Materials and Methods

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.

The initial total drug concentrations used in our experiments ranged from 1 to 1500 nM. At a 20% free fraction in culture medium (Song et al., 1996), the range of free drug concentrations was 0.2 to 300 nM. In comparison, the total drug concentrations in patients range from 230 to 14,000 nM attained immediately after drug infusion to ∼30 nM observed at 24 h postinfusion (Sonnichsen and Relling, 1994; Kearns et al., 1995). At the terminal half-life of 6 h, the expected drug concentration at 48 h is ∼2 nM. At a free fraction of 5 to 10% in human plasma (Longnecker et al., 1987; Jamis-Dow et al., 1993; Song et al., 1996), the free drug concentrations range from 0.1 to 1400 nM in patients. Hence, the concentrations used in our experiments are within the clinically relevant range.

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.

Determination of intracellular binding constants requires knowledge of the intracellular free drug concentration. For cells that have negligible Pgp expression (i.e., no active transport), the intracellular free drug concentration equals the extracellular free drug concentration at equilibrium and, therefore, can be obtained by measuring the extracellular concentration when the intracellular and extracellular concentrations are under a steady-state condition (Kuh et al., 2000). For Pgp-rich cells where the drug is transported out of the cell by Pgp-mediated efflux, the intracellular free drug concentration is lower than the extracellular free drug concentration. Hence, determination of intracellular binding constants in Pgp-rich cells requires a method different from that in Pgp-negative cells. The present study used the following approach. We first established two intracellular pharmacokinetic models, one for cells that have negligible Pgp expression and one for cells with enhanced Pgp expression. For this purpose, we used MCF7 cells, which have negligible Pgp expression and negligible Pgp-mediated efflux, and BC19 cells, which are the mdr1-transfected variant of MCF7 cells and display a 150-fold higher mdr1 mRNA level and a >10-fold higher level of Pgp compared with MCF7 cells (Fairchild et al., 1990;Li et al., 1998; Kuh et al., 2000). The intracellular binding and passive diffusion constants obtained in the Pgp-negative cells were then applied to the intracellular pharmacokinetic model for the Pgp-expressing cells to solve for the Pgp kinetic parameters. To verify the assumption that there were no differences in the Pgp-independent parameters (i.e., intracellular binding and passive diffusion rate constants) between the two cells, we then used a Pgp inhibitor to abolish the Pgp-mediated efflux in the Pgp-rich cells and analyzed the intracellular pharmacokinetic data for these parameters. As shown below, the Pgp-independent parameters in the Pgp-rich cells were identical to the parameters in the Pgp-negative cells.

The computation model for the intracellular paclitaxel pharmacokinetics in MCF7 cells has been described (Kuh et al., 2000). This model was modified to include the Pgp-mediated efflux. Equation 1describes the saturable Pgp-mediated efflux rate (Hunter et al., 1993).Pgp­mediated efflux rate=Jmax·Cfree,cKM,Pgp+Cfree,c Equation 1where J_max is the maximum efflux rate per cell and K_M,Pgp is the dissociation constant of Pgp-mediated efflux.C_free,c is the free drug concentration in cells.

Equations 2 and 3 are the mass balance equations that describe the changes in the amounts of paclitaxel in cells (Amt_total,c) and in medium (Amt_{total, m}), as a function of time.C_total,c andC_total,m are the total (i.e., free plus bound) drug concentrations in cells and medium, respectively.C_free,m is the free drug concentration in medium. V_c is the total cell volume. V_m is the volume of medium and remained constant (i.e., <10% change after 24 h). CL_f,d is the clearance of free drug by passive diffusion.dAmttotal,cdt=Vc·dCtotal,cdt+Ctotal,c·dVcdt Equation 2=CLf,d·Cfree,m−CLf,d·Cfree,c−Jmax·Cfree,cKM,Pgp+Cfree,c·cell number dAmttotal,mdt=Vm·dCtotal,mdt Equation 3=−CLf,d·Cfree,m+CLf,d·Cfree,c+Jmax·Cfree,cKM,Pgp+Cfree,c·cell number Equations 4 and 5 expressC_total,c andC_total,m as functions ofC_free,c andC_free,m, respectively.B_max,c andK_d,c are the Michaelis-Menten constants of drug binding to cellular components, andB_max,m andK_d,m are the binding constants to proteins in medium. NSB is the proportionality constant for the nonsaturable binding in cells.Ctotal,c=Cfree,c+Bmax,c·Cfree,cKd,c+Cfree,c+NSB·Cfree,c Equation 4Ctotal,m=Cfree,m+Bmax,m·Cfree,mKd,m+Cfree,m Equation 5As shown in our previous study (Kuh et al., 2000), the total cell number increased with time at low initial total extracellular drug concentration (1 and 10 nM) due to continued cell proliferation and decreased with time at high initial total extracellular drug concentration (100 and 1000 nM) due to the antiproliferative and/or cytotoxic drug effects. Changes in cell number were represented by changes in total cell volume,V_c. Equation 6 describes the time-dependent changes in V_c at different extracellular drug concentrations. V_{one cell} is the average cell volume and was 2.09 μl per 10⁶ cells for MCF7 cells in log growth phase (Kuh et al., 2000). Using the method described previously, the average volume of BC19 cells in log growth phase was determined to be 1.96 μl per 10⁶ cells. ICN is the initial cell number at time 0, and k_{cell number} is the rate constant for changes in cell number. Note that the values ofk_{cell number} depend on the pharmacological effect of paclitaxel. At low paclitaxel concentrations, cells continue to proliferate, in which case k_{cell number} shows positive values. In the case of higher drug concentrations (i.e., ≥100 nM), cell number decreases, thus resulting in negative values for k_{cell number}.Vc=Vone cell·cell number=Vone cell·ICN·ekcell number·t Equation 6Microtubule mass is enhanced by paclitaxel in a concentration-dependent manner (Jordan et al., 1993; Kuh et al., 2000). We found that treatment with 1000 nM paclitaxel resulted in an enhancement in tubulin concentration linearly with time up to the last time point at 24 h (Kuh et al., 2000). This relationship is described by eq. 7.B_max,c(t) andB_{max,c, initial} are the maximal saturable binding sites at time t and time 0, respectively, whereas k_Bmax,c is the rate constant for increases of B_max,c. Note thatk_Bmax,c varied with drug concentration (Kuh et al., 2000).Bmax,c(t)=Bmax,c,initial·(1+kBmax,c·t) Equation 7Substitution and rearrangement of eqs. 4 through 7 into eqs. 2and 3 yielded eqs. 8 and 9, which describe the time-dependent changes in intracellular and extracellular drug concentrations, respectively, as a function of cell volume, binding affinity and capacity, and Pgp-mediated efflux. These equations were used to simulate the intracellular and extracellular drug concentration-time profiles.dCtotal,cdt=CLf,d·X−CLf,d·Y−Jmax·YKM,Pgp+Y·1Vone cell−kcell number·Ctotal,c Equation 8dCtotal,mdt=−CLf,d·X+CLf,d·Y+Jmax·YKM,Pgp+Y·ICN·ekcell number·tVm Equation 9whereX=−(Kd,m+Bmax,m−Ctotal,m)+(Kd,m+Bmax,m−Ctotal,m)2+4·Kd,m·Ctotal,m 2 Y=−Z+Z2+4·(1+NSB)·Kd,c·Ctotal,c2·(1+NSB) Z=(1+NSB)·Kd,c+Bmax,c,initial·(1+kBmax,c·t)−Ctotal,c

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 ofk_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.

The Pgp efflux parameters, i.e., J_maxand K_M,Pgp, were obtained by model simulation. We first calculated initial estimates of these parameters and then substituted these estimates into eqs. 8 and 9 to generate model simulations. The values of these parameters were altered until the model-predicted data closely aligned with the experimental data. The values that yielded the best fits between simulated data and experimental data, as indicated by the lowest sum of squared errors, were identified as the final model parameters. To obtain the initial estimates of the two Pgp efflux parameters, the intracellular and extracellular free drug concentrations were calculated from the total intracellular and extracellular drug concentrations obtained at the 4-h time point or when these concentrations reached a pseudo-steady state with <10% changes in concentrations within 2 h. Under these conditions, the rate of concentration change is negligible and was set to zero. Accordingly, eqs. 2 and 3 were reduced to eq. 10, and a plot of the Pgp efflux rate versus C_free,cprovided the initial estimates of the Pgp efflux parameters.Pgp­mediated efflux rate=CLf,d·(Cfree,m−Cfree,c) Equation 10=Jmax·Cfree,c(KM,Pgp+Cfree,c)

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.CLPgp=Jmax/(KM,Pgp+Cfree,c) Equation 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

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; Table1), 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.

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Figure 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 and9. Mean ± S.D. (n = 3). S.D. in most cases is smaller than the symbols.

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Figure 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).

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.

The lower intracellular free drug concentrations compared with extracellular free drug concentrations in BC19 cells indicate that the efflux was against the concentration gradient, consistent with an active carrier-mediated transport mechanism.

Contribution of Pgp-Mediated Efflux to Total Efflux.

Table3 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. Figure3 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.

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Figure 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

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 apparentK_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.