Chemosphere 54 (2004) 1255–1265 www.elsevier.com/locate/chemosphere
Effect of temperature and dissolved oxygen on the growth kinetics of Pseudomonas putida F1 growing on benzene and toluene Gunaseelan Alagappan, Robert M. Cowan
*
Department of Environmental Sciences, Cook Campus, Rutgers––The State University of New Jersey, 14 College Farm Road, New Brunswick, NJ 08901, USA Received 3 July 2002; received in revised form 19 August 2003; accepted 9 September 2003
Abstract Batch experiments were conducted to determine the effect of temperature and dissolved oxygen concentration on the rates of growth and substrate (benzene and toluene) degradation by the toluene degrading strain, Pseudomonas putida F1. Over a range of temperature from 15 to 35 C the maximum specific growth rate followed the Topiwala–Sinclair relationship when either benzene or toluene served as the sole carbon and energy source. Oxygen limited growth followed Monod saturation kinetics with the specific growth rate given as a function of the dissolved oxygen concentration. The oxygen half-saturation coefficient was found to be approximately 1 mg/l regardless of whether benzene or toluene was the substrate. Similar experiments with Burkholderia (Ralstonia) pickettii PKO1 for grown on toluene revealed an oxygen half-saturation coefficient of 0.7 mg/l. 2003 Elsevier Ltd. All rights reserved. Keywords: P. putida F1; Kinetic models; Temperature; Dissolved oxygen; Arrhenius; Topiwala–Sinclair
1. Introduction Contamination of soil and groundwater due to accidental spills and leaking underground storage tanks is a widespread threat to the environment. The presence of microorganisms in nature that are capable of breaking down various chemical components of gasoline (chiefly benzene, toluene, ethyl benzene, and xylene congeners) is fairly well recognized as a major agent for decontamination (Bossert and Bartha, 1984). However, the length of time required for the removal of these compounds in the environment depends on various factors that affect the growth kinetics of the participating microorganisms, such as substrate concentration, moisture
*
Corresponding author. Tel.: +1-732-822-8111. E-mail address:
[email protected] (R.M. Cowan).
level, temperature, electron acceptor, pH, presence of toxic intermediates, and the availability of mineral nutrients. Any one of these factors or a combination of them can play a role in limiting the rate of biomass growth and substrate biodegradation. In this study the focus is given to the effect of temperature and dissolved oxygen (electron acceptor) concentration on the growth kinetics of a toluene degrading strain capable of mineralizing both benzene and toluene. It is well known that the growth rate of aerobic heterotrophs is hampered when the oxygen concentrations are low. Therefore an adequate oxygen supply must be ensured whenever aerobic processes are relied upon, whether in a biological reactor or in the subsurface environment. While toluene is known to be biodegradable under most other electron acceptor conditions (nitrate reducing (Jørgensen et al., 1995), iron reducing (Phelps and Young, 1999), sulfate reducing (Reinhard et al.,
0045-6535/$ - see front matter 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.chemosphere.2003.09.013
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1997), and methanogenic (Ahad et al., 2000)), benzene has been shown to degrade under methanogenic, sulfatereducing, and iron-reducing conditions (Kazumi et al., 1997) at much slower rates. Hence, it has been argued that while anaerobic degradation in the subsurface is possible (and may be a significant mechanism in some cases), it is aerobic metabolism that accounts for the bulk of naturally occurring biodegradation of most groundwater plumes, and therefore is the mechanism of choice for almost all enhanced in situ bioremediation. Aerobic, in situ remediation is more challenging, since various non-target sinks such as reduced metals and background organic matter also compete for the available oxygen. Relatively few studies have been reported in the literature fully assessing the effect of temperature on the kinetic and stoichiometric coefficients of aerobic microorganisms, such as maximum specific growth rate, specific decay rate, growth yield and half-saturation coefficient. The equation most commonly used to quantify the effect of temperature on the maximum specific growth rate is that of Arrhenius (1889), as given in Eq. (1): l^ ¼ A eEa =RT
ð1Þ
where l^ is the temperature dependent maximum specific growth rate, A is an exponential factor, Ea is the activation energy for cellular multiplication, R is the universal gas constant, and T is the absolute temperature. This growth model implies an exponential increase in growth rate of the organisms with rising temperature. It is well recognized that the Arrhenius function fails once the temperature approaches the value of optimum activity because it cannot represent the fall in rates at higher temperatures. Due to this limitation, alternate models have been proposed which can predict the drop in rate following the optimum. Two of these models are reviewed here and applied to our data. This trend is well explained by the extended model proposed by Topiwala and Sinclair (1971), as given in Eq. (2): l^ ¼ A eEa =RT B eEb =RT
ð2Þ
where Eb is the activation energy for thermal denaturation processes, which is usually higher than the activation energy for multiplication (De Ory et al., 1998). It is believed that when the temperature rises above the optimum, the cellular decomposition reactions are favored, resulting in irreversible damage to plasma membranes, loss of metabolites, and reduced metabolic function. Mayo (1997) modified the Arrhenius function based on the premise that the active fraction of the enzymes involved in the growth limiting reaction decreases when the temperature exceeds the optimum. This expression, as shown in Eq. (3), is also able to predict a
drop in the maximum specific growth rate when the temperature exceeds the optimum. l^ ¼
A0 eðE1 =RT Þ ½1 þ k eðE2 =RT Þ
ð3Þ
In this equation, the parameters A0 , E1 , k, and E2 have the same meaning as A, Ea , B, and Eb , respectively, in the Topiwala and Sinclair model. The inverse of the denominator term in this equation is the mathematical expression for the enzyme active fraction. The nomenclature for each model was retained as given in the original work in order to distinguish them, and because some differences were found for the two models in the regression analysis results of the same data set. In this work, we investigate the effects of temperature and oxygen concentration on a solvent degrading strain, from a pollutant remediation viewpoint.
2. Materials and methods 2.1. Microorganism strain and growth conditions The strains Pseudomonas putida F1 and Burkholderia pickettii PKO1 were obtained as frozen cultures from Dr. Jerome Kukor at the Biotechnology Center for Agriculture and Environment at Rutgers, The State University of New Jersey. The former strain utilizes toluene dioxygenase in its metabolic pathway to oxidize the aromatic ring structure before the substrate enters the energy yielding steps (Yeh et al., 1977) and the latter contains toluene-3-monooxygenase (Olsen et al., 1994) to initiate oxygenation of aromatic compounds. Daigger mineral salts medium (Daigger, 1979) was used to grow and adapt the culture to the experimental conditions. All experiments were carried out in batch mode using automated aerobic respirometers with adjustable temperature controlled water baths. Non-inhibitory concentrations of both benzene and toluene (16 and/or 32 mg/l) were used as the initial substrate concentration in all the experiments (Goudar and Strevett, 1998; Alagappan and Cowan, 2003). To determine the influence of temperature on the growth rate, studies were carried out in the range of 15–35 C. In the oxygen limitation studies, dissolved oxygen concentrations from that of air saturated water to values less than 1 mg/l were included. 2.2. Reaction equipment, conditions, and data analysis Aerobic respirometers (Comput-Ox, N-CON Systems Inc., Atlanta, Ga, USA) were used to collect oxygen uptake data for both temperature and oxygen limited studies. The principles of aerobic respirometry are described elsewhere (Li and Zhang, 1996; Smets et al., 1996). The valve coefficients used for the oxygen
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metering valves were calibrated at 25 C and adjusted using the ideal gas law to calculate values for the other temperatures. The batch vessels used were 600 ml bottles with 400 ml of liquid volume and 200 ml of headspace gas volume. The carbon substrates used, benzene and toluene, are volatile in nature. Therefore they partition between the liquid and gas phases to different extents, depending on the temperature. In order to account for this, dimensionless Henry’s law coefficients for each compound at each temperature were obtained from the literature. Table 1 contains a summary of literature values, their source, and the dimensionless Henry’s law coefficients employed. All the experiments utilized active seed cultures that were well acclimated (3–4 generations) to the substrate on which the biomass was grown during the experiment. The seed cultures were grown at the temperature at which the experiments were to be carried out. The contents of the batch experimental vessels, i.e., the mineral media, the substrate, and the headspace air, were equilibrated in the water bath prior to inoculation at the beginning of the experiment. The oxygen uptake data obtained from each experiment was used to obtain stoichiometric and kinetic parameters with mass balance based mathematical models. In the case of temperature studies, model fits were regressed to the maximum specific growth rate values as a function of their corre-
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sponding temperatures. The oxygen uptake data were analyzed with MicroMath Scientist (1995), a simulation software for non-linear data analysis. The Monod model incorporates mass balance relationships between the oxygen demand, substrate utilization, biomass accumulation, and product formation (Appendix A). For the oxygen concentration limited growth studies, the inoculated reactor was first deoxygenated by sequential vacuum degassing and nitrogen purge (see next section). Following this, a known quantity of oxygen was injected into the individual reactors to achieve the desired dissolved oxygen concentration based on equilibrium between the aqueous solution and the headspace. The substrate was added to the reactor at this point, and both oxygen and substrate in the headspace and liquid were then allowed to come into equilibrium at the experimental temperature. The headspace oxygen concentration was analyzed and the test started. At the end of the experiment, the headspace oxygen levels were reanalyzed to confirm whether or not they remained constant throughout the experiment. 2.3. Purging–degassing system for oxygen elimination For the oxygen limitation study, a nitrogen purging and degassing arrangement was designed (Fig. 1). In this set up, the airtight batch vessels were connected to a 00 system of manifolds via a side arm with 12 mm (0.469 )
Table 1 Average dimensionless Henry’s law constants used for benzene and toluene at different temperatures Temperature (C)
Benzene
Reference
Toluene
Reference
15
0.159
Ashworth et al. (1988) Turner (1995) Sanemasa et al. (1982) Brown and Wasik (1948)
0.19
Turner (1995) Sanemasa et al. (1982)
0.191
Leighton and Calo (1981)
17.8 20
0.185
Ashworth et al. (1988) Brown and Wasik (1948)
0.23
Ashworth et al. (1988) Brown and Wasik (1948) Schoene and Steinhauses (1985)
25
0.22
Ashworth et al. (1988) Mackay et al. (1979) Robbins et al. (1993) Howe et al. (1987) Mackay and Shiu (1981)
0.267
Ashworth et al. (1988) Robbins et al. (1993) Mackay et al. (1979) Howe et al. (1987) Turner (1995) Sanemasa et al. (1982)
30
0.278
Ashworth et al. (1988) Robbins et al. (1993) Saylor et al. (1938) Tucker et al. (1981)
0.33
Ashworth et al. (1988) Robbins et al. (1993)
35
0.344
Turner (1995) Saylor et al. (1938) Sanemasa et al. (1982)
0.422
Robbins et al. (1993) Sanemasa et al. (1982) Turner (1995)
Values given here are arithmetic mean calculated from those given in the listed references.
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Fig. 1. Schematic of the purging and degassing setup used for preparation of the oxygen limited growth rate study. A––nitrogen tank; B––vacuum pump; C––magnetic stirrer; D––respirometer bottle with mineral medium; E––soda lime; F––clamped tubing; G––side arm with septa; H––three-way valve; I––tubing manifold.
diameter high temperature low bleed septum (Hamilton Co., Nevada, USA). The manifold inlet could be switched between a vacuum pump (for eliminating gas from the headspace), and a nitrogen gas cylinder (for purging the system). By alternating between degassing and nitrogen purging of the headspace of the batch vessels, the oxygen in the system is gradually replaced by nitrogen. By this process, the concentration of oxygen in the headspace (and thereby the equilibrium dissolved oxygen concentration) dropped to near zero. Each cycle of vacuum degassing (15 min) and N2 purge (5 min) is carried out for 20 min. Depending on the level to which the oxygen concentration needs to be lowered, many cycles of purging and degassing were applied to each vessel. At the end of each cycle, a headspace gas sample was taken and analyzed by gas chromatography to determine whether the target level was achieved.
spectrophotometric method recommended by the manufacturer (HACH, 1998).
3. Results and discussion 3.1. Kinetics of benzene and toluene degradation Studies were performed to determine the intrinsic kinetic parameters of P. putida F1 when grown on both benzene and toluene under aerobic condition at 20 C. The mean ± standard error kinetic parameter values with benzene were as follows: l^ ¼ 0:36 0:01 h1 ; Ks ¼ 2:45 0:21 mg/l; Yg ¼ 0:69 (fixed for simulation); X0 ¼ 2:7 0:1 mg COD/l; b ¼ 0:01 h1 (fixed for simulation). The values obtained with toluene were 0.48 ± 0.01, 0.70 ± 0.14, 0.649 ± 0.006, 1.61 ± 0.06, and 0.041 ± 0.002, respectively.
2.4. Determination of oxygen, substrate and biomass Headspace gas samples were analyzed by gas chro00 matography using a molecular sieve 5A (2 m · 1/8 inner 00 diameter, 60/80 mesh) and Haysep DB (10 m · 1/8 inner diameter, 100/120 mesh) columns with thermal conductivity detector (TCD). The operating conditions were: column temperature ¼ 40 C; injector/detector temperature ¼ 20 C; TCD current ¼ 70 mA; helium as carrier gas flowing at 30 ml/min; 570 kPa. The initial and final substrate and biomass concentrations were measured as their chemical oxygen demand. The closed reflux method was used with low range (0–150 mg/l) HACH COD vials following the
3.2. Effect of temperature on the maximum specific growth rate of P. putida F1 grown on benzene and toluene With both benzene and toluene as the sole carbon and energy sources, the maximum specific growth rate for P. putida F1 showed a clear trend when grown at various temperatures. Fig. 2 shows oxygen uptake data plotted as oxygen uptake rate versus oxygen uptake at different temperatures with benzene as the substrate. The data are plotted in this manner to provide for a direct visual comparison of the effect of temperature on specific growth rate. As is described in Smets et al. (1996) the slope of the data presented as the oxygen uptake rate
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Fig. 2. Oxygen uptake rates for P. putida F1 grown at different temperatures. ( )––15 C; (þ)––20 C; ( )––25 C; ()––30 C; ()––35 C.
versus oxygen uptake is directly proportional to the maximum specific growth rate. Note that the oxygen uptake rate increases with temperature. Figs. 3 and 4 represent the maximum specific growth rate data obtained from temperature studies with benzene and toluene, respectively. Included on these figures are least squares regressed models explained later. It is evident in both the cases that the increase in the maximum specific growth rates with temperature from 15 to 30 C follows an exponential trend as predicted by the Arrhenius equation. However, between 30 and 35 C the increase is
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Fig. 4. Effect of temperature on the maximum specific growth rate of P. putida F1 grown on non-inhibitory toluene concentration: (solid line) Topiwala–Sinclair model fit; (long dash) Arrhenius model fit to the first five points (15–30 C); (short dash) Arrhenius model fit to all the data points (15–35 C), and (dash dot dash) Mayo model.
clearly not exponential, which suggests that the optimum temperature might fall between 30 and 35 C. Based on the equation derived by Mayo (1997), the optimum temperatures for the F1 culture when grown on benzene and toluene were calculated to be 33.49 and 33.89 C, respectively, and their corresponding l^ values at those temperatures were 1.52 and 1.39 h1 respectively. The correlation coefficients obtained for the Mayo model fits of the data were 0.99903 and 0.99816 respectively for growth on benzene and toluene. These values lie within a range typical for mesophilic microorganisms (De Ory et al., 1998; L€ oser et al., 1998). The models proposed by Topiwala and Sinclair (1971) and Mayo (1997) predicted this deviation, since they take thermal denaturation into account. The coefficients for the Arrhenius model, Topiwala and Sinclair model, and Mayo model are given in Table 2. Note that the values Table 2 Temperature coefficients for P. putida F1 grown on benzene and toluene Benzene
Toluene
A, h B Ea , kJ/mol Eb , kJ/mol
1.2E + 15 4.8E + 161 87 ± 4.7 954
5.1E + 11 7.9E + 160 68 952
A0 , h1 k E1 , kJ/mol E2 , kJ/mol
1.25E + 15 3.65E + 160 87.3 948.2
5.21E + 15 2.99E + 160 67.8 949.7
1
Fig. 3. Effect of temperature on the maximum specific growth rate of P. putida F1 grown on non-inhibitory benzene concentration: (solid line) Topiwala–Sinclair model fit; (long dash) Arrhenius model fit to the first five points (15–30 C); (short dash) Arrhenius model fit to all the data points (15–35 C), and (dash dot dash) Mayo model.
Values are given as mean ± standard error.
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for the parameters corresponding to thermal denaturation for the latter two models (Ea and E1 ; Eb and E2 ; A and A0 ) were virtually identical, except for the constants B and k. This difference in prediction is apparent with both benzene and toluene data in the temperature region beyond the point of optimum temperature. Unfortunately the relevance of this difference is impossible to decipher because in both cases there is only one data point available in the superoptimal temperature range. Although the scarcity of data available in the supraoptimal temperature range may be cause for some concern regarding the analysis given, there is sufficient information in the literature to support that this is the most likely reason for the observed trend seen in the data. The rapid decrease in specific growth rate with temperature increase above the Arrhenius range is a phenomenon well recognized by microbiologists (Verrips and Kwast, 1977; Brock et al., 1994). Differential scanning calorimetry of the whole cells and various organelles has been used to determine various cellular and molecular events that might occur when the cells grow within the range of cardinal temperatures (Mackey et al., 1991). Ribosomes and rRNA in a wide range of taxonomically unrelated bacteria have been shown to degrade during thermal injury (Tomlins and Ordal, 1976). Bacterial cell membranes were also found to undergo substantial alterations in their properties, both functional and structural. This, along with inactivation of some cytoplasmic enzymes, would result in lack of control over the materials, which permeate in and out of the cell (Verrips and Brevoort, 1979). Haight and Morita (1966) have demonstrated that DNA along with other intracellular components leaked from cells of Vibrio marinus held at elevated temperatures. This would result in an overall drop in activity of the cell before complete thermal inactivation occurred. 3.3. Effect of temperature on b, Yg , and Ks
Fig. 5. Effect of temperature on: (a) the specific decay rate, (b) the true growth yield, and (c) the half-saturation coefficient (COD basis) of P. putida F1 with benzene as the sole carbon and energy source.
The changes observed in the kinetic parameters b, Yg , and Ks as a function of temperature for P. putida F1 when grown on benzene and toluene as sole carbon and energy sources are shown in Figs. 5 and 6 respectively. With benzene, the specific decay rate showed an exponential increasing trend from 15 to 35 C, which is explained by the Arrhenius model with activation energy of 89 ± 11 kJ/mol. The correlation coefficient found for this least squares regression based model fit was 0.9885. The specific decay rate showed a uniform polynomial increase with increase in temperature when toluene was used as the substrate. With benzene and toluene as sole substrate, no significant change (weighted null hypothesis testing) was observed in the growth yield values (0.603 ± 0.033 and 0.592 ± 0.048 respectively). With benzene, the half-saturation coefficient increased with temperature up to 25 C, but dropped and remained
constant at 30 and 35 C. With toluene, the half-saturation coefficient dropped drastically between 17.8 and 20 C, and increased steadily between 20 and 35 C. The increase in Ks values between 20 and 35 C is explained with the Arrhenius model, with an activation energy coefficient of 65 ± 7 kJ/mol. Based on what has been observed by other researchers so far, temperature is expected to have a similar effect on the specific decay rate and the maximum specific growth rate. The activation energy for b in the case of heterotrophs in general is expected to be 1.1 times the activation of l^, and the typical value is reported to be 65.8 kJ/mol (Grady et al., 1999). The average value of Ea for b with benzene as the sole carbon and energy source is 1.02 times the value for l^ (Table 2),
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perature on specific decay rate, b, when grown on toluene. Growth yields did not change significantly with temperature upon using either benzene or toluene as the sole substrate. The effect of temperature on the halfsaturation values appears to be random, which has been corroborated by other reports in the literature (Sock, 1993; Grady et al., 1999). 3.4. Effect of dissolved oxygen on the growth kinetics when grown on benzene and toluene The oxygen uptake data for P. putida F1 when grown on either benzene or toluene showed a correlation between the oxygen uptake rate and the dissolved oxygen concentration (Fig. 7). From the oxygen uptake data obtained, the average specific growth rate was determined for benzene (Fig. 8) and toluene (Fig. 9). For benzene, the maximum specific growth rate (mean ± standard error) was found to be 0.34 ± 0.03 h1 , and the oxygen half-saturation coefficient as 1.2 ± 0.3 mg/l. With toluene, the values were 0.42 ± 0.06 h1 and 1.1 ± 0.47 mg/l respectively. Although the typical oxygen half-saturation values for aerobic heterotrophs are reported to be 0.10–0.2 mg/l as dissolved oxygen when oxygen is required as terminal electron acceptor for cytochrome oxidase (Grady et al., 1999), this is not exactly the case with the degradation of aromatic substrates like benzene or toluene. When oxygen is also used as co-substrate for an oxygenase system, the Monod half-saturation coefficient for oxygen was in the range of 0.3–2.2 mg O2 /l (Shaler and Klecka, 1986). The oxygen half-saturation coefficients observed in this study with growth on both benzene and toluene were similar and fell within the range of values reported. Fig. 6. Effect of temperature on: (a) the specific decay rate, (b) the true growth yield, and (c) the half-saturation coefficient (COD basis) of P. putida F1 with toluene as the sole carbon and energy source.
which is consistent with the expected trend. But, the activation energy for l^ is applicable only in the temperature range of 15–30 C, whereas for b it is applicable uniformly up to 35 C. With the models of Topiwala and Sinclair or Mayo (extended Arrhenius models incorporating activation energy for thermal denaturation), it is reasonable to anticipate the coefficients Eb or E2 obtained from l^ versus temperature data to be correlated to the Arrhenius coefficient Ea obtained with b versus temperature data. However, the values Eb and E2 (950 kJ/mol) are about 11 times higher than the Ea value obtained with b. It is therefore likely that b and its temperature coefficients are not indicative of thermal denaturation. The Arrhenius or other temperature effect models discussed in this work cannot explain the effect of tem-
Fig. 7. Oxygen uptake data showing the effect of oxygen concentration on the growth rate of P. putida F1 grown on benzene.
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Fig. 10. Effect of oxygen concentration on the specific growth rate of B. pickettii PKO1 grown on toluene at 20 C. Fig. 8. Effect of oxygen concentration on the specific growth rate of P. putida F1 grown on benzene at 20 C.
PKO1) for instance. The latter strain was enriched from a contaminated soil microcosm under hypoxic conditions. When PKO1 was grown on different concentrations of oxygen in the presence of toluene (Fig. 10), it showed better affinity for oxygen than F1. This is apparent from the oxygen half-saturation coefficient determined for PKO1, i.e., 0.74 mg/l (compared to 1.1 mg/l for F1). Kukor and Olsen (1996) have already shown this qualitative difference between the strains by comparing the oxygen half-saturation values of the ring cleavage enzyme, extradiol C230, from both strains with catechol (a common intermediate) as the substrate. The half-saturation values for the whole cells determined in this work are much higher than those reported by the above mentioned authors, possibly due to the requirement for oxygen by the initial oxygenation step and other oxygen demanding activities. Fig. 9. Effect of oxygen concentration on the specific growth rate of P. putida F1 grown on toluene at 20 C.
Acknowledgements Understanding the dependence of specific growth rate on limited oxygen concentration is of relevance for the removal of contaminants from the subsurface environment. Where available oxygen does not get replenished at the rate at which it is utilized by various processes (chiefly biological), the concentration would decrease within a plume. Oxygen-restricted growth would result, and the oxygen utilization rate would depend on reoxygenation at the borders of the plume. Where oxygen dependent metabolism is the primary removal mechanism for a given contaminant, degraders with high affinity for oxygen (low half-saturation coefficient) will be selected in preference to those with lesser affinity. The validity of the above statement is apparent by comparing the oxygen half-saturation coefficients of P. putida F1 and B. pickettii PKO1 (formerly P. pickettii
The authors would like to thank the following people: Professors Gerben Zylstra (Rutgers), Ronald Olson (University of Michigan), and Jerome Kukor (Rutgers, formerly at University of Michigan) for supplying the pure culture toluene degrading bacteria; Professors David Kosson (Vanderbilt University, formerly at Rutgers) and Lily Young (Rutgers) for providing funding through their DARPA grant. Additional support was provided by the New Jersey Department of Environmental Protection, Division of Science and Research (Research Contract #48106000052), the New Jersey Agricultural Experiment Station (NJAES), and the US Department of Defense, Advanced Research Projects Agency, Office of Naval Research, University Research Initiative (Grant # N00014-92-J-1888, R&T Code a40r41ruri).
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Appendix A MicroMath Scientist Monod equation files for analyzing oxygen uptake data obtained from tests using toluene or benzene as their sole carbon and energy source //Respirometer kinetics for volatile organics (toluene)––Monod equation Independent variables: t (time) Dependent variables: O (oxygen uptake), l (specific growth rate) //Dependent variables: O, S, X , P , TS Parameters: lmax (maximum specific growth rate), X0 (initial biomass concentration on a COD basis), Ks (half-saturation coefficient on a COD basis), Yg (biomass growth yield, mg COD biomass produced/mg COD substrate consumed), b (decay coefficient) //all volumes are in liters Yp ¼ 0:05 (product yield) Vg ¼ 0:15 (headspace gas volume) Vl ¼ 0:45 (liquid volume) //H ¼ 0:191 (Henry’s coefficient at 15 C) H ¼ 0:23 (Henry’s coefficient at 20 C) //H ¼ 0:267 (Henry’s coefficient at 25 C) //H ¼ 0:33 (Henry’s coefficient at 30 C) //H ¼ 0:422 (Henry’s coefficient at 35 C) MW ¼ 92:13 (molecular weight) R ¼ 0:082 (gas constant) T ¼ 293:15 (temperature in Kelvin) f ¼ 3:13 (mass of oxygen required to oxidize a unit mass of the compound, g/g) Ho ¼ 0:73911 (Henry’s coefficient of oxygen) TS0 ¼ 100 (initial substrate concentration on a COD basis) //Differential equations TS 0 ¼ X lmax ðTS=ð1 þ H Vg =Vl ÞÞ =ððKs þ ðTS=ð1 þ H Vg =Vl ÞÞÞ Yg Þ X 0 ¼ ðk ðTS=ð1 þ H Vg =Vl ÞÞ =ðKs þ ðTS=ð1 þ H Vg =Vl ÞÞÞÞ X b X P 0 ¼ Yp TS 0 A ¼ ðVl =ð1 þ ðH Vg =Vl ÞÞÞ ð32=ðMW f ÞÞ C ¼ ðR T Vl Þ=ð1000 Vg Ho Þ O ¼ ððTS0 TSÞ ð1 þ ðA ð1 þ CÞÞÞÞ ðX X0 Þ ðP Þ S ¼ TS=ð1 þ H Vg =Vl Þ M ¼ TS 0 Yg =X //Parameter values and constraints lmax ¼ 0:43 Ks ¼ 8:3 Ks > 0 X0 ¼ 2:5
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Yg ¼ 0:71 b ¼ 0:057 //Initial conditions t¼0 P ¼0 TS ¼ TS0 X ¼ X0 //Respirometer kinetics for volatiles (Benzene)–– Monod equation Independent variables: t Dependent variables: O //Dependent variables: O, S, X , P , TS, b Parameters: X0 , Ks , K, b, Yg //all volumes are in liters Yp ¼ 0:05 Vg ¼ 0:2 Vl ¼ 0:40 //H ¼ 0:159 (Henry’s coefficient at 15 C) //H ¼ 0:19 (Henry’s coefficient at 20 C) H ¼ 0:224 (Henry’s coefficient at 25 C) //H ¼ 0:2784 (Henry’s coefficient at 30 C) //H ¼ 0:344 (Henry’s coefficient at 35 C) MW ¼ 78 (molecular weight) R ¼ 0:082 (Gas constant) T ¼ 298:15 (Temperature in K) f ¼ 3:076 (mass of oxygen required to oxidize a unit mass of the compound, g/g) Ho ¼ 0:73911 ((Henry’s coefficient of oxygen) TS0 ¼ 100 (initial substrate concentration on a COD basis) //Differential equations TS 0 ¼ X k ðTS=ð1 þ H Vg =Vl ÞÞ =ððKs þ ðTS=ð1 þ H Vg =Vl ÞÞÞ Yg Þ X 0 ¼ ðk ðTS=ð1 þ H Vg =Vl ÞÞ =ðKs þ ðTS=ð1 þ H Vg =Vl ÞÞÞÞ X b X P 0 ¼ Yp TS 0 A ¼ ðVl =ð1 þ ðH Vg =Vl ÞÞÞ ð32=ðMW f ÞÞ C ¼ ðR T Vl Þ=ð1000 Vg Ho Þ O ¼ ððTS0 TSÞ ð1 þ ðA ð1 þ CÞÞÞÞ ðX X0 Þ ðP Þ S ¼ TS=ð1 þ H Vg =Vl Þ M ¼ TS 0 Yg =X //Parameter values and constraints k ¼ 0:85 Ks ¼ 13 Ks > 0 X0 ¼ 2:5 Yg ¼ 0:5 b ¼ 0:05 //Initial conditions t¼0 P ¼0
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TS ¼ TS0 X ¼ X0
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