Biologically Motivated Computational Modeling of Chloroform Cytolethality and Regenerative Cellular Proliferation

Yu-Mei Tan, Byron E. Butterworth1, Michael L. Gargas2 and Rory B. Conolly3

CIIT Centers for Health Research, 6 Davis Drive, Research Triangle Park, North Carolina 27709

Received February 26, 2003; accepted May 9, 2003

ABSTRACT

Chloroform is a nongenotoxic-cytotoxic carcinogen in rodents. As such, events related to cytotoxicity are the driving force for cancer induction. In this paper we extended an existing physiologically based pharmacokinetic (PBPK) model for chloroform to describe a plausible mechanism linking the hepatic metabolism of chloroform to hepatocellular killing and regenerative proliferation. The key aspects of this mechanism are (1) the production of damage at a rate proportional to the rate of metabolism predicted by the PBPK model, (2) the saturable repair of the damage, (3) the stimulation of the cell death rate by damage, and (4) the stimulation of the cell division rate as a function of the difference between the control and exposed numbers of cells. This extension allows the simulation of the labeling index and comparison with labeling index data. Data from a previously published chloroform-inhalation study with female B6C3F1 mice that determined cytolethality and regenerative cellular proliferation following exposures of varying concentrations and exposure durations were used for model calibration. Both threshold and low-dose linear linkages between chloroform-induced damage and cell death rate provided visually good fits to the labeling index data after formal optimization of the adjustable parameters, and there was no statistical difference between the fits of the two models to the data. Biologically motivated computational modeling of chloroform-induced cytolethality and regenerative proliferation is a necessary step in the quantitative evaluation of the hypothesis that chloroform-stimulated cell proliferation predicts the rodent tumor response.

Key Words: chloroform; physiologically based pharmacokinetic (PBPK) model; pharmacodynamic (PD); regenerative cellular proliferation; inhaled chloroform cytolethality; labeling index (LI); liver.

The hepatic and renal carcinogenicity of chloroform (dichloromethane, CHCl3) at high exposure levels in rats and mice has been reported in several studies (Jorgenson et al., 1985Go; Nagano et al., 1998Go; NCI, 1976Go; Yamamoto et al., 1994Go). A trace amount of drinking water, formed during drinking-water chlorination, results in low-level exposures by both ingestion and inhalation. Although the exposures are low (U.S. EPA, 1998Go), widespread human exposure to a rodent carcinogen generates concern that chloroform may pose a human cancer risk.

The mechanism of chloroform carcinogenicity has been investigated extensively through a large number of genotoxic and cytotoxic assays (Butterworth et al., 1998Go; Jorgenson et al., 1985Go; Larson et al., 1994aGo,bGo,cGo; Pegram et al., 1997Go; Templin et al., 1996aGo,bGo,cGo; Yamamoto et al., 1994Go). The weight of evidence indicates that neither chloroform nor its metabolites are DNA reactive or genotoxic and that cancer induction is secondary to events associated with cytolethality and regenerative cell proliferation (Butterworth and Bogdanffy, 1999Go; ILSI, 1997Go; Reitz et al., 1990Go). Biological activities associated with continual cytolethality and regenerative cellular proliferation include the generation of DNA-reactive oxygen species, the release of nucleases, mutation induction associated with continual forced cell division, and the expression of growth factors (Butterworth et al., 1992Go, 1995Go). These activities may increase the rate of accumulation of procarcinogenic mutations and provide a selective growth advantage to precancerous and cancerous cells.

The amount of regenerative cellular proliferation in the liver at any given level of chloroform exposure can be inferred from labeling index (LI) data. The LI provides an estimate of the percentage of hepatocytes that were in S-phase during the period of exposure to a DNA precursor labeling agent. Regenerative cellular proliferation is a more sensitive indicator of toxicity than a traditional histopathological approach because increased LI can be determined before overt histological changes can be observed (Butterworth and Bogdanffy, 1999Go; Constan et al., 2002Go). As with any biological activity that can lead to cancer, increasing the rate of cell division over time increases the cancer risk but does not always lead to tumor development in a particular tissue. Species and tissue susceptibility, the extent and duration of cytolethality and regenerative cell proliferation, and the stochastic nature of some aspects of carcinogenesis are all important determinants in eventual tumor formation. For a nongenotoxic carcinogen, an elevated cancer risk is anticipated only at cytolethal exposure levels, so that protecting against chloroform cytolethality should also prevent tumor formation. Therefore, induced cell proliferation is an appropriate surrogate for tumor formation in risk assessments. This principle is valuable because induced cell proliferation is far more readily and accurately measured than is induced cancer. For example, the concentration x time cell proliferation studies modeled here would be cost-prohibitive to conduct as cancer studies (Constan et al., 2002Go).

Physiologically based pharmacokinetic (PBPK) models describe the mechanism linking external exposure or applied dose with dose to the target tissue, while pharmacodynamic (PD) models focus on the relationship between target tissue dose and the tissue response of interest. In an earlier PBPK-PD model, Reitz et al. (1990)Go linked chloroform cytotoxicity to hepatocyte killing. The authors assumed that chloroform damages liver cells when chloroform metabolites bind to macromolecules, since a correlation exists between the covalent binding of chloroform metabolites to macromolecules and areas of hepatic and renal necrosis induced by chloroform (Ilett et al., 1973Go). Their model predicted the percentage of cells killed by a single chloroform exposure but was not designed to accommodate multiple exposures or to describe regenerative proliferation. The current model was developed to provide these capabilities, since simulating LI data from multiday exposures was the primary objective.

Constan et al. (2002)Go conducted a concentration x time chloroform-inhalation study in female B6C3F1 mice to define the combinations of atmospheric concentration and duration of exposure necessary to induce liver cytotoxicity. The authors concluded that concentration was more important than duration for liver toxicity. That data set was ideal for the initial development of a biologically motivated computational (PBPK-PD) model of chloroform cytolethality and regenerative proliferation. The objective of our study was to employ that data set to increase our understanding of the relationship between chloroform pharmacokinetics, cytolethality, and regenerative cellular proliferation. Quantitative knowledge of chloroform dosimetry and the associated cellular proliferative response relationship will provide an improved scientific basis for a human cancer risk assessment.

MATERIALS AND METHODS

Animals and Husbandry
Experiments were conducted under the federal guidelines for the humane use and care of laboratory animals (National Institutes of Health, 1985Go) and were approved by the CIIT Institutional Animal Care and Use Committee. Female B6C3F1 mice were obtained from the Charles River Breeding Laboratories, Inc. (Raleigh, NC) and allowed to acclimate for 2 weeks. Seventeen-week-old mice (average body weight = 26.2 ± 3.5 g) were used in the gas uptake study, and 25-week-old mice were used in the tissue:air partition coefficient study. The mice were housed in humidity- and temperature-controlled facilities accredited by the American Association of Accreditation of Laboratory Animal Care. The animals were provided with NIH-07 rodent chow (Ziegler Bros., Gardener, PA) and deionized, filtered tap water ad libitum. The animals were housed individually in stainless-steel hanging wire cages contained within H-1000 stainless-steel chambers. The room in which the chambers were maintained was on a 12-h light–dark cycle at 22.2 ± 4°C and 60 ± 15% relative humidity.

Labeling Index Data
Constan et al. (2002)Go published hepatic LI data obtained from the inhalation exposure of 12-week-old female B6C3F1 mice (average body weight = 21.2 ± 1.2 g) to chloroform concentrations of 10, 30, or 90 ppm for 2, 6, 12, or 18 h/day for 7 consecutive days. Seven combinations of concentration and exposure duration were conducted with five animals in each group (Table 1Go). Regenerative cellular proliferation was evaluated by administering the thymidine analog bromodeoxyuridine (BrdU) via subcutaneously implanted osmotic pumps approximately 3.5 days prior to necropsy. Labeled hepatocytes were identified immunohistochemically in histological sections. BrdU labeling reflects the number of cells replicating their nuclear DNA during exposure to the labeling compound. The LI was then calculated as the percentage of cells that were stained positive for BrdU incorporation to quantify regenerative cellular proliferation induced by chloroform cytotoxicity (Table 1Go).


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TABLE 1 Hepatic Labeling Indices (LI) for Female B6C3F1 Mice following 7 Days of Inhalation of Chloroforma
 
Programming
The model was coded using the graphical simulation tool SIMULINK®, which is part of the MATLAB® technical computing product family (The MathWorks Inc., Natick, MA). Formal optimizations were conducted as described by Conolly et al. (2000)Go. Custom MATLAB® scripts were developed for the optimizations and for specifying initial conditions. All simulations were run on 1700–2000 MHz Pentium® computers using either the Windows 2000® or XP® operating systems. The programs are available from the corresponding author (rconolly{at}ciit.org).

Model Structure
The following provides a detailed description of the structure of the PBPK-PD model (see Fig. 1Go):



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FIG. 1. Structure of the pharmacodynamic model.

 
PBPK model.
Corley et al. (1990)Go described chloroform disposition in male, but not female, B6C3F1 mice. We adapted this model for the simulation of LI data from female B6C3F1 mice. The partition coefficients of blood:air, liver:air, and kidney:air for female B6C3F1 mice were measured as described by Gargas et al. (1989)Go, while the partition coefficients of fat:air and slowly perfused tissue:air for B6C3F1 mice were taken from Corley et al. (1990)Go. The partition coefficient of rapidly perfused tissue:air was set to the value for liver:air. The metabolic rate constants, VmaxC (maximum metabolic rate) and Km (half-maximal concentration), for female B6C3F1 mice were estimated from gas uptake data. Female B6C3F1 mice were exposed in groups of five to nominal initial concentrations of 350, 1050, 1700, 2350, or 3200 ppm in a closed recirculating gas uptake chamber having a volume of 2.6 l. Chloroform was added at the beginning of the exposure, while carbon dioxide and oxygen concentrations were regulated during the exposure.

The PBPK model was fit to the decline of chloroform concentrations in the chamber from all five gas uptake exposures simultaneously by adjusting the VmaxC, Km, and starting concentration values; the values of all other model parameters were fixed until an optimal fit was obtained (Table 2Go). Various starting values of the adjustable parameters were explored throughout the parameter space to ensure that global optima were obtained (Table 3Go).


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TABLE 2 Parameters Used in the Physiologically Based Pharmacokinetic/Pharmacodynamic Model for Chloroform
 

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TABLE 3 Starting Values Used for Optimization of Gas Uptake and Pharmacodynamic Parameters Pharmacodynamic parameters
 
Allowing the starting concentrations to vary improved the overall fits to the gas uptake data but provided estimates of the starting concentrations that were 66–76% of the nominal starting concentrations. The early rapid rates of decline in the closed chamber concentrations (Fig. 2Go) reflect breathing rate, cardiac output, and partitioning into tissues. The more gradual later declines reflect metabolism given that equilibrium with the tissues has been achieved. Allowing the starting concentrations to vary during the estimation of VmaxC and Km is thus not expected to actually provide better estimates of the starting concentrations; rather, variation of the starting concentrations minimizes the effect of lack of model fit to the tissue equilibration phase of uptake on the estimation of the metabolic parameters. The optimized starting concentrations are not viewed, therefore, as necessarily indicating that the actual starting concentrations were consistently lower than the nominal concentrations. All PBPK model parameter values not specified in Table 2Go were taken from Corley et al. (1990)Go.



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FIG. 2. Gas uptake curves at 350, 1050, 1700, 2350, and 3200 ppm for female B6C3F1 mice. The solid lines depict the optimized simulations, and the symbols are experimental data.

 
For the male mouse version of the PBPK model, Corley et al. (1990)Go incorporated equations describing the destruction and resynthesis of the hepatic metabolism capacity for chloroform to improve the fit of the model to the gas uptake data. However, this modification was not necessary to fit the female B6C3F1 mouse data. The structural and mathematical details of the PBPK model can be found in Ramsey and Andersen (1984)Go and Corley et al. (1990)Go.

PD model structure.
A biologically plausible mechanism linking PBPK model-predicted hepatic metabolism of chloroform with cytolethality and regenerative proliferation was incorporated into the liver compartment in the PBPK model. This mechanism has two main components: (1) a linkage between the hepatic metabolism of chloroform and the rate of cell death, and (2) regenerative proliferation. For the purposes of model development, no distinction was made between the various cell types in the liver. Thus, changes in the cell death rate apply equally to all hepatic cells. Since most liver cells are hepatocytes on the basis of both number and volume (Battle and Stacey, 2001Go), this simplification is not likely to be a significant source of model uncertainty.

From metabolism to cell death.
The main metabolites of chloroform, phosgene and protons, damage the liver (Pohl et al., 1977Go). Since this damage is not well characterized at the biochemical level, virtual damage was defined in the model to link chloroform exposure to cytolethality. This "virtual damage" is not directly correlated with any measured end point. The rate of damage formation (damage units/h) is proportional to the rate of chloroform metabolism per tissue volume, and damage is removed by a saturable repair process (Equation 1Go):


(1)

where Adamage is the amount of damage (damage units), kdamage is a proportionality constant (damage units-cm3/mg), Rmet is the rate of chloroform metabolism per tissue volume (mg/h-cm3), kmax is the maximum repair capacity (damage units/h), and k1 is the half-maximal amount of damage (damage units). The cell death rate is a function of the amount of damage. Two alternative functions, threshold (Equation 2Go) and low-dose linear (Equation 3Go), were evaluated for linking the amount of damage to the death rate. The threshold linking function had the following form:


(2)

where ßcfm is the cell death rate (h-1) in the chloroform-exposed liver, ßref is the cell death rate (h-1) of a reference (unexposed) liver, k2 ([damage units-h]-1) determines the linear relationship between the amount of damage and the cell death rate, and Th (damage units) is the threshold level of damage. The linear linking function had the form:


(3)

where k3 ([damage units-h]-1) is a constant.

Regenerative cellular proliferation.
The main challenge in modeling regenerative proliferation was to describe a parsimonious mechanism that could sense the deficit in cell number due to chloroform-induced cytolethality and generate a compensatory increase in the division rate of the surviving cells, with this process damping out as the cell number returned to the control level. Accordingly, each liver cell was assumed to secrete a signal into the blood at a constant rate. This signal is cleared at a first-order rate, and normal liver size is therefore associated with a specific blood level of the signal. When cells are killed by chloroform, the rate of signal production falls, and a difference appears between the control blood level of the signal and that of the chloroform-exposed mice. This difference is used to drive an increase in the cellular division rate, with the process damping out as the blood level of the signal in the chloroform-exposed mice approaches that of the controls. This approach is a modeling convenience and does not represent an established mechanism for the control of liver size. A number of studies have shown, however, that soluble factors in the blood do influence the division rate of hepatocytes (Fausto, 2001Go; Michalopoulos and DeFrances, 1997Go; Pediaditakis et al., 2001Go). A detailed examination of the mechanisms controlling the liver size in mice was beyond the scope of the present study, however.

The blood level of the signal for control (Sref) and chloroform-exposed (Scfm) mice was obtained by using the equation:


(4)

where kp (signal units/cell-h) is the zero-order rate constant for signal secretion into the blood by each liver cell, kcp(h-1) is the first-order rate constant for signal clearance from the blood, and N denotes either Nref or Ncfm.

The rate of change of viable liver cells in the control (Nref) and chloroform-exposed (Ncfm) livers was a function of their respective division ({alpha}ref, {alpha}cfm) and death (ßref, ßcfm) rates (h-1):


(5)

The difference between the control and exposed levels of signal (Sref - Scfm) is the driving force for compensatory regenerative proliferation:


(6)

where {alpha}max is the maximum possible division rate. This equation specifies the minimum ({alpha}ref) and maximum values for the rate of cell division ({alpha}ref + {alpha}max) and a smooth transition between these bounds. We did not search for other expressions that might also have been used to specify {alpha}cfm, although it is likely that a number of such alternatives exist.

The simulated LI expressed in percentage was calculated from the number of cells that replicate their DNA during the 3.5 days of exposure to BrdU:


(7)

where Ndiv(t) is the number of cell divisions that have occurred from the start of simulation (t = 0) through time t (days), Ndiv (t - 3.5) is the total number of divisions from the start of the simulation through (t - 3.5) days, and Ncfm(t) is the number of cells at time t. The factor of 200 is used because the number of labeled cells is twice the number of divisions and LI is expressed as a percentage. Equation 7Go does not track cells that divide twice during the labeling interval. Since the maximum LI described by Constan et al. (2002)Go is about 20%, this is not a serious issue for the current analysis. However, analyses of studies with higher LIs could be confounded by multiple divisions during the labeling period. In such cases it would be appropriate to track separately the pool of cells that have divided at least once during labeling to capture subsequent divisions.

Ndiv is obtained as follows:


(8)

Pharmacodynamic parameter estimation.
No data were available to estimate directly the values of the pharmacodynamic parameters appearing in Equations 1Go–8Go. The threshold model required the estimation of five parameters (kmax, k1, k2, Th, and kcp), while the low-dose linear model required the estimation of four parameters (kmax, k1, k3, and kcp), as shown in Table 2Go. The upper and lower bounds used during optimization were based on prior experience gained through manual interaction with the model. The bounds were set to avoid parameter values where the model became numerically unstable or where manual work with the model had shown that fits to the LI data were poor. A grid search was used to identify the starting values for optimization that led to global optima. The grid consisted of pairs of parameter values (kcp and k2 in the threshold model and kcp and k3 in the low-dose linear model). The remaining adjustable parameters were optimized at all grid points (Table 3Go). The optimal set of parameters from the grid search was then used for a final simultaneous optimization of all of the four or five adjustable parameters. A total of seven LI data points were used for parameter estimation.

RESULTS

Female B6C3F1 Mouse Partition Coefficients
The experimentally measured partition coefficients were as follows: blood:air = 24.1 ± 1.7 (n = 20); liver:air = 16.9 ± 1.1 (n = 11); and kidney:air = 12.2 ± 1.2 (n = 9).

Analysis of Female B6C3F1 Mouse Gas Uptake Data
The gas uptake data for female B6C3F1 mice and optimal simulations are shown in Figure 2Go. The optimized VmaxC was 10.06 mg/h-kg, and the optimized Km was 0.77 mg/l. Compared to the published values for male B6C3F1 mice (Corley et al. [1990]Go: VmaxC = 22.8 mg/h-kg, Km = 0.352 mg/l; Gearhart et al. [1993]Go: Vmax C = 14.2 mg/h-kg, Km = 0.25 mg/l), the female mice have a smaller VmaxC and a larger Km. Since the value of Km is not expected to be sex-dependent, the difference in Km between the male and female B6C3F1 mice presumably reflects experimental variability and perhaps also differences in the software and algorithms used for parameter estimation. Corley et al. and Gearhart et al. used ACSL and the Nelder-Mead algorithm (Aegis Technologies, Huntsville, AL), while the current analysis used MATLAB/SIMULINK and the fmincon algorithm from the MATLAB Optimization toolbox (The Mathworks Inc., Natick, MA).

Optimization of the Pharmacodynamic Parameters and Simulation of the Labeling Index Data
Two linkages between damage and cell death rate were evaluated—threshold and low-dose linear. Identical values were found by grid search optimizations for the common adjustable parameters of the two models (Tables 2Go and 3Go). Thus, the optimized models are identical, except for the presence of the threshold parameter (Th) in the threshold model (Tables 2Go and 3Go). The sums of squares (SS) of the normalized differences between the experimental data and the predictions from both models were compared. The SS for the threshold model was 1721, and for the low-dose linear model it was 1738. These SS were not statistically different (p = 0.295) as evaluated by an F-test (df = 2 for the threshold model and df = 1 for the linear model). This result can be explained by the relatively small value of the threshold parameter.

The simulations of the LI were in good visual agreement with the experimental data from the dose x time study of Constan et al. (2002)Go (threshold model in Fig. 3Go; low-dose linear model in Fig. 4Go). The error bars on the measured LI represent 95% confidence intervals. All of the simulated LI were within the 95% confidence intervals of the measured means.



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FIG. 3. Simulation of LI data from Constan et al. (2002)Go using the threshold model.

 


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FIG. 4. Simulation of the LI data of Constan et al. (2002)Go using the low-dose linear model.

 
DISCUSSION

Reitz et al. (1990)Go were the first to extend a PBPK model for chloroform to describe the relationship between hepatic metabolism and cytolethality. In their model, chloroform-induced cellular damage is defined as a combined function of the rate of chloroform metabolism, the fraction of this rate associated with macromolecular binding, and a normally distributed susceptibility of the cells to damage. These factors together define the fraction of cells in the liver that is damaged. As with the current model, the damage defined in the Reitz et al. model is virtual. Unlike the current model, however, the virtual damage in the Reitz et al. model is not described by a differential equation and does not exist independently of the ongoing metabolism of chloroform. Although a repair process for the damage is not described per se in Reitz et al. (1990)Go, the instantaneous variation in the amount of damage with the rate of chloroform metabolism effectively means that the damage is repairable, since the fraction of damaged cells decreases as the rate of metabolism decreases. The cells in the damaged fraction die at a first-order rate, allowing the calculation of a cumulative fraction of the cells in the liver that have been killed by chloroform exposure. The model of Reitz et al. does not describe regenerative proliferation and so cannot be used for multiple-exposure experiments or for the simulation of LI data.

In the current model, the production and saturable repair of virtual damage are described by a differential equation (Equation 1Go). Damage is produced at a rate proportional to the rate of chloroform metabolism without reference to the fraction of metabolites that bind to macromolecules (Ilet et al., 1973Go). This decision reflected the possibility that protons and associated pH changes may be part of the mechanism of chloroform-mediated cytolethality, as is the case with vinyl acetate (Bogdanffy, 2002Go), and recognition that the stably bound fraction of chloroform metabolites is a small fraction of the total amount metabolized. Presently, while the oxidative metabolism of chloroform is strongly implicated in its cytolethal effects, we do not know the molecular details of this mechanism. A simple linkage of metabolism to the creation of cellular damage without additional specification of details therefore seems most appropriate.

Damage is repaired (Equation 1Go) and can exist independently of the concurrent metabolism of chloroform. Cell killing associated with this damage can occur after the exposure to chloroform has ended and the hepatic metabolism of chloroform has ceased, as long as the level of damage is sufficient. Sufficiency is defined by the function linking damage to cell death rate. Both threshold (Equation 2Go) and low-dose linear (Equation 3Go) linking functions were evaluated. The shapes of these functions define the distributions of sensitivity of liver cells to killing. The parameters of Equations 2Go and 3Go were adjusted to fit the LI data, so the shapes of the sensitivity distributions differ from the normal distribution used by Reitz et al. (1990)Go.

El-Masri et al. (1996)Go described a PBPK-PD model for carbon tetrachloride that has similarities to both the model described by Reitz et al. (1990)Go and to the current model. The model by El-Masri et al. describes cell killing but not regenerative proliferation. The rate of cell killing in this model is a function of the amount of carbon tetrachloride metabolized. The linkage to the amount metabolized, rather than to the time-varying measure of bioactivation, and the lack of description of regenerative proliferation mean that the El-Masri model cannot be used with multidose experiments. A population of damaged cells that are either repaired or die is described. This is functionally similar to the damage compartment of the current model, although the repair process that acts on the damaged cells is first-order.

From the hepatic metabolism of chloroform through cell killing, the models by Reitz et al. (1990)Go, El-Masri et al. (1996)Go, and the current model consist of identical or analogous elements, including xenobiotic metabolism, virtual damage, repair of damage, a linkage of damage to cell killing, and, with the exception of the El-Masri model, a distribution of cellular sensitivity to killing by damage. However, the current model also includes a description of the regenerative proliferation, providing a capability for simulating multiple-exposure experiments and of LI, as described by Constan et al. (2002)Go.

Several reports have used PBPK models to define target tissue dose surrogates that are good predictors of pharmacodynamic end points, such as cytotoxicity and cancer (Delic et al., 2000Go; Meek et al., 2002Go; Reitz et al., 1990Go; Smith et al., 1995Go). The rate of chloroform metabolism generally has been identified as the preferred dose surrogate for correlating pharmacokinetics with the adverse hepatic effects of chloroform. The current model involves no requirement for the identification of a tissue dose surrogate per se. Issues such as whether the cytolethality of chloroform is better correlated with rate of metabolism or with the area under the curve for metabolism are subsumed into the structure of the pharmacodynamic model. The rate of damage repair, the form of the linkage between damage and cellular death rate, and the signal kinetics that drive regenerative proliferation constitute a structural alternative to an empirical correlation between a target tissue dose surrogate and the toxicological end point.

Tissue dose surrogates are useful predictors of effects to the degree that the toxicological end point has a linear correlation with the dose surrogate. Our pharmacodynamic modeling of the relationship between chloroform metabolism, cytolethality, and regenerative proliferation includes several nonlinear steps and provides an accurate simulation of LI data (Figs. 3Go and 4Go). Given the nonlinearities in the pharmacodynamic relationship, any tissue dose surrogate is unlikely to match the LI data as well.

Pharmacodynamic modeling fleshes out an important part of the overall linkage between exposure and response. However, computational modeling studies are most effective when they are part of an iterative process that also involves laboratory experiments. The pharmacodynamic structure described here posits entities such as cellular damage and signal molecules that certainly exist in some form but for which no data are available. Laboratory studies targeted to identify key steps of the mechanism linking chloroform metabolism with cell killing and the regulation of regenerative proliferation are needed. For example, while formal optimization was used to identify values for the adjustable parameters of the pharmacodynamic model, there is at present no way to evaluate how these parameter values correlate with specific biochemical entities. Additional experimental work that characterizes the damage caused by chloroform metabolites and the mechanism of regenerative proliferation would be needed to do so.

A grid search approach was used for optimization (Table 3Go) as a check on the ability of the optimization algorithm to find global optima. We found that the algorithm tended to not move far from the starting points. This could reflect the presence of local optima that trap the optimization algorithm. This result may also suggest that a richer data set is needed to ensure the prediction of global optima.

Our analysis found that low-dose linear and threshold models fit the LI data equally well. We suspect that experimental resolution of the question of the actual shape of the dose–response curve in the low-dose region is unlikely to be achieved by adding more exposure levels to the kind of study described by Constan et al. (2002)Go. One can always argue that small changes in the LI exist that are below the limit of detection. Rather, mechanistic studies are needed that adequately characterize the biochemical damage caused by chloroform metabolites and the sequence of events that leads from this damage to cell death.

Future work will include simulation modeling of other hepatic LI data sets from male and female mice and rats (Larson et al., 1996Go; Templin et al., 1996bGo, 1998Go). The LI data from the kidney (Larson et al., 1996Go; Templin et al., 1996bGo, 1998Go), which is also a target for carcinogenic effects of chloroform, will be modeled as well. A Monte Carlo version of the PBPK model (Delic et al., 2000Go) will be used to examine the extent to which interindividual variability in the mechanisms controlling chloroform pharmacokinetics accounts for variability in the LI. These studies will all contribute to the long-range goal of developing a robust cancer risk assessment for chloroform that makes maximal use of the mechanistic data.

ACKNOWLEDGMENTS

We would like to thank Dr. Alex Constan for valuable discussions and his insight regarding this data set and our modeling efforts. Dr. Barbara Kuyper provided expert editorial assistance with the manuscript, and Dr. Dennis House performed statistical tests.

NOTES

Portions of this paper were presented at the 41st Annual Meeting of the Society of Toxicology, Nashville, TN, March 2002.

1 Present address: Butterworth Consulting, Raleigh, NC 27613. Back

2 Present address: The Sapphire Group, Inc., Beavercreek, OH 45431. Back

3 To whom correspondence should be addressed. Fax: (919) 558-1300. E-mail: rconolly{at}ciit.org. Back

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