Dose-Response Modeling of Cytochrome P450 Induction in Rats by Octamethylcyclotetrasiloxane

Ramesh Sarangapani*, Justin Teeguarden*, Kathleen P. Plotzke{dagger}, James M. McKim, Jr.{dagger} and Melvin E. Andersen{ddagger},1

* The K.S. Crump Group, ICF Consulting, P.O. Box 14348, Research Triangle Park, North Carolina 27709; {dagger} Toxicology, Health and Environmental Sciences, Dow Corning Corporation, Midland, Michigan 48686; and {ddagger} Department of Environmental Health, CETT/Foothills Campus, Colorado State University, Ft. Collins, Colorado 80523

Received August 17, 2001; accepted January 4, 2002


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Inhalation of octamethylcyclotetrasiloxane (D4) induces CYP2B1/2 protein and causes liver enlargement. We have developed a pharmacodynamic (PD) extension to a physiologically based pharmacokinetic (PBPK) model to characterize these dose-response behaviors. The PD model simulates interactions of D4 with a putative receptor, leading to increased production of cytochrome P450 2B1/2. Induction was modeled with a Hill equation with dissociation constant, Kd, and Hill coefficient, N. Both a 1- and a 5-compartment liver model were evaluated. The PBPK model provided excellent simulations of tissue D4 and hepatic CYP2B1/2 protein concentrations following 6 h/day, 5-day inhalation exposures to 0, 1, 7, 30, 70, 150, 300, 500, 700, or 900 ppm D4. Either the 1- or 5-compartment liver model could accurately simulate increases in CYP2B1/2 protein in the liver. With a 1-compartment liver, Kd and N were 0.67 µM (free liver concentration) and 1.9, respectively. The 5-compartment model used higher N-values (~ 4.0) and varied Kd between compartments. The fitted 5-compartment model parameters were Kd = 0.67 µM in the midzonal compartment with geometric differences in Kd between compartments of 2.9. On the basis of unbound (free) plasma concentrations, D4 appeared to be a higher potency inducer than phenobarbital (PB). Dose-response curves for increased liver weights had N |mS 1.0 and Kd |mS 3.4 µM, very different values from those for enzyme induction. Exposure concentration leading to a 0.1% increase in CYP2B1/2 protein predicted by the 1- and 5-compartment models were 2.1 ppm and 5.1 ppm, respectively. The 1- and 5-compartment liver models provided very similar fits to the whole liver induction data, excluding the lowest dose, but the 5-compartment liver model had the additional advantage of simultaneously describing the regional induction of CYP2B1/2.

Key Words: siloxane; pharmacodynamic; enzyme induction; inhalation; modeling.


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Octamethylcyclotetrasiloxane (D4), a clear, odorless, silicone fluid of molecular weight 296, has alternating silicon-oxygen bonds in a ring (cyclic) arrangement with two methyl groups on each silicone atom (-(CH3)2Si0-)4. This cyclic siloxane is an intermediate in the synthesis of polydimethylsiloxane, a silicone polymer that is used widely in industrial and consumer applications (Stark et al., 1982Go), and is itself an ingredient in many consumer products and precision cleaning products. Inhalation exposure of rats to D4 induces cytochromes P450 2B1/2 and 3A in the liver and causes hepatomegaly and transient increases in hepatocyte proliferation (McKim et al., 2001Go). This response pattern, similar to that seen with phenobarbital (PB), is consistent with a receptor-dependent process, presumably mediated by the constitutive androstenedione (CAR) receptor (Waxman, 1999Go) that regulates the PB responses.

Tissue responses to compounds, such as D4, depend on the interplay of pharmacokinetic (distribution, metabolism, clearance) and pharmacodynamic (receptor binding, protein induction, hypertrophy, and hyperplasia) processes. Of interest for a risk assessment for D4 is whether the resulting dose-response curves for these receptor-mediated responses are linear or nonlinear in the low dose region. Pharmacokinetic and pharmacodynamic models of biological responses constructed based on a clearly articulated hypothesis relating to a receptor-mediated mode of action for D4 could be utilized to develop biologically based dose-response (BBDR) models for predicting low dose behavior. The development of BBDR models is consistent with risk assessment guidance noted in the proposed U.S. EPA guidelines for risk assessment with carcinogens (EPA, 1996Go).

Studies were conducted measuring D4 tissue concentrations and hepatic induction of CYP2B1/2 protein and activity in female Fisher F344 rats following repeated inhalation exposure to D4 (McKim, 1998Go). Andersen et al. (2001) developed a physiologically based pharmacokinetic (PBPK) model for the disposition of D4 in rats after single and multiple inhalation exposure. In this present work, we coupled this PBPK model with a pharmacodynamic (PD) model for hepatic enzyme induction by D4. The objectives of this study were threefold: (1) to use a 1-compartment liver model to analyze and compare both the induction of CYP2B1/2 protein in the liver and increases in liver weight, (2) to compare the 1-compartment liver model to a 5-compartment model that accounted for regional variations in protein induction patterns in the liver, and (3) to describe and compare the low dose behavior predicted by these two models.


    MATERIALS AND METHODS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Experimental data.
The data modeled in this analysis were from female Fischer 344 rats exposed by inhalation to 0, 1, 7, 30, 70, 150, 300, 500, 700, or 900 ppm D4 vapors 6 h/day for 5 consecutive days (McKim, 1998Go). D4 concentrations in the blood, liver, and fat were determined immediately after the cessation of the last exposure by GC/MS (Table 1Go). Tissue samples for determination of CYP2B1/2 protein and 7-pentoxyresorufin O-dealkylation (PROD), a marker for CYP2B1/2 activity, were collected approximately 18 h after the end of the last exposure (Table 1Go). The CYP2B1/2 protein was measured in isolated microsomal protein by Western blotting with a polyclonal antibody specific to CYP2B1/2, and activity of CYP2B1/2 was measured using a standard assay for PROD activity.


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TABLE 1 Experimentally Measured Tissue D4 Concentrations and CYP2B1/2 Protein and Activity Levels (McKim, 1998Go)
 
The results for induction of CYP2B1/2 proteins show some interesting behaviors (Table 1Go). At maximum induction, concentrations of CYP2B1/2 protein were approximately 40-fold greater than basal levels. Maximum induction of these proteins was attained at exposures of approximately 500 ppm D4. The total liver D4 concentration required for this maximal induction of CYP2B1/2 protein was about 76 µg D4/ml tissue (~ 256 µM). The plasma concentration of D4 at maximal induction was 5.65 µg/ml (~ 19 µM). In these studies, PROD activity increased proportionately with CYP2B1/2 protein levels for liver concentrations below 256 µM; at higher concentrations PROD activity actually declined (Table 1Go). It was also apparent that D4 induction of CYP2B1/2 protein in the liver followed a regional pattern when evaluated by immunohistochemical techniques (Fig. 1Go).



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FIG. 1. Immunohistochemical localization of CYP2B1/2 expression in rat liver following inhalation exposure to Control (A), 30 ppm (B), 300 ppm (C), or 700 ppm D4 (D) for 6 h/day for 5 days per week. Expression is regional rather than homogeneous. D4 induction of CYP2B1/2 increases expression from near basal levels (Panel A), limited to areas surrounding the central vein, to higher levels (Panels B–D) with expression extending to the periportal region at high concentrations.

 
Immunohistochemical staining for CYP2B protein was conducted using the DAKO LSAB®2 Kit. The median lobe liver sections from control, D4, and phenobarbital exposure groups were randomized and evaluated by quantitative light microscopy using the BioQuant Image Analysis System. The percent area stained for CYP2B1/2 protein in the liver was calculated in three fields per slide, and mean values were calculated for each treatment group. Evaluation of the group means for area labeled showed a significant increase in the mean percent area stained in animals treated with D4 to control animals, except for the group receiving 1 ppm D4. There was a significant dose response to D4, with mean percent area stained increasing with inhalation exposure until a maximum of 76.9 ± 6 % of the liver was induced at 700 ppm (Fig. 1Go). Control rats showed centrilobular expression with a mean percent area stained of 21.3 ± 15% (Fig. 1Go).

Model development.
The dose-response analysis of hepatic induction requires knowledge of the concentrations and time course of D4 in liver. The high lipid solubility and low blood:air partition coefficient of D4 result in atypical distribution in the body following inhalation exposure, compared to most inhaled compounds. To describe the time course behaviors with inhaled D4, Andersen et al. (2001) developed a PBPK model with standard compartments such as fat, lung, liver, and richly perfused and poorly perfused tissues, which also included deep tissue compartments in lung and liver, multiple fat compartments, and a mobile lipoprotein pool in the blood. This PBPK model structure was adopted here to study protein induction in the liver following multiple inhalation exposure of D4 in F344 rats. A brief description of this model (Fig. 2Go) is provided here.



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FIG. 2. Schematic of the physiologically based pharmacokinetic/pharmacodynamic (PBPK/PD) model used to simulate hepatic induction of CYP2B1/2 protein in rats. PK model based on the structure developed by Andersen et al. (2001). PD model for hepatic CYP2B1/2 induction was formulated as both a 1- and 5-compartment model; the latter model was used to simulate the observed regional pattern of induction in the liver. Blood perfusion occurs sequential from compartment #1 to #5 in the 5-compartment liver model. Several deep tissue compartments were included to describe the pharmacokinetics of D4. The lung and liver were formulated with shallow and deep compartments (separated by dotted line), and a diffuse fat and blood lipoprotein pool were added to represent additional deep lipid compartments.

 
The lung compartment equilibrates inhaled D4 with arterial blood. In this model, there is no formal volume assigned to the arterial blood compartment. The arterial blood supplies D4 to the fat, liver, richly perfused tissue compartments, and poorly perfused tissue compartments, each with its characteristic tissue to blood partition coefficient. A formal venous blood compartment with volume (Vb) receives effluent venous blood from each tissue. Metabolism of D4 occurs in the liver by a single metabolic pathway following Michaelis-Menten kinetics. Because D4 is highly lipophilic, a sizable fraction of inhaled D4 is sequestered in various fat stores in the body. The PBPK model partitions the liver and lung into a shallow and a deep compartment to account for the tissue-lipid fraction. A similar strategy was employed with methylene chloride (Angelo and Pritchard, 1984Go). A lipoprotein pool in the blood compartment accounts for transported blood lipids produced in the gut and the liver. The total blood concentration includes both the lipoprotein-bound D4 and free D4 that can be exhaled or passed on to the arterial blood. Mass balance equations for the rate of change of the amount of D4 in the various compartments have been described elsewhere (Andersen et al., 2001Go). Only equations for CYP2B1/2 induction and PROD activity are described here. The model was coded in ACSL (Advanced Continuous Simulation Language, Aegis, Inc., Huntsville, AL), and the resulting series of differential equations solved by numerical integration using the Gear algorithm for stiff systems.

In this PBPK description, two different measures of liver tissue D4 concentration were calculated: total D4 and free D4. The total D4 concentration is the volume-averaged composite of D4 in shallow liver and deep liver compartments. Thus, total D4 concentration includes liver D4 that is not partitioned into tissue (free D4), nonspecifically bound D4 in the shallow liver (equivalent to tissue partitioning), and D4 in the deep tissue pool. Free D4 in the shallow liver compartment equilibrates with the venous blood exiting the compartment. Free venous D4 is available for gas exchange in the lung. The shallow and deep pool blood:tissue partition coefficients for liver are 16 and 100, respectively (Andersen et al., 2001Go). The free and total D4 concentration in liver varies by about a factor of 20 or more.

Modeling CYP2B induction using the 1-compartment liver model.
Pharmacodynamic approaches to modeling hepatic protein induction have been developed previously (Andersen et al., 1997aGo,bGo; Kohn et al., 1993Go; Wang et al., 1997Go). In these reports, induction of proteins by 2,3,7,8-tetrachlorodibenzo-p-dioxin in liver was described as a receptor-mediated process resulting in transcriptional activation of genes coding for the proteins. Binding of ligand to receptor was described with a Hill equation. In the absence of knowledge of binding constants for the D4 receptor complex or concentrations of specific binding proteins, presumably the CAR receptor (Waxman, 1999Go) or some associated proteins, the fractional occupancy (FO) of the DNA promoter elements by the D4 receptor complex was related to either the free or total tissue concentration of the parent compound (D4). The FO was calculated from liver D4 concentration by a Hill equation, with an apparent dissociation constant (Kd) and a Hill coefficient (N).

((1))

Here, D4:R:DNA is the concentration of DNA ligand binding sites bound with the putative D4 receptor complex and DNAtotal is the total concentration of binding sites for this complex. The rate of change of total amount of CYP2B1/2 protein in the liver was related to basal production rate (K0), the induced rate (proportional to the fractional occupancy of the DNA binding site), and first order degradation rate constant (kelim) of CYP2B1/2 protein, as follows:

((2))
where Kmax is the maximal rate of synthesis with full occupancy of the promoter sites. The units for the various parameters used in the above two equations are presented in Table 2Go. Since the appearance of new protein in the cell is a result of many steps, a finite time delay (3 h) was included between the transcription of the gene and measurable increases in cellular protein.


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TABLE 2 Parameters for the Multicompartment Liver Model to Simulate Protein Induction and PROD Activity following Inhalation Exposure to D4
 
Modeling dose-dependent PROD inhibition using the 1-compartment liver model.
PROD is a relatively specific enzymatic measure of CYP2B1/2 activity. PROD activity was measured using liver microsomal samples collected at the end of a 5-day exposure to D4 (Table 1Go). PROD activity is assumed to be proportional to the concentration of CYP2B1/2 protein. The PROD activity increases with D4 exposure concentration up to 500 ppm and thereafter decreases with increasing exposure concentration of D4. This decrease in activity at higher concentrations was modeled as either competitive inhibition by D4 that was carried through the preparation procedure or suicide inhibition. Either competitive or suicide inhibition model formulation could successfully describe the dose dependence. For the case of competitive inhibition, D4 was assumed to be carried through from the intact liver to the microsomal preparation without substantial decreases in its microsomal phase concentration due to very low solubility in water. PROD activity for a given substrate concentration, [PROD]sub, was formulated as follows (units for the various parameters used in this equation are presented in Table 2Go):

((3))

In the competitive inhibition model, the only extra parameter required is the inhibition dissociation constant of D4 for binding the enzyme and inhibiting pentoxyresorufin metabolism (Kinh, in µM). The proportionality constant (ß), relating the protein activity units to the amount of protein, is computed based on the basal level of CYP2B1/2 protein and PROD activity. Models with noncompetitive or uncompetitive inhibition could also describe the data since we have no constraints on values of binding constants or exact concentrations of D4 in the microsomal preparations. Equations for suicide inhibition (Appendix) required an unusual depiction of the dose dependence of inactivation of the enzyme by D4. Usually suicide inhibition is described in relation to the rate of metabolism of substrate by the protein that is lost during the inhibition (Lilly et al., 1998Go). In the present case, only descriptions based on free D4 concentrations were successful in reproducing the dose response for diminished activity. This point is discussed further below.

Multicompartment liver model.
A 5-compartment liver model was used to account for regional induction of the CYP2B1/2 proteins. In the 5-compartment model, the compartment numbered 1 surrounded the portal triad and the compartment numbered 5 surrounded the central vein. The intermediate compartments 2, 3, and 4 were interposed between compartments 1 and 5. The geometric analysis with portal triad regions draining to two central veins gave three star-shaped concentric regions around the central vein and one triangular shaped region around the portal triad. Compartment 2 became distributed throughout the entire 2-dimensional liver. Based on computing surface areas for these two-dimensional compartments and scaling them to three-dimensional cylinders, the volume for the 5 compartments was estimated as 13.5, 25.5, 33.9, 20.3, and 6.8% of total liver, respectively, going in order from the periportal to the centrilobular regions. The 5-compartment liver model used in this study was adopted directly from an earlier description for TCDD (Andersen et al., 1997bGo).

The mathematical formulation of the pharmacokinetics of the multicompartment liver closely parallels that of the single-compartment liver model. The multicompartment liver model partitions the liver into individual regions; each contains a shallow and deep tissue compartment (Fig. 2Go). The shallow liver compartment is perfused by the arterial blood and transports D4 to the deep compartment by diffusional transfer. In the multicompartment liver model the five compartments are perfused by blood sequentially, with compartment 1 (i.e., periportal region) receiving the arterial blood. Venous blood exits the liver from compartment 5 (i.e., centrilobular region). The rate of change of D4 in each of the shallow liver compartments is determined by the amount gained due to blood flow, the amount lost due to metabolism, the amount transferred to the deep compartment, and the amount lost by elimination into the mobile lipid pool in the blood perfusing the shallow compartment.


((4))

Here vli is the volume of the ith liver compartment in ml, Cvli and Cvli-1 are the venous concentration (µg/ml) of D4 exiting the ith and the (i–1)th compartment, respectively, Cdli is the concentration (µg/ml) of D4 in the ith deep compartment, kld is the transfer coefficient (h-1) between the shallow and deep compartments, klb is the first order elimination (h-1) of D4 from the liver to the blood via lipid pool transfer, and Vmi and Km are the kinetic parameters for D4 metabolism in the ith compartment.

Andersen et al. (2001) found it necessary to include induction of D4 metabolism to improve fits to liver tissue and plasma concentrations following multiday inhalation exposures of male and female rats to D4. In order to fit these tissue concentrations following 700 ppm exposures, the Vmax had to be increased by 2.0-fold for the female F344 rats in the inhalation model (Andersen et al., 2001Go). For the present study, the increase in D4 metabolism due to enzyme induction in the liver was expressed empirically by the equation:

((5))
where Vo is the basal metabolic activity (mg/ml/ml tissue), and INDmax is the dimensionless maximal fractional increase in metabolic capacity due to induction. A trial and error method was adopted to assign the appropriate functional form of INDmax that provided good fits to the pharmacokinetic data on D4 disposition and to the protein induction and activity data. After exploring several alternate formulations, INDmax was assumed to be equal to the ratio of the instantaneous concentration in liver, CYP2B(t), divided by the maximal concentration, CYP2Bmax, at full induction (INDmax = CYP2B(t)/CYP2Bmax). As a natural outcome of this formulation, INDmax was constrained to be a maximum of 1.0. This is consistent with earlier modeling results of a twofold increase in Vmax at high dose in female rats. This formulation for INDmax is different for earlier formulations that varied induction only as a function of time at high exposure concentrations without considering the dose dependent dynamics of induction (Andersen et al., 2001Go). The induction of CYP2B1/2 and the PROD activity in the multicompartment liver model was formulated similar to those described for the single compartment liver (Appendix).

Model parameterization.
The parameters used in the PBPK model were from Andersen et al. (2001). Parameters for the pharmacodynamic submodel were either obtained from literature (below) or were estimated by fitting the PD model to the induction dose-response data. The pharmacodynamic parameters for induction were the basal CYP2B1/2 protein production rate, the degradation rate constant for the protein, the delay time from transcriptional activation to appearance of functional protein, and the maximum zero-order production rate due to induction. The increase in production rate due to changes in FO is described in Equation 1Go with the Hill coefficient (N) and the apparent dissociation constant (Kd). Similarly, quantitative estimation of PROD activity requires parameter estimates for the competitive inhibition constant, Kinh.

Radiolabeling studies have been used to determine the degradation rate of cytochromes P450, including CYP2B1/2 protein. Shiraki and coworkers administered NaH14CO3 to male Sprague Dawley rats after a 5-day treatment with PB (80 mg/kg) or vehicle. Radiolabeled CYP2B1/2 was immunoprecipitated from isolated hepatic micorosomes at various times after administration of the radiolabel and plotted as a function of time to determine the half-life. The measured half-lives for CYP2B1 and CYP2B2 were between 37 to 50 h (Parkinson et al., 1983Go; Shiraki and Guengerich, 1984Go). The optimal fit to the half-life from the present studies, 22 h, was fairly close to this range.

The basal production rate of CYP2B1/2 protein and the proportionality constant relating CYP2B1/2 protein and PROD activity were derived using basal CYP2B1/2 and PROD data collected by McKim (1998). The amount of basal CYP2B1/2 protein in the liver of female F344 rats was determined by laser scanning densitometry, and reported as15.1 area-under-curve (AUC) units/µg protein (AUC = pixels x signal strength product; McKim, 1998Go). The basal CYP2B1/2 protein production rate is uniquely determined by the product of the protein degradation rate and the basal CYP2B1/2 level, giving an estimate of 0.45 AUC/h/µg protein for K0. The basal PROD activity in the uninduced liver was 2.45 pmoles/h/µg protein in female F344 rats (McKim, 1998Go). The proportionality constant is uniquely determined by the ratio of the basal PROD activity to the basal level of CYP2B1/2 protein, resulting in a value of 0.16 pmoles/h/AUC for ß.

Other values, the maximum CYP2B1/2 production rate, the Hill coefficient, and Kd, were not available from the literature. These three parameters were estimated simultaneously using the dose-response data for CYP2B1/2 protein induction (McKim, 1998Go). For the inhibition models, neither the inhibitory dissociation constant for D4 nor the second order rate constant for inactivation of CYP2B1/2 protein were available from any other studies. These constants were estimated by optimizing the model output against measured PROD activity for a wide range of D4 doses. The initial values for all the above parameters were estimated by visually fitting model predicted CYP2B1/2 induction and PROD activity to measured data. These initial values were used as seed values for parameter estimations conducted using the Nelder-Mead algorithm in ACSL-Optimize (Advanced Continuous Simulation Language, Aegis, Inc., Huntsville, AL). The optimized parameters were within10% of the initial estimates obtained using the manual visual fits. The only additional parameters to be estimated for the 5-compartment liver model, compared to the 1-compartment model, are the individual Kd for the various regional compartments in the liver. The process adopted to estimate these values in the 5-compartment model is similar to that in the 1-compartment model and are elaborated in the Results section. The parameters for the PD submodel are listed in Table 2Go.


    RESULTS
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Tissue Concentrations
Simulations with the PBPK model were compared with plasma and tissue concentration data from McKim (1998), presented in Table 1Go. The plasma and liver simulations agreed with the data at higher inhaled D4 concentrations. However, systematic errors were noted with the data for fat. The model, using a constant volume for the fat compartment, overestimated D4 concentrations in fat at low exposure concentrations and underestimated the D4 concentrations in fat at the higher exposure concentrations (Fig. 3Go). McKim (1998) found no significant alteration in body weight over the 5 exposure days. However, there was a substantial increase in liver size, up to 24% increase at the highest dose, following a 5-day inhalation exposure to D4. A better description of D4 concentration in fat was obtained when changes in the size of the fat compartment were assumed to parallel a similar organ-level effect (in this case, changes in liver–body weight ratio; Fig. 3Go). Assuming the energy for liver growth is partly generated by depletion of the fat reserves in the body, the fat volume was decreased in the model, in direct proportion to the measured dose-dependent increases in liver size (Table 1Go). Simulations with the PBPK model provided good fits to concentration data for all three tissue compartments (liver, plasma, and fat) when the dynamic fat compartment was implemented (Fig. 4Go). By incorporating coordinate changes in liver and fat, fat concentrations increase by about 40% at the high exposure concentrations where there are the largest changes in liver volume.



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FIG. 3. Comparison of observed total D4 concentrations in fat with those simulated using a model with a static (solid line) or dynamic (dotted line) fat compartment following inhalation exposure to D4 for 1 week (6 h/day, 5 days/week). For the dynamic fat compartment simulations, the size of the fat compartment was inversely proportional to the liver-body weight ratio. Changes in the size of the fat compartment were assumed to parallel changes in liver weight to body weight ratio, a similar organ-level effect. Points, observed data; bars are SEs.

 


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FIG. 4. Comparison of simulated and observed total D4 in liver, plasma and fat following exposure to various concentrations of D4 for 1 week (6 h/day, 5 days/week). Slightly nonlinear behavior in liver concentration reflects saturation of metabolism as exposure concentration exceeds 300 ppm. Dominance of the partition coefficient in determining blood concentrations during inhalation exposure limits experimental variability, resulting in small SEs for the observed data. Points, observed data; bars are SEs.

 
The variability in tissue concentration in Figures 3 and 4GoGo is remarkably small. The tight range for the mean blood and tissue D4 concentrations can be explained primarily by the inhalation route of exposure and the low blood:air partition coefficient (PC). For compounds with low blood:air PC, metabolic clearance has little influence on achieved arterial blood concentration (Andersen, 1981Go). The only factors that have a large influence on the plasma and tissue concentrations are the inhaled concentration and the partition coefficients. The slight nonlinearity in the liver curve results from saturation of metabolism at higher concentrations.

Protein Induction
CYP2B1/2 protein increased to a maximum following exposure to D4 of 500 ppm and greater concentrations (Fig. 5Go). PROD activity increased monotonically with increasing inhaled concentration up to 500 ppm and declined at higher concentrations (Fig. 6Go). The liver induction model was applied to estimate the dose dependence of total CYP2B1/2 protein and PROD activity using two different measures of dose, either total D4 concentration or free D4 concentration in the liver. Free liver concentration gave a better fit to the dose-response data (Figs. 5 and 6GoGo). Based on free D4 concentration in the liver, optimized estimates for the Kd and N were 0.67 µM and 1.9, respectively. The estimated inhibitory dissociation constant for D4 in the PROD assay was 1.69 nM free D4. Blood and tissue concentrations were not changed significantly when D4 inhibition was included in the model. Even though there is nearly a 35-fold increase in PROD activity, the estimated increase in D4 metabolism is only about twofold. The percent inhibition in PROD is actually quite small, about 20%. These small changes in metabolic clearance of a poorly soluble volatile will have minimal effects on blood concentrations and kinetics of the parent compound (Andersen, 1981Go).



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FIG. 5. Comparison of simulated and observed total hepatic CYP2B1/2 protein as a function of inhaled D4 concentration assuming that either free (solid line) or total (dotted line) D4 is pharmacologically active. The CYP2B1/2 protein was measured approximately 18 h after a 6 h/day, 5-day exposure in female F344 rats. The pharmacodynamic model provided the best fit to observed protein induction assuming that free D4 rather than total D4 is pharmacologically active. Protein levels were quantified using densitometry and are reported here as the AUC (total pixel density) per µg protein. Points, observed data; bars are SEs.

 


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FIG. 6. Comparison of simulated and observed hepatic CYP2B1/2 activity (measured using a standard assay for PROD activity) as a function of inhaled D4 concentration assuming free (solid line) or total (dotted line) D4 is pharmacologically active. The CYP2B1/2 activity was measured approximately 18 h after a 6 h/day, 5-day exposure in female F344 rats. The pharmacodynamic model provided the best fit to observed induction CYP2B1/2 activity when free D4 rather than total D4 was assumed to be pharmacologically active. All simulations include D4 inhibition of CYP2B1/2 activity. Points, observed data; bars are SEs.

 
The model simulations described above were conducted for 6 h/day, 5 consecutive day exposures. The influence of exposure conditions on the predicted dose-response pattern for CYP2B1/2 induction was evaluated by comparing continuous exposure (i.e., 24 h/day) to intermittent exposures (6 h/day) for a total of 5 days and the PROD activity was plotted as a function of dose 18 h postexposure (Fig. 7Go). Induction is increased with a longer exposure duration each day, reflecting a longer time when liver concentrations are maintained at high levels by the inhaled D4.



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FIG. 7. Predicted dose-response relationship for CYP2B1/2 activity (measured as PROD metabolism) following continuous (24 h/day) and intermittent (6 h/day) exposures. Activity is simulated without correcting for inhibition. The CYP2B1/2 activity was measured approximately 18 h after a 6 h/day, 5-day exposure in female F344 rats. Activity is increased (due to increase in induction) with longer exposure durations since liver D4 concentration are maintained at high level for a longer time. Also superimposed is measured CYP2B1/2 activity following treatment with PB (ip, 3 days at 80 mg/kg/day, McKim et al., 1998). Continuous exposure to concentrations of D4 greater than ~ 100 ppm are expected to lead to activities that are similar to levels induced by PB. Points, observed data; bars are SEs.

 
Liver Weight Changes
Increases in relative liver size occurs in response to many hepatic enzyme inducing compounds, including TCDD and PCB (Carthew et al., 1998Go; Peng et al., 1997Go; Sweeney et al., 1978Go). The increase can result from increases in the number of cells (hyperplasia), the size of cells (hypertrophy), or some combination of both. To compare the dose response for liver weight changes (a physiological level response of the organ) with CYP2B1/2 induction (a biochemical level response of cells), the measured liver weight to body weight ratio (LWBWR) dose-response curve (Table 1Go) was also fit to a Hill equation. Parameters for the Hill model were not known. Optimal values of Kd and the maximum LWBWR were determined using ACSL Optimize assuming an N of either 1 or 2. Assuming an N of 1 provided good fits to the observed data (Fig. 8Go) and resulted in a Kd of approximately 1 µg free D4/ml tissue (~ 3.36 µM) and a maximum LWBWR of 0.049 (i.e., 41% increase over control). Assuming an N of 2 did not provide a fit to the data (fit not shown). Hence, the N for liver weight changes is close to 1, with a half maximal saturation point (Kd) of 3.36 µM. The N and Kd for these increases in the LWBWR (organ level effect) are significantly different than the values determined for CYP2B1/2 induction (biochemical effect).



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FIG. 8. Estimation of the Hill coefficient and maximum induction level and half-maximal effect level (Kd) for liver enlargement following inhalation exposure to D4 for 1 week (6 h/day, 5 days/week). The parameters of a hill model applied to liver weight/body weight ratio (LWBWR) changes were explored to determine the similarities or differences of this organ level effect with enzyme induction. Optimal values of Kd and the maximum LWBWR were determined using ACSL Optimize assuming an N of either 1 or 2. Values of Kd (693 ppm exposure concentration that is approximately 3.36 µM free D4 liver tissue concentration) and maximum LWBWR (0.049) determined assuming an N of 1, provided much better fits to the observed data than those for N = 2 (data not shown). Points, observed data; bars are SEM.

 
Multicompartment Models for Regional Induction
Heterogeneous enzyme induction throughout the liver is a prominent feature of many liver tumor promoters (Bars et al., 1992Go). At low concentrations of D4, induction occurs preferentially in the centrilobular region and moves progressively outward toward the periportal region as the dose increases (Fig. 1Go). The 5-compartment liver model simulated this heterogeneous induction. The regional induction dose response in individual compartments is also determined by a Hill coefficient (N) and a dissociation constant, Kd. Variation in Kd among the compartments leads to the different regional sensitivities and predictions of regional induction by the PD model. Consistent with work with TCDD (Andersen et al., 1997aGo), the Kdi for the individual compartments were estimated by geometrically varying the Kd between adjacent compartments by a constant factor ({Delta}Kd). In such a formulation, increasing {Delta}Kd increases the differences in affinity between compartments and spreads whole liver induction over a greater range of exposure concentration. On the other hand, increasing the Hill coefficient increases the steepness of the induction dose response, leading to sharper boundaries between adjacent compartments. To model the regional induction, the Hill coefficient (N) for all the five compartments was set to a high value (4.0). The dissociation constant for the central compartment (#3) and the geometric difference, {Delta}Kd, between adjacent compartments were obtained by fitting these parameters to the measured data on overall induction in the liver. The optimized values for Kd3 and {Delta}Kd are 0.67 µM free D4 and 2.9, respectively.

Low Dose Responses
Low-dose behavior of the 1- and 5-compartment liver models were compared by determining the inhaled concentration required to provide a 10, 1, or 0.1% of maximum increase in CYP2B1/2 induction in rats (i.e., ED10, ED01, or ED001). The ED10, ED01, and ED001 estimated using the 1-compartment PBPK/PD models were 24.1, 6.9, and 2.1 ppm, respectively, and those estimated using the 5-compartment model were 25.1, 9.3, and 5.1 ppm, respectively (Table 3Go). The effective dose for a given percent increase in response differs between the 1- and the 5-compartment models more significantly at low dose than at high dose. Induction dose-response data was also fit to a Hill equation (U.S. EPA BMDS v1.2) to derive empirical estimates of effective dose, resulting in ED10, ED01, and ED001 values of 28.5, 7, and 1.8 ppm, respectively. These equate to concentrations that give a 10, 1, or 0.1% increase in induction and compare directly with the ED values calculated using the model.


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TABLE 3 Effective Dose for Fixed Percent Change in Hepatic Enzyme Induction Estimated Using a PBPK/PD Model with 1-Compartment Liver, 5-Compartment Liver, and Benchmark Analysis
 
Sensitivity Analysis
Many of the input parameters to the PD model were estimated based on model fits to the CYP2B1/2 induction and PROD activity data. Sensitivity analysis is a tool to analyze the effect of individual model parameters on model predictions. A sensitivity analysis was conducted by measuring the change in the estimated CYP2B1/2 and PROD levels for a prespecified change in a particular pharmacodynamic parameter when all the other model parameters were held constant. The sensitivity coefficients represent the percent change in the CYP2B1/2 and PROD levels for a 1% change in the listed parameter (Table 4Go). A sensitivity coefficient of 1 indicates that there is a one-to-one correlation between change in the parameter and model output. A positive value for the sensitivity coefficient indicates that the dose metric and the corresponding model parameter are directly correlated and a negative value indicates they are inversely correlated.


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TABLE 4 Sensitivity Analysis for the PD Model Parameters toward Induction of CYP2B1/2 and PROD Activity in Rats following Exposure to D4 Concentrations of 10 and 700 ppm
 
To examine PD model behavior at low and high exposure concentration, the sensitivity coefficients (SC) were calculated following exposure in rats to 10 and 700 ppm, respectively. The SCs toward CYP2B1/2 induction and PROD activity for all the PD model parameters were computed separately at the two different exposure concentrations for the 1-compartment liver model (Table 4Go). The sensitivity analysis was conducted using both the 1- and 5-compartment liver model and the results were qualitatively similar. Among the group of fitted parameters, dissociation constant (Kd) and Hill coefficient (N) are the most sensitive parameters at low exposure concentrations and the maximum production rate (Kmax) and elimination rate constant (Kelim) are the most sensitive parameters at high exposure concentrations when CYP2B induction is saturated. Of the measured parameters, basal CYP2B levels affects model predicted CYP2B induction at low exposure concentration, but not at high exposure concentration when induction is saturated. Measured basal PROD activity that determines the proportionality constant for PROD activity impacts these model estimates in direct proportion at both low and high exposure concentrations. The remaining model parameters that form part of the competitive or suicide inhibition formulations had negligible sensitivity on the model derived dose metrics.


    DISCUSSION
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Pharmacodynamic models simulate biological effects in response to internal (i.e., tissue) exposures. Here we integrated a PD model to an existing PBPK model to study induction of CYP2B1/2 following exposure to D4. In addition to testing model performance in simulating tissue D4 concentrations, CYP2B1/2 induction, and PROD activity data, other issues, such as the comparison of potency of D4 and PB and the impact of regional induction on low-dose responses, were also explored.

Comparative Induction Characteristics of D4 and PB
Dose-dependent induction of CYC2B1/2 by PB has been well characterized. Two published reports on PB induction of CYP2B1/2 were used to estimate Kd and Hill coefficients for PB induction. Nims and coworkers treated F344 rats with PB at feed concentrations of between 6.17 and 1500 ppm in the diet for 2 weeks (Nims et al., 1993Go). CYP2B1 protein was determined in microsomal protein preparations by Western blot using a mouse monoclonal CYP2B1 antibody. The experiment was also conducted with hepatocytes from F344 rats at nominal PB concentrations between 1 and 1000 µM in the media. The Kd for induction was 14.5 µM in vitro and the Kd for induction based on serum concentration was 10 µM in vivo. Kocarek and coworkers exposed primary hepatocytes from male Sprague-Dawley rats to nominal PB concentrations ranging from 1–500 µM in the media and measured CYP2B1 mRNA by Northern blot (Kocarek et al., 1990Go). The Kd for PB induction of CYP2B1 in this study was approximately 15 µM.

The CYP2B1 induction data from these two reports can also be used to determine Hill coefficients. The values of N determined for the in vivo and in vitro protein induction experiments (Nims et al., 1993Go) were 1.5 and 2.0, respectively. These values are similar to the N value (1.7) determined using the in vitro CYP2B1 mRNA induction data (Kocarek et al., 1990Go). Thus, Hill equations also adequately accounted for the induction of hepatic CYP2B1/2 induction by PB with an N value close to 2.0. The Kd for CYP2B1 induction by PB, expressed as plasma PB concentration, is in the range of 10 to 15 µM.

Using the free D4 concentration in liver to fit the dose response, the optimized values for Kd and N were 0.67 µM free D4 and 1.9, respectively. In addition to fitting the PBPK model to the data, empirical fits of D4 CYP2B1/2 induction data to a Hill equation were made using ACSL Optimize. These induction data were fit to several exposure metrics: exposure concentration (in ppm), free liver D4, total liver D4, free plasma D4, and total plasma D4 concentrations. With the exception of total plasma D4, the resulting optimized values of the Hill coefficient for D4 were between 1.55 and 1.67 (average = 1.6, SD = 0.06). The similarity in the Hill coefficient for PB and D4 implies that a similar ligand-receptor process could be involved in induction with both compounds. The Kd for PB in relation to plasma concentration is approximately 15 times higher than is the Kd for D4 expressed in relation to free concentrations of D4 in the liver.

McKim et al. (1998) compared maximum CYP2B1/2 induction caused by D4 and PB at the end of 3 days following either repeated daily inhalation exposures to 700 ppm D4 for 6 hrday or a repeated ip administration at 80 mg/kg/day for 3 days. The maximal increase with PB was three to four times greater than from D4 in both male and female F344 rats. It would be easy to conclude that the maximal induction with D4 was lower than with PB. However, this comparison is misleading since PB concentrations in plasma following ip administration for 3 days saturate the receptor over most of the 24 h. In contrast, the 6-h exposure regimen with D4 produces maximally inducing concentrations for little more than the 6-h period due to rapid exhalation of D4 at the cessation of exposure leading to a duration effect on maximal induction for D4 (Fig. 7Go). Currently, our D4 modeling results indicate that D4 is a somewhat more potent inducer of CYP2B family proteins than is PB and that the two ligands cause similar levels of maximal induction when the pharmacokinetics of inhalation are taken into consideration. Interestingly, the Hill coefficient of close to 2 differs from that for hepatic induction with TCDD where the Hill coefficient was closer to 1.0 (Kohn et al., 1993Go). This observation may indicate that a dimeric form of liganded receptor is involved in transcriptional regulation of CYP2B proteins by these inducers.

D4 Inhibition of Induced PROD Activity
High dose D4 inhibition of CYP2B1/2 activity was modeled to evaluate mechanisms of inhibition and the potential impact of inhibition on D4 pharmacokinetics. Blood and tissue concentrations were not affected by including D4 inhibition of CYP2B1/2. It is difficult to establish a mechanism for the inhibition of PROD by D4 at high concentrations. The carryover of D4 to a microsomal preparation is likely given the poor water solubility of D4 (Andersen et al., 2001Go) and the lipophilic nature of the microsomal preparation required for the PROD analysis. D4 concentrations in these microsomes have been measured, but not compared directly to concentrations in the livers before sacrifice of the animals. The present estimate of the inhibitory dissociation constant would need further study to determine the D4 concentrations in microsomes derived after different inhalation exposures. Suicide inhibition or competitive inhibition by D4 was explored as possible modes of inhibition. Either competitive or suicide inhibition model formulation could successfully describe the dose dependence (Fig. 9Go). However, we believe that the competitive inhibition is more likely than suicide inhibition for two reasons, namely, the nature of intermediate metabolites for D4 and the dose dependence of inhibition. Oxidative metabolism of D4 is believed to hydroxylate a methyl group, leading to rearrangement to a methoxy substituent, and hydrolysis of the ring. These intermediates should not be sufficiently reactive to irreversibly inhibit the enzyme by covalent modification. The dose response for suicide inhibition should also reflect the rate of production of the metabolite rather than D4 concentration as required to fit the inhibition dose response.



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FIG. 9. Comparison of observed hepatic CYP2B1/2 activity (measured as PROD metabolism) and activity predicted using a pharmacodynamic model that assumes the mechanism of high dose D4 inhibition of activity is either competitive, noncompetitive, or uncompetitive (dotted line) or suicide (solid line) inhibition. The mechanism of inhibition was not identifiable by modeling. Points, observed data; bars are SEs.

 
Protein Induction and Liver Enlargement
Smooth endoplasmic reticulum (SER), the cellular organelle containing the CYP2B enzymes, increases in response to these inducers (Peng et al., 1997Go). In part, cell hypertrophy is believed to result from the increase in SER (Peng et al., 1997Go). The dose-response curves for protein induction and liver enlargement had very different characteristics, with different values of N and Kd. Enlargement and CYP2B induction appear to be associated with different processes. CYP2B induction is at 90% of its maximum value by 300 ppm. Enlargement is less than 50% maximum at this concentration (Table 1Go) and continues to increase after induction has leveled off. Thus, cellular hypertrophy and changes in liver size do not appear to be directly related to the molecular processes that mediate induction of CYB 2B family enzymes. It is possible that the increase in smooth endoplasmic reticulum is dominated by the induction of other proteins by an alternative process with a N value near 1.

Regional Induction
Accounting for regional induction leads to predictions of markedly nonlinear dose response behavior in the low dose region. TCDD induction of CYP1A1 had an N value of close to 1.0 when modeled as a homogenous liver (Tritscher et al., 1992Go). However, intercompartmental N values of 4 are necessary to simulate regional induction in a 5-compartment liver (Andersen et al., 1997aGo). Our analysis of the PB induction data in vitro and in vivo also demonstrates that PB-type induction is nonlinear, whether it is modeled as a homogenous or regional process. For D4, the Hill coefficient of 1.9 for the 1-compartment model leads to considerable nonlinearity at low doses even for the homogenous liver. The 5-compartment liver model uses a large Hill coefficient (N = 4.0) to achieve a demarcation of responses among the compartments. The interpretation of the Hill coefficient in these two formulations differs subtly. For the 1-compartment model, the Hill coefficient of close to 2.0 indicates a level of cooperativity between binding proteins or other components in the promotional machinery for the CYP2B1/2 genes. In the 5-compartment description, Andersen and coworkers have interpreted the high N-value as representing a switching process initiated by interaction of the ligand with the receptor protein that sets off a cascade of processes in the cell (Andersen et al., 1997aGo).

With the modeling of tetrachlorodibenzo-p-dioxin, the 5-compartment liver model provided a better fit to the regional induction and to the low dose induction of the CYP 1A1 message (Andersen et al., 1993Go). As parameterized for D4, the 5-compartment model underestimates the amount of CYP2B1/2 at the lowest dose while the 1-compartment model provides a good fit (Fig. 10Go). One explanation is that the fraction of the liver induced in the 5-compartment model at the lowest dose is lower than the observed amount, a reflection of the current distribution of compartment sizes and Kds associated with them. While the 5-compartment model could be optimized to fit the data, such optimization requires quantitative data on compartment level regional induction (Fig. 1Go) that is not available.



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FIG. 10. Simulated dose response for the induction of hepatic CYP2B1/2 protein using a 1-compartment model and a 5-compartment model that accounts for the observed regional pattern of induction. Both models provide good fits to total hepatic CYP2B1/2 protein. Fitting both the total hepatic CYP2B1/2 protein and the regional induction pattern with the 5-compartment model results in a nonlinear dose response in the low dose region that is different than the 1-compartment model. Points, observed data; bars are SEs.

 
Another concern is that protein induction, as measured here, may not be the optimal experimental measure to distinguish between the two models. With TCDD, CYP1A1 mRNA induction was evaluated at low doses (Vanden Heuvel et al., 1994Go). The sensitivity and specificity of mRNA induction versus increases in protein concentration for a gene with little constitutive expression allowed more definitive evaluation of the 1- and 5-compartment models and indicated that the multiple-compartment model provided a better description of the induction data over a wide dose range (Andersen et al., 1997bGo). Similar studies could be done in the low concentration region for D4 with evaluation of mRNA for CYP 2B1 and CYP 2B2. Other mechanistic studies employing primary hepatocytes in culture are now providing mechanistic information to assess the induction dose-response behavior for individual cells (French et al., in press). These in vitro studies easily evaluate protein and message induction in populations of hepatocytes and in individual cells.

Comparative Dose Response
Expressing doses normalized to a given response level facilitates comparison of dose-response relationships in a selected portion of a dose-response curve. The effective dose that results in a 10% (ED10) or 1% (ED01) response can be used to compare unit potency within and below the range of experimental observation, respectively. Benchmark dose methods currently employed for risk assessment use empirical fitting to estimate effective doses, relying on extrapolations to estimate effective doses below the range of the observed data (EPA, 1996Go). Data in the experimental range (ED10 and higher) are used to guide extrapolation below the ED10, but the approach is statistical in nature rather than being informed by explicit knowledge of the underlying biological processes that determine the shape of the curve in the low-dose region. An alternative approach for calculating ED01 values is to use PBPK/PD models. The basal level of CYP2B1/2 in the liver in control rats is approximately 15 AUC/µg protein and the maximum measured CYP2B1/2 in rats exposed to high concentrations of D4 is approximately 600 AUC/µg protein. A 1% increase in induction is then equal to the basal protein level plus 1% of dynamic range (maximum protein level – basal protein level). Hence, ED01 is the D4 exposure that will result in a CYP2B1/2 of 15 + 6 or 21 AUC/µg protein.

The effective dose causing a specified increase in response differs for the 1- and the 5-compartment liver models (Table 3Go). The 5-compartment liver model predicts a larger nonlinearity in the response at low dose compared to the 1-compartment liver model, resulting in a larger effective dose for a given response. Empirical benchmark analysis using a Hill-type model fit to the induction data resulted in a lower ED as compared to those estimated using the 5-compartment liver PBPK/PD model. The model-based approach for calculating effective dose is an improvement over empirical models because it captures nonlinearities in the underlying biological processes to predict low-dose behavior. Our best representation of the fundamental processes, such as receptor occupancy and basal and maximal induction rates, rather than the statistical approach, determine the shape of the dose response in the low-dose region.

Uncertainties in Pharmacodynamic Representations of Biological Responses
These physiologically based PD models for enzyme induction by D4 attempt to convert qualitative hypotheses regarding modes of action into quantitative structures that can be evaluated, compared to available data and used to design targeted research. These models have several layers of uncertainty: the most important of which is the question of whether the model structure itself is actually correct. The present work includes specific components to evaluate fat concentrations, to assess mechanisms of inhibition of enzyme activity, and to assess mechanisms of total and regional induction in the liver. In each area alternate model forms were evaluated.

For fat concentrations, the original PBPK model that assumed constant fat compartment volume over time, while liver compartment volumes changed, slightly underestimated fat concentrations. The parameters that influence the achieved D4 concentration in fat are fat compartment volume and fat:blood partition coefficient. The alteration in volume in concert with liver volume changes is a more tenable idea than alterations in fat:blood partitioning in an otherwise time-invariant compartment. The basic assumption of contrasting changes in fat and liver compartment might be more readily examined in studies with inducers that cause larger increases in liver weight, such as peroxisomal proliferators (Van Rafelghem et al., 1987Go), or by carefully evaluating lipid content of the body minus liver in rats after PB-type induction. While the overall improvement in fit to fat data is relatively small, the ability to draw inferences with tissue concentration data with such small standard deviations makes these exercises especially valuable with a highly lipophilic compound such as D4.

The modeling of PROD inhibition represents implementation of several hypotheses regarding modes of inhibition coupled with considerations of biological plausibility. The favored mode of action relates to potential inhibition by D4 that is carried over in preparation of microsomal samples. This hypothesis can be tested by adding D4 to microsomes derived from PB-treated rats before conducting PROD determinations. The requirement in the PBPK model to include deep tissue stores for D4 in the liver is consistent with sequestration of D4 in cell membranes and potential for carryover to microsomal preparations.

Undoubtedly, the most significant decisions in our PD modeling effort with D4 was implementation of the presumed receptor-based mode of action of D4 and the comparison of a 1- and 5-compartment description of the liver acinus. The similarities with the induction pattern with PB, the degree of liver enlargement, and the similarity in the Hill term for overall induction by D4 and PB are all consistent with a PB-like response working through the same CAR receptor that regulates PB responses. While full induction requires many steps, our receptor model captures the binding interactions as the primary determinant of the dose response. More detailed studies, especially with in vitro preparations, should add more molecular detail to this macroscopic formulation of induction. The present PD model did clearly show that the maximal induction for PB and D4 were similar, although initial empirical estimates would have presumed D4 to have a lower maximal induction.

The receptor-based gene induction model was then embedded into a larger model to evaluate responses of the entire liver. Which macroscopic liver model is preferred? The most obvious visual characteristic of induction is the nonuniform response with increasing dose. This behavior cannot be reproduced in any description that regards the liver as a single, uniformly responding organ. The multicompartment model (Andersen et al., 1997bGo) was developed because of the regional induction noted with Ah receptor regulated induction. This model was motivated by a desire to have a description that provided a smooth increase in induced area as dose increased with a minimum number of parameters. Five compartments provided the ability to describe relatively smooth induction (at three compartments the induction looks more stair stepped) with only two parameters, the binding affinity in compartment 3 and the difference in affinity between adjacent compartments.

The restriction that the relative affinities between compartments are fixed limits the freedom of the model to fit the low dose data point even though this model worked better than a 1-compartment model for dioxin. Despite the difficulty with the single data point, a multicompartment model is clearly essential to provide descriptions that recapitulate regional induction (Fig. 1Go). Future studies of regional induction that utilize a variety of in vivo methods to visualize and quantify induction in individual cells and in specific regions in vivo will be important for extending this multicompartment model and to make it more flexible. At this point, manipulation of compartment parameters to fit the single point does not seem warranted until more molecular information on induction is accrued by in vitro and in vivo methods.

The largest mechanistic uncertainty with this regional induction model is in the decision to alter Kd throughout the five regions to achieve variable sensitivity. Other changes could be made to achieve the same end, such as variability in receptor concentrations or CAR receptor protein interaction with other transcriptional actors. However, each has the same mechanistic uncertainty. Our belief is that resolution of these uncertainties will require new methods to examine responses of individual cells undergoing induction (French et al., 2002Go). The real issue with the single and multicompartment liver induction models is in the process of induction. The former regards induction as a smooth dose-response curve where individual cells have all possible levels of induction. The latter is based on the premise that induction occurs as an all-or-none switch, moving the cell to a new phenotypic state. The regional induction data argues persuasively for the latter type model. The details now need to be examined by appropriate molecular studies.

Model development includes trial and error; the final model is the one most consistent with both the available experimental data and current mechanistic information on the biological processes under investigation. Our model reflects a working hypothesis regarding induction in the intact rat. Modeling the observed regional pattern of hepatic CYP2B1/2 induction clearly requires a multicompartment liver model. However, the hypothesis that Kds are different in the various compartments is a possibility that needs confirmation. Despite some uncertainties at the molecular level of detail, the model presented here is completely consistent with the experimental data on induction on whole liver and regional basis and reflects our best understanding of the biochemical processes controlling induction.


    APPENDIX
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
Suicide inhibition is the inactivation of the enzyme by irreversible modification of the enzyme during metabolism of a substrate. For suicide inhibition, it is necessary to calculate amounts of total protein, inhibited protein and catalytically active protein. The rate of change of inactive CYP2B1/2, described by a second order process, is proportional to the concentration of active enzyme and the liver D4 concentration. Thus, the equations for PROD activity are:

((A-1))


((A-2))

Here ksui is a second-order rate constant for suicide inhibition, and ß is proportionality constant relating the protein activity units to the amount of protein. Since [CYP]inactive is zero in control animals (i.e., when D4 exposure concentration is zero), ß is the ratio of the baseline PROD activity to the baseline CYP2B1/2.

In the 5-compartment liver model, induction of CYP2B1/2 and the PROD activity in each of these compartments is directly related to the free D4 concentration in the respective compartment, similar to those described for the single compartment liver. Hence the rate of change of CYP2B1/2 protein and PROD activity with suicide inhibition in any given liver compartment is given by the following equations:

((A-3))


((A-4))


((A-5))
where [CYP2B1/2]i is the total CYP in the ith compartment, PRODi is the activity in the ith compartment, [D4]i is the concentration of the parent compound in the ith compartment, and Kdi is the dissociation constant for the binding between the ligand-receptor complex and the response element in the ith compartment. Kdi is altered in the various hepatic subcompartments to simulate the differential dose response for induction in the various liver regions. The total amount of CYP2B1/2 and PROD activity are estimated by summing the five compartment values.


    ACKNOWLEDGMENTS
 
We thank Dow Corning Corporation for support of this work and Dr. Bruce Allen for conducting empirical and statistical analysis on the induction dose-response data. The Silicones Environmental Health and Safety Council of North America provided support for portions of this work.


    NOTES
 
1 To whom correspondence should be addressed. Fax: (970) 491-8304. E-mail: andersenme{at}aol.com. Back


    REFERENCES
 TOP
 ABSTRACT
 INTRODUCTION
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 REFERENCES
 
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