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THE USE OF SANDWICH-CULTURED RAT HEPATOCYTES TO DETERMINE THE INTRINSIC CLEARANCE OF COMPOUNDS WITH DIFFERENT EXTRACTION RATIOS: 7-ETHOXYCOUMARIN AND WARFARIN

Institute for Risk Assessment Sciences, Utrecht University, Utrecht, the Netherlands (N.T., H.v.H., A.B., B.J.B.); and National Institute for Public Health and the Environment, Bilthoven, the Netherlands (J.C.H.v.E.)

(Received February 21, 2005; accepted June 8, 2005)

	Abstract

Top Abstract Materials and Methods Results Discussion Appendix References

 
The application of sandwich-cultured rat hepatocytes for the identification of the hepatic intrinsic clearance of compounds with widely varying extraction ratios was investigated. We previously showed the applicability of this in vitro system, in combination with a model describing molecular diffusion, hepatocyte/medium partition, and nonsaturated metabolism, which resulted in a successful identification of this parameter for tolbutamide. This approach is further validated using the compounds 7-ethoxycoumarin and warfarin, covering a 100-fold range of extraction ratios. Clearance of these two substrates could be reliably determined, but only if the depletion of the parent compound in medium as well as in the hepatocyte sandwich was measured. Sensitivity analyses showed that the time course of depletion of the parent compound in medium, especially for warfarin, is insensitive to the partition and diffusion parameter values, whereas depletion in the hepatocyte sandwich was far more sensitive. When varying the volumes of collagen in the sandwich culture, it appears that the most reliable kinetic parameters could be obtained by fitting the data with the smaller collagen volume and that these parameters obtained from fitting to data of the larger volumes generally cannot be verified satisfactorily with the data of the smaller volumes. The values of hepatic clearance that were obtained after extrapolation of the intrinsic clearance to the hepatic clearance from blood were comparable within a factor of 2 to hepatic clearance data in the literature. This indicates that this sandwich culture and modeling system can be applied for the identification of the hepatic intrinsic clearance rate of the total range from low to high clearance compounds.

Recently, we have successfully developed the alternative approach of using sandwich-cultured rat hepatocytes in determining the in vitro intrinsic clearance of the slowly metabolized compound tolbutamide (Treijtel et al., 2004). The sandwich culture is a long-term in vitro system allowing for long incubation periods. Besides prolonged cell viability, other advantages of this system are cellular morphology comparable to the in vivo situation, including cellular polarity, physiological levels of protein secretion, development of an extensive bile canalicular network, and expression of drug transporter proteins. Furthermore, the most important phase I enzyme activities remain better expressed for several days as compared with hepatocytes cultured without collagen (Koebe et al., 1994; Kern et al., 1997), whereas phase II glutathione S-transferase activity is stably expressed for over 14 days (Beken et al., 1997b).

In this alternative approach, the use of data on substrate depletion was chosen rather than the use of data on metabolite formation. Using data on metabolite formation may cause practical problems when analytical methods or standards to study the kinetics of metabolite formation are not fully optimized. Since these problems were confirmed in our previous study with tolbutamide where three unexpected metabolites were detected (Treijtel et al., 2004), the same depletion approach was also chosen in this study. Substrate depletion data obtained from sandwich-cultured rat hepatocytes were incorporated into a mechanistic model. This model takes into account the system-dependent processes, viz., molecular diffusion through the medium and collagen layers, protein binding, and partitioning to the cell lipid fraction. Ignoring these system-dependent processes could disturb the calculation of the true intrinsic clearance parameter (Treijtel et al., 2004).

The aim of this study was to further develop this promising approach in the prediction of the intrinsic clearance of slowly metabolizing compounds. Moreover, to investigate the applicability of the sandwich culture to a possibly wide range of metabolizing kinetics, the prediction of a fast metabolizing compound also was included.

There is a great variety of the collagen layer volume in sandwich cultures that is applied between various studies and laboratories (Berthiaume et al., 1996). Thus, another aim was to study the effect of this variation and to understand the limitations the variation of the layer volume imposes. In this perspective, the collagen volumes applied in the sandwich culture were varied and the effects of this barrier were studied especially with respect to the difficulty this barrier could impose on gaining accurate experimental data.

Two reference compounds, warfarin and 7-ethoxycoumarin, were used in this study, because they cover a wide range (100-fold) of extraction ratios, warfarin being the slow metabolizing compound and 7-ethoxycoumarin the fast metabolizing compound. Moreover, these compounds were widely used in the estimation of kinetic parameters in other in vitro systems, allowing for comparison of our results with values from the literature. The concentrations used in this study for warfarin and 7-ethoxycoumarin, 100 µM and 0.45 µM, respectively, were both below the Michaelis-Menten constant, K_m, and the metabolism rate was assumed to be linear.

Once the intrinsic clearance of a compound is determined from an in vitro experiment, its value can be used to parameterize an in vivo physiologically based pharmacokinetic model or to estimate the value of the classical kinetic hepatic clearance parameter. For tolbutamide, Treijtel et al. (2004) showed the successful in vitro-in vivo extrapolation of the intrinsic hepatocyte clearance that was found experimentally to a physiologically based pharmacokinetics model of the disposition of tolbutamide in the rat (Sugita et al., 1982). In this study, intrinsic clearance of warfarin and 7-ethoxycoumarin was estimated and extrapolated to a hepatic in vivo clearance.

	Materials and Methods

Top Abstract Materials and Methods Results Discussion Appendix References

 
Chemicals. Fetal calf serum and Dulbecco's modified Eagle's medium were purchased from Invitrogen (Breda, The Netherlands). Insulin, glucagon, hydrocortisone, gentamycin, glutathione, bovine serum albumin, collagenase type 1A, and testosterone and its metabolites were obtained from Sigma-Aldrich (St. Louis MO). Collagenase type B was purchased from Roche (Roche Diagnostics Nederland B.V, Almere, the Netherlands). Warfarin and p-chlorowarfarin were obtained from Sigma Chemical (Zwijndrecht, the Netherlands), as well as 7-ethoxycoumarin, 10-hydroxycoumarin, and methoxycoumarin. All other chemicals were of analytical grade.

Preparation of Rat Tail Tendon Collagen. Type I collagen was prepared from rat tail tendons as described by Koebe et al. (1994) by a modified procedure of Elsdale and Bard (1972). This preparation yields type I collagen, mostly in its native, not cross-linked, triple-helical form (Beken et al., 1997a).

Isolation of Hepatocytes. Male Wistar rats (CPB:uWU) from the Central Animal Laboratory (Utrecht University), weighing 190 to 250 g, were used for hepatocyte isolation. Acidified water and food was provided ad libitum before the liver perfusion.

The rats were anesthetized by injecting pentobarbital i.p. (Nembutal; Ceva Sante Animale, Brussels, Belgium), 120 mg/kg body weight. Rat hepatocytes were isolated using the two-step collagenase perfusion technique as described by Seglen (1976) and modified according to Paine et al. (1979).

Hepatocyte Culture. Collagen gel was prepared by mixing 1 part DMEM (10x, pH 7.4) and 9 parts collagen solution of 1.11 mg/ml on ice (yielding a solution of 1.0 mg/ml collagen). The cells were seeded on tissue culture dishes with a diameter of 60 mm, precoated with 0.25, 0.50, or 1.0 ml of collagen (underlay), at a density of 4 x 10⁶ cells/dish in 4 ml of DMEM. DMEM was supplemented with 10% fetal calf serum (FCS), 0.5 U/ml insulin, 0.007 µg/ml glucagon, 7.5 µg/ml hydrocortisone, and 50 µg/ml gentamycin.

After 4 h of incubation, cultures were washed twice with DMEM (without FCS), and 0.25, 0.50, and 1.0 ml of collagen was added as a top layer on the dishes (overlay) that were precoated with an equal volume. Cultures were placed in the incubator (37°C, 5% CO₂) for 1 h to allow gelation. Subsequently, 4 ml of DMEM (without FCS) was added.

Cell Viability and Enzyme Activities. On each day, cultures incubated with warfarin (100 µM) or 7-ethoxycoumarin (0.45 µM), as for the substrate depletion experiments, were tested for viability, cell number, and biotransformation capacities. Cell viability was determined by trypan blue exclusion. Testosterone hydroxylation activity was determined according to the method of Wortelboer et al. (1990). Cytosolic protein was used to estimate cell number and measured according to Lowry et al. (1951) using bovine serum albumin as a standard.

Kinetic Profiles of Warfarin and 7-Ethoxycoumarin in the Sandwich Rat Hepatocyte Culture. Twenty-four hours after cell isolation, sandwich cultures were incubated with 4 ml of 100 µM warfarin or 0.45 µM 7-ethoxycoumarin in DMEM. For the different volumes of collagen used in our experiments, the actual initial values determined were 104, 100, and 101 µM for warfarin and 0.40, 0.48, and 0.49 µM for 7-ethoxycoumarin for collagen volumes of 0.5, 1.0, and 2.0 ml, respectively. For warfarin, after 0, 2, 5, 15, 30, 60, 90, 240, 480, 960, 1440, 1920, 2130, and 2880 min of incubation, for cultures with a collagen volume of 1.0 and 2.0 ml, and after 0, 10, 30, 60, 240, 420, 1320, 1500, 1860, and 2990 min for sandwich cultures with a collagen volume of 0.5 ml, a culture was terminated. For 7-ethoxycoumarin, after 0, 1, 2, 4, 6, 10, 15, 25, 40, 60, 90, 120, 180, 270, 360, and 480 min of incubation, a culture was terminated. The medium was aspirated and 2 ml were transferred to a glass centrifuge tube. The sandwich, i.e., the total of collagen and hepatocyte layers, was transferred to a glass centrifuge tube as well. All the tubes were ice-cold and stored at –20°C immediately after harvesting. The experiments were carried out in duplicate at n = 2.

Analysis of Warfarin and 7-Ethoxycoumarin. The sandwich samples were thawed and 1.5 ml of a collagenase-Krebs solution (100 U/ml) was added. The samples were incubated at 37°C for 60 min, after which all collagen was digested. A total of 40 µl of 10% acetic acid and 20 µl of ß-glucuronidase was added to the 7-ethoxycoumarin samples. The samples were incubated at 37°C for 20 h to allow the phase II products formed during the kinetic experiments to be deconjugated to hydroxycoumarin. An internal standard solution (50 µl) of p-chlorowarfarin (80 ng/ml in acetonitrile) was added to the warfarin samples, and 10 µl of methoxycoumarin (80 µM in methanol) was added to the 7-ethoxycoumarin samples. Subsequently, the sandwich samples and the medium samples were extracted with 8 ml of a mixture consisting of diethyl ether/dichloromethane/iso-propanol in a 60:40:1 ratio (v/v). After separation and evaporation of the organic layer, the residue of the warfarin samples was dissolved in eluent (acetonitrile and H₂O/H₃PO₄, pH2.7; 1:2.4) and the residue of 7-ethoxycoumarin samples was dissolved in 50% methanol (v/v). Calibration curves of warfarin covered a concentration range of 0 to 150 µM in both medium and sandwich matrix. This concentration range was linear, and the limit of detection was 2 µM. For 7-ethoxycoumarin and hydroxycoumarin, linear calibration curves covered a concentration range of 0 to 1.5 µM in both matrices, with a limit of detection of 0.025 µM.

HPLC Analysis. Twenty microliters of the warfarin samples was injected into an HPLC system consisting of a Chromosphere C18 analytical column (100 x 3 mm), with a mobile phase of 0.5% phosphoric acid/acetonitrile (63:37, v/v), at a flow rate of 1 ml/min. The eluent was monitored with a fluorimetric detector operating at a wavelength of 313 nm for excitation and a wavelength of 400 nm for emission.

7-Ethoxycoumarin and hydroxycoumarin were separated by an HPLC method with fluorimetric detection, slightly modified from Yamazaki et al. (1999). A volume of 10 µl was injected into the HPLC system consisting of a Chromosphere C18 column (100 x 3 mm). The mobile phase consisted of mobile phase A (methanol/milliQ, 25:75, v/v) and mobile phase B (methanol/acetonitrile/deionized water, 64:6:30, v/v). Initially, 85% of mobile phase A and 15% of mobile phase B was used. At 3.6 min, 50% of mobile phase A and 50% of mobile phase B was used, and at 11.0 min, the gradient returned to 85% A and 15% B and re-equilibrated after 9 min. The eluent was monitored with a fluorimetric detector operating at a wavelength of 338 nm for excitation and a wavelength of 458 nm for emission.

Mathematical Model. Three processes determine the time course of a parent compound in the medium-sandwich experimental model: transport, partitioning, and biotransformation. The interplay of these processes typically leads to a biphasic concentration-time course in both medium and the sandwich culture. During the first phase, the concentration in medium rapidly decreases by uptake into the sandwich. The characteristic time of this phase is the sum of the characteristic times of diffusion and biotransformation. The terminal phase is characterized by exponential depletion in both medium and sandwich culture. The exponential rate of this phase, which can be observed from the experiment, multiplied by the medium volume or sandwich culture volume, determines the clearance from medium or sandwich, respectively. Just as, for example, the hepatic clearance from blood is determined by the liver's intrinsic clearance (biotransformation), the blood free fraction (partition), and the blood volumic flow through the liver (transport), the clearance from medium is determined by the hepatocyte's intrinsic clearance, the ratio of distribution volume of medium and of the medium-sandwich culture volume of distribution and molecular diffusion. In the Appendix, the influence of diffusion and distribution volume on the clearance from medium is shown. When the parameter values neither for partition nor for diffusion are known, it is necessary from an experimental point of view to sample not only during the terminal phase, but also during the initial phase of distribution. The interpretation of data, i.e., the identification of the hepatocyte's intrinsic clearance, necessitates the mathematical formulation of the depletion experiment, its implementation in a computer program, and fitting the unknown values of the parameters for clearance, partition, and diffusion to the experimental data.

Transport takes place by molecular diffusion both in medium and sandwich. Based on our experience with tolbutamide, it is assumed that the values of the molecular diffusion coefficient in medium and sandwich are the same.

Partitioning between the different constituents of the sandwich culture, i.e., medium, collagen and hepatocytes, is assumed to be caused by differences in their protein binding capacity and their lipid content. Since neither medium nor collagen contains binding proteins or a lipid fraction, the partitioning between these two phases is assumed to be 1. The hepatocytes contain both binding proteins and a lipid fraction.

In the model, the clearance per unit volume of hepatocytes is parameterized, which allows for a straightforward in vitro-in vivo extrapolation once the relative volume of hepatocytes in the liver is known. To account for the decrease in cell number, cell variability, and biotransformation capacity in vitro, the true clearance parameter is corrected by multiplying with the corresponding fractions found; i.e., in the computer model, the specific clearance f_n f_v f_aK_h is the product of the true intrinsic specific clearance K_h with the correction factors for fraction of cells (f_n), fraction of viable cells (f_v), and fraction of cell activity (f_a).

The mathematical model description, including the modification with respect to the partitioning of the model in Treijtel et al. (2004), can be found in the Appendix. [In the model equations in Treijtel et al. (2004), the division sign, /, between the concentration in sandwich and the sandwich/medium partition coefficient is omitted.] The model parameters for transport (D_m), partition between hepatocytes and medium (P_hm), and specific intrinsic hepatocyte clearance, i.e., the intrinsic clearance per unit of volume of hepatocytes (K_int,h) were identified by fitting them to the sampling data in medium and sandwich. The volume of hepatocytes was estimated from the number of cells in the culture (4 x 10⁶) and cell volume (7500 µm³; cell diameter about 24 µm). The fitting criterion was the optimization of the loglikelihood of the set of parameters. Model calculations and model fits were performed using the ACSL-Optimize suite (Aegis Technologies Group, Huntsville, AL).

In Vitro-in Vivo Extrapolation. For 7-ethoxycoumarin and warfarin, the specific intrinsic hepatocyte clearance was extrapolated to the intrinsic liver clearance by accounting for the volume fraction of hepatocytes in the rat liver (about 90%) and rat liver volume. Next, this estimate of the intrinsic liver clearance was used for an estimation of the hepatic clearance of the compounds, using both a well stirred and a parallel tube liver model (Wilkinson, 1987).

The well stirred model assumes instantaneous and complete mixing and reads

(1)

Here, CL_h is the hepatic clearance from blood, Q_h is the hepatic blood flow, and f_u is the free fraction in blood. The parallel tube model assumes piston flow through parallel tubes, causing a concentration gradient in the blood flow direction because of loss due to clearance in the lateral direction and reads

(2)

Note that when f_uCL_int becomes small compared with the blood flow Q_h, both models converge to the same value: Q_h = f_uCL_int.

Rat cardiac output (110 ml/min), relative hepatic blood flow (18.3%), and relative liver volume (3.4%) were taken from Brown et al. (1997). Standard rat weight is 250 g and the tissue specific density was taken to be 1. The free fractions of 0.22 for 7-ethoxycoumarin and 0.017 for warfarin (mean of 0.023 for R-warfarin and 0.011 for S-warfarin) were taken from Ito and Houston (2004).

Parameter Sensitivity Analysis. To obtain more insight into the reliability of the parameter values that are obtained by fitting the model to the experimental data, parameter sensitivity was analyzed. This sensitivity concerns the relative variation in the concentration-time course in medium and sandwich due to a relative variation in a parameter value:

(3)

Here, s is the relative sensitivity, t is time, p is a generic parameter representing specific clearance, partition, or diffusion, and C is the concentration in medium or sandwich. From this expression follows,

(4)

So, at any time t, the relative sensitivity at that time point relates a relative variation in the parameter value of interest to the corresponding relative change in the concentration. Samples taken at time points where the sensitivity s(t) is small for the given parameter, p, poorly contribute to the identification of that parameter, whereas samples taken at time points where the sensitivity is large contribute well to the parameters identification. Since the sensitivity depends on the value of the nominal parameters, too, i.e., varying the value of the nominal parameters leads to a variety of sensitivities, one can only check the appropriateness of sampling strategy a posteriori, unless one knows a fair estimate of the nominal values a priori.

	Results

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Cell Number, Cell Viability, Enzyme Activity, and Cell Volume. The results of the following measurements were used for the correction factors (f_n, f_v, and f_a) of the clearance parameter as described under Materials and Methods.

Cell number was estimated by protein determination and decreased from 100% at day 1, to 80% at day 2 and 70% at day 3. Cell viability decreased only slightly: 90% at day 1 and 80% at days 2 and 3. Phase I activity decreased significantly over time. As for both 7-ethoxycoumarin and warfarin, different cytochrome P450 enzymes are involved (Yamazaki et al., 1996; Ngui et al., 2001; Takahashi and Echizen, 2003). The clearance parameter was corrected for the mean decrease in activity of the subtypes measured. A decrease of approximately 50% after 4 h of isolation was observed, after which it further decreased to 40% at days 1 and 2, and to 25% on the third day after isolation. Assuming a hepatocyte cell diameter of 25 µm, the total cell volume of the hepatocytes plated (about 4 x 106 cells) was roughly estimated to be 30 µl.

View larger version (24K): [in this window] [in a new window]   FIG. 1. Concentration-time curves of 7-ethoxycoumarin (left) and warfarin (right) in medium (solid line, closed circles) and sandwich (broken line, open circles) for total collagen volumes of 0.5 (upper panels), 1.0 (middle panels), and 2.0 (lower panels) ml. The lines represent model calculations with the optimized parameter values, and the symbols represent experimental values.

The initial decrease from medium is mostly due to diffusion from medium to sandwich, resulting in a corresponding initial increase in sandwich. This initial phase is followed by a terminal phase of decrease in both medium and sandwich due to metabolism. The model calculations were performed using the result of fitting the model to the data of depletion both in medium and sandwich and from each individual collagen volume taken together, taking into account the corresponding collagen volume for each of the three data sets. From a Bayesian statistics point of view, this is the better procedure since in this way the individual sets mutually serve as a condition in the fitting procedure. The values found by fitting all data together resulted in a value for the intrinsic clearance per unit of hepatocyte volume of 6.0 [–/min] (45 µl/min/1 x 10⁶ cells), a value for the hepatocyte-collagen partition coefficient of 29, and a value for the diffusion coefficient of 1.0 x 10^–3 [cm²/min].

Substrate Depletion of Warfarin. The experimental data on depletion of warfarin in medium and sandwich for collagen volumes of 0.5, 1.0, and 2.0 ml are shown in Fig. 1 (right), together with the corresponding concentration-time course model calculations (the same general remarks as for 7-ethoxycoumarin apply). The values found by fitting all data together resulted in a value for the intrinsic clearance per unit of hepatocyte volume of 0.073 [–/min] (0.55 µl/min/1 x 10⁶ cells), a value for the hepatocyte-collagen partition coefficient of 4.9, and a value for the diffusion coefficient of 0.69 x 10^–3 [cm²/min].

In Vitro-in Vivo Extrapolation. For 7-ethoxycoumarin the hepatic clearance was estimated to be 6.7 ml/min/SRW = 27 ml/min/kg using the well stirred liver model and 7.9 ml/min/SRW = 32 ml/min/kg using the parallel tube liver model. For warfarin the hepatic clearance was estimated to be 0.0095 ml/min/SRW = 0.038 ml/min/kg for both the well stirred liver model and the parallel tube liver model. Table 1 shows both the intrinsic clearance and the predicted hepatic clearance of our results compared with the clearances from the literature.

Sensitivity Analysis. Sensitivity analysis was performed both for 7-ethoxycoumarin and for warfarin using the "sensitivity analysis" option of ACSL-Optimize. The nominal parameter values that were varied were those obtained by fitting the model to the data. The results for an applied collagen volume of 0.5 ml are depicted in Fig. 2 for 7-ethoxycoumarin and Fig. 3 for warfarin.

View larger version (7K): [in this window] [in a new window]   FIG. 2. Sensitivity of concentration-time course in medium (left) and sandwich (right) of 7-ethoxycoumarin to variation in the values of intrinsic clearance (solid line), hepatocyte/medium partition (dotted, broken lines) and diffusion (broken line) for 0.5 ml of collagen. The asterisks show the sampling time points.

View larger version (7K): [in this window] [in a new window]   FIG. 3. Sensitivity of concentration-time course in medium (left) and sandwich (right) of warfarin to variation in the values of intrinsic clearance (solid line), hepatocyte/medium partition (dotted, broken line), and diffusion (broken line) for 0.5 ml of collagen. The asterisks show the sampling time points.

The sensitivity to hepatocyte/medium partition is likewise complex. For this parameter, sensitivity for the concentration in medium initially will be negative because of more extended depletion of parent compound, but finally it will be positive because elimination is of the free fraction in the aqueous phase only. So, the greater the partition coefficient, the less effective metabolism will be. However, as in the experiment, the total sandwich is sampled, rather than the hepatocytes and collagen layers separately, the combined partition of the collagen and hepatocyte layers, i.e., the sandwich/medium partition, is much smaller than the hepatocyte/medium partition. Thus, because of this "dilution" of hepatocytes, the sensitivity of the hepatocyte/medium partition for the concentration in medium will always be small compared with the sensitivity of clearance and diffusion. The sensitivity for the concentration in sandwich, however, will always be positive, initially because of the more extended depletion out of the medium and finally because of the less effective metabolism. Moreover, since this parameter determines the concentration in sandwich rather than in medium, it may be expected to be more sensitive for the concentration in sandwich than in medium.

Comparing Figs. 2 and 3 clearly shows the dependence of the sensitivities to the nominal parameter values. Note the differences between 7-ethoxycoumarin and warfarin in the scales of both the time and the sensitivity axes. Also note the differences in sensitivity for warfarin in medium and sandwich in the scale of the y-axis.

	Discussion

Top Abstract Materials and Methods Results Discussion Appendix References

 
In a previous study (Treijtel et al., 2004), the clearance estimation of the slow metabolizing compound tolbutamide using a sandwich-culture-based approach proved to be useful. From this study it was clear that the specific system parameters for this in vitro approach (viz. the volumes of medium, collagen, and cell, the diffusion of compounds in the system, as well as the metabolic clearance in the cells) are determining factors in the successful determination of the true intrinsic clearance. Therefore, the in vitro system needed to be complemented with a mathematical modeling approach, taking into account the interplay of these parameters.

Sandwich-cultured rat hepatocytes, besides cryopreserved hepatocytes, were also used by Lau et al. (2002) to study clearance parameters. However, in their approach, the system-dependent parameters that are mentioned above are not taken into account and are therefore obscuring the true intrinsic clearance value. Another difference between both approaches is the longer incubation times that were used in our study compared with the study of Lau et al. (2002), in which samples were incubated for only 120 minutes. This is the major advantage of this culture system.

Our approach was further explored with two reference compounds, warfarin and 7-ethoxycoumarin, because of their divergent extraction ratios covering a 100-fold range. Metabolism of warfarin in vivo is even slower than that of tolbutamide (Obach, 1999), whereas 7-ethoxycoumarin is a very fast metabolizing compound in vivo (Carlile et al., 1998). The concentrations used in this study for warfarin and 7-ethoxycoumarin (100 µM and 0.45 µM, respectively) were both below the Michaelis-Menten constant, K_m. Therefore, metabolism was assumed to be linear. The K_m of 7-ethoxycoumarin was 0.8 µM for hepatocytes (Worboys et al., 1996) and 1.3 µM (Worboys et al., 1995) for liver slices in rat. The K_m of warfarin hydroxylation in fresh rat hepatocytes ranged from 83 µM for 7-OH warfarin formation to 1452 µM for 10-OH warfarin, and from 113 µM for 6-OH warfarin to 339 µM for 10-OH warfarin in cryopreserved hepatocytes (Griffin and Houston, 2004). However, the model could easily be adapted to the case of saturated metabolism.

For warfarin and 7-ethoxycoumarin, a consistent clearance estimation of 0.073/min (45 µl/min/1 x 10⁶ cells) and 6.0/min (0.55 µl/min/1 x 10⁶ cells), respectively, was obtained when fitting on both medium and sandwich data. Model calculations were performed using the result of fitting the model to the data of depletion both in medium and sandwich and from each collagen volume taken together. Due to the relative insensitivity of the concentration-time course in medium to the value of the hepatocyte-collagen partition coefficient, no consistent estimate could be obtained using data of depletion in medium only. When using data of depletion in medium only, the model verification on the sandwich data, using the parameters thus obtained, failed.

For tolbutamide, an in vivo physiologically based pharmacokinetic model was presented by Sugita et al. (1982). This model allowed the straightforward in vitro-in vivo extrapolation of tolbutamide (Treijtel et al., 2004) with a fair comparison to the experimental data. However, to our knowledge, for neither warfarin nor 7-ethoxycoumarin is such a model, together with experimental data, available. Nevertheless, the parameters resulting from the in vitro experiments for 7-ethoxycoumarin and warfarin were extrapolated to the corresponding value for in vivo hepatic clearance in blood, using the well stirred and parallel tube liver models, and compared with literature values, which were also extrapolated using both liver models. For 7-ethoxycoumarin, the hepatic clearance values estimated from sandwich-cultured rat hepatocytes were 6.7 and 7.9 ml/min/SRW for the well stirred and the parallel tube model, respectively, whereas Carlile et al. (1998) estimated a hepatic clearance of 12 ml/min/SRW. Axelsson et al. (2003) estimated a hepatic clearance of 9.8 ml/min/SRW and De Kanter et al. (2004) estimated a hepatic clearance of 3.1 ml/min/SRW. For warfarin, a hepatic clearance of 0.0095 ml/min/SRW was calculated for both models. De Kanter et al. (2004) estimated a hepatic clearance of 0.01 ml/min/SRW. Two important issues should be considered when comparing these literature values, which are summarized in Table 1. For 7-ethoxycoumarin there is a difference in the clearance based on substrate depletion or metabolite formation, such as in Worboys et al. (1995, 1996). For warfarin it is important to use data on the racemic mixture instead of only one of the enantiomers. When comparing the appropriate literature values, which are in accordance (within a factor of 2) with the estimated values (Table 1), this approach proved to be reliable in clearance estimation.

The sensitivity of the nominal parameters was studied. For ease of phrasing, a parameter will be referred to as sensitive during some time interval when relatively small variations of that parameter will cause relatively large deviations in the concentration-time course during that time interval. Data points sampled at time points when a parameter is insensitive will not contribute to its identifiability. In this perspective, the different experimental setups, with different volumes of collagen applied, were also studied.

With respect to the concentration in medium, the hepatocyte/medium partition is rather insensitive throughout the whole experimental period, and the more so for warfarin than for 7-ethoxycoumarin. This explains the observation that when some value for this parameter has been found by fitting to data in medium only, it may happen that verification with respect to the concentration in the hepatocyte sandwich fails. For the concentration in the hepatocyte sandwich, the hepatocyte/medium partition is (far) more sensitive. Thus, fitting to data in both medium and hepatocyte sandwich results in a more reliable parameter value estimation. However, when applying greater volumes of collagen, this parameter also becomes insensitive for the concentration in the hepatocyte sandwich, due to increasing dilution of the hepatocytes in the sandwich, which argues for applying the smaller collagen volume. In the Appendix (Fig. A1), a simulation of depletion from medium of a parent compound with the same characteristics as 7-ethoxycoumarin, except for a 10-fold higher hepatocyte/medium partition, is shown. In such a case, i.e., when a drug is lipophilic, not only is the apparent clearance much smaller, but also the sensitivity of the partition is much greater.

View larger version (7K): [in this window] [in a new window]   FIG. A1. Left panel: variation of diffusion with respect to nominal value. Upper line, molecular diffusion 10 times slower; middle line, nominal value; lower line, molecular diffusion 10 times faster. Right panel: variation of hepatocyte/medium partition with respect to nominal value. Final lower line, partition 10 times smaller; final middle line, nominal value; final upper line, partition 10 times greater.

During the very initial phase of distribution, the intrinsic clearance is rather insensitive, due to the relatively small amount of parent compound that has reached the metabolizing sites. But soon, the sensitivity increases with increasing time. Apparently, the sensitivity for warfarin is an order of magnitude lower. However, if one would scale the time for the two drugs corresponding to their half-lives, the sensitivities would be similar.

This approach is suited to predict the intrinsic clearance of slow metabolizing compounds such as tolbutamide and warfarin but can also be used to predict the clearance of fast metabolizing compounds such as 7-ethoxycoumarin. The advantages of using sandwich-cultured rat hepatocytes are the longer incubation periods. This is an important aspect in drug development since most pharmaceutical compounds are low clearance drugs. The fact that this culture system is also suitable for the prediction of high-clearance drugs makes it an all-around system that can be used for the testing of a broad variety of compounds. This is a clear advantage compared with liver slices, which do not allow for incubation periods over 24 h and usually underpredict high-clearance compounds due to diffusional limitations (Worboys et al., 1995, 1996).

Thus, the approach described here is suited to predict the intrinsic clearance of slow metabolizing compounds, such as tolbutamide and warfarin, but can also be used to predict the clearance of fast metabolizing compounds such as 7-ethoxycoumarin.

	Appendix

Top Abstract Materials and Methods Results Discussion Appendix References

 
In the first section of this appendix, it is shown that both diffusion and partition also determine the exponential rate of depletion. The parameter values for specific clearance, hepatocyte/medium partition, and diffusion as found for 7-ethoxycoumarin serve as nominal values. In this comparison, it is assumed that a compound differs in its physicochemical properties only with respect to its diffusion (left panel, Fig. A1) or to its partition (right panel, Fig. A1). When one determines the exponential rate from the data and, multiplied by the medium volume, interprets this as the intrinsic clearance, one would conclude a specific intrinsic clearance of 1.7 (D_m = 0.1D_m), 3.9 (D_m = D_m), 4.4 (D_m = 10D_m), 4.4 (P_hm = 0.1P_hm), 3.9 (P_hm = P_hm), and 1.8 (P_hm = 10P_hm), whereas in fact, the specific clearance = 6 (–/min).

Unfortunately, the mathematical analysis of diffusion problems is cumbersome. However, when one approximates molecular diffusion by a simple mass transfer between medium and the sandwich culture (which is at least in the initial phase incorrect), then one can derive that the clearance from medium is described by

(A1)

Here, CL_m denotes clearance from medium, K is the mass transfer coefficient (transport), V_m/V_d is the ratio of the medium and total system distribution volume (partition), and CL_h the hepatocyte intrinsic clearance (biotransformation). The similarity with eq. 1 in the main text is obvious. Note that when transport is much faster with respect to clearance, then CL_m = V_m/V_dCL_h and still partition is involved in clearance. In the other extreme case, clearance is much faster; then CL_m = , totally independent of the hepatocyte's clearance.

The model that is described in the text, under Materials and Methods, with molecular diffusion instead of mass transfer, reads

(A2)

The first line of this equation describes transport by diffusion through the medium layer of the free concentration f_mC_m. In these experiments the medium (DMEM) contains no binding sites and f_m = 1; however, the model can equally well describe culture medium that contains binding sites.

The second line describes the sandwich. Although actually this layer is subdivided into three sublayers consisting of the hepatocyte layer in between two collagen layers, the description assumes a "homogenized" layer with the hepatocytes distributed at random in a layer of collagen. This assumption is only valid when the thickness of the top and bottom layer of the sandwich is the same (Treijtel et al., 2004).

The free concentration that is not dissolved in a lipid fraction is the total concentration C divided by the medium/sandwich partition coefficient. As it is assumed that collagen does not contain binding sites, nor has a lipid fraction, P_s = (V_c + P_hV_h)/(V_c + V_h), or equivalently, the distribution volume of the sandwich P_s(V_c + V_h) equals the sum of the distribution volumes of the collagen layers and the layer of hepatocytes V_c + P_hV_h. The hepatocyte/medium partition P_h = P_hm/f_h, where P_hm is the lipid/water solubility-based hepatocyte/medium partition and f_h is the free fraction in hepatocytes.

The first term in the right-hand side of the second line in eq. A2 describes transport by diffusion in the sandwich layer. As the separate identification of the diffusion coefficients in medium and sandwich is not possible, it assumed that D_s = D_m. The second term describes the clearance per unit of volume K_s = CL_int,h/V_s, where CL_int,h is the intrinsic clearance of the layer of hepatocytes, CL_int,h = V_hK_int,h, and K_int,h is the specific intrinsic clearance of hepatocytes, i.e., their clearance per unit of volume.

The third line shows the initial conditions: the compound dissolved only in medium with initial concentration C_m,0.

The fourth line of eq. A2 describes the conditions at the medium-sandwich interface. The first equality shows continuity of flux of the compound over the interface, i.e., the absence of sources or sinks at the interface. The second equality shows instantaneous equilibration of the free, non-lipid-soluble fraction of the concentrations at the interface.

The last line shows that there is no transport over the top boundary of the medium layer, nor over the bottom layer of the sandwich.

	Acknowledgments

 
We thank Wouter Gebbink and Sandra Nijmeijer for technical assistance. We also thank Minne Heringa for a critical review of the manuscript.

	Footnotes

 
Article, publication date, and citation information can be found at http://dmd.aspetjournals.org.

doi:10.1124/dmd.105.004390.

ABBREVIATIONS: CL_bile, biliary clearance (ml/min/kg body weight); CL_hep, hepatic clearance (ml/min/kg body weight); CL_int, intrinsic clearance (ml/min); C_m, concentration medium (µM); C_s, concentration sandwich (µM); D_m, diffusion coefficient in medium (cm²/min); D_s, diffusion coefficient in sandwich (cm²/min); f_a, fraction of cell activity; f_m, free fraction medium; f_h, free fraction hepatocytes; f_n, fraction of cells; f_s, free fraction sandwich; f_u, free fraction in blood; f_v, fraction of viable cells; K_h, specific clearance (–/min); K_l, specific intrinsic clearance of the liver (–/min; –/h); K_m, Michaelis-Menten constant (µM); K_ow, partition coefficient octanol-water; K_s, first-order metabolism (–/min); L_m, medium layer thickness (cm); L_s, sandwich layer thickness (cm); PBPK, physiologically based pharmacokinetics; P_cm, collagen-medium partition coefficient; P_hm, hepatoycte-medium partition coefficient; P_sm, sandwich-medium partition coefficient; P, parameter value; Q_h, hepatic blood flow (l/h); s, sensitivity; SRW, standard rat body weight (250 g); V_c, volume of collagen (ml); V_h, volume of hepatocytes (ml); V_m, volume of medium (ml); V_max, maximum rate of metabolism (µM/min); V_s, volume sandwich (ml); DMEM, Dulbecco's modified Eagle's medium; FCS, fetal calf serum; HPLC, high-performance liquid chromatography.

Address correspondence to: Bas J. Blaauboer, Institute for Risk Assessment Sciences, Utrecht University, Yalelaan 2, PO Box 80176, 3508 TD Utrecht, the Netherlands. E-mail: B.Blaauboer{at}iras.uu.nl

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