Introduction

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Paclitaxel, one of the most important anticancer drugs developed in the past two decades, is active against multiple types of human solid tumors (Rowinsky et al., 1993). Paclitaxel enhances tubulin polymerization, promotes microtubule assembly, binds to microtubules, stabilizes microtubule dynamics, induces mitotic block at the metaphase/anaphase transition, and induces apoptosis (Parness and Horwitz, 1981; Manfredi et al., 1982; Jordan et al., 1993, 1996; Derry et al., 1995). Intracellular paclitaxel concentration is important for drug activity; drug resistance in several resistant sublines is correlated with reduced intracellular drug accumulation compared with the sensitive parent cell line (Lopes et al., 1993; Bhalla et al., 1994; Jekunen et al., 1994; Riou et al., 1994; Speicher et al., 1994). We have also shown that the slow release of paclitaxel from intracellular binding sites contributes to its antitumor activity, observed after the drug is removed from extracellular fluid (Kuh et al., 2000).

Paclitaxel is a substrate for the mdr1 Pgp (Gottesman and Pastan, 1993; Bradley and Ling, 1994). Enhanced Pgp expression, leading to enhanced drug efflux and reduced drug accumulation, is considered a major mechanism of resistance to paclitaxel; several in vitro studies have shown that cotreatment with Pgp inhibitors such as verapamil, cyclosporin A, PSC833, or LY335979 results in reversal of paclitaxel resistance in Pgp-expressing cells (Jachez et al., 1993; Cardarelli et al., 1995; Dantzig et al., 1996).

The kinetics of Pgp-mediated efflux of paclitaxel and the contribution of Pgp to the overall drug efflux are not known. This information is important for determining the clinical usefulness of combining Pgp inhibitors with paclitaxel. For example, the combination is more likely to produce beneficial therapeutic effects if the Pgp-mediated efflux constitutes a major efflux mechanism. Furthermore, a 3-h intravenous infusion of paclitaxel produces a >10,000-fold range of plasma concentrations in patients (Sonnichsen and Relling, 1994; Kearns et al., 1995). It is conceivable that the Pgp efflux plays different roles at different drug concentrations; the Pgp pump may be saturated and becomes a minor efflux mechanism at higher paclitaxel concentrations. Hence, identification of the plasma paclitaxel concentration ranges where the Pgp efflux represents the major and minor efflux mechanisms may provide the basis for selecting the dosage and schedule for administering a Pgp inhibitor. For example, administration of Pgp inhibitors should be such that these compounds are present when paclitaxel is present in a concentration range where the Pgp efflux is the major mechanism, rather than when the Pgp efflux becomes a minor mechanism.

The objective of the present study was to determine the kinetic parameters of the Pgp-mediated efflux of paclitaxel and the relative contribution of the Pgp efflux to the overall efflux of paclitaxel at clinically relevant concentrations. We used human breast BC19 carcinoma cells, which are the mdr1-transfected variant of MCF7 cells and display a 150-fold higher expression of mdr1 and a >10-fold higher Pgp level compared with MCF7 cells (Fairchild et al., 1990; Li et al., 1998). A computational model, similar to the one previously described for the MCF7 cells that have negligible Pgp expression (Kuh et al., 2000), was developed to establish the dissociation constant and the maximum efflux rate by the Pgp pump. These data were then used to calculate the contribution of Pgp efflux to the overall efflux. Potential applications of the computational model are discussed.

	Materials and Methods

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Chemicals and Cell Culture. The sources of chemicals and reagents and the cell culture conditions are as described previously (Kuh et al., 2000). The human breast MCF7 and BC19 carcinoma cells were kindly provided by Dr. Kenneth Cowan at the National Cancer Institute (Bethesda, MD).

Uptake and Efflux of Paclitaxel in Monolayer Cell Cultures. The uptake and efflux of [³H]paclitaxel were studied as described previously (Kuh et al., 2000). Briefly, cells were seeded in six-well plates (10⁵-10⁶ cells in 1 ml of culture medium per well). One day later, the medium was replaced with 1 ml of medium containing [³H]paclitaxel. To determine drug efflux, cells were treated with the drug for 24 h, washed, and then incubated in drug-free medium. To analyze the extracellular drug concentration, aliquots (100 µl) of medium were removed at predetermined times. The remaining medium was aspirated. Cells were washed twice with ice-cold Versene (Life Technologies, Grand Island, NY), harvested using trypsinization, and mixed with Solvable tissue gel solubilizer and Atomlight (DuPont Biotechnology Systems, Boston, MA). The cellular radioactivity was determined using liquid scintillation counting. As 95% of the radioactivity was represented by paclitaxel and its epimerization product, 7-epitaxol (Kuh et al., 2000), and because 7-epitaxol has microtubule binding affinity and cytotoxicity similar to that of paclitaxel (Ringel and Horwitz, 1987), the total radioactivity was expressed in paclitaxel equivalents. The intracellular drug concentration was calculated as total radioactivity divided by total cell volume.

Model Development. As shown below, the intracellular pharmacokinetics of paclitaxel in Pgp-rich cells are determined by multiple kinetic processes, including saturable and nonsaturable intracellular and extracellular binding and drug transport by passive diffusion and Pgp. The model uses a total of 10 parameters. Four of these parameters can be determined experimentally. Because the measurement of intracellular free drug concentration is not technically feasible, we used simulation techniques to obtain the remaining six parameters (see below). Three parameters describe the intracellular binding, one parameter describes the passive diffusion across cell membrane, and two parameters describe the Pgp efflux.

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

Calculation of Model Parameters. As discussed above, for the model parameters that are not Pgp-dependent, i.e., B_max,c, K_d,c, NSB, CL_f,d, B_max,m, and K_d,m, we used the values obtained previously for MCF7 cells (Kuh et al., 2000). Increase in tubulin concentration is dependent on extracellular paclitaxel concentration but is not cell-type-specific (Jordan et al., 1993; Kuh et al., 2000). Furthermore, a preliminary study showed a similar enhancement of tubulin concentration due to paclitaxel treatment in MCF7 and BC19 cells. Hence, we used the value of k_Bmax,c for MCF7 cells (Kuh et al., 2000). Changes in cell number due to paclitaxel treatment were cell-type-dependent and were determined for BC19 cells at each initial extracellular drug concentration; k_{cell number} was calculated as the slope of the log-linear plot of cell number versus time.

(10)

Verification of Model Assumption. The kinetic model was developed under the assumption that MCF7 and BC19 cells differed only in their Pgp function and that these cells showed identical intracellular binding constants and passive diffusion across cell membrane. To verify this assumption, we determined the values of these constants in BC19 cells after the Pgp efflux was abolished by a Pgp inhibitor. Ideally, the inhibitor should completely inhibit Pgp function, should be devoid of cytotoxicity, and should not affect the intracellular binding of paclitaxel. A preliminary study showed that PSC833, a cyclosporin A derivative, did not affect cell growth for at least 3 days at 1 µg/ml, but reduced cell growth by 50% after 2 days at 5 µg/ml. Subsequent studies used the 1 µg/ml concentration. At this concentration, PSC833 did not alter the intracellular accumulation of paclitaxel in MCF7 cells (Kuh et al., 2000) and, therefore, did not affect intracellular drug binding.

Contribution of Pgp Efflux to Overall Efflux of Paclitaxel. The clearance of paclitaxel from the intracellular compartment by the Pgp efflux, CL_Pgp, was calculated using eq. 11. The ratio of Pgp-mediated clearance to the total drug efflux clearance (i.e., sum of clearance by passive diffusion and by Pgp) provided the measurement of the contribution of Pgp-mediated efflux to the overall drug efflux.

(11)

Validation of Kinetic Model. The intracellular pharmacokinetic model was used to predict the effect of cell density on drug accumulation and the effect of intracellular-to-extracellular concentration gradient on drug efflux in the Pgp-expressing BC19 cells. The model-predicted data were then compared with experimental results to evaluate the validity of the model.

Data Analysis. For model fitting and simulation, we used the numerical integration method of WinNonlin (SCI Software, Lexington, KY), and used 1/concentration or 1/(amount)² as the weight.

	Results

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Verification of Model Assumption. Treatment of BC19 cells with PSC833 enhanced the intracellular paclitaxel concentrations to a level that was nearly identical to the concentrations in MCF7 cells (Fig. 1; Table 1), and diminished the differences between the intracellular and extracellular free drug concentrations in BC19 cells (Fig. 2). These results indicate that PSC833 abolished the Pgp-mediated efflux in BC19 cells. Analysis of the intracellular and extracellular drug concentration-time profiles in the PSC833-treated BC19 cells yielded the Pgp-independent kinetic parameters that are indistinguishable from the values obtained for MCF7 cells (Table 2). This confirms the model assumption that MCF7 and BC19 cells have identical Pgp-independent kinetic parameters.

View larger version (20K): [in this window] [in a new window]   Fig. 1.   Intracellular and extracellular concentrations of paclitaxel during uptake. MCF7 (closed circles) and BC19 (open circles) cells were incubated with 1 to 1000 nM paclitaxel. Separate samples of BC19 cells were also treated with PSC833 (open squares). The concentrations of paclitaxel in cells (left panel) and culture medium (right panel) were measured for 24 h. Note the different units for intracellular and extracellular concentrations. Symbols represent experimental data. Lines are computer-simulated lines using eqs. 8 and 9. Mean ± S.D. (n = 3). S.D. in most cases is smaller than the symbols.

View larger version (17K): [in this window] [in a new window]   Fig. 2.   Relationship between intracellular and extracellular free drug concentrations. Free drug concentrations in cells and culture medium at 4 h were calculated from total drug concentrations as described under Methods. BC19 cells (open circles). PSC 833-treated BC19 cells (open squares).

View this table: [in this window] [in a new window]   TABLE 2 Kinetic parameters in MCF7, BC19, and PSC 833-treated BC19 (PSC-BC19) cells The definition of the model parameters and their values were as described under Materials and Methods. For Bmax,c, Kd,c, NSB, CLf,d, Jmax, and KM,Pgp, the results represent the mean ± S.D. for the values determined from analyzing the four profiles obtained for four initial extracellular drug concentrations (i.e., 1, 10, 100, and 1000 nM). For kcell number and kBmax,c, the values obtained for the four initial extracellular drug concentrations are provided. The extracellular binding constants to proteins in the culture medium are not cell-type specific and, as determined previously, are 3.94 µM for Bmax,m and 781 nM for Kd,m (Kuh et al., 2000).

Kinetics of Pgp-Mediated Efflux. Figure 1 shows the intracellular and extracellular concentration-time profiles of paclitaxel in MCF7 and BC19 cells in the uptake study. Table 1 compares the intracellular drug concentrations determined at 4 h. As would be expected, the intracellular concentrations in the Pgp-rich BC19 cells were lower than those in the Pgp-negative MCF7 cells, with an up to 2.5-fold lower concentration in BC19 cells. Differences in the concentrations in the two cells decreased from 56 to 16% as the initial extracellular drug concentration increased from 1 to 1500 nM. The diminishing differences between two cell lines at high extracellular concentrations suggest saturation of the Pgp-mediated efflux in BC19 cells. A plot of the calculated intracellular free drug concentration versus extracellular free drug concentration at 4 h shows lower intracellular concentrations compared with extracellular concentrations in BC19 cells, whereas the PSC833-treated BC19 cells show approximately equal intracellular and extracellular free drug concentrations (Fig. 2). The plot also shows a biphasic line for the BC19 cells; the first phase showed a slope of less than unity at intracellular free drug concentration of <100 nM, and the second phase showed a slope approaching unity, as in the case of the PSC833-treated BC19 cells. These data suggest a saturation of the Pgp efflux at the 100 nM intracellular free drug concentration. Table 2 summarizes the kinetic parameters for the Pgp efflux.

Contribution of Pgp-Mediated Efflux to Total Efflux. Table 3 shows that in BC19 cells, the ratio of clearance due to Pgp efflux to total clearance decreased with increasing intracellular free drug concentration and increasing extracellular concentrations. Within the clinically relevant plasma (i.e., extracellular) concentration range of 200 to 1000 nM, the contribution of Pgp efflux to the overall drug efflux decreased from >70 to <30%. These data indicate that the importance of the Pgp-mediated efflux is highly dependent on the paclitaxel concentration.

Validation of the Intracellular Pharmacokinetic Model. Two studies comparing the model-predicted data with subsequently obtained experimental data were performed to evaluate the validity of the model. We have shown that the kinetics of paclitaxel uptake and efflux are affected by cell density and the intracellular-to-extracellular concentration gradient (created by using different volumes of wash-out medium, i.e., 1 and 3 ml) (Kuh et al., 2000). First, our model predicted that the extensive drug accumulation in BC19 cells, due to the higher extent of intracellular binding compared with the extracellular binding, would reduce the total drug concentration in medium (10 nM initial extracellular concentration); the extent of reduction ranged from 5% for a cell density of 0.1 × 10⁶ cells/ml to 52% at a cell density of 2 × 10⁶ cells/ml, at 4 h. This reduction in total extracellular drug concentration in turn would result in a 2-fold decrease in drug accumulation in BC19 cells. Second, our model predicted different kinetics of paclitaxel efflux at different intracellular-to-extracellular concentration gradients. Figure 3 compares the model-predicted data and the experimental data. In both studies, the model-predicted data deviated from the experimental data by about 6%. The close agreement between the model-predicted and the experimental data indicates the validity of the model.

View larger version (12K): [in this window] [in a new window]   Fig. 3.   Validation of intracellular pharmacokinetic model. Left panel, drug uptake as a function of cell density in culture medium. BC19 cells were seeded at different densities and treated with 10 nM paclitaxel in 1 ml of culture medium for 4 h. The intracellular drug concentrations attained at 4 h were analyzed. Right panel, drug efflux as a function of time and intracellular-to-extracellular concentration gradient. BC19 cells were treated with 10 nM paclitaxel for 24 h. The drug-containing medium was then replaced with 1 and 3 ml of drug-free medium; the larger medium volumes were used to reduce the extracellular concentration and thereby increase the intracellular-to-extracellular concentration ratio. Both panels: symbols represent experimental data. Lines represent the model-predicted data. Mean ± S.D. (n = 3). S.D. is smaller than the symbols in most cases.

	Discussion

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The present study establishes the kinetics of Pgp-mediated efflux of paclitaxel in intact cells. Our results show that the Pgp-mediated efflux is saturable at the clinically relevant concentration range and that the importance of the Pgp-mediated efflux is dependent on extracellular drug concentration. For BC19 cells, the Pgp-mediated efflux accounted for >70% of total drug efflux at extracellular drug concentrations between 1 and 200 nM, but became saturated and accounted for <30% of total efflux at 1000 nM extracellular concentration. The clinical implications of our findings depend on the Pgp levels in patient tumors. For example, for tumors that show similar Pgp expression and function as BC19 cells, our data suggest a limited role of Pgp in the efflux of paclitaxel and a limited utility of Pgp inhibitors at the high end of the clinically relevant concentration range, e.g., >200 nM, where the Pgp efflux is saturated; and that the drug efflux by Pgp can be minimized by using high intensity infusions that deliver high drug concentrations. Studies to compare the Pgp expression in human and BC19 tumors, and to evaluate the possibility that the Pgp-related resistance can be overcome by altering the treatment schedule, are ongoing.

The dissociation constant of paclitaxel from Pgp found in the present study for BC19 cells is about 1000-fold lower than the apparent K_m reported for human intestinal epithelial Caco2 cell monolayer (14 nM versus 16.5 µM) (Walle and Walle, 1998). One possible cause of the difference is the different cell types. For example, Caco2 cells showed a 20- to 40-fold lower dissociation constant for vinblastine, compared with human renal epithelial Madin-Darby canine kidney cells (Hunter et al., 1993). Another possible cause is the different methods used to determine the dissociation constant. The earlier study calculated the apparent K_m of Pgp as half the difference between the apical-to-basal and basal-to-apical transport rates, based on the assumption that Pgp-mediated transport was the only difference between the bidirectional transport. This assumption, in turn, is based on two other assumptions, i.e., identical intracellular drug concentration for transport in both directions and linear transport in both directions. These assumptions are invalid for the following reasons. First, because of the Pgp-mediated transport, the intracellular concentration for the apical-to-basal transport will be higher than the concentration for the basal-to-apical transport. Second, the plot of the apical-to-basal transport rate versus paclitaxel concentration was linear in the same concentration range where the basal-to-apical transport showed saturation, indicating that there are other factors in addition to Pgp that accounted for the difference in the bidirectional transport. The earlier method also assumes a cell as a single homogenous compartment from the kinetic standpoint and views Pgp as a transport barrier (i.e., a single compartment representing only the Pgp binding sites). Our previous (Kuh et al., 2000) and present studies show that, kinetically, a cell consists of multiple compartments including saturable binding sites, nonsaturable binding sites, and Pgp binding sites. Hence, the apparent Pgp transport rate determined in the earlier study represents a hybridized rate comprised of binding and transport rates. Accordingly, the dissociation constant of Pgp found in the earlier study is confounded by the kinetics of drug binding to intracellular binding sites. In contrast, the present study used intracellular free drug concentration to specifically measure the dissociation constant of Pgp efflux, separately from drug binding to intracellular binding sites. Hence, the dissociation constant found in the present study is less likely to be error-prone compared with the earlier approach.

A review of the literature data indicates that most of the published studies on the mechanism of paclitaxel resistance address only the effect of altering either Pgp expression or the binding affinity/capacity on intracellular drug accumulation. On the other hand, simultaneous changes in the Pgp level and in the number of total tubulins have been reported in paclitaxel-resistant cells obtained by single-step exposure to paclitaxel (Dumontet et al., 1996). Hence, there is a need to understand the inter-relationship between changes in these biological factors and intracellular paclitaxel pharmacokinetics. The present study describes the establishment of the computational intracellular pharmacokinetic model that depicts the intracellular paclitaxel concentration as a function of extracellular drug concentration, drug transport, and intracellular and extracellular drug binding. This model provides the means to predict the intracellular drug concentration as a function of Pgp expression and amount and binding affinity of tubulins/microtubules. Because these biological changes can be represented mathematically by altering the values of the kinetic parameters, computer simulations can be performed to elucidate the effect of changing these parameters, separately or simultaneously. An ongoing study in our laboratory uses this model to address questions such as the net effect of changing the Pgp level and changing the binding affinity/capacity of intracellular binding sites on the intracellular pharmacokinetics, and whether omission of one or more of the biological changes in the study design would lead to erroneous conclusions on the role of the other biological changes.