Increasing importance has been given in the past few years to active drug transport processes in pharmacokinetics (Chandra and Brouwer, 2004; Shitara et al., 2006). In addition to metabolism, elimination of drugs can be strongly dependent on hepatic and/or renal transport processes and drug-drug interactions can be transporter-related as well (Petzinger and Geyer, 2006; Poirier et al., 2007). In the liver, the interplay between uptake and export processes influences the drug intracellular concentration and thereby the amount of drug available for metabolic elimination and/or biliary excretion. Therefore, hepatic uptake of new chemical entities is increasingly studied in preclinical development.

Primary hepatocytes, plated or in suspension, as well as cell lines overexpressing individual transporters, are widely used to assess active hepatic uptake processes (Komai et al., 1992; Ismair et al., 2001; Shitara et al., 2003; Ho et al., 2006; Poirier et al., 2007). Nevertheless these cellular systems represent only one component of the dynamic and interlinked processes occurring in liver tissue. Therefore, it remains a major challenge to predict quantitatively hepatic transport processes based on in vitro data (Bentz et al., 2005; Hallifax and Houston, 2006; Liu and Pang, 2006; Ekins et al., 2007; Webborn et al., 2007). Additional processes, such as nonspecific binding and bidirectional passive diffusion between medium and cells need to be assessed separately from active transport to enable proper mechanistic scaling. In particular, for lipophilic compounds, extensive adsorption to cells and culture materials is often observed (Ishiguro et al., 2006).

In hepatocytes, passive processes are typically assessed in a parallel incubation at 4°C to disable any active transport proteins (Komai et al., 1992; Ismair et al., 2001; Shimada et al., 2003; Lancon et al., 2004; Treiber et al., 2004; Ho et al., 2006). However, whereas active transport is inhibited at low temperature, passive processes might also be altered as membrane fluidity decreases (Frezard and Garnier-Suillerot, 1998; Neuhoff et al., 2005; Webborn et al., 2007). Nevertheless, these limitations in the control incubations performed at low temperature have not been addressed systematically in uptake experiments up to now. Alternatively, active transport processes might be inhibited by specific inhibitors to assess the remaining passive processes. However, such selective inhibitors are not yet available for many of the transporters relevant in drug distribution and elimination (Hirano et al., 2006; Webborn et al., 2007). In addition they might also influence many other processes in the cell systems used (Boelsterli et al., 1988; Ratanasavanh et al., 1996). Optionally, passive processes can be assessed by including in the experiment high concentrations in which active transport processes are saturated, allowing the determination of passive diffusion processes (Hirano et al., 2004; Yamashiro et al., 2006). However, the high substrate concentrations used in this approach may lead to a deviation from a linear uptake rate, in particular for highly lipophilic compounds (Baker and Parton, 2007; Parker and Houston, 2008) (see Fig. 5). Therefore, the typically performed single incubation time points are not appropriate and linear conditions, resulting in true initial transport rates, cannot be assumed. Mechanistic approaches to analyze in vitro transport data have hence been discussed recently (Gonzalez-Alvarez et al., 2005; Baker and Parton, 2007).

Kinetic parameters of drug transporters are usually assessed in a stepwise procedure. Initial uptake rates are determined on the basis of a single incubation time point for multiple concentrations, followed by a determination of the basic Michaelis-Menten parameters (K_m and V_max) in a second step (Komai et al., 1992; Ismair et al., 2001; Treiber et al., 2007). However, initial rates based on multiple measured time points are rarely established, although they are an important prerequisite of Michaelis-Menten kinetics, and for many compounds the assumption of linear initial transport rates might be violated in the presence of the bidirectional passive diffusion, the nonspecific binding, and the decrease in extracellular concentration. In the proposed mechanistic model, using multiple time points determined in vitro, such time-dependent nonlinearities can be described and the underlying processes can be better quantified.

In the present study, the experimental setup for in vitro assays was optimized with respect to both active and passive processes. Taurocholate, estrone-3-sulfate, CCK8, deltorphin II, fexofenadine, napsagatran, pravastatin, pitavastatin, and fluvastatin were chosen as well known substrates of multiple uptake transporters (van Montfoort et al., 2003; Kopplow et al., 2005). In addition, two proprietary compounds and propranolol, as a highly permeable compound, were included to cover a broad range of physicochemical parameters. A mechanistic mathematical model addressing the time-dependent changes in compound concentrations and the underlying passive (P_dif) and active processes was developed. It allowed a standardized assessment of in vitro transport data to derive V_max, K_m, P_dif, and nonspecific binding values. The robustness of the approach was tested using both experimental data from in vitro transport experiments and theoretical transport data. The improved experimental conditions in conjunction with the mechanistic model for data evaluation were found to deliver transport kinetic data of greatly improved quality, a prerequisite for subsequent extrapolation to in vivo using physiologically based pharmacokinetic models.

Materials and Methods

Materials. [³H]Fexofenadine and [³H]pravastatin were obtained from Moravek Biochemicals (Brea, CA); [³H][d-Ala2]-deltorphin II, [³H]taurocholic acid, [³H]propranolol, and [³H]estrone-3-sulfate were from PerkinElmer Life and Analytical Sciences (Waltham, MA); [³H]pitavastatin calcium was from American Radiolabeled Chemicals (St. Louis, MO); [³H]CCK8 was from GE Healthcare (Chalfont St. Giles, UK); pravastatin and pitavastatin calcium were from APIN Chemicals Ltd. (Abingdon, Oxon, UK); [d-Ala2]-deltorphin II and CCK8 were from Bachem (Bubendorf, Switzerland); and propranolol, fexofenadine, estrone-3-sulfate, and taurocholic acid were from Sigma-Aldrich (Buchs, Switzerland). [¹⁴C]Napsagatran and napsagatran were produced in house (structure in Ries and Wienen, 2003). All cell culture media and reagents were purchased from Invitrogen (Paisley, UK), and standard tissue culture flasks and 24-well plates were from BD (Franklin Lakes, NJ).

PAMPA Experiments. As described previously (Fischer et al., 2007), for the PAMPA assay, a “sandwich” was formed from a 96-well filter plate and a 96-well in-house-made Teflon plate, such that each well is divided into two chambers: donor at the bottom and acceptor at the top, separated by a microfilter with a pore size of 0.45 μm polyvinylidene fluoride from Millipore Corporation (Billerica, MA), coated with a 10% (w/v) egg phosphatidylcholine and 0.5% (w/v) cholesterol dissolved in dodecane. Compounds were introduced as 10 mM DMSO stock solutions in a 96-well microtiter plate. An automated liquid handling system draws an aliquot of the DMSO and mixes it into a buffer solution [0.05 M 3-(N-morpholino)-2-hydroxypropanesulfonic acid with 0.5% (w/v) glycocholic acid at pH 6.5], so that the final sample concentration is 150 μM and the DMSO concentration is 1.5% (v/v). A part of the sample solution was filtered, using a 96-well polyvinylidene fluoride filter plate from Corning Inc. (Corning, NY), and added to the donor compartments. In the acceptor compartment the same buffer system at the same pH but devoid of glycocholic acid is used as in the donor compartment. After an 18-h incubation at 4°C or 37°C, the sandwich plates were separated, and both the donor and acceptor compartments were measured for the amount of material present, by comparison with the UV spectra (250–500 nm) obtained from reference standards. All measurements were done in triplicate. Effective permeability values (Pe) were calculated as described previously (Avdeef et al., 2001; Fischer et al., 2007). PAMPA Evolution Software (version 3.3; pION Inc., Woburn, MA) was used for all Pe calculations.

OATP-Expressing Cell Lines. Chinese hamster ovary (CHO) cells overexpressing Oatp1a1 or OATP1B1 were transfected, respectively, with a pTriEx-3 Neo-Oatp1a1 or OATP1B1 construct as described previously (Noe et al., 2007). Single clones were selected on the basis of functional activity and characterized. The CHO cells overexpressing Oatp1b2 and OATP1B3 were obtained from the laboratory of Peter Meier-Abt (University of Zürich, Zürich, Switzerland). Culturing of the cells was performed as described previously (Noe et al., 2007). CHO cells were grown in Ham's F-12K medium-2.5 g/l sodium bicarbonate, supplemented with 10% fetal calf serum, penicillin-streptomycin solution plus geneticin (0.5 mg/ml) for CHO-Oatp1a1, CHO-OATP1B1, and CHO-OATP1B3 or hygromycin (0.5 mg/ml) for CHO-Oatp1b2 cells. Cells were cultivated at 37°C in a humidified 5% CO₂ cell culture incubator. For the transport assay, cells were split as follows: cells from a confluent 75-cm² flask (detached with trypsin-EDTA) were uniformly resuspended in the desired volume of Ham's F-12K medium. One milliliter of the uniformly resuspended cells (2 × 10⁵ cells/ml) was added to each well of a 24-well plate. The cells were used for transport assays 38 to 42 h later, when they were 80 to 90% confluent.

Preparation and Plating of Primary Rat Hepatocytes. Isolation and conventional primary culture of rat hepatocytes were performed as described previously (Luttringer et al., 2002; Blanchard et al., 2004). Hepatocytes were isolated from adult male Wistar rat (∼250 g) liver by a previously described two-step collagenase perfusion method (Seglen, 1979; Luttringer et al., 2002). Cell viability was determined from exclusion of erythrosine-B by the cell membranes. Only the cell preparations that exhibited a viability more than 80% were retained for further studies. Freshly prepared hepatocytes were seeded at 4 × 10⁵ cells/well on precoated 24-well plates (BD BioCoat Collagen I). Cells were cultured for 3 h in a humidified chamber maintained at 37°C and 5% CO₂ in attachment medium composed of Williams' E medium supplemented with 10% fetal calf serum, 0.5% streptomycin/penicillin, insulin (1.2 μM), and glutamine (400 μM).

In Vitro Uptake Experiments. Recombinant cells or hepatocytes were prepared as outlined above, and the uptake assays were performed as described previously with minor modifications (Noe et al., 2007). Assays were run using two or three wells as one set. The medium was removed from the wells by aspiration. The wells were washed once at 37°C with 1 ml of Hanks' balanced salt solution (HBSS) (Invitrogen, Carlsbad, CA) for cell lines or HBSS containing calcium and magnesium for hepatocytes. The uptake experiment was started by aspiration of wash buffer and addition of 150 μl of a prewarmed 37°C (or ice-cold for 4°C incubation) HBSS solution containing the substrate of interest. The plate was transferred on a 37°C heating block (Eppendorf) (or on ice for 4°C incubation). After the incubation time, the plate was removed from the heating block and immediately 1 ml of ice-cold PBS containing 0.2% bovine serum albumin (BSA) was added to stop the transport activity with the ice-cold buffer and the large volume of PBS effectively diluting the compound (stop step). The solution was removed by aspiration. BSA was also included in the subsequent washing buffer to minimize background due to nonspecific binding of radiolabeled compound. The following washing steps were performed rapidly with warmed (37°C) or ice-cold (4°C) buffer as indicated in the respective experiments. The cells were washed twice with PBS containing 0.2% BSA, with 2 ml each (first and second wash steps), and once with PBS without BSA (3 ml) to remove added BSA protein (third wash step). Then 0.5 ml of 1% Triton X-100 was added to solubilize the cells. After incubation for 15 min on a heated shaker at 60°C, 0.25 ml of the solubilized cell mix was added to 4 ml of scintillation fluid and radioactivity was determined by liquid scintillation counting. Protein content was determined for each well using the Pierce BCA assay (Pierce, Rockford, IL) with BSA as the standard according to the manufacturer's protocol.

Kinetic in Vitro Experiment. Kinetic experiments were carried out as described above on 24-well plates. One experiment consisted of the drug of interest incubated at six to eight different concentrations, which were adjusted after a first experiment to cover K_m and P_dif evaluation. Three different time points were used per drug concentration (usually 30, 60, and 90 s), and each time point was done in duplicate. Kinetic parameters were calculated from three independent experiments using either different batches of cells or hepatocytes prepared from three different rats.

Data Analysis of Kinetic Experiments and Mechanistic Model. The cellular uptake process consists of both an active, saturable process, and a passive component. The active transport can be characterized by Michaelis-Menten parameters (V_max and K_m), whereas the passive process is represented by the passive diffusion P_dif. Two different methods, the conventional two-step approach and a mechanistic model, were compared for the estimation of V_max, K_m, and P_dif.

Conventional two-step approach. The kinetic analysis of experimental data consisted of two consecutive steps. In the first step, measured compound accumulation in cell reported as milligrams of protein (B_intracell in picomoles per milligram) was plotted against time for each incubation medium concentration (C_me in micromolar concentrations, nominal values). This intracellular accumulation was assumed to be the sum of an initial binding α and a linear increase with time at a constant rate v₀. The following equation (eq. 1) was used to fit α and v₀ for each C_me tested:

In this first step, duplicates for each of the three time points were fitted, corresponding to six data points per concentration. In the second step, initial uptake rates were plotted against medium concentrations, and V_max, K_m, and P_dif were fitted according to eq. 2. It was assumed in this model that the initial uptake rate (v₀) is a function of the medium concentration, with contributions of active uptake (Michaelis-Menten) and passive unidirectional diffusion (from medium into cells). The number of points available for fitting in the second step depended on the number of medium concentrations tested (six to eight). V_max was expressed in picomoles per minute per milligram, K_m as a micromolar concentration, and P_dif in microliters per minute per milligram.

Mechanistic model. The in vitro assay was described by two compartments corresponding to the incubation medium for one well (volume V_me, nominal value of compound concentration C_me as a micromolar concentration) and intracellular space of all cells in one well [volume V_intracell, quantity of compound in one well, A_intracell, in picomoles, and compound concentration as a micromolar concentration: C_intracell = (A_intracell/V_intracell)] as depicted in Fig. 1. The volume V_me was 150 μl. For the determination of V_intracell (in microliters), the total quantity of protein per well (U_intracell in milligrams) was converted to number of cells by applying an experimentally determined constant of 1 mg of protein/1 million rat hepatocytes [1.06 ± 0.18 mg/10⁶ cells (n = 5), similar to a reported value (Shitara et al., 2004)] or 0.15 mg/1 million CHO cells (0.152 ± 0.032 mg/10⁶cells, n = 11). A cell volume of 3.9 μl/1 million hepatocytes (Reinoso et al., 2001) or 1.40 μl/1 million CHO cells [mean of two publications: 1.28 μl (Sarkadi et al., 1984) and 1.53 μl (Vickers et al., 1993)] was then applied to calculate the intracellular volume in microliters in one well (V_intracell).

The time course of the quantity of compound in the intracellular compartment was modeled by the following differential equation: In eq. 3 bidirectionality of passive diffusion was included by the introduction of the last, time-dependent, term in this equation (-P_dif × C_intracell). In control cells (i.e., CHOneo cells incubated at 4 or 37°C or rat hepatocytes incubated at 4°C) the active uptake process was omitted and the following equation was used to estimate P_dif: In eqs. 3 and 4, V_max was expressed in picomoles per minute, K_m as a micromolar concentration, and P_dif in microliters per minute and were calculated parameters for a one-well equivalent. Thus, with U_intracell being the total amount of protein in one well (milligrams), the V_max and P_dif obtained in eqs. 3 and 4 needed to be converted as follows:

A nonzero initial condition for the intracellular amount was used for eqs. 3 and 4 to account for nonspecific binding (to cells and/or experimental supports). The amount of compound bound initially was assumed to be proportional to C_me and V_intracell with the constant f_b being the bound fraction (eq. 5).

This mechanistic in vitro model was implemented in ModelMaker (version 4; FamilyGenetix Ltd., Wallingford, Oxfordshire, UK). Numerical integration was performed using the Runge-Kutta method. The Marquardt optimization algorithm was used to simultaneously estimate the parameters f_b, V_max, P_dif, and K_m. In a typical kinetic experiment using this method, all data points were fitted in a single step using eq. 3, with duplicates for each of the three time points for each concentration, resulting in 36 to 48 data points.

Computer generation of virtual data sets. To cover extended compound properties, eight different scenarios of P_dif, nonspecific binding, V_max, and K_m were generated, each of which consisted of six sets of data. One data set consisted of seven concentrations (C_me) (0.3–300 μM) with three time points each (30, 60, and 90 s) and duplicate C_intracell per time point, corresponding to one virtual experiment (42 C_intracell or 42 virtual wells). The data sets were generated (using the random number generation function of Excel) through random sampling, assuming normal distribution with an S.D. of 10% and solving of eq. 3 to generate the intracellular concentration as a function of time. Each data set was then analyzed with both the conventional two-step approach and the mechanistic model.

Statistical Evaluation of Data. S.D.s were calculated for all parameters obtained from the individual experiments. Triplicate experiments were run, and mean values were calculated for all parameters. The S.D.s were propagated following the rules of propagation of errors (Lindberg, 1997) to account for the uncertainty due to the measurement.

To compare the mean P_dif calculated in different experimental conditions, Student's t test was used to test the equality of the means. To compare the accuracy of the two different approaches of kinetic analysis, Student's t test was used to test the equality of the coefficient of variation in each population. To compare the ability of evaluating an identical K_m for selective substrates, Student's t test was used to test the equality of the K_m in CHO-Oatp1b2 cells and rat hepatocytes for CCK8 and deltorphin II for each data analysis method separately. For all tests, the null hypothesis was rejected for p ≤ 0.05.

Results

Reduction of Nonspecific Binding to Cells and Cell Culture Plates. Typically, much less than 0.1% of the radiolabeled substrate supplied in the incubation medium enters the cells. Efficient washing of excess substrate is therefore of particular importance when cell-associated compound is assessed. In initial experiments, high nonspecific binding was observed to cells, to culture plates, and to the collagen layer for hepatocytes. This nonspecific binding was compound- and temperature-dependent and therefore difficult to control, in particular for highly lipophilic compounds incubated with hepatocytes.

To reduce nonspecific binding to cell culture plates, binding of deltorphin II, CCK8, taurocholic acid, and pravastatin to collagen-coated and noncoated plates was assessed using different washing temperatures. These empty plates were treated the same as plates with cells. A significant decrease in nonspecific bound radioactivity was observed for all substrates tested (67 ± 12% mean decrease) if washing of the plate was performed at 37°C instead of at 4°C.

A similar effect was seen for plates containing cells. Although the last wash step was virtually devoid of radioactivity (0.02–0.09%), suggesting efficient washing of nonspecifically bound radioactivity, the overall recovery of radioactivity could be improved from 80 to 96% at 4°C to 85 to 100% at 37°C. This increased efficiency of washing at 37°C was seen particularly if high drug concentrations were tested.

To ensure that the reduced residual cellular substrate levels were not due to increased cell leakage at 37°C, the first wash step was extended over 7 min to follow radioactive substrate leakage over this prolonged time interval. Comparable leakage was observed irrespective of the temperature for several compounds and cell lines, including rat hepatocytes. The example of deltorphin II in CHOneo (control) and CHO-Oatp1b2 cells is shown in Fig. 2. By comparing the extended washings at 4 and 37°C, an equivalent slope and, hence, leakage were seen irrespective of the washing temperature. The initial difference in cell-associated compound is considered to be due to improved efficiency of the washing at 37°C. By keeping each wash step as short as possible in routine assays, the leakage can be minimized and the nonspecific binding reduced by the washing at 37°C.

Evaluation of P_dif in Cell Lines and Hepatocytes. The passive diffusion was assessed at 37 and 4°C using an artificial phospholipid membrane (PAMPA), different cell lines, and hepatocytes for five transporter substrates plus propranolol as a high passive permeability compound. A significant temperature-dependent difference in drug uptake was observed in PAMPA and CHOneo cells, believed not to express any drug transport activity (Fig. 3). For all compounds a linear, concentration-dependent increase of cell-associated compound was observed in CHOneo cells, without indication of any saturable process. The passive diffusion of these compounds in the cellular system resulted in a ranking comparable to the one obtained on the basis of measured permeabilities for artificial membranes (Pe from PAMPA), supporting the fact that mainly passive diffusion was observed in those CHOneo cells. A statistically significant underestimation of both P_dif and Pe was observed when CHOneo cells and artificial membranes were incubated at 4°C instead of 37°C (Fig. 3). The temperature-dependent effects were particularly high for fluvastatin and fexofenadine with 7.6- and 16-fold decreased apparent “uptake” in the 4°C control incubation of CHOneo cells. On the other hand, the smallest temperature effects were observed for compounds with extreme permeability values, either low (estrone-3-sulfate and taurocholate) or very high (propranolol).

The passive diffusion of three Oatp transporter substrates was evaluated using CHO control cells and the same cells overexpressing either Oatp1a1 or Oatp1b2 transporter. Kinetics were determined at 37°C in triplicate for each compound, and the passive diffusions were evaluated using either eq. 3 for the Oatp-overexpressing cells or eq. 4 for the CHO control cells (Fig. 4A). Low passive diffusion was observed for deltorphin II and CCK8 (all <0.1 μl/min/mg), whereas fexofenadine had a higher passive diffusion of approximately 7 μl/min/mg. For each compound, a comparable passive diffusion could be observed in CHO-Oatp cells using eq. 3, which includes active and passive transport, and in CHOneo cells using eq. 4, which includes only passive transport. These results support the assumption that CHOneo cells do not express significant amounts of transport protein and can therefore be used to study passive diffusion. Because for hepatocytes the typical negative control in transport studies is a parallel incubation at 4°C, the passive diffusion was compared under these conditions for the same three Oatp substrates (Fig. 4B). A statistically higher P_dif was observed for the 37°C incubations for all compounds. Deltorphin II and CCK8 showed low absolute values of P_dif (<1 μl/min/mg), and negligible P_dif relative to the active uptake into the cell. However, for fexofenadine, which showed a higher absolute P_dif (∼2 μl/min/mg at 37°C), the estimated parameter from

the 4°C incubation was approximately 3 times lower than the value obtained at 37°C (Fig. 4B).

Analysis of Kinetic Experiments and Testing of the Mechanistic Model. A mechanistic model addressing the different interrelated and time-dependent processes of active uptake, nonspecific binding and passive diffusion was used to evaluate in vitro transport data as described under Materials and Methods. The validity of the model and the sensitivity of individual parameters were tested by analyzing different real and virtual data sets.

Sensitivity analysis. A sensitivity analysis was performed to investigate the impact of P_dif, K_m, and V_max on the cellular uptake parameters evaluated using the mechanistic model. Thus, the model was tested for ranges of values typically observed in in vitro experiments: P_dif was varied from 0 to 70 μl/min/mg, K_m from 1 to 1000 μM, and V_max from 10 to 3000 pmol/min/mg (Fig. 5). For low to medium P_dif values (i.e., up to 15 μl/min/mg), the intracellular concentration was strongly influenced by active transport. At low extracellular medium concentrations, K_m had a major impact (Fig. 5A), whereas V_max was more important at high extracellular medium concentrations (Fig. 5C). On the other hand, for higher P_dif values (>15 μl/mg/min, e.g., very lipophilic), the impact of active transport is very unlikely to be detectable even if it contributes significantly to the overall transport into the cell, because the assay sensitivity would be insufficient to detect the correct K_m and V_max (Fig. 5, B and D). In consequence, with a high P_dif, Michaelis-Menten parameters would not be accurately estimated, independently of their value. Overall the model behaved as expected and showed that a broad concentration range is required to accurately estimate P_dif, K_m, and V_max within a single experiment, and the optimal concentration range preferably needs to be determined in a pilot experiment.

The impact of the hepatocyte volume, which is used to calculate the intracellular volume per well (V_intracell in microliters), on the estimation of the uptake parameters was further investigated. The hepatocyte volume values reported in the literature ranged from 2.19 to 6.54 μl/10⁶ hepatocytes (Brosnan and Qian, 1994; Reinoso et al., 2001; Baker and Parton, 2007). It is interesting to note that P_dif, V_max, and K_m remained constant over this range of values. In the present work, an intermediate volume of 3.9 μl/1 million cells was used (Reinoso et al., 2001). The impact of the accuracy of V_intracell, which is calculated on the basis of the measured protein level per well, was also assessed. K_m remained very stable over a wide range of V_intracell values (0.04–12 μl), whereas P_dif and V_max increased with increasing V_intracell. Therefore, protein levels should be measured for each experiment (mean values per plate can be used) to calculate the respective V_intracell by applying the scaling factors as outlined.

Data analysis of computer-generated set of data. Data for eight virtual compounds covering a wide range of active and passive transport properties and different nonspecific binding were generated on the computer. These numerically generated data were then analyzed using both the conventional stepwise approach and the mechanistic model. The results are summarized in Fig. 6. Significant differences were seen in the estimation of P_dif, V_max, and K_m between the two approaches. As this comparison was done with a virtual set of data, the estimated parameters could be directly compared with the initially selected values. The parameters estimated from the mechanistic model were always closer to the expected values. Furthermore, the mechanistic model resulted in statistically better precision than the conventional approach. The two methods gave similar results when P_dif was negligible, although both accuracy and precision were superior with the mechanistic model. For compound 3, with low passive diffusion (P_dif = 0.01 μl/min/mg, K_m = 32 μM), the mechanistic model yielded a K_m of 31.5 ± 2.9 μM, whereas the two-step approach yielded 26.8 ± 7.5 μM. For a compound with high P_dif (compound 4, P_dif = 14 μl/mg/min, V_max = 550 pmol/min/mg), V_max was estimated to be 546 ± 86 pmol/min/mg by the mechanistic model, whereas the two-step approach gave a V_max of 109 ± 1580 pmol/min/mg. No significant difference could be observed when the incubation time points were changed, indicating the robustness of the approach based on the underlying mechanistic assumptions.

Analysis of Data from in Vitro Transport Experiments. In vitro uptake data were generated for the selected uptake transporter substrates CCK8, fexofenadine, pitavastatin, deltorphin II, napsagatran, and proprietary compound B using either primary rat hepatocytes or rat Oatp1b2- or Oatp1a1- or human OATP1B1- or OATP1B3-overexpressing cells. The kinetic studies were done under optimized experimental conditions in triplicate as detailed under Materials and Methods. The data were analyzed using both the step-wise conventional approach and the mechanistic model to determine P_dif, K_m, and V_max. Experimental data from one experiment each are shown in Fig. 7 with the respective fitting using the mechanistic model, and all mean parameters are summarized in Table 1. Pitavastatin (Fig. 7H) showed low P_dif (0.909 ± 1.043 μl/min/mg) and a fraction bound of 0.21 ± 0.10. Much lower affinity and intracellular concentrations and a negligible P_dif were measured for CCK8 in CHO cells (Fig. 7, B and C). For compound B, a high P_dif (22 ± 10 μl/min/mg) was found. This compound contains a carbonic acid moiety, has a clogP of 4.9, and showed extensive distribution to liver tissue in rats. The high lipophilicity is probably responsible in part for these properties. It showed a rapid deviation from linearity of cellular uptake (data not shown), and the relatively high uncertainty in the estimated kinetic parameters (K_m = 373 ± 137 μM, V_max = 28,000 ± 9300 pmol/min/mg, and f_b = 0.15 ± 0.47 in a single pilot experiment) indicated limitations in the approach for such compounds.

Analysis of the experimental in vitro data by the two approaches allowed comparison of the resulting K_m values between expressed systems and rat hepatocytes for the two Oatp1b2-selective substrates, CCK8 and deltorphin II, for which it should be identical (Table 1). Student's t test showed a statistically different K_m for CCK8 with the two-step approach, whereas with the mechanistic model it was identical between CHO-Oatp1b2 and rat hepatocytes. For deltorphin II the K_m values were similar using the mechanistic model, whereas with the conventional approach they were spread apart, although statistically not significantly different because of the high variance. Fexofenadine transport data from rat Oatp1a1-expressing cells cannot be compared directly to hepatocyte transport data, because rat Oatp1a4 is also involved in fexofenadine transport (Cvetkovic et al., 1999). In addition, specific scaling factors, compensating for differences in transporter expression levels, have to be established to make a quantitative comparison of transport rates across these experimental systems. For all compounds the accuracy of both methods was assessed by comparing the coefficient of variation (CV) of the estimated parameters. Significant differences were seen in the accuracy of the estimation of V_max and K_m for which the mean CVs on the estimates were 19 and 23% with the mechanistic model and 58 and 115% with the stepwise approach. The individual CVs on the P_dif parameter estimates were extreme and different between the two methods; however, they were spread across a too large range of values to show a statistically significant difference. For example, in the case of CCK8 and deltorphin II, two compounds with a very low P_dif, the estimation using the mechanistic model was significantly more precise (i.e., deltorphin II Oatp1b2-associated V_max was estimated to be 82.6 ± 23.3 pmol/mg/min with the mechanistic model and 56.1 ± 39.2 pmol/mg/min with the two-step approach), whereas for fexofenadine, characterized by a medium P_dif in rat hepatocytes (2.08 ± 0.67 μl/mg/min), the difference in K_m estimation by the two methods was larger (271 ± 35 and 27.2 ± 29.2 μM for the mechanistic model and the two-step approach, respectively). In addition, the estimate obtained from the two-step approach was associated with a high uncertainty (CV = 107%).

Discussion

The quantitative assessment of active transport requires careful evaluation of the experimental procedure as well as an appropriate mathematical model to quantify and integrate both passive and active processes. Therefore, the conditions for in vitro uptake studies were optimized, and data were analyzed with a mechanistic model to quantify in one single step the passive and active processes derived from the in vitro cellular uptake assays. In addition, this mechanistic model includes disappearance of compound from the incubation medium, bidirectional passive diffusion, and nonspecific binding.

Optimization of Experimental Conditions for the in Vitro Assessment of Active Drug Uptake. In cellular uptake assays nonspecific binding often leads to high apparent intracellular concentrations, misleading the subsequent data analysis because of an elevated background (Obach, 1996). This problem is especially critical for higher substrate concentrations and for compounds with higher lipophilicity. Therefore, experimental conditions, in particular the washing steps, were modified to reduce such nonspecific binding. The optimization of the washing steps showed that the temperature of the wash buffer in particular influenced the efficiency of the washing. An increased efficiency was seen if wash buffer was used at 37°C rather than at 4°C. The potential of leakage of intracellular compound during the washing at elevated temperature was found to be similar at either temperature of the washing buffer used (Fig. 2). In any case, the washing should be fast to avoid significant levels of compound leakage. Remaining nonspecifically bound material was taken into account during the kinetic analysis of transport data.

Different methods are used to assess passive diffusion independently from active transport in cellular uptake assays. Cell lines overexpressing individual transporters have in theory the advantage that any passive processes, such as nonspecific binding and passive diffusion, can be assessed by using the parental cell lines in parallel uptake studies. For primary cells, such as hepatocytes, the passive processes are more difficult to assess. In this respect control incubations at 4°C are often performed to assess passive diffusion (Komai et al., 1992; Ismair et al., 2001; Shimada et al., 2003; Lancon et al., 2004; Treiber et al., 2004; Ho et al., 2006). For many transporter model substrates, such as taurocholate and estrone-3-sulfate, which have negligible passive diffusion, this approach is appropriate. However, for many other, more lipophilic, compounds characterized by potentially higher passive permeabilities, this approach is questionable. Thus, for such compounds the passive diffusion was found to be considerably lower at 4°C than at 37°C in parent cell lines and artificial PAMPA membranes (Figs. 3 and 4B), indicating that such conditions would not be appropriate as a control incubation for some compounds. In this study, P_dif values were obtained for three transporter substrates, CCK8, deltorphin II, and fexofenadine, in both the control CHOneo cells, in which only P_dif was estimated, and the CHO-Oatp cells, in which P_dif and active processes were estimated simultaneously with the proposed mechanistic model (Fig. 4A). These values were not statistically different, but because of the high variability for the low P_dif values (CCK8 to deltorphin II), the study was underpowered to detect a difference. However, both estimations yielded a medium P_dif for fexofenadine and extremely low values for CCK8 and deltorphin II. For rat hepatocytes incubated at 37°C, the P_dif was assessed by the same approach and was different from the P_dif measured at 4°C (Fig. 4B). Therefore, in all following in vitro experiments, P_dif was assessed together with V_max and K_m in the same experiment, without using control CHO control cells or rat hepatocytes at 4°C.

Analysis of Data from in Vitro Transport Experiments. Often in vitro uptake transport data are evaluated by a step-wise approach. The initial transport rates are determined, often in single time point experiments, followed by a secondary plot of these rates versus substrate concentrations. Kinetic parameters (V_max and K_m) and P_dif are then calculated by regression analysis using eq. 2 (Komai et al., 1992; Ismair et al., 2001; Treiber et al., 2007; Webborn et al., 2007). This approach assumes linear conditions for the determination of initial uptake rates, and it proved to produce reliable parameters for compounds for which P_dif and nonspecific binding were negligible (compound 3 in Fig. 6 and CCK8 and deltorphin II in Table 1). However, for compounds with higher permeability the assumption of linearity of the initial uptake is not valid because of the physiological bidirectionality of P_dif. The usual assumption underlying this approximation is that within the very short time of an uptake experiment (<2 min), a concentration gradient driving the export of the drug through passive diffusion is negligible. However, in the experimental setup used in this study in which the incubation medium volume was approximately 150-fold higher than the intracellular volume (V_me = 150 μl; V_intracell =∼1 μl), the incubated drug rapidly reached very high intracellular concentrations relative to extracellular concentrations, so that the passive diffusion of the compound back into the extracellular medium becomes significant and leads to nonlinear uptake rates. For example, pitavastatin incubated in rat hepatocytes showed intracellular concentrations of 9 μM after a 30-s incubation for a C_me of 0.6 μM, whereas for fexofenadine the intracellular concentration was 3.5 μM after a 30 s incubation for a C_me of 2 μM. This rapid intracellular accumulation of some substrates leads to a nonlinear uptake rate as seen for fexofenadine, pitavastatin, and compound B (Fig. 7, G and H), which warrants kinetic determination of the uptake with multiple time points. For low permeability compounds such as the classic model substrates used in uptake transport studies, e.g., estrone-3-sulfate, taurocholate, and also CCK8 (Fig. 7, A–C), this nonlinearity is not seen because uptake is then mainly driven by the active transport component.

Mechanistic Two-Compartment Model Describing Bidirectional Passive Permeability and Active Transport. A mechanistic model able to incorporate nonlinearities by addressing the underlying physiologic processes involved is proposed in this article. One main advantage of this model is the possibility of describing the time course of the relevant passive and active physiological processes observed under the experimental conditions, including active transport, bidirectional passive diffusion, and adsorption to cells and supportive materials in one single step. In addition, the model accounts for the time-dependent disappearance of compound from the incubation medium, which was incorrectly considered to be stable in the classic approach. This mechanistic model allows analysis of the whole set of raw data in one step, without any prior data transformation. The model allowed us to determine the kinetic parameters for compounds with many diverse properties (P_dif up to 15 μl/mg/min, nonspecific binding, and diverse K_m and V_max) with higher precision than with the conventional step-wise approach.

The assessment from virtual data sets generated for eight compounds with different properties indicated that the kinetic parameters calculated using the mechanistic model were always closer to the initial values and much more accurate and precise than those calculated with the two-step approach (Fig. 6). The analysis of in vitro transport data for five diverse compounds, using primary rat hepatocytes and CHO cells overexpressing Oatp/OATP transporters, clearly supported the advantages of the mechanistic model over the conventional two-step approach. For CCK8 and deltorphin II, which are selective substrates of Oatp1b2 (our own data; Ismair et al., 2001), the mechanistic model yielded comparable K_m values in rat hepatocytes and in CHO-Oatp1b2 cells, whereas the two-step approach resulted in 2- to 3-fold different K_m values (Table 1). Most important, in all cases, the variation in K_m and V_max was significantly lower if the mechanistic model was used for data evaluation.

A similar mechanistic approach was recently published by Baker and Parton (2007). In contrast to the model proposed by these authors, in which intra- and extracellular protein binding is modeled on the basis of association and dissociation kinetics (k_on and k_off rates), a single parameter was chosen in the present study to describe adsorption to the cells and other nonspecific binding to reduce the number of parameters. The present in vitro experimental setup has been developed for the evaluation of uptake transport parameters only, and no protein was added in the incubation. In contrast to the study of Baker and Parton (2007), the validity of the present model was demonstrated for several drugs, with some of them being studied in three different cell types. The present study also used a different experimental in vitro approach. Plated cells, whether freshly isolated primary rat hepatocytes or cell lines overexpressing different transporters, were used here rather than suspensions. This approach allows for the assessment of transport under the same experimental conditions and gives the possibility of reducing nonspecific binding by multiple washing steps.

In addition to evaluation of experimental data, the mechanistic model can be used to optimize the experimental design (i.e., optimal sampling times and medium concentrations) on the basis of compound properties, such as solubility, lipophilicity, and expected permeability. The analysis with the mechanistic model also shows one important limitation in the estimation of transport parameters when P_dif values increase beyond 15 μl/mg/min (Fig. 5, B and D) as shown, for example, for compound B. Furthermore, the model allows us to quantify the impact of the uncertainty associated with some parameters.

The mechanistic model was set up for two compartments describing the situation in cellular uptake transport studies. Further refinement of the model will be required in the future to assess data from different in vitro assays. Thus, the analysis of in vitro transport data coming from cells seeded on filter inserts requires a third compartment as suggested by Sun and Pang (2008), Bentz et al. (2005), and Gonzalez-Alvarez et al. (2005).

In conclusion, the in vitro experimental protocol to assess uptake transport more quantitatively has been optimized in this study. Furthermore, the present mechanistic model proved to be a major improvement over the conventional two-step approach. It allowed precise and accurate estimation of in vitro transport parameters from cellular uptake transport processes in one step, including bidirectional passive diffusion and nonspecific binding. The analysis with the mechanistic model has also highlighted some limitations in the estimation of kinetic parameters in vitro. This quantitative evaluation of the kinetic transport parameters provides the basis for solid physiologically based pharmacokinetic modeling of active drug transport processes in connection with major parameters of drug metabolism with the aim of better prediction of overall hepatic drug elimination.