The need to incorporate the fraction unbound in microsomes (fu_mic) to obtain meaningful drug concentrations for the prediction of intrinsic clearance and cytochrome P450 inhibition potential is widely accepted (Obach, 1996; Ito and Houston, 2005; Rostami-Hodjegan and Tucker, 2007). Recently, two equations based on drug lipophilicity have been developed for prediction of fu_mic (Austin et al., 2002; Hallifax and Houston, 2006) that avoid experimental determinations. The limitations of these empirical predictive tools and their applicability for fu_mic predictions over a range of lipophilicity and microsomal protein concentrations have been addressed (Gertz et al., 2008).

Analogous to applying a correction for microsomal drug binding to in vitro clearance and inhibition parameters, it is important that the fraction unbound in hepatocyte incubations (fu_hep) is also considered for in vitro-in vivo extrapolation (McGinnity et al., 2006; Brown et al., 2007b). However, this need has yet to be broadly applied, perhaps due to the lack of comprehensive demonstration of its value. In a recent study by Austin et al. (2005), the extent of binding between the microsomal and hepatocyte incubations was compared using hepatocyte data (n = 14) and the corresponding fu_mic from a previous study (Austin et al., 2002). The authors proposed a linear 1:1 relationship between microsomal and hepatocyte binding for incubations of 1 mg/ml and 10⁶ cells/ml, respectively, indicating that the fu_hep can be extrapolated from microsomal studies. However, the applicability of this correlation has been questioned because of the small number of compounds investigated (Hallifax and Houston, 2007).

To further explore the relationship between binding in microsomal and hepatocyte systems, a detailed analysis was carried out involving 39 drugs. A nonlinear empirical equation is proposed as an alternative to the linear relationship to relate binding between the two systems. In addition, prediction of fu_hep directly from the logP/D metric is assessed over a wide range of lipophilicity (-0.13 to 5.93). The implications of these findings on the estimation of hepatocellular drug concentration for intrinsic clearance and inhibition parameter predictions are discussed.

Materials and Methods

A database of 39 drugs and their corresponding fu_mic and fu_hep values was collated either from in house data or from the literature (Austin et al., 2002, 2005; Brown et al., 2007a; Hallifax and Houston, 2007). In the aforementioned studies, different methods were used to determine the drug binding in hepatocyte incubations, namely oil centrifugation (using live cells), dialysis (using dead cells), and ultrafiltration (using dead cells). Microsomal and hepatocyte binding are defined by eqs. 1 and 2, respectively: where K_a represents microsomal protein binding affinity, P the microsomal protein concentration (mg/ml), K_p the hepatocyte/medium concentration ratio, and V_R a V_cell/V_inc ratio, where V_cell is the cell volume and V_inc the incubation volume (Brown et al., 2007b; Hallifax and Houston, 2007). V_R is 0.005 at the cell concentration of 10⁶ cells/ml (Brown et al., 2007b). Where multiple fu_mic/hep values were obtained, a mean value was used for the comparison. In cases where the fu_mic or fu_hep were obtained at different microsomal protein or cell concentrations, reported values were standardized to give fu_mic or fu_hep values at 1 mg/ml and 10⁶ cells/ml, respectively.

To investigate the relationship between drug binding in hepatocytes and microsomes, an equation was obtained by dividing eq. 2 by 1 and rearranging it to produce: To allow the calculation of fu_hep from drug lipophilicity, the fu_mic term in eq. 3 was substituted with the Hallifax and Houston (2006) equation (eq. 4). This fu_mic predictive equation is based on either logD_7.4 (for acidic and neutral drugs) or logP (for bases) as descriptors for drug lipophilicity:

The final equation for the prediction of fu_hep directly from logP/D data is eq. 5: Predicted fu_hep for 39 drugs was compared with the observed values and their respective logP/D, ranging from -0.13 to 5.39.

Results and Discussion

The database (Table 1) covered a range of physicochemical properties, including 8 acids, 18 bases, and 13 neutrals. The fu_mic ranged from 0.01 to 1.00 for astemizole and warfarin, respectively, whereas the fu_hep ranged from 0.03 to 0.99 for α-naphthoflavone and tolbutamide, respectively.

At the conditions investigated by Austin et al. (2005), that is, at P = 1 mg/ml and cell concentration of 10⁶ cells/ml, the nonlinear relationship (eq. 3) between the experimentally obtained fu_mic and fu_hep was found to be a better descriptor than the proposed linear relationship. Figure 1A shows the data for 39 drugs together with the nonlinear fit using eq. 3 with a K_p/K_a ratio of 125 and V_R/P of 0.005; also shown is the linear relationship (line of unity). The proposed relationship between fu_mic and fu_hep (eq. 3) results in predictions for 87% of the compounds investigated within 1.5-fold of the observed value. When a linear relationship between microsomal and hepatocyte binding is assumed, the proportion outside 1.5-fold from the line of unity is higher (28% in comparison with 13% in the case of nonlinear equation). However, in both cases the outliers include drugs with a logP/D >3, with astemizole, fluoxetine, and quinine as drugs with the most pronounced discrepancy between fu_mic and fu_hep. In addition, the precision error (Fig. 1B) for linear relationship is greater, in particular for drugs with fu_hep <0.4. Equation 3 allows the prediction of fu_hep from existing microsomal binding data.

Equation 3 was extended to allow calculation of fu_hep directly from drug lipophilicity by substituting the fu_mic term by the Hallifax and Houston (2006) equation (eq. 4). This equation was selected over the equation proposed by Austin et al. (2002), as recent analysis has shown that this tool provided more accurate fu_mic predictions, in particular for lipophilic drugs (logP/D = 2.5–5) and at higher microsomal protein concentrations (Gertz et al., 2008). The resulting nonlinear empirical model (eq. 5) allowed the prediction of fu_hep directly from logP/D.

The ratio of predicted (eq. 5) to observed fu_hep values was compared with the respective drug lipophilicity ranging from -0.13 to 5.93 (caffeine and miconazole, respectively). Figure 2 shows the relationship between the predicted/observed fu_hep and the logP/D for the 39 drugs investigated. The prediction accuracy of the derived equation is high for relatively hydrophilic drugs (logP/D ≤ 2.5), with 89% falling within 1.5-fold of the line of unity. The only outlier in this lipophilicity range is cortisol, where the predicted fu_hep is 4.4-fold greater than the observed value. In the intermediate lipophilicity range (logP/D = 2.5–5), 35% of the compounds are outside 2-fold of the predicted/observed ratio. Less accurate prediction of the fu_hep for lipophilic drugs (logP > 3) is consistent with the limitations observed for microsomal binding predictions (Gertz et al., 2008). In addition, the impact of variability in the logP/D estimates on the prediction of fu_hep was investigated. Analogous to microsomal binding situation (Gertz et al., 2008), a propagation of 20% variation in logP had a negligible effect on fu_hep at low lipophilicity. However, at increasing lipophilicity (logP ≥ 5), 20% variation on logP resulted in more than 15-fold difference in the fu_hep predictions.

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Fig. 1.

A, comparison of binding in hepatocytes at a concentration of 10⁶ cells/ml and binding in microsomes at a concentration of 1 mg/ml for 39 drugs. Data shown as fractions unbound in the respective incubations. The solid line represents the fit to eq. 3 with a K_p/K_a ratio of 125 and dashed line represents the line of unity. B, comparison between precision error (expressed as predicted/observed value on a log scale) and predicted fu_hep for 39 drugs. • and ○ represent predicted fu_hep using either nonlinear (eq. 3) or linear empirical model, respectively.

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Fig. 2.

Comparison between precision error (expressed as predicted/observed fu_hep ratio) and lipophilicity (logP/D) using eq. 5. Areas of low (logP/D ≤ 2.5), intermediate (logP/D = 2.5–5), and high (logP/D ≥ 5) lipophilicity are indicated. Dashed and dotted lines indicate 1.5- and 2-fold of the line of unity, respectively.

In conclusion, a nonlinear empirical equation has been proposed that allows successful prediction of fu_hep using either fu_mic or a lipophilicity metric. The nonlinear equation shows comparable accuracy to microsomal binding prediction equations and results in lower bias in the fu_hep prediction in comparison with a previously proposed linear relationship. This is particularly evident for drugs with fu_hep <0.4, for which the accurate assessment of nonspecific binding will have a significant impact on prediction of intrinsic clearance. Prediction of hepatocyte binding must be undertaken with caution for drugs with logP/D ≥3 because of the impact of inaccuracies in logP/D estimates and the general inaccuracy of the predictive tools in this lipophilicity area. Based on the current data set, this is evident for basic and neutral drugs, whereas hydrophilic acidic drugs tend to have high fu_hep (fu_mic) values and are generally well predicted. In addition, for drugs for which hepatocellular uptake is not limited to simple partitioning [e.g., lysosomal uptake for bases at low drug concentrations (Hallifax and Houston, 2007) or active uptake in hepatocytes (Hirano et al., 2006; Ho et al., 2006)], the prediction of fu_hep will be further complicated. However, as a general guide, eqs. 3 and 5 provide a reasonably accurate and straightforward method to calculate fu_hep to allow correction of hepatocellular drug concentration for intrinsic clearance and inhibition parameter predictions.