Evaluation of Isotopic Enrichment Factors for the Biodegradation of

ELIZABETH A. EDWARDS, ⊥. AND. BARBARA SHERWOOD LOLLAR* , |. Stable Isotope Laboratory, University of Toronto,. 22 Russell Street, Toronto Ontario, ...
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Environ. Sci. Technol. 2006, 40, 3886-3892

Evaluation of Isotopic Enrichment Factors for the Biodegradation of Chlorinated Ethenes Using a Parameter Estimation Model: Toward an Improved Quantification of Biodegradation PENNY L. MORRILL,† BRENT E. SLEEP,‡ GREGORY F. SLATER,§ ELIZABETH A. EDWARDS,⊥ AND B A R B A R A S H E R W O O D L O L L A R * ,| Stable Isotope Laboratory, University of Toronto, 22 Russell Street, Toronto Ontario, Canada, M5S 3B1

A model was developed to predict the concentrations of chlorinated ethenes and ethene during sequential reductive dechlorination of tetrachloroethene (PCE) from stable carbon isotope values using Rayleigh model principles and specified isotopic enrichment factors for each step of dechlorination. The model was tested using three separate datasets of concentration and isotope values measured during three experiments involving the degradation of PCE to vinyl chloride (VC), trichloroethene (TCE) to ethene, and cis1,2-dichloroethene (cDCE) to ethene. The model was then coupled to a parameter estimation method to estimate values for the isotopic enrichment factors of TCE, cDCE, and VC when they are intermediates in the dechlorination to ethene. The enrichment factors estimated for TCE and cDCE when they were intermediates in biodegradation experiments were close to or within the published range of enrichment factors determined from experiments where TCE or cDCE were the initial substrates. In contrast, the enrichment factors determined by parameter estimation for experiments in which VC was an intermediate in biodegradation experiments were consistently more negative (by ∼10‰) than the most negative published enrichment factor determined from experiments where VC was the initial substrate. This finding suggests that the range of enrichment factors for VC dechlorination may not be as narrow as previously suggested (-21.5‰ to -26.6‰) and that fractionation during VC dechlorination when VC is an intermediate compound may be significantly larger than when VC is the initial substrate. These findings have important implications both for the current practice of extrapolating laboratory-derived isotopic * Corresponding author phone: (416)978-0770; fax: (416)978-3938; e-mail: [email protected]. † Geophysical Laboratory, Carnegie Institution of Washington, Washington, DC 20015. ‡ Department of Civil Engineering, University of Toronto, Toronto, Ontario, Canada, M5S 1A4. § School of Geography and Geology, McMaster University, Hamilton, Ontario, Canada, L8S 4K1. ⊥ Department of Chemical Engineering and Applied Chemistry, University of Toronto, Toronto Ontario, Canada. | Stable Isotope Laboratory, University of Toronto, 22 Russell Street, Toronto Ontario, Canada, M5S 3B1. 3886

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enrichment factors to quantify biodegradation of chlorinated ethenes in the field and for understanding the details of enzymatic reductive dechlorination.

Introduction The chlorinated solvents tetrachloroethene (PCE) and trichloroethene (TCE) are two of the most frequently detected groundwater contaminants at hazardous waste sites in North America (1). PCE and TCE are potential carcinogens and classified as priority pollutants by the United States Environmental Protection Agency (2). Under anaerobic conditions, the primary mechanism for the degradation of PCE and TCE in the environment is reductive dechlorination (3). Reductive dechlorination involves the sequential replacement of chlorine atoms with hydrogen atoms, resulting in the transformation of PCE to TCE, TCE to cis-1,2-dichloroethene (cDCE), cDCE to vinyl chloride (VC), and VC to nontoxic ethene. The reductively dechlorinating microorganisms that mediate these reactions use chlorinated ethenes as electron acceptors and a range of substrates (e.g., lactate, methanol, H2) as electron donors. To date, microorganisms that can reduce chlorinated ethenes completely to nontoxic ethene are restricted to the Dehalococcoides (DHC) group of bacteria (4). KB-1, a mixed microbial culture, contains DHC strains and has demonstrated in laboratory batch experiments (5, 6) and field studies (7) the ability to completely dechlorinate PCE to ethene. Current methods used to assess and monitor biodegradation at chlorinated ethene contaminated sites include biotreability studies, detection of specific DHC 16SrRNA genes, and more recently nucleic acid probe detection of specific dehalogenase genes. Modeling the fate and transport of chlorinated ethenes, including the effects of biodegradation, dissolution, sorption, and volatilization, is another line of evidence required for regulatory approval of monitored natural attenuation (8). However, differentiating between degradative and nondegradative processes is difficult using concentration data alone. A method that could uncouple concentration changes due to degradative and nondegradative processes (i.e., to estimate changes in concentration due to degradation exclusively) would improve modeling of the fate and transport of chlorinated ethenes. Carbon compound specific isotope analysis (CSIA) is a method that has the potential to differentiate between chlorinated ethene degradation and other nondegradative processes of mass loss. Laboratory studies have shown large shifts in the stable carbon isotope values of PCE, TCE, cDCE, and VC during reductive dechlorination of these compounds (9-11). In contrast, nondegradative processes such as sorption, dissolution, and volatilization involve only relatively small isotopic shifts at equilibrium, which in many cases are less than analytical uncertainty (12-16). CSIA measures the ratio of 13C to 12C for an individual compound in a sample. The isotopic ratio is expressed in δ13C notation

δ13C )

(

)

Rsample - 1 × 1000 Rstd

(1)

where Rsample is the 13C/12C ratio in a given compound and Rstd is the 13C/12C ratio of the international standard, V-PDB. The δ13C value is expressed in units of permil (‰). The analytical error associated with stable carbon isotope analysis by CSIA is (0.5‰. This error incorporates both the internal 10.1021/es051513e CCC: $33.50

 2006 American Chemical Society Published on Web 05/19/2006

reproducibility on duplicate measurements and the accuracy of the measurement with respect to international standards (17). A shift in the ratio of heavy to light isotopes is known as isotopic fractionation. During degradation, for instance, 12CCl bonds are broken faster than 13C-Cl bonds due to lower activation energy. For example, during the degradation of PCE, the undegraded substrate will become more enriched in 13C as the reaction progresses. The product, TCE, will initially be more depleted in 13C with respect to the initial isotope value of the substrate PCE due to the preferential incorporation of 12C into the product. Subsequently as TCE is degraded to cDCE, the isotope value of TCE will become more enriched in 13C and the δ13CTCE will become less negative than its initial value, δ13CTCEo. This pattern of isotopic fractionation has been observed in laboratory studies during each of the reductive dechlorination steps of PCE, TCE, cDCE, and VC (9-11). The isotopic fractionation of a substrate during its transformation can be determined using a Rayleigh model (18). According to the Rayleigh model the isotope value of a substrate is given by

R ) Rof(R-1)

(2)

where R is the stable carbon isotope ratio (13C/12C) at a remaining fraction of substrate f, Ro is the initial isotope ratio, and the R is the fractionation factor. Fractionation factors are often converted to enrichment factors () where  ) 1000(R - 1). In this simple form the Rayleigh model can be used to quantify the enrichment factor for the initial dechlorination step (e.g., PCE for the degradation of PCE to TCE or TCE for the degradation of TCE to cDCE) but not for an intermediate dechlorination step where a compound is simultaneously formed and degraded (e.g., the TCE for the degradation of PCE to TCE to cDCE). In laboratory studies, degradation of many organic contaminants, including the chlorinated ethenes, has been shown to fit a Rayleigh model. This means that the enrichment factor remains constant over the course of a reaction and can be calculated using eq 2. Using the Rayleigh equation (eq 2) as well as isotope and concentration data from batch degradation studies using KB-1, Slater et al. (11) determined enrichment factors for each step of PCE biodegradation to ethene by spiking batch cultures with PCE, TCE, cDCE, and VC. These data added to the range of enrichment factors previously published by Bloom et al. (10) for chlorinated ethene reductive dechlorination by KB-1 (see Supporting Information, Table 1) and reported the first enrichment factors for PCE reductive dechlorination. In field studies, the Rayleigh model has been used to estimate the extent of degradation remaining during biodegradation of PCE to TCE and TCE to cDCE (19, 20) as well as estimate first-order biodegradation rate constants for the degradation of cDCE to VC (21). While useful, these applications of the Rayleigh model to estimate the extent of biodegradation and biodegradation parameters are limited to the first reaction in a sequence of reactions such as the partial dechlorination of PCE to TCE. As noted, the Rayleigh model represented in eq 2 cannot strictly estimate the extent of degradation or degradation parameters of an intermediate compound that is simultaneously formed and degraded. Recognizing the need for degradation estimates for intermediate compounds for each step of the sequential reaction of PCE dechlorination to ethene, Hunkeler et al. (9) applied an approximation that uses a point by point calculation of  (22) whereby

product/substrate = δ13Cproduct - δ13Csubstrate

(3)

to estimate enrichment factors from isotope values measured during the reductive dechlorination of PCE to ethene (see Supporting Information, Table 1). For carbon isotope effects, the difference between eq 3 and the full expression for  is small and eq 3 is conventionally used (22). This does not affect the application of this model to carbon isotope effects. Recently, Be´ranger et al. (23) developed a 1-dimensional, analytical, multistep reactive transport model to simulate concentrations and isotope values of PCE and its degradation products during PCE reductive dechlorination based on firstorder kinetics and Rayleigh fractionation. This model was coupled to a global search method with a gradient-based minimization method to estimate degradation rate constants and enrichment factors from a data set consisting of measured concentrations and isotope values of PCE and dechlorination products (23). These concentrations and isotope values were measured during a column study where PCE was dechlorinated by an ethanol enrichment culture. The enrichment factors for PCE and TCE dechlorination determined from this parameter estimation are listed in Table 1 of the Supporting Information (23). These enrichment factors were within the range of other published enrichment factors. While the method developed by Be´ranger et al. (24) is appropriate for modeling concentration values of chlorinated ethenes and determining all of the parameters required for a reactive transport model, the method requires some knowledge of the degradation rate constants and was not designed to model batch systems. In another recent paper Van Breukelen et al. (25) described a multistep isotope fractionation reactive transport model, which similarly requires some knowledge of degradation rate constants, which incorporates isotopic fractionation of both parent compounds and intermediates. This model was applied to determine isotopic and kinetic degradation parameters for a laboratory batch experiment and at a complex field site and test transport scenarios involving degradation, sorption, and mixed sources. The first objective of this study was to use the relationship between stable carbon isotope values and the extent of biodegradation estimated by the Rayleigh equation to develop a model that predicts changes in concentration of parent and daughter products during reductive dechlorination and does not require prior knowledge of degradation rate constants. The model was tested using three separate experimental data sets from Slater et al. (11) which included concentration and isotope values measured during the degradation of PCE to VC, TCE to ethene, and cDCE to ethene. Published enrichment factors determined from the initial dechlorination steps of TCE, cDCE, and VC as well as enrichment factors approximated from a small subset of the data set using eq 3 after Hunkeler et al. (9) were used as model inputs. The second objective of this study was to create an optimization model by coupling the concentration prediction model to a parameter estimation method that uses all of the data in each data set to estimate isotopic enrichment factors for intermediate compounds and compare modeled predictions to these estimated enrichment factors. The third objective was to compare the difference between enrichment factors estimated using the parameter estimation method, enrichment factors approximated using two data points from each of the data sets and eq 3, and published enrichment factors determined from laboratory degradation studies of Bloom et al. (10) and Slater et al. (11). This optimization model is a new tool to estimate isotopic enrichment factors for degradation of intermediate compounds from measured data based on degradation of parent compounds in batch laboratory experiments. While it is designed for evaluation of laboratory experimental data, it nonetheless has important practical applications for the field. Quantification of reductive dechlorination of chlorinated ethenes in the field is currently dependent on extrapolation VOL. 40, NO. 12, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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of laboratory-derived enrichment factors to field data (19, 21, 26, 27). The underlying assumption in these studies is that isotopic enrichment factors determined in experiments where the compounds are present as parent compounds can be extrapolated to systems where the compounds are intermediates. Hence, there is a need for tools to evaluate how applicable that assumption is and how well laboratoryderived enrichment factors extrapolate to the field. The optimization model developed in this study provides a tool for evaluating the extrapolation central to field applications of quantification of biodegradation of chlorinated ethenes using CSIA.

Methodology Model Development. A model was developed to predict concentration values of chlorinated ethenes during reductive dechlorination using the established relationship between stable carbon isotope values and the extent of biodegradation expressed by the Rayleigh model. For simplicity, the following model describes the calculation of PCE, TCE, cDCE, VC, and ETH concentrations during the degradation of PCE to ETH. The model inputs include the measured isotope values for parent and degradation products (δ13C) at each time interval (t), enrichment factors () for each dechlorination step, and the initial concentration of all substrates C0PCE, C0TCE, C0DCE, C0VC, and C0ETH. Using the δ13C input values, the model calculates the isotope ratios for each compound at each time interval (RPCEn, RTCEn, RDCEn, RVCn, and RETHn) by solving for Rsample in eq 1. From the concentration at the beginning and isotope ratio at the beginning of time step n (n ) 0, 1, ...), the model calculates the concentrations of 13Cn and 12Cn for each ethene compound at the end of each time step. For PCE the equation is

RpiTCEn+1 ) RPCE × RPCEn

(11)

and enrichment factors () can be related to fractionation factors (R) by  ) 1000(R - 1). Similarly, using eqs 8 and 10 one can derive an equation for 13XPCE. Next, eqs 6 and 7 can be used to calculate 12CPCEn+1 and 13CPCEn+1 and subsequently Cn+1PCE as their sum. After calculating the PCE concentrations for time step n + 1, the TCE concentrations can be calculated in a similar fashion, but one must account for the simultaneous formation and degradation of TCE. Given 12CTCEn and 13CTCEn calculated from the previous time step or from the initial concentrations and isotopic signatures of TCE if n ) 0, the new concentrations of TCE can be calculated from 12

CTCEn+1 ) 12CTCEn + 12XPCE - 12XTCE

(12)

13

CTCEn+1 ) 13CTCEn + 13XPCE - 13XTCE

(13)

Dividing eq 13 by eq 12 and using eq 8, the following relationship 13 13 XTCE DCEformed RpiDCE ) 12 ) formed 12 DCE XTCE

(14)

gives 13

RTCEn+1 )

CPCEn + RpiTCE 12XPCE - RpiDCE 12XTCE 12

CTCEn + 12XPCE - 12XTCE

(15)

Rearranging gives 12

13

12

RPCEn × CPCEn

n

CPCE )

n

RPCE + 1

CPCEn ) CPCEn - 13CPCEn

XTCE )

(4)

RTCEn+1 - RpiDCE (5)

The concentrations of the PCE isotopic species (12CPCEn+1 and 13CPCEn+1) at the end of time step n + 1 are found from

CPCEn+1 ) 12CPCEn - 12XPCE

(6)

CPCEn+1 ) 13CPCEn - 13XPCE

(7)

12

13

where 12XPCE and 13XPCE are the amounts of 12PCE and 13PCE degraded in the time step n + 1. The instantaneous product ratio (Rpi) for TCE can be written as 13 XPCE TCEformed ) formed 12 TCE XPCE

13

RpiTCEn+1 ) 12

(8)

Dividing eq 7 by eq 6 and using eq 8, one can write

CPCEn+1

13 12

CPCE

n+1

13

) RPCEn+1 )

CPCEn - RpiTCE12XPCE 12

CPCEn - 12XPCE

RTCEn+1(12CTCEn + 12XPCE) - 13CPCEn - RpiTCE 12XPCE

(9)

(16)

Using eqs 14 and 16, one can also calculate 13XTCE, and eqs 12 and 13 can be used to calculate 12CTCEn+1 and 13CTCEn+1 and subsequently Cn+1TCE. Similar equations can be derived to calculate CDCEn+1, CVCn+1, and CETHn+1. These equations are applied for each of the time steps at which isotopic measurements are made to predict the concentrations as a function of time. This model is appropriate for any set of isotopically fractionating (i.e.,  > 0‰), sequential, linear (nonbranching) reactions during which mass balance is maintained. It was developed specifically to model the linear reductive dechlorination pathway that is a major anaerobic degradation pathway for a key group of priority pollutantss the chlorinated ethenes. Parameter Estimation. The concentration simulation model was coupled to a gradient-based minimization technique known as the Levenberg-Marquardt method (28) to estimate the unknowns, in this case the enrichment factors of the intermediate products, during the reductive dechlorination of PCE to ethene. A least-squares approach was used so that the objective function minimized was nc nt

∑∑(C

mi,j

- Cdi,j)2

(17)

i)1 j)1

Rearranging to solve for 12

XPCE )

12X

PCE

gives

RPCEn+1 12CPCEn - 13CPCEn RPCEn+1 - RpiTCEn+1

(10)

The instantaneous product ratio is related to R as follows (18) 3888

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where the subscript i is the compound (i.e., PCE, TCE, cDCE, VC, or ethene), j is the temporal sampling interval, and C is the modeled (m) and measured (d) concentration data in total micromoles or chlorinate ethenes per bottle. The minimum value for the objective function corresponds to the best estimate of the unknown parameters (also known as the fitness). Since the problem is nonlinear, the search for

TABLE 1. Enrichment Factors for Intermediate Compounds Determined Using a Range of Initial Guesses and the Fitness of Each Simulation (numbers in parentheses refer to citations in the reference list) experiment 3

2

reaction

initial E (11) (‰)

cDCE f ETH cDCE ) -20.4 cDCE f ETH cDCE f ETH cDCE f ETH TCE f ETH TCE ) -13.8 TCE f ETH TCE f ETH TCE f ETH

1

PCE f VC PCE f VC PCE f VC PCE f VC

PCE ) -5.5

initial guess E (‰)

fitnessa (using initial guesses)

ETCE (‰) ( std. error

EcDCE (‰) ( std. error

EVC (‰) ( std. error

fitnessa (using parameter estimations)

415 294 442 359 252

n/a n/a n/a n/a n/a

n/a n/a n/a n/a -15.8 ( 0.9

-36.3 ( 3.4 -36.3 ( 3.4 -36.3 ( 3.4 -36.3 ( 3.4 -36.7 ( 2.2

231 231 231 231 109

237

n/a

-15.8 ( 0.9 -36.7 ( 2.2

109

242

n/a

-15.8 ( 0.9 -36.7 ( 2.2

109

215

n/a

-15.8 ( 0.9 -36.7 ( 2.2

109

VC ) -21.5 (10) VC ) -26.6 (10) VC ) -20.7b VC ) -23.5c cDCE ) -14.1 (10) VC ) -21.5 (10) cDCE ) -20.4 (11) VC ) -26.6 (10) cDCE ) -16.1b VC ) -21.8b cDCE ) -16.7c VC ) -23.5c TCE ) -2.5 (10) cDCE ) -14.1 (10) TCE ) -13.8 (11) cDCE ) -20.4 (11) TCE ) -1.8b cDCE ) -13.6b TCE ) -7.6c cDCE ) -16.7c

57

-1.5 ( 1.1 -10.0 ( 3.9

n/a

55

126

-1.5 ( 1.1 -10.0 ( 3.9

n/a

55

56

-1.5 ( 1.1 -10.0 ( 3.9

n/a

55

81

-1.5 ( 1.1 -10.0 ( 3.9

n/a

55

a Fitness values determine from objective function (eq 17). b Enrichment factors approximated using eq 3 for the intermediate compounds (see text). c Mean value of published enrichment factors for the first dechlorination step of the chlorinated ethene of interest using KB-1 (10, 11). n/a ) not applicable.

a minimum is iterative. This method requires good initial guesses of the unknown parameters (in this case the enrichment factors) or the solution may not converge. The initial guesses for the enrichment factors to be entered into the parameter estimation model for each of the intermediate products formed during the reductive dechlorination of PCE were taken from the range of published values in the literature (see Supporting Information, Table 1) (9-11). Data Sets Modeled. In this study, three separate experimental data sets from Slater et al. (11) were modeled to determine enrichment factors for the intermediate compounds being simultaneously formed and degraded. The experimental data sets included the reductive dechlorination of PCE to VC (experiment 1), TCE to ethene (experiment 2), and cDCE to ethene (experiment 3). Enrichment factors for the initial substrate dechlorination of PCE (PCE), TCE (TCE), and cDCE (cDCE) were previously determined from Rayleigh regressions of the data (11) and are reported in Table 1 in the Supporting Information. The mean total concentrations of ethenes (micromoles per bottle) per experiment were used as the initial concentration for each simulation. Since gas chromatographic (GC) methods measure the total carbon (12C and 13C) while CSIA is precisely measuring the ratio of 13C/12C (global average ≈ 98.9/1.1), the detection limit for GC is approximately 2 orders of magnitude better than for CSIA. In addition, theoretically at a very low fraction of substrate remaining the stable carbon isotope value of that substrate will become exponentially large. Therefore, when the concentration of a chlorinated ethene degraded below the detection limits of CSIA but was still quantifiable by gas chromatography, an enriched isotope value of 50‰ was used as input into the model.

Results To test if the relationship between isotopic fractionation and concentration changes described by the model equations was valid, the uncoupled concentration estimation model was used to predict the concentration values measured by Slater et al. (11) during each reductive dechlorination experiment including PCE to VC (experiment 1), TCE to ethene (experiment 2), and cDCE to ethene (experiment 3). Concentration values were calculated using the isotope measurements, enrichment factors for the first dechlorination

step from Slater et al. (11) (Table 1, column 3), and a variety of selected enrichment factors for the dechlorination of intermediate compounds as input. The selected enrichment factors for the intermediate compounds (initial guesses reported in Table 1, column 4) included the largest and smallest published enrichment factors, enrichment factors determined using eq 3 after Hunkeler et al. (9), and the mean of the published enrichment factors. The fitness (eq 17) of the modeled concentration data to the measured concentration data was determined for each type of enrichment factor used (Table 1, column 5). The comparison of fitness values determined for each type of enrichment factor showed that no one initial guess consistently provided a better fit than the others. Each data set (consisting of concentration and isotope values and an enrichment factor for the first dechlorination step) from each experiment (experiments 1-3) were individually entered into the concentration estimation model coupled to the parameter estimation method to determine enrichment factors for the dechlorination of intermediate compounds (Table 1, columns 6-8). The enrichment factors for intermediate compounds determined using this coupled model produced better fitness values compared to all other methods (compare column 9 with column 5). When simulations using the coupled model were run with the published data from the degradation of cDCE to ethene (experiment 3), only one parameter needed to be estimated, the enrichment factor for the dechlorination of intermediate VC (VC). Four different initial guesses for the VC enrichment factor were used: the smallest and largest published enrichment factors, the enrichment factor calculated using eq 3, as well as the mean of the published enrichment factors (Table 1, column 4). All four simulations with different initial guesses converged on the same enrichment factor for VC, -36.3‰ (Table 1, column 8). This estimated enrichment factor for the dechlorination of the intermediate VC is more negative (by 9.7‰) than the most negative published enrichment factor (-26.6‰ (10)) determined when VC was the initial dechlorination substrate. Similarly, when the TCE data set (experiment 2) was used as input into the coupled model to determine enrichment factors for the dechlorination of the two intermediates cDCE and VC (cDCE and VC, respectively), all four simulations with VOL. 40, NO. 12, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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different sets of initial guesses for the enrichment factors converged on one unique estimate for each compound, -15.8‰ for cDCE and -36.7‰ for VC (Table 1). While the cDCE is within the range of published cDCE enrichment factors determined when cDCE was the initial dechlorination substrate, VC is consistently more negative (in this case by 10.1‰) than the most negative published VC enrichment factor (-26.6‰ (10)) determined when VC was the initial dechlorination substrate. Finally, when the PCE data set (experiment 1) was used as input in the coupled model to determine enrichment factors for the dechlorination of two intermediates TCE and cDCE (TCE and cDCE, respectively), all four simulations with different sets of initial guesses for the enrichment factors converged on one unique estimate for each compound, -1.5‰ for TCE and -10.0‰ for cDCE (Table 1). The estimated enrichment factor for TCE was just outside of the published range determined when TCE was the initial dechlorination substrate (see Supporting Information, Table 1). The estimated enrichment factor for cDCE was also just outside of the published range for the initial dechlorination of cDCE determined when cDCE was the initial dechlorination substrate (see Supporting Information, Table 1).

Discussion Enrichment factors determined by the optimization model for TCE and cDCE as intermediates for experiments 1, 2, and 3 all agreed well with published enrichment factors determined in experiments where the compounds were present as parent compounds (Table 1). Hence, this model suggests that extrapolation of experimentally derived enrichment factors for these compounds to the field is justified. Given that this reflects the current practice in published studies (19, 21, 26, 27), this is an important finding. For experiments 2 and 3, however, the optimization model predicted enrichment factors for VC as an intermediate that are consistently larger (by 9.7‰ and 10.1‰, respectively) compared to those produced in the laboratory where VC is added as a parent compound. Since the results of these two experiments then are particularly important, the measured data, the fit to the optimization model, and validation with respect to the Rayleigh model for the degradation of TCE and cDCE are plotted in Figure 1 and in the Supporting Information. Published Rayleigh enrichment factors have been used to estimate the extent of biodegradation and first-order degradation rate constants during the dechlorination of chlorinated ethenes (19-21, 26). While useful, these applications of the Rayleigh model are limited to the first reaction of the sequence of reactions. Therefore, the Rayleigh model, as presented in eq 2, technically cannot be used to estimate the extent of degradation or degradation parameters for an intermediate compound which is simultaneously formed and degraded. During this study a model was developed to predict the concentrations of chlorinated ethenes and ethene during reductive dechlorination using an established relationship between stable carbon isotope values and the extent of biodegradation. The model was tested using the data set of Slater et al. (11). The model was subsequently coupled to a parameter estimation method to determine enrichment factors for the dechlorination of intermediate compounds that best fit the modeled data to the measured data. The estimated enrichment factors for TCE and cDCE determined in this study were either within, or close to, the published range of enrichment factors determined from Rayleigh regressions of data collected when TCE and cDCE were added as initial substrates to KB-1. The estimated enrichment factors for these two compounds were also similar to the enrichment factors determined by point by point calculations using eq 3. This suggests that on the whole 3890

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FIGURE 1. Comparison of measured concentration values from experiment 2 (solid squares) versus simulated values using the Rayleigh Model (dashed lines) and the optimization model (solid lines). Error bars on measured concentrations represent (5% reproducibility. The optimization model (solid line) provides a good fit to the measured data points. In addition, the standard Rayleigh model curve (eq 2) for the data from Slater et al. (11) is shown in dashed lines for the parent compound. The Rayleigh curve necessarily falls directly on the data points since it is derived from them. The fact that the Rayleigh curves and optimization model curves show good agreement is an additional validation of the optimization model. However, the optimization model is more conservative in its estimate of the extent of biodegradation. This is due to the fact that the Rayleigh model simulations are based on measured experimental data (with inherently imperfect mass balance), while the optimization model assumes complete mass balance. Hence, the Rayleigh curves and optimization curves will always be slightly offset to a degree to which the experimental data does not fit perfect mass balance. In the case of this experimental data, where the total mass balance was slightly greater than 100% over the 600 h of the experiment, the Rayleigh curves are always slightly below the curves produced by the optimization model. In contrast, for any experiment where the mass balance is less than 100% during the experiment, the Rayleigh curve might be slightly higher than the curves produced by the optimization model. the data for enrichment factors published to date are a good representation of the isotopic fractionation of TCE and cDCE during reductive dechlorination by the mixed microbial culture, KB-1. In contrast, the estimated enrichment factors determined for VC as an intermediate of TCE and cDCE degradation by

KB-1 were consistently more negative (by ∼10‰) than the most negative published enrichment factor (-26.6‰ (10)) determined from Rayleigh regressions of data collected when VC was added as the initial substrate to KB-1. The fact that the use of the parameter estimation model on two discrete sets of experimental data yielded similar results strengthens this conclusion. The larger, more negative enrichment factors estimated in this study for VC degradation suggests that the range of enrichment factors for this process is not as narrow as the previously published range (-21.5‰ (10) to -26.6‰ (10)). The difference in previously published VC enrichment factors and those determined in this study could be due to the presence of multiple chloroethene dechlorinating enzymes, each of which may have a different affinity for the VC substrate and therefore may impart a different isotopic fractionation. Currently it is known that at least two different VC reductive dehalogenase genes have been detected in KB1, one by Muller et al. (29) and the other by KrajmalnikBrown et al. (30). Additional putative reductive dehalogenase genes have been detected in KB-1 (31). Regulation of the expression of these genes is currently unknown but may depend on the presence and concentration of specific chlorinated substrates, redox potential, or other environmental conditions. Therefore, is it plausible that a different set of dechlorinating enzymes is induced depending on the conditions when the initial reactants are TCE or cDCE, and VC is present as an intermediate compound, versus when VC is added to the culture directly. Alternatively, it is also possible that the larger, more negative enrichment factors determined in this study for VC when VC was an intermediate compound versus the smaller, less negative published enrichment factors determined when VC was the initial substrate is due to the location of the dechlorinating enzymes with respect to the cell membrane, which is still under investigation for dechlorinated microorganisms (29, 30, 32-36). One way this could occur is if the VC reductively dechlorinating enzyme was located facing the interior rather than the exterior of the cytoplasmic membrane. Any compound degraded by an enzyme located on the interior of the cell membrane would initially have to diffuse through the cell membrane. For example, VC added directly to the culture would have to diffuse through the cell membrane prior to biodegradation. In contrast, VC produced as an intermediate would not undergo this diffusion step since it would be produced intracellularly from more chlorinated compounds that had already entered the cell and undergone biodegradation. The process of diffusion has been shown to reduce the observable isotopic fractionation associated with enzymatic reactions (36, 37). Constraining the conditions under which different fractionation factors are observed is essential to the application of stable carbon isotope values to estimate the extent of biodegradation and other biodegradation parameters such as first-order degradation rate constants. Determining the conditions under which a larger isotopic fractionation will be expressed versus a small isotopic fractionation will allow for more accurate biodegradation estimates and lead to better predictive modeling of chlorinated ethene biodegradation (23-25). This study confirmed that the current range of published enrichment factors is a good representation of the isotopic fractionation of TCE and cDCE during reductive dechlorination by mixed microbial culture, KB-1. In contrast, this study also suggests that there is a difference in the VC enrichment factors depending on whether VC is the initial contaminant or an intermediate compound of reductive dechlorination. This phenomenon may be consortium specific. Recently two completely independent microcosm studies that were modeled estimated enrichment factors for the reductive dechlorination of the intermediate VC. While

Hunkeler et al. (38) derived estimates similar to those of this study (-32.6‰), perhaps supporting the idea that the range of enrichment factors for VC dechlorination may not be as narrow as previously thought, Van Breukelen et al.’s (25) estimates were significantly lower (-14.7‰). Future studies need to focus on experiments to determine if different chlorinated ethenes do indeed induce different reductively dechlorinating enzymes and whether those reductive dechlorinating enzymes impart different isotopic fractionations to the measured VC. Additional experiments will be performed to determine whether the isotopic fractionation measured during reductive dechlorination of VC in whole cell versus cell free extracts of KB-1 reflect differences due to the hypothesized effects of diffusional transport across the cell membrane.

Acknowledgments The authors gratefully acknowledge funding provided by the Natural Science and Engineering Research Council of Canada (NSERC) Strategic Projects Program.

Supporting Information Available Summary of published enrichment factors and comparison of measured concentration values from experiment 2 versus simulated values using the Rayleigh model and the optimization model. This material is available free of charge via the Internet at http://pubs.acs.org.

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Received for review August 1, 2005. Revised manuscript received April 13, 2006. Accepted April 18, 2006. ES051513E