P-Glycoprotein Deficient Mouse in situ Blood-Brain Barrier Permeability and its Prediction using an in combo PAMPA Model

Abstract

The purpose of the study was to assess the permeability of mouse blood-brain barrier (BBB) to a diverse set of compounds in the absence of P-glycoprotein (Pgp) mediated efflux, to predict it using an in combo PAMPA model, and to explore its role in brain penetration classification (BPC). The initial brain uptake (K_in) of 19 compounds in both wild-type and Pgp mutant [mdr1a(−/−)] CF-1 mice was determined by the in situ brain perfusion technique. PAMPA measurements were performed, and the values were used to develop an in combo model, including Abraham descriptors. Published rodent K_in values were used to enhance the dataset and validate the model. The model predicted 92% of the variance of the training set permeability. In all, 182 K_in values were considered in this study, spanning four log orders of magnitude and where Pgp decreased brain uptake by as much as 14-fold. The calculated permeability-surface area (PS) values along with literature reported brain tissue binding were used to group molecules in terms of their brain penetration classification. The in situ BBB permeability can be predicted by the in combo PAMPA model to a satisfactory degree, and can be used as a lower-cost, high throughput first-pass screening method for BBB passive permeability.

INTRODUCTION

Discovery of central nervous system (CNS) drugs is challenging due to the complexity of neurological disorders, the paucity of pre-clinical models with proven human translational value, and the persistent difficulty of delivering drug molecules across the blood-brain barrier (BBB) to achieve optimal CNS exposure. There is an intricate debate taking place in the recent literature regarding how best to interpret the results obtained from in vitro, in situ, and in vivo blood-brain transport methodologies, to identify properties most relevant to successful CNS drug delivery, both in terms of the rate and the extent of penetration (Hammarlund-Udenaes et al. 2008; Martin 2004; Liu et al. 2005, 2008; Hitchcock 2008; Jeffrey et al. 2007; Cecchelli et al. 2007; Maurer et al. 2005; Pardridge 2007; Reichel 2009).

The brain-to-plasma distribution ratio has been widely used in drug discovery as an index of brain penetration (K_p = AUC_tot,brain/AUC_tot,plasma, where AUC is the area under the total drug concentration-time curve in the corresponding tissue over a dosing interval; also called log BB – see Glossary). However, K_p used in isolation is a misleading parameter since it is generally accepted that it is the unbound drug that exerts the physiological effect (Hammarlund-Udenaes et al. 2008; Martin 2004). Efforts to optimize CNS candidate selections based solely on K_p “may actually lead to unproductive/counterproductive design of drugs that are unnecessarily basic, lipophilic, and have greater degree of nonspecific partitioning into brain tissue” (Maurer et al. 2005). Increasing lipophilicity does not necessarily lead to increased efficacy (Summerfield et al. 2006), and may lead medicinal chemists astray in a chemical space that is hardly druggable due to poor solubility and metabolic instability.

A number of CNS drug discovery groups (Liu et al. 2005, 2008; Jeffrey et al. 2007; Summerfield et al. 2006) have proposed optimization strategies based on an integrated use of BBB permeability, the effect of efflux transport, and nonspecific plasma and brain tissue binding, to ultimately characterize brain penetration in terms of unbound drug brain distribution: K_p,uu^{in vitro} = C_u,brain/C_u,plasma, where C_u,brain and C_u,plasma are the unbound concentrations in the brain (blood-free) homogenate and plasma, respectively. Ideally, a CNS drug would achieve a K_p,uu^{in vitro} close to unity within a relatively short time to maximize CNS exposure. In practice, this would also maximize peripheral safety margins by minimizing differences in peak unbound concentrations between brain and plasma. For instance, BBB efflux makes K_p,uu^{in vitro} < 1, requiring higher plasma concentrations to elicit a CNS effect.

In vivo microdialysis has been the long standing and labor-intensive standard methodology to measure unbound concentrations in living brain (Hammarlund-Udenaes et al. 2008; Fridén et al. 2007; Benveniste and Huttemeier 1990). A more refined consideration of the in vivo ratio, K_p,uu (cf., Glossary), draws a distinction between the concentration in the brain homogenate and the brain interstitial fluid (ISF), since the process of homogenization blends the intra- and extracellular brain fluids, which is relevant to compounds with poor cell membrane permeability that may distribute poorly to intracellular compartments. Nevertheless, there is cumulating evidence that suggests measurement of K_p,uu^{in vitro} can be used to approximate free exposure in a pharmacologically meaningful manner. In vitro methods to assess the unbound drug fractions in plasma, f_u,plasma, and brain tissue homogenates, f_u,brain, have been extensively investigated (Liu et al. 2005, 2008; Jeffrey et al. 2007; Maurer et al. 2005; Kalvass and Maurer 2002; Mahar Doan et al. 2004; Kalvass et al. 2007; Wan et al. 2007; Summerfield et al. 2007).

Many different in vitro BBB models have been developed and proposed to measure permeability, some based on human brain endothelial cells (Terasaki et al. 2003; Garberg et al. 2005; Weksler et al. 2005; Abbott 2007). Despite limited successes, these models generally suffer from a significant loss in transporter function and poor tight junction organization (leakiness) as compared to the in vivo BBB. Many drugs companies simply use epithelial cells transfected with P-glycoprotein (MDCK or LLC-PK1) to conduct permeability screening in CNS drug discovery.

Kalvass et al. (2007) provided an integrated approach for assessing CNS steady-state distribution of drugs. They combined the Pgp efflux ratio, ER, with in vitro-measured unbound plasma and brain tissue concentrations. A plot of ER versus C_u,plasma/C_u,brain is divided into four brain penetration classifications (BPC) using 3-fold cutoffs as delineators.

In a similar example of integrative approach to better understand CNS exposure, Liu et al. (2005,2008) incorporated independent measures of BBB permeability by brain perfusion in their physiologically based pharmacokinetic (PBPK) model, and calculated brain equilibration half-time as t_1/2,eq = const. / (PS·f_u,brain), where the unbound brain fraction, f_u,brain = C_u,brain/C_tot,brain. PS is the product of BBB permeability and the microcapillary specific surface area.

Given the number of compounds to test in early drug discovery, costly and labor-intensive in vivo measurements of CNS pharmacokinetic properties are impractical, and in vitro BBB models rely on relatively time-consuming cell culture. Useful in silico predictions of in vivo BBB transport properties could substitute for direct measurements in initial screening. In silico methods to predict K_p exist (Bendels et al. 2008, Zhang et al. 2008, Kortagere et al. 2008), but have not been applied to K_p,uu. The prediction of PS_passive has been the subject of a number of studies (Clark 2003; Abraham 2004; Lanevskij et al. 2008; Di et al. 2008). In silico attempts have been made to estimate the influence of Pgp on in vitro substrate transport (Didziapetris et al. 2003; Garg and Verma 2006).

The most reliable published PS data come from rodent in situ brain perfusion studies (Takasato et al.1984; Gratton et al.1997; Wu et al. 1998; Murakami et al. 2000; Bourasset et al. 2003; Cisternino et al. 2003, 2004; Youdim et al. 2004; Dagenais 2000; Dagenais at al. 2000, 2001, 2002, 2004, 2005; Cisternino et al. 2004; Liu, et al. 2005; Parepally et al. 2006; Bihorel et al. 2007; Obradovic et al. 2007). The modified Takasato method (Takasato et al. 1984) has been adapted to the mouse by Dagenais and Rousselle (Dagenais et al. 2000b), and applied to study BBB efflux using various knockout mouse models. This technique requires special surgical skills, is labor and animal intensive, and time consuming. Unless radiolabeled compounds are used, significant bioanalytical resources are required (e.g., liquid chromatography-mass spectrometry). Rodent brain perfusion studies are not performed routinely in the pharmaceutical industry.

As a cost-effective high-throughput alternative to in vitro and in situ methods to estimate BBB permeability, PAMPA (parallel artificial membrane permeability assay) could be used to assess PS_passive (Kansy et al. 1998; Avdeef 2003, 2005; Di et al. 2003,2008; Bermejo et al. 2004; Avdeef et al. 2005; Youdim et al. 2003; Ruell et al. 2004; Avdeef et al. 2004). PAMPA membranes are based on a mixture of phospholipids deposited into lipophilic microfilters, and contain net-negative lipid charge, mimicking some of the properties of endothelial cell membranes. Di et al. (2003) adapted porcine brain lipid extract dissolved in n-dodecane (2% w/v) as their PAMPA membrane barrier and demonstrated that molecules can be successfully binned into CNS+ and CNS− classes. The early attempts to establish a numerical relationship between PAMPA and Caco-2 cellular assays have shown considerable promise, with high linear correlations reported (Bermejo et al. 2004). An in combo PAMPA method (hybrid “combination” of in silico and in vitro methods) has been described, where it was possible to separate some active and passive components of cellular permeability (Avdeef et al. 2005).

In this study, we report 38 new in situ PS measurements performed on 19 compounds in wild-type (WT) and Pgp-deficient [mdr1a(−/−)] CF-1 mice (so called mutants equivalent in phenotype to the corresponding “knockout” model). One aim of the study was to quantify the influence of Pgp on PS values by comparing the mouse genotypes. The second aim was to use PS_passive values from the Pgp deficient data to train the in combo PAMPA procedure, followed by enhancement and validation based on additional published rodent values. We were interested in developing a practical, cost-effective, and rapid quantitative in combo assay which could be used in early screening for passive BBB permeability, and which could over time assist medicinal chemists with structure modification to improve a key determinant of CNS exposure for test compounds downstream in the discovery process, as part of an integrated BBB penetration model, incorporating PS_passive along with possibly ER, f_u,brain, and f_u,plasma. Finally we explored the implicit contribution of passive BBB permeability in the brain penetration classification (BPC), which has not been discussed in the published literature.

MATERIALS AND METHODS

Drugs and Chemicals

The unlabeled chemicals used in this study (training set) were purchased from Sigma-Aldrich/RBI (St. Louis, MO, USA) and Tocris Bioscience (Ellisville, MO, USA), and used as received, except that analytical-grade amitriptyline and indinavir (Merck), astemizole, domperidone and galanthamine (Janssen-Ortho), clozapine (Novartis), gabapentin and sertraline (Pfizer), ritonavir (Abbott), saquinavir (Roche), and terfenadine (Aventis), were kindly provided by their manufacturer. PAMPA lipid (lecithin mixture) was obtained from pION (PN 110669), and was stored at −20°C when not used. The pH of the assayed donor solutions was adjusted with a universal buffer (pION, PN 100621). A buffer solution at pH 7.4 containing a chemical scavenger to simulate tissue binding and maintain sink conditions (pION ASB-7.4 buffer, PN 110139) was used as the receiver solution.

Animals

Adult male CF-1 mice (wild type and mdr1a(−/−), 30-40 g, 6-8 weeks old) were obtained from Charles River Laboratories (Wilmington, MA, USA). Animals were housed in a room with a controlled environment (22 ± 3° C; 55 ± 10% relative humidity) and maintained under a 12-h dark:light cycle (light from 6 a.m. to 6 p.m.). Animals had access to food and tap water ad libitum. All animal experiments were evaluated and approved by the Institutional Committee for Good Animal Practices (UQAM, Montréal, Québec, Canada).

Mouse Brain Perfusion Technique

Surgical Procedure and Transport Studies

The in situ mouse brain perfusion has been described in detail elsewhere (Dagenais 2000; Dagenais et al. 2000). Briefly, mice were anesthetized with intraperioneal ketamine/xylazine (140/8 mg/kg). The right hemisphere was perfused through the right common and internal carotid arteries following ligation of the external branch. The cardiac ventricles were severed immediately before brain perfusion (Krebs-bicarbonate buffer gassed to pH 7.4 with 95% O₂ and 5% CO₂ at 37° C) at 2.5 mL/min via a syringe pump. Test compounds were spiked in perfusate at a targeted concentration of 1 μM from a DMSO or dilute acetic acid stock solution (400-fold dilution). The perfusions were terminated by decapitation. Single time point experiments were performed (1, 2 or 3 minutes) based on the molecular properties of the compounds and their expected permeability category (low, intermediate, high). Previous studies were used to gauge the length of perfusion most likely to be within the linear portion of the uptake curve. The brain was removed from the skull and dissected on ice to isolate the right hemisphere. At this point, a sample of perfusion fluid was collected at the tip of the catheter by activation of the infusion pump. Samples were frozen in liquid nitrogen and maintained at −80°C until analysis by LC/MS or LC/MS/MS.

Sample Preparation and Bioanalysis

The generic sample preparation and bioanalysis procedures have been reported in detail elsewhere (Dagenais et al. 2002, 2004). As appropriate, samples of perfusion fluid were acidified with 1% v/v glacial acetic acid, and diluted with the mobile phase used at the start of gradient elution without further preparation. Brain samples (ca. 150 mg) were homogenized in 4 volumes of aqueous buffer, followed by protein precipitation with 2 volumes of ice-cold acetonitrile. Following centrifugation, the supernatant was either injected directly onto the HPLC system, or evaporated and reconstituted in 40% acetonitrile/ 60% water with 0.1% formic acid. All in vivo samples were quantified by LC/MS or LC/MS/MS using an Agilent 1100 LC/MSD system (Agilent Technologies, Wilmington, DE), or a PE-Sciex API-3000 MS/MS system (Applied Biosystems, Foster City, CA) fitted with a Shimadzu LC-10 HPLC system (Shimadzu Scientific Systems, Columbia, MD) and a CTC-Pal autosampler (Leap Technologies, Carrboro, NC). Gradient elution (1 to 2 mL/min) using admixtures of 0.1% formic acid or 25 mM acetate, and acetonitrile or methanol , was applied to high performance analytical columns (Agilent Zorbax C-18, YMC NH2 or Agilent Zorbax Extend C-18, all 4.6 mm × 50 mm). Parent ion monitoring (i.e., selective ion monitoring, MS) or multiple reaction monitoring (MS/MS) were used for mass spectrometric detection. Diclofenac was used as the internal standard. Typical run times were between 2 and 8 minutes per sample. Calibration curves were fit using linear or quadratic relationships with standard software from the instruments' manufacturer. A deviation of 20% or less from the predicted curve was considered acceptable for points on the calibration curve. Samples were re-assayed after appropriate dilution if the concentration could not accurately be interpolated or extrapolated.

Calculation of the in situ BBB Permeability

Initial uptake data from brain perfusion experiments can be assimilated to a pharmacokinetic tissue uptake clearance (Dagenais 2000; Dagenais et al. 2000), but traditionally have been referred to as K_in values, which can be estimated from single time point experiments using the following relationship (Dagenais 2000; Dagenais et al. 2000), K_in = ( X_br / T ) / C_pf, where X_br is parenchymal brain concentration (mol/kg units) of the tracer, C_pf is the perfusion fluid (analogous to arterial) concentration (mol/L) of the test compound collected at the tip of the infusion catheter, T is the perfusion time (min), and K_in is the initial rate of brain uptake. Parenchymal brain concentration is obtained by subtracting from the total concentration, the contribution from the vascular volume, X_br = X_total − V_vasc C_pf. A vascular volume of 1 mL/100g was used to correct total brain concentrations.

Using the Crone-Renkin equation, the rate constant is defined as K_in = F_pf ( 1 − e ^−PS/Fpf ), where F_pf is the regional cerebral flow of perfusion fluid, and PS is the capillary permeability-surface area product. Usually, diazepam is used as a flow marker to determine F_pf, since its uptake clearance is expected to be maximal (Dagenais 2000; Dagenais et al. 2000). However, in the training set used in this study, three compounds (amitriptyline, buspirone, chlorpromazine) had brain uptake clearances that were greater than that of diazepam (255 mL/100 g/min in the mouse; Dagenais 2000; Dagenais et al. 2000). Since the results tend to be more variable and sensitive to changes in experimental conditions under a flow-limited situation, the regional cerebral flow, F_pf, was taken to be 430 mL/100g/min for the purpose of the training set conversions. This value was selected so that all of the measured K_in may be converted to PS values. This choice did not alter the ranking of the PS values, as considered below.

In order to apply the Abraham descriptors, the PS value were temporarily converted to the intrinsic scale (Avdeef et al. 2005), according to the equation P_o^BBB = (PS / S) ( 1 + 10^±(pH-pKa)), with the '+' used for acids, and the '−' sign used for bases, and where S = brain capillary surface area, assumed to be 100 cm²/g (Ohno et al. 1978).

Pgp Effect

In addition to Pgp deficient (mdr1a(−/−)) data, wild-type mouse uptake clearance data were measured in this study. The results from Pgp-deficient mice were expected to result in a better estimate of passive permeability. The Pgp effect is defined by the ratio of the Pgp-deficient uptake clearance to that of wild-type up uptake clearance.

PAMPA Method

Data Collection

The PAMPA Evo instrument from pION INC (Woburn, MA, USA) was used in this study. The 96-well microtitre plate “sandwich” (pION, PN 110212, preloaded with magnetic stirrers) filters were coated with a 20% (w/v) alkane solution of a lecithin mixture containing an excess of negatively-charged constituents (pION, PN 110669). Sample concentrations in the buffer solutions for the compounds with low-UV absorption were about 500 μM (e.g., gabapentin, DPDPE, meperidine). However, for most of the compounds, UV sensitivity was good, and the typical concentrations were about 50 μM. DMSO-free stock solutions were prepared for some of the compounds (buspirone, colchicine, quinidine, tolbutamide, U69593, fentanyl, sertraline, ritonavir, astemizole, clozapine, deltorphin II, DPDPE, gabapentin, galanthamine, indinavir), to improve on UV sensitivity in the 210-240 nm part of the spectrum. The donor solutions were varied in pH (NaOH-treated universal buffer), while the receiver solutions had the same pH 7.4. This was necessary in order to correct the effective permeability values for ionization and aqueous boundary layer (ABL) effects (Avdeef et al. 2004, 2005). The pK_a^flux-centered (see below) gradient pH values were selected by the pOD procedure (Ruell et al. 2003). The receiver solutions contained a surfactant mixture (“lipophilic sink”) to mimic tissue binding (Avdeef 2003). Vigorous stirring was employed in the assay, with stirring speed set to produce an ABL thickness < 50 μm, to minimize the ABL contribution to the measured permeability. The PAMPA sandwich was assembled and allowed to incubate for 30 minutes for highly permeable molecules (e.g., amitriptyline, chlorpromazine, loperamide, sertraline, probenecid and verapamil), and 15 h for poorly permeable molecules (e.g., galanthamine, DPDPE, deltorphin II, indinavir), in a controlled-environment chamber (pION PN 110205) with a built-in magnetic stirring mechanism. Both the donor and receiver wells were assayed for the amount of material present, by comparison with the UV spectrum (210 to 500 nm) obtained from a reference standard. Permeability values were corrected for membrane retention (Avdeef 2003).

Correcting PAMPA Permeability for the ABL and Charge Effects by the pK_a^flux Method

In brain endothelial microcapillaries, the ABL thickness is likely to be < 1 μm (given that the radius of the human microcapillaries is about 3 μm), whereas in unstirred PAMPA, the ABL thickness can be as high as 4000 μm (Avdeef et al. 2004). By taking PAMPA (stirred or unstirred) data over a range of pH, it is possible to correct for the effect of the ABL, by applying the pK_a^flux method (Avdeef 2003; Avdeef et al. 2004, 2005; Ruell et al. 2003), briefly described below.

In the analysis of PAMPA data, four types of permeability values are considered: (a) the effective permeability coefficient, P_e (which is directly determined); (b) the aqueous boundary layer permeability, P_ABL, based on the resistance of the water layer adjacent the membrane; (c) the membrane permeability, P_m (which depends on pH with ionizable molecules); and (d) the intrinsic permeability, P_o, which is the permeability of the uncharged species (the maximum possible value of P_m at the pH where an ionizable molecule is uncharged). ABL-limited transport is often observed for lipophilic molecules, when P_o >> P_ABL. The basic equation describing permeability is (Avdeef et al. 2005)

$$\log {\mathrm{P}}_{\mathrm{e}}=\log {\mathrm{P}}_{\mathrm{e}}^{\max }-\log ({10}^{\pm \left(\mathrm{pH}-{\mathrm{pK}}_{\mathrm{a}}^{\mathrm{flux}}\right)}+1)$$ (1)

which is valid provided that P_o > 10 P_ABL (lipophilic molecules). The maximum possible effective (measured) permeability, P_e^max, is defined as log P_e^max = log P_ABL − log ( 1 + P_ABL / P_o ). When P_o >> P_ABL (highly permeable molecules), P_e^max, ≈ P_ABL. The “flux” ionization constant, pK_a^flux, refers to the pH value where the resistance to transport across a permeation barrier is 50% due to the ABL and 50% due to the membrane (Avdeef 2003).

In silico Model Building Software and the in combo Strategy

PS Training and Test Set Selection Criteria

Our core computational object was to model PS_passive values. From a survey of the published literature, 507 PS values were identified, based on in vivo intravenous injection (i.v.), bolus carotid artery injection (BUI), and in situ brain perfusion methods, for rats, mice, guinea pigs, rabbits, dogs, and cats. It was decided to focus only on rat (n=335, 66%) and mouse (n=131, 26%) data, accounting for about 92% of the collected values.

It is hypothesized here that mouse and rat data are comparable for the purposes of our prediction study. This may be reasonable, as suggested by Murakami et al. (2000). For their reported rat and mouse permeability values (21 compounds), the linear regression of rat vs. mouse logarithm of the intrinsic (defined below) permeability coefficients yielded the intercept = 0.21 ± 0.24 and slope = 1.01 ± 0.05.

Since plasma protein binding lowers values of PS (in comparison to protein-free perfusate experiments), i.v. data were not used for lipophilic compounds. Compounds that had reported saturable transport were also excluded. Since we were interested to select in situ data as free of efflux effects as practical, we chose our training set PS values from studies which used some sort of transport inhibition (e.g., Pgp-KO, cyclosporine A, PSC833, GF120918, self-inhibition by using high concentrations). Also, simple amino acids and dipeptides were excluded, except for those with reported non-saturable K_d values. In our own data, the L-isomer of p-F-phenylalanine was excluded from the training set, since comparison with the D-isomer clearly indicated that its transport was facilitated. As an added pruning, several compounds were excluded from the training set on the suspicion that carrier-mediated transport was possible, by comparisons of structures to known transport-mediated molecules. Out of the starting set of 507 PS values, a total of 182 “passive” rodent values were selected in our study, including the in situ measurements reported here.

The in combo PAMPA model was trained with a set of 80 compounds: 31 bases, 11 acids, 15 ampholytes, and 23 neutral molecules (encompassing 130 different measured PS values). In addition to the 130-PS training set, an additional 52 molecules (Summerfield et al. 2007; Gratton et al. 1997; Obradovic et al. 2007) were taken to serve as the test set. Table 1 contains physical properties and the Abraham (2004) descriptors of the training and test set molecules.

Table 1.

Physical Properties, Abraham Descriptors, and PAMPA ^a

COMPOUND	MW	logPoct	logDoct	pKa		f	(Q)	α(A)	β(B)	π(S)	R(E)	Vx	logPoPAMPA	SD	Ref
TRAINING SET
1-aminocyclohexanecarboxylic acid	143	−1.6	−1.6	9.1	2.1	1.00	(±)	0.78	0.93	0.98	0.56	1.16	−7.05	b	--
3-hydroxykynurenine	224	−2.6	−2.6	9.9	2.3	0.95	(±)	1.31	1.71	2.19	1.70	1.63	−8.65	b	--
amitriptyline	277	4.9	3.5	9.49		0.96	(+)	0.00	0.77	1.31	1.71	2.40	1.30	0.04	d
antipyrine	188	0.8	0.8			1.00	(0)	0.00	1.28	1.75	1.42	1.48	−5.69	0.03	e
astemizole	459	5.5	3.9	8.60	5.84	0.94	(+)	0.13	1.64	2.70	3.10	3.56	1.00	0.10	f
bremazocine	315	3.4	3.2	10.3	8.5	0.66	(0)	0.73	1.35	1.28	1.82	2.58	−1.49	0.07	c
buspirone	386	2.7	2.2	7.60		0.67	(+)	0.00	2.16	2.18	2.22	3.03	−2.88	0.08	c
carbamazepine	236	2.5	2.5			1.00	(0)	0.39	0.92	2.06	2.12	1.81	−3.73	0.17	c
cetririzine	389	2.6	−0.4	7.9	3.8	0.76	(±)	0.57	1.76	2.24	2.05	2.94	−3.24	b	--
chlorpromazine	319	5.4	3.7	9.24		0.98	(+)	0.00	0.99	1.83	2.26	2.41	1.62	0.08	e,g
cimetidine	252	0.7	0.6	6.93		0.80	(0)	0.74	1.86	1.87	1.66	1.96	−6.20	0.08	h
clozapine	327	3.1	2.6	7.90	4.40	0.71	(+)	0.18	1.44	1.82	2.46	2.43	−0.39	0.09	c
colchicine	399	1.2	1.2			1.00	(0)	0.26	2.08	3.32	2.17	2.99	−5.40	0.01	c
creatinine	113	−1.1	−1.1	9.2	4.8	1.00	(0)	0.39	1.31	1.04	1.04	0.84	−7.52	0.10	c
deltorphin II	783	−0.8	−3.5	10.10	4.27	0.56	(−)	3.30	5.53	8.18	4.06	6.03	−6.37	0.02	c
diazepam	285	2.8	2.8	3.40		1.00	(0)	0.00	1.04	1.72	2.11	2.07	−2.44	0.29	c
digoxin	781	1.4	1.4			1.00	(0)	1.58	4.32	4.46	3.67	5.75	−5.78	0.08	c
diltiazem	415	3.1	2.4	8.02		0.80	(+)	0.00	2.12	2.55	2.42	3.14	−1.33	0.01	h
diphenhydramine	255	3.5	2.2	9.10		0.95	(+)	0.00	0.95	1.43	1.36	2.19	−0.71	0.08	d
domperidone	426	4.2	3.9	8.10		0.51	(+)	0.72	1.83	3.13	3.11	3.06	−2.78	0.11	c
doxepin	279	4.1	2.7	9.5		0.96	(+)	0.00	0.98	1.46	1.75	2.32	0.44	0.08	g
DPDPE	646	−0.9	−3.7	10.1	3.5	0.55	(−)	2.30	4.04	5.81	3.87	4.77	−7.31	0.19	c
estradiol	272	3.1	3.1	10.4		1.00	(0)	0.81	0.95	2.30	1.85	2.20	−3.08	0.02	c
etoposide	589	0.6	0.6	10.0		1.00	(0)	0.60	3.23	4.11	3.38	3.90	−5.22	0.01	c
fentanyl	336	4.0	3.4	8.10		0.76	(+)	0.00	1.33	2.18	1.86	2.84	−0.95	0.07	c
fexofenadine	502	4.8	2.2	7.84	4.3	1.00	(±)	1.20	2.12	2.48	2.72	4.09	−5.17	0.03	c
flurbiprofen	244	3.9	0.7	4.18		1.00	(−)	0.57	0.58	1.51	1.50	1.84	−1.78	0.01	g
gabapentin	185	0.2	0.2	10.6	3.8	1.00	(±)	0.78	0.96	1.02	0.59	1.58	−3.36	0.31	c
galanthamine	287	1.2	−0.1	8.6		0.96	(+)	0.31	1.45	1.92	1.89	2.17	−3.15	0.04	c
glibenclamide	494	4.4	2.1	5.90		0.97	(−)	0.85	2.01	3.84	2.64	3.56	−2.54	0.08	f
grepafloxacin	359	0.2	−2.1	8.5	6.0	0.91	(±)	0.73	1.88	2.43	2.23	2.59	−4.87	b	--
haloperidol	376	3.7	2.7	8.65		0.88	(+)	0.31	1.45	2.08	2.00	2.80	0.05	0.05	d
HSR-903	386	−0.1	−2.2	10.6	6.1	0.86	(±)	0.98	2.24	2.78	2.80	2.72	−5.46	b	--
hydroxyzine	375	3.2	3.1	7.5		0.84	(0)	0.23	1.80	2.01	2.12	2.92	−1.50	0.12	c
ibuprofen	206	3.4	0.4	4.59		1.00	(−)	0.57	0.51	1.01	0.78	1.78	−2.11	0.09	g,i
imatinib	494	3.7	3.3	7.6	4.7	0.61	(+)	0.54	2.63	3.64	3.83	3.85	−1.40	0.30	c
indinavir	614	3.3	3.3	6.2		0.91	(0)	0.98	3.59	4.27	3.63	4.90	−3.57	0.07	c
indomethacin	358	4.4	1.6	4.57		1.00	(−)	0.57	1.24	2.49	2.44	2.53	−1.65	0.25	e, g
lidocaine	234	2.2	1.6	7.95		0.76	(+)	0.26	1.17	1.50	1.10	2.06	−1.42	0.15	d
L-kynurenine	208	−2.2	−2.2	9.9	2.3	0.98	(±)	0.96	1.60	2.06	1.50	1.57	−7.82	b	--
L-leucine	131	−1.8	−1.8	9.1	2.1	1.00	(±)	0.78	0.97	0.92	0.39	1.13	−7.25	b	--
loperamide	477	4.7	3.8	8.5		0.88	(+)	0.31	1.88	2.90	2.76	3.77	0.15	0.06	c
L-phenylalanine	165	−1.4	−1.4	9.23	2.20	0.98	(±)	0.78	1.02	1.39	0.95	1.31	−5.36	0.06	c
L-valine	117	−2.2	−2.2	9.1	2.1	1.00	(±)	0.78	0.97	0.92	0.39	0.99	−7.54	b	--
M6G	461	−1.6	−4.2	8.22	2.77	0.78	(±)	1.64	2.84	2.96	3.10	3.11	−7.66	b	--
maprotiline	277	5.1	2.2	10.4		1.00	(+)	0.13	0.68	1.27	1.76	2.33	1.99	0.06	g
melphalin	305	−0.3	−0.3	9.1	2.1	0.98	(±)	0.78	1.37	1.90	1.43	2.22	−5.87	b	--
meperidine	247	2.6	1.3	8.58		0.94	(+)	0.00	0.97	1.26	0.99	2.05	0.79	0.20	c
methadone	309	3.9	2.6	8.99		0.95	(+)	0.00	1.09	1.72	1.51	2.71	0.08	0.03	c
morphine	285	0.9	0.3	9.46	8.13	0.76	(+)	0.50	1.47	1.59	2.23	2.06	−3.59	0.12	g
naltrindole	414	3.3	2.3	10.0	8.3	0.89	(+)	1.04	1.92	3.16	3.53	2.98	−0.94	0.10	c
naringenin	272	2.5	2.5	10.4	8.9	0.97	(0)	1.30	1.14	2.19	2.23	1.89	−3.71	0.06	c
perphenazine	404	4.2	3.6	7.9		0.75	(+)	0.23	1.84	2.33	2.87	3.02	0.81	0.14	c
p-F-Phe(D)	183	−1.5	−1.5	9.2	2.2	0.98	(±)	0.78	1.02	1.36	0.87	1.33	−6.73	0.09	c
phenytoin	252	2.3	2.3	8.36		0.89	(0)	0.44	1.14	2.04	1.94	1.87	−4.32	0.01	g
prazosin	383	0.9	0.8	7.14		0.80	(0)	0.23	2.17	3.59	2.94	2.74	−2.58	0.03	g
probenecid	285	2.9	−0.7	3.16		1.00	(−)	0.57	1.29	1.92	1.25	2.16	−1.83	0.20	g
propranolol	259	3.0	0.9	9.53		0.99	(+)	0.29	1.36	1.44	1.76	2.15	0.43	0.38	g,h
quercetin	302	1.9	1.3	9.40	6.90	0.74	(−)	1.88	1.63	2.64	2.68	1.96	−4.77	0.22	c
quetiapine	384	2.4	2.4	7.30	2.27	0.99	(0)	0.23	2.01	1.93	2.72	2.91	−1.85	0.02	c
quinidine	324	2.9	1.6	8.55	4.09	0.94	(+)	0.23	1.81	1.71	2.40	2.55	−1.56	0.07	g
quinine	324	2.9	1.6	8.55	4.09	0.94	(+)	0.23	1.81	1.71	2.40	2.55	−1.05	0.08	i
risperidone	410	2.9	2.1	8.2		0.86	(+)	0.00	1.70	2.23	2.59	3.04	−2.01	0.07	c
ritonavir	693	4.9	4.9	4.1		1.00	(0)	0.88	3.11	5.05	3.69	5.27	−1.68	0.18	c
salicylic acid	138	2.4	−1.6	3.02		1.00	(−)	0.70	0.40	1.10	0.91	0.99	−2.64	0.13	i
saquinavir	671	4.0	4.0	6.8		0.86	(0)	1.46	3.89	5.55	4.09	5.30	−3.69	0.07	c
sertraline	306	4.9	2.8	9.5		0.99	(+)	0.13	0.67	1.44	1.83	2.26	2.10	0.09	c
SNC121	452	4.5	3.6	7.7	4.1	0.86	(+)	0.00	2.11	2.47	2.12	3.84	−1.24	0.09	c
sumatriptan	295	1.3	0.0	9.64	8.93	0.95	(+)	0.68	1.61	2.05	1.90	2.27	−4.18	0.09	j
terfenadine	472	5.8	3.5	9.86		1.00	(+)	0.63	1.80	2.04	2.55	4.01	2.63	0.17	g,k
testosterone	288	3.1	3.1			1.00	(0)	0.31	1.01	2.27	1.55	2.38	−2.83	0.01	c
theophylline	180	0.1	0.1	8.70		0.95	(0)	0.35	1.29	1.99	1.46	1.22	−5.99	0.02	d
thioridazine	371	6.2	4.2	8.82		0.99	(+)	0.00	1.13	1.93	2.70	2.90	1.81	0.17	c
tiagabine	376	5.8	3.3	9.0	3.7	0.99	(±)	0.57	1.02	1.60	1.77	2.89	0.32	b	--
tolbutamide	270	2.3	0.1	5.20		0.99	(−)	0.59	1.15	2.21	1.33	2.06	−3.70	0.02	c
U69593	357	3.6	2.4	9.3		0.94	(+)	0.00	1.49	2.07	1.73	2.92	0.37	0.18	c
verapamil	455	4.3	2.9	9.07		0.96	(+)	0.00	1.89	3.00	1.76	3.79	0.26	0.12	g,h
vinblastine	811	4.1	3.8	7.4	6.0	0.50	(0)	0.54	4.01	3.72	4.46	6.07	−0.42	0.05	c
vincristine	825	3.1	2.8	7.4	5.4	0.51	(0)	0.54	4.25	4.30	4.59	6.08	−2.72	0.06	c
warfarin	308	2.9	−0.2	4.97		1.00	(−)	0.31	1.23	2.28	1.98	2.31	−2.59	0.06	g
zidovudine	267	0.0	0.0			0.93	(0)	0.47	1.70	1.77	1.62	1.82	−5.79	0.17	c
TEST SET
amantadine	151	2.4	−0.4	10.5		1.00	(+)	0.21	0.64	0.68	0.84	1.29	−1.12	b	--
amoxapine	314	2.1	1.8	7.6		0.54	(+)	0.16	1.43	1.68	2.25	2.25	−1.89	b	--
atomoxetine	255	3.6	1.5	10.3		0.99	(+)	0.13	0.90	1.36	1.37	2.19	−0.13	b	--
AZ 11003	503	5.0	3.1	8.10		0.99	(+)	0.41	1.95	2.83	1.84	3.92	0.58	b	--
AZ 12002	393	2.7	−0.4	3.20		1.00	(−)	0.57	1.43	2.14	2.28	2.40	−3.14	b	--
AZ 13007	163	2.4	−0.4	10.10		1.00	(+)	0.21	0.73	0.75	1.11	1.32	−1.12	b	--
AZ 22001	216	−0.2	−4.3	5.30		1.00	(−)	0.23	1.17	2.50	1.21	1.41	−4.91	b	--
AZ 26006	637	5.4	3.4	8.91		0.99	(+)	0.43	3.18	3.74	2.79	4.80	0.96	b	--
AZ 95005	251	1.5	1.5			1.00	(0)	0.48	1.33	1.87	1.18	2.08	−4.40	b	--
brompheniramine	319	3.2	1.5	9.2		0.98	(+)	0.00	1.02	1.57	1.70	2.26	−0.37	b	--
bupropion	240	2.9	1.6	8.8		0.95	(+)	0.13	0.94	1.32	1.07	1.94	−0.94	b	--
chlorpheniramine	275	3.1	1.3	9.2		0.98	(+)	0.00	1.02	1.49	1.52	2.21	−0.51	b	--
citalopram	324	3.8	1.9	9.4		0.99	(+)	0.00	1.08	1.87	1.66	2.53	0.16	b	--
clemastine	344	5.6	3.4	9.6		1.00	(+)	0.00	0.97	1.55	1.70	2.76	1.82	b	--
donepezil	379	3.9	2.5	9.2		0.96	(+)	0.00	1.50	2.49	2.12	3.03	0.08	b	--
ergotamine	582	1.7	1.6	6.9		0.81	(0)	0.79	3.69	4.60	4.56	4.21	−4.71	b	--
erythritol	122	−2.2	−2.2			1.00	(0)	1.08	1.20	1.23	0.82	0.91	−8.50	b	--
ethanol	46	−0.2	−0.2			1.00	(0)	0.31	0.31	0.45	0.21	0.45	−5.68	b	--
ethosuximide	141	0.4	0.4	9.3		0.99	(0)	0.34	0.93	0.94	0.74	1.12	−5.23	b	--
ethylene glycol	62	−1.3	−1.3			1.00	(0)	0.54	0.58	0.71	0.41	0.51	−6.91	b	--
fluoxetine	309	4.2	2.0	9.6		0.99	(+)	0.13	0.78	1.19	1.01	2.24	0.35	b	--
fluphenazine	438	4.4	3.8	7.9		0.75	(+)	0.23	1.80	2.00	2.40	3.09	0.05	b	--
isocarboxazid	231	1.7	1.7	2.8		1.00	(0)	0.39	1.38	2.16	1.61	1.74	−4.18	b	--
isopropanol	60	0.3	0.3			1.00	(0)	0.31	0.34	0.43	0.22	0.59	−5.25	b	--
lamotrigine	256	2.4	2.4	5.5		1.00	(0)	0.45	0.93	2.13	2.40	1.65	−3.62	b	--
loratidine	383	5.0	5.0	5.0		1.00	(0)	0.00	1.14	2.09	2.19	2.87	−0.69	b	--
loxapine	328	2.7	2.6	6.7		0.86	(0)	0.00	1.49	1.67	2.30	2.39	−2.70	b	--
mannitol	182	−3.2	−3.2			1.00	(0)	1.62	1.81	1.75	1.23	1.31	−10.09	b	--
meprobamate	218	1.0	1.0			1.00	(0)	0.89	1.12	1.62	0.71	1.73	−5.43	b	--
mesoridazine	387	4.5	2.5	9.4		0.99	(+)	0.00	1.69	2.97	2.87	2.96	0.73	b	--
metoclopramide	300	2.5	0.7	9.2		0.98	(+)	0.50	1.63	2.31	1.50	2.34	−1.75	b	--
midazolam	326	3.0	3.0	6.4		0.96	(0)	0.00	0.80	1.76	2.41	2.26	−2.45	b	--
mirtazapine	265	3.1	2.8	7.5		0.55	(0)	0.00	1.22	1.67	2.08	2.11	−2.32	b	--
olanzapine	312	2.7	2.2	7.8		0.72	(+)	0.13	1.45	1.59	2.30	2.37	−1.30	b	--
pemoline	176	0.2	0.2	1.3		1.00	(0)	0.21	1.22	1.45	1.48	1.26	−5.21	b	--
pergolide	314	5.1	4.3	8.7		0.86	(+)	0.31	1.01	1.48	2.22	2.54	0.61	b	--
phenelzine	136	1.1	0.5	7.9		0.76	(+)	0.34	0.99	1.02	0.98	1.20	−3.00	b	--
pyrilamine	285	3.1	1.6	8.8		0.96	(+)	0.00	1.45	1.73	1.66	2.39	−0.61	b	--
rizatriptan	269	2.4	1.1	8.7		0.95	(+)	0.31	1.28	2.05	2.21	2.14	−1.63	b	--
selegiline	187	2.9	2.6	7.3		0.56	(0)	0.09	0.71	1.00	1.00	1.72	−2.64	b	--
sucrose	342	−3.4	−3.4			1.00	(0)	2.01	3.43	2.63	2.32	2.23	−10.86	b	--
tacrine	198	2.8	0.3	9.9		1.00	(+)	0.23	0.76	1.52	1.88	1.60	−0.91	b	--
temazepam	301	2.1	2.1	1.5		1.00	(0)	0.17	1.34	1.76	2.24	2.13	−3.47	b	--
thiothixene	444	4.1	3.3	8.1		0.83	(+)	0.00	2.19	2.59	2.94	3.36	0.10	b	--
thiourea	76	−1.0	−1.0			1.00	(0)	0.42	0.82	0.97	1.07	0.57	−6.53	b	--
thymine	126	−0.7	−0.7			1.00	(0)	0.44	0.90	1.41	0.88	0.89	−6.27	b	--
trazodone	372	3.5	3.4	7.0		0.81	(0)	0.00	1.92	2.47	2.64	2.73	−2.01	b	--
trifluoperazine	408	5.1	4.3	10.0		0.85	(+)	0.00	1.42	1.79	2.17	2.89	1.02	b	--
urea	60	−1.6	−1.6			1.00	(0)	0.72	0.69	1.17	0.63	0.46	−7.43	b	--
venlafaxine	277	3.3	2.4	8.7		0.90	(+)	0.31	1.16	1.23	1.20	2.37	−0.91	b	--
zaleplon	305	1.8	1.8	1.6		1.00	(0)	0.00	1.42	2.60	2.36	2.31	−3.52	b	--
ziprasidone	413	4.6	4.3	7.7		0.52	(0)	0.48	1.65	2.67	3.38	2.92	−1.65	b	--

^aThe octanol-water partition coefficients, log P_oct, the octanol-water distribution coefficients at pH 7.4, log D_oct, pK_a values in italics, the pH 7.4 fraction, f, of the compound in the charge state Q (indicated in parentheses), and the Abraham descriptors (α, β, π, R, V_x – alternate names in parentheses after the symbol) were calculated using the ADME Boxes V4.9 program (Pharma Algorithms). The non-italic pK_a values were taken from Avdeef 2003, and were adjusted to 0.01 M ionic strength. Ref refers to logP_o^PAMPA source.

^blog P_o^PAMPA calculated by the pCEL-X program (pION).

^cThis work.

^dAvdeef et al. 2006.

^eAvdeef et al. 2004.

^fBendels et al. 2006.

^gRuell et al. 2004.

^hAvdeef et al. 2005.

ⁱRuell et al. 2003.

^jAvdeef 2005.

^kAvdeef et al. 2007.

Linear Free Energy Relations (LFER) Descriptors “Boosting” PAMPA Measured Values

Abraham's linear free energy relations (LFER) applied to a BBB permeability model may be stated as (Abraham 2004)

$$\log {{\mathrm{P}}_{\mathrm{o}}}^{\mathrm{BBB}}\left(\mathrm{LFER}\right)={\mathrm{c}}_{\mathrm{o}}+{\mathrm{c}}_1\mathrm{R}+{\mathrm{c}}_2\pi +{\mathrm{c}}_3\alpha +{\mathrm{c}}_4\beta +{\mathrm{c}}_5{\mathrm{V}}_{\mathrm{x}}$$ (2)

where c₀…c₅ are the multiple linear regression (MLR) coefficients, and where R (dm³ mol⁻¹ / 10; also called E) is the excess molar refraction, which models dispersion force interaction arising from pi- and n-electrons of the solute, π (also called S) is the solute polarity/polarizability due to solute-solvent interactions between bond dipoles and induced dipoles, α (also called A) is the solute H-bond acidity, β (also called B) is the solute H-bond basicity, and V_x is the McGowan molar volume (dm³ mol⁻¹ / 100) of the solute.

Eq. (2) uses intrinsic BBB permeability values, P_o^BBB, rather than PS values. This is because the Abraham molecular descriptors have been developed for uncharged species, and so it was decided to convert all permeability values (PS and PAMPA) to intrinsic values, P_o^BBB and P_o^PAMPA, in order to develop the computational model. This may seem unnecessary, given that the environment of the BBB is very close to pH 7.4. However, the transformation is solely a computational strategy, in order to take full advantage of the Abraham descriptors. After the model was developed, the calculated intrinsic values were converted back to PS scale. In effect, by these transformations, we have adapted the Abraham molecular descriptors for charged molecules.

In addition to the LFER model, we explored how well PAMPA measurements, augmented with one (or two) of Abraham's solvation molecular descriptors, can predict PS_passive values. The combination of measured PAMPA and a calculated LFER descriptor defines the in combo method below. A trial-and-error testing of various combinations of one or two Abraham descriptors and PAMPA was tried, using

$$\log {{\mathrm{P}}_{\mathrm{o}}}^{\mathrm{BBB}}\left(\mathrm{in}\mathrm{combo}\right)={\mathrm{a}}_{\mathrm{o}}+{\mathrm{a}}_1\log {{\mathrm{P}}_{\mathrm{o}}}^{\mathrm{PAMPA}}+(\text{one}∕\text{two Abraham descriptors})$$ (3)

where a₀, a₁… are MLR coefficients. The usefulness of such an approach has been discussed elsewhere (Avdeef et al. 2005). Fewer MLR coefficients are necessary in eq. 3, compared to eq. 2, because P_o^PAMPA already encodes for some of the transport characteristics common to the permeability models.

The best prediction model was validated by testing its ability to predict BBB permeability of compounds not used in the training set.

The Abraham descriptor calculation and the computational model testing used the Algorithm Builder V1.8 and ADME Boxes V4.9 computer programs (Lanevskij et al. 2008; Didziapertris et al. 2003) from Pharma Algorithms (Toronto, Canada). Since the 52-molecule test set and ten of the zwitterionic training set molecules were not available to us for PAMPA measurement, the pCEL-X program (pION) was used to predict the missing PAMPA values.

RESULTS AND DISCUSSION

Pgp-Deficient Mouse Measurements and the Pgp Effect

The brain uptake values (K_in) for the wild type and the Pgp-deficient mouse data, listed in Table 2, were converted to PS values (Table 3).

Table 2.

in situ Brain Perfusion Data in CF-1 Pgp Deficient and Wild Type Mice

COMPOUND	Wild-Type Kin (mL/100g/min)	SD	Pgp Mutant Kin (mL/100g/min)	SD	Pgp Effect	Tperf (s)	Cperf (μM)
amitriptyline	335	44	408	45	1.2	60	1.0
astemizole	112	5	123	20	1.1	120	0.7
buspirone	325	30	341	8	1.0	120	1.1
carbamazepine	173	3	184	10	1.1	120	1.1
chlorpromazine	300	94	295	39	1.0	60	1.0
clozapine	118	44	90	16	0.8	120	0.8
diltiazem	65	14	130	21	2.0	180	1.2
domperidone	3.1	1.0	9.5	2.3	3.1	180	0.9
gabapentin	15	6	26	5	1.7	60	0.08
galanthamine	19	5	20	2	1.1	60	0.9
indinavir	0.52	0.12	2.4	0.5	4.6	180	0.7
p-F-D-phenylalanine	8.4	1.4	8.9	0.3	1.1	120	0.07
p-F-L-phenylalanine	127	16	142	22	1.1	60	0.09
probenecid	0.069	0.060	0.098	0.067	1.4	180	0.9
ritonavir	1.8	0.5	15	1	8.3	180	1.5
saquinavir	2.9	0.4	11	1	3.8	180	1.0
sertraline	205	29	210	58	1.0	60	1.1
terfenadine	126	35	129	26	1.0	120	1.2
tolbutamide	0.91	0.10	1.1	0.2	1.2	180	0.9

Table 3.

Training Set Data

COMPOUND	Rodent	Comment a	logPS(calc) (mL/g/s)	logPS(obs) (mL/g/s)	REF	COMPOUND	Rodent	Comment a	logPS(calc) (mL/g/s)	logPS(obs) (mL/g/s)	REF
1-aminocyclohexanecarboxylic acid	rat	Kd	−3.5	−4.00	c	meperidine	mouse	mdr1a(−/−)	−0.63	−1.28	j
3-hydroxykynurenine	rat	Kd	−4.3	−4.49	d	methadone	mouse	mdr1a(−/−)	−1.47	−1.63	j
amitriptyline	rat	5-50uM	−1.17	−1.05	e	morphine	mouse	mdr1a(−/−)	−3.38	−3.66	r
amitriptyline	mouse	mdr1a(−/−)	−1.17	−0.66	b	morphine	mouse	mdr1a(−/−)	−3.38	−3.67	j
antipyrine	rat		−2.81	−2.00	f	morphine			−3.38	−3.30	s
antipyrine	rat		−2.81	−1.97	g	morphine	mouse	mdr1a(−/−)	−3.38	−3.51	n
antipyrine	rat		−2.81	−2.00	h	morphine	rat	not saturable	−3.38	−4.23	t
antipyrine	rat	CsA	−2.81	−2.34	i	morphine	mouse	mdr1a(−/−)	−3.38	−3.49	o
astemizole	mouse	mdr1a(−/−)	−0.49	−1.55	b	naltrindole	mouse	mdr1a(−/−)	−2.33	−1.98	j
bremazocine	mouse	mdr1a(−/−)	−2.18	−1.89	j
buspirone	mouse	mdr1a(−/−)	−2.05	−0.94	b	naringenin	rat	PSC833,GF120918	−1.67	−2.60	u
carbamazepine	rat	5-50uM	−1.69	−1.75	e	perphenazine	rat	5-50uM	−0.50	−1.27	e
carbamazepine	mouse	mdr1a(−/−)	−1.69	−1.26	b	p-F-Phe(D)	mouse	mdr1a(−/−)	−3.37	−2.82	b
cetririzine	rat	CsA	−3.1	−3.72	i	phenytoin			−2.12	−2.30	s
chlorpromazine	rat	5-50uM	−0.80	−1.20	e	phenytoin	rat		−2.14	−2.20	h
chlorpromazine	mouse	mdr1a(−/−)	−0.80	−1.08	b	Phenytoin	rat	5-50uM	−2.14	−2.07	e
cimetidine	mouse		−3.42	−4.10	k	prazosin	mouse	30uM	−2.38	−2.55	v
cimetidine	rat		−3.42	−4.05	k	probenecid	mouse	mdr1a(−/−)	−3.87	−4.79	b
clozapine	rat	5-50uM	−1.02	−1.29	e	propranolol	rat		−2.15	−1.15	f
clozapine	mouse	mdr1a(−/−)	−1.02	−1.73	b	propranolol			−2.15	−1.95	s
colchicine	rat	PSC833	−3.24	−3.24	l	propranolol	rat		−2.15	−1.20	h
colchicine	mouse	mdr1a(−/−)	−3.24	−3.12	m	quercetin	rat	PSC833,GF120918	−2.45	−3.50	u
colchicine	mouse	PSC833	−3.24	−3.06	n	quetiapine	rat	5-50uM	−1.87	−1.33	e
colchicine	mouse	mdr1a(−/−)	−3.24	−3.14	o	quinidine	mouse	mdr1a(−/−)	−2.40	−2.13	r
creatinine	rat	i.v.	−3.49	−4.55	p	quinidine	rat	GF120918	−2.40	−2.66	w
creatinine	rat	i.v.	−3.49	−4.70	p	quinine	mouse		−2.11	−2.59	k
deltorphin II	mouse	mdr1a(−/−)	−4.60	−4.36	j	quinine	rat		−2.11	−2.63	k
diazepam	mouse	mdr1a(−/−)	−1.35	−1.19	q	risperidone	rat	5-50uM	−2.10	−1.81	e
diazepam	rat	5-50uM	−1.35	−1.37	e	ritonavir	mouse	mdr1a(−/−)	−2.41	−2.59	b
digoxin	mouse		−4.79	−4.48	k	salicylic acid	rat		−4.18	−3.40	h
digoxin	rat		−4.79	−4.30	h	saquinavir	mouse	mdr1a(−/−)	−3.76	−2.73	b
digoxin	rat		−4.79	−4.14	k	sertraline	rat	5-50uM	−0.81	−0.71	e
diltiazem	mouse	mdr1a(−/−)	−1.68	−1.52	b	sertraline	mouse	mdr1a(−/−)	−0.81	−1.13	b
diphenhydramine	rat	CsA	−1.98	−1.21	i	SNC121	mouse	mdr1a(−/−)	−1.39	−1.44	j
domperidone	mouse	mdr1a(−/−)	−3.16	−2.79	b	sumatriptan	rat	5-50uM	−4.40	−4.60	e
doxepin	rat	5-50uM	−1.04	−1.31	e	terfenadine	rat	CsA	−1.66	−1.39	i
DPDPE	mouse	mdr1a(−/−)	−4.09	−3.97	j	terfenadine	mouse	mdr1a(−/−)	−1.66	−1.52	b
DPDPE	rat		−4.09	−3.60	h	testosterone	rat		−1.41	−1.10	h
estradiol	rat		−1.37	−0.83	f	theophylline	mouse		−2.89	−3.26	k
etoposide	mouse	mdr1a(−/−)	−3.96	−3.91	x	theophylline	rat		−2.89	−2.90	h
fentanyl	mouse	mdr1a(−/−)	−1.30	−1.02	j	theophylline	rat		−2.89	−2.81	k
fexofenadine	rat	CsA	−3.78	−4.08	i	thioridazine	rat	5-50uM	−0.89	−1.37	e
flurbiprofen	rat	not saturable	−2.59	−1.80	y	tiagabine	rat	5-50uM	−2.2	−2.46	e
gabapentin	rat	5-50uM	−3.45	−2.56	e	tolbutamide	mouse	saturable	−2.72	−2.60	k
gabapentin	mouse	mdr1a(−/−)	−3.45	−2.34	b	tolbutamide	mouse	mdr1a(−/−)	−2.72	−3.74	b
galanthamine	mouse	mdr1a(−/−)	−3.32	−2.46	b	tolbutamide	rat	saturable	−2.72	−2.84	k
glibenclamide	mouse		−2.56	−3.27	k	U69593	mouse	mdr1a(−/−)	−1.72	−2.01	j
glibenclamide	rat		−2.56	−2.77	k	verapamil	mouse	mdr1a(−/−)	−1.67	−1.33	r
grepafloxacin	rat	2 mM	−3.3	−2.91	z	verapamil	mouse	mdr1a(−/−)	−1.67	−1.42	m
haloperidol	rat	5-50uM	−1.50	−1.46	e	vinblastine	mouse		−2.96	−3.32	k
HSR-903	rat	20 mM	−3.7	−3.14	aa	vinblastine	rat	PSC833	−2.96	−3.36	l
hydroxyzine	rat	CsA	−1.86	−1.41	i	vinblastine	mouse	mdr1a(−/−)+GF120918	−2.96	−3.12	n
ibuprofen	rat	Kd	−2.32	−2.03	y	vinblastine	rat		−2.96	−3.27	ff
imatinib	mouse	mdr1a(−/−)	−2.07	−2.11	bb	vinblastine	mouse	GF120918	−2.96	−3.25	v
indinavir	mouse	mdr1a(−/−)	−3.52	−3.40	b	vinblastine	mouse	mdr1a(−/−)	−2.96	−3.31	o
indomethacin	rat	not saturable	−2.36	−2.19	y	vinblastine	rat		−2.96	−3.49	k
lidocaine	rat		−1.64	−1.90	cc	vincristine	mouse		−4.04	−4.12	k
L-kynurenine	rat	Kd	−3.9	−4.16	dd	vincristine			−4.04	−4.00	s
L-leucine	rat	Kd	−3.7	−4.08	ee	vincristine	mouse	mdr1a(−/−)	−4.04	−3.82	n
loperamide	mouse	mdr1a(−/−)	−1.48	−1.66	j	vincristine	mouse	mrp1(−/−)	−4.04	−4.25	x
L-phenylalanine	rat	Kd	−3.32	−3.74	dd	vincristine	rat		−4.04	−3.91	ff
L-valine	rat	Kd	−3.7	−4.41	ee	vincristine	rat		−4.04	−4.10	k
M6G	mouse	mdr1a(−/−) /glucose	−5.2	−5.17	gg	warfarin	mouse	saturable	−2.29	−2.10	k
maprotiline	rat	5-50uM	−2.28	−1.37	e	warfarin	rat	saturable	−2.29	−1.99	k
melphalin	rat	Kd	−3.3	−3.28	hh	zidovudine	rat	i.v.	−3.07	−3.99	ii

^aK_d indicates that the PS value was the nonsaturable component taken from a Michaelis-Menten analysis; mdr1a(−/−) are Pgp-deficient (knockout) mouse data; CsA, PSC833,GF120918 indicate that efflux was inhibited by cyclosporin A, valspodar, and elacridar, respectively; 5-50 μM, 2 mM, 20 mM indicate self-inhibition suppression of transporter effects; i.v. indicates intravenous injection method, for compounds not likely to be strongly bound to serum proteins, and thought to be weak substrates for transporters.

^bThis work.

^cAoyagi et al. 1988.

^dFukui et al. 1991.

^eSummerfield et al. 2007 (please note that the original publication has an error in Table 1 in situ units: cm/min are correct, not cm/s - Summerfield S., private correspondence).

^fGratton et al. 1997.

^gTakasato et al.1984.

^hLiu et al. 2004.

ⁱObradovic et al. 2007.

^jDagenais et al. 2004.

^kMurakami et al. 2000.

^lCisternino et al. 2003.

^mDagenais 2000.

ⁿCisternino et al. 2001.

^oCisternino et al. 2004.

^pLevin 1980.

^qDagenais et al. 2000.

^rDagenais et al. 2001.

^sFernstermacher 1989.

^tBickel et al. 1996.

^uYoudim et al. 2004.

^vCisternino et al. 2004.

^wChen et al. 2002.

^xCisternino et al. 2003.

^yParepally et al. 2006.

^zTamai et al. 2000.

^aaMurata et al. 1999.

^bbBihorel et al. 2007.

^ccPardridge et al. 1990.

^ddMomma et al. 1987.

^eeSmith et al. 1986.

^ffGreig et al. 1990.

^ggBourasset et al. 2003.

^hhGreig et al. 1987.

ⁱⁱWu et al. 1998.

The PS parameter is an indicator of early access into the CNS. The short time over which the measurement is performed minimizes egress from brain to blood. As such, this parameter is independent from, and cannot predict the extent of brain distribution at steady-state, even if there is some overlap in the properties that impart high affinity for brain tissue and high passive BBB permeability. Two additional considerations further support this statement. First, the upper limit of the observed BBB permeability in vivo is cerebral blood flow. Therefore, compounds may have a similarly high permeability, but very different affinity for brain tissue, as illustrated by the lipophilic amine sertraline which has a very high brain volume of distribution, in comparison to the neutral compound diazepam (low to intermediate). Second, apparent permeability is the net result of passive and when applicable, carrier-mediated transport components, as indicated in Table 2. Hence a Pgp substrate may have low apparent permeability, but high affinity for brain tissue, which would obscure any underlying correlation that may have existed with respect to passive permeability.

The Pgp effect (Table 2) is an index of the magnitude of efflux under initial uptake conditions. It has been suggested than under initial brain uptake conditions and in the absence of plasma protein binding, the Pgp effect is an underestimate of the steady-state situation (Dagenais et al. 2001). Moreover, deriving the Pgp effect from the nonlinear PS value scale (in contrast to K_in) would yield much higher ratios for compounds that go from low or intermediate extraction to high extraction when efflux is removed, so it should be used to rank compounds based on their efflux potential, not in absolute terms. The compounds represented a wide range of Pgp effects ranging from no interaction (ratio of 1) to a 14-fold difference (based on K_in values), with K_in values spanning four log orders of magnitude.

PAMPA Measurements

Table 1 lists the PAMPA intrinsic permeability values. The values for doxorubicin and gabapentin are poorly determined, as indicated by the standard deviations (SD). This was due to the low UV absorbance of the molecules. Figure 1 shows the PAMPA log P_e as a function of pH for twelve of the studied molecules. Morphine, naltrindole, and bremazocine are ampholytes, and are characterized by parabolic-shaped profiles. The bases in Figure 1 are characterized by an ascending hyperbolic curves with increasing pH.

Fig. 1.

The log permeability vs. pH plots of twelve of the 42 molecules measured by the PAMPA method. The pH was varied to assess the contribution of the aqueous boundary layer. The best-fits of eq. 1 to the measured effective permeability data are represented by the solid curves, and the ABL-corrected log P_m - pH curves are represented by dashed curves. The dotted lines correspond to the log P_ABL values, derived from the refinement model based on eq. 1. The maximum point in the log P_m curves corresponds to the intrinsic permeability coefficient, log P_o, which characterizes the transport of the neutral form of an ionizable molecule. The intersections of the horizontal and the diagonal tangents occur at pH values corresponding to the pK_a in the dashed curves and pK_a^flux in the solid curves.

The best-fits of eq. 1 to the data are represented by the solid curves, and the derived lipid membrane-based log P_m - pH curves are represented by dashed curves. The horizontal dotted lines correspond to the log P_ABL values, resulting from the regression analysis based on eq. 1. The maximum point in the log P_m curves corresponds to the intrinsic permeability coefficient, log P_o.

in combo PAMPA Method Throughput

The PAMPA method described here may appear to be low-to-medium throughput, since for most of the compounds, permeability was determined in 3-12 different pH buffers (cf., Fig. 1). This was done to reconcile the substantial difference between the aqueous boundary layer thickness in PAMPA (1500-4000 μm in unstirred plates) and in the in situ assay (< 1 μm). Some pharmaceutical companies perform PAMPA measurements in duplicate at one pH in high-throughput assays (often without stirring). To match such a throughput, it can be proposed here that PAMPA be done at two pH values as singletons with the pH values selected to straddle the pK_a^flux value, as described by Ruell et al. 2003. This would be sufficient to correct the data for the effects of the aqueous boundary layer, to better match the in situ conditions. Furthermore, if vigorous stirring were used for lipophilic compounds during the assay, the method could have up to 100-fold increase in the dynamic range of the effective permeability, with a concomitant decrease in the permeation time. Such a proposed procedure would have nearly the same workload as the commonly used high-throughput protocol, and thus could be considered high throughput. (Given that PAMPA values themselves can be predicted (e.g., pCEL-X), our proposed PS_passive prediction model can be done entirely as a very fast in silico method, perhaps suitable for ranking molecules in virtual compound libraries.)

Abraham LFER and in combo PAMPA Models

Comparisons of log P_o^BBB and log P_o^PAMPA were explored according to eq. 3, using various combinations of “booster” LFER descriptors. Combinations of log P_o^PAMPA and the H-bond Abraham descriptors produced the lowest r² values. Using both α and β descriptors, the best-model multiple linear regression coefficients resulting from the search produced r² = 0.80 and s = 0.79 (Table 5). By comparison, the five-descriptor Abraham model yielded r² = 0.69 and s = 0.99 (Table 5). Inspection of the residuals suggested that the acid compounds appeared to have higher than expected passive permeability, compared to the other compounds in the training set. This may be due to the anisotropic properties of the biological membranes, consisting of various bilayer-forming amphiphilic lipids and membrane-anchored proteins. The distribution of the lipids and proteins is complex and uneven in the BBB membranes. It may be that acids, bases, neutral molecules, and zwitterions undergo passive diffusion that can best be described by different mixes of physical property descriptors. To test this hypothesis, the 130-PS training set was then partitioned into four groups: acids, bases, neutrals, and zwitterions.

Table 5.

Passive BBB Permeability in combo Model ^a

Data Partitioning	a0	a1	a2	a3	r2	s	F	n
neutral	−1.60	0.40	+0.21	−0.75	0.78	0.51	55	50
cations(bases)	−1.59	0.57	−0.93	−0.29	0.86	0.52	90	47
anions(acids)	−0.02	0.50	−0.48	−0.33	0.90	0.66	37	17
zwitterions	−3.52	0.21	−0.69	−0.17	0.66	0.54	8	16

^alog P_o^BBB (in combo) = a₀ + a₁ log P_o^PAMPA + a₂ α + a₃ β. The linear correlation coefficient is r²; s = standard deviation; F = “F” statistic; n = number of training set compounds in the group. Data partitioning is determined on the basis of predominant charge at pH 7.4 (cf., Table 1). When all compounds are combined in one set, the calculated result is log P_o^BBB (in combo) = −1.20 + 0.50 log P_o^PAMPA +0.365 α −0.76 β: r² = 0.80, s = 0.79, F = 167. The Abraham model produces log P_o^BBB (LFER) = −3.66 −0.53 α −3.23 β +0.50 π +0.15 R +1.69 V_x: r² = 0.69, s = 0.99, F = 55.

The partitioned-set regression analyses led to an improved overall model, and the individual set parameters are listed in Table 5. The anions and cations had the highest correlation coefficients, 0.90 and 0.86, respectively. For the zwitterions, the 0.21 coefficient for the log P_o^PAMPA term was considerably lower than those of the other three groupings. Also, the contribution due to H-bond donor strength (α) varied extensively across the four types of charge groups, with neutral compounds appearing to have enhanced BBB permeability with increased H-bond donor strength, contrary to expectations. The zwitterion set had the poorest r² of the four groups. Abraham et al. (1997) noted that the LFER descriptors were not ideally suited for these charged species. Also, the log P_o^PAMPA descriptors for many of the zwitterions were calculated using pCEL-X (whereas those of the other training-set molecules were measured), and thus are less accurate. After the in combo model was developed, the calculated results were transformed back to the PS scale.

Figure 2a is a plot of observed and calculated intrinsic permeability coefficients, using the charge-partitioned models in Table 5. The combined statistics indicate r² = 0.92 and s = 0.51. Figure 2b is the plot of the observed log PS as a function of the calculated values (filled circles). The transformed PS values indicated r² = 0.80 and s = 0.51.

Fig. 2.

Prediction of the Pgp deficient mouse brain perfusion log PS values of the 130 measurements training set (filled circles; Table 3) and the 52 compound test set (yellow squares; Table 4: data of Summerfield et al. 2007, Gratton et al. 1997, and Obradovic et al. 2007) with the in combo PAMPA model (Table 5). In the training set, red symbols correspond to acids (negative charged at pH 7.4), blue symbols to bases (positively charged at pH 7.4), orange to zwitterions and green to uncharged drugs. The upper frame (a) is the prediction based on the intrinsic permeability values, and the lower frame (b) has the predicted values converted back to the PS scale.

External Test Set Validation

Figure 2 (yellow squares) shows the relationship between the in combo model predicted and observed test set permeability values (Summerfield et al. 2007; Gratton et al. 1997; Obradovic et al. 2007) from Table 4. For the charge-partitioned prediction, r² = 0.59, and s = 0.67 in the PS form (Fig. 2b), and r² = 0.82 in the intrinsic permeability form (Fig. 2a). This may be considered an adequate validation of the in combo training set. The largest test-set residuals were seen with AZ13007, pemoline, and lamotrigine.

Table 4.

Test Set Data

COMPOUND	Rodent	Comment a	logPS(calc) (mL/g/s)	logPS(obs) (mL/g/s)	Ref	COMPOUND	Rodent	Comment a	logPS(calc) (mL/g/s)	logPS(obs) (mL/g/s)	Ref
amantadine	rat	5-50uM	−3.73	−2.71	b	loxapine	rat	5-50uM	−1.32	−1.45	b
amoxapine	rat	5-50uM	−1.37	−1.18	b	mannitol	rat		−4.19	−5.01	c
atomoxetine	rat	5-50uM	−2.60	−1.39	b	meprobamate	rat	5-50uM	−2.35	−3.09	b
AZ 11003	rat		−0.99	−1.53	c	mesoridazine	rat	5-50uM	−1.71	−1.81	b
AZ 12002	rat		−3.82	−3.49	c	metoclopramide	rat	5-50uM	−3.44	−2.67	b
AZ 13007	rat		−3.53	−1.57	c	midazolam	rat	5-50uM	−0.40	−1.17	b
AZ 22001	rat		−3.35	−2.92	c	mirtazapine	rat	5-50uM	−1.49	−1.39	b
AZ 26006	rat		−3.20	−3.31	c	olanzapine	rat	5-50uM	−0.85	−1.29	b
AZ 95005	rat		−2.34	−2.61	c	pemoline	rat	5-50uM	−1.76	−3.45	b
brompheniramine	rat	CsA	−1.88	−1.38	d	pergolide	rat	5-50uM	−1.80	−1.00	b
bupropion	rat	5-50uM	−1.82	−1.52	b	phenelzine	rat	5-50uM	−2.63	−2.67	b
chlorpheniramine	rat	CsA	−1.98	−1.65	d	pyrilamine	rat	CsA	−1.88	−1.47	d
citalopram	rat	5-50uM	−2.27	−1.99	b	rizatriptan	rat	5-50uM	−3.03	−3.76	b
clemastine	rat	CsA	−1.17	−1.16	d	selegiline	rat	5-50uM	−1.00	−1.39	b
donepezil	rat	5-50uM	−1.89	−1.50	b	sucrose	rat		−5.71	−5.30	c
ergotamine	rat	5-50uM	−1.44	−2.06	b	tacrine	rat	5-50uM	−2.99	−2.02	b
erythritol	rat		−3.47	−4.57	c	temazepam	rat	5-50uM	−1.42	−1.37	b
ethanol	rat		−1.90	−1.52	c	thiothixene	rat	5-50uM	−1.29	−1.15	b
ethosuximide	rat	5-50uM	−2.39	−2.47	b	thiourea	rat		−2.69	−3.36	c
ethylene glycol	rat		−2.58	−2.99	c	thymine	rat		−2.57	−1.93	c
fluoxetine	rat	5-50uM	−1.65	−1.18	b	trazodone	rat	5-50uM	−1.20	−1.47	b
fluphenazine	rat	5-50uM	−1.09	−1.87	b	trifluoperazine	rat	5-50uM	−1.90	−1.88	b
isocarboxazid	rat	5-50uM	−1.78	−1.24	b	urea	rat		−2.75	−3.79	c
isopropanol	rat		−1.83	−1.66	c	venlafaxine	rat	5-50uM	−2.34	−1.98	b
lamotrigine	rat	5-50uM	−1.12	−2.67	b	zaleplon	rat	5-50uM	−1.77	−2.25	b
loratidine	rat	CsA	−0.42	−1.49	d	ziprasidone	rat	5-50uM	−1.48	−1.73	b

^aCsA indicates that Pgp efflux was inhibited by cyclosporin A; 5-50 μM indicates self-inhibition suppression of transporter effects.

^bSummerfield et al. 2007.

^cGratton et al. 1997.

^dObradovic et al. 2007.

Rank Order Model

Figure 3 shows a rank-ordered comparison of predicted and observed in situ PS values, using a “low,” “intermediate,” and “high” designations. The classification boundaries were selected by inspection, and in the figure, the PS range (in 10⁻⁴ mL/g/s units) 0 to 20 defines the low class; the high class is defined by PS above 70 for the predicted set and above 150 for the observed set. The intermediate class is the zone between the high and low boundaries.

Fig. 3.

Rank order comparison of in combo PAMPA predicted PS values and various measured in vivo PS values. The vertical axis cut-off values are 20 and 150; the horizontal axis cut-offs are 20 and 70.

For the training set (Table 3), there were three false negatives (galanthamine, buspirone, and terfenadine) and four false positives (vinblastine, gabapentin, naltrindole, and ritonavir). This corresponds to about 18% misclassification. The origin of these discrepancies is unclear. The rest of the training set compounds (82%) were correctly classified: 37% as high, 11% as intermediate, and 34% as low.

Also included in the figure are some of the test-set molecules, indicated by italic text. These were similarly distributed as those of the training set.

The underlined compounds in Figure 3 were those of the training set, where both the wild-type (not used in model training) and the Pgp-deficient results were predicted in the same class. Largely, these are compounds that do not appear to be substrates of Pgp in the in situ method.

The seven compounds designated with an asterisk in Figure 3 are based on wild-type PS values (not used in the training), and reveal a down-step in classification. The corresponding values of the Pgp effect ratios (Table 2) are: quinidine 14.2, ritonavir 8.3, loperamide 10.4, verapamil 6.4, diltiazem 2.0, SNC121 8.6, and methadone 2.6.

Influence of Non-Pgp Transport Systems

Despite the fact that some training set compounds are known substrates of putative transport systems in the BBB, the model performs relatively well. Even if there is a non-Pgp efflux, or active or facilitated uptake process, the molecular properties of the compounds (and apparent permeability values) span a much broader range than the efflux ratios at the BBB. For this reason DPDPE, probenecid, gabapentin, tolbutamide, and M6G were not excluded, even though these are known to be substrates of transport systems (Deguchi et al.1997; Sun et al. 2001; Takanaga et al. 1998; Luer et al. 1999; Uchino et al. 2002; Su et al. 1995; Ohtsuki and Terasaki 2007). DPDPE was shown to be substrate of a saturable uptake system (Dagenais et al. 2002). Passive diffusion of DPDPE is negligible without this transport system. The estimated transport parameters, along with the highest concentration tested, 150 μM, suggest a K_in of 0.0862 mL/100g/min for DPDPE, which may be reasonable to use, in place of the higher value in Table 2. Probenecid is an organic anion efflux substrate and inhibitor (Deguchi et al. 1997; Sun et al. 2001). Since gabapentin is a substrate of the large neutral amino acid transporter (LNAAT; system L), the K_in value in Table 2 probably overestimates passive permeability. This is nicely illustrated by the difference in BBB permeability between p-F-L- and p-F-D-phenylalanine in Table 2; due to its enantiomeric form, only the former is a recognized substrate of the LNAAT. Tolbutamide appears to be a non-Pgp efflux substrate (Takanaga et al. 1998). M6G appears to have an uptake transporter (Bourasset et al. 2003). Quantitatively, how transporters affect the blood-brain transport of these compounds in relation to intrinsic BBB permeability should be further explored as more in vivo data become available.

Two Possible Uses of the Predicted PS_passive Values

It's clear that there is a cost and speed advantage in using in combo PAMPA to predict BBB permeability, compared to in vitro, in situ or in vivo methods. Since PAMPA can only address the passive permeability component in the overall transport process, it's best to use it for virtual screening of large sets of compounds, or in a supportive role. For example, when an in vivo, in situ, or in vitro permeability measurement is made, it may be difficult to be certain to what extent the result represents a passive, a carrier-mediated, or an active influx/efflux process. Combining the PAMPA-predicted permeability with the more biomimetic measured values can sometimes shed light on the contributions of several components of transport, as illustrated previously (Bermejo et al. 2004; Avdeef et al. 2005). The two examples below illustrate the use of PS_passive determined by the in combo PAMPA, in the first case to indicate transporter effects (influx and efflux), and in the second case to indicate BPC classification using different parameters from those used by Kavlass et al. (2007)

Possible Recognition of Active Transport

Compounds that are Pgp specific (Pgp effect > 1.5 in Table 2) will have attenuated brain uptake. Their predicted PS_passive will exceed the measured PS value, as illustrated by the asterisked compounds in the ranking scheme in Figure 3. Figure 4 shows a quantitative plot of the Pgp effect with the down-pointing (blue) triangle symbols. For this set of compounds, the vertical axis represents the measured PS values (WT), whereas the horizontal scale represents the PS_passive values calculated by the in combo PAMPA model, drawing on training set of measurements performed with KO mice or rodents where some inhibition of transport was implemented. The further the down-triangle symbols are displaced from the solid diagonal line, the more the compound indicates a Pgp effect. The dashed diagonal lines represent a threefold difference, where compounds falling below the threshold line show a significant Pgp effect.

Fig. 4.

Comparison of active vs. passive permeability. For the down-pointing (blue) triangle symbols, the vertical axis represents the measured PS values (WT), whereas the horizontal scale represents the PS_passive values calculated by the in combo PAMPA model. The dashed diagonal lines represent a three-fold difference, where compounds falling below the threshold line show a significant Pgp effect. Compounds that may be uptaken by some carrier-mediated (CM) process in in situ brain perfusion measurements are indicated as upward displacements by upward-pointing (red) triangles. For the CM set, the calculated PS_passive underestimates the observed permeability values.

Compounds that are actively uptaken in in situ brain perfusion measurements are indicated as upward displacements by upward-pointing (red) triangles in Figure 4. The calculated PS_passive underestimates the observed permeability values. Most of the examples are amino acids. But there are some other examples, e.g., doxorubicin, daunomycin, and mitoxanthrone. These compounds have been extensively studied in terms of efflux specificity, but very little has been reported regarding their being influx transported by a facilitated process.

Brain Penetration Classification (BPC) Model Enhancement

The BPC scheme described by Kalvass et al. (2007) assesses the role of Pgp and other putative processes in “impairing” (or compensating) brain penetration. Their scheme was presented in terms of a plot of the Pgp efflux ratio (ER), defined as the ratio of K_p between KO and WT mice, versus the ratio of the unbound drug concentrations in plasma and brain tissue (the inverse of K_p,uu^{in vitro}). The horizontal and vertical lines indicate an efflux ratio of 3, and ratio of unbound plasma-to-brain concentrations of 3, respectively. The different quadrants delineate various CNS penetration characteristics: 1) impaired by Pgp and/or other active process(es); 2) impaired by non-P-gp mechanism; 3) no impairment; and 4) Pgp, but no impairment due to compensatory mechanism.

Their BPC plot for 34 compounds is reproduced in Figure 5, but with two additional parameters, PS_passive (determined by in combo PAMPA) and t_1/2,eq (calculated from PS_passive and f_u,brain using the method and data from Liu et al. 2005) superposed on the compound symbols: (a) the size of the symbols is proportional to log PS_passive; (b) the values of log t_1/2,eq are proportionally represented by the “cross” symbol, with the largest cross symbol representing 624 min (ivermectin) and the smallest cross symbol representing 2 min (meperidine). We acknowledge that PS_passive is an overestimate of the true in vivo permeability for efflux substrates, which at first consideration appears to bias the estimate of t_1/2,eq by shortening it. However, while a decrease in BBB permeability due to Pgp efflux may be expected intuitively to result in lengthening of t_1/2,eq modeling of blood-brain transport in this specific case suggests that the effect would be more or less reversed depending on the magnitude of the increase in blood-to-brain egress (Syvänen et al. 2006). Although the relative balance between these two parameters is unknown for the Pgp substrates in Figure 5, we still considered the exercise conceptually useful, especially to qualify Class 3 compounds.

Fig. 5.

The BPC scheme of Kalvass et al. 2007 with two additional parameters, PS_passive (this study) and t_1/2,eq (Liu et al. 2005), superposed on the compound symbols: (a) the size of the symbols is proportional to log PS_passive; (b) the values of log t_1/2,eq are proportionally represented by the dimensions of the “cross” symbol.

In the BPC plot in Figure 5, Classes 3 and 4 on the left side are characterized by unbound drug concentration in the brain of about 30% or more that in the blood. These two classes may be designated “CNS+”. Conversely, the other classes on the right side of the plot can be designated “CNS−“ for the purpose of the present discussion. Di et al. (2003) were able to differentiate CNS+ from CNS− groups using PAMPA. In the present study, PS_passive was used to define class boundaries in the BPC scheme in Figure 5.

Inspection of Figure 5 indicates that the most intrinsically permeable compounds are associated with BPC Class 3 (no impairment to brain penetration). However, intermediate to high PS_passive values also are associated with Class 1 (Pgp impaired penetration), simply reflecting that PS_passive is not a predictor of Pgp efflux ratio. However, it should be noted that for compounds that can bind to Pgp, the residence time in the cell membrane (a direct function of PS_passive) must be sufficient for an interaction to occur and result in significant efflux. For instance, although some high permeability compounds may display affinity for Pgp and act as inhibitors, they display little or no apparent efflux due to passive escape. The three-fold off-diagonal (outside of the dashed-line boundary in Fig. 5) compounds generally have very low PS_passive, suggesting it is also a contributor to poor CNS penetration. Evidently PS_passive alone cannot differentiate impaired from non-impaired compounds in the BPC scheme. The average values of PS_passive, f_u,brain and t_1/2,eq (a combination of the first 2 parameters) for the 34 compounds in Figure 5 were compiled for each of the BPC groups, along with the 68% probability ranges, and are listed in Table 6. Conceptually, t_1/2,eq is shortest when both permeability and free fraction in brain are high. As mentioned above, there is some overlap in the molecular properties that govern the latter two parameters, but that can be obscured by active efflux or uptake. There cannot be permeability if the compound is unable to partition in cell membranes, which is to a large extent analogous to partitioning in brain tissue. The optimal CNS candidate has good permeability, moderate affinity for brain tissue and no efflux, which appears to be the hallmark of Class 3 compounds. One notes that Class 1 (impaired) and Class 3 (unimpaired) have large differences in the average PS_passive (68 vs. 430, 10⁻⁴ mL/g/s units), perhaps suggesting that these compounds have a slightly longer residence time in the luminal cell membrane that maximizes interactions with Pgp as discussed above. From the PS parameter ranges, 170 appears to be a good boundary value to differentiate the two classes. Another important difference between the two classes is the value of brain tissue binding. This binding in Class 1 compounds is notably greater (average f_u,brain = 6%) than those in Class 3 (average f_u,brain = 19%), but the two ranges overlap significantly. Perhaps these two measured quantities could be used in drug discovery in the following way: a compound is very likely not to be brain penetration impaired (Class 3) if PS_passive > 170 × 10⁻⁴ mL/g/s and f_u,brain > 16%. Class 4 (unimpaired due to compensation mechanisms) and Class 3 (unimpaired) both have high PS_passive, with considerable overlap in permeability values. However, the average values of f_u,brain for the two classes are quite different. In such a comparison, a test compound is more likely to be Class 4 than Class 3 if f_u,brain < 3.4% and PS_passive < 180 × 10⁻⁴ mL/g/s. Classes 2 and 1b are characterized by low values of PS_passive, again suggesting that this parameter contributes at least in part to poor brain penetration. However, the values of f_u,brain are dramatically different in the two classes (Table 5).

Table 6.

Brain Penetration Classification (BPC) and the Rate of Penetration ^a

BPC Class	PS (mL/g/s)		fu,br * 100%		t1/2,eq (min)		BBB Penetration
1	68	(2 - 160)	6	(0.05 - 16)	70	(8 - 170)	impaired by Pgp
1b	6	(0.5 - 16)	2	(0.01 - 6)	340	(110 - 570)	impaired by Pgp + other
2	5	(0.1 - 15)	39	(10 - 68)	58	(5 - 110)	impaired by non-Pgp
3	430	(180 - 690)	19	(0.2 - 41)	10	(2 - 24)	not impaired
4	200	(12 - 500)	2	(0.4 - 3.4)	58	(12 - 500)	not impaired – compensating mechanism

^aThe four classes in the extent of brain penetration, according to Kalvass et al. 2007. Listed for each of the three properties are the mean values and the 68%-probability range, based on the 34-compoud set from Kalvass et al. 2007.

Although the overall number of compounds used to create the BPC probably has to be increased in order to confirm the rules we suggest, the empirical observations above may be useful in drug discovery applications, since PS_passive (PAMPA) and f_u,brain (brain homogenate dialysis) can be measured at high-throughput speeds at a relatively low cost.

CONCLUSION

There exist multiple and complementary methodologies to study BBB transport and distribution in various brain compartments. The ability to cross the BBB at a sufficiently high rate (i.e., permeability) to avoid excessive blood-brain equilibration delays, unhindered by efflux processes, is a pre-requisite for CNS active compounds to distribute to brain, and exert their pharmacological action while maximizing peripheral safety margins. We used a mouse brain perfusion technique to estimate the BBB permeability of drugs and drug-like compounds with a wide range of molecular properties, and enhanced this dataset with published rodent values. We have demonstrated that the in combo PAMPA method, trained with 130 in situ P-glycoprotein deficient/inhibited rodent brain perfusion data, was able to predict 82% of the variance in the intrinsic BBB permeability of 52 external test compounds, whose permeability values were not used in the original training. Our investigation, based on 182 rodent brain perfusion results, is one of the largest PS-based published study to date used to develop a BBB permeability prediction model. The passive permeability predictions allowed us to further qualify and understand the brain penetration classification suggested by other investigators. Based on correlation plots (Fig. 2), the rank order comparisons (Fig. 3) and the transporter effect considerations (Fig. 4), we conclude that we have met the objectives of our study: to develop a practical, low-cost, and fast quantitative method which could be used for early passive BBB permeability screening, and for assisting medicinal chemists with structure modification to improve the BBB permeability of test compounds downstream in the CNS drug discovery process.

GLOSSARY

ER

efflux ratio

K_p

total brain/plasma concentration ratio at steady state; K_p = AUC_tot,brain/AUC_tot,plasma; sometimes a single time point determination at distribution equilibrium is used, with the parameter called log BB

K_p,uu

in vivo unbound brain ISF/unbound plasma concentration ratio at steady state = ratio of sum of all passive and active influx clearances, minus possible active efflux clearances, divided by the sum of all elimination clearances from the brain (passive, active BBB transport, metabolism, and elimination via ISF bulk flow); K_p,uu = AUC_u,brainISF/AUC_u,plasma

K_p,uu^{in vitro}

in vitro unbound blood-free brain/unbound plasma concentration ratio at steady state based on brain homogenate method; K_p,uu^{in vitro} = C_u,brain/C_u,plasma

AUC_tot,brain

area under the concentration-time curve of the total concentration in brain

AUC_tot,plasma

area under the concentration-time curve of the total concentration in plasma

AUC_u,brainISF

area under the concentration-time curve of the unbound concentration in brain ISF

AUC_u,plasma

area under the concentration-time curve of the undbound concentration in plasma

f_u,plasma

in vitro fraction of unbound drug in plasma; f_u,plasma = C_u,plasma/C_tot,plasma

f_u,brain

in vitro fraction of unbound drug in undiluted brain (ISF + ICF); f_u,brain = C_u,brain/C_tot,brain

C_tot,plasma

in vitro total concentration in plasma

C_u,plasma

in vitro unbound concentration in plasma

C_tot,brain

in vitro total concentration in brain; C_tot,brain = total amount of drug in blood-free brain homogenate divided by the volume of undiluted blood-free brain homogenate

C_u,brain

in vitro unbound concentration in brain (excluding blood) homogenate, determined by equilibrium dialysis

ISF

brain interstitial fluid; i.e., brain extracellular fluid not including blood

ICF

intracellular fluid

t_1/2,eq.

half-time

PS

permeability surface area product

K_in

brain uptake clearance