This article is part of the monograph on Mathematical Modeling in Environmental Health Studies.
Address correspondence to M.C. Kohn, Laboratory of Computational Biology and Risk Analysis, NIEHS, PO Box 12233, Mail Drop A3-06, Research Triangle Park, NC 27709-2233 USA. Telephone: (919) 541-4929. Fax: (919) 541-1479. E-mail: kohn@valiant.niehs.nih.gov
Received 16 February 2000; accepted 12 May 2000.
1,3-Butadiene, a gaseous hydrocarbon used in the production of synthetic rubber, has been found to be carcinogenic at multiple sites in mice (
1) and rats (
2) and is associated with leukemia in humans (
3). This carcinogenicity has been attributed to the formation of reactive epoxide intermediates that alkylate DNA bases (
4). As these epoxide metabolites are soluble in most tissues (
5-7), concentrations of circulating epoxides might be a useful measure of carcinogenic risk consequent to butadiene exposures.
Early physiologically based pharmacokinetic (PBPK) models of the disposition of butadiene (5,6,8) predicted 6- to 26-fold higher blood concentrations of 1,2-epoxybut-3-ene than were subsequently measured in mice and rats exposed to butadiene (9). This discrepancy indicates that the metabolic parameters that enabled these models to reproduce the uptake of epoxybutene from closed chambers leads to underprediction of the rate of metabolism of epoxybutene produced in situ. Several strategies have been used to obtain a better fit to the experimental data. Sweeny et al. (7) proposed that about 75% of the butadiene taken up by the animal is converted to an unidentified product other than epoxybutene. Johanson and Filser (5) suggested that some of the epoxybutene formed from butadiene may be sequestered in an "intrahepatic compartment."
The earlier model that includes sequestration of epoxybutene (5) did not specify the mechanism for this sequestration in the model's differential equations. Instead, it estimated (assuming a steady state) the concentration of the postulated "intrahepatic" pool by an algebraic function of the total liver epoxybutene and treated that pool as the sole substrate for epoxide hydrolase. Although Csanády et al. (10) suggested that sequestration may be due to formation of a complex between the cytochrome P450 that produces epoxybutene and the epoxide hydrolase that consumes it, a mathematical representation of the behavior of this complex was not given. There is experimental evidence for a transient complex between these two enzymes (11,12), suggesting the possibility of "channeling" of the newly synthesized epoxide to the epoxide hydrolase in competition with dissociation of the epoxide from the endoplasmic reticulum membrane. The goal of the present modeling effort was to represent in differential equations this molecular mechanism of sequestration, namely, privileged access of endoplasmic reticulum membrane-bound epoxide to the active site of a transiently associated epoxide hydrolase molecule. The predictions of the model representing this mechanism were compared with data for butadiene uptake and clearance and for circulating epoxide concentrations in mice and rats.
The model described here is an extension of a previous PBPK model (
13,14) and includes compartments for blood, lung, gastrointestinal (GI) tract, liver, kidney, and other rapidly perfused tissues, as well as fat and other slowly perfused tissues. The blood was distributed among arterial and venous spaces and compartments for the capillary spaces in each tissue. Arterial blood flow in this model branches to the capillary beds associated with tissue compartments. Capillary flow empties into the venous space except in the case of the GI tract where venous effluent empties into the liver capillary space, resulting in 80% of hepatic perfusion via the portal vein and 20% via the hepatic artery.
Because each organ or organ system is divided into blood and tissue spaces, arterial blood entering the capillaries can either be transported into the tissue or swept out into the venous blood. As the rates of these two processes are not necessarily the same, the model includes an extraction ratio, the fraction of material in the blood taken up by the tissue on the first pass through the organ. Transfer of butadiene between tissue and capillary blood spaces was represented as proportional to the permeability ¼ of the capillary membrane to the specific chemical.
where 
is the extraction ratio and Qt is the tissue blood flow rate (14). The net rate of transport is given by
where Ab and At are the amounts of chemical in the capillary blood and tissue spaces, respectively, Vb and Vt are the respective volumes of those spaces, and Pt is the tissue:blood partition coefficient. Because reliable data for the concentrations of butadiene and its epoxides in most tissues are not available, it was not possible to uniquely determine extraction ratios for each tissue individually. Therefore, the extraction ratios for butadiene, epoxybutene, and 1,2;3,4-diepoxybutane were each assumed to be the same for all tissues and were adjustable parameters in this model. The net rates of transport differ among organs because transport is a function of tissue blood flow rate, tissue concentration of the permeant, and the tissue:blood partition coefficient.
The lung in this model also had an associated compartment for the alveolar space, which exchanged gas (butadiene and/or epoxybutene) with the ambient air at a rate proportional to the alveolar ventilation rate. Net uptake of a gas from the chamber air into the alveolar space is given by
Qv is the alveolar ventilation rate--70% of total ventilation rate (15,16); Achamber and Aa are the amounts of gas in the chamber and alveolar air; Vchamber and Va are the volumes of the chamber and alveolar space. Although inspired gases must traverse the respiratory epithelium to enter the blood, this epithelium constitutes a small fraction of the lung compartment volume. Also, gases may penetrate the epithelium by a paracellular route. Therefore, material was represented as directly transferred between the alveolar air and the lung blood at a rate given by
where Pair is the blood:air partition coefficient. Transport of the chemical into the total lung tissue was treated in the same manner as for other organs.
It has been observed that the measured rate of clearance of a number of gases is only 60% of that predicted by a simple inhalation model that assumes instantaneous equilibration of the chemical between air and circulating blood (17). This effect was ascribed to a transient adsorption of the chemical on the walls of the airway (17). In accordance with this hypothesis, several modelers (5-7,10) have reduced the measured alveolar ventilation rate by 40% in their inhalation models. However, there is no direct evidence for adsorption on the airway, and it is unlikely that the same 40% reduction in gas delivery should be obtained for substances of widely varying lipophilicity. It was previously shown that distribution of the blood among arterial, venous, and capillary spaces and inclusion of extrahepatic metabolism permitted fitting observed rates of gas uptake by adjusting the extraction ratio but without altering the measured values for the ventilation rate or the biochemical kinetic constants (14). In vitro studies (see below) have demonstrated extrahepatic metabolism of butadiene and its epoxide derivatives in mice and rats. The extraction ratio only affects the rate of approach to equilibrium distribution between blood and tissues, whereas altering the ventilation rate affects the rate of delivery of chemical to tissues. Therefore, the measured alveolar ventilation rates were not reduced for use in the privileged access model.
Average reported values for the alveolar ventilation rates of 20.2 and 20.0 L/hr/kg0.7 in mice and rats, respectively, were used. The literature averages of 15.3 and 14.7 L/hr/kg0.7 in mice and rats, respectively, were used for the cardiac output. Body weights were fixed at the measured values for the experiments being simulated--25-29 g for mice and 215-360 g for rats. The values used in this model for other physiological parameters are given in Table 1.
Metabolism of butadiene and its epoxide derivatives has been observed in extracts from liver, lung, and kidney (5,18-22). Therefore, the full metabolic pathway was replicated in each of these organs with the exception that oxidation of epoxybutene to diepoxybutane was omitted in the lung because it could not be observed experimentally. The activities of the metabolizing enzymes have been reported as normalized by the amount of protein recovered. The microsomal enzyme activities were multiplied by 30, 9, or 9 mg microsomal protein/g tissue for liver (23), lung (24), and kidney (25), respectively. The same values were used for both mice and rats. The glutathione S-transferase activities were multiplied by 82.8 or 108 mg cytosolic protein/g tissue for mice and rats, respectively (18).
Cytochrome P450-catalyzed oxidation of butadiene and epoxybutene and epoxide hydrolase-catalyzed hydrolysis of both epoxybutene and diepoxybutane were described by Michaelis-Menten kinetics. It is possible that alternative substrates compete for access to the metabolizing enzymes, but there are no kinetic data for metabolism of two of these substrates simultaneously. Filser et al. (26) suggested that competition between substrates would lead to a compensatory rise in their blood (hence tissue) concentrations. This increase is necessary to maintain a rate of metabolic clearance equal to the rate of delivery or production of the substrate. In addition, butadiene and epoxybutene are metabolized by several isozymes (19,20,27), and it is unknown if the contribution of each isozyme to the overall metabolic rate is changed by competition among alternative substrates. Because of these unknown factors, substrate competition was not included in the enzymatic rate equations in this model.
Although terminal olefins often act as suicidal inhibitors of P450, conjugated olefins such as isoprene (2-methyl-1,3-butadiene) do not exhibit that activity (28). There is no evidence for inactivation of P450 by epoxybutene. When suicidal inactivation of P450 by epoxybutene was included in the model, there remained insufficient enzymatic activity to reproduce the observed uptake of this chemical from closed chambers (29,30). But-3-ene-1,2-diol (the product of epoxybutene hydrolysis) does inactivate P450 (31), but it is a minor product of butadiene metabolism (32) and is unlikely to have a significant effect at the low concentrations achieved in tissues. Therefore, suicidal inhibition was not included in this model.
Conjugation of each epoxide with glutathione (GSH) was represented by an ordered bi-bi mechanism with glutathione binding first--it exhibits ping-pong kinetics only at GSH concentrations below 0.2 mM (33). The apparent Km (i.e., concentration giving the half-maximal reaction rate) reported for the epoxide substrate was corrected for the required prior activation by glutathione binding by solving the ordered bi-bi rate equation (see "Appendix") for the actual Km that would yield a half-maximal reaction rate.
where S0.5 is the epoxide substrate concentration at half-maximal enzymatic rate and glutathione is the GSH concentration in the assay.
GSH production is limited by the activity of 
-glutamyl synthetase, which was modeled with Michaelis-Menten kinetics (cysteine Km = 0.35 mM) and noncompetitive inhibition (Ki = 2.3 mM) by the GSH product (34). Averages of many literature values for tissue cysteine concentrations were 0.193 (liver), 0.171 (lung), and 0.28 mM (kidney) in mice and 0.195 (liver), 0.127 (lung), and 0.326 mM (kidney) for rats. The maximal rates of GSH synthesis used were 102 (liver), 26.4 (lung), and 75.6 (kidney) nmol/hr/mg cytosolic protein for mice (35) and 396 (liver), 50 (lung), and 6,080 (kidney) nmol/hr/mg cytosolic protein, the averages of several literature values, for rats.
Measured values of the partition coefficients of butadiene and epoxybutene vary substantially. For example, Johanson and Filser (5) reported tissue:air partition coefficients for butadiene and epoxybutene in rats of 3.03 ± 0.27 and 83.4 ± 17.3, respectively, for blood and 0.73 ± 0.35 and 59.9 ± 2.0 respectively for muscle. Medinsky et al. (6) reported values of 1.49 ± 0.06 and 50.4 ± 2.5, respectively, for blood and 1.47 ± 0.18 and 19.8 ± 6.0, respectively, for muscle in rats. These quantities correspond to a 4-fold difference between the two laboratories in the muscle:blood partition coefficient for butadiene and a 2-fold difference for epoxybutene. The average of literature values for the partition coefficients (5,6) were used in this model (Table 2), but the effects of varying these quantities were determined empirically (see below). The partition coefficients for diepoxybutane (Table 2) were taken from Sweeny et al. (7). The same partition coefficient values were used for mice and rats.
The products formed from oxidation of butadiene and of epoxybutene were represented (Figure 1) as bound to the endoplasmic reticulum membrane. Dissociation from the membrane was modeled with first-order kinetics. The rate constants for release of the epoxides into the bulk cytosol were adjustable parameters in the model.
Both bound and cytosolic pools of epoxybutene and diepoxybutane were considered to be substrates for epoxide hydrolase. Because of the proximity of the epoxide hydrolase and P450 proteins, the apparent Km of epoxide hydrolase for its membrane-bound substrate should be smaller than its value for cytosolic substrate. The ratio of the substrate Km values
was an adjustable parameter in the model and reflects the increased availability of membrane-bound epoxide. The same ratio was used for epoxybutene and diepoxybutane.
Parameters in the model fall into three classes--well-established physiological and biochemical parameters, chemical-specific parameters with conflicting measured values, and parameters whose values were not measured. Where conflicting values had been reported for a particular parameter, the behavior of the model was systematically investigated. The value of the parameter in question was fixed at each reported value in turn, and the unmeasured parameters in the model were estimated to yield the best fit to measured gas uptake data. As the activities of epoxide hydrolase and glutathione S-transferase were not measured in the kidney, those quantities also were adjustable parameters in the model.
The models for mice and rats were encoded as chemical equations in the SCoP (Simulation Control Program; Simulation Resources Inc., Redlands, CA, USA) language (36) that were translated into C language code for the corresponding differential equations by the SCoP software (37). The forms of these equations are given in the "Appendix." The unmeasured parameters were optimized with SCoPfit, using iteratively reweighted least squares, to obtain the best fit to uptake of butadiene and epoxybutene from closed chambers by mice and rats and steady-state concentrations of epoxybutene and diepoxybutane in the blood of mice and rats exposed nose only to butadiene.
In the course of estimating the free parameters for the mouse, it was observed that the optimal values for the renal activities of epoxide hydrolase and glutathione
S-transferase toward diepoxybutane were such that the ratio of the effective first-order rate constant (
Vmax/
Km) for the two epoxide substrates in the kidney was the about the same as was observed in the liver. Therefore, these two
Vmax values were calculated to maintain this ratio (Table 3) instead of being optimized. This behavior was not detected in the rat model, however. It was also observed that the optimized values of the adjustable parameters varied greatly, depending on which of the conflicting experimental values for chemical-specific parameters were used. The measured biochemical parameter values that resulted in the best fit were used in this model (Table 3). The final optimal parameter values are listed in Table 4.
|
Figure 1. Scheme for proposed metabolic pathway for butadiene. Abbreviations: BD, butadiene; EB, epoxybutene; DEB, diepoxybutane; EH, epoxide hydrolase; GST, glutathione S-transferase.
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The simulated uptake of butadiene and epoxybutene from closed chambers by mice and rats is compared to experimental data in Figures 2 and 3, respectively. The fits to blood concentrations of butadiene, epoxybutene, and diepoxybutane following nose-only exposures are given in Table 5. A wide range of values for each extraction ratio could fit the data with similar accuracy. Judicious selection among measured biochemical parameter values and optimization of free parameters could compensate for differences in the extraction ratios. The values selected were those that produced the best fit to the data. On the other hand, the fits to the data were sensitive to the maximal velocities of the metabolizing enzymes (see below).
Most of the computed steady-state blood concentrations agree with their observed values. The computed blood butadiene concentration for the rat is consistently about double that measured, similar to the values obtained with other (7,10) models, and the computed blood diepoxybutane concentration at the lowest dose is underpredicted for the mouse. No choice among the published values of the metabolic parameters was found that would correct the defects in the fit, but the fit could be improved by altering the biochemical kinetic constants from their experimentally determined values. The fit could also be improved if larger values of the tissue:blood partition coefficients for butadiene were used in the model, but this would exacerbate the over-prediction of blood butadiene. As the measured partition coefficients varied by as much as a factor of 4 among different laboratories, use of the average values may not reflect their true values.
Figure 2. Clearance of butadiene from closed 6.4 l dessicators. (A) Eight mice, observed values from Kreiling et al. (49). Initial chamber concentrations (ppm), standard error of estimates (ppm): 
: 5,000, 391; 
: 2,000, 94; 
: 1,000, 28; 
: 500, 17.3; 
: 250, 4.41; 
: 100, 3.14. (B) Two rats, observed values from Bolt et al. (50). Initial chamber concentrations (ppm), standard error of estimates (ppm): : 4,000, 230; : 2,300, 60.6; : 1,100, 24.6; : 400, 9.9; 
: 200, 9.8; 
: 90, 6.1.
Figure 3. Clearance of epoxybutene from closed 6.4 l dessicators. (A) Eight mice, observed values from Kreiling et al. (29). Initial chamber concentrations (ppm), standard error of estimates (ppm): : 2,000, 144; : 850, 26.7; : 450, 23.2; : 200, 25.2; : 90, 23.2. (B) One rat, observed values from Filser and Bolt (30). Initial chamber concentrations (ppm), standard error of estimates (ppm): : 3,100, 78.0; : 1,500, 23.2; : 700, 14.1; : 200, 9.8.
The existing butadiene models are structurally different, are based on different mechanistic hypotheses, and employ different simplifying assumptions. Experiments that could test the critical assumptions in each model are necessary to discriminate among these models. For example, is metabolism of butadiene or its epoxide derivatives truly negligible in tissues other than the liver (
10)? Is competition among reactants for access to the metabolizing enzymes an important factor in butadiene disposition? Is the rate of microsomal production of butenediol from butadiene faster than that from exogenous epoxybutene at the same concentration as achieved by supplying butadiene as suggested by the present model?
Computed blood butadiene concentrations are somewhat higher than observed for the rat, and some computed blood epoxide concentrations are lower than observed. These concentration effects would be exacerbated if the model included competition among alternative substrates for the metabolizing enzymes. The blood concentration of a chemical depends on its concentration in metabolizing tissues, which in turn is affected largely by the apparent Km. This suggests that either the measurements of the apparent Km values already account for such competition or the enzyme is far from saturation and the reaction rate is effectively first order. Simultaneous time courses of the circulating metabolic intermediates could help resolve this question.
The reliability of this or any PBPK model of butadiene disposition in rodents depends on the quality of the data used in the construction of the model. The partition coefficients for butadiene and epoxybutene measured in different laboratories vary by up to 4-fold. These uncertainties may be the origin of the systematic deviation from data of computed blood butadiene concentrations in the rat. This modeling effort revealed that the choices among measured values of the partition coefficients and the metabolic parameters have strong effects on the values of the free parameters obtained by fitting gas uptake data.
Corresponding biochemical constants measured in vitro by different laboratories range from close agreement, e.g., P450 oxidation of butadiene in mouse liver (5,18), to a factor of 26 difference, e.g., GSH conjugation of epoxybutene in rat lung (18,19). Even measurements made in the same laboratory are sometimes not reproducible, e.g., cytochrome P450 oxidation of epoxybutene (18,20). Verification of any model of butadiene disposition must await accurate and reproducible measurements of the biochemical kinetics of the metabolizing enzymes in various tissues.
Adjusting parameters for which there are inconsistent measurements (see above) to their various experimental values indicated that the model's predictions most strongly depend on the maximal velocities of the metabolizing enzymes. The partition coefficients, especially for blood:air, are the next most important. The choice among the experimental values (or taking an average) has a major effect on the ability of the model to reproduce the data. The extraction ratios are less important. Comparable fits to the data can be achieved with a range of values, confirming the notion that these parameters affect only the rate of equilibration of chemical between blood and tissues and not its rate of delivery to tissues.
The model was modified by assuming that membrane-bound epoxybutene has privileged access to the P450 that oxidizes that chemical to diepoxybutane. No improvement in the fit to the data was observed with this modification. The corresponding ratio of Km values of bound:free substrate had an optimal value of 1.0, indicating the lack of privileged access for the second oxidation step.
Removal of the P450-epoxide hydrolase privileged access mechanism from the model resulted in an order of magnitude overprediction of circulating epoxides regardless of the choice of values for the parameters with conflicting measurements. Blood epoxide levels are determined by their cytosolic concentrations and the partition coefficients. The cytosolic concentrations of epoxides in metabolizing tissues are set by the apparent Km values of enzymes that utilize cytosolic substrates (e.g., epoxide hydrolase and glutathione S-transferase). Only a mechanism than prevents epoxide produced in situ from mixing with the cytosolic pool can duplicate the observed circulating concentrations. This property of the model supports the hypothesized mechanism for epoxide metabolism.
The parameter values R and krelease are not well determined. Experiments with the model revealed that a wide range of values could reproduce the data. Changes in one parameter could compensate for changes in the other. The information content of the experimental data is insufficient to specify a unique set of parameter values. This lack of identifiability is a common problem in PBPK modeling, and no statistical approach can provide reliable parameter estimates. Chamber uptake and steady-state epoxide data are inadequate for the estimation of mechanistic parameters. Simultaneous time courses of multiple responses to butadiene exposure are needed to resolve these outstanding issues.
This section describes the forms of the rate equations for the disposition of chemicals in various compartments (amount is denoted by A). Uptake from ambient air and exhalation are restricted to butadiene and epoxybutene. Tissue cysteine values were obtained from the literature. The basal rate of GSH utilization was calculated to maintain a steady state in the absence of epoxides. Compartment volumes are denoted by Vtissue, and organ blood flow rates are denoted by Qtissue. Alveolar ventilation is Qv. First-pass extraction ratios are e. Metabolic rate equations are repeated in liver, lung, and kidney, except that diepoxybutane production is not included for the lung. Maximal velocities are denoted by Venzyme, and the net reaction rate is denoted by venzyme.
Exchange between blood and air
Transport between blood and tissues
Butadiene and epoxide
Metabolic intermediates
Glutathione metabolism
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Last Updated: October 9, 2000
