microsome composition-based model as a mechanistic tool to predict nonspecific binding of drugs in...

Microsome Composition-Based Model as a Mechanistic Tool toPredict Nonspecific Binding of Drugs in Liver Microsomes

PATRICK POULIN,1 SAMI HADDAD2

1Consultant, 4009 Sylvia Daoust, Quebec City, Quebec, Canada

2Departement de Sante Environnementale et Sante au Travail, IRSPUM, Faculte de Medecine, Universite de Montreal,Montreal, Quebec, Canada

Received 1 April 2011; revised 21 April 2011; accepted 22 April 2011

Published online 13 May 2011 in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/jps.22619

ABSTRACT: The purpose of this study was to investigate the ability of the microsomecomposition-based model to predict the unbound fraction determined in vitro in microsomalincubation system (fuinc). Another objective was to make a comparative assessment between theproposed mechanistic method and three empirical methods published in the literature, namelythe models of Austin et al. (2002, Drug Metab Dispos 30:1497–1503), Turner et al. [2007, DrugMetab Rev 38(S1):162], and Halifax and Houston (2006, Drug Metab Rev 34:724–726), whichare based solely on physicochemical properties. The assessment was confined by the availabilityof measured fuinc data in rat and human at diverse microsomal protein concentrations for 132compounds. The proposed microsome composition-based model can be viewed as a combina-tion of two distinct processes, namely the nonspecific binding to neutral lipids and the ionicbinding to acidic phospholipids. Across methods, the maximum success rate in predicting fuinc

of all compounds was 98%, 91%, and 84% with predictions falling within threefold, twofold,and 1.5-fold error of the observed fuinc, respectively. The statistical analyses suggest that theprediction models are more effective at computing fuinc (i) for rat as compared with human,and (ii) for acids and neutral drugs as compared with strong basic drugs. In addition, on thebasis of the comparisons made using all datasets, the method that made use of microsomecomposition data compares well with those methods that relied solely on physicochemistry. Thesensitivity analysis demonstrated the importance of the compound properties and physiologicalparameters reflective of specific mechanistic determinants relevant to prediction of fuinc valuesof drugs. Overall, the results obtained with our proposed model demonstrate a significant steptoward the development of a generic and mechanistic model of fuinc for liver microsomes, whichshould provide rationale extrapolation procedures of hepatic clearance using a physiologically-based pharmacokinetics (PBPK) modeling approach. © 2011 Wiley-Liss, Inc. and the AmericanPharmacists Association J Pharm Sci 100:4501–4517, 2011Keywords: distribution; microsomes; clearance; metabolism; metabolic clearance; unboundfraction; computational ADME; in vitro–in vivo extrapolation; IVIVE; pharmacokinetics; PBPKmodeling

INTRODUCTION

Kinetic measurements using liver cell subfractions(microsomes and hepatocytes) are being increasinglyused to predict the clearance of drugs in humansunder in vivo conditions.1–3 The results of these invitro assays are corrected through a variety of fac-tors to facilitate their in vitro–in vivo extrapolation.

Correspondence to: Patrick Poulin (Telephone: + 418-802-3985;E-mail: [email protected])Journal of Pharmaceutical Sciences, Vol. 100, 4501–4517 (2011)© 2011 Wiley-Liss, Inc. and the American Pharmacists Association

Of those factors, the inclusion of correction for non-specific binding to microsomes and/or hepatocytes iswell documented.4–11 For accurate in vitro–in vivoextrapolation of metabolic clearance, the unboundfraction (fu) of a drug in the incubation mediumshould be taken into account in the upscaling pro-cess of the in vitro intrinsic metabolic clearance ofthe drugs.1–12 Several empirical relationships for theprediction of the unbound fraction in microsomalincubations (fuinc) have been developed in the lastdecade.4–9 The predictive tools are based upon read-ily available physicochemical properties as defined

JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 100, NO. 10, OCTOBER 2011 4501

4502 POULIN AND HADDAD

by the ionization state, lipophilicity and class of thecompounds studied, and the microsomal protein con-centration (Cp). Although there were some empiricalrules that could be followed to ensure the predictionof fuinc, there has been no initiative to our knowledgefor the development of realistic or mechanistic mod-els for predicting fuinc. In other words, the value ofmechanistic understanding, which one gains by usingphysiologically-based prediction models, might pro-vide more in-depth understanding of the process andextrapolation procedures (e.g., in vitro to in vivo, an-imals to humans, adult to children, and healthy vol-unteer to patient). Therefore, the involvement of thisaspect in the prediction of nonspecific binding to liverpreparations was considered likely for drugs.

In the in vitro kinetic studies, a drug incubatedwith preparations of microsomes distributes amongdifferent phases: mainly lipids (i.e., nonspecific bind-ing), proteins (i.e., specific binding), and aqueous(i.e., solubilization in buffer). In the context of drugmetabolism, it is the concentration of the drug in thephase available to the enzyme site of action that is ofinterest. This should theoretically be the concentra-tion of the drug in the aqueous phase of the medium.In an incubation medium, the fraction of the drug thatis present in the aqueous phase is commonly knownas the unbound fraction.

The mechanistic algorithms or tissue composition-based equations developed for predicting drug tissuedistribution are based on the fundamental principlethat the concentration (or solubility) of a compoundin a biological matrix can be expressed as the sumof its concentration in the respective components ofthe matrix (i.e., water, neutral lipids, charged phos-pholipids, and plasma proteins).13,14 These equationswere initially developed for calculating the tissue—plasma partition coefficients (PCs) of drugs and en-vironmental chemicals. As fuinc is also an importantparameter for drug distribution, an extension of therecently developed tissue composition-based modelsfrom the whole organ to microsomes was necessary.

The purpose of this study was to investigate theability of the microsome composition-based model topredict fuinc determined in vitro in rat and humanmicrosomal incubation for several structurally unre-lated drugs (acids, bases, and neutrals). The secondobjective was to make a comparative assessment be-tween the mechanistic model proposed in this studyand existing empirical models published in the lit-erature. Thus, it is of interest to assess the predic-tion of fuinc for drugs using mechanistic and empiricalmodels.

METHODS

The overall strategy is divided into two steps. Thefirst step consists of adapting a recently published

unified algorithm of drug distribution based on tissuecomposition data, which facilitates the computation ofmacro and micro level PCs,13 for predicting fuinc. Thesecond step compares the prediction performance ofthe proposed mechanistic method with three empiri-cal methods published in the literature, namely themodels of Austin and coworkers,6-8 Turner et al.,4 andHalifax and Houston5 and Houston and coworkers,9

which are based on physicochemical properties only.

Datasets

Large, diverse, and published datasets were collected.Therefore, the rat and human datasets publishedin the literature were reinvestigated in the presentstudy, bringing the total number of drugs studied to132 (38 acids, 60 neutrals, and 34 bases).1,3–11 Thedatasets are compiled in Tables 1 and 2. Compoundswere divided into acidic, basic, and neutral classes.For each of these classes, a generic prediction modelwas built for fuinc. All compounds represent thosedrugs available in the literature, for which the in-put parameters and in vitro fuinc were available. Theexperimental in vitro data comprised fuinc measure-ments with rat and human liver microsomes at Cpranging from 0.1 to 10 mg/mL.1,3–11

Development of the Microsome Composition-basedModel for Prediction of Fuinc

The incubation system in the in vitro studies is a non-saturable microsomes aqueous phase equilibrium,which can be expressed in the form of PC. Therefore,this PC was computed for the prediction of fuinc usinga microsome composition-based model.13

Theoretical Background

The microsomes contain neutral lipids (including neu-tral phospholipids), acidic phospholipids, and bind-ing proteins. Therefore, it was assumed that nearly100% of the weight of the incubation medium (mi-crosomes + buffer) can be accounted for by aque-ous phase, lipids, and proteins. Drug concentrationin the incubation medium was defined on the basisof the corresponding fractional content of and par-titioning/binding into aqueous phase, neutral lipids,phospholipids (neutral and acidic), and proteins.Accordingly, in the incubation medium, the cen-tral compartment is aqueous phase, where ioniz-able molecules exist in ionic and nonionic forms,which equilibrate with the other constituents. Sim-ilarly, in the hydrophilic group of the phospholipids(e.g., phosphomonoester) and proteins, both ionic andnonionic forms can be present. The nonionic formsof all classes of chemicals are more easily solubi-lized in the neutral lipids and in the hydrophobicgroups (e.g., glyceride) of the neutral phospholipids.The ions produced by the dissociation of bases haveelectrostatic interactions with acidic phospholipids

JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 100, NO. 10, OCTOBER 2011 DOI 10.1002/jps

PREDICTION OF UNBOUND FRACTION IN MICROSOMES 4503

Table 1. Rat Dataset∗

fuinc Microsomes

Physicochemistry [Prot.] Observed Predicted

Compounds

LogPow at25◦C

LogPow at37◦C

LogDow at37◦C pKa Class Pea

Cp(mg/mL) In vitro

MCM(this

study)Halifax and

Houston Turner et al. Austin et al.

Bumetanide 3.21 3.32 0.42 4.5 A – 1 0.92 1.00 0.92 0.88 0.940.25 0.95 1.00 0.98 0.97 0.98

4 0.83 1.00 0.75 0.65 0.79Cerivastatin 4.54 4.65 1.80 4.55 A – 1 0.65 0.97 0.86 0.80 0.72

0.25 0.87 0.99 0.96 0.94 0.914 0.42 0.89 0.60 0.50 0.39

Cinoxain 0.59 0.70 –2.0 4.7 A – 1 0.92 1.00 0.90 0.96 1.00Glipizide 1.64 1.75 0.23 5.9 A – 1 0.96 1.00 0.93 0.94 0.95Glyburide 4.29 4.40 2.29 5.3 A – 1 0.82 0.91 0.80 0.82 0.57Glyburide 0.25 0.93 0.98 0.94 0.95 0.84Glyburide 4 0.64 0.73 0.49 0.53 0.25Indomethaci 3.79 3.90 1.00 4.5 A – 1 0.81 1.00 0.91 0.85 0.88Ketoprofen 2.71 2.82 0.02 4.6 A – 1 0.92 1.00 0.93 0.90 0.96Losartan 4.13 4.24 0.94 4.1 A – 1 0.9 1.00 0.91 0.83 0.88Oxaprozin 4.81 4.92 1.72 4.2 A – 1 0.87 0.98 0.86 0.78 0.74

0.25 0.9 0.99 0.96 0.94 0.924 0.77 0.91 0.61 0.47 0.41

Piroxicam 0.82 0.93 –0.21 6.3 A – 1 0.92 1.00 0.93 0.96 0.97Sulfadoxine 0.93 1.04 –0.62 5.75 A – 1 0.97 1.00 0.93 0.96 0.98Sulindac 2.86 2.97 0.07 4.5 A – 1 0.86 1.00 0.93 0.90 0.96Tolmetin 2.88 2.99 –0.91 3.5 A – 1 0.94 1.00 0.93 0.90 0.99Warfarin 3.15 3.26 0.86 5 A – 1 0.94 1.00 0.91 0.89 0.89Ethoxybenzamide 1.34 1.45 1.45 – N – 1 0.98 0.99 0.88 0.87 0.80

0.25 0.97 1.00 0.97 0.97 0.944 0.95 0.97 0.65 0.64 0.50

Albendazole 3.29 3.40 3.40 – N – 1 0.56 0.62 0.54 0.47 0.240.25 0.8 0.87 0.82 0.78 0.56

4 0.24 0.29 0.23 0.18 0.07Alprazolam 1.84 1.95 1.95 – N – 1 0.82 0.98 0.84 0.80 0.68Carbamazepine 1.54 1.65 1.65 – N – 1 0.87 0.99 0.87 0.85 0.75Colchicine 0.82 0.93 0.93 – N – 1 0.94 1.00 0.91 0.92 0.89Diazepam 2.8 2.91 2.91 – N – 0.5 0.781 0.91 0.81 0.75 0.55Dichloraphe −0.32 –0.21 –0.21 – N – 1 0.94 1.00 0.93 0.98 0.97Indapamide 1.76 1.87 1.87 – N – 1 0.96 0.98 0.85 0.82 0.70

0.25 0.92 1.00 0.96 0.95 0.904 0.81 0.93 0.58 0.53 0.37

Isradipine 3.75 3.86 3.86 – N – 1 0.34 0.37 0.38 0.35 0.150.25 0.58 0.70 0.71 0.68 0.42

4 0.08 0.13 0.14 0.12 0.04Mebendazol 2.9 3.01 3.01 – N – 1 0.7 0.80 0.65 0.57 0.35Methocarb 0.36 0.47 0.47 – N – 1 0.84 1.00 0.92 0.95 0.93Metyrapone 1.37 1.48 1.48 – N – 1 0.97 0.99 0.88 0.87 0.79

0.25 0.97 1.00 0.97 0.96 0.944 0.92 0.97 0.65 0.63 0.49

Phensuximi 0.68 0.79 0.79 – N – 1 0.75 1.00 0.91 0.93 0.90Zolpidem 2.43 2.54 2.54 – N – 0.5 0.938 0.96 0.86 0.81 0.66Trioxasalen 3.47 3.58 3.58 – N – 1 0.38 0.52 0.48 0.42 0.20Omeprazol 2.23 2.34 2.34 4 WB – 0.5 0.929 0.95 0.88 0.84 0.72Betaxolol 2.59 2.70 0.69 9.4 SB 5.91 1 0.62 0.53 0.73 0.74 0.44

0.25 0.89 0.82 0.91 0.92 0.764 0.35 0.22 0.40 0.42 0.17

Verapamil 3.79 3.90 2.76 8.5 SB 13.5 1 0.37 0.29 0.37 0.36 0.14Propranolol 3.65 3.76 1.65 9.5 SB 7 1 0.44 0.48 0.42 0.41 0.17Imipramine 4.8 4.91 2.80 9.5 SB 21 1 0.16 0.21 0.10 0.13 0.04

∗Data were obtained from the literature.4–11,15,16 If more than one value is available, the average value was considered. For imipramine and propranol,however, drug blood–plasma ratio and fup used to calculate Pea were available at the incubated drug concentration (1:M).17 Log Pow37◦C was calculated asstated in the methods. Log Dow = log Pow–log(1 + 10pKa–pH) for a base, and log Dow = log Pow–log(1 + 10pH–pKa) for an acid (pH = 7.4).

Pea, erythrocyte:aqueous phase PC; A, acid; N, neutral; WB, weak base; SB, strong base; MCM, microsome composition-based model.

DOI 10.1002/jps JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 100, NO. 10, OCTOBER 2011


Table 2. Human Dataset∗

fuinc Microsomes


Compounds

LogPow at25◦C

LogPow at37◦C


Cp(mg/mL) In vitro

MCM(this

study)Halifax and


Naproxen 2.8 2.91 –0.29 4.2 A – 1 0.99 1.00 0.93 0.90 0.97Phenytoin 2.47 2.58 2.53 8.3 A – 1 0.85 0.86 0.76 0.91 0.50Tolbutamide 3.13 3.24 1.10 5.27 A – 1 0.97 0.99 0.90 0.89 0.86Diclofenac 4.49 4.6 1.20 4 A – 0.1 1 1.00 0.99 0.98 0.98

1 0.87 0.99 0.90 0.81 0.850.3 1.0 ± 0.13 1.00 0.97 0.93 0.95

Gembifrodil 3.4 3.51 0.81 4.7 A – 0.1 0.97 1.00 0.99 0.99 0.991 0.77 1.00 0.91 0.87 0.90

Ibuprofen 3.98 4.09 1.09 4.4 A – 2 0.84 ± 0.13 0.99 0.82 0.73 0.76Myco.acid 2.8 2.91 2.91 9.76 A – 0.1 0.94 0.96 0.95 0.99 0.86

1 0.79 0.72 0.68 0.90 0.38Tolbutamide 3.13 3.24 1.10 5.27 A – 10 0.95 ± 0.03 0.94 0.48 0.44 0.38Tenoxicam 1.9 2.01 –0.10 5.3 A – 10 0.78 ± 0.03 1.00 0.58 0.58 0.74Warfarine 3.15 3.26 0.86 5 A – 0.1 0.99 1.00 0.99 0.99 0.99

10 0.47 ± 0.05 0.97 0.51 0.44 0.4610 0.99 0.97 0.51 0.44 0.46

Dexamethasone 1.87 1.98 1.98 – N – 5 1.0 ± 0.07 0.90 0.51 0.44 0.29Prednisone 1.6 1.71 1.71 – N – 5 0.20 ± 0.02 0.94 0.56 0.51 0.36Diazepam 2.8 2.91 2.91 – N – 5 0.28 ± 0.05 0.51 0.30 0.23 0.11

0.5 0.745 0.91 0.81 0.75 0.55Midazolam 3.8 3.91 3.91 – N – 0.1 0.97 0.84 0.85 0.84 0.62

1 0.88 0.34 0.37 0.34 0.141 0.54 0.34 0.37 0.34 0.14

Methoxsale 1.97 2.08 2.08 – N – 0.5 0.94 ± 0.11 0.99 0.90 0.88 0.78Alprazolam 1.84 1.95 1.95 – N – 5 0.66 ± 0.04 0.90 0.51 0.45 0.29Triazolam 2.4 2.51 2.51 – N – 0.1 1 0.99 0.97 0.96 0.91

1 0.78 ± 0.09 0.93 0.76 0.69 0.501 0.84 0.93 0.76 0.69 0.50

Oxazepam 2.24 2.35 2.35 – N – 0.1 0.83 0.99 0.97 0.96 0.931 0.72 0.95 0.79 0.73 0.55

Zolpidem 2.43 2.54 2.54 – N – 5 0.58 ± 0.10 0.71 0.38 0.31 0.160.5 0.939 0.96 0.86 0.81 0.66

Amobarbital 2.07 2.18 2.18 – N – 10 0.76 ± 0.08 0.74 0.30 0.24 0.13Hexobarbital 1.98 2.09 2.09 – N – 5 0.81 ± 0.05 0.87 0.48 0.41 0.26Methohexital 2.35 2.46 2.46 – N – 1 0.86 ± 0.13 0.94 0.77 0.71 0.52Naphthofavone 4.65 4.76 4.76 – N – 0.1 0.2 0.42 0.60 0.68 0.36

1 0.07 0.07 0.13 0.17 0.05Simvastastin 4.68 4.79 4.79 – N – 0.1 0.39 0.41 0.59 0.67 0.35

1 0.06 0.06 0.12 0.17 0.05Indinavir 2.79 2.90 2.87 6.2 WB – 0.1 1 0.97 0.96 0.94 0.86

1 0.88 0.74 0.69 0.60 0.39Saquinavir 4.5 4.61 4.49 6.89 WB – 0.1 0.59 0.41 0.70 0.71 0.44

1 0.1 0.06 0.19 0.20 0.07Ritonavir 3.9 4.01 4.01 2.56 WB – 0.1 0.87 0.67 0.83 0.82 0.59

1 0.38 0.17 0.33 0.32 0.13Buspirone 2.3 2.41 2.36 6.5 WB – 0.1 0.94 0.99 0.97 0.96 0.92

1 0.85 0.90 0.79 0.72 0.55Rosiglitazone 2.62 2.73 2.68 6.5 WB – 0.1 0.93 0.98 0.96 0.95 0.89

1 0.72 0.82 0.73 0.64 0.45Omeprazole 2.23 2.34 2.34 4 WB – 0.5 0.975 0.95 0.88 0.84 0.72Caffeine –0.091 0.02 –2.98 10.4 SB 1.56 1 0.96 0.91 0.93 0.99 0.96Amitryptiline 4.9 5.01 3.00 9.4 SB 13.8 0.5 0.15 ± 0.04 0.48 0.16 0.21 0.07

1 0.35 0.32 0.09 0.12 0.04Nortriptyline 4.28 4.39 2.09 9.7 SB 45.8 1 0.35 0.12 0.22 0.23 0.08Chrlopromaz 5.42 5.53 3.23 9.7 SB 38.3 1 0.11 ± 0.02 0.14 0.03 0.06 0.02Propafenone 4.24 4.35 2.05 9.7 SB 12.4 0.5 0.26 ± 0.04 0.51 0.37 0.39 0.16Verapamil 3.79 3.90 2.76 8.5 SB 7.86 0.5 0.43 ± 0.10 0.63 0.54 0.53 0.25

(Continued)



Table 2. Continued

fuinc Microsomes


Compounds

LogPow at25◦C

LogPow at37◦C


Cp(mg/mL) In vitro

MCM(this

study)Halifax and


0.1 0.83 0.89 0.86 0.85 0.631 0.47 0.46 0.37 0.36 0.14

Diphenhydramine 3.31 3.42 1.83 8.98 SB 3.5 6 0.29 ± 0.02 0.28 0.16 0.15 0.05Lorcainide 4.85 4.96 2.85 9.5 SB 3.26 1 0.52 ± 0.03 0.70 0.10 0.12 0.04Diltiazem 2.67 2.78 2.30 7.7 SB 5.33 2 0.76 ± 0.10 0.40 0.55 0.56 0.26

0.2 0.863 0.87 0.92 0.93 0.78Desipramine 4.9 5.01 2.11 10.3 SB 19.5 0.5 0.21 ± 0.01 0.39 0.16 0.21 0.07

0.1 0.65 0.76 0.49 0.57 0.291 0.21 0.24 0.09 0.12 0.04

Imipramine 4.8 4.91 2.80 9.5 SB 9.74 0.1 0.91 0.87 0.54 0.60 0.311 0.45 0.40 0.10 0.13 0.04

Ketamine 2.18 2.29 1.93 7.5 SB 0.78 1 0.49 ± 0.02 1.00 0.80 0.83 0.57Quinidine 3.44 3.55 0.95 10 SB 5.36 5 0.32 ± 0.17 0.21 0.16 0.15 0.05

0.1 0.86 0.93 0.91 0.90 0.731 0.56 0.58 0.49 0.48 0.21

Clozapine 3.42 3.53 3.05 7.7 SB 13.8 5 0.13 ± 0.01 0.08 0.16 0.16 0.05Nicardipine 3.82 3.93 2.70 8.6 SB 8.89 0.2 0.129 0.79 0.74 0.73 0.45Carvedilol 4.19 4.30 3.52 8.1 SB 14.2 0.1 0.58 0.80 0.76 0.77 0.50

1 0.1 0.29 0.24 0.25 0.09Naloxone 2.1 2.21 1.59 7.9 SB 2.52 0.1 0.87 0.97 0.98 0.98 0.94

1 0.87 0.78 0.81 0.85 0.60

∗Data were obtained from the literature.4–11,15–17 If more than one value is available, the average value was considered. For propafenone, however, fup usedto calculate Pea was obtained at the incubated drug concentration (1:M) because it is highly concentration-dependent.18 Log Pow37◦C was calculated as statedin the methods. Log Dow = log Pow–log(1 + 10pKa–pH) for a base, and log Dow = log Pow–log(1 + 10pH–pKa) for an acid (pH = 7.4).

Pea, erythrocyte:aqueous phase; A, acid; N, neutral; WB, weak base; SB, strong base; MCM, microsome composition-based model.

(phosphatidylserine, mono- and diphosphatidylglyc-erol, phosphatidylinositol, and phosphatidic acid).The accumulation of cations in the acidic phos-pholipids is a major mechanism for distributionof a strong basic drug (at least one pKa of 7 orgreater).13,14 Consequently, for a neutral and an acidiccompound, the binding to acidic phospholipids is ne-glected. Therefore, the concentration of a drug in theincubated microsomes can essentially be described asthe sum of the concentration of the drug that is freelydistributed within the aqueous and lipid phases (i.e.,the nonspecific binding) and the concentration of thedrug that is bound to macromolecules (i.e, the specificbinding to proteins). Therefore, at equilibrium, thetotal concentration in the incubated medium can becomputed on the basis of the concentration of the non-ionic form in the aqueous phase (which is buffer) asper the unified algorithm developed by Peyret et al.13

as follows:

Cm = Cna · (1 + Im) · Fwm + Cna · Pnla · Fnlm + Cna

·Im · Papla · Faplm + Cna · (1 + Im) · Ppra · Fprm

(1)

where Cm is the total concentration in the incubationmedium m; Cna is the concentration of the nonionic

form in the aqueous phase (buffer) of the incubationmedium; Fwm is the fractional volume of water equiv-alent in the incubation medium; Fnlm is the fractionalvolume of neutral lipids equivalent in the incubationmedium; Faplm is the fractional volume of acidic phos-pholipids equivalent in the incubation medium; Fprmis the fractional volume of binding proteins in the in-cubation medium; Im is the ionization term for theincubation medium m; Pnla is the neutral lipid–aque-ous phase PC for the incubation medium; Papla is theacidic phospholipid–aqueous phase PC for the incuba-tion medium; and finally Ppra is the protein–aqueousphase PC for the incubation medium.

In Eq. 1, the ionization term of the medium (Im) wascalculated using the Henderson–Hasselbach equationas follows, knowing the pH of the in vitro incubationstudies (7.4) and pKa of a drug.1,3–11 For the purposeof the present study, the monoacid, monobase, andneutral forms were considered13:

Im = 0forneutrals (2)

Im = 10pKa−pHformonoproticbases (3)

Im = 10pH−pKaformonoproticacids (4)



Dividing Eq. 1 (total concentration in the medium)by the free drug concentration in the aqueous phaseyields, after rearrangement, the following algorithmfor computing the medium–aqueous phase PC (Pma)at equilibrium13:

Pma =(1 + Im) · Fwm + Pnla · Fnlm + Im · Papla · Faplm + (1 + Im) · Ppra · Fprm

(1 + Ia)

(5)

where Ia is the ionization term for the aqueous/bufferphase of the incubation medium. Because the micro-somes were incubated in an excess of buffer solution,it was assumed that the aqueous phase is similar inboth the numerator and the denominator of Eq. 5.Consequently, Im and Ia are identical. In addition, itis known that for small chemical molecules, distribu-tion is typically driven by nonspecific binding to lipids;however, pharmacological target binding is generallyof minor relevance in terms of their contribution tothe distribution. Therefore, the extent of binding tothe proteins in microsomes was set to zero for all com-pounds studied (i.e., Ppra, the protein–aqueous phasePC, was set to zero). In other words, the fraction of thedrug that would bind to macromolecules appears tobe negligible as compared with that being distributedinto lipids. Consequently, Eq. 5 reduces to

Pma = Fwm + Pnla · Fnlm + Im · Papla · Faplm

1 + Im(6)

As mentioned for a neutral and acidic drug, Eq.7 should apply considering the mechanism of drugdistribution into neutral lipids equivalent:

Pma = Fwm + Pnla · Fnlm

1 + Im(7)

and for an ionized base, Eq. 6 is proposed.Simply, fuinc (the ratio of free concentration over the

total concentration) was calculated as follows fromPma:

fuinc = 1Pm:a

(8)

These microsome composition-based equations canbe used to compute fuinc by using the correspondingphysiological and physicochemical input parameters.

Estimation of the Physiological Specific InputParameters

A literature search was performed to obtain ratand human composition data for the erythrocytesand representative of the incubation medium whichcontains the microsomes (Table 3). For rat micro-somes, the lipid composition data were found from

two sources19,20 and consequently, the minimum andmaximum values were presented from two batches ofliver microsomes. For the main purpose of the presentstudy, the average value was used for the computationof fuinc for the rat dataset of drugs. However, the lipidcomposition data for human microsomes were foundin only one source15 and consequently, only one batchof liver microsomes was considered for the computa-tion of fuinc for the human dataset. The lipid com-position data for microsomes were reported on a ba-sis of mg protein (Table 3). Therefore, the computa-tion of fuinc could be performed at any microsomalprotein concentration (Cp; mg protein/mL buffer). Inother words, the calculation of fuinc was adjusted toCp reported in the original in vitro studies (Tables 1and 2).

Estimation of the Chemical Specific Input Parameters

To use the proposed microsome composition model forany drug, the value of each physicochemical propertyonly is needed. The physicochemical properties, whichwere computed in this study or obtained followinga review of the literature, are listed, respectively, inTables 1 and 2 for the rat and human datasets ofdrugs.4–11,15–18,21

Calculation of pnla

As mentioned, Pnla refers to the ratio of a drug be-tween the neutral lipids and aqueous phase in theincubation medium, which was estimated from the n-octanol–buffer PC (Pow). Because in vitro incubationstudies are performed at body temperature, values oflog Pow obtained at a temperature of 25◦C were ad-justed to 37◦C based on the temperature dependencyof log Pow published by Leo et al.21 (i.e., log Pow37◦C =log Pow25◦C + 0.009/◦C × ∆◦C). The original values oflog Pow at 25◦C were obtained from the literature.

Calculation of papla

Papla refers to the ratio of a drug between the acidicphospholipids and aqueous phase in the incubationmedium, and it was used only for the strong basicdrugs with at least one pKa ≥ 7. Peyret et al.13 andRodgers and Rowland14 used the blood–plasma ra-tio (RBP) determined in vitro to estimate the extentof binding to acidic phospholipids in any biologicalmatrix. The main reason is that the erythrocyte alsocontains such ionic lipids that provide high-affinitybinding sites for basic drugs. Accordingly, the blood—plasma ratio is converted to the erythrocyte–aqueousphase PC for the unbound drug (Pea) using the mea-sured value of unbound fraction in plasma (fup) andthe erythrocyte content in blood (45%):

Pea =[

(RBP − (1 − 0.45))/0.45fup

](9)



Table 3. Composition of the Incubation Medium and Erythrocyte∗

Composition Data

Anl (mg NeutralLipid/mgProtein)a

Apl (mg TotalPhospholipid /mg

Protein)a

Fnl (Fractionof Neutral Lipid

Equivalent)b

Fapl (Fractionof Acidic

Phospholipid)c

Fw (Fractionof Water

Equivalent)d

Liver cellsHuman microsomes-batch 1 0.235 0.797Rat microsomes-batch 1 0.118 0.500Rat microsomes-batch 2 0.345 1.155Rat microsomes-average 0.232 0.828Incubation medium (m)e

Human microsomes-batch 1 4.74e-4∗Cp 1.43e-4∗Cp ∼1Rat microsomes-batch 1 2.68e-4∗Cp 0.82e-4∗Cp ∼ 1Rat microsomes-batch 2 6.92e-4∗Cp 1.89e-4∗Cp ∼ 1Rat microsomes-average 4.8e-4∗Cp 1.36e-4∗Cp ∼ 1Blood cells (e)f

Human erythrocytes 0.0024 0.00057 0.63Rat erythrocytes 0.0013 0.0005 0.60

∗Data for rat and human microsomes and erythrocytes were obtained from the literature.14,19,20

aFor microsomes, data are given in mg lipid/mg microsomal protein.19,20 In the case of Chidozie et al.,19 a standard conversion factor of 40 mgprotein/g liver was used to convert mg lipid/g liver to mg lipid/mg protein.

bThe term Fnl corresponds to the fractional volume of neutral lipids plus 30% of the content of phospholipids. This is because it was assumed thatthe phospholipids behave similarly as a mixture of 30% neutral lipids and 70% of water.13,14 For rat and human microsomes incubated in themedium, Fnl as a function of the microsomal protein concentration (Cp) is equal to

Fnl = (mgneutral lipid equivalent/gmedium)= [(Anl + 0.3Apl) (mgneutral lipid/mgprotein) × Cp (mgprotein/mLwater)]/1000 mg water × (mgwater/mLwater)cThe acidic phospholipid represents respectively 18% and 16.4% of the total phospholipids in human and rat microsomes.19 For rat and human

microsomes incubated in the medium, Fapl as a function of the microsomal protein concentration (Cp) is equal toFapl = (mgacidic phospholipid/gmedium)= [0.18 or 0.164 Apl (mgacidic,phospholipid/mgprotein) × Cp (mgprotein/mLwater)]/1000 mg water × (mgwater/mLwater)dThe term Fw corresponds to the fractional volume of water plus 70% of the content of phospholipids. This is because it was assumed that the

phospholipids behave similarly as a mixture of 70% of water and 30% neutral lipids.13,14 For rat and human microsomes incubated in the medium,Fw is equal to

Fw = (mgwater equivalent/gmedium)= 1–Fnl–Fapl–Fpr + 0.7Fpl, whereFpr = Cp (mgprotein/mLwater)] / 1000 mg water × (mgwater/mLwater)Fpl = [Apl (mgtotal,phospholipid/mgprotein) × Cp (mgprotein/mLwater)] / 1000 mg water × (mgwater/mLwater).For the range of Cp investigated (Cp ranges from 0.1 to 10 mg/mL), Fw of the medium is about unity.eComposition data used to estimate fuinc.fComposition data used to estimate Pea.

Indeed Pea was used to estimate Papla13,14:

Papla =[Pea − (1 + Ie) · Fwe + Pow · Fnle

1 + Ip

]

· 1 + Ip

Ie · Faple(10)

where e is erythrocyte; Faple is the fractional contentof acidic phospholipids equivalent in the erythrocyte;Fnle is the fractional content of neutral lipid equiva-lent in the erythrocyte; Fwe is the fractional contentof water equivalent in the erythrocyte; Ie is the ion-ization term for the erythrocyte; and Ip is the ioniza-tion term for the plasma p. Again, Ie and Ip of eachstrong basic drug was calculated using the Hender-son–Hasselbach equations (Eq. 3), knowing the pH ofthe erythrocyte and plasma to be 7.22 and 7.4, respec-tively. For plasma, only a trace of acidic phospholipidis present13 and consequently, this was neglected.

Comparative Assessment of Prediction Methodsof Fuinc for Microsomes

We made a first attempt to get information on thepredictive performance of the proposed microsomecomposition-based method by comparing its predic-tive performance to the previously published empir-ical methods. As mentioned, the predictive perfor-mance of the proposed method was compared withother calculation methods like the models of Austinet al., Turner et al., and Halifax and Houston,4–9 forthe same dataset of drugs. For comparability reasons,all equations of these additional prediction models arepresented in the Appendix.

Evaluation of Predictive Performance

The prediction accuracy was assessed by comparingpredicted versus observed values of rat and humanfuinc, by using several statistical parameters. Thesame statistical evaluation, as already described byPoulin and Theil,15 was also performed in the presentstudy. Therefore, the following statistical parameterswere calculated and presented for each prediction



Microsome composition- based model

0.001

0.01

0.1

1

10

0.01 0.1 1 10Predicted fuinc

Ob

serv

ed fu

inc

Figure 1. Comparison between predicted and observedhuman fuinc for the proposed microsome composition-basedmodel (n = 132) (r = 0.85). Data were obtained fromTables 1 and 2 for the rat and human datasets used in thecomparative assessment. The solid line indicates the bestfit (unity). Dashed lines on either side of the unity includea factor of two and three, respectively.

method studied: average-fold error (AFE), absoluteaverage-fold error (AAFE), root mean squared error(RMSE), correlation of coefficient (r), and concordancecorrelation coefficient (CCC). Specific fold-errors ofdeviation between the predicted and observed values(% fold-error ≤1.5, ≤2, ≤3, and ≤10) were also calcu-lated. Finally, plots of predicted versus observed fuincvalues were also made.

Sensitivity Analysis

The impact of lipophilicity (log Pow value), binding pa-rameter to acidic phospholipids (Pea value), and mi-crosome composition on fuinc predictions was inves-tigated. A dataset of fuinc was simulated using theprediction methods applicable by varying these pa-rameters. Three drug examples were considered forthis exercise, namely, a neutral, an acidic (pKa set at3), and a strong base (pKa set at 9.5).

RESULTS

Comparative Assessment for Various PredictionMethods of Fuinc

A total of four prediction methods of rat and humanfuinc were evaluated in the present study for a totalof 132 drugs. In this study, all methods were com-pared using the same datasets. Comparative assess-ment was made on the basis of several statisticalparameters. The observed rat and human fuinc foreach compound, together with the predicted fuinc fromeach model are listed in Tables 1 and 2. The overallstatistical summary in terms of accuracy, precision,and correlation are listed in Table 4. The plots of ob-served versus predicted fuinc values for each methodare shown in Figures 1–4.

Halifax and Houston5

0.001

0.01

0.1

1

10


Ob

serv

ed fu

inc

Figure 2. Comparison between predicted and observedhuman fuinc for the Halifax and Houston model (n = 132)(r = 0.83). Data were obtained from Tables 1 and 2 for the ratand human datasets used in the comparative assessment.The solid line indicates the best fit (unity). Dashed lines oneither side of the unity include a factor of two and three,respectively.

Turner et al.4

0.001

0.01

0.1

1

10


Ob

serv

ed fu

inc

Figure 3. Comparison between predicted and observedhuman fuinc for the Turner et al. model (n = 132) (r = 0.8).Data were obtained from Tables 1 and 2 for the rat andhuman datasets used in the comparative assessment. Thesolid line indicates the best fit (unity). Dashed lines on ei-ther side of the unity include a factor of two and three,respectively.

Austin and coworkers6–8

0.001

0.01

0.1

1

10


Ob

serv

ed fu

inc

Figure 4. Comparison between predicted and observedhuman fuinc for the Austin et al. model (n = 132) (r = 0.8).Data were obtained from Tables 1 and 2 for the rat andhuman datasets used in the comparative assessment. Thesolid line indicates the best fit (unity). Dashed lines on ei-ther side of the unity include a factor of two and three,respectively.



Table 4. Comparative Assessment of Four Calculation Methods used to Predict fuinc in Rat and Human Microsomes for the CurrentDatasets of Drugs

Prediction of fuinc

% ≤ 1.5-Fold % ≤ 2 -Fold % ≤ 3 -Fold % ≤ 5 -Fold % ≤ 10 -Fold AFE AAFE RMSE r CCC

All datasets (n = 132)MCM (this study) 84.1 91.2 97.7 99.2 100 1.10 1.25 0.16 0.85 0.84Halifax and Houston 79.6 90.9 95.5 98.5 100 0.94 1.29 0.19 0.83 0.79Turner et al. 78.0 88.6 95.5 99.2 100 0.94 1.31 0.19 0.80 0.77Austin et al. 57.6 69.7 86.4 93.2 98.5 0.64 1.67 0.33 0.80 0.65

Human dataset (n = 78)MCM (this study) 76.9 87.2 96.2 98.7 100 1.10 1.32 0.20 0.80 0.80Halifax and Houston 68.0 84.6 92.2 97.4 100 0.91 1.42 0.24 0.79 0.73Turner et al. 66.7 80.8 92.3 98.7 100 0.92 1.45 0.23 0.75 0.71Austin et al. 47.4 61.5 79.5 88.5 97.4 0.57 1.90 0.39 0.77 0.59

Rat dataset (n = 54)MCM (this study) 94.4 98.2 100 100 100 1.11 1.15 0.08 0.93 0.92Halifax and Houston 96.3 100 100 100 100 1.0 1.11 0.07 0.91 0.94Turner et al. 94.4 100 100 100 100 0.96 1.13 0.07 0.90 0.94Austin et al. 72.2 81.5 96.3 100 100 0.75 1.38 0.20 0.87 0.76

Neutrals + weak bases (n = 60)MCM (this study) 86.7 93.3 98.3 100 100 1.07 1.22 0.14 0.85 0.89Halifax and Houston 80.0 91.7 98.3 100 100 1.0 1.25 0.15 0.81 0.83Turner et al. 76.7 88.3 96.7 100 100 0.95 1.32 0.18 0.76 0.77Austin et al. 55.0 75.0 88.3 96.7 100 0.64 1.64 0.28 0.76 0.69

Acids (n = 38)MCM (this study) 94.7 94.7 100 100 100 1.13 1.14 0.09 0.46 0.21Halifax and Houston 94.7 100 100 100 100 0.96 1.12 0.08 0.59 0.55Turner et al. 92.1 94.7 100 100 100 0.93 1.14 0.10 0.59 0.52Austin et al. 84.2 89.5 100 100 100 0.88 1.19 0.14 0.63 0.44

Strong bases (n = 34)MCM (this study) 67.7 85.3 94.1 97.1 100 1.13 1.43 0.23 0.76 0.67Halifax and Houston 61.8 79.4 85.3 94.1 100 0.84 1.58 0.29 0.79 0.64Turner et al. 64.7 82.4 88.2 97.1 100 0.91 1.49 0.26 0.80 0.68Austin et al. 32.4 38.2 67.6 79.4 94.1 0.43 2.52 0.50 0.80 0.45

AFE, average-fold error; AAFE, absolute average-fold error; RMSE, root mean square error; r, correlation coefficient; CCC, concordance correlationcoefficient; MCM, microsome composition-based model.

There was not simply one method that predictsfuinc accurately for all compounds. Across methods,the maximum success rate in predicting rat and hu-man fuinc of all compounds was 98%, 91%, and 84%with predictions falling within threefold, twofold, and1.5-fold error, respectively, of the observed fuinc. Ingeneral, a high degree of prediction accuracy was ob-tained in this study for the current datasets, whichshould satisfy the requirements of fuinc predictions indrug discovery and early drug development.

On the basis of the comparisons made using alldatasets, the method that made use of microsomecomposition data was slightly more predictive thanthose methods that relied solely on physicochemi-cal data. In other words, the proposed model fairedwith the correlation principles of Halifax and Hous-ton and Turner et al., whereas the model of Austinet al. was less predictive. This is reflected by thevalues of % fold-error, AFE, AAFE, RMSE, r, andCCC (Table 4), as well as graphically (Figs. 1–4).

This is also reflected by the fact that the Austinet al. model incorrectly predicted the rat and humanfuinc by a factor of 10-fold or greater for some drugs,which was not the case for the other models. Fur-thermore, the model of Austin et al. tends to under-predict fuinc (AFE values lower than unity), in con-trast to the other models (AFE values closer to unity).It is useful to take a closer look at the performanceof the different approaches applied in this study(see below).

Rat Versus Human Datasets

One aspect of interest was to determine if the com-putation methods provided a similar prediction per-formance for fuinc in human as compared with thatin rat. Generally, the prediction performance was su-perior for the rat dataset as compared with that forhuman for the four methods tested (Table 4). Thisis expected considering the greater variability in hu-mans. These methods produced predicted fuinc values



with an accuracy of >96% within 1.5-fold, 100%within twofold, and 100% within threefold for the ratdataset, whereas these values decreased to 77%, 86%,and 96%, respectively, for the human dataset.

In particular, for the human dataset, the predic-tion of fuinc was improved by accounting for micro-some composition data as compared with the empir-ical models (at least for the 1.5-fold error). However,for the rat dataset, all methods were equivalent ex-cept the one of Austin et al. Therefore, the model ofAustin et al. was again the least successful testedmethod.

Classes of Drugs

Another aspect of interest was to determine whetherthe computation methods provided a similar predic-tion performance across the classes of drugs. Theclasses of drugs investigated in the present study(acids, bases, and neutrals) presented different pre-diction performance (Table 4). In general, predictionaccuracy was highly dependent on the properties ofthe compounds investigated. In this context, moreaccurate predictions were obtained for neutral (andweak bases) and acidic compounds as compared withstrong basic compounds (at least in terms of fold-error, AFE, AAFE, and RMSE values). However, theacids demonstrated a lower measure of correlationand global concordance (lower r and CCC values) ascompared with the other classes of compounds. Again,the microsome composition-based model, Halifax andHouston model, and Turner et al. model showed a sim-ilar level of accuracy, which is superior to the modelof Austin et al.

Prediction of Fuinc for Particular Drugs

For some basic compounds (chlorpromazine,imipramine, and lorcainide), the use of the em-pirical models (Halifax and Houston, Turner et al.,and Austin et al.) provided a greater inaccuracyof human fuinc (relevant under-prediction by about2–10-fold) as compared with the mechanistic modelbased on microsome composition (Table 2). It appearsthat these basic compounds do not totally followa relationship with drug lipophilicity as suggestedby these empirical models. In contrast, the moreaccurate prediction observed with the microsomecomposition-based model would suggest some biolog-ical underpinning, for example, the significant ionicbinding to acidic phospholipids, which is specificallyconsidered by this model. However, this is not alwaystrue because for nicardipine, another strong basicdrug, all models showed inaccurate prediction ofhuman fuinc.

Sensitivity Analysis

The sensitivity analysis demonstrated the impor-tance of the compound properties and physiologi-

Rat dataset

0.1

1

10

0 1 2 3 4 5 6Log Pow

Co

mp

ute

d f

uin

c

Figure 5. Relation between log Pow37◦C and computed fuinc

for the microsome composition-based model (cross) and Hal-ifax and Houston correlation principle (square). The ratdataset of drugs is investigated.

cal parameters reflective of specific mechanistic de-terminants relevant to prediction of fuinc values ofdrugs. Both lipophilicity and microsome compositionaffected the fuinc predictions, and this is more notice-able at higher log Pow values and concentrations of mi-crosomal protein and lipid. Furthermore, for a strongbasic drug the binding to acidic phospholipids is pre-dominant. This is further detailed below.

Impact of Lipophilicity on the Prediction of Fuinc

The prediction of fuinc over a large range of log Powvalues was assessed. For the rat dataset of drugs,Figure 5 illustrates that the empirical model ofHalifax and Houston and the proposed microsomecomposition-based model produced in several casesrelatively similar fuinc predictions at the same druglipophilicity, indicating the similar prediction perfor-mance. In addition, a simulated rat fuinc dataset wasgenerated using each model over a representativerange of log P values (–5–10) for three drug exam-ples (i.e., a neutral, an acid with pKa = 3, and astrong base with pKa = 9.5 and Pea = 1) (Fig. 6).The fuinc value decreases significantly with increas-ing lipophilicity, particularly in the lipophilic area,suggesting that caution should be applied in pre-dicting fuinc while using predicted log Pow valuesinstead of measured log Pow values as input. How-ever, the sensitivity to drug lipophilicity became morepronounced at log Pow values ranging from about1 to 6, especially for the Halifax and Houston andTurner et al. equations as compared with the micro-some composition-based model for the simulation sce-narios studied. Furthermore, the Halifax and Hous-ton model performs differently at values of log Powparticularly lower than zero, and its nonlinear formlacks experimental support. Even if this is accept-able, this model cannot be further verified in thisarea of hydrophilicity because the current datasetis poor in term of highly polar compounds. In theFigure 6, three drug examples were used to



(a) Neutral

0

0.2

0.4

0.6

0.8

1

1.2

-5 0 5 10

Log P

Cal

cula

ted

rat

fu

(b) Acid (pKa = 3)

0

0.2

0.40.6

0.8

1

1.2

-5 0 5 10

Log P

Cal

cula

ted

rat

fu

(c) Strong base (pKa = 9.5, Pea = 1)

00.20.40.60.8

11.2

-5 0 5 10

Log P

Cal

cula

ted

rat

fu

Figure 6. Predictions of rat fuinc simulated over a large range of log Pow values for three drugexamples, using the physiological and empirical models investigated in this study. (a) Neutraldrug, (b) acid (pKa set to 3), and (c) strong base (pKa and Pea set to 9.5 and 1, respectively).A value of Cp equal to 1 mg/mL was used for the simulations. Solid line (blue) represents themicrosome composition-based model, whereas the dashed (orange) and dotted (green) linesrepresent the Turner et al., and Halifax and Houston model, respectively.

simulate rat fuinc, considering Cp sets equal to 1 mg/mL and the average microsomal lipid composition,and consequently, these findings would change withother examples. In this context, the two following sec-tions present evidences that among different simula-tion scenarios, there is a difference in the findings.

Impact of Microsome Composition on thePrediction of Fuinc

The sensitivity analysis indicated that the predictionperformance was affected by both microsomal proteinand lipid concentrations. The current human datasetshowed that the fold-error of deviation (predicted/observed fuinc) is generally lower than unity, par-ticularly at high microsomal protein concentration,which is generally applicable to the empirical models(Austin et al., Turner et al. and Halifax and Houston)(Fig. 7). In addition, the impact of lipid concentra-tion on the predictions of rat fuinc was simulated. Inthe two batches of rat liver microsomes (Table 3), thelipid concentration varied at least by 100%, providinga representative distribution across this species of in-

terest. Each class of drugs is affected by a change offuinc due to a variation in the lipid concentration in ratliver microsomes (Fig. 8). This is particularly ampli-fied at the highest microsomal protein concentration(consequently at the highest lipid concentration simu-lated). In this case, the fold difference of fuinc betweenthe two batches of liver microsomes varies by a factorof up to three using the microsome composition-basedmodel.

Impact of Binding to Acidic Phospholipidson the Prediction of Fuinc

In the rat and human datasets of basic drugs, thevalue of Pea generally ranges from 1 to 50 (Tables1 and 2). Therefore, the calculated fuinc changed bya factor up to 10-fold over Pea values ranging onlyfrom 1 to 50 (Fig. 9). This is particularly noticeable atthe highest Pea values (and consequently, this shouldalso be noticeable at the highest lipid and microso-mal protein concentrations). Here, the impact of Peaon fuinc predictions is particularly important at logPow values below 7. At greater log Pow values, the



Austin and coworkers6–8

0.1

1

10

0 2 4 6Log Pow

Fo

ld-e

rro

r (p

red

./o

bs.

)

Microsome Composition-based model

0.1

1

10

0 2 4 6Log Pow

Fo

ld-e

rro

r (p

red

./o

bs.

)

Halifax and Houston5

0.1

1

10

0 2 4 6Log Pow

Fo

ld-e

rro

r (p

red

./o

bs.

)

Turner et al.4

0.1

1

10

0 2 4 6Log Pow

Fo

ld-e

rro

r (p

red

./o

bs.

)

Figure 7. Relationship between log Pow37◦C, fold-error of deviation (predicted/observed fuinc)and microsomal protein concentration (Cp for the microsome composition-based model andHalifax and Houston, Turner et al., and Austin et al. models. Open square represents Cp <

2 mg/mL and full square represents Cp ≥ 2 mg/mL. Dashed lines on either side of the unityinclude a factor of two and three, respectively. The human dataset of drugs is investigated.

impact of Pea is negligible (Fig. 9). In other words, atthat point, the ionic binding to acidic phospholipids(i.e., the term in the composition-based model con-sidering Pea) became negligible as compared with thehydrophobic binding to neutral lipids (i.e., the termin the composition-based model considering log Pow)for the current scenario.

DISCUSSION

Several extrapolation procedures (e.g., in vitro to invivo, animal to human, adult to children, and healthyvolunteer to patient) are still not fully resolved in thecase of drug clearance and drug–drug interactions.1–3

One important factor that should be theoreticallytaken into account in such studies is the fractionunbound in the incubation medium and in the me-tabolizing tissue.1–12 The limitation of fuinc data is,nevertheless, a common trend in the drug develop-ment. As a high number of drugs in development areintended for metabolic studies, fuinc is typically notassessed for all drugs at early stages. To address thisissue, a number of empirically-based methods havebeen developed and implemented for the computa-tion of fuinc.1–12,22 The main focus of this study wasto develop a mechanism-based prediction model forfuinc and assess the predictive performance of variousmethodologies reported in the literature to predict

rat and human fuinc using a large dataset of drugs.The assessment was confined by the availability ofmeasured fuinc data in rat and human at diverse Cpfor 132 compounds. The intended scientific benefit ofthis study was to obtain a greater appreciation of thepredictive performance of mechanistic and empiricalmethods of fuinc for liver microsomes.

Results from the literature4,9 show that fuinc pre-dicted solely from physicochemical data provide a su-perior degree of prediction accuracy for the models ofHalifax and Houston and Turner et al. as comparedwith Austin et al., and the results from our evalua-tion support these observations (Table 4). These em-pirical models provide consistently optimized equa-tions for the calculation of fuinc based mainly on druglipophilicity. Therefore, the difference in the degree ofaccuracy might partly be due to the fact that thesethree models rely not just on the same drug datasetsin the optimization procedures.4–9 Relying on readilyavailable physicochemical properties (class, pKa, andlog Pow) can be valuable during early discovery whenmeasured fuinc data are not available, and it is pos-sible to obtain accurate predictions of fuinc (Table 4).However, such empirical models should only be usedfor the chemical space covered by the optimizationprocedures.

Here, we describe the prediction of hepatic fuincbased also upon physicochemical (class, pKa, and log



(a) Neutral

0

1

2

3

−5 0 5 10

Log P

Fo

ld d

iffer

ence

in r

at fu

(b) Acid (pKa = 3)

0

1

2

3

−5 0 5 10

Log P

Fo

ld d

iffer

ence

in r

at fu

(c) Strong base (pKa = 9.5, Pea = 10)

0

1

2

3

−5 0 5 10

Log P

Fo

ld d

iffer

ence

in r

at fu

Figure 8. Fold-difference in rat fuinc simulated over a range of log Pow values, which accountsfor the variability in liver microsome composition. The simulations were performed using thecurrent composition-based model. The fold-difference represents the ratio of fuinc calculated be-tween the two batches of liver microsomes. Two batches of rat liver microsomes were obtainedfrom Table 3, and the lipid concentration was calculated according to the microsomal proteinconcentration (Cp = 0.5, 1, and 10 mg/mL). Solid line represents the highest protein concentra-tion (10 mg/mL), whereas the dashed and dotted lines represent the intermediate (1 mg/mL) andlower protein concentrations (0.5 mg/mL), respectively. Three drug examples are considered. (a)Neutral drug, (b) acid with a pKa = 3, and (c) strong base with a pKa = 9.5 and Pea = 10.

Strong base (pKa = 9.5)

0123456789

10

−5 0 5 10

Log P

Fo

ld im

pac

t in

rat

fu

calc

ula

ted

Figure 9. Fold-impact in rat fuinc simulated over a rangeof log Pow values, which accounts for different values ofPea. The simulations were performed using the currentcomposition-based model. The fold-impact represents thefactor by which a change in the Pea value relative to unityimpacts fuinc predictions. A strong base (pKa set to 9.5) isinvestigated. Cp = 1 mg/mL is considered. Lines representPea values set equal to 50, 25, 10 and 5 from the upper tolower panel, respectively.

Pow) and/or biochemical (Pea) properties. However, in-formation on microsome composition data was alsoconsidered to develop a mechanistic model. Osten-sibly, it was observed that the proposed microsomecomposition-based model appeared to be as predic-tive as the previously published empirical modelsof Halifax and Houston and Turner et al., in gen-eral (Table 4). The consideration of other datasetsof drugs may change the conclusion of this study.However, even while acknowledging that this couldbe important, it appears that the current microsomecomposition-based model compares well to the em-pirical models. Nevertheless, some may conclude thatthere is little point in further pursuing the microsomecomposition-based model, which requires a much bet-ter mechanistic understanding and additional inputdata (i.e., Pea). However, unlike the empirical model,which cannot be significantly improved more, mi-crosome composition-based modeling for fuinc is stillin its relatively early stages of application to drug



discovery and development, and the predictive capa-bility of this type of mechanistic model is likely toincrease as our mechanistic understanding improves.That is, a relatively similar level of accuracy betweenthe current microsome composition-based model andpublished correlation principles (Halifax and Hous-ton and Turner et al.) might also be an indicationthat the empirical finding by correlating fuinc withdrug lipophilicity data is also reflected by the mecha-nisms considered in the microsome composition-basedmodel. In this sense, the physiological and physic-ochemical determinants of fuinc used in the currentmicrosome composition-based model seem to explainthe published models by relating the empirical na-ture to potential biological meaning. This is expectedbecause drug partitioning into lipids and ionic bind-ing to acidic phospholipids, which are the main as-sumed mechanistic determinants of fuinc, would gen-erally vary with drug lipophilicity.13–14,16,23,24 More-over, Figures 5 and 6 illustrates that the empiri-cal models and the proposed microsome composition-based model provided sensibly the same fuinc predic-tions at the same drug lipophilicity, particularly whenlog Pow values are greater than zero. The presentdatasets are mainly constituted of drugs in this rangeof lipophilicity.

In this context, we explored how sensitive is the mi-crosome composition-based method as compared withthose of Houston and Halifax and Turner et al. tochanges in log Pow values (Fig. 6). It seems that eachmodel is sensitive to log Pow, but for the current mi-crosome composition-based model, this is noticeableat greater log Pow values as compared with the em-pirical models. Therefore, the microsome composition-based model seems relatively less sensitive to druglipophilicity, particularly in the low to medium rangeof log Pow values. The latter is important because cal-culated log Pow values are used in early drug discoveryand they are not always that accurate because differ-ences of one unit between calculated and measuredvalues are not uncommon.

In this study, all approaches were compared usingthe same drug datasets limiting at least the corre-sponding variability. However, analysis of the currentdatasets of drugs has been limited to prediction of themean, without consideration of variability and uncer-tainty especially for the physiological input parame-ters. Once the issues of variability and uncertaintyare addressed, it will be feasible to assess predic-tions more objectively. Because all physiological andphysicochemical input parameters can be consideredseparately in the proposed microsome compositionmodel, a more rationale prediction of fuinc could beachieved by allowing the consideration of variabilityand uncertainty in predictions. Therefore, relying onmicrosome composition data in a mechanistic frame-work might represent a relevant benefit also at the

later stage of drug development and in clinical study,particularly to conduct more rationale extrapolationprocedure particularly when the interspecies and/orinterindividual variations are relevant (e.g., animalto human, adult to children, and healthy volunteer topatient). Therefore, the differences in sex and ethnicalong with species and individual differences shouldbe closely taken into account in subsequent predic-tions. At present, however, the literature indicatesthat the lipid content and composition of microsomesvaries with age in rat, and across species (rat andhuman) as well as rat batches of liver.19,20 Also, itmight be assumed that the microsome compositionwould be affected by disease states, for example, livercirrhosis and cancer. Therefore, once a discrepancybetween estimated and experimental fuinc data is ob-served, it is an indication that variability or othermechanisms could be involved and their contribu-tion may, hence, be further investigated with sucha mechanistic model when the needed data becomeavailable. Future efforts should be given to determinethe lipids content and composition in microsomesfor additional prediction scenarios. Consequently, theproposed generic and mechanistic model would notpredict a single fuinc value, but rather a range of val-ues based on the observed variability. Conversely, thepublished empirical models may only predict a singlevalue of fuinc because they are based solely on physic-ochemical data.

One way to investigate how sensitive is fuinc tochanges in lipid concentration and composition in themicrosomes is presented in Figure 8. For rat, moredata on microsome composition were readily availablefrom the literature. Computing fuinc in rats by con-sidering two batches of rat liver microsomes reportedfrom the literature (Table 3), we demonstrate that thecalculated value of fuinc may change by a factor of up tothreefold due to differences in composition. Therefore,this exercise validates the hypothesis that variabilityin the microsome composition can be reflected in thepredictions of fuinc of drugs. Only one batch of livermicrosomes was considered for the lipid compositionin human in contrast to rat, for which two batches ofliver microsomes were considered. Then, this mightpartly explain why the prediction performance is rel-atively superior for rat as compared with the humandataset of drugs. The experimentally determined fuincwas obtained from more than one in vitro study1,3–11

and consequently, more than one batch of human livermicrosomes were used.

In addition, we explored the interspecies differ-ences in fuinc. In this context, Zhang et al.25 showedthat the species differences in fuinc of drugs are gen-erally small (i.e., within twofold). This is not surpris-ing because the rat and human microsome composi-tions seem relatively similar on an average (Table 3).Therefore, a similar value of fuinc was simulated in



rat and human. Nevertheless, there are exceptionslike some lipophilic strong bases. For amiodarone,the animal and human fuinc obtained experimentallydeviated by a factor of up to 10-fold,25 whereas forimipramine, the deviation is about threefold (thisstudy). For example, fuinc of imipramine showed a rel-evant interspecies difference (rat, 0.16; human, 0.46)at the same Cp (1 mg/mL), to which only the pro-posed microsome composition-based model predictedthis difference. The rationale of this interspecies dif-ference is explained below. As mentioned, the accu-mulation of cations in the acidic phospholipids is amajor mechanism for distribution of a strong basicdrug (at least one pKa ≥ 7).13,14,16,24 Moreover, theinput parameter (Pea) used to estimate the binding toacidic phospholipids impacts the prediction of fuincto a significant extent (Fig. 9). It is common thatthe value of Pea varies significantly across species(e.g., imipramine) and consequently, this may ex-plain why the microsome composition-based modelpredicted better the significant species differences infuinc observed with imipramine. In addition, it hasbeen observed that the value of Pea may significantlyvary with drug concentration.26 Another aspect thatmight be of interest for a basic drug is the poten-tial impact of stereoselectivity on the prediction offuinc. It is known that stereoselectivity influences theionic binding to acidic phospholipids for strong ba-sic drugs, which affects the input parameter Pea be-cause it may also vary significantly across the enan-tiomers (e.g., R and S).16 In this study, however, onlythe racemic mixture has been investigated based onthe availability of data. Hence, another advantage ofthe microsome composition-based model as comparedwith the published empirical models is its capacityto consider a potential change in Pea that may affectfuinc predictions and consequently, hepatic clearance(CL) predictions. The latter is important because ba-sic amines require knowledge of Pea (to get an esti-mate of Papla) and that information may not alwaysbe gathered routinely in drug discovery. Because thisinput parameter seems highly relevant for a strongbasic drug based on this study, its estimation becameessential. In this case, in vitro studies are availablein the literature.14,16,26

The use of information on Pea or log Pow to estimatethe binding of a basic drug to the acidic phospholipidsis probably not as simple as suggested. In other words,relying on drug lipophilicity (Halifax and Houstonand Turner et al.) or to the erythrocyte–buffer ra-tio (this study) might provide a rough estimate ofthis process in liver microsomes in more or less cases.Moreover, it has been reported that specific strong ba-sic drugs (e.g., antiarrhythmic agents) may not onlybind to the acidic phospholipids, but also to some addi-

tional binding targets like particular ion channels orcation transporters, which affected the prediction ofdrug distribution.16 Such additional binding targets,which might also be present in the endoplasmic retic-ulum, have not been considered in this study. Theseaspects may explain why the prediction performanceobtained from the basic drugs that are mainly in theirionized form at the physiological pH was in generalrelatively lower than those obtained for the acidicand more neutral compounds for all models tested(Table 4).

Finally, we explored how sensitive is fuinc tochanges in Cp (Fig. 7). Recently, Gertz et al.9 madea comparative assessment of the models of Austinet al. and Halifax and Houston for several classesof drugs (acid, base, and neutral). These authorsfound that both models investigated showed very goodagreement in the fuinc estimates especially at lowCp (<0.5 mg/mL), in particular for drugs with lowlipophilicity. As overall prediction accuracy was thehighest at low Cp and for low lipophilicity drugs, itwas suggested that it is probably not prudent to per-form fuinc estimates at the highest Cp for new chem-ical entities that are relatively lipophilic.9 The cur-rent dataset is particularly poor in terms of highlyhydrophilic (log Pow < 1) and highly lipophilic (logPow > 5) drugs. Nevertheless, for log Pow values rang-ing from 2 to 5, fuinc has mostly been under-predictedat the highest Cp by the empirical models, which doesnot seem to be the case for the microsome composition-based model (Fig. 7). Again, this could be another ad-vantage of the proposed composition model.

Special consideration was given to the develop-ment of a microsome composition-based model forrat and human. Therefore, one may need to extendthe current microsome composition-based model toother species. The principle of the proposed micro-some composition-based model is applicable to otherspecies such as mouse, dog, and monkey. This canbe applied as soon as the essential physiological in-put data on the content of lipids in microsomes be-come available in the literature. In addition, for abiprotic acid, biprotic base, and zwitterion, a micro-some composition-based model can also easily be im-plemented just by estimating the specific ionizationterm used in the microsome composition-based model(Im, Ie, Ip) as Peyret et al.13 recently did for tissuedistribution prediction. Finally, a recent study haspointed toward an essential contribution of fuinc ina physiologically-based model of liver for simulationof drug–drug interaction at the subcellular level.12

Consequently, we consider that a combination of thisnovel liver model with this present study can pro-vide a meaningful physiological model for drug–druginteraction.



CONCLUSION

In summary, analysis of the current rat and humandatasets suggests that prediction of fuinc in incubatedmedium based on microsome composition data is fea-sible, considering the relatively high level of accu-racy obtained in this study. The proposed model canbe viewed as a combination of two distinct processes,namely, the nonspecific binding to neutral lipids andionic binding to acidic phospholipids. The microsomecomposition-based model and correlation proceduresfrom Halifax and Houston and Turner et al. werethe best performing prediction methods. The statisti-cal analyses conclude that the prediction models aremore effective at computing fuinc for rat as comparedwith that for human, and for acids and neutral drugsas compared with that for strong basic drugs. Thisis to be expected, given the challenging physicochem-ical properties of relatively lipophilic ionized bases.The sensitivity analysis should facilitate the identifi-cation and prioritization of the determinants of drugpartitioning into liver microsomes. Both lipophilicityand microsome composition affected the fuinc predic-tions, and this is more noticeable at higher log Powvalues and concentrations of microsomal protein andlipid. Furthermore, for a strong basic drug the bind-ing to acidic phospholipids is predominant. There arealways opportunities to improve predictive models be-cause there is the issue of variability and uncertainty.However, by using a mechanistic approach, this wouldhelp considering this issue across drug development.Overall, the results obtained with our proposed modeldemonstrate a significant step toward the develop-ment of a generic and mechanistic model of rat andhuman fuinc for liver microsomes, which should pro-vide more rationale extrapolation procedures of hep-atic clearance using a physiologically-based pharma-cokinetics modeling approach.

APPENDIX

The appendix contains the equations of the empir-ical prediction models of fuinc investigated by otherauthors, namely, the models of Austin et al., Turneret al., and Halifax and Houston.4–9

Prediction Model of Austin Et Al.

The Austin et al. model use log Pow or log Dow as acovariate of fuinc:

fuinc =[

11 + Cp × 100.56×LogPow/Dow −1.41

](11)

where Cp is the microsomal protein concentration re-ported in the in vitro studies and log Pow and log Doware the log n-octanol–buffer ratio corresponding to theunionized and ionized drugs at pH 7.4, respectively

(Tables 1 and 2). Log Pow is used with all basic andneutral drugs, whereas log Dow is used with all acids.For comparability reason with this present study, dataon drug lipophilicity at 37◦C were used (Tables 1 and2).

Prediction Model of Halifax and Houston

Similarly, the Halifax and Houston model use log Powor log Dow as a covariate of fuinc:

fuinc =[1

1 + Cp × 100.072×LogPow/D2ow+0.067×LogPow/Dow−1.126

]

(12)

Prediction Model of Turner Et Al.

The Turner et al. model (also named the Simcypmodel4) use log Pow alone for each ionization stateclass (acid, base, and neutral) as a covariate of fuinc.

predominantly Ionized Bases (pKa ≥ 7.0)

fuinc =[

11 + Cp × 100.58×LogPow−2.02

](13)

predominantly Ionized Acids

fuinc =[

11 + Cp × 100.20×LogPow−1.54

](14)

predominantly Neutral Compounds

fuinc =[

11 + Cp × 100.46×LogPow−1.51

](15)

ACKNOWLEDGMENTS

The authors would like to kindly offer their gratitudeto Rudolfo Gasser, Christoph Funk, and Thierry Lave,at F. Hofmann-la Roche, Basel, Switzerland, for theirassistance and support. This study was supported bya Discovery Grant from the National Sciences andEngineering Research Council of Canada (NSERC).

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