Prediction of Chemical Biotransfer of Organic Chemicals from Cattle

Biotransfer factors (BTFs) represent the ratio of the concentration of a chemical found in animal tissues such as beef or milk to the animal's daily i...
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Environ. Sci. Technol. 1996, 30, 984-989

Prediction of Chemical Biotransfer of Organic Chemicals from Cattle Diet into Beef and Milk Using the Molecular Connectivity Index DEANNA L. DOWDY, THOMAS E. MCKONE,* AND DENNIS P. H. HSIEH Risk Sciences Program, Department of Environmental Toxicology, University of California, Davis, Davis, California 95616

Biotransfer factors (BTFs) represent the ratio of the concentration of a chemical found in animal tissues such as beef or milk to the animal’s daily intake of that chemical. Using currently available citations for BTFs in meat and milk, the use of molecular connectivity indices (MCIs) as a quantitative structureactivity relationship (QSAR) for predicting the BTFs for organic chemicals is evaluated. Based on a statistical evaluation of correlation, residual error, and cross validation, this evaluation reveals that the MCI provides both higher reliability and a fast and cost-effective method for predicting the potential biotransfer of a chemical from environmental media into food. When compared to the use of Kow as a predictor of BTFs, the analysis here indicates that MCI can substantially increase the reliability with which BTFs can be estimated.

Introduction Chemical contaminants of human health significance are released into the environment from both natural and anthropogenic sources. For many of these environmental contaminants, the food chain is a potential source of human exposure. For lipophilic contaminants (such as dioxins, furans, polychlorinated biphenyls, organic pesticides) and for metals (such as lead and mercury), exposures through the food chain have been demonstrated to be a dominant contributor to the total dose received by nonoccupationally exposed populations (1). However, the uncertainty in estimating potential dose through food chain exposure is much larger than the uncertainty associated with other exposure pathways (2-5). Because of the importance of food chain exposure and as a result of the low precision associated with the estimation of such exposures, there is a continuing need to develop methods that can both identify with high reliability the types of chemicals capable of biotransfer from environmental media into food chains and more accurately quantify the extent of such a biotransfer. * Corresponding author fax: (510) 642-5815; e-mail address: [email protected].

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The biotransfer factor (BTF) is defined as the ratio of a tissue concentration to the daily intake. The numerator of this ratio is the concentration of chemical found in animal tissues (such as meat) or fluids (such as milk), and the denominator is the quantity of an animal's daily intake of the chemical. The experimental measurement of BTF values requires long-term animal testing. Ideally, a feeding study to measure biotransfer from a dietary exposure into fat requires multiple groups of animals receiving different long-term daily doses of the chemical of interest. It is necessary to monitor each animal’s body weight and food intake throughout the exposure. A long-term study should last over a period of several months to ensure that a steady state has been attained. At the end of the long-term exposure, the organs of the animal should be homogenized, and the chemical of interest should be extracted from the homogenate and quantified. Because this type of experiment is both expensive and time-consuming, it is desirable to estimate biotransfer values using physical-chemical properties that can serve as predictors of a chemical’s partitioning and reactivity. It is important to keep in mind that although it is advantageous to be able to estimate biotransfer, estimation methods rarely have the reliability or credibility of experimental measurements. The octanol/water partition coefficient (Kow) represents the tendency of a chemical to partition between octanol and water and has been considered to be a good indicator of biotransfer potential because partitioning into the octanol phase is assumed to mimic partitioning into fat (6). Travis and Arms (7) have shown that there is a correlation between the base 10 logarithm of the BTF and the base 10 logarithm of the octanol/water partition coefficient (log Kow). Based on this observed correlation, Travis and Arms developed a geometric least squares fit for estimation of log BTF from log Kow (7). A number of issues limit the reliability of Kow as a BTF predictor. Measured Kow values have been observed to vary by as much as several orders of magnitude for the same compound depending upon the method used to obtain them (8). This high degree of uncertainty associated with measured values of Kow presents reliability problems when Kow is used for predicting BTFs. Travis and Arms (7) argued that using the geometric least squares fit can address this uncertainty problem. However, McKone (4) has shown that the estimated error is not reduced significantly by using the geometric least squares fit. In addition, Kow values are often obtained without measurement using estimation methods that can also have low precision. If Kow values are used to obtain biotransfer information, then any uncertainty inherent to Kow can be carried in the biotransfer estimates. Since a precise, reliable quantification of biotransfer is crucial to exposure and risk assessment, there is a need to relate biotransfer to a parameter quantified easily and with relatively high precision. It would be particularly advantageous if this parameter could be easy and inexpensive to quantify and applicable to a wide variety of chemicals. In light of these observations, we pose here the premise that a simple structure-based index, the molecular connectivity index (MCI), offers greater utility to predict BTFs than a does a measure of lipid/water solubility. Statistical comparison of the model reliability associated with both

0013-936X/96/0930-0984$12.00/0

 1996 American Chemical Society

Kow and MCI as predictors of biotransfer is used below to demonstrate that the MCI can be a more reliable predictor of biotransfer than Kow.

Methods Calculation of Biotransfer Factors (BTFs). A literature search was carried out to obtain measured biotransfer values. From these data, BTFs were calculated as

BTF )

Ct (mg/kg) Io (mg/d)

(1)

where Ct is the concentration of chemical (in mg/kg) measured in the tissue of interest (meat or milk in this case) and Io represents the daily intake of the chemical (in mg/d). Mean values of the log BTF and standard errors of log BTF were calculated for each chemical. For those chemicals with only one or two BTF values available, the standard error was assigned a default value. This value was equal to the average standard deviation for the remaining BTF set. For biotransfer data to be included in the calculation set, it was required that the cited experiment be a long-term cattle feeding study. From each individual study, the data representing the longest exposure time to the cattle were selected and considered the most representative of biotransfer under steady-state conditions. For those meat studies that reported chemical concentrations both in fat and meat, concentrations in fat were selected and considered more representative of the biotransfer potential. Measured concentrations of organics in meat fat or milk fat were converted to the concentrations in fresh meat or whole milk by assuming, where necessary, that the fat content of meat and milk is 25% and 4%, respectively. Daily intakes were computed, where necessary, by assuming an average dry feed ingestion rate of 16 kg/d for lactating cows and 8 kg/d for non-lactating cattle (7). Biotransfer data are inherently variable, partially because of the difficulties involved in obtaining biological data and partially because of the wide variety of test methods used to obtain the data. Because of the general lack of data in this area, no judgments were made regarding the quality of available data. Thus, any readily available measured values within the stated criteria were used. These default values for ingestion rates as well the assumption that biotransfer factors do not need to be normalized by the weight of the animal were the method of BTF calculation used by Travis and Arms (7). Their assumptions were adopted so that the two methods would be consistent in the area of data calculation, lending credibility to the statistical comparison. Calculation of Molecular Connectivity Indices (MCIs). To adequately assess the risk associated with exposure to a chemical, it is necessary to know its basic physicalchemical properties. These data are not always readily available, in particular for the many organic chemicals that are newly formulated every year. Quantitative structureactivity relationship (QSAR) methods are a class of property estimation methods that categorize molecules based on structural characteristics, which are then correlated to property values (9). The resulting statistical model is used to predict properties for structurally similar chemicals for which the property of interest has not been measured. QSAR methods are useful for setting research priorities, designing experiments, and assessing associated risks. Chemical properties commonly estimated by QSAR methods include

solubility in water, octanol/water partition coefficient, adsorption coefficient for soil, bioconcentration in aquatic organisms, and many other factors relevant to exposure and risk assessments. The QSAR method utilized in the present study is based on the Randic branching index (10), which was developed to address how the relative degree of branching among a series of alkanes influences certain physical properties. From the Randic branching index, Kier and Hall (9) developed a simple index based on molecular structure. To use this index, the structural formula is written out as a hydrogen-suppressed molecular skeleton in which all atoms are equivalent. Each atom is then designated by a δ value. In this particular case, the δ value is equal to the number of adjacent or formally bonded atoms. Each bond is designated by the δ values of the two atoms that form the bond. Using the Randic algorithm, values for the bond fragments are then computed. The index (χ) is the sum of bond values over the entire molecule: 1

χ)

∑(δ × δ )

-0.5

i

(2)

j

where i and j represent adjacent atoms (10) and the prefix of 1 (1χ) indicates an index that utilizes one-bond dissections of the molecule. Previous studies have shown this index to be correlated with size, branching, molar volume, and surface area (9). Molecular connectivity indexes have been used to predict bioconcentration factors (BCFs) in fish (11, 12), indicating that they may be viable as predictors of BTFs for terrestrial animals. The study reported here found that the normal path first-order molecular connectivity index (henceforth called MCI) could reliably predict biotransfer for nonpolar compounds without any need for correction factors. However, extension of this predictive model to estimate biotransfer for polar compounds requires an adjustment of the index with correction factors to account for polar group effects. Because the chemical set used in this study was not large enough to allow a valid statistical determination of these factors independently from the nonpolar regression, existing polar correction factors from the literature were applied to our data set. The existing factors used in this study are taken from a set developed by Meylan et al. (14), who used the MCI as a predictor of soil sorption coefficients (Koc) for a set of 189 nonpolar organics. Meylan et al. (14) also fit 205 polar chemicals to their nonpolar regression by developing a set of polar fragment correction factors. These factors were applied to the MCI of each polar chemical as an adjustment factor for the estimation of BTFs. Our data set was analyzed both with and without these correction factors. This analysis confirmed the need to apply such factors to take into account the presence of certain polar groups and their strong influence on the dependence of BTF on MCI. When polar correction factors taken from the Meylan et al. study (14) are applied to our regression, good correlations between MCI and both meat and milk BTFs result. Table 1, which is an abbreviated list of the Meylan et al. correction factors, lists all correction factors used in this study set. It is of interest that a set of polar correction factors that was developed for a partitioning relationship in soil proved to be applicable here. In order to understand how this could come about, it should be noted that observed variations in biotransfer among chemicals likely result

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TABLE 1

Polar Fragments and Polarity Correction Factors Used in This Study no.

fragment

factor

1 2 3 4 5 6 7

With N and C nitrile/cyanide nitrogen to noncyclic aliphatic carbon nitrogen to cycloalkane nitrogen to nonfused aromatic ring pyridine ring with no other fragments aromatic ring with 2 N triazine ring

-0.722 -0.124 -0.822 -0.777 -0.700 -0.965 -0.752

8

nitro

-0.632

9 10

With N, C, O urea (N-CO-N) acetamide, aliphatic carbon (N-CO-C)

-0.922 -0.811

11 12 13 14 15 16

ether, aromatic ether, aliphatic ester aliphatic alcohol carboxylic acid carbonyl

-0.643 -1.264 -1.309 -1.519 -1.751 -1.200

d

17

With P and O organophosphorus [P)O], aliphatic

-1.698

a, g

18 19

With P and S organophosphorus [P)S], aliphatic organophosphorus [P)S], aromatic

-1.263 -2.330

a h

With N and O

With C and O

With C and S 20

a b

log Koc ) a′(1χ) + a′′

a, b c

With S and O

log BTF ) a′(1χ) + a′′

a f

χpc ) (1χ) + a′′′

mainly from (a) variations in uptake and distribution and (b) variations in metabolism rates. Since the variation in Kow used by Travis and Arms (7) did not fully capture the observed variation of BTF values, it is likely that metabolism variations are an important contribution to BTF variations. The MCI index used here has two components: (a) the nonpolar MCI regression term and (b) the polar correction factors term. Uptake and distribution are highly influenced by relative solubility in lipid and water phases. Since Koc depends to a large extent on partitioning between water and organic phases, the fact that the Koc correction factors work for BTF indicates that the nonpolar (uncorrected) MCI regression is likely accounting for variations in metabolism and that the polar correction derived from Koc is needed to account for uptake/distribution variations. The Meylan et al. (14) equation for the regression of MCI as a predictor of soil sorption coefficients is of the form f

(3)

where Koc represents the soil sorption coefficient, 1χ

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(4)

f

(5)

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∑(P N)] + b f

(6)

where m is the general slope factor for the polar-corrected MCI term in the brackets and a′′′ is a constant that must be estimated in the regression analysis. The term 1χpc is defined to represent the polar-corrected normal path firstorder MCI: 1

Counted only once per structure, regardless of the number of occurrences. b Any nitrogen attached by a double bond is not counted, carbonyl and thiocarbonyl are not counted as carbons. c Counted only when no other fragments in this list are present. d Either one or both carbons aromatic: if both carbons aromatic, cannot be cyclic. e This fragment was used if more than one ester was present. If one ester was present, the ester was regarded as if it were an ether and a carbonyl group. f Not included in regression derivation; estimated from other carbonyl fragments; counted only when no other carbonyl-containing fragments are present. g This is the only fragment counted, even if other fragments are present. h The value of this factor is the average deviation of this set of compounds from our curve, all other polar correction factors were developed by Meylan et al. (14).

∑(P N) + 0.62

∑(P N) + b

log BTF ) m[(1χ) + a′′′

e

a

log Koc ) 0.53(1χ) +

f

with allowance for different values of a′, a′′, and b. Since the present study makes use of the Meylan et al. polar correction factors, Pf, the generalized regression for both meat and milk is of the form

-0.995

sulfone

∑(P N) + b

If we assume that the dependence of BTF on 1χ and on the Pf parameters is analogous to Koc, then we can substitute BTF for Koc in eq 4, which then becomes

-1.100

thiocarbonyl

21

note

represents the normal path first-order MCI, and ∑(PfN) represents the summation of the products of all applicable correction factors multiplied by the number of times (N) that a fragment occurs in the structure. The factor 0.53 is the slope and 0.62 is the intercept. Generalizing this relationship gives

∑(P N) f

(7)

In order to relate MCI and BTF, the regression relationship in eq 6 was optimized both to maximize the correlation coefficient, r2, and to minimize the residual error or standard error of the estimator (SEE). We first optimized based on r2 to determine that the best value for a′′′ is equal to 1.89 for both the beef and milk BTF regressions. We then optimized using a linear least squares fit to find appropriate values of the slope (m) and intercept (b) of the regressions. Once the correlations were obtained, 1χpc and Kow were compared as predictors of chemical biotransfer. The correlation coefficient (r2) represents the fraction of the overall variance in log BTF accounted for by the regression model. The SEE represents the average residual error between the measured log BTF and the log BTF that is estimated using the regression (15). SEE is calculated as

x

n

∑(log BTF

SEE of log BTF )

msd

- log BTFest)2

i)1

(n - 2)

(8)

where n is the number of chemical samples used in the estimation protocol, and (log BTFmsd - log BTFest) is the difference between the logarithms of measured and estimated value of BTF. Smaller standard errors indicate higher model reliability. The statistical parameters r2 and SEE were calculated for the MCI-based data set and also for the data of Travis and Arms (7).

Results and Discussion Regression Equations. The calibration set of chemicals selected for demonstrating the correlation between BTF and 1χpc and the pertinent data are given in Table 2. For Aroclor 1254 and toxaphene, which as complex mixtures have no unique structure, the MCI is based on the most

TABLE 2

Data for Meat and Milk BTF Regressionsa chemical

1χ pc

Aldrin Aroclor 1254 benzoylprop-ethyl chlordane chloropropylate chlorpyrifos clopidol coumaphos 2,4-D DDD DDE DDT dicamba 3,6-dichloropicolinic acid dieldrin endosulfan endrin famphur fenitrothion fenoprop fenthion fenvalerate flamprop flamprop-isopropyl flamprop-methyl heptachlor heptachlor epoxide kerb lindane malathion MCPA mirex oxadiazon PCNB phosphamidon 2,4,5-T TCDD toxaphene trichlopyr 3,5,6-trichloropyridinol

8.3 8.4 3.1 8.1 5.7 4.0 3.7 1.4 1.6 8.6 8.6 8.9 1.6 1.8 8.8 6.8 8.7 2.2 2.0 2.4 3.1 7.3 4.4 3.4 2.6 7.7 8.2 4.8 5.5 1.6 1.6 9.5 4.2 5.2 2.6 2.0 8.5 7.2 2.0 3.3

factors

12, 4, 16 16, 12 5, 19 5 19, 16, 12 15, 11

11, 15 15, 5 21 19, 20 8, 19 11, 15 19 12, 11, 16, 1 16, 4, 15 16, 4, 12 16, 4, 12 16, 2 13, 18 11, 15 11, 16, 12 8 17, 16, 2 11, 15 11, 15 5

no. of std mean log beef error log BTF(beef) values BTF(beef)

no. of std mean log milk error log BTF(milk) values BTF(milk)

beef refs

-1.076 -1.298 -4.718 -1.830

6 9 3 12

0.102 0.040 0.054 0.167

16, 17, 18 20 21 17, 18, 22

-3.100 -4.576 -5.415 -4.998 -1.939 -1.301 -1.490 -5.283 -5.244 -1.165 -3.145 -1.846 -4.083

15 2 2 3 1 1 27 1 2 28 1 16 1

0.051 0.327 0.211 0.138 0.240 0.240 0.029 0.240 0.040 0.074 0.240 0.059 0.240

24, 25 24 27 28 30 30 17, 18, 32-35 38 24 17, 18, 34, 39-41 42 17, 43, 44 27

-4.255 -4.626 -3.098

3 1 5

0.062 0.240 0.099

28 27 48

-4.129

4

0.075

21

-1.892 -0.822 -3.102 -1.820 -5.039

14 8 6 6 12

0.064 0.049 0.126 0.122 0.086

17, 41, 50 17, 53 56 17 58

-1.281 -3.231 -2.740 -4.806 -4.695 -0.961 -1.886 -5.551 -4.071

2 3 4 1 5 1 14 1 3

0.253 0.022 0.037 0.240 0.200 0.240 0.030 0.240 0.151

59 61 62 63 24, 28 24 17, 18 24 24

milk refs

-1.743 -1.915 -4.602 -3.339 -3.058 -4.681

7 9 1 3 1 1

0.046 0.010 0.244 0.298 0.244 0.244

16,19 20 21 22 23 26

-5.325 -5.432 -2.519 -2.353 -2.494 -4.681

1 2 3 6 27 1

0.244 0.073 0.035 0.191 0.048 0.244

27 29 30 30, 31 19, 30, 31, 33-37 38

-1.924

21

0.048

19, 31, 34, 39-41

-2.678 -5.122 -5.133 -5.085 -4.175 -3.218 -4.903 -4.426 -4.727 -2.846 -1.650 -3.778 -2.666 -5.778 -4.966 -1.749 -3.683 -3.804

25 1 3 3 4 5 1 1 1 14 12 1 5 8 4 3 1 2

0.091 0.244 0.095 0.124 0.087 0.098 0.244 0.244 0.244 0.129 0.143 0.244 0.062 0.052 0.115 0.317 0.244 0.077

31, 43-45 27 46 29 46, 47 48, 49 21 21 21 19, 41, 51, 52 31, 53, 54,55 56 31, 57 58 29 59, 60 61 62

-4.705 -2.097 -3.196

13 17 16

0.056 0.038 0.025

29 64 65

a χ represents the polar corrected normal path first-order MCI which is equal to [(1χ) + 1.89∑(P N)]. Number of values available for beef or milk pc f indicates the total number of BTFs available for each particular chemical.

abundant chemical structure present in the mixture. BTF values for beef and milk are plotted as a function of 1χpc in Figures 1 and 2. In these figures, each plotted log BTF value represents the average of all log BTF values available for a particular chemical, and the standard error of the log BTF data set for that chemical is shown by a vertical error bar. Table 3 provides a comparison of r2 and SEE for the MCI-based and Kow-based methods of predicting biotransfer. The polar-corrected MCI predicts the biotransfer of chemicals into beef (Figure 1) with the regression equation of

log BTF(beef) ) 0.525(1χpc) - 5.904

(9)

with an r2 of 0.90 and an SEE of 0.49, which corresponds to a geometric error in BTF(beef) of 100.49 or 3.1. In comparison, Kow used by Travis and Arms (7) to predict the biotransfer of organic chemicals into beef has the regression equation

log BTF ) 0.834(log Kow) - 6.887

(10)

with an r2 of 0.65 and an SEE of 0.92, which corresponds to a geometric error in BTF(beef) of 100.92 or 8.3. The polar-corrected MCI predicts the biotransfer of chemicals into milk (Figure 2) with the regression equation of

log BTF ) 0.421(1χpc) - 5.879

(11)

with an r2 of 0.89 and an SEE of 0.43, which corresponds to a geometic error in BTF(milk) of 100.43 or 2.7. In contrast, the regression of biotransfer to milk based on Kow is

log BTF ) 0.731(log Kow) - 6.786

(12)

with an r2 of 0.54 and an SEE of 0.92, which corresponds to a geometric error in BTF(milk) of 100.92 or 8.3. It was found that for both milk and meat the polarcorrected MCI method yielded both a higher r2 and a lower standard error of the estimator than the Kow method. The r2 results indicate that the MCI model accounts for more of the variance in biotransfer data than the Kow method. The SEE results indicate that with the MCI regression,

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TABLE 3

Comparison of 1χpc and Kow as Predictors of Biotransfer to Beef and Milk statistical parameter

this paper

Travis and Arms (7)

N r2 SEEa

Beef 35 0.90 3.1

36 0.65 8.3

N r2 SEEa

Milk 34 0.89 2.7

28 0.54 8.3

a The numbers listed in this table for SEE are based on the SEE of the log BTF but are transformed to reflect the geometric deviation in the estimate of BTF according to the transformation 10[SEE(log BTF)].

1χ

pc

FIGURE 1. Log beef biotransfer factors correlated with the polarcorrected MCI, 1χpc. The polar-corrected MCI, 1χpc, predicts the biotransfer of organic chemicals into beef with a regression equation of log BTF ) 0.525(1χpc) - 5.904 and an r2 of 0.903. 1χpc represents the polar-corrected normal path first-order MCI and is equal to [(1χ) + 1.89∑(PfN)].

of a simulated validation set through cross validation. Cross validation creates a number of modified observations from the existing data set in such away that each observation is taken away once and only once. One model is developed for each reduced data set, and the response values (log BTF) of the deleted observations are predicted from the model. The squared differences between predicted and “actual” values are summed into the Predictive REsidual Sum of Squares (PRESS). According to Wold (66), for regression models such as those posed here, PRESS is calculated as n

PRESS )

∑[(y - yˆ ) /(1 - h ) ] 2

i

i

2

ii

(13)

i)1

where yi and yˆi are respectively the observed and predicted outcomes, and hii is the diagonal elements of the “hat” matrix, which is calculated as

H ) X(X′X)-1X′

1χ

pc

FIGURE 2. Log milk biotransfer factors correlated with the polarcorrected MCI, 1χpc. The polar-corrected MCI, 1χpc, predicts the biotransfer of organic chemicals into milk with a regression equation of log BTF ) 0.421(1χpc) - 5.879 and an r2 of 0.887. 1χpc represents the polar corrected normal path first-order MCI and is equal to [(1χ) + 1.89∑(PfN)].

because of much lower residual error, there is higher model reliability than with the Kow regression. Model Validation. As has been noted by Wold (66), having an r2 close to 1 and a small SEE are necessary but not sufficient conditions to demonstrate the validity of a QSAR model, since these parameters do not necessarily demonstrate the absence of chance correlations. Ideally, there is a need for a large validation set of chemicals. However, the paucity of data on chemical biotransfer prevents this option at this time. Wold (66) points out that, in the absence of a real validation set, one can make use

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(14)

where X is a two-column and n-row matrix in which the first column is filled with 1’s corresponding to the intercept (b) and the second column is the n predictors, which is the corresponding values of 1χpc. X′ refers to the transpose of X. Wold (66) notes that when PRESS is smaller than the SSY, the sum of the squares of the responses (the log BTFs in our case), then the model predicts better than chance. For the log BTF(beef) and log BTF(milk) considered here, the ratios of PRESS to SSY for the 1χpc-based models are 0.01 and 0.02, respectively. These are both well below the 0.1 ratio, which, according to Wold (66), is the indication of an “excellent model” in terms of cross validation. Discussion. This study demonstrates that there is a strong correlation between the polar-corrected MCI of a chemical and its biotransfer to beef and milk. Due to the paucity of available data, both this study and that of Travis and Arms (7) are constrained to small sets of chemicals. Nevertheless, the results of the statistical analysis show that the 1χpc method gives a much better estimation of dietary biotransfer than does the Kow method and that the MCI is a more accurate predictor of cattle dietary biotransfer than is Kow. When MCI is used in place of Kow as an estimator of potential chemical biotransfer from environmental media into animal products, the estimation of BTF can be more accurate, faster, easier to carry out, and more cost-effective. For those chemicals without biotransfer values reported in the literature, this method can be used to estimate these values. The use of MCI instead of Kow as an input parameter

in exposure assessment models can improve the reliability of the model outputs.

Acknowledgments Funding was provided in part by the State of California Department of Toxic Substances Control (DTSC) through Contract Agreement 92-T0105. This work was also performed under the auspices of the U.S. Department of Energy (DOE) through Lawrence Livermore National Laboratory under Contract W-7405-Eng-48. However, any views or policies stated or implied by this paper are those of the authors and not necessarily those of the DTSC or the DOE. We would like to also thank the three reviewers for their very instructive and useful comments.

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Received for review July 3, 1995. Revised manuscript received October 18, 1995. Accepted October 18, 1995.X ES950398C

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Abstract published in Advance ACS Abstracts, January 1, 1996.

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