Simulation of Trichloroacetic Acid Kinetics in the Isolated Perfused Rat Liver Using a Biologically Based Kinetic Model

Corike Toxopeus* and J. M. Frazier{dagger},1

* McLaughlin Research Institute, Great Falls, Montana 59405; and {dagger} Air Force Research Laboratory, Wright-Patterson Air Force Base, Ohio 45433-7400

Received December 14, 2001; accepted July 30, 2002


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Trichloroacetic acid (TCA) is a contaminant of drinking water. It induces peroxisome proliferation in livers of rats and mice and is hepatocarcinogenic in the latter species. Previous experimental studies of the kinetics of TCA in the isolated perfused rat liver (IPRL) at two doses have been reported. To gain more insight into the mechanistic processes controlling TCA kinetics in the liver a biologically based kinetic (BBK) model for the IPRL was used to analyze the experimental data. The IPRL was exposed to 25, 250, or 1000 µM TCA for 2 h in a recirculating perfusion system. These doses were not cytotoxic. The BBK model simulated the TCA concentration in perfusion medium and liver, and the biliary excretion of TCA. Separate protein binding studies showed that over 90% of TCA was bound to albumin in the perfusion medium whereas binding in liver homogenate was much lower. Integrating the information on protein binding into the BBK model, the hepatic uptake of TCA and its biliary excretion could be fitted assuming asymmetrical saturable transport at the sinusoidal membrane and linear transport at the bile canalicular membrane. To validate the BBK model, additional washout experiments were conducted in which the perfusion medium was replaced with TCA-free medium after 30 min of exposure of the liver to 1000 µM TCA. This approach illustrates the usefulness of BBK modeling for analyzing experimental kinetic data and gaining insight in kinetic mechanisms controlling the behavior of a chemical in the liver.

Key Words: TCA; isolated perfused rat liver; kinetics; modeling; transport parameters; protein binding.


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Trichloroacetic acid (TCA) has been investigated as a potential health hazard. TCA is formed by metabolism of trichloroethylene in mammalian systems (Dekant et al., 1984Go) and by chemical reactions during chlorination of drinking water (Quimby et al., 1979Go). Mice exposed to TCA develop liver tumors (Bull et al., 1990Go), while TCA is not a hepatocarcinogen in rats (DeAngelo et al., 1997Go). However, exposure of rats to TCA does cause pathological changes in their livers, e.g., lipid peroxidation (Larson and Bull, 1992Go), peroxisome proliferation (DeAngelo et al., 1989Go), and liver hypertrophy and glycogen accumulation (Mather et al., 1990Go). To better understand the disposition of TCA in the liver, detailed studies using the isolated perfused rat liver (IPRL) system were performed in which rat livers were exposed to TCA concentrations of 25 and 250 µM (Toxopeus and Frazier, 1998Go). These studies showed that during a 2-h period only a small fraction of the total TCA dose was taken up and excreted in bile by the liver. Theoretical calculations indicated that there was a positive concentration gradient of free TCA from the perfusion medium into the liver intracellular water space, suggesting that TCA uptake may involve asymmetrical transport at the sinusoidal membrane. The concentration of TCA in bile was calculated to be similar to that of the free TCA in the liver intracellular water space, suggesting that the transport of TCA through the canalicular membrane may be passive. Binding of TCA to bovine serum albumin (BSA) in the perfusion medium was high, over 90% bound (Toxopeus and Frazier, 1998Go), and was a dominant factor controlling the kinetics of TCA in the IPRL system.

The IPRL system is a useful tool for investigating metabolism and kinetics of chemicals in the liver. A biologically based kinetic (BBK) model of the IPRL that includes metabolism, membrane transport, and protein binding of chemicals has been developed for water-soluble compounds (Frazier 1998Go). A schematic diagram of the BBK model for the IPRL system is shown in Figure 1Go.



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FIG. 1. Schematic diagram of the generic BBK model for the IPRL (adapted from Frazier, 1998Go).

 
To gain more insight into the mechanisms controlling TCA kinetics in the liver, a BBK model was used to analyze experimental data from the IPRL system. Data obtained at three doses of TCA, corresponding to initial concentrations of 25, 250, and 1000 µM TCA in the perfusion medium, were analyzed. These three doses of TCA were chosen based on serum concentrations of TCA 30 min after dosing with 6.1, 61, and 306 µmol/kg (Yu et al., 2000Go). Parameters for binding of TCA to BSA in perfusion medium and to liver homogenates were obtained in separate binding experiments. The concentration of TCA in perfusion medium and liver, and the cumulative TCA excretion in bile were simulated for a 2-h period. The transport parameters for uptake and biliary excretion were adjusted to fit the experimental data. The estimated values for membrane transport parameters were validated by simulating TCA kinetics in separate washout experiments.


    MATERIALS AND METHODS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
Experimental Methods
Materials.
Low endotoxin BSA, taurocholic acid, and TCA (purity 99.0+%) were purchased from Sigma Chemical Co. (St. Louis, MO). Heparin (1,000 U/ml) was obtained from Solopak Laboratories, Inc. (Elk Grove Village, IL). Pico Fluor-40 was purchased from Packard Instrument Co. (Meriden, CT). Labeled TCA ([1-14C]TCA; specific activity = 55 mCi/mmole) was obtained from American Radiolabel Chemicals Inc. (St. Louis, MO). All other chemicals used were of analytical grade.

Animals.
Male Fischer 344 rats weighing between 220 and 290 g were used for liver isolations. Rats had free access to food and water purified by reversed osmosis. Animal use described in this study was conducted in accordance with the principles stated in the Guide for the Care and Use of Laboratory Animals (National Research Council, 1996Go) and the Animal Welfare Act of 1966, as amended.

Liver isolation and perfusion.
Liver surgery was performed as described previously (Toxopeus and Frazier, 1998Go). The liver perfusion cabinet was the same as described by Wyman et al. (1995)Go. Sterile Krebs-Ringer buffer (200 ml) supplemented with 4% (w/v) low endotoxin BSA and 11.5 mM glucose was used to perfuse the liver during experiments. The flow rate of the perfusate was 40 ml/min and the perfusate temperature was maintained at 37°C. To sustain bile production, taurocholate was infused into the perfusion medium at a rate of 33.5 µmol/h. The medium was oxygenated by passing it through a gas exchange apparatus and equilibrated with 95% O2/5% CO2. Medium pH was maintained between 7.37 and 7.42. Temperature, pH, and the percentage oxygen saturation of the perfusion medium and hydrostatic pressure on the liver were constantly monitored. Body weight of donor rats, liver weight, and liver water content are summarized in Table 1Go.


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TABLE 1 Physiological Parameters for Isolated Perfused Rat Liver Studies
 
Viability Parameters
To evaluate the quality of the livers during perfusion, the following parameters were monitored:

Liver water content.
An aliquot of approximately 1 g liver was collected from the liver at the end of the experiment, weighed (wet weight, W), dried for 4 days at 120°C in a vacuum oven and weighed again (dry weight, D). The percentage water content was calculated as:


(1)

All abbreviations used in Equations 1–10GoGoGoGoGoGoGoGoGoGo are listed in Table 2Go.


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TABLE 2 Abbreviations used in Equations 1–10GoGoGoGoGoGoGoGoGoGo
 
Enzyme leakage.
Samples of perfusion medium (0.5 ml) were collected every 30 min and the activity of LDH was determined as described by Korzeniewski and Callewaert (1983)Go. The percentage LDH leakage during the experiment was calculated as the percentage of activity in perfusion medium at time t (AP(t)) relative to the total LDH activity. The total LDH activity is the sum of the activity in the perfusion medium at the end of the experiment (AP(120)) plus the total activity in the liver at the end of the experiment (AL(120)) calculated from the enzyme activity in liver homogenate. Thus,


(2)

Bile flow.
Bile was collected in preweighed microcentrifuge tubes over intervals of 15 or 30 min. Bile flow was expressed as µl/(min x g) liver, assuming that the density of bile is 1.0 g/ml.

Kinetic studies.
In order for the liver to recover from surgery, kinetic studies were started 1 h after connecting the excised liver into the perfusion system. Time is measured relative to the time that the chemical is dosed into the reservoir (t = 0). Exposures were started by adding 5, 50, or 200 µmol of TCA dissolved in approximately 1 ml nanopure H2O to the reservoir that contained 200 ml perfusion medium. These dosages resulted in initial concentrations of 25, 250, or 1000 µM, respectively. To determine the time course of chemical concentration in the perfusion medium, samples (1 ml) were taken from the reservoir at 2, 5, 10, 20, 30, 60, 90, and 120 min after TCA addition. In washout experiments, not only were samples taken at the standard times, but additional samples were collected immediately after the perfusion medium was switched to TCA-free medium at t = 30 min and at 45, 75, and 105 min. Bile was collected over intervals of 30 min in the standard experiments. In the washout experiments bile was collected at 15-min intervals. All samples were kept on ice until analyzed. At the end of the 120-min experiment, the liver was perfused with 10 ml ice cold chemical-free perfusion medium to flush the sinusoids free of TCA. The liver was homogenized in 0.9% NaCl (1 g liver to 3 ml saline). TCA concentrations in the liver are reported as average liver concentration (CL-AVG (µmol/kg)) and as the theoretical concentration in intracellular water:


(3)
where CLI-TOTAL (µM) is the total concentration of TCA in the hepatic intracellular water space, assuming that (1) all TCA in the liver is in the intracellular space after flushing the sinusoids with buffer, and (2) there is 0.58 l/kg of intracellular water in the liver – total water content of liver (0.79 l/kg, Table 1Go) less the volume of the vascular space and space of Disse (0.21 l/kg of liver; Goresky, 1980Go).

Binding Studies in Vitro
The binding of TCA to protein (BSA) in perfusion medium and liver homogenates was investigated. The procedures used were similar to those reported in (Templin et al. 1995)Go.

Perfusion medium.
Perfusion medium used in binding studies was sterile Krebs-Ringer buffer supplemented with 4% (w/v) low endotoxin BSA and 11.5 mM glucose, identical to that used for liver perfusion studies.

Liver homogenate.
Rats were anesthetized with diethyl ether and the portal vein was cannulated using an 18-gauge 2-inch catheter. The liver was flushed with 2 ml prewarmed heparin/saline solution (500 U heparin/ml in 0.9% NaCl). Following severance of the inferior vena cava, the liver was perfused with ice cold Krebs-Ringer medium supplemented with 11.5 mM glucose and saturated with 95% O2/5% CO2, pH 7.40, at a flow rate of 25 ml/min. The liver was excised, minced, and homogenized (1 g of minced liver to 3 ml ice-cold buffer) using a Potter-Elvehjem tissue grinding chamber (Thomas; No. A 62247) and motor driven teflon pestle (AHT Co.; Model S 756). The liver was kept on ice throughout all procedures. Homogenates were stored at 80°C and used in binding studies within two weeks after preparation.

Binding studies.
An aliquot (400 µl) of perfusion medium or liver homogenate containing radiolabeled TCA, ranging in concentration from 3 µM to 20 mM, was incubated for 60 min at 37°C on an incubator shaker. A sample (40 µl) of this mixture was transferred to a scintillation vial, mixed with 5.5 ml Pico Fluor-40 and the radioactivity determined by liquid scintillation counting (Packard Tri-Carb 2200CA). Radioactivity measurements were converted to TCA equivalents using the specific activity and the concentration obtained represented the total TCA concentration. The remaining mixture was centrifuged at 2000 x g for 5 min (perfusion medium) or 30 min (homogenate) at 4°C in Centrifree micropartitioning tubes (Amicon, Inc., MA) to obtain protein-free filtrate. A sample (40 µl) of the filtrate was transferred to a scintillation vial, mixed with 5.5 ml Pico Fluor-40 and assayed for radioactivity. The TCA equivalent concentration in the ultrafiltrate represents the free TCA concentration. The concentration of bound TCA was determined by the difference between the total and the free TCA concentrations.

Binding curve analysis.
Standard binding curves and Schatchard analysis were used to evaluate TCA binding parameters. The binding of TCA in the perfusion medium was analyzed assuming a combination of linear binding and a saturable binding site. The following equation was used to fit the experimental data for binding in the perfusion medium (Taira and Terada, 1985Go):


(4)

BP (dimensionless) is the coefficient for linear binding of TCA in the perfusion medium, and BMAXP (µM) and KDP (µM) are the maximum binding capacity and the dissociation constant for saturable binding, respectively, in the perfusion medium. The parameters were determined by fitting the experimental binding data to Equation 4Go using SigmaPlot version 5.00 (Jandel Scientific, San Rafael, CA). A similar analysis was conducted for TCA binding in the liver homogenate (liver binding parameters are designated by replacing P in Equation 4Go with L).

Experimental determination of TCA binding in the IPRL experiments.
Aliquots of 600 µl of perfusion medium (collected at t = 5 and t = 120 min) or 400 µl of liver homogenate (prepared at the end of the experiment, t = 120 min) were processed as described above for TCA binding in perfusion medium. Since TCA used in the perfusion studies was not radioactive, TCA concentrations were determined in the whole homogenate and the filtrate as described in the analytical methods section below. In order to obtain enough filtrate from liver homogenate samples for analysis, four aliquots of homogenate were centrifuged under identical conditions and the filtrates obtained pooled. The concentration of TCA in the liver homogenate filtrate (CL-FILTRATE) was used to estimate the free TCA concentration in liver intracellular water space:


(5)

The factor of 3.79 is included to correct for dilution of the liver while preparing the homogenate and 0.58 is the ratio of the intracellular water volume of the liver to the weight of the liver.

Analytical methods.
TCA in perfusion medium, bile, liver homogenate, and ultrafiltrates from IPRL experiments was derivatized to methyl esters by dimethyl sulfate under acidic conditions and quantified by GC using electron capture detection (Ketcha et al., 1996Go). To prevent conversion of TCA to DCA, 100 µl of sample was mixed with 100 µl of 20% lead acetate and stored at 20°C. For derivatization, the samples (200 µl) were mixed with 100 µl H2O and 100 µl 2,2-dichloropropionic acid (10 µg/ml), an internal standard. After cooling on ice, 500 µl concentrated sulfuric acid and 100 µl dimethyl sulfate were added. The reaction mixture was shaken for 30 min at 60°C, cooled to room temperature, and 1 ml hexane was added. Samples were extracted on an incubator shaker for 1 h at 30–40°C and centrifuged (10 min, 2000 x g) to separate the aqueous phase from the hexane phase. The hexane layer was analyzed for TCA on a Hewlett Packard 5890 GC (Avondale, PA) equipped with a Hewlett Packard 7673A liquid autosampler and a 30 m x 0.53 mm Supelco Wax column (Bellefonte, PA). Derivatization products were detected by electron capture and concentrations corrected for extraction efficiency using the internal standard.

Model Implementation
The BBK model was coded using Advanced Computing Simulation Language (ACSL level 11, MGA Associates, Concord, MA), a numerical integration package. For details on the model structure see Frazier (1998)Go. The physiological parameters used in the BBK model are shown in Table 3Go. To utilize the BBK model to analyze the experimental data for TCA kinetics in the IPRL, the three important factors that control chemical kinetics (metabolism, protein binding, and membrane transport) were addressed as follows. Metabolism plays a negligible role in TCA kinetics (Larson and Bull, 1992Go; Toxopeus and Frazier, 1998Go). Therefore, the VMAX for TCA metabolism was set to zero in the generic BBK model. Parameters for protein binding were determined experimentally for TCA in both perfusion medium and liver homogenate as described above and subsequently incorporated into the BBK model. The BMAXP and KDP were not allowed to vary in any parameter fitting activities. To our knowledge no parameters for TCA membrane transport have been reported in the literature. Therefore, values for membrane transport of TCA, both at the sinusoidal and canalicular membranes, were derived from fitting TCA kinetics in the IPRL using the BBK model.


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TABLE 3 Physiological Parameters for the Biologically Based Kinetic Model
 
Fitting transport parameters for the sinusoidal membrane.
The fitting of experimental data for the purpose of obtaining transport parameters for TCA transport across the sinusoidal membrane took place in two steps. First, it was assumed that transport of TCA from the perfusion medium into the liver intracellular space involved both linear and saturable transport. In this case, the transport rate was given by


(6)
where CP-FREE (µM) is the concentration of free TCA in perfusion medium; PP-LI (l/[h x kg]) is the linear transport rate constant; UTMAX:P-LI (µmol/[h x kg]) is the maximum rate of saturable transport; KT:P-LI (µM) is the concentration of free TCA in the perfusion medium at half maximum transport rate via the saturable pathway, WL is the weight of the liver, and TP-LI is the apparent transport rate coefficient (l/h) from the perfusion medium into the liver intracellular space and can be CP-FREE dependent. The reverse transport, from the liver intracellular space into the perfusion medium is assumed to involve linear transport only:


(7)

CLI-FREE (µM) is the concentration of free TCA in liver intracellular space; PLI-P (l/[h x kg]) is the linear transport rate constant; and TLI-P (l/h) is the apparent transport rate coefficient from the liver intracellular space into the perfusion medium and is assumed to be independent of CLI-FREE. It is further assumed that the linear transport rate constant, i.e., the diffusion permeability, is equal in both directions:


(8)

Even though the apparent transport rate coefficient, TP-LI in Equation 6Go, may be concentration dependent, it can be considered concentration independent for a particular experiment if the concentration driving the transport is relatively constant during the experiment. For the TCA studies described here, the free concentration in the perfusion medium is relatively constant over the majority of the experiment. Therefore, the experimental data obtained at the three TCA concentrations were individually fitted to obtain the apparent transport rate coefficients at the sinusoidal membrane, TP-LI and TLI-P, for each experiment. The values obtained for TP-LI at the various doses were plotted against the free TCA concentration in the perfusion medium. These data were fitted using Equation 6Go for the membrane transport rates and the average values for PD, UTMAX:P-LI, and KT:P-LI were estimated.

If it is assumed at the mechanistic level that the linear (diffusional) component of sinusoidal transport, PD, is similar between livers, then any variability in the apparent transport rate constant is due to the saturable transport component. In particular, the variability of the apparent transport rate constant in each experiment is most likely due to variability in UTMAX:P-IL. Therefore, the second step in evaluating the sinusoidal transport parameters is to estimate the value of UTMAX:P-LI for each individual experiment. This is accomplished by refitting each experimental data set with PD and KT:P-LI fixed to the average values estimated in the first fitting exercise and varying UTMAX:P-LI. The set of individual values for UTMAX:P-LI obtained from each experiment represent an estimate of the population distribution for this parameter.

Fitting transport parameters for the canalicular membrane.
Since the concentration of TCA in bile was calculated to be similar to that of the free TCA in the liver intracellular water space (Toxopeus and Frazier, 1998Go), experimental data were fitted assuming that the transport of TCA through the canalicular membrane was linear. In this case the rate of transport was given by:


(9)
where PLI-B (l/[h x kg]) is the unidirectional linear transport rate constant for transport of TCA from the liver into the bile, and TLI-B is the apparent transport rate coefficient (l/h).

Sensitivity analysis.
The relative sensitivity of the state variables to variations in the model parameters was investigated. The relative sensitivity is defined as


(10)
where {Delta}SV is the change in the state variable as a result of {Delta}PAR, the change in the model parameter. The variations in the factors, {Delta}SV and {Delta}PAR, are scaled by the magnitude of each factor, SV and PAR, to evaluate changes on a relative basis. Thus, a relative sensitivity of 1.0 implies that the value of the state variable varies by an equal percentage with the change in the model parameter, i.e., when S = 1.0, if the value of the model parameter changes by 10%, then the value of the state variable changes in the same direction by 10%. If the magnitude of the relative sensitivity is less than 1.0 then the state variable changes less in proportion to the change in the parameter and vice versa if S is greater than 1.0. Negative values for S indicate that the state variable changes in the opposite direction to the change in the model parameter, i.e., if S < 0, then an increase in the value of the parameter will result in a decrease in the value of the state variable. Sensitivity analysis of the BBK model for TCA in the IPRL was performed for the lowest and highest TCA concentrations, 25 and 1000 µM.


    RESULTS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
TCA Binding Experiments
In vitro binding studies were conducted to estimate binding parameters. The extent of binding of TCA in perfusion medium was much greater compared to TCA binding in liver (Fig. 2Go). For both perfusion medium and liver homogenate, binding saturation could not be achieved up to concentrations of TCA that caused protein precipitation (results not shown). Only data obtained in the concentration range of TCA utilized in the IPRL studies (<= 1000 µM) were used for curve fitting. Binding data for TCA in perfusion medium were fitted using Equation 4Go. Fitting the binding data with and without the linear binding term indicated that one saturable binding site was adequate to empirically fit the data. Including the linear binding coefficient BP did not significantly improve the fit; therefore, BP was set equal to zero. The parameters obtained for saturable binding of TCA in perfusion medium were BMAXP = 1487 µM and KDP = 155 µM (solid line in Fig. 2Go). The experimentally determined free and bound TCA concentrations in the perfusion medium in the IPRL experiments (represented by the open symbols in Fig. 2Go) are consistent with the predicted curve based on the in vitro studies, although there is a tendency for the experimental data to have slightly higher bound TCA concentrations as compared to the in vitro binding curve. The binding of TCA in liver homogenate was low and exhibited a linear increase with TCA concentration. No evidence of saturable binding was observed. Linear binding in the liver homogenate depended on homogenate dilution. Extrapolating binding data obtained from experiments using different dilutions of liver homogenate to the undiluted condition gives an estimated value for the linear binding constant for TCA in the liver of BL = 0.18 ± 0.04. The experimental data for binding of TCA in liver homogenates prepared from livers used in the IPRL experiments (represented by open squares in Fig. 2Go) are slightly above the range predicted by the in vitro estimations for TCA binding in liver.



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FIG. 2. TCA binding to proteins in perfusion medium and in liver. Experimental data for binding in perfusion medium are shown for in vitro binding studies (closed circles) and for IPRL studies (open circles). The binding curve (solid line) was generated using BP = 0, BMAXP = 1487 µM and KDP = 155 µM. Lower (BL = 0.10) and upper (BL = 0.25) limits for in vitro TCA binding in liver are indicated (BMAXL = 0). TCA binding in the liver at the end of the IPRL studies (t = 120 min) is shown (open squares).

 
Viability Data
To ensure that the experimental data used for fitting TCA kinetics in the BBK model were valid, the viability of livers was closely monitored throughout experimental studies (Fig. 3Go). Leakage of LDH in perfusion medium (Fig. 3AGo) remained very low up to t = 30 min (90 min after liver was placed into the IPRL system). After this time, there was a slow increase in LDH activity in perfusion medium. Throughout the experiments, enzyme leakage in all four experimental groups was not significantly elevated as compared to control livers, indicating that TCA treatment did not alter liver integrity. An additional indicator of liver function is the production of bile (Fig. 3BGo). There were no significant changes in bile production over time, or between TCA treated livers and control livers. This indicates that normal liver function is maintained throughout the experiments and that exposure to TCA did not compromise liver function.



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FIG. 3. Viability of IPRL preparations during TCA kinetic studies. (A) Percentage LDH activity in perfusion medium. (B) Bile production (µl/[min x g liver]). Data are expressed as means ± SD (n = 4 for control livers, n = 3 for 25 µM TCA, n = 4 for 250 µM, n = 4 for 1000 µM, and n = 3 for the washout experiments).

 
Simulation of TCA Kinetics in Parameter Fitting Experiments
Examples of the simulated kinetic curves for the perfusion medium, liver concentrations, and cumulative biliary excretion are shown in Figures 4, 5, and 6GoGoGo, respectively. Representative model simulations of the TCA concentration in the perfusion medium are shown in Figure 4Go for all three doses. The kinetics of TCA are relatively simple in the perfusion medium due to the limited elimination of the chemical from the system as a result of negligible metabolism, low biliary excretion, and the high extent of TCA binding to albumin in the perfusion medium (Toxopeus and Frazier, 1998Go). To facilitate comparison of TCA kinetics at different doses, the ordinates of the kinetic graphs at the two higher doses are scaled relative to the lowest dose in proportion to the TCA dose (i.e., the scale of the middle dose is 10 times that of the lowest dose, and the scale of the highest dose is 40 times that of the lowest dose). Thus, if the kinetics of the system are linear with respect to dose, all three graphs should appear to be similar. One nonlinearity observed in these data is a slight shift in the relative concentration of free TCA in the perfusion medium—the percentage of free TCA increases from 4% of total TCA at the lowest TCA dose to 15% at the highest dose. This increase is predicted by the model and is due to the nonlinearity in TCA binding in perfusion medium (Fig. 2Go).



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FIG. 4. TCA kinetics in perfusion medium. Experimental data and fitted curves for total and free TCA concentration in perfusion medium for: (A) 25 µM TCA, (B) 250 µM TCA, and (C) 1000 µM TCA. After a recovery period of 60 min, the IPRL system was dosed at t = 0 with 5, 50, or 200 µmol of TCA corresponding to initial concentrations of 25, 250, and 1000 µM, respectively. The experiment was terminated at t = 120 min. Results for one experiment at each TCA concentration are shown.

 


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FIG. 5. TCA kinetics in the liver. Experimental data and fitted curves for TCA concentration in the liver at exposures of 25 µM TCA, 250 µM TCA, and 1000 µM TCA. Results are shown for the average total liver TCA concentration, CL-AVG (µmol/kg; closed symbols), and the theoretical free TCA concentration in liver intracellular water, CLI-FREE (µM; open symbols). Experiments were conducted as described in Figure 4Go. Results for one experiment at each TCA concentration are shown.

 


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FIG. 6. Cumulative TCA excretion in bile. Experimental data and fitted curves for cumulative TCA excretion in the bile (MB) at doses of 25 µM TCA, 250 µM TCA, and 1000 µM TCA. Experiments were conducted as described in Figure 4Go. Results for one experiment at each TCA concentration are shown.

 
Figure 5Go illustrates the model simulations of the average TCA concentration in the liver, CL-AVG (µmol/kg; left y-axis), and the calculated free TCA concentration in liver intracellular water, CLI-FREE (µM; right y-axis). Data for these state variables are limited since determination of the concentration of TCA in the liver can be obtained only at the termination of the experiment. However, for the 1000 µM TCA experiment (200 µmol dose), data (shown as squares, mean ± SD) from separate experiments where the livers were perfused with 1000 µM TCA for 30 min are included. Although these data were obtained from separate experiments, they give a reference point for early kinetics. The simulated curves and the 30-min data points for exposure to 1000 µM TCA suggest that TCA quickly enters the liver and a quasi-steady state between the perfusion medium and the liver is rapidly established. Figure 5Go also illustrates the kinetics of the intracellular free TCA concentration. As was previously reported (Toxopeus and Frazier, 1998Go), the intracellular free TCA concentration is 3–4 times greater than the free TCA concentration in the perfusion medium. In the IPRL model for TCA, this effect is a consequence of the asymmetrical transport processes at the sinusoidal membrane. Finally, an estimate of the linear binding constant for TCA in liver, BL, was determined for each experiment by dividing CLI-FREE as determined by the ultrafiltration method by CLI-TOTAL computed from the average liver concentration. The average value for BL, 0.21 ± 0.08, closely matches the value of 0.18 ± 0.04 determined from in vitro binding studies performed with liver homogenates (Fig. 2Go).

The excretion of TCA in bile is linear in time and started almost immediately after TCA was added to the system (Fig. 6Go). The simulated curves closely match the experimental data. The scaled graphs reveal that the relative amount of TCA excreted in bile increased with TCA dose. This increase in biliary excretion rate parallels the increase in free TCA in liver intracellular space. The total amount of TCA excreted during the experiments was approximately 0.05, 0.10, and 0.20% at the 5 µmol, 50 µmol, and 200 µmol doses, respectively. The transport rate coefficient for biliary elimination of TCA corrected for liver weight, TLI-B/WL, from all experiments is estimated to be 0.017 ± 0.006 l/(h x kg); see Table 4Go.


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TABLE 4 Chemical-Specific Parameters for TCA Kinetics in the IPRL System
 
Estimation of Sinusoidal Transport Parameters
TCA transport parameters were estimated by fitting the experimental kinetic data using the two step process described in the Methods section. In the first step, the apparent transport rate coefficients (TP-LI) for each experiment at the three experimental doses were obtained by model fitting as described in the previous section. These estimates of the sinusoidal transport rate coefficient are plotted against the free TCA concentration in perfusion medium (Fig. 7Go). Assuming that both linear and saturable transport are involved in TCA transport from the perfusion medium into the liver intracellular space, the data for the apparent transport rate constant TP-LI were fitted using Equation 6Go. The estimated values for the transport parameters were P = 0.02 l/(h x kg), UTMAX:P-LI = 6.0 µmol/(h x kg), and KT:P-LI = 95 µM.



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FIG. 7. Concentration dependence of the sinusoidal transport rate coefficient. The fitted transport rate coefficients for TCA transport into the liver, TP-LI/WL, are plotted versus the concentration of free TCA in perfusion medium, CP-FREE. The data points were fitted giving an average linear transport rate constant (permeability) for the liver sinusoidal membrane to TCA of PD= 0.02 l/(h x kg), maximum saturable transport rate UTMAX:P-LI = 6.0 µmol/(h x kg), and concentration of free TCA at half maximum saturable transport rate KT:P-LI = 95 µM.

 
The second step in the fitting procedure is to estimate the apparent value for UTMAX:P-LI for each individual experiment. The experimental data were refitted for each kinetic experiment with PD and KT:P-LI fixed at 0.02 l/(h x kg) and 95 µM, respectively, and UTMAX:P-LI allowed to vary. Table 4Go summarizes the results obtained for all three TCA concentrations studied. If the assumptions above are correct, then the average UTMAX:P-LI should be independent of TCA concentration, i.e., the concentration dependency should be accounted for by the mathematical form assumed. The data in Table 4Go suggest this is correct as the average UTMAX:P-LI is not statistically different between the three concentration groups.

TCA Kinetics in Washout Experiments
The IPRL model for TCA kinetics was validated by investigating the simulation of TCA kinetics in the washout experiments where livers were exposed to 1000 µM TCA for 30 min and then perfused with TCA-free medium for an additional 90 min. In Figure 8Go the lower and upper limits were simulated for each state variable in the washout experiments. The lower limit simulation was obtained using the mean minus one SD for UTMAX:P-LI and TLI-B (Table 4Go) in the simulation. The upper limit simulation used the mean plus one SD. For UTMAX:P-LI the values used were 4.0 and 7.4 µmol/(h x kg), and for TLI-B the values were 0.011 and 0.023 l/(h x kg). The values for the other model parameters were the same as those used for fitting the kinetic parameters. The experimental data for three separate washout experiments were also plotted in Figure 8Go as the means ± one SD (n = 3). Both the total and free concentration of TCA in perfusion medium fell within the limits of the simulated curves (Figs. 8A and 8BGoGo). The inserted graph shows in detail the TCA concentration in perfusion medium after switching to clean medium. The model predicts an increase in TCA concentration in perfusion medium as TCA leaks out of the liver. This prediction is confirmed by the experimental data. Figures 8C and 8DGoGo show the simulated curves for CL-AVG and CLI-FREE respectively. The model predicted a rapid decrease in the TCA concentration in the liver after switching the IPRL system to TCA-free perfusion medium. The inserted graphs show that the experimental data for TCA concentration in the liver at the end of the experiment confirmed the decrease in concentration as predicted by the simulations. The experimental data for cumulative TCA excretion in bile fell within the upper and lower simulated limits (Fig. 8EGo). Note, as a result of the rapid washout of TCA from the liver, biliary excretion of TCA immediately ceases after switching to TCA-free perfusion medium at t = 30 min.



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FIG. 8. TCA kinetics in washout experiments. Simulated curves predicting the lower and upper limits for each state variable, and experimental data (mean ± SD, n = 3) for TCA kinetics in washout experiments are plotted. (A) The total concentration of TCA in perfusion medium, CP-TOTAL. (B) The free concentration of TCA in perfusion medium, CP-FREE. (C) The average concentration in the liver, CL-AVG. (D) The free TCA concentration in the liver interstitial space, CLI-FREE. (E) the total cumulative TCA excretion in bile, MB. Following a recovery period of 60 min, the IPRL system was dosed at t = 0 with 200 µmol of TCA corresponding to an initial concentration of 1000 µM. After 30 min of exposure to TCA, the IPRL system was switched to TCA-free medium. The experiment was terminated at t = 120 min. Results are expressed as the means ± SD (n = 3).

 
Sensitivity Analysis
Sensitivity analysis of the BBK model was performed for the lowest and highest TCA concentrations, 25 and 1000 µM. The results for the estimated relative sensitivity are given in Figure 9Go.



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FIG. 9. Sensitivity analysis of the BBK model for TCA kinetics in the IPRL system. Each parameter in the BBK model was increased by 10% and the percentage change in the state variables CP-TOTAL, CP-FREE, CLI-AVG, CLI-FREE, and TCA excreted in bile was determined by model simulation. The relative sensitivity, as defined in Equation 10Go, at the end of the study (t = 120 min) is plotted for each parameter. The analysis was performed for the lowest and highest TCA concentrations, 25 and 1000 µM respectively.

 
Effect of binding parameters on state variables.
The total TCA concentration in perfusion medium, CP-TOTAL, was insensitive to small changes in protein binding parameters (BP, BMAXP, KDP). This is not surprising since the majority of the TCA added to the system remains in the perfusion medium and only a small fraction of the total TCA dose is taken up by the liver and excreted in the bile under all conditions (Toxopeus and Frazier, 1998Go). However, the CP-FREE was sensitive to changes in BMAXP, particularly at the high dose. The relative sensitivity of CP-FREE to a change in BMAXP was about –1.7 for the 1000 µM TCA experiments, as compared to –0.80 for the 25 µM TCA experiments. This is due to the nonlinear nature of the binding relationship. At the 25 µM concentration, binding is relatively linear and an increase in binding capacity in the perfusion medium results in an almost proportional decrease in the free TCA concentration. At the 1000 µM concentration, the relationship between the free and bound forms of TCA in the perfusion medium is highly nonlinear and an increase in binding capacity results in a greater than proportional decrease in free TCA. At even higher total TCA concentrations in the perfusion medium, where the binding capacity is totally saturated and most TCA present is free, the relative sensitivity of free TCA to binding capacity would approach zero. The liver TCA concentrations and cumulative TCA excretion in the bile are also sensitive to changes in CP-FREE, therefore they are also sensitive to changes in BMAXP to about the same extent as CP-FREE.

The sensitivity of CP-FREE, CLI-FREE, and cumulative TCA excretion in the bile to changes in KDP was about 1.0 at 25 µM TCA and about 0.5 at 1000 µM TCA. The lower sensitivity of these state variables to changes in KDP at 1000 µM TCA can be explained by looking at the equation for liver transport (Equation 6Go). KDP and CP-FREE are additive factors in the denominator and as a result the relative contribution of KDP to the denominator is less at higher CP-FREE.

In the standard uptake experiments, the only state variable affected by a change in the linear binding constant for TCA in liver, BL, is CL-AVG with a sensitivity of about 0.15. However, varying BL in the simulation of the washout experiment does affect the final concentration of TCA in the perfusion medium after the switch to clean perfusion medium. This is because BL has a significant influence on how much TCA is loaded into the liver during the 30 min uptake phase of the washout experiment.

Effect of sinusoidal transport parameters on state variables.
The total TCA concentration in perfusion medium was relatively insensitive to changes in the transport parameters PD, KT:P-LI, and PLI-B. The sensitivity of the average liver TCA concentration and the cumulative biliary excretion to a change in PD is about 0.7 for 25 µM TCA and 0.4 for 1000 µM. This indicates that increasing the linear transport rate constant across the sinusoidal membrane decreases the liver intracellular free TCA concentration by allowing more TCA to leak out down the concentration gradient across the sinusoidal membrane. The reduction in intracellular TCA concentration then reduces biliary excretion. This effect is more important at low concentrations where the concentration gradient is greater than at high concentrations.

Average liver TCA concentration and cumulative TCA excretion in bile have similar sensitivities to changes in UTMAX:P-LI, the sensitivity being about 0.73 for 25 µM TCA and 0.43 for 1000 µM. In addition, liver kinetics at 25 µM are more affected by a change in KT:P-LI than at 1000 µM, relative sensitivities being about 0.6 and 0.18 respectively. The reason for this differential sensitivity is the same as for the sensitivity to the binding constant KPD. KT:P-LI and CP-REE are additive factors in the denominator for saturable transport. This makes the relative contribution of KT:P-LI to mediated transport less at higher CP-FREE.

Effects of biliary transport parameters on state variables.
TCA concentration in perfusion medium and liver are relatively insensitive to changes in PIL-B. However, the cumulative excretion of TCA in the bile is highly sensitive to changes in PIL-B; S {approx} 1 for both 25 µM and 1000 µM TCA.


    DISCUSSION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 REFERENCES
 
BBK modeling is a useful tool to integrate various processes that control the kinetic behavior of a chemical in a biological system. The generic BBK model for kinetics of water soluble chemicals in the IPRL (Frazier, 1998Go) was used as the basis to simulate TCA kinetics. Binding parameters were derived from in vitro binding studies and utilized in the model. Since metabolism of TCA is minimal, metabolic parameters were neglected. This leaves membrane transport parameters as the only undetermined chemical-specific parameters in the model. Data for the kinetics of TCA at three different doses were used to fit the transport parameters. The resultant model was then used to predict the kinetic behavior of TCA in washout experiments as a validation test. As has been described in the Results section, the experimental data fell within the lower and upper boundaries predicted by the model. Thus, the BBK model as presented is consistent with the experimental data available.

Consistency of model predictions with experimental data does not prove that a particular model is "correct." However, in this case the BBK model for TCA kinetics in the IPRL is capable of accounting for several subtle features of TCA kinetics suggesting that the assumptions made in constructing the model may be valid. One feature is the slight nonlinearities that are observed with increasing dose. These effects, i.e., the increase in the proportion of free TCA in the perfusion medium at the highest dose and the increase in the proportion of cumulative biliary excretion at the highest dose, can be explained adequately by the nonlinear binding of TCA to albumin in the perfusion medium. CP-FREE increases from 4% of total TCA concentration in the perfusion medium at the 25 µM TCA dose to 15% at 1000 µM TCA, about a four-fold increase in the percentage free. Concurrently, the cumulative TCA excretion in bile increases by a similar factor, increasing from 0.05% of total dose at the 25 µM TCA dose to 0.2% of total dose at the 1000 µM TCA dose. It is clear from these studies that TCA binding to albumin is a major factor controlling TCA kinetics in the IPRL system. This conclusion is also supported by the sensitivity analysis where the average TCA liver concentration and cumulative biliary excretion are highly sensitive to changes in protein binding parameters.

Another interesting issue is the elevated concentration of free TCA in the liver intracellular space relative to the free concentration of TCA in the perfusion medium. This effect has been observed in vivo in rats (Yu et al., 2000Go). The hypothesis proposed to explain this observation is that there is an asymmetry in the transport of TCA across the plasma membrane of the hepatocytes. In the BBK model, this hypothesis is described by assuming that diffusion of TCA occurs in both directions with the same linear rate constant, i.e., diffusional permeability (PD), and that there is also a saturable transport mechanism that can transport TCA into the cell but not in the reverse direction (see Equations 6 and 7GoGo). As a consequence of this hypothesis, the transport rate coefficient in the forward direction into the cell, TP-LI, is greater than the transport rate coefficient in the reverse direction, TIL-P, at equal concentrations of free TCA. Thus, for a quasi-steady state to be established between the perfusion medium and the hepatic intracellular water space, which occurs within the first 30 min of exposure to TCA, the forward and reverse transport rates must be approximately equal. These rates can only be equal if the intracellular free concentration of TCA is significantly greater than the free TCA concentration in the perfusion medium. This conclusion is consistent with the experimental data.

The estimation of the maximum transport rate constant for mediated uptake of TCA across the sinusoidal membrane, UTMAX:P-LI, from the experimental data indicated a significant variation of this parameter between livers. It was suggested that this variability may be related to the variability in the expression of a mediated transport system in the sinusoidal membrane between livers. Although there are several assumptions that are made to arrive at this conclusion (see section on fitting transport parameters for sinusoidal membrane), the concept that the internal dose to the liver may be controlled by a genetic factor regulating membrane transport is intriguing. The sensitivity analysis of the BBK model indicates that the free intracellular concentration of TCA is sensitive to the value of UTMAX:P-LI. Thus, variations in this parameter between individuals would significantly impact on the integrated dose in the hepatic intracellular water space.

In the BBK model, it is assumed that biliary excretion of TCA is linear. If this is correct, then the transport rate coefficient for TCA transport into bile, PLI-B, should be independent of the free intracellular concentration of TCA. There is a tendency for PLI-B to increase with increasing TCA concentrations as shown in Table 4Go, however this increase is not statistically significant. There are no signs of saturation of the rate of TCA transport into bile in these studies. In addition, the concentration of TCA in bile is similar to the concentration of free TCA in the liver water intracellular space, CLI-FREE (Toxopeus and Frazier, 1998Go). Together, these data suggest that TCA may move across the canalicular membrane along with intracellular water as bile is formed and is not excreted into bile via mediated transport processes.

The TCA washout experiment was conducted to validate the BBK model for TCA kinetics in the IPRL. The TCA concentration selected for the validation study, 1000 µM, was chosen to maximize the accumulation of TCA in the liver during the 30-min loading phase to ensure that the leakage of TCA into the perfusion medium could be detected. Although the concentration of TCA used in the validation study corresponded to the highest TCA concentration used in the uptake studies to develop the BBK model, the experimental data were collected in independent experiments using different liver perfusions. The washout data fell within the range of values predicted by the model for all the state variables and are consistent with the model assumptions. The washout of TCA from the liver, as indicated by the increase in TCA concentration in the perfusion medium after switching to TCA free medium, is mainly controlled by the linear transport rate constant at the sinusoidal membrane, PD. The observed kinetic fit substantiates the estimate for PD as obtained from the standard kinetic studies. The cumulative excretion of TCA, which is dependent on several model parameters, behaved as predicted and falls within the upper and lower limit simulated (Figure 8EGo). Although the predictions of the BBK model for TCA are consistent with the washout experiments, the observations are based on relatively high concentrations of TCA. The possibility always exists that high affinity–low capacity nonlinear processes (either protein binding, membrane transport or even metabolism) could be present and would have an impact on chemical kinetics at concentrations below the lowest concentration studied experimentally.

The sensitivity analysis showed that kinetic behavior of TCA in the IPRL system is most sensitive to changes in the albumin binding parameters, BMAXP and KDP, mediated through their effect on CP-FREE. Preliminary binding studies using rat serum albumin indicated that TCA binds to a lower extent to rat serum albumin as compared to BSA (results not shown). Therefore, similar serum concentrations of TCA in the rat in vivo as compared to perfusion medium in the IPRL system will imply greater concentrations of TCA in the liver intracellular water space in vivo than in the liver in the IPRL system. This observation will have implications for interspecies extrapolation, particularly to human beings. The sensitivity of CP-FREE, CLI-FREE, and cumulative TCA excretion in bile to changes in parameters for protein binding in perfusion medium emphasizes the importance of having accurate values for binding parameters for the species of interest.

Parameters for transport of TCA over the sinusoidal membrane and the canalicular membrane have not been published before to our knowledge. The values reported in this paper for TCA transport will be applied to the liver compartment in future fitting of the in vivo rat kinetic data of TCA as reported by Yu et al. (2000)Go.

The generic BBK model for the IPRL used in these studies of TCA kinetics requires further validation using a range of water-soluble chemicals. One feature not investigated in this study is the role of metabolism in chemical kinetics. Additional studies with chemicals that undergo hepatic metabolism will expand the usefulness of this BBK model. Future kinetic studies using the IPRL system and analyzing data using the BBK model will add to our understanding of the role of the liver in systemic kinetics of chemicals.


    ACKNOWLEDGMENTS
 
We thank Frank Dessauer and Marcia Feldmann for their enthusiastic help in performing the IPRL experiments and Christel Zajbel and Gerry Buttler for analytical services. This work was supported by the Air Force Office of Scienctific Research (AFOSR) Predictive Toxicology Project (2312A202) and performed in conjunction with U.S. Air Force Contract No. F41624-96-C-9010 (ManTech/Geo-Centers Joint Venture).


    NOTES
 
1 To whom correspondence should be addressed at AFRL/HEST, Bldg. 79, 2856 G Street, Wright-Patterson Air Force Base, OH 45433-7400. Fax: (937) 255-1474. E-mail: john.frazier{at}wpafb.af.mil. Back


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