* Experimental Toxicology Division and
Reproductive Toxicology Division, National Health and Environmental Effects Research Laboratory, Office of Research and Development, U.S. Environmental Protection Agency, Research Triangle Park, North Carolina 27711
Received May 23, 2000; accepted September 13, 2000
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ABSTRACT |
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Key Words: biologically based dose-response model; 5-fluorouracil (5-FU); deoxyribonucleotide triphosphate (dNTP) pool perturbation; fetal weight deficit; thymidylate synthetase (TS) inhibition.
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INTRODUCTION |
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The mechanism by which 5-FU inhibits TS has been well-characterized (see, for example, Parker and Cheng, 1990). 5-FU is metabolized through a series of steps to 5-fluorodeoxyuridine monophosphate (FdUMP) (Fig. 1), which competes with deoxyuridine monophosphate (dUMP) for TS. TS catalyzes the transformation of dUMP to deoxythymidine monophosphate (dTMP), transferring a methyl group from 5,10-methylene tetrahydrofolate to the 5-carbon of the uracil ring. When FdUMP replaces dUMP in the reaction, a stable ternary complex of TS-FdUMP-folate is produced that has a half-life measured in hours, and depends in part on the concentration of folate (Parker and Cheng, 1990
). The immediate effect of this reaction is to reduce the rate of deoxythymidine monophosphate (dTMP) production. A consequence of TS inhibition is the elevation of dUMP levels, which partially compensates for the TS inhibition, since dUMP and FdUMP compete for binding to TS (Parker and Cheng, 1990
). The regulation of dNTP pool levels involves complex feedbacks among DNA precursors and the enzymes involved in their biosynthesis, including ribonucleotide reductase, TS, and deoxycytidine deaminase (Fig. 2
) (Jackson, 1978
, 1989
; Moore and Hurlbert, 1966
). Ribonucleotide reductase is required for the conversion of ribonucleotides to deoxyribonucleotides, which includes the metabolism of FUDP to 5-fluorodeoxyuridine diphosphate (FdUDP) (Fig. 1
), a precursor to 5-fluorodeoxyuridine monophosphate (FdUMP). Presumably, FUDP competes with UDP in that process. Finally, as thymidine triphosphate (dTTP) levels drop, thymidine salvage pathways may be up-regulated to at least partially restore dTTP pools for DNA synthesis.
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However, these models have made at least two critical assumptions that may not be realistic: first, that the substrate concentrations that we can measure in aggregates of cells correspond to the concentrations in the vicinity of the enzyme molecules, and second, that the kinetics of the enzymes in vivo correspond to those measured in vitro. Although 5-FU itself probably distributes readily throughout various tissue compartments, the intermediate metabolites such as FdUMP may be confined to the intracellular dNTP pools. Hence, FdUMP concentrations should vary across aggregates of cells to the extent that enzymes responsible for the metabolism of 5-FU to FdUMP vary across those cells. Furthermore, it has been hypothesized that some of the enzymes involved in DNA synthesis (including ribonucleotide reductase and TS, among others) form an enzyme complex whose kinetic properties differ from those derived from studies of isolated enzyme components (Fell, 1997; Ovadi, 1991
). Thus, even models in which the fundamental components are substrate concentrations and enzyme kinetics may be inadequate for extrapolation across species without a lot of extra work to adjust, empirically, parameters for the new species. Having to make such empirical adjustments for a large number of parameters in these models would rapidly erode one's confidence in their predictive value.
The alternative explored here for modeling the effect of 5-FU on nucleotide pools is to target a model at higher than the molecular level of biological organization. The model developed in this paper is based on analyzing the causal pathway that links exposure to adverse outcomes into submodels, which are arranged serially so that the outputs of each model but the last form the inputs of the next in the chain. Each submodel, while empirical, is based on underlying biological relationships among the measured variables. The initial submodels in the cascade describe the pharmacokinetics of 5-FU and the active metabolite FdUMP. The next two submodels are based on perturbations or deviations from normal levels of activity (defined here as the Euclidean distance from control levels, where all values are measured on a logarithmic scale). That is, we relate FdUMP concentration to the related perturbation of TS activity, followed by a model that relates perturbations of TS activity to perturbations of the pool of DNA precursors.
The objectives of this research are to:
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MODEL DEVELOPMENT |
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Pharmacokinetics of 5-FU
The pharmacokinetic model used here was based on a 2-compartment physiological model by Collins et al. (1980) of serum levels of 5-FU in humans after intravenous dosing. We adapted this model to pregnant rats by adjusting the tissue volumes and blood flows to values appropriate to the day of gestation being modeled, using the data and relationships described by O'Flaherty et al. (1992). To this basic model, we added a compartment for fetuses, and a compartment with first-order kinetics to allow for subcutaneous dosing.
The maternal portion of this model has a metabolically active (blood, liver, kidney, lung, uterus, and mammary gland) and metabolically inactive (all other maternal tissues) compartment. Maternal clearance of 5-FU, both first-order and saturable (modeled as Michaelis-Menten kinetics) occurs only from the metabolically active compartment: the metabolically inactive compartment serves as a reservoir, from which 5-FU is repartitioned to the blood. Fetal concentrations depend upon flow from the metabolically active maternal compartment, and upon saturable clearance with the same parameters as that for the adult. Figure 3 outlines the proposed pharmacokinetic model. This is encoded in the following set of equations:
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Va refers to the volume of compartment a and Ca refers to the concentration of 5-FU in compartment a, where a may be one of s, c, m, or f, and s refers to the subcutaneous injection region, c to the metabolically inactive maternal compartment, m to the metabolically active maternal compartment, and f to the fetal compartment. a represents the derivative of Ca with respect to time. Qm refers to the blood flow between the maternal compartments, and Qf to the blood flow from the metabolically active maternal compartment to the fetal compartment. Kcs isthe first-order rate constant for the diffusion between the subcutaneous injection region and the metabolically inactive compartment; K4 is the first order rate constant for renal clearance; and A and B are related to conventional Michaelis-Menten kinetic parameters for metabolic transformation of 5-FU by
. Finally, P1 and P2 are empirically determined transfer efficiencies into and out of the fetal compartment, required to account for the slow elimination of 5-FU from fetal tissues in GD 19 data (Boike et al., 1989a,b; see below). The parameters for metabolism of 5-FU are presumed to be the same in maternal and fetal tissues. This is consistent with the GD 19 data from Boike et al. (1989b). In addition, it has been estimated that around 95% of 5-FU is catabolized by dihydropyrimidine dehydrogenase (Naguib et al., 1985
). Although there does not seem to be any information about the activity of this enzyme in fetuses, rats between 3 weeks and > 60 weeks have been found to have constant levels of activity of this enzyme (Tateishi, et al. 1997
). Note that, among other simplifications, the model represents metabolism of 5-FU as a single Michaelis-Menten expression, although in reality the metabolism of 5-FU is carried out by multiple pathways, only some of which end up producing FdUMP.
Parameter estimation.
Tissue volumes and blood flows specific to the gestational stage are based upon formulas given by O'Flaherty et al. (1992). Other parameters were estimated in 2 steps. First, parameters for first-order clearance and for transfer efficiency, both into and out of the fetal compartment (P1 and P2), were estimated using data from Boike et al. (1989a,b) who evaluated the pharmacokinetics of 5-FU in pregnant rats and their fetuses after a single intravenous dose on GD 19. Next, parameters for metabolism were estimated using data reported by Lau et al. (2001) on maternal serum 5-FU concentrations, after a single dose administered on GD 14. In this study, multiple observations of serum concentration were available for each individual animal. Serum concentrations differed significantly among dams given the same dose and observed at the same time, so mixed-effects models (statistical models that allow some model parameters to vary among subjects) were used to account for inter-individual variation (Davidian and Giltinan, 1995).
The submodels are all described as systems of ordinary differential equations (ODEs). To get model predictions, the system was solved numerically using the ODE solver CVODE (Cohen and Hindmarsh, September 1994, available through the Netlib repository at the University of Tennessee at Knoxville/Oak Ridge National Laboratories, http://www.netlib.org). Parameters for the pharmacokinetic model were estimated using nonlinear mixed-effects models (function "nlme" in Splus Version 3.4, Mathsoft, Seattle, Washington, run on a Sun Sparcstation 20 under version 2.3 of the Solaris operating system). The values and the origins for all the parameters of the pharmacokinetic submodel are in Table 1.
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Lau et al. (2001) showed that maternal serum 5-FU concentrations peaked within about 15 min of dosing, and essentially became undetectable within 1 h of drug administration. Boike et al. (1989b) showed that on GD 19, fetal 5-FU levels peaked just minutes after the maternal peak. Yet, in GD-14 data (Lau et al., 2001), TS inhibition in embryos did not peak until 3 to 5 h after drug administration. If we can assume that, similar to the findings of Boike et al. (1989b) on GD 19, and as predicted by the pharmacokinetic model described above, the GD-14 embryonic levels of 5-FU closely parallel those of maternal serum, then some mechanism is required to account for the delay in time between the peak 5-FU concentration and the peak TS inhibition. The metabolism of 5-FU to FdUMP requires a minimum of 4 steps (Fig. 1
), and it is plausible that this could account for the time delay.
In this model, the metabolism to FdUMP has been simplified to 2 steps: saturable metabolism from 5-FU to an intermediate compound and subsequent linear first-order metabolism of the intermediate to FdUMP. Clearance of FdUMP from fetal tissues (by all routes) is also assumed to be linear. The resulting equations are:
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Here t1/2,I is the half-life for the metabolism of the intermediate compound to FdUMP, and t1/2,FdUMP is the half-life for the clearance of FdUMP from fetal tissues. Note that the main function of this submodel is to introduce a time delay between the 5-FU concentration and TS inhibition, and the form of this submodel does not depend critically upon the delay being due to metabolism.
Inhibition of TS by FdUMP is a fairly complicated process. The initial ternary complex of TS-folate-FdUMP is gradually converted to a covalently bound complex, so that the inhibition has both competitive and non-competitive characteristics (Danenberg, 1977). The affinity of the TS-folate complex for FdUMP is substantially higher when higher glutamate forms of folate participate in the complex. Furthermore, the half-life of the covalently bound complex depends in part by the concentration of folate (Parker and Cheng, 1990
). Finally, TS activity varies through the cell cycle, apparently increasing during S-phase (Nagarajan and Johnson, 1989
). The model for the inhibition of TS used here supposes that, at the level of detail considered, the main effect of FdUMP is to reduce the availability of TS enzyme protein. A simple way to model the relationship between TS activity and embryonic FdUMP concentration under this assumption is:
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where V0 represents the "normal" level of TS activity (TS inhibition is estimated as the log of the ratio of the enzyme activity in a treated group to that in the control group, so V0 need not be estimated.), KI is the concentration of FdUMP that would result in half the normal level of TS activity, and g is an additional parameter to help adjust the shape of the relationship.
Parameter estimation.
The 4 unknown parameters in Equations 2 and 3, g, KI, t1/2,FdUMP, and t1/2,I, cannot all be estimated uniquely, because neither the concentration of the intermediate compound nor that of FdUMP have been directly measured. Fixing one parameter (in this case, t1/2,I) to an arbitrary value (120 min) allowed the other 3 to be estimated. Any value for t1/2,I yields estimates for the other 3 parameters, giving the same model predictions; however, the arbitrariness means that the parameter values cannot be compared to estimates derived from other sources. The remaining 3 parameters were estimated by fitting a model consisting of the pharmacokinetic model described by Equation 1
with parameters estimated from the pharmacokinetic data described above, combined with the submodel described by Equations 2 and 3
to data on TS kinetics described in Lau et al. (2001). To accommodate the experimental design for the data, the model was expressed as the sum of a term that gave the mean log TS activity level in the control group for a specific block and time and a term contributed by the model (i.e., equations 1, 2, and 3
) for the specific dose and time after dosing. This eliminates the term V0 from equation 3
. The log transformation of the parameters in the submodel was estimated to ensure that the kinetic-parameters estimates remained positive, and to improve the distributional properties of the estimates.
Parameters were estimated using nonlinear least squares (function "ms" in SPlus Version 3.4). Confidence intervals for the parameters are based on an estimate of the covariance matrix for the estimated parameters computed from the inverse of the matrix of second derivatives of the sum of squared deviations with respect to the parameters, a standard approach for nonlinear least square estimation (Davidian and Giltinan, 1995). Point-wise confidence limits for the predicted value from the model were computed by simulation. Five thousand samples from a multivariate normal distribution given by the mean and covariance matrix for the estimated parameters were drawn, and predicted values were computed for a finely spaced set of times and all doses considered in this study using the model and each of the simulated parameter sets. Confidence intervals at each time point were estimated from quantiles of the resulting distribution of predicted values.
Parameter estimates are shown in Table 2 with their approximate 95% confidence intervals. The resulting model predictions are shown in Figure 4
. Although the data set used for these parameter estimates stops at 12 h, the model predictions for later time points are qualitatively consistent with data from a longer duration study (Table 1
in Lau et al., 2001). The model captures the basic shape of the TS inhibition curves well, with perhaps a tendency to under-predict the inhibition at later time points in the 10-mg/kg dose group, and to under-predict the early inhibition in the highest-dose group.
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The first scenario assumes that developmental toxicity is related to dTTP as alteration of this deoxyribonucleotide is the direct and immediate product of TS inhibition. The second scenario assumes that deficits of any dNTP would translate into interruption of DNA synthesis; hence, both dTTP and dGTP are included in the model. The third scenario simply assumes that any alteration of the dNTP pool would impede the normal process of cell replication; thus, deviation of all 4 species of DNA precursors are taken into consideration in the model. The submodel developed here is intended to apply to any of these measures (represented by Nuc in the equations below). The measure of TS inhibition at time t and administered dose dose used here is:
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First, for small perturbations of TS activity from normal, Nc increases proportionally to the TS perturbation, but the effect of the deviation of TS activity from normal on N
c becomes proportionately less for larger changes of TS activity. Mathematically, this is expressed as
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Finally, inhibition of TS increases the concentration of dUMP and results in the up regulation of salvage pathways. Both activities tend to reduce Nuc. In this model, the variable "U" represents these tendencies. U increases with a rate proportional to the level of inhibition of TS, while the rate of increase for a given level of TS inhibition declines with increasing values of U. U adds a negative component to the rate of increase of the deoxyribonucleotide pool perturbation, which is proportionately smaller for greater values of TS and U and larger for greater levels of Nuc. This is expressed quantitatively as
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These three terms, and the consideration about the rate of change of U give the following system to describe the change of deoxyribonucleotide pool perturbations:
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Parameter estimation.
Parameters for the deoxyribonucleotide pool-perturbation model were estimated in 3 stages. First, mean contrasts (on a log scale) of dNTP between control and various 5-FU dose groups were computed using the method for repeated measures to allow for covariances among dNTP levels in the same sample ("lme" in SPlus) described in Lau et al. (2001). Next, the 3 dNTP perturbation functions were computed at each time point and dose. Approximate covariances were computed for each measure, using the method of statistical differentials (see, e.g., Elandt-Johnson and Johnson 1980, pp 6972). Finally, parameters for the dNTP perturbation model (composed of Equations 1, 2, and 3 using previously estimated parameters, and Equation 4
) were estimated by generalized least squares, and weighted by the inverse of the covariance matrix of the computed perturbation measures calculated in the previous step. Confidence intervals for predicted values in this model were estimated by generating at least 100 simulated data sets based on the original dNTP data, and recomputing each step in the process just described using each simulated data set. Table 3
shows estimates for parameters of the model in Equation 4
using the data presented in (Lau et al., 2001, Table 2
and Figure 5
).
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Relationship between Measures of Nucleotide Pool Perturbation and Endpoints of Developmental Toxicity
Although a complete data set for the entire mechanistic pathway of 5-FU toxicity is not yet available, one can begin to evaluate the associations between various intervening steps and the overt toxic outcomes, despite remaining data gaps. One gross measure of normal growth and development is fetal weight, and 5-FU produced fetal weight deficits at term, in a dose-dependent manner (Shuey et al., 1994). The relationships between fetal weight deficit and the 3 scenarios of dNTP alteration (derived from the mathematical model) are illustrated in Figure 6
. Within the dose range examined, fetal weight deficit increases smoothly with increasing dNTP pool perturbation. This model predicts a smooth (non-threshold) relationship between administered dose and dNTP pool perturbation. Furthermore, generally dNTP pool sizes are so small that they can support replication of only about 1% of their genome (Kornberg and Baker, 1992
). Thus, even quite small perturbations in the dNTP pool regulation are likely to be transduced into effects at the cellular level. If a threshold for the effect of 5-FU on fetal weight is to be found, it will appear either as the result of a more sophisticated model of the consequences for dNTP pool regulation of TS inhibition than that presented here, or as the presence of an active mechanism that compensates for the cellular effects that result from dNTP pool perturbations, and which is essentially saturated at the lowest dose studied here.. Thus, reassessing the fetal weight data in light of mechanistic information (instead of administered doses of 5-FU) reveals additional properties of this data set for risk assessment consideration.
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DISCUSSION |
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Ideally, the current model would be extended to link nucleotide pool perturbation to events downstream, ultimately to predictions of incidence of malformations or weight deficits. However, the details of the mechanism(s) linking nucleotide pool perturbation and the prevalence of adverse effects are unknown. There are several interesting possibilities, all beginning with perturbation of DNA synthesis due to an imbalance of nucleotide pools. The next step could be a slowing down of the cell cycle, or perhaps DNA damage and subsequent triggering of apoptosis. Perhaps the most straightforward consequence of these events to consider is that they might critically reduce a population of cells required for normal development. However, there are other possibilities. For example, a temporary block of cell cycling in early S-phase would result in a population of partially synchronized cells. This partial synchronization could interfere with cellcell signaling or perhaps other processes critical to development. For now, we have contented ourselves with examining the dose-response relationships between different metrics of dNTP pool perturbation and developmental effects.
The relationships between measures of dNTP pool perturbation and adverse outcomes can tell us something about the processes involved, and suggest where further investigation might help to clarify the dose response for this chemical. In the end, this model of dNTP pool perturbation predicts that the magnitude of pool imbalance, regardless of how it is defined, increases with administered dose. Quite a different conclusion was possible. With the right parameter values, the submodel that relates TS inhibition to dNTP pool perturbation can yield a threshold-like response, allowing dNTP pool perturbations only when TS inhibition exceeds a critical level. Had such a threshold been determined, and had it been low enough to be consistent with the dose-response for fetal weight alteration, it would be a natural candidate for a regulatory point of departure, instead of the usual NOAEL or benchmark dose derived from the more usual developmental endpoints. On the other hand, a sufficiently high threshold would be inconsistent with the dose-response for fetal weight, and would suggest that fetal weight and malformations proceed from fundamentally different processes. However, given the current model, the data we collected were not consistent with a threshold in the relationship between administered dose and dNTP pool perturbation. Thus, to the extent the general relationships among the important moieties, described in the text preceding Equations 4, hold true for smaller perturbations of TS activity, there can be no threshold in the relationship between administered 5-FU dose and nucleotide pool perturbation. If it were important to establish the existence of a threshold for the effect of 5-FU on fetal weight, it would therefore most profitably be sought in the processes that link nucleotide pool perturbation to fetal weight deficits.
All these conclusions are contingent on the validity of our model, which can only be assessed by the degree to which it passes tests in which it is called upon to predict the results of experiments that were not used in its construction. For the current model this testing might include explorations of how different dosing schedules and days, and the use of different TS inhibitors, affects measures of nucleotide pool perturbations. The current version of this model is intended to describe the relationship between a single bolus dose of 5-FU on the 14th day of gestation and subsequent perturbation of nucleotide pools. Therefore, to generalize the model for different exposures of 5-FU, the pharmacokinetic submodel needs to be modified to allow for different tissue volumes and blood flows, and for the changes of maternal and fetal tissues that occur during development. This work is currently ongoing in our laboratory. However, since the remaining submodels were not derived explicitly assuming a particular stage in development, as long as 5-FU is used as the TS inhibitor, and the test species and strain remains the same, the parameterization derived here should be applicable to other dosing schedules and times and could be used for testing the model.
A critical assumption of this model is that nucleotide pool perturbation can be quantified somewhat "generically," that is, for the purpose of predicting adverse outcomes; the details of how the individual nucleotides change after exposure is not as important as an overall measure of perturbation. This strong assumption requires testing, perhaps by quantifying the relationship between measures of nucleotide pool perturbation and adverse effects on GD-14 for other agents that are known to perturb nucleotide pools. Work of this nature has begun in our laboratories for a folate analog that is also a TS inhibitor.
The approach to modeling exemplified here requires that a large number of parameters be estimated. As it happened, at least one parameter in the model t1/2,I was not identifiable or estimable using the dose-response designs. Additional experiments, for example, measuring the half-life of the metabolic process that leads from 5-FU to FdUMP would be required to estimate these unknown parameters. Thus, the remaining parameter values depend to varying degrees on the value assumed for the unknown parameter. The remaining parameters were estimated in a nested sequence of models: pharmacokinetics, pharmacokinetics + metabolism and TS inhibition, pharmacokinetics + metabolism and TS inhibition + dNTP pool perturbation. In each model in the sequence, parameters that had already been estimated in the previous model were fixed at their estimated values, and new parameters were estimated assuming the other values were correct. The alternative approach, that of estimating all parameters simultaneously, would have been substantially more difficult because of the variety of experimental designs involved, and because the final endpoints involved derived variables. Nevertheless, a consequence of this approach to parameter estimation is that the quantification of the uncertainty of the parameter estimates in the latter 2 models is likely to be understated, though the quantification of the uncertainty in the predictions is probably relatively unaffected. Although it is particularly apparent in this model, because the parameters treated as fixed were themselves estimated from data in this study, this problem is not unique. It is shared by most physiological models that use standard estimates of tissue volumes and blood flows, and base estimates of other model parameters on fitting model predictions to data sets.
We began the 5-FU modeling project to develop a better idea of how to construct mechanistic models for developmental endpoints to facilitate health effects, dose-response assessment. 5-FU was selected as the model compound because of its large database and relatively well understood dynamics. Clearly, the resulting model presented here, while still incomplete, already has given us some insights into the biology of the processes being modeled, as well as on how such models might be used in human health, dose-response assessment. We entered the project with the idea that we would construct a model that would predict the incidence of developmental abnormalities subsequent to 5-FU exposure, at least in rats, for a particular well-defined exposure. We believed that a generalization of this process is how such models would be used in dose-response assessment. This was probably optimistic. What the modeling process undoubtedly can do for dose-response assessment is to focus attention toward the processes that affect the shapes of dose-response curves, as well as to identify gaps in our knowledge of toxicological processes. Too often, we were able to find a qualitative statement in the literature about relations among variables, unaccompanied by any useful quantification. Yet, as the bulk of our knowledge of interactions grows, from gene networks to the proteins they control and their interactions to determine the behavior of cells and tissues, it will be the quantitative relationships among components that will usually determine the final behavior of biological systems. Only when we can understand and develop models for the quantitative relationships in biological systems, shall we be able to make dramatic improvements in our ability to predict the consequences for human health of exposures to toxic agents.
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ACKNOWLEDGMENTS |
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NOTES |
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1 To whom correspondence should be addressed at Mail Drop 74, U.S. Environmental Protection Agency, Research Triangle Park, NC 27711. Fax: (919) 541-5394. E-mail: setzer.woodrow{at}epa.gov.
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