Introduction

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Recent advance in the recombinant DNA technology to prepare the chimeric mouse-human antibodies provided a means to use such Mabs in the diagnosis and/or treatment of solid tumors (Colcher et al., 1989, Amstutz et al., 1993). For a safe and efficient treatment of a tumor in humans, it is important to know the kinetic parameters for the disposition of Mabs within the tumor. Such kinetic understanding is further necessary to design appropriate delivery systems with Mabs as vectors (Suzuki et al., 1996). Based on these requirements, Dedrick and his collaborators previously investigated the disposition of Mabs in tumor-bearing mice based on a hybrid model in which physiological factors (such as the volume of extracellular fluid and lymph flow rate in tumor) as well as the parameters characteristic of the Mabs (such as tumor capillary permeability and binding parameters) were considered (Sung et al., 1990, 1992; Shockley et al., 1992). They found a discrepancy between in vivo and in vitro in the BP of Mabs, which was defined as the number of binding sites divided by the dissociation rate constant; the BP of an immunotoxin determined in vivo being 530 times lower than that determined in vitro (Sung et al., 1990). Moreover, the in vivo BP of several antibodies was 15 to 70 times lower than the in vitro BP, even if the difference in antigen expression level between both experimental conditions was considered (Sung et al., 1992; Shockley et al., 1992). This finding was ascribed to the sequestration of the Mabs by tumor cells and/or to the in vivo inaccessibility of the Mab molecules to their binding sites (Sung et al., 1990, 1992; Shockley et al., 1992). Other theoretical and experimental studies with a more elaborate microscopic pharmacokinetic model in which the diffusion of Mab molecules within the tumor tissue was considered also supports the latter hypothesis (Fujimori et al., 1990). Based on this model, these investigators suggested that the binding of Mabs to the antigen in the immediate proximity of the blood vessels significantly reduces the number of diffusible Mab molecules available for the penetration into the deeper part of the tumor tissues (Juweid et al., 1992; Weinstein and Osdol, 1992).

In essentially all of the studies reported previously, however, the kinetic analysis was based on the Langmuir isotherm for the reversible and saturable binding of Mabs to the tumor cells (Thomas et al., 1989; Fujimori et al., 1990; Sung et al., 1990, 1992; Juweid et al., 1992; Shockley et al., 1992; Weinstein and Osdol, 1992). However, it is well established that the Mab molecules bound to the cell surface antigen are internalized via a clathrin-dependent (Press et al., 1988) and/or clathrin-independent manner (Byers et al., 1991) and then are subjected to the lysozomal degradation. Separate estimation of the surface-bound and internalized Mab molecules should be important when the mechanism of the pharmacological activity of Mabs is considered; if the tumor is treated with immunotoxins, the internalized amount might be related to the therapeutic efficacy (Lambert et al., 1985; Wargalla and Reisfeld, 1989). By contrast, surface-bound Mab molecules might be important if the immune system of the host is involved in the reduction of tumor size, because complements recognize the antigen-antibody complex on the tumor cell surface (Roitt, 1988). Although Fujimori et al. (1989) theoretically examined the influence of antibody sequestration in the tumor on the tumor disposition, no experimental studies have been performed to separately determine surface bound and internalized Mab molecules.

Previously, we investigated the hepatic disposition of growth factors which are internalized via receptor-mediated endocytosis (Kato et al., 1992; Liu et al., 1995; Sugiyama and Kato, 1995). In these studies, a pharmacokinetic model incorporating the initial binding, internalization and degradation processes of Mab molecules was used. The purpose of the present research was to analyze the tumor disposition of Mabs with use of such a comprehensive pharmacokinetic approach. As a model Mab, we used MRK16, an IgG_2a Mab against P-glycoprotein (P-gp), which mediates the efflux of anticancer drugs (such as adriamycin and vinca alkaloids) from multidrug-resistant cells (Hamada and Tsuruo, 1988). The in vivo pharmacological activity of MRK16 was demonstrated in nude mice bearing P-gp positive human tumor cell lines; the growth of adriamycin-resistant ovarian carcinoma cells (2780^AD) (Tsuruo et al., 1989) and MDR 1 gene-transfected colorectal carcinoma cells (HT-29^{mdr 1}) were markedly reduced by the i.v. administration of MRK16 (Pearson et al., 1991). Furthermore, we demonstrated the in vivo efficacy of MRK16 against the P-gp positive colorectal carcinoma cell line (HCT-15) in nude mice, along with its accumulation in the tumor after i.v. administration (Iwahashi et al., 1993). In the present study, we determined the kinetic parameters for the binding, internalization and degradation of MRK16 in HCT-15 cells in vitro, and predicted its in vivo disposition.

	Materials and Methods

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Animals and tumor cells. Six-week-old female BALB/c nu/nu mice weighing 20 to 22 g were purchased from Japan Laboratory Animals Inc. (Tokyo, Japan). HCT-15 and another human colorectal carcinoma cell line which does not express P-gp to a significant level, COLO205, were purchased from American Type Culture Collection (Rockville, MD). These cell lines were cultured in RPMI 1640 (Nikken Bio Medical Laboratory, Tokyo, Japan), supplemented with 10% fetal bovine serum (Irvine Scientific, Santa Ana, CA).

Mabs. MRK16 was purified from an MRK16-producing hybridoma subclone (Iwahashi et al., 1993) that grows stably in serum-free RPMI 1640 supplemented with insulin (5 mg/l), transferrin (10 mg/l), sodium serenate (4.3 µg/l) and aprotinin (10,000 units/l). Conditioned medium was applied to a Protein A-Sepharose column (IPA-400 FAST FLOW Immobilized Protein A, Repligen, MA), equilibrated with 0.1 M Tris-HCl buffer (pH 3.0). The fraction containing MRK16 was eluted with 0.1 M Tris-HCl buffer (pH 3.0), then the pH of the antibody containing fraction was adjusted to 7.0 by the addition of Tris-HCl buffer. The purity of Mab preparations used in the present study was determined by means of a gel filtration method with high-performance liquid chromatography (Iwahashi et al., 1993) and was found to be more than 99% pure. UPC-10, an IgG_2a isotype Mab against mouse whole serum, was purchased from Sigma Co. Ltd. (St. Louis, MO).

Radiolabeling of MRK16. MRK16 was radiolabeled by the Iodo-gen method (Iwahashi et al., 1993). Fifty micrograms of purified antibody, dissolved in 100 µl of PBS (137 mM NaCl, 26.8 mM KCl, 9.66 mM NaHPO₄, 1.15 mM KH₂PO₄; pH 7.2), were incubated with 0.5 mCi of ¹²⁵I-Na (Amersham International, Buckinghamshire, U.K.) for 8 min on ice, in glass tubes coated with 2.5 µg of Iodo-gen reagent (1,3,4,6-tetrachloro-3d,6d-diphenyl glycoluril; Pierce Chemical Co, Rockford, IL). Radiolabeled antibody was separated from free iodine by use of PD-10 columns (Pharmacia Biotech, Uppsala, Sweden), which had been pre-equilibrated with 1% BSA/PBS. The fraction of incorporated radioiodine was determined by the TCA precipitation method: 150 µl of TCA solution (15% w/w) was added to 150 µl of each specimen, which was prepared by diluting 75 times with 1% BSA/PBS, and then the mixture was incubated for 10 min at a room temperature. After centrifugation, the radioactivity associated with the supernatant and precipitant was measured in a gamma counter (model ARC-300, Aloka, Tokyo, Japan); more than 99% of radioactivity was associated with the Mab. The specific activity was 4.8 to 5.8 µCi/µg IgG, which suggested that 0.8 to 1.0 iodine molecules were bound to one MRK16 molecule. The fact that the binding activities of MRK16 to P-gp were not inhibited by the radiolabeling procedure was confirmed by means of an enzyme-linked immunosorbent assay, wherein 1.3 µM ¹²⁵I-labeled or unlabeled MRK16 was incubated with HCT-15 cells (2 × 10⁴ cells/well) for 1 hr. After removal of the medium, the cells were washed three times with PBS, then the cells were incubated with an anti-mouse peroxidase-conjugated rabbit immunoglobulin to mouse immunoglobulin (130 µg/ml, P260, DACO, Glostrup, Denmark) for another hour at a room temperature. The enzymatic activity, determined with 3,3,5,5-tetramethyl benzidine dihydrochloride as a substrate, was similar between ¹²⁵I-labeled and unlabeled MRK16.

In vitro binding experiments. To perform in vitro experiments with confluent cells, 1 × 10⁵ of HCT-15 cells were seeded 4 days before the experiment. The binding reaction was initiated by adding [¹²⁵I]MRK16 to produce a final concentration of 0.6 µg/ml in 0.5 ml medium (RPMI 1640 containing 1% BSA), then the cells were incubated at 37°C under 5% CO₂. At specified times, the medium was removed and then the cells were washed three times with 1 ml of ice-cold PBS. To determine the amount of [¹²⁵I]MRK16 associated with the cell surface from that internalized into the cells, an acid-wash method (Wargalla and Reisfeld, 1989), a trypsin-wash method (Kyriakos et al., 1992) and an acid papain-wash method (Press et al., 1988) were examined. In the acid-wash method, 500 µl of acid buffer (0.5 M NaCl and 0.2 M acetic acid in PBS) was added to each well before incubation on ice; preliminary experiments indicated that an 8-min incubation was sufficient to remove the surface-bound antibodies. In the trypsin-wash method, 500 µl of trypsin (10 mg/ml in PBS) was added to each well before incubation at 37°C for 10 to 30 min. In the acid papain-wash method, 500 µl of papain solution (2.5 mg/ml in RPMI 1640 containing 1 N HCl) was added to each well and incubated for 8 min at 37°C. After these three kinds of treatment, radioactivity associated with the cells was determined after solubilizing them by the addition of 2 N NaOH (500 µl) followed by the incubation for 30 min at 60°C. After incubating the cells with MRK16 for 6 hr, the membrane-bound fraction was determined to be 0.75, 0.50 and 0.73 for the acid-wash, trypsin-wash and acid papain-wash methods, respectively. The fraction of MRK16 released from the cells (0.50) was lowest when the trypsin-wash method was used, which suggests that this method may not be sufficient to remove all of the surface-bound antibody. Although we do not have any evidence that the surface-bound antibody can be completely removed by the acid-wash and acid papain-wash methods, these two methods should be superior to the trypsin-wash method, because 73 to 75% of MRK16 molecules was removed by these methods. Because only these three methods have been previously used to separately determine membrane-bound and internalized Mabs (Wargalla and Reisfeld, 1989; Kyriakos et al., 1992; Press et al., 1988), we selected the acid-wash method because the highest fraction of MRK16 was released from the incubated cells.

Disposition of FITC-labeled Mabs in HCT-15 cells. MRK16 or UPC-10 each (300 µg) was incubated in 0.5 M bicarbonate buffer (0.3 ml; pH 9.2) containing 0.59 mg of FITC (Wako Pure Chemical Industries, Osaka, Japan) for 24 hr at room temperature and a concentration of 1.97 mg FITC/mg IgG. The labeled Mabs were separated from free FITC by dialysis. The molar ratio of FITC to Mab in the FITC-Mab conjugate was 1.9 to 2.3. To investigate the disposition of FITC-labeled Mabs in confluent HCT-15 cells, 1 × 10⁴ HCT-15 cells were seeded 4 days before the experiment. The binding reaction was initiated by adding FITC-labeled Mabs to produce a final concentration of 2 µg/ml in 0.2 ml medium (RPMI 1640) at 37°C in 5% CO₂. Twelve hours after initiation of the experiment, the medium was removed and the cells were washed three times with 0.5 ml of ice-cold PBS. Then, cells were examined in a laser scanning confocal microscopy (MRC-600, Bio-Rad Laboratories, Hercules, CA) at excitation and emission wavelengths of 488 and 515 nm, respectively.

In vivo study. Nude mice were inoculated subcutaneously with 5 × 10⁶ HCT-15 and COLO205 cells suspended in 0.2 ml of PBS solution into the right and left flanks, respectively. After 14 days, the tumor grew up to 0.5 to 0.8 g. The mice received an i.v. injection of [¹²⁵I]MRK16 (0.6 µg/mouse) through a tail vein before the sacrifice at specified time points. Blood was collected from a tail vein and plasma was separated from blood by centrifugation. Tumor specimens were removed and rinsed with PBS before analysis. The radioactivity associated with the plasma and tumors was counted in a gamma counter (model ARC-300, Aloka). The tissue-to-plasma concentration ratio of [¹²⁵I]MRK16 was determined by dividing the radioactivity associated with 1 g of tissue by that associated with 1 ml of plasma.

Kinetic analysis. The in vitro binding of MRK16 with HCT-15 cells was kinetically analyzed based on a model shown in scheme 1, where L represents the concentration of [¹²⁵I] MRK16 in the medium. The clearance for the binding of MRK16 to membrane-associated P-gp was defined as k_onR, where k_on represents the association rate constant between MRK16 and P-gp and R represents the amount of unoccupied antigen (P-gp) on the cell surface. The antigen-bound MRK16 molecules (LR_s) are assumed to be internalized or dissociate with the rate constants of k_int or k_off, respectively. The internalized complex (LR_i) may be degraded within the cell or released into the medium with the rate constant of k_eff.

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	Results

Top Abstract Introduction Materials & Methods Results Discussion References

In vitro experiments. In HCT-15 cells, the amount of [¹²⁵I]MRK16 in the acid-releasable and -resistant fractions increased with time (fig. 1) and reached 140 and 50 ng/mg protein at 12 hr, respectively. The amount of acid-releasable and -resistant fractions of [¹²⁵I]MRK16 to COLO205 cells was 2.5% and 0.5% of those in HCT-15 cells, respectively. Saturation of [¹²⁵I]MRK16 binding was not observed by the addition of unlabeled MRK16 up to a concentration of 105 µg/ml. In pulse-chase experiments, acid-releasable and -resistant radioactivity decreased with time and reached approximately 47% and 52% of the initial value at 6 hr after initiation of the chase incubation, respectively (fig. 2). The fraction of [¹²⁵I]MRK16 released into the medium increased with time. At 6 hr, approximately 85% of the radioactivity released in the medium was associated with the TCA-precipitable fraction. The binding capability of the released radioactivity to HCT-15 cells was approximately 88% of that of intact [¹²⁵I]MRK16.

View larger version (15K): [in this window] [in a new window]   Fig. 1.   Time profiles for cell surface-bound and intracellularly internalized MRK16 in HCT-15 cells. Confluent HCT-15 cells were incubated in the medium (RPMI1640 with 1% BSA) containing 0.6 µg/ml of [125I]MRK16 at 37°C. Surface-bound () and internalized () MRK16 were determined separately by means of an acid-wash method. Solid lines represent the best fit of the data to equations 1 and 2. Each point and vertical bar represent the mean ± S.E. of three independent experiments.

View larger version (13K): [in this window] [in a new window]   Fig. 2.   Time profiles for distribution of MRK16 in the pulse-chase study. Confluent HCT-15 cells were incubated in the medium (RPMI 1640 with 1% BSA) containing 0.6 µg/ml of [125I]MRK16 for 6 hr at 37°C. The cells were washed with PBS, and then were incubated for the specified times at 37°C in the same medium but is free from [125I]MRK16. Surface-bound (), internalized () MRK16 and medium () radioactivity were measured by means of an acid-wash method. Solid lines represent the best fit of the data to equations 1, 2 and 3. Each point and vertical bar represent the mean ± S.E. of three independent experiments.

View larger version (10K): [in this window] [in a new window]   Fig. 3.   Estimation of the initial model parameter values. Panel A shows the initial slope of the amount of surface-bound MRK16 versus 0T L(t) dt to estimate the initial value of konR. Panel B shows the initial slope of the amount of LRi at time T versus 0T LRs (t) dt to determine the initial estimation of kint. Panel C shows the initial slope of ln LRs versus time to estimate the sum of kint + koff. The solid lines represent the best fit of the data. Each point and vertical bar represent the mean ± S.E. of three independent experiments. Data were taken from figures 1 and 2.

Disposition of FITC-labeled Mabs in HCT-15 cells. To investigate whether the acid-resistant portion of MRK16 is responsible for the internalized molecules, the cellular distribution of FITC-labeled MRK16 was measured. The intracellular fluorescence of FITC-MRK16 was detectable at the cell surface (fig. 4A); by contrast, the intracellular fluorescence intensity of FITC-UPC-10 was minimal (fig. 4B).

View larger version (111K): [in this window] [in a new window]   Fig. 4.   Disposition of FITC-labeled Mabs into HCT-15 cells. Confluent HCT-15 cells were incubated in the medium (RPMI 1640 with 1% BSA) containing 2 µg/ml of FITC-labeled Mabs [MRK16 (A) and UPC-10 (B)] at 37°C. At 12 hr, the cells were washed with PBS and then examined by laser-scanning confocal microscopy at excitation and emission wavelengths of 488 and 515 nm, respectively. Left and right panels show the observation by microscopy and laser-scanning confocal microscopy, respectively.

In vivo disposition of [¹²⁵I]MRK16. After i.v. administration, the plasma concentration [C_p (t)] of [¹²⁵I]MRK16 declined biexponentially (fig. 5). Nonlinear least-square regression analysis revealed that C_p (t) (in µg/ml) was described as a function of time (t in hr): C_p (t) = 0.182e^0.0105t + 0.269e^0.301t. The initial volume of distribution (53.2±9.6 ml/kg) was similar to the plasma volume (40 ml/kg). The terminal plasma half-life (66 hr) was approximately 60% smaller than that reported previously (168 hr; Iwahashi et al., 1993). More than 98% of the radioactivity in plasma 24 hr after injection of [¹²⁵I]MRK16 was TCA-precipitable. Furthermore, the radioactive material in plasma obtained 24 hr after injection of [¹²⁵I]MRK16 had the same binding activity to HCT-15 cells as freshly prepared [¹²⁵I]MRK16, which suggested that the radioactivity in plasma represents intact [¹²⁵I]MRK16.

View larger version (22K): [in this window] [in a new window]   Fig. 5.   Time profiles for plasma and tumor concentrations of [125I]MRK16 after intravenous injection. [125I]MRK16 (0.6 µg/ml) was intravenously injected into mice bearing tumors (HCT-15 and COLO205). At specified time points, mice were sacrificed and the [125I]MRK16 concentration in plasma (), HCT-15 () and COLO205 () was measured. The solid line represents the plasma concentration fitted to a biexponential equation; the dotted line represents [125I]MRK16 concentration in HCT-15 tumor and ECF; and the dashed line represents the [125I]MRK16 concentration in COLO205 tumor and ECF. The dotted and dashed lines were calculated by equations 5 through 8 together with the parameters listed in table 2. Each point and vertical bar represent the mean ± S.E. of three independent experiments.

View larger version (14K): [in this window] [in a new window]   Fig. 6.   Tumor-to-plasma concentration ratio of MRK16 after intravenous injection. [125I]MRK16 (0.6 µg/ml) was injected intravenously into mice bearing tumors (HCT-15 and COLO205). Based on the data shown in figure 5, the tumor-to-plasma concentration ratio of [125I]MRK16 for HCT-15 () and COLO205 () were calculated by dividing the [125I]MRK16 concentration in tumor by that in plasma. Solid lines represent the predicted tumor-to-plasma concentration ratio of [125I]MRK16 in HCT-15 and COLO205 tumors. Calculations were performed by equations 5 through 8 with the parameters listed in table 2. Each point and vertical bar represent the mean ± S.E. of three independent experiments.

View larger version (20K): [in this window] [in a new window]   Fig. 7.   Initial in vivo uptake of Mabs into HCT-15 tumor. The tumor-to-plasma concentration ratio at time T versus [plasma AUC up to T divided by Cp (T)] obtained from figure 5 is plotted. The y-intercept and the slope provide Vcap and Kin, respectively.

View larger version (28K): [in this window] [in a new window]   Fig. 8.   Sensitivity analysis of the tumor-to-plasma concentration ratio against parameters involved in the prediction. Panels A, B, C, D, E, F, G and H indicate the sensitivity to the alteration in clearance for influx (Kin), clearance for efflux (Kout), lymph flow rate (QL), clearance for binding (konR), dissociation rate constant (koff), internalization rate constant (kint), efflux rate constant (keff) and fractional ECF space in tumor tissue (VECF), respectively. Calculations were performed with equations 5 through 8 with the parameter values listed in table 2.

	Discussion

Top Abstract Introduction Materials & Methods Results Discussion References

In the present study, we determined the kinetic parameters for the disposition of MRK16 in HCT-15 cells in vitro, and predicted the in vivo tumor association of this Mab. In the in vitro binding study, the volume of distribution of MRK16 in HCT-15 cells at pseudo steady state, defined as the amount of MRK16 associated with the tumor cells (surface plus internalized) divided by the concentration in the medium, was calculated to be 323 µl/mg protein, by considering MRK16 concentration in the medium (0.6 µg/ml; fig. 1). Based on the fact that the intracellular volume of HCT-15 cells is 3.2 µl/mg protein, the apparent cell-to-medium concentration ratio of MRK16 is about 100. Approximately 75% of cell-associated radioactivity was acid-releasable, which indicated that a large fraction of the apparent accumulation was caused by the surface binding of MRK16 to P-gp (fig. 1). In contrast, approximately 25% of the cell-associated radioactivity (acid-resistant fraction) may represent the intracellular MRK16 (fig. 1). This assumption was also supported by the observation with laser scanning confocal microscopy (fig. 4).

Based on the model analysis, the rate constant for internalization of MRK16 was determined to be 0.149 hr¹ (table 1). The half-life of the internalization, in turn, was estimated to be 4.65 hr. This result is consistent with the previous observation that the turnover rate of cell surface glycoproteins, whose physiological function is not mediated by its internalization, is relatively slow in most cases; e.g., for hgp85 and M_r =110,000 glycoprotein approximately 41 and 43 hr in hepatoma cells (Tauber et al., 1989) and hepatocyte bile canaliculus (Diamond et al., 1987), respectively. In contrast, it has been reported that the internalization rate constant of Mabs against the transferrin receptor is 7.5 min (Hopkins and Trowbridge, 1983) as the internalization of Mab is accompanied by that of receptor. Since the turnover rate of P-gp has not yet been reported, it cannot be determined whether this internalization rate is associated with the constitutive turnover of P-gp or the internalization of P-gp is induced by the binding of MRK16.

The in vitro kinetic analysis, however, has limitations. First, the calculated value of k_off is unreliable (table 1), because the data in figures 1 and 2 cannot provide the time profiles from which the k_off value can be directly determined. This is in marked contrast to the ready estimation of other parameters. For example, the time profiles for the initial uptake of MRK16 by HCT-15 cells provides an excellent estimation of k_onR, i.e., k_onR is given by equation 4. To obtain a direct k_off estimate, we attempted to determine the kinetic parameters (K_d and R) for the saturable binding of MRK16 to HCT-15 cells. Because k_off can be given as K_d/k_on, k_off can be determined in a reliable manner by this method. The binding of MRK16 to HCT-15 cells, however, was not saturated in the presence of 105 µg/ml of MRK16 and, therefore, we could not determine the K_d value. Previously, Hamada and Tsuruo (1986) reported that the binding of MRK16 to P-gp was not saturated up to 50 µg/ml, irrespective of its high specificity against P-gp.

Second, we have no explanation why surface-bound MRK16 is underpredicted in figure 2. However, one possible explanation for this discrepancy may be the presence of another pool for the membrane-bound MRK16; if some portion of the membrane-bound MRK16 is not releasable, the data in figure 2 can be explained.

Finally, in the present analysis, we assumed no intracellular degradation of the antibody. However, because we found that 12 to 15% of the [¹²⁵I]MRK16 released into the medium in the pulse-chase experiment may represent degradation product, intracellular degradation may affect the analysis.

Accumulation of MRK16 by HCT-15 cells was also observed in the in vivo experiments (figs. 5 and 6). After i.v. administration of MRK16 into tumor-bearing mice, the tumor-to-plasma concentration ratio of this Mab was 0.583 and 0.254 in HCT-15 and COLO205 cells at 72 hr, respectively (fig. 6). These in vivo observations are in marked contrast to the in vitro data, in that the apparent in vitro accumulation of MRK16 in HCT-15 cells is approximately 40 times higher than in COLO205 at steady state. Because the binding of MRK16 to HCT-15 cells was not saturated up to 105 µg/ml (see "Results") and the initial plasma concentration of MRK16 was 0.451 µg/ml (fig. 5), saturation of the binding may not affect the analysis.

To account for this in vivo and in vitro discrepancy, we performed additional kinetic analysis. With the kinetic parameters listed in tables 1 and 2, the time profiles for the tumor concentration of MRK16 were estimated (fig. 5). At 72 hr, the tumor-to-plasma concentration ratio was calculated to be 0.83 and 0.31 for HCT-15 and COLO205, respectively. This predicted 2.6-fold difference between the two tumor cell lines was similar to the observed 2.3-fold difference in vivo (fig. 6). The analysis revealed that, at this time point, the MRK16 concentration in the HCT-15 ECF (0.66 ng/ml) is apparently 13 times lower than that in COLO205 ECF (8.6 ng/ml), i.e., the tumor-to-ECF concentration ratio of MRK16 in HCT-15 tumor (106) was 34 times higher than that in COLO205 tumor (3.14), which was similar to the in vitro observations. Collectively, the observed minimal difference in vivo is accounted for by the fact that the ECF is not in rapid equilibrium with the plasma, i.e., the penetration of MRK16 across the tumor capillary is restricted.

This suggestion was supported further by the sensitivity analysis (fig. 8). The tumor-to-plasma concentration ratio of MRK16 was most sensitive to K_in but not to Q_L, k_onR or k_off values (fig. 8). This result can be accounted for by considering the fact that the k_onR value (13.5 ml/hr/g tumor) is much higher than Q_L (0.048 ml/hr/g tumor) and K_out (= K_in, 0.012 ml/hr/g tumor) (table 2); because almost all the MRK16 molecules upon entering tumor ECF and/or released from the cells are bound to the cell surface antigen and cannot be eliminated by lymph flow and/or efflux across the capillary, the tumor-to-plasma concentration ratio is most sensitive to K_in (Miyauchi et al., 1988). These results suggest that the previously reported variations in Q_L value depending on the tumor cell lines (0.048-0.222 ml/hr/g tumor; Butler et al., 1975; Sung et al., 1990; Shockley et al., 1992) as well as the 0.4- to 3.5-fold difference in the antigen expression level between in vitro and in vivo (Shockley et al., 1992) might not alter the prediction (fig. 8). In the same manner, the variation in V_ECF value might not affect the calculation (fig. 8).

Under the condition that K_in equals 0.0120 ml/hr/g tumor, the tumor disposition of MRK16 was affected by k_int and k_eff, along with k_onR (fig. 8). The higher tumor-to-plasma concentration ratio was associated with the lower k_int values (fig. 8), which can be accounted for by considering that approximately 73% of the tumor tissue-associated MRK16 is present as the surface-bound form if the k_int value equals 0.149. At higher k_int values, the internalization of the surface-bound MRK16 is accelerated, and this, in turn, is eliminated from the tumor cells. The decrease in k_eff resulted in an increase in the tumor-to-plasma concentration ratio (fig. 8), which can be accounted for by the intracellular MRK16 being maintained at lower k_eff values.

In the present analysis, we assumed that the in vitro 40-fold difference in the associations of MRK16 between HCT-15 and COLO205 cells is ascribed to the difference in k_onR values and that the k_int and k_eff values are the same for the two tumor cell lines, because of the difficulty in determining each parameter value in COLO205 cells as a result of the low association of MRK16. Kinetic considerations (fig. 8), however, suggest that both the in vitro and in vivo data may be accounted for by another set of parameter values. For example, higher k_int and k_eff values in COLO205 cells compared with HCT-15 cells could account for the present data if one assumes restricted penetration of MRK16 across the tumor capillary (K_in = 0.0120 ml/hr/g tumor; fig. 7 and table 2).

As shown in figure 6, the predicted line overpredicted the actual data by approximately 43% at 72 hr. However, it is possible that an error in the estimation of K_in values could result in this overestimate because the prediction is very sensitive to the K_in value (fig. 8A). Reducing the K_in value to improve the prediction of the results at later time points, however, results in the poor fit to the earlier time point data. The simulation suggested that the late time point data can be predicted by increasing the k_int value to 0.24 hr¹. If the standard deviation of the k_int value determined in vitro (k_int = 0.149 ± 0.046 hr¹, table 1) is considered, it is possible that the later time point data can be predicted more accurately by larger k_int values.

In addition, because we found that 12 to 15% of the [¹²⁵I]MRK16 was released into the medium in the pulse-chase experiment, the discrepancy may be related to the deiodination of [¹²⁵I]MRK16. Alternatively, some additional physiological and/or anatomical factors (e.g., in vivo inaccessibility of MRK16 to their binding sites; Fujimori et al., 1990) to describe the ligand disposition within the solid tumor might be required to improve the model. In addition, it is plausible that the reduction in tumor size produced by MRK16 (Iwahashi et al., 1993) may be related to this discrepancy.

In the present analysis, the K_in values were determined from the initial uptake of MRK16 into the tumor (fig. 7). For HCT-15 and COLO205 cells, the K_in values were 0.012 and 0.008 (ml/hr/g tumor), respectively (table 2). These values are consistent with the previously reported values for several Mabs; although the K_in values depend on cell type (Shockley et al., 1992), tumor size (Nakagawa et al., 1987) and/or localization of the xenograft (Blasberg et al., 1987), the value is within the range of 0.0078 to 0.142 (Nakagawa et al., 1987; Sung et al., 1990; Shockley et al., 1992). In the same manner, V_cap values were determined to be 0.035 and 0.028 (ml/g tumor) for HCT-15 and COLO205 tumor, respectively (table 2), which were slightly larger than those reported previously [0.0023-0.0125 (ml/g tumor); Sung et al., 1990; Shockley et al., 1992]. This discrepancy may be accounted for by the difference in the vascularization of the tumor as discussed by Gabbert et al. (1982), because Sung et al. (1990) and Shockley et al. (1992) examined the Mab disposition in the tumor whose size is much smaller (4-12 mg) than that used in the present study (500-800 mg).

In conclusion, we describe a pharmacokinetic model in which the physiological parameters (such as capillary blood flow and lymph flow) and the parameters specific for MRK16 (such as permeability-surface area product and the kinetic parameters determined in vitro) are incorporated. Based on this model, it is suggested that the observed difference in the tumor association of an antibody between in vitro and in vivo might be ascribed to the restricted penetration across the tumor capillary. The methodology provided in the present study might be useful to analyze the tumor disposition of Mabs.