Abstract
Knowledge of free drug intracellular concentration is necessary to predict the impacts of drugs on intracellular targets. The goal of this study was to develop models to predict free intracellular drug concentrations in the presence of apical efflux transporters. The apical efflux transporter P-glycoprotein (P-gp), encoded by human gene multidrug resistance 1 (MDR1), was studied. Apparent permeabilities for 10 compounds in Madin-Darby canine kidney (MDCK) and MDR1-MDCK cell monolayers were obtained experimentally. Six of these compounds were evaluated additionally in the presence of the P-gp inhibitor cyclosporine A. A three-compartment model was developed, and passive and apical efflux clearances (CLd and CLae, respectively) were estimated. Endogenous canine transporters also were delineated. The three-compartment model was unable to simulate experimentally observed lag times and exhibited systematic bias across the simulations. Next, a five-compartment model with explicit membrane compartments was developed. This model resulted in lower systematic errors and simulated the lag time observed experimentally. Apical efflux was modeled out of the cell or out of the membrane. The five-compartment model with apical efflux out of the membrane predicted marked differences in unbound intracellular concentrations between the apical-to-basolateral and the basolateral-to-apical directions. Upon apical drug addition, large decreases in intracellular concentrations were observed with the efflux transporter. No such difference was predicted upon basolateral drug addition. This is consistent with experimental differences in the impact of P-gp on hepatic and brain distribution and supports the hypothesis that apical efflux occurs out of the apical membrane.
Introduction
Most efforts in the area of drug metabolism and pharmacokinetics have the ultimate goal of predicting or measuring the pharmacokinetics of the drug in humans. Knowledge of the time course and concentrations of the drug at the target along with the target response profile is used to predict the pharmacodynamic effect of a drug. Membrane transporters are key determinants of pharmacokinetic and pharmacodynamic profiles of numerous drugs (Giacomini et al., 2010). In general, total plasma drug concentrations are used to characterize drug disposition and function. However, the need for free tissue drug concentrations, especially at the site of drug clearance and/or drug action, is increasingly being recognized. Correlation between in vitro experiments and in vivo parameters (in vitro-in vivo correlation; IVIVC) can be improved greatly by taking into consideration unbound plasma and tissue concentrations, unbound substrate concentrations in in vitro experiments, and unbound intracellular concentrations in whole-cell experiments (Obach, 1999). To predict the impact of a drug on an intracellular target, the free intracellular concentration must be known (Lam et al., 2006; Giacomini et al., 2010).
Obtaining intracellular concentrations experimentally is difficult, and a few studies have attempted the prediction of concentrations across cell monolayers. The interplay between drug transport and metabolism has been modeled previously (Fan et al., 2010). The authors showed that intracellular concentrations drove both transport and metabolism; therefore, a reciprocal relationship exists between metabolite production (fraction metabolized) and active efflux clearance. Efflux ratio estimations were conducted with assumptions of sink conditions and a lack of cell accumulation or nonspecific binding. Another study evaluated the presence of endogenous transporters in MDR1-MDCK cells toward drugs such as loperamide and digoxin with enzyme kinetic analysis (Acharya et al., 2008). Enzyme kinetic modeling has predicted drug concentrations across cell monolayers in both apical-to-basolateral (A-B) and basolateral-to-apical (B-A) directions. Another example is a study wherein hepatobiliary disposition of troglitazone and its metabolites was evaluated in human sandwich-layered hepatocytes (Lee et al., 2010). Pharmacokinetic modeling and simulations based on hepatocyte data indicated that intracellular drug concentrations would increase if biliary excretion decreased. Finally, drug absorption in the presence of efflux transporters was modeled compartmentally with nonlinear fluxes across Caco-2 cells with an antibiotic as a transporter substrate (Komin and Toral, 2009).
Thus, mathematical modeling to predict intracellular drug disposition has been conducted by a few researchers. To our knowledge, however, modeling efforts to predict the impact of transporters on free intracellular concentrations have not been reported. In addition, estimating passive and active clearances can help to predict drug-drug interactions due to transporter inhibition. We therefore aimed to develop models to predict free intracellular drug concentrations in the absence and presence of apical efflux transporters. In addition, we aimed to estimate both passive and apical efflux clearances for drug disposition across cells. The transporter studied in the present work was the apical efflux transporter P-glycoprotein (P-gp) encoded by the human gene multidrug resistance 1 (MDR1; ABCB1).
The present work describes transport assays for 10 compounds in Madin-Darby canine kidney (MDCK) and MDR1-MDCK cell monolayers. Assays were conducted in the absence and presence of cyclosporine A (CsA), an inhibitor of P-gp. Mathematical models were developed to estimate passive and apical efflux clearances as well as free intracellular concentrations. The contribution of endogenous transporters in MDCK cells also was delineated.
Materials and Methods
Chemicals and Reagents.
Reference compounds were supplied by Sigma-Aldrich (St. Louis, MO). Cell culture reagents were purchased from Invitrogen (Carlsbad, CA). MDCK cells were obtained from the American Type Culture Collection (Manassas, VA). MDCK cells transfected with the MDR1 gene (MDR1-MDCK) were obtained from the National Institutes of Health (Bethesda, MD). Transwell plates (12-well, 11-mm diameter, 0.4-μm pores) were purchased from Corning Costar (Cambridge, MA).
Cellular Transport Studies.
MDCK and MDR1-MDCK cells were cultured, and transport experiments were conducted as described by Wang et al. (2008). All of the cells were maintained in high glucose (4.5 g/l) Dulbecco's modified Eagle's medium supplemented with 10% fetal bovine serum, 1% nonessential amino acids, 1% l-glutamine, penicillin (100 U/ml), streptomycin (100 g/ml) at 37°C in a humidified incubator with 5% CO2. All of the cells were seeded at a density of 60,000 cells/cm2 onto collagen-coated, microporous, polycarbonate membranes in 12-well Transwell plates. Cells were used between passages 10 and 14. The culture medium was changed 24 h after seeding to remove cell debris and dead cells; afterward, the medium was changed every other day for 6 days. The permeability assay buffer was Hanks' balanced salt solution containing 10 mM HEPES and 15 mM glucose at pH 7.4. The test compounds were prepared in this buffer to a final concentration of 5 μM each.
Test compounds were dissolved in dimethyl sulfoxide and then diluted in Hanks' balanced transport buffer (pH 7.4) (Mediatech, Herndon, VA). The amount of dimethyl sulfoxide in the final transport solution was 1% (v/v). The test compounds (5 μM final concentration) were dosed on either the apical side (A-B transport) or the basolateral side (B-A transport) and incubated in a humidified atmosphere at 37°C with 5% CO2. Samples were collected at the end of 90 min for experiments in each direction. All of the experiments were conducted in triplicate, and estimated means and standard deviations were calculated. A total of 10 compounds were evaluated (experiment 1; Table 1). For permeability experiments, data are not accepted if recovery is <80%. For the determination of lag time, A-B experiments were repeated with sampling at 15, 30, 60, and 90 min. To determine the possible impact of endogenous canine transporters, the permeabilities of six compounds across MDCK and MDR1-MDCK cells were evaluated in the presence and absence of CsA, an inhibitor of both canine and human P-gp (experiment 2) (Hegewisch-Becker, 1996; McEntee et al., 2003). These compounds were atorvastatin, digoxin, labetalol, loperamide, minoxidil, and pitavastatin. Target drug concentrations were analyzed by liquid chromatography-tandem mass spectrometry using a Xevo TQ MS Acquity UPLC System (Waters, Milford, MA) triple-quadrupole mass spectrometer fitted with an electrospray ionization probe operated in the positive ion mode (Li et al., 2010). The mobile phase consisted of two solvents: 0.1% formic acid in water (A) and 0.1% formic acid in acetonitrile (B). The gradient profile was 0 to 5.5 min 10% B, 5.5 to 6.5 min linear gradient to 90% B, 6.5 to 7.0 min 90% B, and 7.0 to 8 min 10% B. Saturable transport was checked in separate experiments with radiolabeled atorvastatin and digoxin. The experimental methods for cell assays were the same as those described above, except 0.5 and 5 μM initial concentrations were used. Radiolabeled substrates in these studies were quantified with liquid scintillation counting.
Model Development: Three-Compartment Model.
A simple model first was developed for diffusion across the cell, as well as for diffusion and apical efflux across the cell (Fig. 1A). This model is structurally similar to that developed by Fan et al. (2010). All of the passive diffusion clearances were assumed to be identical. Changes in free fractions due to membrane partitioning were assumed to be minimal. Back diffusion from the receiver compartment was modeled explicitly; therefore, the assumption of sink or steady-state conditions was not necessary. For this model, when diffusion is the only clearance mechanism (active efflux = 0), the following differential equations can be written: where are the rates of change of apical concentration (CA), cellular concentration (Ccell), and basolateral concentration (CB) with time (t), respectively; VA, Vcell, and VB are volumes of the apical, cellular, and basolateral compartments, respectively; and CLd is the passive diffusion clearance. Equations 1 to 3 were solved to obtain explicit solutions for CA, CB, and Ccell as a function of time. All of the derivations were conducted with Mathematica 8.0 (Wolfram, Research, Inc., Champain, IL). Thus, for apical dosing where the initial concentration at time 0 in the apical compartment is CA(0) and that in the receiver basolateral compartment is 0, the following expressions are derived for CA(t), Ccell(t), and CB(t):
Likewise, upon basolateral dosing, where the initial concentration at time 0 in the basolateral compartment is CB(0) and that in the receiver apical compartment is 0, the following expressions are derived for CA(t), Ccell(t), and CB(t): where
For the model in Fig. 1A, when passive diffusion plus apical efflux occurs, the following differential equations can be written:
For passive diffusion plus apical efflux: where CLae is the apical efflux clearance from the cellular compartment to the apical compartment. Equations 10 to 12 were solved to obtain explicit solutions for CA, CB, and Ccell as a function of time. Thus, for apical dosing where the initial concentration at time 0 in the apical compartment is CA(0) and that in the receiver basolateral compartment is 0, the following expressions are derived for CA(t), Ccell(t), and CB(t):
Likewise, upon basolateral dosing, where the initial concentration at time 0 in the basolateral compartment is CB(0) and that in the receiver apical compartment is 0, the following expressions are derived for CA(t), Ccell(t), and CB(t): where (for eqs. 13–18)
Numerical Simulations for the Three-Compartment Model To Obtain Estimates of CLd and CLae.
Estimates of CLd and CLae were obtained iteratively as follows.
Step 1: estimation of CLd.
The following constants were substituted into eqs. 1 to 3: VA = 0.5 ml, VB = 1.5 ml, Vcell = 0.002 ml, and t = 90 min. The apical and basolateral volumes were standard for the 12-well plates (VA = 0.5 ml and VB = 1.5 ml), and the cell volume was set to 2 μl. CLd was optimized iteratively to obtain experimental receiver concentrations for each drug at t = 90 min upon apical or basolateral dosing in MDCK cells. CLd estimates thus were obtained for experiments in either direction. The arithmetic mean of these CLd estimates was used in step 2 below to obtain an estimate of CLae.
Step 2: estimation of CLae.
The following constants were substituted into eqs. 10 to 12: VA = 0.5 ml, VB = 1.5 ml, Vcell = 0.002 ml, and t = 90 min, and CLd = constant (from step 1). Estimates of CLae for each drug were calculated to explain the experimentally observed drug efflux ratio at t = 90 min in MDR1-MDCK cells. This CLae predicted receiver concentrations upon apical or basolateral drug dosing. Predicted receiver concentrations were compared against experimentally observed values to check goodness of fit for this model. The model additionally provided predicted intracellular concentrations.
When necessary, estimates of Cld and CLae were obtained by simultaneously solving eqs. 19 and 20. These equations result from the following constants substituted into expressions for receiver compartment concentrations (eqs. 15 and 16): VA = 0.5 ml, VB = 1.5 ml, Vcell = 0.002 ml, and t = 90 min; further, for eq. 15 (apical dosing), CA(0) = 5 μM, Ccell(0) = 0, and CB(0) = 0, and for eq. 16 (basolateral dosing), CB(0) = 5 μM, Ccell(0) = 0, and CA(0) = 0.
These substitutions in eqs. 15 and 16 resulted in the following simplified equations: where
Experimental receiver concentrations upon apical dosing (CB in eq. 19) as well as basolateral dosing (CA in eq. 20) for each drug then were substituted simultaneously into eqs. 19 and 20 to solve for CLd and CLae. Thus, for example, endogenous canine transport clearances were solved with this method.
Model Development: Five-Compartment Model.
Next, the three-compartment model was expanded to include explicit compartments for apical and basolateral membranes, resulting in a five-compartment model (Fig. 1B). Back diffusion from the receiver compartment was modeled explicitly, and therefore the assumption of sink or steady-state conditions was not necessary. Membrane partitioning for each drug was determined as follows: where fum is the unbound drug fraction in microsomes, Va is the volume of the partitioning incubation, and Vm is the volume of cell membranes. For this model when diffusion is the only clearance mechanism, the following differential equations can be written:
For passive diffusion only: where are the rates of change of apical membrane concentration (CAM) and basolateral membrane concentration (CBM) with time (t), respectively; VAM and VBM are volumes of the apical membrane and basolateral membrane compartments, respectively; and all of the other terms are as defined previously. Equations 22 to 26 were solved to obtain explicit solutions for CA, CAM, Ccell, CBM, and CB as a function of time.
With apical efflux, the following differential equations can be written for the five-compartment model:
For passive diffusion plus apical efflux out of the cell:
In addition, eqs. 23, 25, and 26 remain the same for this model.
For passive diffusion plus apical efflux out of the membrane:
In addition, eqs. 24 to 26 remain the same for this model.
All of the differential equations for a particular five-compartment model were solved simultaneously to obtain explicit expressions for CA(t), CAM(t), Ccell(t), CBM(t), and CB(t) upon apical or basolateral dosing. These expressions are too complex to be listed here and do not easily lend themselves to explicit solutions. Therefore, numerical estimation of CLi, CLo, and CLae was conducted iteratively with an automated program within Mathematica 8.0. The general steps for optimization are as follows.
In step 1, passive permeability with MDCK cells was used to parameterize CLi and CLo (eq. 21). The value for fum was determined experimentally or estimated from each drug's apparent volume of distribution and plasma protein binding. With only passive diffusion occurring (eqs. 22–26), experimentally observed receiver compartment drug concentrations were used to obtain “best fit” estimates of CLi and CLo. These estimates were obtained for experiments in both A-B and B-A directions, and the averages of CLi and CLo estimates (averages of estimates from A-B and B-A experiments) were used in step 2 below.
In step 2, estimates of CLi and CLo were fixed, and CLae was optimized to explain the experimentally observed drug efflux ratio in MDR1-MDCK cells (eqs. 27–30, modeling efflux either out of the apical membrane or out of the cell). This CLae predicted receiver concentrations upon apical or basolateral drug dosing. Because the model is significantly more complex than the three-compartment model, it was necessary to add a damping function to the iterative optimization program to ensure convergence. Predicted receiver concentrations were compared against experimentally observed values to check goodness of fit for the model. The model additionally predicted unbound intracellular concentrations.
The five-compartment models were derived with cellular lipid contents of 10, 20, and 40%. The data presented are only for the 40% lipid calculations. As the lipid content is decreased, the five-compartment model collapses to the three-compartment model with CLd = CLi/2.
Results
Estimation of Clearances and Free Intracellular Concentrations with the Three-Compartment Model.
The first dataset includes A-B and B-A receiver concentrations at 90 min and apparent permeabilities for 10 compounds in both MDCK and MDR1-MDCK cells (experiment 1; Table 1). All of the drugs were P-gp substrates with efflux ratios (ER = B-A/A-B) in MDR1-MDCK cells between 5.2 and 240. In addition, efflux ratios in control MDCK cells were >1 for nine of 10 drugs, presumably due to endogenous canine P-gp in the MDCK cells. The efflux ratio for pitavastatin was 0.65 in MDCK cells, possibly due to endogenous apical uptake or basolateral efflux activity.
Using the model in Fig. 1A, eqs. 1 to 3 were used to numerically simulate the concentration profile for passive diffusion in MDCK cells (CLae = 0). Values for CLd then can be calculated to provide the appropriate receiver concentration at 90 min in MDCK cells for both A-B and B-A directions (CLdAB and CLdBA in Table 2). The most permeable compound, verapamil (apparent permeability Papp = 18 × 10−6 cm/s), gave a diffusion clearance of 4.5 μl/min, and the least permeable compound, labetalol (Papp = 0.26 × 10−6 cm/s), gave an average diffusion clearance of 0.068 μl/min (Table 2). Next, the average CLd values were fixed to calculate CLae for the MDR1-MDCK permeability data. Apical efflux clearance values (CLae) were optimized to obtain the appropriate efflux ratio (ER = B-A/A-B). The resulting CLae values (Table 2) ranged from 0.18 μl/min for minoxidil (ER = 2.6) to 540 μl/min for amprenavir (ER = 240). The intracellular concentrations were 2- (minoxidil) to 120-fold lower (amprenavir) in the presence of expressed efflux transporter. There was very little difference in the calculated intracellular concentrations between apical and basolateral dosing simulations.
Because CLae was optimized to provide the correct ER and we have both A-B and B-A concentrations, we have another degree of freedom that can be used to check the internal consistency of the simulation. The ratio of the calculated receiver concentrations to the experimental values (error) for the MDR1-MDCK cells is provided in Table 2. Because a perfect fit would give a value of 1, the data in Table 2 show that the errors are not random. Seven of the compounds have errors between 1.1 and 2.9, and three have errors between 23 and 34. None of the compounds have errors <1, suggesting a systematic bias in the simulations.
Contributions of Endogenous Canine Transporters.
To determine the origins of these errors, a second set of experiments was performed with six of the substrates (experiment 2). Three of the compounds with low errors, digoxin, loperamide, and minoxidil, were analyzed along with the three compounds with high errors, atorvastatin, labetalol, and pravastatin. The data for these experiments are shown in Table 3. In general, the efflux ratios for all of the compounds were lower than those in experiment 1. The presence of CsA dramatically decreased the efflux ratios for all of the drugs in MDR1-MDCK cells. CsA also decreased the efflux ratio for all of the drugs in MDCK cells, confirming the presence of canine P-gp activity in the control cells. The efflux ratios for MDCK + CsA were between 0.21 and 1.2, suggesting that apical uptake or basolateral efflux transporters could be involved as well.
Again, the errors in the model fit based on predicted receiver concentrations were nonrandom and >1 after fitting the data to the three-compartment model in Fig. 1A (Table 4). The three compounds with high errors in experiment 1, atorvastatin, labetalol, and pravastatin, had errors between 9 and 12 in experiment 2. Digoxin and minoxidil had similar errors (2.0–3.3) to those observed in experiment 1. Loperamide, which had a relatively low error in experiment 1, has an error of 11 in experiment 2.
The permeability data in the presence of CsA were used to determine whether the errors in the fits were due to endogenous canine transporters. Atorvastatin, digoxin, minoxidil, and pitavastatin have efflux ratios <1 for MDCK cells in the presence of CsA (Table 3). Because CsA inhibits both canine and human P-gp, efflux ratios <1 could be due to basolateral efflux or apical uptake. The clearance for these possible canine transporters can be calculated from the MDCK + CsA data, because we have two known receiver concentrations and two variables, CLd and canine basolateral efflux clearance (CLbec) or canine apical uptake clearance (CLauc). Equations 19 and 20 were solved simultaneously with the MDCK + CsA receiver concentrations and provided values for CLd and either CLbec or CLauc. The values for CLd and CLbec are given in Table 5. The canine efflux transporter clearances were calculated by adding the basolateral efflux clearance and canine apical efflux clearance pathways to the model in Fig. 1A, deriving symbolic equations similar to eqs. 19 and 20, and solving simultaneously with the MDCK + CsA permeability data. The canine apical efflux clearances (CLaec) are provided in Table 5. Finally, the MDCK and MDR1-MDCK data from experiments 1 and 2 could be described by a model that includes canine and human transporters using the calculated values for CLbec and CLaec. The resulting data are given in Table 5. Inclusion of canine transporters did not reduce the errors in the fits but instead increased them by approximately 10%. Inclusion of the canine transporters did increase the consistency of the passive diffusion clearances for the A-B and B-A directions. The average error without canine transporter clearances was 2.6-fold, and it decreased to 1.8-fold with canine clearances included in the model.
Because the errors in the simulations could not be explained by canine transporters, we considered whether the systematic errors could be saturable transport. Permeabilities for atorvastatin and digoxin were measured with initial concentrations of 0.5 and 5 μM. Radiolabeled compounds were used to increase the sensitivity for quantification. No differences in errors were observed, and similar values of CLd and CLae were calculated (data not shown), suggesting that the saturation of transport is not responsible for fitting errors.
The Three-Compartment Model Did Not Explain Experimentally Observed Lag Times.
Experimentally, we observe significant lag times for both highly permeable and poorly permeable compounds. Verapamil, labetalol, and minoxidil all showed lag times of 15 to 30 min when measuring permeability in MDCK cells (data not shown). Lag times in experiments with monolayers have been commonly reported (Knipp et al., 1997). In addition to the nonrandom errors of our modeling efforts, the three-compartment model in Fig. 1A does not accurately predict experimental lag times. The concentration-time profiles for the verapamil simulations are shown in Fig. 2A, and the receiver profiles for labetalol are shown in Fig. 2B. Verapamil has high permeability and therefore a high calculated CLd, and the intracellular concentration rapidly equilibrates with the apical and basolateral compartments. The result is that the simulation shows a very short lag time for the receiver concentration profile (Fig. 2A). Alternatively, labetalol has low passive permeability, resulting in a significant lag time calculated for the MDCK cell experiment (Fig. 2B). A lag time was not observed for the MDR1-MDCK cells, because the efflux transporter dramatically decreases intracellular concentrations, allowing equilibrium to be reached rapidly.
Estimation of Clearances and Free Intracellular Concentrations with the Five-Compartment Model.
Because the observed lag times could be due to the partitioning of drugs into the membranes, we used the model in Fig. 1B for additional simulations. In this model, the membranes are considered to be explicit compartments, resulting in five-compartment models. With these explicit membrane compartments, two different models for apical efflux can be considered. For the first, the efflux transporter can bind drug in the cytosol and transport it across the membrane to the apical compartment. For the second, the transporter can bind drug in the membrane and transport it into the membrane to the apical compartment (Fig. 1B). Both possibilities were modeled.
Data for the five-compartment model fit with apical efflux from the cell are shown in Table 6. The most striking difference from the three-compartment model (Table 2) is the lower error of the fit. The average error for the three-compartment model is 9.0, whereas the average error for the five-compartment model is 2.5. Three drugs had errors <1, suggesting less of a systematic bias for this model. Calculated unbound intracellular concentrations were similar (usually within 2-fold) for the A-B and B-A experiments. The ratios of the concentrations in the absence and presence of transporters (Ccell ratios) were independent of directionality and ranged from 1.4 for minoxidil (ER = 3.1) to 68 for amprenavir (ER = 240).
Table 7 shows the five-compartment model fits with apical efflux from the apical membrane. Again, the errors (average = 3.4) are much lower than those for the three-compartment model (Table 2). The most striking difference between transport from the cell (Table 6) and transport from the membrane (Table 7) is the difference in unbound intracellular concentrations between the A-B and the B-A directions. Apical addition gave Ccell AB ratios between 1.8 and 54, whereas apical efflux from the membrane had almost no effect on free intracellular concentrations for basolateral addition (Ccell AB ratios between 1.0 and 2.4).
In contrast to the three-compartment model, all of the compounds show significant lag times for the five-compartment models. The calculated concentration-time profiles for verapamil and labetalol are shown in Fig. 3. Results for models with transport from the membrane are shown, but models with transport from the cell gave similar profiles (data not shown). Although the intracellular concentrations can be very different for the A-B and B-A directions, the lag time profiles are very similar.
A plot of the efflux ratio versus the ratio of intracellular concentrations in MDCK to MDR1-MDCK cells (Ccell ratio) is shown in Fig. 4. For the three-compartment model (Fig. 4A), the decrease in intracellular concentration is proportional to the efflux ratio in both the A-B and the B-A directions. This is expected, because the rate of flux into the receiver is proportional to the intracellular concentration. For the five-compartment model with efflux from the cytoplasm (Fig. 4B), the Ccell ratios are not consistently proportional to efflux ratios, but high efflux ratios (>20) result in large decreases in intracellular concentration (>5-fold). In addition, similar decreases were seen for both the A-B and the B-A directions. For the membrane efflux model, only apical addition results in large changes in intracellular concentration (Fig. 4C). Basolateral addition resulted in Ccell ratios <2.5 for all of the compounds, with many compounds showing little or no change.
Discussion
Free or unbound concentration is generally assumed to be the relevant concentration needed to describe activity at target macromolecules (e.g., enzymes and receptors). With some in vitro systems (e.g., membrane preparations, plasma, and brain tissue), free drug concentrations can be measured experimentally by equilibrium dialysis. For compounds that readily cross membranes and are not substrates for transporters, free plasma concentrations can approximate free intracellular concentrations. For cells and tissues with active transport processes, the free intracellular concentration can be significantly different from the extracellular concentration. These differences can be particularly important when predicting target activities and absorption, distribution, metabolism, and elimination processes such as clearance, drug-drug interactions, and blood-brain barrier (BBB) penetration. The goal of this research was to develop models to predict free intracellular concentrations in the presence of transporters.
Several models for permeability and transport are being studied, and the first two of these models (Fig. 1) are presented here. In the simplest three-compartment model (Fig. 1A), passive diffusion through a cell is represented by a single clearance term CLd, and apical efflux is represented by CLae. The equations defining this model are complex (eqs. 1–20) but can be used to solve for CLd and CLae from single-point permeability data (Tables 2 and 4). With multiple datasets such as MDCK, MDR1-MDCK, and CsA inhibition data, we also can solve for clearances due to endogenous canine transporters (Table 5). A similar model has been used by Pang and colleagues (Sun et al., 2008a,b; Pang et al., 2009; Fan et al., 2010) to describe combinations of permeability, transport, and metabolism. However, the three-compartment models have deficiencies. Simultaneously modeling both MDCK and MDR1-MDCK results in large systematic errors, suggesting that inappropriate assumptions are made and/or the model is incomplete. In addition, highly permeable compounds have a much smaller predicted lag time than is observed experimentally.
Using permeability data in the presence of CsA, we were able to sequentially quantify canine basolateral and apical transporter activity (Table 5). Such activity has been deduced previously in MDCK cells (Acharya et al., 2008). Although the inclusion of these terms did not decrease the systematic errors of the three-compartment model, they increased the consistency of passive diffusion clearances in both directions. Therefore, these methods can be used to delineate contributions of multiple transporters in permeability experiments. For this dataset, the calculated contributions of canine apical transporters ranged from 0.03 to 5% for all of the drugs except minoxidil, which had canine contributions of 17 and 28% from apical uptake and basolateral efflux transporters, respectively. Whether this higher relative contribution for minoxidil is due to species differences in activity or greater relative error in the predicted values for lower efflux compounds is unknown.
The five-compartment models (Fig. 1B) incorporate explicit membrane compartments and use an experimental membrane partitioning term (fum) to parameterize the ratio of clearance into and out of the membrane. Although it is generally assumed that substrate binding to P-gp occurs from the plasma membrane (Gottesman et al., 1995, 1996; Hennessy and Spiers, 2007), we modeled efflux from both the membrane and the cell. Both models have decreased systematic errors and show significant lag times for drug appearance in the receiver compartments. However, there is a significant difference in the intracellular concentrations for the two models when dosed from the basolateral membrane.
Apical efflux from the cell would result in decreased cell concentrations irrespective of apical or basolateral dosing (Fig. 4B). However, efflux from the apical membrane prevents most of the drug from reaching the cell after apical addition (Fig. 4C, A-B). For basolateral addition (Fig. 4C, B-A), intracellular concentrations should decrease a maximum of 2-fold, because the drug is entering the cell from only one membrane instead of two (eq. 24, with CAM → 0). This is consistent with data in Table 7 (Ccell BA ratio).
A review of the impact of P-gp activity on both the liver and the BBB provides support for efflux directly from the membrane. For hepatocytes, the basolateral membrane faces the hepatic sinusoid and is proximal to the plasma. The apical membranes form bile canaliculi, and apical efflux transporters, such as P-gp, promote biliary secretion. For the BBB, the apical membrane is adjacent to the blood, and apical efflux transporters transfer drugs back into the blood. Our models suggest that efflux activity should significantly hinder P-gp substrates from crossing the BBB and show little effect on hepatic metabolism.
This is consistent with a report on the distribution of P-gp substrates in mdr1a(+/+) and mdr1a(−/−) mice (Schinkel et al., 1995). The ratios of brain and liver concentrations in knockout to wild-type mice were 35 and 2.0, respectively, for digoxin. These values are consistent with the average calculated intracellular ratios of 31 and 1.5 for A-B and B-A, respectively (Table 7). For CsA, the brain and liver ratios were 17 and 1.2, respectively, and dexamethasone, a moderate P-gp substrate, gave brain and liver ratios of 2.5 and 1.1, respectively (Schinkel et al., 1995). Several other studies have been reviewed (Girardin, 2006; Urquhart and Kim, 2009), showing that murine mdr1a has a major impact on BBB penetration. Loperamide showed a 65-fold increase in brain concentration in the knockout mouse (Kalvass et al., 2004). The calculated loperamide A-B cell concentration ratio in Table 7 is 33. A human positron emission study with [11C]verapamil revealed that P-gp inhibition with CsA results in a 13-fold increase in brain verapamil concentration (Hsiao et al., 2006). Again, this is consistent with the calculated A-B cell concentration ratio of 15 (Table 7).
Although there is no direct evidence that P-gp does not greatly affect human intracellular liver concentrations, support is provided by IVIVCs. Obach (1999) reported the correlation between microsomal clearance and human in vivo clearance for 29 drugs. The IVIVC incorporated binding to both plasma proteins and microsomal membranes. Seven of these drugs are known P-gp substrates (chlorpromazine, verapamil, diltiazem, desipramine, quinidine, clozapine, and dexamethasone). If P-gp significantly decreases the free intracellular concentration of these drugs, then clearance would be overpredicted by microsomal activity. Most predictions for these compounds were within 2-fold of the in vivo clearance, and none was overpredicted.
In a recent report (Agarwal et al., 2011), brain concentrations in single and dual knockout mice for dual P-gp and breast cancer resistance protein (BCRP) another BBB apical efflux transporter) substrates were discussed. For nine of 10 dual substrates, increases in brain concentrations were small for single knockout mice relative to those for dual knockout mice. We simulated dual P-gp and BCRP transport by adding another apical efflux transporter (with identical CLae) to the membrane compartment of the verapamil simulations. Blocking one transporter resulted in a 1.9-fold increase in intracellular concentration, whereas blocking both resulted in a 29-fold increase. If we add the second transporter to the cell compartment instead, blocking either the cell or the membrane transporter resulted in 18- and 20-fold increases, respectively. Blocking both resulted in a 310-fold increase. Thus, two transporters in the same compartment will buffer each other, preventing large changes when one is inhibited, whereas transporters in the membrane and cell compartments are sequential and are essentially multiplicative. This analysis suggests that BCRP also effluxes substrates from the apical membrane.
It should be noted that these results are preliminary and based on an artificial system. Although the predicted intracellular concentration ratios correlate well with the observed effects of P-gp on brain and liver concentrations, more data are needed. Experimentally, MDR1-MDCK cells were used, because they constitute a relatively simple model (compared with, for example, sandwich-cultured hepatocytes), which permits the identification and evaluation of the interaction of drugs with individual transporters. MDR1-MDCK cells maintain stable P-gp expression, as opposed to primary cultures, which lose transporter expression (Swift et al., 2010). In addition, through the formation of tight junctions, MDR1-MDCK cells develop good barrier properties and avoid appreciable passive paracellular diffusion that can enhance the difficulty of data interpretation. In addition, the model in Fig. 1B does not represent the actual structure of an epithelial cell or a hepatocyte. Although the model in Fig. 1B includes an explicit membrane compartment, the actual plasma membrane is only a small fraction of the total membranes in a cell. Most of the membranes in a cell comprise the endoplasmic reticulum and other organelles. We are currently evaluating other models for permeability and transport for a future report. Finally, to validate any model, it will be necessary to predict the activities of other uptake and efflux transporters.
In summary, a three-compartment model was developed, and passive and apical efflux clearances (CLd and CLae, respectively) were estimated. Endogenous canine transporters were additionally delineated. The three-compartment model was unable to simulate experimentally observed lag times and exhibited a systematic bias across simulations. A five-compartment model with explicit membrane compartments had a lower systematic error and simulated the lag time observed experimentally. The five-compartment model with apical efflux out of the membrane predicted marked differences in unbound intracellular concentrations between the A-B and the B-A directions. The data are consistent with in vitro and in vivo BBB and hepatic clearance data, supporting the hypothesis that apical efflux occurs out of the apical membrane.
Authorship Contributions
Participated in research design: Korzekwa, Nagar, Weiskircher, Bhoopathy, and Hidalgo.
Conducted experiments: Tucker.
Performed data analysis: Korzekwa and Nagar.
Wrote or contributed to the writing of the manuscript: Korzekwa, Nagar, Tucker, Weiskircher, Bhoopathy, and Hidalgo.
Acknowledgments
We thank Qing Wang and Libin Li (Absorption Systems, L.P.) for expert technical assistance.
Footnotes
Article, publication date, and citation information can be found at http://dmd.aspetjournals.org.
ABBREVIATIONS:
- IVIVC
- in vitro-in vivo correlation
- A-B
- apical-to-basolateral
- B-A
- basolateral-to-apical
- BBB
- blood-brain barrier
- CsA
- cyclosporine A
- MDCK
- Madin-Darby canine kidney cells
- MDR1
- multidrug resistance protein 1
- P-gp
- P-glycoprotein
- BCRP
- breast cancer resistance protein
- CLd
- passive diffusion clearance
- CLae
- apical efflux clearance.
- Received December 13, 2011.
- Accepted January 25, 2012.
- Copyright © 2012 by The American Society for Pharmacology and Experimental Therapeutics