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, 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). The intracellular concentration of paclitaxel is critical for its pharmacological effect. Drug resistance in several resistant sublines is correlated with reduced intracellular drug accumulation compared with the sensitive parent cell lines (Lopes et al., 1993; Bhalla et al., 1994; Jekunen et al., 1994; Riou et al., 1994; Speicher et al., 1994).

One of the challenges regarding the clinical use of paclitaxel is the identification of optimal treatment schedules; multiple treatment schedules with different infusion duration (1, 3, 24, and 96 h) and different treatment frequency (daily, weekly, and every 3 weeks) are under evaluation in patients. The difficulty is in part due to the lack of a precise understanding of the pharmacodynamics of paclitaxel, i.e., drug effect as a function of drug concentration and treatment duration. For example, the importance of treatment duration on the antitumor effect of paclitaxel has been controversial; some studies in cultured cells indicate that prolonging the treatment duration did not enhance the drug effect (Cohen and Duke, 1984; Roberts et al., 1990), whereas other studies indicate the opposite (Rowinsky et al., 1988; Liebmann et al., 1993; Lopes et al., 1993; Milas et al., 1995). We have shown that this controversy is likely due to the delayed cytotoxicity of paclitaxel that is exhibited after termination of treatment. The delayed effect is due in part to the slow manifestation of apoptosis and in part to the slow release of paclitaxel from its intracellular binding sites (Au et al., 1998). These findings indicate that the elucidation of paclitaxel pharmacodynamics requires a better understanding of its intracellular pharmacokinetics on a quantitative level. For example, the intracellular drug concentration-time profile is needed to predict the drug effect at various time intervals during and after drug administration.

Several laboratories, including ours, have studied various aspects of intracellular pharmacokinetics of paclitaxel in cultured cells, such as the binding of paclitaxel to extracellular and intracellular macromolecules (Manfredi et al., 1982; Jordan et al., 1993; Song et al., 1996) and the effect of overexpression of the multidrug resistance of P-glycoprotein (Pgp) on drug efflux (Bhalla et al., 1994; Speicher et al., 1994). Although these studies have led to a better understanding of the determinants of intracellular paclitaxel pharmacokinetics on a conceptual level, they do not provide the means to depict quantitatively how changes in these determinants will alter intracellular pharmacokinetics. For example, it is known that: 1) changes in tubulins alter drug binding and accumulation in cells (Haber et al., 1995; Dumontet et al., 1996; Dumontet and Sikic, 1999); 2) the presence of Cremophor micelles decreases the free fraction of paclitaxel available to enter cells (Knemeyer et al., 1998); and 3) displacement of paclitaxel from plasma protein binding sites by other highly protein-bound drugs such as cisplatin increases the free fraction. However, because the quantitative relationship between these determinants and intracellular drug accumulation is unknown, it is not possible to design treatment schedules to accommodate changes in the determinants.

The goal of this study was to establish a computational model of intracellular paclitaxel pharmacokinetics that could be used to quantify the relative importance of various determinants. As a first study, the model was developed for a system where drug efflux does not involve active drug transport by the Pgp efflux pump, and the required experimental data were obtained using human breast adenocarcinoma MCF7 cells, which have negligible Pgp expression (Fairchild et al., 1990; Li et al., 1998).

	Materials and Methods

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Chemicals and Reagents. Paclitaxel was a gift from Bristol-Myers Squibb Co. (Wallingford, CT) and the National Cancer Institute (Bethesda, MD); 3"-[³H]paclitaxel (specific activity, 19.3 Ci/mmol) from the National Cancer Institute; and PSC833 from Novartis Inc. (Summit, NJ). 7-Epitaxol was purchased from Hauser Chemicals (Boulder, CO); cefotaxime sodium from Hoechst-Roussel (Somerville, NJ); gentamicin from Solo Pak Laboratories (Franklin Park, IL); all other cell culture supplies including Versene from Life Technologies (Grand Island, NY); Solvable tissue gel solubilizer and Atomlight scintillation fluid from DuPont Biotechnology Systems (Boston, MA); and all other chemicals and -tubulin monoclonal antibody from Sigma (St. Louis, MO). All chemicals and reagents were used as received. 7-Epitaxol was >99.2% pure, as determined by high pressure liquid chromatographic (HPLC) analysis.

Cell Culture. Human breast MCF7 tumor cells were a gift from Dr. Kenneth Cowan (National Cancer Institute). Cells were maintained in RPMI-1640, supplemented with 9% heat-inactivated fetal bovine serum, 2 mM glutamine, 90 µg/ml gentamicin, and 90 µg/ml cefotaxime sodium, in a humidified atmosphere at 37°C and 5% CO₂. For experiments, cells were harvested from subconfluent cultures using trypsin and resuspended in fresh medium before plating. Cells with greater than 90% viability, as determined by trypan blue exclusion, were used. The doubling time of MCF7 cells, during the exponential growth phase, was 24 h.

Cell Volume Measurement. The volume of MCF7 cells in the exponential growth phase was determined using the Samba Image Analyzer 4000 (Imaging Products International, Inc., Chantilly, VA). Because the drug-induced reorganization of microtubules has no effect on cell volume (Brown et al., 1985; Mills, 1987), cell volume was determined using untreated cells. Cells were harvested with trypsin, stained with toluidine blue (0.2% in 10% methanol), and diluted with PBS. The Samba 4000 quantified the distance as the number of pixels, i.e., 164 pixels per 200× microscopic field. The maximum (L) and minimum (W) diameters of a cell, which were determined by counting the number of pixels and converting the value to micrometers, were used to calculate the cell volume. Equation 1 describes the calculation of the volume (V) of ellipsoid cells. MCF7 cells in the log growth phase showed an average volume of 2.09 ± 0.431 µl/10⁶ cells (mean ± S.D.; n = 232; median, 2.11 µl).

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Uptake and Efflux of Paclitaxel. Cells were plated at densities of 10⁵ to 10⁶ cells/well in 1 ml of culture medium in six-well plates. One day after seeding, the medium was replaced with 1 ml of medium containing [³H]paclitaxel. Nonradiolabeled paclitaxel was added when necessary. The final specific activity of [³H]paclitaxel ranged from 0.04 to 19.3 Ci/mmol. Drug uptake experiments used drug concentrations (total concentration) that are within the therapeutic range of 1 to 5000 nM (Kearns et al., 1995). To determine drug efflux, cells were treated with 10 nM [³H]paclitaxel for 24 h, then washed twice with 1 ml of ice-cold drug-free medium, followed by incubation in drug-free medium with agitation every 15 min for 2 h and every hour thereafter. For both uptake and efflux studies, aliquots (100 µl) of medium were removed at predetermined times. After the remaining medium was aspirated, cells were washed twice with 0.25 ml of ice-cold Versene and then harvested as a suspension after trypsinization. Cell number was measured by hemocytometer or by Coulter Counter (Coulter Electronics Inc., Hialeah, FL) after a 20-fold dilution with Isotone (Coulter Electronics Inc.). Samples were dissolved in 0.5 ml of Solvable tissue gel solubilizer, mixed with 10 ml of Atomlight, and processed by liquid scintillation counting.

Sample Extraction and Analysis. Paclitaxel and its reversible epimerization product, 7-epitaxol, were extracted using ethyl acetate and ammonium acetate buffer (0.01 M, pH 5.0). The latter was added to minimize epimerization (Leslie et al., 1993). The organic extract was evaporated to dryness. After being reconstituted with 16% acetonitrile in ammonium acetate, the sample was loaded on BondElut CN solid-liquid phase extraction cartridges (Varian, Harbor City, CA) pre-equilibrated sequentially with 2 ml of acetonitrile, 2 ml of methanol, and 3 ml of ammonium acetate buffer. After being washed with 2 ml of ammonium acetate buffer and 2 ml of 25% acetonitrile in the same buffer, the analytes were eluted with 70% acetonitrile in water. The eluent was evaporated to dryness and reconstituted in the HPLC mobile phase (49% acetonitrile in water). The extraction recovery was >90% for both culture medium and cell samples. An aliquot was analyzed by HPLC using a reversed phase µBondapak C18 column (Waters Association, Milford, MA) and UV absorbance at 229 nm. The flow rate of the mobile phase was 1 ml/min, and the retention times for paclitaxel and 7-epitaxol were 13.6 and 21.9 min, respectively. More than 95% of the radioactivity recovered in the HPLC-eluting fractions corresponded to paclitaxel and 7-epitaxol. 7-Epitaxol accounted for less than 10% of the total radioactivity at 4 h. Because paclitaxel and 7-epitaxol together accounted for almost all of the recovered radioactivity and because paclitaxel and 7-epitaxol are pharmacologically equivalent, with identical microtubules binding affinity and cytotoxicity (Ringel and Horwitz, 1987), the total recovered radioactivity was considered equivalent to paclitaxel without further correction in subsequent studies.

Confirmation of Negligible Pgp-Mediated Paclitaxel Efflux in MCF7 Cells. The MCF7 cells used in this study are known to have negligible Pgp expression (Fairchild et al., 1990). A separate study using Western blot analysis confirmed that the Pgp level in these cells was barely detectable (Li et al., 1998). To determine whether Pgp-mediated efflux significantly contributed to the efflux of paclitaxel, we compared the intracellular concentration-time profiles in the absence or presence of a known Pgp inhibitor, PSC833 (Boesch et al., 1991). A preliminary study showed that PSC833, at 0.5, 1, and 5 µg/ml, did not affect the growth of MCF7 cells for at least 2 days. Subsequent studies used 1 µg/ml PSC833. In the uptake study, PSC833 was administered with paclitaxel. In the efflux study, cells were first treated with paclitaxel for 24 h; the paclitaxel-loaded cells were then placed in PSC833-containing medium.

Analysis of Total and Polymerized Tubulin. Total (free plus polymerized) and polymerized tubulin were analyzed as previously described (Thrower et al., 1991), with the exception that cells were lysed by four to five cycles of freezing, thawing, and vortexing. More than 90% of the cells were lysed, as indicated by the uptake of trypan blue dye. Tubulin was analyzed by an enzyme-linked immunoadsorbent assay using a monoclonal antibody to -tubulin (IgG, Tub2.1). Bovine brain tubulin was used as the tubulin standard due to the unavailability of human tubulin. Hence, we were not able to determine the absolute concentration/amount of tubulin in human cells. Accordingly, changes in the tubulin concentration/amount were reported as changes relative to the control value.

Model Development. We constructed an intracellular pharmacokinetic model to describe the factors that determine the kinetics of paclitaxel uptake, binding, and efflux from cells. The model included: 1) saturable binding of paclitaxel to proteins in the extracellular compartment (Song et al., 1996), 2) saturable and nonsaturable binding of paclitaxel to cellular components (Manfredi et al., 1982), 3) time- and concentration-dependent changes in microtubule mass (Jordan et al., 1993; Derry et al., 1995), and 4) time- and concentration-dependent changes in cell number (see Results). We assumed that a) drug uptake is by passive diffusion because sodium azide treatment, which depletes ATP, has minimal effect on intracellular drug accumulation (Manfredi et al., 1982); b) drug efflux is by passive diffusion because Pgp-mediated drug efflux was insignificant in MCF7 cells (see Results); and c) only free drug participates in the uptake and efflux processes.

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(8)

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Determination of Model Parameters. Several model parameters were determined experimentally, as follows: B_max,m and K_d,m were determined by analyzing our previously published data on paclitaxel binding to proteins in cell culture medium (Song et al., 1996) using eq. 5; k_{cell number} was calculated for each initial C_total,m as the slope of the log-linear plot of [cell number] versus [time]; and k_Bmax,c was calculated for each initial C_total,m as the slope of the plot of [concentration of total tubulin] versus [time].

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

Application of Intracellular Pharmacokinetic Model. The intracellular pharmacokinetic model was used to demonstrate the effects of changing several parameters (i.e., number and dissociation constant of intracellular binding sites, free fraction of drug in extracellular fluid, and extracellular drug concentrations) on intracellular drug concentrations. These simulations were accomplished by altering the values of B_max,c, K_d,c, B_max,m-to-K_d,c ratio, and initial C_total,m, respectively. Simulations were conducted for initial cell density of 10⁶ cells/ml of medium volume.

Computer Simulation. For model fitting and simulations, we used WINNONLIN with 1/concentration as the weight.

	Results

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Verification of Model Assumption. Paclitaxel is a substrate for Pgp but not for multidrug resistance-associated protein, another drug efflux membrane protein (Breuninger et al., 1995). The assumption of a negligible Pgp-mediated drug transport in MCF7 cells was verified with an inhibitor study. Treatment of MCF7 cells with the Pgp inhibitor PSC833 at 1 µg/ml did not alter the intracellular accumulation of paclitaxel. For the control and the PSC833-treated cells, the areas under the intracellular concentration-time profiles were 79 ± 8 and 84 ± 7 µM · h, respectively (mean ± S.D., n = 3). A separate study showed that PSC833 at this concentration completely inhibited the Pgp-mediated efflux in the mdr1-transfected subline of the MCF7 cells (i.e., BC19 cells), which showed a 9-fold higher Pgp expression and 60% lower drug accumulation (Jang et al., 1998; Li et al., 1998). These data rule out significant Pgp-mediated efflux and support the assumption that paclitaxel is removed from MCF7 cells by passive diffusion.

Kinetics of Paclitaxel Accumulation and Binding. Figure 1 shows the kinetics of paclitaxel accumulation in MCF7 cells. The extensive drug accumulation in cells, indicated by the high intracellular-to-extracellular concentration ratios (Table 1), resulted in significant depletion of paclitaxel from the medium, i.e., >70% depletion at 1 and 10 nM and ~40% depletion at 1000 nM. The depletion occurred even though the volume of the drug-containing medium was more than 500 times the cell volume, a condition that is commonly used in cell culture studies. The intracellular concentration increased with time and approached plateau levels between 1 and 4 h, with the longest time to reach plateau levels at the lowest extracellular concentration. The intracellular-to-extracellular concentration ratio at 4 h decreased 13-fold when the extracellular concentration increased from 1 to 1000 nM. However, when the extracellular concentration was further elevated to 2000 and 5000 nM, the intracellular-to-extracellular concentration ratio remained relatively constant at ~75. As shown below, these concentration-dependent changes in concentration ratios are due to the saturation of the saturable binding sites at higher extracellular drug concentrations and to the linear increase of nonsaturable binding with extracellular concentration.

View larger version (15K): [in this window] [in a new window]   Fig. 1.   Intracellular and extracellular concentrations of paclitaxel during uptake. MCF7 cells were incubated with 1 to 1000 nM paclitaxel. The concentration of paclitaxel in cells (left panel) and culture medium (right panel) were monitored for 24 h. Note the different units for intracellular and extracellular concentrations. Symbols are the experimental data. Lines are computer-simulated data using eqs. 8 and 9. Mean ± S.D. (n = 3). All S.D. values are smaller than the symbols.

Effect of Paclitaxel Treatment on Tubulins/Microtubules. In untreated cells, the polymerized tubulin represented ~75% of total tubulin. Treatment with 1 and 10 nM paclitaxel did not increase the total tubulin nor the extent of polymerization, whereas treatments with 100 and 1000 nM paclitaxel significantly enhanced the polymerization (Table 4). Treatment with 1000 nM paclitaxel for 24 h further increased the amount of total tubulin, whereas shorter treatments with 1000 nM or treatments with lower drug concentrations did not. This indicates the induction of tubulin production over time at high paclitaxel concentration. The increase in tubulin polymerization at 1000 nM paclitaxel occurred within 1 h or before significant tubulin production was detected. This indicates a rapid polymerization of pre-existing tubulin by paclitaxel in MCF7 cells and confirms that this drug effect, previously observed in a cell-free system (Derry et al., 1995), also occurs in intact cells.

Development and Validation of a Computational Intracellular Paclitaxel Pharmacokinetic Model. Figure 1 shows the model-simulated intracellular and extracellular drug concentration-time profiles, which superimposed the experimental data points. Table 3 lists the model parameters.

View larger version (11K): [in this window] [in a new window]   Fig. 2.   Comparisons of model-predicted and experimental data. Left panel, drug uptake as a function of cell density and amount of drug in culture medium. MCF7 cells were seeded at different densities and treated with 10 nM paclitaxel in either 1 or 10 ml of culture medium for 4 h. The intracellular drug concentrations attained at 4 h are shown. Right panel, drug efflux as a function of time and intracellular-to-extracellular concentration gradient. MCF7 cells were treated with 10 nM paclitaxel for 24 h. The drug-containing medium was then replaced with 1, 2, and 4 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. Symbols are the experimental data. Lines represent the model-predicted data. Mean ± S.D. (n = 3). Most S.D. values are smaller than the symbols.

View larger version (10K): [in this window] [in a new window]   Fig. 3.   Effects of cell density and microtubule mass on model prediction. Intracellular drug concentration-time profile in MCF7 cells treated with paclitaxel for 24 h. Symbols are the experimental data. Left panel, lines represent the model-predicted data with (solid) and without (dotted) the increase in cell number as described by eq. 6 at 1 nM extracellular drug concentration. Right panel, lines represent the model-predicted data with (solid) and without (dotted) the increase in tubulin concentration as described by eq. 7 at 1000 nM extracellular drug concentration. Mean ± S.D. (n = 3). Most S.D. values are smaller than the symbols.

Examples of Application of a Computational Intracellular Paclitaxel Pharmacokinetic Model. The computational intracellular pharmacokinetic model can be used to depict changes in intracellular drug concentration as a function of extracellular concentration, time, number and binding affinity of binding sites, and cell density. To demonstrate its use, we performed the following simulations.

View larger version (16K): [in this window] [in a new window]   Fig. 4.   Application of computational model: effects of altering intracellular and extracellular binding on intracellular drug accumulation. Simulations were performed using parameters obtained in MCF7 cells at two initial extracellular concentrations (i.e., 1 and 1000 nM) as described in Table 3. Left panel, effect of changing the value of Bmax,c from 60 µM (actual value for MCF7 cells, solid line) to 30 µM (broken line) and 120 µM (dotted line). Middle panel, effect of changing the value of Kd,c from 5 nM (actual value for MCF7 cells, solid line) to 20 nM (dotted line). Right panel, effect of changing extracellular free fraction from 20 (actual value, solid line) to 5% (dotted line).

View larger version (15K): [in this window] [in a new window]   Fig. 5.   Application of computational model: relationship between extracellular and intracellular drug concentration. Effect of changing extracellular drug concentration on intracellular drug concentration at 4 h, or when the intracellular and extracellular drug concentrations approached a pseudo-steady state.

	Discussion

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Relationship Between Cell Density, Tubulin Polymerization/Production, and Drug Accumulation. The intracellular concentration-time profiles, depicted in Fig. 1, showed two unusual features. First, the intracellular paclitaxel concentration attained at 1 and 10 nM extracellular concentrations reached a maximum value at 4 h and subsequently declined by 23 and 10%, respectively, by 24 h (Table 1). Second, the intracellular concentrations attained at 100 and 1000 nM extracellular concentrations continued to increase with time by about 20 and 50% between 4 and 24 h, respectively (Table 1). These profiles differ from the more commonplace situation where intracellular drug concentration increases with time to reach and remain at a plateau level. This study showed that the decrease in intracellular drug accumulation with time at low drug concentration was due to an increase in cell number as cell proliferation continued (i.e., cell number increased by 36 and 23% over 24 h at 1 and 10 nM, respectively, see Table 1), whereas the increase in drug accumulation with time at high drug concentration was due to paclitaxel-induced increases in total tubulin (Table 4).

Comparison of Paclitaxel Accumulation Data in MCF7 Cells with Previous Data in Other Cells. To determine whether the intracellular pharmacokinetic model is applicable to human cancer cells in general or only to the MCF7 cells, we compared the accumulation of paclitaxel and drug-induced changes in tubulin polymerization and production in MCF7 cells with the results of an earlier study in HeLa cells (Jordan et al., 1993). The unusually high drug accumulation in MCF7 cells is similar to the finding in HeLa cells; the intracellular-to-initial medium concentration ratios in MCF7 cells, attained at 10 to 1000 nM initial medium concentrations, ranged from 115 to 464 at 24 h (calculated from data in Table 1), whereas the same ratios in HeLa cells ranged from 111 to 480 at 20 h. In both cell lines, prolonged treatment (20-24 h) with paclitaxel at higher concentrations (100 nM) induced tubulin production and polymerization and increased microtubule concentration. The enhancement in microtubule concentration in MCF7 cells was lower than in HeLa cells, i.e., a 2-fold enhancement at an initial extracellular concentration of 1000 nM in MCF7 cells versus a 5-fold enhancement in HeLa cells. This 2.5-fold greater enhancement is mainly due to the higher concentration of pre-existing free tubulin available for polymerization in the HeLa cells; free tubulin represents 67% of total tubulin in HeLa cells (Jordan et al., 1991; Thrower et al., 1991) and 25% in MCF7 cells (Table 4). Correction for this factor showed that the enhancement in total tubulin was almost identical in the two cell lines, i.e., 1.8-fold in MCF7 for 24 h versus 1.7-fold in HeLa cells for 20 h (calculated from the literature data; Jordan et al., 1991, 1993; Thrower et al., 1991).

Conclusions. The intracellular pharmacokinetic model of paclitaxel described here takes into account the known determinants of drug accumulation in Pgp-negative cells, and therefore can be used to depict intracellular drug concentration-time profiles. As shown in this study, a computational intracellular pharmacokinetic model has the versatility to predict the kinetics of paclitaxel uptake, binding, and efflux in cells under various conditions. The ability to predict intracellular drug concentrations as a function of extracellular drug concentrations such as those in plasma enables the comparison of intracellular concentrations attained at different treatment schedules, e.g., a long infusion that delivers a low plasma concentration for a long duration versus a shorter infusion that delivers a higher plasma concentration for a shorter duration. The ability to predict intracellular drug accumulation as a function of extracellular drug binding enables the evaluation of drug-drug interaction due to alteration of free fraction of paclitaxel in plasma by the presence of Cremophor or cisplatin. The ability to relate the intracellular bound concentrations to changes in microtubules enables us to quantify the effects of changes in tubulins on the kinetics of drug accumulation and efflux in cells. Our long-term goal is to develop a model that links the intracellular pharmacokinetics with pharmacodynamics and allows the antitumor effects of selected treatment schedules to be depicted.