methods

Data

This work was performed within the framework of the Dutch Top Institute Pharma project: Mechanism-based PK–PD modeling (http://www.tipharma.com). This mechanism-based PKPD modeling platform involves leading pharmaceutical companies worldwide, and academic institutes from the Netherlands. Three pharmaceutical companies who are the members of this mechanism-based PK–PD modeling platform, namely, Janssen Research and Development - Belgium, Merck Sharp and Dohme - The Netherlands and Pfizer Worldwide Research and Development – USA, provided human plasma concentration data for haloperidol (HAL), risperidone (RIS) and paliperidone (PAL, in extended release formulation) and helped with collection of human D₂ and 5-HT_2A receptor occupancy data. Clozapine (CLZ), HAL, olanzapine (OLZ), RIS, extended release formulation of PAL and quetiapine (QTP) were used in this study as model antipsychotic drugs. The observed human D₂RO for these antipsychotics were taken from the literature (2,13–24). For risperidone (RIS), human D₂RO was provided from the pharmaceutical companies who are involved in this project.

Population pharmacokinetic (PK) parameters for CLZ, OLZ, QTP and RIS were obtained from literature (1,25,26). However, no population PK models have been reported in literature for HAL and PAL. So, for these compounds in-house population PK models were developed. The population PK model for haloperidol was developed on the basis of data from 7 studies, comprised of 122 individuals [healthy volunteers (n = 20) and schizophrenic patients (n = 102)] and 515 plasma concentrations obtained across a wide dose range of 1 to 60 mg/day administered either as single or multiple doses. The population PK model for paliperidone-extended release was developed on the basis of data from 3 studies, comprised of 870 individuals and 4169 plasma concentrations obtained across a wide dose range of 3 to 15 mg/day administered as an OROS® once daily formulation.

Physiology-Based PKPD Model Structure

A PBPKPD model was previously developed and evaluated for its usefulness in describing the time course of brain concentration and D₂RO in rats (7). This model contains expressions to describe the kinetics in brain-vascular, brain-extravascular, striatum-free and striatum-bound compartments (Fig. 1). Following administration, drug is transported from the plasma compartment to the brain-vascular compartment; this process is assumed to be determined only by the cerebral blood flow. Only the unbound drug in this vascular compartment crosses the BBB and is transported into the brain-extravascular compartment, which is governed by the brain-extravascular clearance (CL_bev). Furthermore, drug is transported from the brain-extravascular compartment to the striatal-free compartment. The brain-extravascular and striatum-free compartments were assumed to be equilibrating rapidly. In striatum-bound compartment, drug can reversibly bind to the dopamine receptor complex (Fig. 1). The receptor association and dissociation processes were described using k_on as the receptor association rate constant (nM⁻¹h⁻¹), k_off as the receptor dissociation rate constant (h⁻¹) and D₂ receptor density in striatum (nM).

Fig. 1

A schematic representation of the PBPKPD model. The model incorporates different processes to explain the time course of D₂RO. The brain pharmacokinetics describes the processes involved in the transport of drug from plasma to brain, and the striatum compartment explains the drug binding to receptors through the binding constants.

In addition to the previously developed rat PBPKPD model structure, an active efflux clearance (CL_eff) component between brain-extravascular and brain-vascular compartments was included in this predictive model to reflect the active drug transport from brain, when appropriate (i.e., for RIS and PAL). Additionally, this rat PBPKPD model structure was extended to account for binding of RIS and PAL to the 5-HT_2A receptor (8). This extended model included two additional compartments (cortex-free and cortex-bound). Binding to 5-HT_2A receptors was described using association and dissociation constants and receptor density values specific for 5-HT_2A receptors. This extended model structure was used to predict both D₂ and 5-HT_2A receptor occupancy in humans in this simulation study.

Human D₂RO predictions

The rat PBPKPD model structure (Fig. 1) was used to predict the D₂RO versus time profile of antipsychotics in humans by substituting all parameters of the rat model by their human analogues, according to the following methods:

• (1) Human population PK parameters estimated using total plasma concentrations were obtained either from models developed in-house or from published literature (Table I).

• (2) Physiological parameters, such as blood flow to the brain and the brain volumes were obtained from literature (Table II).

• (3) Passive permeability transport across the BBB was scaled from in vitro or in vivo rat to in vivo human based on the assumption that permeability for passive diffusion per cm² of brain endothelial surface area is identical the between different systems.

• (4) Active efflux transport for PAL and RIS was scaled using pertinent information on Pgp protein expression in the different systems as a scaling factor.

• (5) Receptor binding was either derived from in vitro Ki values or in vivo Kd values corrected for differences between the in vitro and the in vivo system of the same species.

• (6) Experimentally determined values of the fraction unbound in human plasma and in rat brain were obtained from the literature. Unbound fraction in human brain is assumed to be equal to the unbound fraction in rat brain.

Table I Human Population Pharmacokinetic Parameters (Inter-Individual Variability as % Coefficient of Variation) Used in the Human D₂RO Predictive Model

Table II Physiological Values Used in the Human D₂RO Predictive Model

Different approaches were used to obtain human parameters and they were detailed as Approaches A-C in this section.

• Approach A was based only on human in vitro information (in vitro apparent permeability, efflux ratio (ER), in vitro Ki and k_off).

• Approach B was based on the in vivo parameters (rCL_bev, rCL_eff, Kd_rat, k_off-rat) obtained from the rat PBPKPD model.

• Approach C was aimed at using minimal information to get the best predictions of human D₂RO by integrating approaches A and B.

All the parameters values used for these simulations are presented in Table III.

Table III In Vitro, In Vivo and Ex Vivo Values Estimates Used in the Human D₂RO Predictive Model

Approach A: Human D₂RO predictions based on in vitro information

Passive drug transport at the BBB

Experimentally determined in vitro apparent permeability (Papp) values were used to predict passive transport of antipsychotics across the BBB. Specifically, values of the v permeability across multidrug resistance Madin-Darby canine kidney (MDR1-MDCK) type II cell monolayers were obtained from Summerfield et al. (32). Permeability determined while attenuating transporters denotes the ability of the molecule to traverse membranes by passive means (41). These Papp values were translated to a meaningful parameter of human brain extra-vascular clearance (hCL_bev) across the BBB by taking the product of Papp and human brain endothelial surface area of 20 m² (27).

Passive and active drug transport at the BBB

For the antipsychotics PAL and RIS that are known to have both active and passive transport across the BBB, the drug transport component was derived from Papp and in vitro efflux ratio (ER) determinations. ER is commonly used as an indicator of active drug transport in CNS drug discovery. ER is calculated as the ratio of effective permeability for a drug from the basal side to the apical side to that in the opposite direction (37). ER was used to calculate the human active efflux clearance (hCL_eff) of RIS and PAL. The parameters describing hCL_bev and hCL_eff accounting for active transport were derived based on Kwon et al. (42), underlying derivations are presented in Appendix 1.

$$ hC{L}_{bev}\left(\frac{L}{h}\right)=\frac{2*{P}_{app}* HBSA}{ER+1} $$

(Eq 1)

$$ hC{L}_{eff}\left(\frac{L}{h}\right)=\frac{2*{P}_{app}* HBSA*\left(ER-1\right)}{ER+1} $$

(Eq 2)

hCL_bev and hCL_eff represent the passive permeability and active transport clearance across the BBB in humans, respectively. Papp represents the in vitro apparent permeability and HBSA represents human brain endothelial surface area of 20 m^2..

Receptor binding parameters

In vitro Ki_human values were used as the parameter Kd (equilibrium constant). If available, in vitro or ex vivo experimentally determined k_off values were used in these simulations (Table III). If experimental k_off values were not available, then calculated k_off values based on Ki and k_off correlation of different antipsychotics were used, as reported previously (5).

Approach B: Human D₂RO predictions based on in vivo information

The appropriateness of using the available rat hybrid PBPKPD model to determine in vivo parameters for human D₂RO predictions was assessed. Binding constants (K_on and K_off) and clearances (rCL_bev and rCL_eff) were obtained using PBPKPD models developed by us previously (7,8). This in vivo model based information was only available for OLZ, PAL and RIS.

Passive drug transport to the brain

Calculated Papp (Papp_calc) values were derived as the ratio between PBPKPD model-estimated in vivo rCL_bev and rat brain endothelial surface area (150 cm²/g) and then normalized for an average rat brain weight of 2 g/250 g of rat (32). The product of Papp_calc and the human brain endothelial surface area (20 m²) was used as the hCL_bev - the passive transport clearance across the human BBB.

Active drug transport from the brain

Human active efflux clearance was predicted based on the PBPKPD model-estimated rCL_eff and mdr1a protein expression in micro vessels in mouse. Mdr1a expression values for rats were not available; hence, mdr1a expression in rat brain was assumed to be equal to that of mouse. Mouse mdr1a expression was documented as 14.1 fmol/μg of protein, and MDR1 expression in human brain was documented as 6.06 fmol/μg of protein (11). The following Eq. (Eq 3) describes the assumed relationship that was used to derive the hCL_eff.

$$ hC{L}_{eff}\left(\frac{L}{h}\right)=rC{L}_{eff}\left(\frac{L}{h}\right)*\frac{MDR1\; expression\; in\; human\; brain}{Mdr1a\; expression\; in\; rat\; brain} $$

(Eq 3)

Receptor binding parameters

Model estimated in vivo k_on-_rat and k_off-rat values were used as in vivo human k_on and k_off assuming that these drug-specific parameters do not require any scaling between species (9). For OLZ, model estimated in vivo Kd_rat and k_off-rat values were taken from our previous publication (7). For RIS and PAL, in vivo binding constants were obtained from the extended model structure where the time courses for D₂ and 5-HT_2A receptor binding were modeled together (8). These parameters are shown in Table IV.

Table IV Brain PKPD Model Parameter Estimates (% Relative Standard Error) Obtained from rat PBPKPD Model and Used in the Human D₂RO Predictive Model (Approach B)

Approach C: Human D₂RO predictions integrating in vitro and in vivo information

Passive and active drug transport to the brain

Scaling and calculation used in Approach A were also applied in the integrated Approach C.

Receptor binding parameters

In vivo Kd_human parameters were corrected for the differences between in vitro and in vivo scenarios by normalizing model estimated in vivo Kd_rat and in vitro Ki values for rat and human, as shown in Eq. (Eq 4).

$$ K{d}_{human}(nM)= Invitro\;K{i}_{human}*\frac{Invivo\;K{d}_{rat}}{Invitro\;K{i}_{rat}} $$

(Eq 4)

In vivo k_off-human values were assumed to be equal to in vitro or ex vivo experimentally determined k_off values.

Human 5-HT_2ARO predictions

The objective of this exercise was to check the utility of the extended model structure to predict human D₂RO and 5-HT_2ARO. In vitro Ki_human and Ki_rat for PAL were 0.250 nM (43). In vitro Ki_human and Ki_rat for RIS were 0.160 and 0.210 nM, respectively (43,44). We were unable to find k_off value for 5-HT_2A binding from any in vitro source and so, the in vivo based Approach B and the integrated Approach C were applied for these predictions.

Human D₂ receptor occupancy simulations

For each approach (A-C), 1000 human D₂RO- time course curves were simulated at clinically relevant doses, administered orally. Differential equations (Appendix 2) explaining the pharmacokinetics and pharmacodynamics of antipsychotics were used in these simulations as implemented in R (Version 3.1.0) using the deSolve package (45). Inter-individual variability (IIV) in the population pharmacokinetic parameters was accounted for in these simulations. The predictive power of this translational approach was determined by comparing these simulations with observed human D₂RO. In clinical trials, human D₂RO information were collected after repeated dosing and at steady state conditions. Hence, time course of D₂RO was simulated and results at steady state (achieved within 2 or 3 weeks of repeated drug dosing) were compared with the observed steady state RO.

Predictions of human RO were performed for CLZ (500 mg/day), HAL (2 mg/day), OLZ (10 mg/day), PAL (9 mg/day), QTP (750 mg/day) and RIS (4 mg/day) dose levels and compared graphically with observed D₂RO. Additionally, for OLZ, RIS and PAL box plots of prediction errors were made to compare the applicability of the different approaches and their predictive power. For this purpose, D₂RO or both D₂RO and 5-HT_2ARO predictions were made for a drug treatment of 3 weeks, at a single time point (12 h after the last dose of OLZ, RIS and 2 h after the last dose of PAL). These predictions were then compared with the median of the actual observations. The selection of dose and time points was based on the availability of data.

% Prediction Error (PE) was calculated as follows:

$$ \%\mathrm{P}\mathrm{E}=100*\frac{\mathrm{Median}\;\mathrm{Predicted}\;\mathrm{R}\mathrm{O}-\mathrm{Median}\;\mathrm{O}\mathrm{bserved}\;\mathrm{R}\mathrm{O}}{\mathrm{Median}\;\mathrm{O}\mathrm{bserved}\;\mathrm{R}\mathrm{O}} $$

(Eq 5)

The median D₂RO observed experimentally for OLZ, PAL and RIS were 54.9, 77.4, 75.8%, respectively. The 5-HT_2ARO observed for RIS was 100% (46).

Results

Human D₂RO predictions

Approach A

This approach predicted the time course of human D₂RO well for five of the antipsychotics, but not for HAL, as depicted in Fig. 2. The percentage prediction bias of these predictions is depicted for OLZ, PAL and RIS in Table V and Fig. 3.

Fig. 2

Observed and predicted steady-state D₂ receptor occupancy in humans after oral administration of antipsychotics at clinically relevant doses. Simulations were performed using the rat PBPKPD model structure integrated with in vitro apparent permeability, efflux ratio and in vitro binding information (Approach A). Depicted are the observed D₂RO (dots) and the shaded area represent the 95% prediction limits of the simulated D₂RO. The medians of the simulated D₂RO are represented as a solid line.

Table V Prediction Bias (in %) Across Different Approaches Used for Predicting Human D₂RO

Fig. 3

Box plots representing the % prediction error (PE) for different approaches where in vitro, in vivo and integrated in vitro and in vivo information were used to predict the human D₂RO. Letters A, B and C denotes the three different approaches, Approach A, Approach B and Approach C, respectively.

Approach B

The predictive model based on in vivo model estimated parameters under-predicted the human D₂RO for OLZ, RIS and PAL (Table V, Fig. 3).

Approach C

The predictive model using the “corrected” in vivo Kd_human estimates predicted human D₂RO for OLZ are at the best when compared to the other approaches (Fig. 3). For PAL and RIS, the D₂RO was slightly over-predicted and the prediction bias was large in comparison to Approach A (Figs. 3 and 4) and Table V.

Fig. 4

Observed and predicted steady-state D₂ receptor occupancy (D₂RO) in humans after oral administration of risperidone or paliperidone at clinically relevant doses. Depicted are the observed D₂RO (dots) and the shaded area represent the 95% prediction limits of the simulated D₂RO. The medians of the simulated D₂RO are represented as a solid line. Panel (a) and Panel (b) represent the human D₂RO predictions for paliperidone achieved by approaches A and C, respectively. Panel (c) and Panel (d) represent the human D₂RO predictions for risperidone based on approaches A and C, respectively.

Human 5-HT_2ARO predictions

The extended predictive model using the “corrected” in vivo Kd_human estimates predicted the human 5-HT_2ARO for risperidone better than approach B. Human D₂RO predictions were similar to that of the model which only accounts for the D₂ receptor binding, although the prediction bias for Approach B is lower (Table V, Fig. 5).

Fig. 5

Box plots represent the % prediction error (PE) for human D₂RO and 5-HT_2ARO predictions of risperidone at 4 mg/day dose. % PE for human D₂RO predictions obtained by both D₂ model structure (D₂MS) and an extended model structure including 5-HT_2ARO (5-HT_2AMS) are compared in the left hand panel. Right hand panel represents the human 5-HT_2ARO predictions of risperidone obtained from the extended model structure using approach B and C.

Discussion

This study aimed to utilize the recently proposed rat PBPKPD model structure (7,8) in a translational framework to scale pharmacokinetic and pharmacodynamic information from rats to human. The objective of this work was also to determine the minimal information required to be included in this translational framework to predict the D₂RO during the early drug discovery phase, while taking into account distribution to the brain and receptor binding.

In this simulation study, three approaches (A, B and C) were used to predict D₂RO in human. Approach A uses information based on in vitro studies, Approach B uses information obtained from in vivo studies based on rats and Approach C integrates both in vitro and in vivo based information. Due to limitation of in vivo based information, Approach B and Approach C were applied only for olanzapine, risperidone and paliperidone. The following part discusses the implementation of these approaches to translate permeation of drugs to brain and their binding to D₂ receptors.

Translation of passive drug transport at the BBB

It is well known that tight junctions and active efflux transporters present at the luminal surface of the BBB are involved in the distribution of any substance to the brain. Hence, hCL_bev and hCL_eff were included in this model structure to explain passive permeability across the BBB and active efflux processes in a mechanistic manner.

In vitro effective permeability of compounds with various characteristics across human primary brain endothelial cells was comparable to those obtained with bovine and rat capillary endothelial cells (10). So, a simplistic way of translation of passive permeability across the BBB between species is by accounting for the differences in system-specific brain endothelial surface area and utilize the in vitro effective permeability information without any scaling between species. In Approach A, passive permeability of the compounds across the BBB was calculated as the product of human brain endothelial surface area and Papp values obtained from in vitro MDR1-MDCK.

Approach B used the passive permeability of compounds across the BBB under in vivo conditions. This was achieved by estimating model parameter explaining the passive transport of drugs across the BBB by fitting a PBPKPD model to plasma and whole brain concentration data obtained from rats. Papp_calc (permeability across the BBB in vivo) values were derived from PBPKPD model-estimated in vivo rCL_bev and rat brain endothelial surface area.

The hCL_bev values calculated based on in vitro Papp or Papp_calc (calculated based on rCL_bev) values were different (Table III) and this could direct towards a theory on different efficiency of drug transport in in vitro and in vivo systems. However, it should be noted that the PBPKPD model-based estimate rCL_bev (and thereby Papp_calc) was based on whole brain concentration and therefore this data do not differentiate the influence of the cerebrospinal fluid barrier and other microenvironment conditions on the transport of drug at the BBB. In addition, Papp_calc was derived using reported rat brain endothelial surface area, which ranges from 100 to 240 cm² per g brain tissue (47,48). These underlying assumptions and lack of information limited the application of Approach B. Notwithstanding this limitation, deriving a relationship between model-estimated rCL_bev (and thereby Papp_calc) and in vitro Papp based on more compounds might help to improve the translation approach. However, the limited number of compounds used in our PKPD analysis did not allow us to elicit such a relationship. So, in the absence of such a relationship, it seems to be more appropriate to base the scaling of in vitro Papp values to hCL_bev on human brain endothelial surface area only. Hence, while integrating in vitro and in vivo information (i.e., Approach C), the calculated hCL_bev was based only on in vitro Papp value and human brain endothelial surface area.

Translation of active drug transport at the BBB

Predicting active efflux clearance at the human BBB using in vitro information was challenging and complicated. In this simulation study, in vitro ER was used to account for the active drug transport out of the brain. In Approach A, in vitro ER was used to calculate the drug transport across the BBB by means of active transport. Derivation based on Kwon et al. (42) explains the transport of compound across membranes under in vitro conditions using Papp and ER and by using this derivation and HBSA, the parameters hCL_bev and hCL_eff were calculated for human conditions. This translation approach is simple and based only on information from in vitro. Hence, this will be a useful tool to predict brain transport in human brain environment at early stages of drug development. Nevertheless, it should be noted that this translation approach accounts only for differences in brain endothelial surface area between species and excludes differences in transporter expression levels. Extension of this approach accounting for those differences on microenvironment levels between different species would help to improve predictions of drug transport at BBB.

Subsequently, active efflux transport was also scaled to the human conditions based on the estimates obtained from the rat PBPKPD model parameters and expression of mdr1a protein in both species (i.e., Approach B). As described earlier, this PBPKPD model-based estimate of rCL_bev (and thereby Papp_calc) and rCL_eff were based on whole brain concentration and therefore had no ability to differentiate microenvironment conditions at the BBB. In addition, due to non-availability of the appropriate mdr1a expression data in rats, it was assumed that it is equal to that of mouse. Additionally, the active transport was included as a linear process rather than non-linear as usually described for in vitro systems, since the free concentrations of drug at the BBB (in rats) were much lower than the concentrations used in vitro, and remain most likely below the Km (concentration require for the half -maximal transport) for the transporter, which makes this assumption acceptable. A proper evaluation of these assumptions would help to substantiate the claims, however due to lack of human brain drug exposure information these assumptions are seldom evaluated. Nevertheless, this work provides a framework to account for the active drug transport in humans. It is noteworthy that both these approaches (Approach A and B) are plausible because of their mechanistic basis.

Translation of receptor binding properties

Danhof et al. (49) proposed that the values of drug-specific parameters such as target affinity are likely to be identical between species and individuals. This would imply that the binding rate constants estimated in rats could be used to extrapolate the pharmacodynamics from rat to human. Hence, it is appropriate to include in vitro or in vivo binding constants in this model structure to predict human D₂RO. This predictive model structure was obtained from a preclinical system where the drug binding to D₂ receptors was explained by accounting for the association and dissociation rates of antipsychotics. The model estimated in vivo Kd_rat values for OLZ were close to in vitro Ki_rat values (rat cloned D_2L system – 17 nM), but in vitro Ki_human values (human cloned D_2L system- 5.1 nM) were different from both these values of the rat system. Additionally, PAL and RIS in vitro Ki_rat values (most commonly reported as 2 nM) are different from the model estimated in vivo Kd_rat values (0.364 nM). The human D₂RO predictions for OLZ, RIS and PAL were not consistent with the observed human D₂RO data when model estimated in vivo Kd_rat was used as the in vivo Kd_human parameter in the predictive model. This challenges the general belief that drug-specific parameters like Kd can be used across species without any scaling. However, this difference between the in vivo and in vitro scenario for the same species could arise from the assumptions used in both in vitro calculations and model estimations. Additionally, radio-ligand selection and disturbances in assumed equilibrium conditions in in vitro and in vivo systems could lead to biased or inappropriate Ki calculations (50).

Extension of predictive model

It has been demonstrated that the binding to both D₂ and 5-HT_2A receptors (extended model) was essential to explain the relationship between drug exposure and receptor occupancy in the preclinical system with good precision (8). The model estimates of in vivo Kd_rat for RIS are influenced by the brain distribution kinetics and it was elucidated that the brain-to-plasma ratio (in rats) is not constant for RIS, suggesting an influence of specific binding to receptors on the brain-kinetics (8). Hence, an extended model structure was used to predict both D₂ and 5-HT_2A receptor occupancy in humans. The extended structure predicted 5-HT_2ARO well. Surprisingly, the D₂RO predictions achieved by using these two different model structures (D₂ alone versus D₂ + 5-HT_2A) remained close to each other; and this extension, which was essential for model fitting in a preclinical system, did not significantly improve the human D₂RO predictions (atleast for Approach C). Nevertheless, this extended model structure underscores the ability of this model framework to be flexible and extendable to other receptor types.

Our objective was also to study the minimal information required to predict human D₂RO. In general, human D₂RO was predicted well for all compounds except haloperidol when only in vitro information (Approach A) was used in the simulations. This demonstrates the ability of this model structure to predict human D₂RO with minimal in vitro information.

In this simulation study, the time course of plasma concentrations was obtained from available population pharmacokinetic parameters. It is also possible to predict these pharmacokinetic parameters based on in silico and in vitro information using commercially available tools, like Simcyp (Simcyp Ltd., Sheffield, UK). So, the requirement of population pharmacokinetic parameters obtained from clinical studies is not essential.

For HAL, D₂RO predictions were lower than the observations. This may be related to the high ratio of unbound concentrations of HAL in brain and plasma, which is close to 4 in rats (51). This high brain to plasma ratio may indicate a unique active influx transport to the brain. In addition, it has been documented that the metabolism of HAL involves a conversion of HAL to reduced haloperidol, and back-conversion of reduced haloperidol to HAL (52) in the brain of guinea pigs. Accounting for this metabolism and/or active influx transport may help to improve predictions. Extending this predictive model structure to include such complexity is practically possible, if sufficient information about each related process is available beforehand.

Applications of this predictive tool are not limited to only predicting D₂RO in early drug discovery but also in selecting appropriate first in human doses based on pharmacodynamics. It is not anticipated that predictive tools will completely replace the need for experiments, though it is plausible that this tool can help to design more informative and more efficient clinical studies.

Conclusion

A general translational framework was developed which is based on a mechanism-based approach and accounts for the different processes involved in the transport of drug to the brain. Based on, in vitro information (Papp, ER and Ki), the model was able to predict the human D₂RO for drugs distributed to the brain by passive permeability and active transport processes. This model structure with an appropriate extension also predicted the human 5-HT_2ARO well.

Appendices

APPENDIX 1

Derivation of the relationship between CL_bev, CL_eff, Papp, SA and ER

1. Relationship between CL_bev, CL_eff, PS and PS_pgp

The derivation is based on the model described by Kwon et al. (42). The model describes the passive and active transport from the apical side (A) to the basal side (B) of enterocytes. A similar model was described by Kalvass et al. (53) for various situations where efflux transporters such as P-glycoprotein (Pgp) are involved, including the blood–brain barrier.

Equation (Eq 2) of Kwon et al. (42) describes the net change of the amount in the cells (M), i.e., the rate of accumulation in the cell.

$$ \frac{dM}{dt}=PS1*{C}_A-PS2*{C}_{ent}-P{S}_{pgp}*{C}_{ent}+PS4*{C}_B-PS3*{C}_{ent} $$

(A1)

where C_A and C_B are the extracellular concentration at the apical and basal side, respectively, C_ent is the intracellular concentration, PS1, PS2, PS3 and PS4 are the products of membrane permeability and surface area for passive transport from A to intracellular, from intracellular to A, from intracellular to B and from B to intracellular, respectively, and PS_pgp is the product PS for active transport from intracellular to A by the transporter Pgp.

In situations where the concentrations at both sides A and B are constant, C_ent will be constant, and the net change of M will be zero. For dM/dt = 0, Eq. (Eq 5) can be rearranged and simplified to:

$$ {C}_{ent}=\frac{C_A+{C}_B}{2+\frac{P{S}_{pgp}}{PS}} $$

(A2)

The net transport over the basal membrane in the direction from apical to basal side is

$$ Net\; basal\; membrane\; flu{x}_{AB}=PS*{C}_{ent}-PS*{C}_B $$

(A3)

Replacing C_ent by Eq. (A1)

$$ Net\; basal\; membrane\; flu{x}_{AB}=\frac{PS*{C}_A-\left(PS+P{S}_{pgp}\right)*{C}_B}{2+\frac{P{S}_{pgp}}{PS}} $$

(A4)

The net transport over the apical membrane in the direction from apical to basal side is

$$ Net\; apical\; membrane\; flu{x}_{AB}=PS*{C}_A-\left(PS+P{S}_B\right)*{C}_{ent} $$

(A5)

Replacing C_ent by Eq. (A1) yields the same result as Eq. (A3), since it was assumed that there is no accumulation in the cells.

The passive diffusion clearance CL_bev is defined as the passive membrane flux from A to B divided by the concentration C_A, so it follows from Eq. (A3):

$$ C{L}_{bev}=\frac{PS}{2+\frac{P{S}_{pgp}}{PS}} $$

(A6)

The active efflux clearance CL_eff is defined as the efflux by Pgp of C_B, so from Eq. (A3):

$$ C{L}_{eff}=\frac{PS}{2+\frac{P{S}_{pgp}}{PS}} $$

(A7)

Equations (A5) and (A6) define the relationship between the model parameters CL_bev and CL_eff, and their determinants, PS and PS_pgp.

Note that the passive CL_bev is dependent on PS_pgp. This is due to the fact that the active efflux lowers the intracellular concentration C_ent, reducing the effective concentration gradient over the basal membrane. As a result, the passive transport is lower compared to the situation in the absence of active efflux.

2. Efflux Ratio

The Efflux Ratio is defined as the ratio of the transport clearance (CL_BA) from B to A if C_A = 0 and the transport clearance (CL_AB) from A to B if C_B = 0 (37). From Eqs. (A3), (A5) and (A6) the following equations can be derived:

$$ Efflux\; Ratio\;(ER)=\frac{PS+P{S}_{pgp}}{PS} $$

(A8)

$$ Efflux\; Ratio\;(ER)=\frac{C{L}_{bev}+C{L}_{eff}}{C{L}_{bev}} $$

(A9)

$$ P{S}_{pgp}=PS*\left(ER-1\right) $$

(A10)

$$ C{L}_{eff}=C{L}_{bev}*\left(ER-1\right) $$

(A11)

From Eqs. (A3) and (A7) it can be derived that the ratio C_A/C_B (plasma/brain ratio) at steady state is equal to the efflux ratio ER.

3. Relationship between Papp and PS

The apparent permeability Papp is determined by measuring the net flux over the cell layer in the absence of active efflux (PS_pgp = 0). In this case Eq. (A3) can simplified to:

(A12)

Papp is obtained by dividing by the concentration gradient, after normalizing for surface area (SA):

$$ {P}_{app}=\frac{PS}{2*SA} $$

(A13)

Or

$$ PS=2*{P}_{app}*SA $$

(A14)

The factor 2 reflects the passage over two membranes in series.

4. Relationship between CL_bev, CL_eff, Papp and ER

Combining Eqs. (A5), (A6), (A9), (A10) and (A13) yields the following equations:

$$ C{L}_{bev}=\frac{2*{P}_{app}*SA}{ER+1} $$

(A15)

$$ C{L}_{eff}=\frac{2*{P}_{app}*SA*\left(ER-1\right)}{ER+1} $$

(A16)

Equations (A14) and (A15) can be used to calculate the model parameters CL_bev and CL_eff from the experimentally obtained values Papp and ER.

APPENDIX 2

PBPKPD model used to predict human D₂RO is defined by the following differential equations:

$$ \begin{array}{l}d\left({A}_{bv}\right)/dt=\left(C{L}_{bv}/{V}_{plasma}\right)\ast {A}_{plasma}-\left(C{L}_{bv}/{V}_{bv}\right)\ast {A}_{bv}-\left(C{L}_{bev}/{V}_{bv}\right)\ast f{u}_{plasma} \ast {A}_{bv}+\left(C{L}_{bev}/{V}_{bv}\right)\ast f{u}_{brain} \ast {A}_{bev}+\left(C{L}_{bev}/{V}_{bv}\right)\ast f{u}_{brain} \ast {A}_{bev}\kern1em \\ {}d\left({A}_{bev}\right)/dt=\left(C{L}_{bev}/{V}_{bv}\right)\ast f{u}_{plasma} \ast {A}_{bv}-\left(C{L}_{bev}/{V}_{bev}\right)\ast f{u}_{brain} \ast {A}_{bev}-\left(C{L}_{eff}/{V}_{bv}\right)\ast f{u}_{brain} \ast {A}_{bev}-\left(C{L}_{st}/{V}_{bev}\right)\ast f{u}_{brain} \ast {A}_{bev+}\left(C{L}_{st}/{V}_{stf}\right)\ast f{u}_{brain}\ast {A}_{stf}\kern1em \\ {}d\left({A}_{stf}\right)/dt=\left(C{L}_{st}/{V}_{bev}\right)\ast f{u}_{brain}\ast {A}_{bev}-\left(C{L}_{st}/{V}_{stf}\right)\ast f{u}_{brain}\ast {A}_{stf}-{k}_{on}\ast f{u}_{brain}\ast {A}_{stf}\ast \left({B}_{max}-CB\right)+{k}_{off}\ast {A}_{stb}\kern1em \\ {}d\left({A}_{stb}\right)/dt={k}_{on}\ast f{u}_{brain}\ast {A}_{stf}\ast \left({B}_{max}-CB\right)-{k}_{off}\ast {A}_{stb}\kern1em \end{array} $$

Where,

subscripts plasma, bv, bev, stf, sb represent volume (V) and amount (A) of drug in plasma, brain-vascular, brain-extravascular, striatum-free and striatum-bound compartments, respectively;

CL_bv, CL_bev, CL_st represent transport clearance of drug to brain-vascular, brain-extravascular, striatum-free compartments, respectively;

CL_eff represents the active efflux transport clearance of drug from brain-extravascular compartment;

B_max is the dopamine D₂ receptor density in nM;

CB is the concentration bound to receptor as (A_stb/V_stb)/ (MW/1000) in nM;

MW is the molecular weight of the drug;

D₂RO is calculated as CB/B_max*100%.