Article pubs.acs.org/est
The Gompertz Function Can Coherently Describe Microbial Mineralization of Growth-Sustaining Pesticides Anders R. Johnsen,*,† Philip J. Binning,‡ Jens Aamand,† Nora Badawi,† and Annette E. Rosenbom† †
Department of Geochemistry, Geological Survey of Denmark and Greenland (GEUS), Øster Voldgade 10, DK-1350 Copenhagen K, Denmark ‡ Department of Environmental Engineering, Technical University of Denmark, DTU Environment, Miljøvej Building 113, DK-2800 Kgs. Lyngby, Denmark S Supporting Information *
ABSTRACT: Mineralization of 14C-labeled tracers is a common way of studying the environmental fate of xenobiotics, but it can be difficult to extract relevant kinetic parameters from such experiments since complex kinetic functions or several kinetic functions may be needed to adequately describe large data sets. In this study, we suggest using a two-parameter, sigmoid Gompertz function for parametrizing mineralization curves. The function was applied to a data set of 252 normalized mineralization curves that represented the potential for degradation of the herbicide MCPA in three horizons of an agricultural soil. The Gompertz function fitted most of the normalized curves, and trends in the data set could be visualized by a scatter plot of the two Gompertz parameters (rate constant and time delay). For agricultural topsoil, we also tested the effect of the MCPA concentration on the mineralization kinetics. Reduced initial concentrations lead to shortened lag-phases, probably due to reduced need for bacterial growth. The effect of substrate concentration could be predicted by simply changing the time delay of the Gompertz curves. This delay could to some extent also simulate concentration effects for 2,4-D mineralization in agricultural soil and aquifer sediment and 2,6-dichlorobenzamide mineralization in single-species, mineral medium.
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INTRODUCTION The use of radioactive 14C-tracers is a common way to quantify the potential for degradation of pesticides and other organic pollutants in soil, sediment, and water. The principle1 is simple: the pesticide is spiked with a chemically identical 14C-tracer, and the mixture of radioactive and nonradioactive pesticide is added to an environmental sample in an appropriate concentration. The sample is placed in an airtight container where microorganisms in the sample mineralize the 14C-tracer to 14CO2, which is captured in a base trap and quantified. Down-scaling of the mineralization assay to microplate formats2−4 has greatly increased the number of samples that can be handled, and it is no longer exceptional to generate hundreds of mineralization curves in a single experiment (e.g., refs 5−7). This raises the question of how one should parametrize and evaluate such large numbers of curves. Mineralization curves may be compared by their direct visual differences. This is a common but subjective approach that works well only when few curves are compared and when the differences are obvious. Fitting of kinetic functions is a more consistent way of evaluating mineralization curves. First-order kinetics are often the preferred model, for instance, in the approval procedure for pesticides in the European Union,8 but first-order kinetics are only appropriate when the half-life is independent of time and concentration, i.e., when the density © 2013 American Chemical Society
of degrader organisms does not change. Many pesticides, however, sustain growth of the degrader organisms so that the growing populations lead to sigmoid mineralization curves rather than first-order curves. As an alternative to the first-order kinetics, it has been suggested that variations of the sigmoid Gompertz function9 may describe the degradation10−12 and mineralization13−16 of organic pollutants when the microbial degrader density increases. In this article, we show that the Gompertz function in its simplest form may be used for parametrizing and comparing large numbers of such sigmoid pesticide mineralization curves. The Gompertz function may furthermore be used to estimate how mineralization would proceed at other pesticide concentrations than the one tested. The aim of our study was thus to test whether the twoparameter sigmoid Gompertz function can be used to fit and interpret the mineralization of 14C-labeled pesticides by environmental microorganisms, and in particular, focus on the ability of the function to parametrize mineralization for all samples of large data sets. Received: Revised: Accepted: Published: 8508
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MATERIALS AND METHODS MCPA Mineralization in Agricultural Soil − One Concentration. The applicability of the Gompertz function was tested on a previously published data set5 where the herbicide 2-methyl-4-chlorophenoxyacetic acid (MCPA) was mineralized in 0.2-g soil samples in microplates. The initial MCPA concentration was 10 mg kg−1. The soil came from an agricultural field (sandy loam), where 84 subsamples were sampled in 6.5 × 10.5 cm2 arrays at five depths. We used data from depths of 8, 28, and 48 cm giving a total of 252 mineralization curves. We used data only from the initial 120 days incubation due to the risk of producing artifacts by prolonged incubation. Mineralization was considered significant only when it exceeded 3% of the added 14C-label. MCPA Mineralization in Agricultural Topsoil − Concentration Effects. We carried out an additional mineralization experiment to test the effect of substrate concentration on the mineralization kinetics. Fresh ploughlayer soil was collected from the same field as above, and a 50-g subsample was thoroughly homogenized by triple sieving through a 2 mm mesh. Portions of 1 g were then transferred to 20-mL glass scintillation vials and spiked with 100 μL aqueous MCPA solution (42 Bq) giving final concentrations of 0.1, 0.3, 1, 3, and 10 mg kg−1. Five replicates were tested for each concentration. One-milliliter glass tubes containing 0.5 mL NaOH (0.5 M) were placed inside the vials for trapping the produced 14CO2. The NaOH was replaced over time, and the trapped radioactivity quantified by liquid scintillation counting. The scintillation liquid (Optiphase HiSafe3, PerkinElmer) was made basic (pH > 10) by addition of NaOH before mixing with the trapped 14CO2. A series of incubations were also set up to test if any MPCA remained in the soil when mineralization leveled off. The conditions were identical to the 0.1 and 10 mg kg−1 incubations above except that 917 Bq was added to each vial, and triplicate controls were immediately inactivated by adding sodium azide (70 μL, 2% w/v). Sodium azide was added to the mineralization vials when the mineralization ceased. Remaining MCPA was then extracted by adding water (1 mL) followed by overnight shaking. The MCPA concentration in the extracts was determined by thin-layer chromatography (TLC, 100 μL per lane) followed by digital autoradiography using a Cyclone scanner (Packard Bioscience). The remaining MCPA was calculated in percent of the 14C-signal in the inactivated controls. The TLC quantification limit (0.3 Bq) corresponded to 0.6% of the added MCPA. Effects of Concentration on the Mineralization of Other Pesticides. Comparable pesticide mineralization data, where pesticides were added in varying concentrations, has previously been published. In one study,17 phenoxyalcanoic acid herbicides (mecoprop, 2,4-D, and 2,4,5-T) were mineralized in sandy, agricultural topsoil, and sandy aquifer sediment. In another study, the herbicide degradation product 2,6-dichlorobenzamide (BAM) was mineralized by a pure culture of Aminobacter sp. in liquid mineral medium.18 Mineralization data from the two articles was extracted from the published graphics by using the freeware Tracer 2.0 (Marcus Karolewski, http://sites.google.com/site/ KalypsoSimulation). The Gompertz Function. The original Gompertz function (eq 1) is a three-parameter sigmoid function where Y(t) [%] is the amount of pesticide mineralized to 14CO2 at time t [day], a
[%] is the upper asymptote, t0 [day] sets the horizontal displacement (time-delay), and b [day] sets the rate of increase: Y (t ) = ae−e
−((t − t0)/ b)
(1)
Note that eq 1 is presented in a slightly different form to that presented in some papers (e.g., refs 13,14). We assumed that the growth-sustaining pesticides MCPA, 2,4-D, and BAM were fully degraded when the mineralization eventually leveled off. The upper asymptote (a) was therefore given a value of 1 so that the mineralization proceeded from 0 to 1. For the soil horizons data set, most curves showed a plateau of 40% mineralization. This value was therefore used to normalize data from samples where the mineralization was too slow to reach a plateau within the 120 days incubation. By normalizing the mineralization data, we could quantify each mineralization curve by only two Gompertz parameters, t0 and b (eq 2).
Y (t ) = e − e
−((t − t0)/ b)
(2)
This function was fitted to the normalized mineralization data by using the custom fit option in Sigmaplot 10 (Systat Software Inc., San Jose, USA). The time delay of the mineralization curve, which is described by t0 (Figure S1A), may be interpreted as the need for bacterial adaptation and growth. The slope of the function is maximal at t = t0 (Figure S1B) where the slope equals b−1 (see Supporting Information for details). This means that Y(t) becomes less sensitive to b as b increases.
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RESULTS AND DISCUSSION MCPA Mineralization in Agricultural Soil − One Concentration. We applied the two-parameter Gompertz function for parametrization of a comprehensive data set where the mineralization of the herbicide MCPA was tested in 0.2-g agricultural soil samples that represented three depths. Examples of the raw mineralization data, normalized mineralization data, and fitted Gompertz functions are depicted in Figure 1. The initial increases in mineralization rates in the sigmoid mineralizations probably reflected growth of degrader bacteria, whereas the almost constant mineralization rates in the linear mineralizations indicated degrader populations that were almost constant over time. Soil samples from the plough layer (8 cm depth) all showed fast, sigmoid mineralization that leveled off at approximately 40% (Figure 1A), and the Gompertz function could easily fit the normalized version of these data (Figure 1B, R2 = 0.987− 1.000, average 0.999, n = 84). Samples from the upper Bhorizon (28 cm depth, Figure 1A) showed either sigmoid mineralization, slow almost linear mineralization that did not exceed 5−10% within the 120 days incubation, or no mineralization (R2 = 0.731−0.999, average 0.953, n = 61). For this depth, the Gompertz function slightly underestimated the initial mineralization in the sigmoid curves (Figure 1B), and slightly overestimated mineralization when mineralization ceased during incubation in some of the nongrowth curves. The potential for MCPA mineralization was generally very low in the lower B-horizon (48 cm depth) where most samples were mineralization-negative. Some samples showed slow nongrowth mineralization, and only one sample showed sigmoid mineralization (R2 = 0.697−0.992, average 0.858, n = 19). As far as we are aware, there are no ordination methods available that can provide overviews of mineralization data sets, 8509
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days, average 233 ± 63 days), and curves from the upper Bhorizon are somewhat intermediary (b−1: 0.0040−0.38 day, average 0.096 ± 0.10 day; t0: 22.0−323 days, average 119 ± 89 days). A possible explanation for the observed pattern might be that sigmoid growth in the B-horizon could be dependent on hydraulic contact with the plough layer. Soil particles, degrader cells, and nutrients may be washed down from the plough layer to the B-horizon through biopores and drought cracks, resulting in a mosaic pattern of zones of high degradation capacity close to the pores, and zones of low capacity in the bulk soil. Once in the B-horizon, the degrader cells may still be able to grow on MCPA and produce sigmoid mineralization curves, but the initial density of degrader cells would be lower, giving increased t0-values, and the general growth conditions in the mineral soil would be less favorable, giving smaller b−1 values. This interpretation would suggest that only one (t0 = 32 days, b−1 = 0.16 day) of the 84 lower B-horizon samples had direct hydraulic contact with the plough layer. MCPA Mineralization in Agricultural Topsoil − Concentration Effects. The maximum allowed dose of MCPA in Denmark is 2.0 kg ha−1. With a soil density of approximately 1.5, this dose corresponds to an average of 13 mg kg−1 if distributed in the upper centimeter, and 0.13 mg kg−1 in the upper meter. The 252 mineralization curves above were all generated by adding MCPA at a concentration of 10 mg kg−1, which thus corresponded only to the situation in the upper few centimeters right after spraying. We therefore carried out an additional experiment to see how reduced MCPA concentrations would change the course of mineralization. The concentration effect on the normalized Gompertz functions was mainly a shift in time delay (Figure 3). One-way ANOVAs
Figure 1. A. Examples of 14C-MCPA mineralization curves from the plough layer (8 cm depth, black symbols) and the upper B-horizon (28 cm depth, white symbols). B. Their conversion to normalized Gompertz functions.
and it may therefore be difficult to recognize patterns and interpret large data sets. As a simple alternative, we suggest plotting the maximal mineralization rate (b−1) against the delay time (t0), as shown in Figure 2 for all the mineralization curves
Figure 2. Distribution of b−1 (maximal mineralization rate) and t0 (time delay) from 6 × 11 cm arrays of 84, 0.2-g samples from the plough layer (8 cm depth, n = 84), the upper B-horizon (28 cm depth, n = 61), and the lower B-horizon (48 cm, n = 18).
from the three depths. The plot provides a clear visual separation of the growth-associated, sigmoid mineralizations (b−1 > 0.02 day, t0 < 100 days) and the slow, almost linear mineralizations (b−1 < 0.02 day, t0 > 100 days). It is also seen that the mineralization curves from the plough layer fall in one group (b−1: 0.17−0.43 day, average 0.34 ± 0.07 day; t0: 8.5− 27.0 days, average 14.7 ± 4.4 days), the curves from the lower B-horizon with one exception fall in another group (b−1: 0.0035−0.0093 day, average 0.0055 ± 0.0016 day; t0: 148−354
Figure 3. Effect of 14C-MCPA concentration on mineralization. A. raw mineralization data (n = 5, ±1 standard deviation). B. normalized mineralization (symbols) and their corresponding Gompertz fits (lines). 8510
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showed that the means were concentration-dependent for both b−1 and t0 (P < 0.001), but Tukey’s post hoc test showed that t0 was more affected by the MCPA concentration than b−1, i.e., the different concentrations were all well separated with respect to t0 but overlapping for b−1 (Tables S1 and S2). This is also apparent when the complete data set is visualized in a b−1 versus t0 scatter plot (Figure 4).
Figure 5. Simulated effect of MCPA concentration. The symbols show the normalized mineralization data (from Figure 3) and dashed lines show the simulated Gomperz functions derived from the 10 mg kg−1 fit (solid line).
concentration only, an estimate of the decrease in t0 for reduced initial concentrations may be simulated by assuming that t0 in that sample is reduced proportionately to eq 3: Figure 4. Effect of MCPA concentration on the Gompertz parameters where b−1 is the maximum mineralization rate and t0 denotes the time delay.
t0(C1) = t0(C2) ·
(4)
C1 is the initial concentration where a mineralization estimate is wanted, C2 is the initial concentration where mineralization data is available for Gompertz curve-fitting, and t0(C2) is the fitted time-delay value that is specific for the sample at concentration C2. The simulated t0(C1) and the fitted b can now be used to calculate qualified predictions of how mineralization would proceed at different initial concentrations of MCPA. Such a prediction is depicted in Figure S3, where the concentration effect was simulated for an upper B-horizon sample. Concentration Effects on the Mineralization of Other Pesticides. We searched the literature for appropriate data to test the validity of eq 4. Concentration effects have previously been published for phenoxyalcanoic acid herbicide mineralization in samples of sandy, agricultural topsoil (5−25 cm depth) and the underlying aquifer sediment from a depth of 3 m.17 The sigmoid mineralization of 2,4-dichlorophenoxyacetic acid (2,4-D) in both topsoil at 10 °C (Figure 6), 20 °C (Figure S4),
Estimates on the potential for growth of MCPA degraders may be calculated by assuming the dry-weight of one cell to be 5 × 10−10 mg and a yield of 0.5. The potential increase would be 107 cells g−1 for 10 mg kg−1 of MCPA, 106 cells g−1 for 1 mg kg−1, and 105 cells g−1 for 0.1 mg kg−1. Given that the average, initial degrader population was only 610 cells g−1,5 it seems plausible that the initial degrader population was probably a main limiting factor, i.e., the increase in t0 with increasing MCPA concentration was caused by increased growth at higher concentrations. The type of degrader bacteria, nutrient availability, water content, and other soil parameters that may influence b seems to have been less impacted by decreasing MCPA concentration; b may therefore be interpreted as a characteristic of the specific degrader community under the specific conditions in the soil sample. Mineralization experiments are often carried out with only one concentration of pesticide, but Figures 3 and 4 suggest that, by changing t0, we might be able to come up with simulations of how mineralization would proceed at other concentrations. The MCPA concentration-dependence of t0 in the homogenized plough layer soil can be expressed by a logarithmic function (Figure S2, eq 3) of the initial MCPA concentration C [mg kg−1]: t0(C) = 1.9199 ln(C) + 7.4563
1.9199 ln(C1) + 7.4563 1.9199 ln(C2) + 7.4563
(3)
The effect of the initial MCPA concentration on the course of mineralization could then be simulated by using b from the 10 mg kg−1 curve and t0(C) from eq 3 (Figure 5). Rather good predictions were obtained, even for a 100-fold reduced concentration. It may seem more intuitive to have done the simulation from the 1 mg kg−1 curve, so that the differences up and down in concentration would only be 10-fold, but we chose the 10 mg kg−1 curve because mineralization data in the literature generally are generated from unrealistically high pesticide concentrations. Equation 3 describes only how t0 depends on C in a specific soil sample. For other samples where we have data for one
Figure 6. Concentration dependence of 2,4-D mineralization in sandy plough layer samples (0.05−0.25 m depth, n = 3, 10 °C).17 Simulated degradation curves (dashed line) were calculated from a fitted 10 mg kg−1 curve (solid line) in conjunction with the concentration dependence from MCPA mineralization in soil (eq 4). 8511
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and in sediment at 10 °C (Figure 7) showed pronounced concentration dependence in the 0.1 to 10 mg kg−1 range. For
Figure 8. Concentration dependence of 2,6-dichlorobenzamide (BAM) degradation by Aminobacter sp. MSH1 in liquid mineral salts medium, n = 3.18 Simulated degradation curves (dashed lines) were calculated from a fitted 10 mg kg−1 curve (solid line) in conjunction with the concentration dependence from MCPA mineralization in soil (eq 4).
Figure 7. Concentration dependence of 2,4-D mineralization in sediment samples (3 m depth, n = 3, 10 °C). 17 Simulated degradation curves (dashed lines) were calculated from a fitted 10 mg kg−1 curve (solid line) in conjunction with the concentration dependence from MCPA mineralization in soil (eq 4).
simplicity. Complex kinetic functions with more parameters like the three-half-order model,19 the extended three-half-order model,20 and the modified Gompertz models13,14 will fit most mineralization curves with greater accuracy, but it is more complicated to interpret the effect of their parameters when comparing large numbers of curves, or when applying different functions to different samples. Alternatively, the simple Gompertz model may allow direct visualization of all mineralization curves in b−1 versus t0 plots and simulation of concentration effects, but at the expense of precision in the curve fitting. It is worth noting that the normalization has no effect on the b and t0 values so that the b−1 versus t0 plots will be the same with normalized and non-normalized data, but the normalization may often allow the parametrization of mineralization when not all curves show a plateau (Figure 1). The Gompertz equation, however, cannot describe slow nongrowth systems where no curves reach a plateau. For the data-normalization, we presumed that the MCPA was fully degraded when the mineralization eventually plateaued. This is mainly due to the fact that, when growthsustaining pesticides are mineralized, a large proportion of the carbon goes into new biomass instead of 14CO2, resulting in plateaus substantially below 100% mineralization. There may be other explanations for the reduced 14CO2 plateaus. Accumulation of metabolites in the soil, for instance, would lead to reduced 14CO2 yield. Though not complete mineralization, this is also degradation sensu lato and therefore acceptable for the normalization. Often, the metabolites may accumulate only temporarily so that the effect would be slower kinetics rather than reduced 14CO2 plateaus. Aging processes in soil, where a fraction of some pesticides may become permanently sorbed in micropores,21 would also result in a low and stable 14CO2 plateau with incomplete degradation. This would violate the partial-mineralization-butfull-degradation assumption, but then the sorbed pesticide would probably be of little ecological relevance.21 Such aging of phenoxy alcanoic acids in soil is probably very limited since nearly all soil-bound residue is of biogenic origin.22 In our experiment, the full-degradation-but-partial-mineralization assumption was confirmed by thin-layer chromatography where both MCPA and metabolites were undetectable after incubation for initial concentrations of 10 and 0.1 mg kg−1.
both topsoil temperatures (Figure 6 and Figure S4), the Gompertz function deviated from the data with measured mineralization not reaching a clear plateau. The simulated concentration effect, however, corresponded closely to the experimental data in the lower part of the curves. 2,4-D mineralization in the sediment samples had a clear plateau (Figure 7). The fitted curve (10 mg kg−1) and the simulated experiment with a 1 mg kg−1 initial concentration followed the experimental data, whereas simulations of experiments with 0.1 mg kg−1 initial concentrations showed mineralization that is too fast compared to the experimental data. This discrepancy may have been an artifact caused by the specific setup where the sediment was covered by stagnant water. Diffusion in water is slow compared to diffusion in the gas phase, so we suspect that 14CO2 diffusion through the water to the CO2-traps probably could not keep up with the 14CO2production, resulting in apparently delayed mineralization. Data on concentration effects are also available in the literature for mineralization of the pesticide metabolite 2,6dichlorobenzamide (BAM) under controlled conditions in single-species, mineral medium.18 BAM mineralization was strongly concentration dependent, and the simulated concentration effect corresponded closely to the experimental data in the 0.1 to 10 mg L−1 range (Figure 8). The simulated BAM mineralization for the smallest concentration of 0.0015 mg L−1 was very poor (Figure S5), and the highest concentration of 50 mg L−1 also showed poor correspondence between simulated and measured values (Figure S5). This is not surprising since both curves are outside the concentration range that was used to derive eq 4. Overall, it was quite surprising that the empirical concentration-dependence of t0 from MCPA in agricultural topsoil (eq 4) had any predictive power for 2,4-D in aquifer sediment and BAM in liquid single-species culture. The reason is probably that the limiting factor was the initial size of the microbial degrader populations, so the increase in pesticide concentration was reflected in the time needed for growth. Premises and Limitations. We chose the simplest version of the Gompertz function as a trade-off between accuracy and 8512
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This proved that all MCPA (>99.4%) was degraded when mineralization ceased even when the final 14CO2-plateaus decreased with decreasing concentration (Figure 3). A similar effect was shown in a previous study18 where the 14CO2 yield was determined for BAM mineralization at 50, 10, 1, 0.1, and 0.0015 mg L−1 in liquid pure-culture, i.e., a soil-less system where aging processes could not take place. The final 14CO2 level decreased from 64% to only 13% with decreasing initial BAM concentrations, but when the final BAM concentrations were determined chemically, it turned out that ≥99.9% was degraded, except for the lowest initial concentration of 0.0015 mg L−1 where 95.6% was degraded. The fraction mineralized to 14 CO2 is generally expected to increase with decreasing initial substrate concentration because an increasing fraction goes to the cell’s basal metabolism. At present, there is no plausible explanation for the decreasing plateaus seen for MCPA and BAM at decreasing concentrations. Mineralization of the phenoxyalcanoic acid herbicide 2,4,5-T showed nongrowth kinetics in both topsoil and aquifer sediment for all substrate concentrations ranging from 0.0001 mg kg−1 to 10 mg kg−1.17 The Gompertz function can be used to fit these almost linear mineralization curves, enabling direct comparison of both growth and nongrowth curves, but the dependence of t0 on C given by eq 4 is not applicable to the nongrowth situation. The Gompertz function also should not be applied for the mineralization of mixed enantiomer substrates that may produce double-sigmoid mineralization curves as reported for the racemic mixture found in the phenoxyalcanoic acid herbicide mecoprop.17 Complex kinetics may also be found where sorption is strong, but reversible. In this case, the mineralization may be controlled by the limited mass-transfer rate, and the flux of carbon to the degrader cells may after some initial growth equal the basic metabolic demand so that almost all substrate is converted to CO2 without cell growth.23 In this case, the fitted Gompertz curves will reflect bioavailability rather than growing degrader populations. The concentration dependence shown in (eq 4) also should not be extrapolated outside the concentrations used for deriving it. As described above, the mineralization of 2,4-D in topsoil and aquifer sediment17 was concentration dependent in the 10 to 0.1 mg kg−1 range, but there was no clear difference in the 0.01−0.0001 mg kg−1 range. A likely explanation may be that the low amount of substrate did not sustain growth of the indigenous degrader population, so that the kinetics approached first-order rather than sigmoid mineralization. The concentration dependence (eq 4) therefore works well only when the initial microbial population is small compared to the simulated amount of added carbon, which is typical for pesticide degradation in agricultural soil. First-Order Kinetics or Gompertz Kinetics? As pointed out in the Introduction, first-order kinetics and Gompertz kinetics are different models with respect to the growth of the degrader organisms. First-order kinetics requires constant degrader populations so that the half-life is constant over time and at different substrate concentrations. Gompertz kinetics, in contrast, works well when the potential for degradation increases over time. To illustrate the difference between growth and nongrowth kinetics, we have fitted a firstorder nongrowth model to the data for the different initial MCPA concentrations. For the lowest concentration of 0.1 mg kg−1 in the topsoil, normalized first-order kinetics fitted the data well (Figure 9A, R2 = 0.99), suggesting that growth of
Figure 9. Fitting of a first-order kinetic model to the normalized mineralization data from Figure 3 (panel A, soil from the A-horizon), and from Figure 1 (panel B, soil from the A-horizon and upper Bhorizon, 10 mg kg−1).
degraders was not important. As the MCPA concentration and the potential degrader growth increased, the first-order model gave increasingly bad fits so that the R2 decreased to 0.73 for 10 mg kg−1. The limitations of the first-order model were also reflected in increasing half-lives with increasing concentration (0.1 mg kg−1: 4.0 days; 0.3 mg kg−1: 5.3 days; 1 mg kg−1: 7.1 days; 3 mg kg−1: 9.3 days; 10 mg kg−1: 11.6 days). The firstorder fits were even worse for the slow samples from the Bhorizon (Figure 9B, R2 = 0.51). Fitting of first-order kinetics to our sigmoid mineralization data would lead to initial overestimation of MCPA removal, and later a serious overestimation of MCPA persistence in soil. The Gompertz model, in contrast, gave good fits both at low (Figure 3, 0.1 mg kg−1, R2 = 0.99) and high (Figure 3, 10 mg kg−1, R2 = 1.00) MCPA concentrations. In general, we recommend to apply growth-based models for growthsustaining pesticides, for instance in numerical modeling.
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ASSOCIATED CONTENT
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AUTHOR INFORMATION
S Supporting Information *
Additional equations for the first derivative function of eq 1, and additional tables and figures concerning the effect of pesticide concentration on normalized mineralization. This material is available free of charge via the Internet at http:// pubs.acs.org. Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest. 8513
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mineralization of mecoprop, 2,4-D and 2,4,5-T in soil and aquifer samples. Environ. Pollut. 2007, 148, 83−93. (18) Sørensen, S. R.; Holtze, M. S.; Simonsen, A.; Aamand, J. Degradation and mineralization of nanomolar concentrations of the herbicide dichlobenil and its persistent metabolite 2,6-dichlorobenzamide by Aminobacter spp. isolated from dichlobenil-treated soils. Appl. Environ. Microbiol. 2007, 73, 399−406. (19) Brunner, W.; Focht, D. D. Deterministic three-half-order kinetic model for microbial degradation of added carbon substrates in soil. Appl. Environ. Microbiol. 1984, 47, 167−172. (20) Trefrey, M. G.; Franzmann, P. D. An extended kinetic model accounting for nonideal microbial substrate mineralization in environmental samples. Geomicrobiol. J. 2003, 20, 113−129. (21) Alexander, M. How toxic are toxic chemicals in soil? Environ. Sci. Technol. 1995, 29, 2713−2717. (22) Nowak, K. M.; Miltner, A.; Gehre, M.; Schäffer, A.; Kästner, M. Formation and fate of bound residues from microbial biomass during 2,4-D degradation in soil. Environ. Sci. Technol. 2011, 45, 999−1006. (23) Harms, H.; Bosma, T. N. P. Mass transfer limitation of microbial growth and pollutant degradation. J. Indust. Microbiol. 1997, 18, 97− 105.
ACKNOWLEDGMENTS This study was funded by the Villum Foundation via the Center for Environmental and Agricultural Microbiology (CREAM).
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REFERENCES
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dx.doi.org/10.1021/es400861v | Environ. Sci. Technol. 2013, 47, 8508−8514
