A Cometabolic Kinetics Model Incorporating Inhibition, Inactivation, and Recovery: II. Degradation Experiments

Roger L. Ely,' Michael R. Hyman? Daniel J. Arp? Ronald 6. G~enther,~and Kenneth J. Williamson'* Departments of 'Civil Engineering, 'Botany & Plant Pathology, and 3Mathematics Oregon State University, Corvallis, Oregon 9733 1 Received June 6, 7994lAccepted December 13, 1994

A cometabolism enzyme kinetics model has been pre- fects included assumptions requiring experimental verifica- sented which takes into account changes in bacterial ac- ti~n.~Among them was the assumption that, although in- tivity associated with enzyme inhibition, inactivation of hibition, inactivation, and recovery create an inherently enzyme resulting from product toxicity, and respondent synthesis of new enzyme. Although this process is inher- nonequilibriurn, unsteady-state condition, changes in en- ently unsteady-state, the model assumes that cometa- zyme levels, specifically changes in concentrations of en- bolic degradation of a compound exhibiting product tox- zyme/substrate complexes (ES, El, and ESZ), occur slowly icity can be modeled as pseudo-steady-state under cer- enough that the process may be modeled as pseudo-steady- tain conditions. In its simplified form, the model also state provided that enzyrnehbstrate associatiorddissocia- assumes that enzyme inactivation is directly proportional to nongrowth substrate oxidation, and that recovery is tion reactions are fast compared to the net rate of change of directly proportional to growth substrate oxidation. In enzyme quantities. Also, the amount of enzyme inactivated, part 1, model derivation, simplification, and analyses E', was assumed to equal some function, h, of the non- were described. In this article, model assumptions are growth substrate oxidized, P,; and the amount of new en- tested by analyzing data from experiments examining E,,,, trichloroethylene (TCE) degradation by the - zyme synthesized, in response to inactivation, was oxidizing bacterium europaea in a quasi- assumed to equal some function, g, of the growth substrate steady-state bioreactor. Model solution results showed oxidized, P,. In simplifying the model, it was assumed that TCE to be a competitive inhibitor of ammonia oxidation, h was equal to a constant fraction, f, representing the with TCE affinity for ammonia monooxygenase (AMO) amount of enzyme inactivated per nongrowth substrate ox- being about four times greater than that of ammonia for idized, that is, E' = jP2. It was assumed also that g was the enzyme. Inhibition was independent of TCE oxidation and occurred essentially instantly upon exposure to TCE. equal to a constant fraction, fs, representing the amount of In contrast, inactivation of AM0 occurred more gradually new enzyme synthesized, in response to inactivation, per and was proportional to the rate and amount of TCE ox- growth substrate oxidized, that is, En,, = fpl.Using these idized. Evaluation of other 0,-dependent and assumptions, equations were derived to describe cometa- electron transport proteins suggested that TCE-related damage was predominantly confined to AMO. In re- bolic transformation rates in general and rates of ammonia sponse to inhibition and/or inactivation, bacterial recov- and TCE oxidation by N. europaea in particular, in the ery was initiated, even in the presence of TCE, implying absence of significant cell growth or death. that membranes and protein synthesis systems were N. europaea are autotrophic, ammonia-oxidizing bacte- functioning. Analysis of data and comparison of model ria. Ammonia monooxygenase (AMO) catalyzes the reduc- results showed the inhibition/inactivation/recovery con- tion and insertion of an oxygen atom from molecular 0, cept to provide a reasonable basis for understanding the effects of TCE on AM0 function and bacterial response. into ammonia, oxidizing the ammonia to hydroxylamine. The model assumptions were verified except that ques- As indicated in Figure 1, oxidation of NH, to NH20H is a tions remain regarding the factors controlling recovery reductant-consuming step, requiring two electrons that must and its role in the long term. 0 1995 John Wiley & Sons, Inc. be supplied by the subsequent oxidation of hydroxylamine Key words: Nitrosomonas europaea ammonia oxida- to nitrite. l1 Two other electrons obtained in oxidizing hy- tion kinetics model trichloroethylene cometabolism TCE droxylamine to nitrite enter the electron transport chain, providing energy for cell growth and maintenan~e.~ INTRODUCTION AND BACKGROUND Many metabolic and phylogenetic similarities exist be- Derivation of a cometabolism enzyme kinetics model incor- tween ammonia-oxidizing and -oxidizing ba~teria,~ porating bacterial inhibition, inactivation, and recovery ef- but much more is known about the soluble and particulate methane monooxygenases (sMMO and pMMO) found in * To whom all correspondence should be addressed. methane-oxidizing than about AMO. AM0 is

Biotechnology and Bioengineering, Vol. 46, Pp. 232-245 (1995) 0 1995 John Wiley & Sons, Inc. CCC 0006-3592195lO30232-14 Quasi-Stead y- Sta te Reactor Experiments

N. europaea cells were grown axenically in batch cultures (1.5 L) as described previously. lS The growth medium con- sisted of 25 mM (NH4),SO4, 3 mM KH2P0,, 735 @I MgSO,, 200 pA4 CaCl,, 10 @I FeSO,, 17 @I EDTA, 0.7 To Electron pA4 CuSO,, and 0.04% (wt/vol) Na2C03, and was buffered 2 e- Transport Chain with a phosphate solution (pH 8.0) to final concentrations of 43 mM potassium phosphate and 4 mM sodium phosphate. Figure l. Reactions catalyzed by N, europaea in converting ammonia to Cells were harvested by centrifugation at or near the end of nitrite. AM0 is ammonia monooxygenase. HA0 is hydroxylamine oxi- doreductase. the log-growth phase 3 days after inoculation; washed with 500 mL of solution containing 80 mM phosphate and 100 mM carbonate buffers (pH 7.8); centrifuged again; and re- membrane bound as is pMMO, and its substrate is thought suspended in 500 mL of the same phosphateicarbonate so- to be NH, rather than NH: .24 AM0 catalyzes the insertion lution, except that 80 mM phosphate and 50 mM HEPES of from 1802into NH, to produce NH,'80H." In buffer (pH 7.8) were used in experiments 6 through 9. Cell addition, it catalyzes the oxidation of many nongrowth suspensions were sealed within the reactor vessel and used substrates such as methane and other n- (to c,), immediately after harvesting. n-alkenes (to C,), aromatics, and halogenated hydrocar- The reactor vessel (Wheaton Double-Sidearm Cellstir) bons, including TCE.4,6,'4,'6"'7.'9.22,27Whereas evidence had a total volume of 1.67 L comprised of 0.5 L of liquid suggests considerable similarity between AM0 and (the cell suspension) and 1.17 L of headspace (see Fig. 1). p~~~,12,13,18,21,2S,26 . its ability to catalyze the oxidation The top of the reactor was sealed with a Teflon-lined, gas- of aromatic hydrocarbons and straight-chain alkanes above keted cap. The two upper reactor sidearms were sealed with C, indicates that, catalytically, AM0 may be more similar screw-cap, septum vial caps fitted with Teflon-gasketed to sMMO than to the less versatile pMMO system. Mininert valves, and the lower sidearm was sealed with a N. europaea were used in this study for four major rea- hypo-vial Mininert valve (Supelco). Silicone septa in the sons: (1) Nitrifying bacteria are particularly attractive for in Mininert valves were replaced immediately prior to each situ processes because they are ubiquitously experiment. Turbulent mixing of the reactor liquid, with present in natural environments and their activity can be extreme vortexing and air entrainment, was provided by a stimulated by adding ammonia and oxygen; (2) substrate Teflon-coated, 3-in. magnetic stirring bar operated at high utilization and other laboratory experiments may be con- speed by a magnetic stirrer. ducted with them under a variety of conditions without sig- This mixing method, selected after conducting gas-liquid nificant changes in cell concentrations because they grow mass transfer evaluations of several mixer and baffle con- slowly (generation time of about 8 h); (3) inherent compli- figurations, accomplished complete gas-liquid equilibrium cations of interpreting results from mixed culture experi- in less than 2 min after a pulse injection of carbon tetra- ments can be avoided because methods and techniques have chloride (CT) into the reactor (data not shown). This indi- been developed for maintaining and employing pure cul- cates that, while a brief time period was necessary to tures of this species under laboratory conditions; and (4) achieve equilibrium after a pulse addition of volatile com- they may function as a model for other monooxygenase- pound, gas-liquid mass transfer retardation effects were not and dioxygenase-utilizing bacteria. The goals of this re- significant during the much slower process of TCE degra- search were: (1) to distinguish and quantify the processes dation. A syringe pump arrangement delivered, at a con- affecting bacterial activity during TCE cometabolism in the stant rate, a solution containing ammonium sulfate in 80 absence of significant cell growth or death; (2) to determine mM phosphate/100 mM carbonate buffer (pH 7.8). The sy- the kinetics of TCE degradation by ammonia-oxidizing bac- ringe pump contained a lO-mL, gas-tight, her-lock, glass teria; (3) to investigate conditions potentially conducive to syringe fitted with a stainless-steel hypodermic needle (22- sustainable cometabolic TCE oxidation; and (4) to evaluate gauge by 12 in.). All experiments were conducted at am- the model (and the assumptions included in it) under various bient temperature (about 22°C). experimental conditions of TCE degradation by ammonia- Initial samples were collected as described below, after oxidizing bacteria. which experiments were initiated by inserting the ammonia solution feed needle, turning on the syringe pump, and EXPERIMENTAL SECTION manually injecting an initial pulse of ammonium sulfate/ buffer solution. By feeding ammonia at rates less than the maximum oxidation rate, stable nitrite production and 0, Model Equations uptake rates were attained after about 60 to 90 min. Begin- For the particular experimental system used in this study, ning at r = 90 min (i.e., 90 min after initiating an exper- model equations were obtained from the general model as iment), nitrite concentration and 0, uptake rate measure- described elsewhere.' ments were taken at 15-min intervals. After verifying

ELY ET AL: COMETABOLISM MODEL, PART II 233 steady-state conditions for another 40 to 50 min, CT was ary phase, 15 m X 0.53 mm, Catalog #16851) and was injected into the system to a liquid concentration of about 1 operated isothermally at 50°C with a carrier gas ppm. CT at this concentration was determined not to inhibit flow of 3.5 mL/min. Detection was by flame ionization. ammonia oxidation significantly (data not shown). Because CT is more volatile and more diffusive than TCE, it served as a conservative, volatile tracer to indicate the absence or Hydroxylamine Oxidoreductase Activity Experiments presence of reactor leaks. (No leakage was detected in any experiments.) Also, CT could be used essentially as an It was important to evaluate whether decreases in culture internal standard in the reactor. activity were attributable to changes in specific activity, that The system was monitored for an additional 30 min to is, to partial loss of AM0 activity within live cells, as confirm that the steady-state condition had not been upset represented in the model, or to partial death of the culture. by the CT addition, at which time a pulse of TCE was Because N. europaea do not grow particularly well, espe- injected (r = 170 rnin). Nitrite concentration and 0, uptake cially on plates, and presumably would be even less likely rate measurements continued at 15-min intervals and TCE to grow when stressed or injured, ability to grow could not and CT concentrations were monitored at 5- to 10-min in- be used as a reliable indicator of whether the cells were dead tervals for the balance of the experiment (70 or 85 min). or alive. Instead, cell viability was evaluated by examining Experiments were conducted for a total time of either 240 or the integrity of 0,-dependent electron transport proteins 255 min. Final pH measurements were taken immediately (other than AMO) before and after partial culture inactiva- after experiments were concluded. This experimental ap- tion by exposure to TCE. The reasoning for this approach proach allowed examination of: (1) ammonia oxidation ki- was as follows. Although it has not yet been purified or netics in the absence of TCE; (2) immediate and developing fully characterized, it is known that AM0 is a membrane- TCE effects on culture activity in real time; and (3) TCE bound protein, that substrate (hydroxylamine) must pass degradation kinetics in the presence of ammonia. from AM0 to HAO, that electrons must pass back from Initial reactor liquid samples consisted of a 10-mL sam- HA0 to AMO, and that no energy is gained by the cell in ple of the cell suspension for protein analysis and a 3-mL transferring these electrons (Fig. 1). Therefore, it seems sample for initial nitrite concentration and initial 0, uptake probable that AM0 and HA0 (which is located in the rate measurements. Protein content was determined using periplasm) are closely associated in the cell, perhaps near the Biuret assay procedure’ after solubilizing the cells in 3 the periplasmic surface of the cell membrane, and perhaps M NaOH for 60 rnin at 60°C. (Protein analyses were con- even as a complex of some sort. Because of its likely prox- ducted at the conclusion of several experiments as well, to imity to AM0 and its relatively large size (200 kDa), it also confirm that significant cell growth did not occur during seems probable that, if a reactive, short-lived product of experiments. Protein measurements were not used to assess TCE oxidation were to diffuse away from the AM0 active cell viability. Cell viability, i.e., the extent of TCE-related site and cause damage to other cellular constituents, HA0 cellular injury, was evaluated by examining the integrity of would be a likely target. The integrity of HA0 (and other the electron transport chain, as will be discussed more fully HAO-dependent electron transport proteins to the terminal below.) Of the 3-mL sample, 1 mL was microcentrifuged electron acceptor) can be evaluated by blocking AM0 ac- for 2 min to remove the cells, after which triplicate aliquots tivity, providing an alternative HA0 substrate, and measur- of the supernatant were analyzed colorometrically for nitrite ing HAO-dependent activity. If HAO-dependent activity re- concentration. lo The remaining 2 mL were injected directly mains essentially unchanged after culture exposure to TCE into the evacuated 1.8-mL chamber of an 0, electrode ap- (and our reasoning is correct), this suggests insignificant paratus consisting of a water-jacketed glass cell (Gilson damage to HAO-dependent components, which in turn im- Medical Electronics, Inc.) fitted with a Clark electrode plies confinement of TCE-associated damage primarily to (Yellow Springs Instrument Co.) for 0, uptake rate mea- AM0 components, and continued viability of the cells. surement. 0, uptake rate measurements were made at 30°C To examine HAO-dependent activity before and after using the cell suspension and buffer solution as taken di- culture exposure to TCE, some 0, uptake rate measure- rectly from the reactor. All reactor liquid samples (3 mL ments were modified by providing hydrazine as an alterna- each) were removed from the reactor via the lower sidearm tive reductant after specifically blocking AM0 activity with using a syringe with a hypodermic needle inserted through ally1 thiourea (ATU), as described previo~sly.~~Reactor the Mininert valve and were analyzed likewise for nitrite cell suspension samples (2 mL) were placed into the 0, concentration and 0, uptake rate. Immediately after remov- electrode and 2 to 3 minutes were allowed for a determina- ing samples, fresh buffer solution was injected into the re- tion of ammonia-dependent 0, uptake rates. ATU then was actor to replace the volume removed. Reactor headspace added to a concentration of 100 pA4 to inhibit ammonia- samples (200 pL) were collected through an upper sidearm dependent 0, uptake, after which hydrazine was added as using a glass, gas-tight Hamilton syringe (500 kL) and an alternative HA0 substrate to a concentration of 750 pA4 injected directly into a gas chromatograph for analysis of and hydrazine-dependent 0, uptake rates were determined. CT and TCE. The chromatograph (Hewlett Packard Model In this manner, the effects of TCE on hydrazine-dependent 5830A with 18850A integrator) contained a capillary col- oxidation activity were evaluated as ammonia oxidation was umn (Alltech, 5 pm RSL 160 polydimethylsiloxane station- progressively inactivated by TCE in the reactor.

234 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 46, NO. 3, MAY 5, 1995 Figure 2. Experimental setup for conducting quasi-steady-state reactor experiments.

0, Electrode Experiments very sensitive to minor errors in nitrite concentration mea- Separate experiments were conducted in the 0, electrode to surements, especially when nitrite concentrations were high determine the rapidity with which cell metabolism was ef- or after TCE inactivation when changes in nitrite concen- fected by exposure to low concentrations of TCE. In these tration over a time interval were small. Therefore, calcu- experiments, 2-mL cell suspension samples, functioning at lated nitrite production rates were much more variable and quasi-steady-state and not previously exposed to TCE, were less reliable than the directly measured 0, uptake rates. To taken from the reactor and injected into the 0, electrode as counter this difficulty, all data analysis, curve fitting, and described above. After allowing about 3 to 4 minutes to modeling used directly measured 0, uptake rates which define initial 0, uptake rates, various amounts of TCE were were converted to nitrite production rates according to mea- injected and immediate changes in 0, uptake rates were sured O,-to-NO, stoichiometry . (Average observed 0,-to- assessed. NO, stoichiometry was 1.63 ? 0.15 for all experiments, close to the theoretical value of 1.5.) This method allowed 0, uptake rate to serve as a reliable, surrogate parameter for Model Solution and Estimation of Parameters nitrite production rate and provided an independent, rapid Three curves of experimental data were produced in each indication of bacterial activity. Estimated 0, uptake asso- experiment; nitrite concentration, TCE concentration, and ciated with TCE oxidation was included in all calculations; ammonia-dependent 0, uptake activity versus time. Using however, it was insignificant, amounting to on the order of known initial conditions and Eqs. (37) and (38) from part 1% of the total O2 uptake, as indicated by the reaction rates ratio, 8.7 1 ,7 a time-step analysis was performed for each experiment to obtain fitted model curves and estimated parameter val- To fit the model curves by minimizing x2 as described ues as described previ~usly.~ previ~usly,~data variances were estimated as follows. Be- Except for Km, which was constrained to 40 pM * lo%, cause nitrite concentration measurements were done in trip- confidence limits (see Table 11) were determined for each licate, a variance could be calculated for each nitrite data parameter in all experiments. Using the Solver optimization point. Nitrite concentration coefficients of variation were routine in Excel, each parameter, in turn, was perturbed, generally in the 1% to 2% range. 0, uptake rate variances that is, increased or decreased, away from its optimum were estimated from deviations about the mean, quasi- value and held there while the other parameters were ad- steady-state (i.e., pre-TCE), oxygen uptake rate. An 0, rate justed to obtain a new “minimum” x2 (larger than the coefficient of variation of about 2% was found to be typical optimum x2). Using this approach, and assuming that data and was used to calculate the 0, x2 in all experiments. TCE errors are normally distributed, statistical significance is variances were assumed comparable to variances in CT indicated by the amount of increase in x2 caused by pertur- data, which were estimated from the deviations about the mean CT level in the reactor. TCE coefficients of variation bation of one of the parameters.20 A Ax2 2 1 is statistically significant and marks the 68% (one standard deviation; one averaged about 8%. degree of freedom) confidence interval of the parameter. In RESULTS these experiments, 95% confidence intervals were deter- mined, corresponding to a Ax2 of 3.843. Quasi-Steady-State Reactor Experiments Nitrite production rates calculated from changes in mea- Multiple experiments were conducted without TCE to as- sured cumulative nitrite concentrations were found to be certain baseline performance characteristics of the system,

ELY ET AL: COMETABOLISM MODEL, PART It 235 Table I. Experimental conditions."

Calculated quasi-steady-state NH, feed Specific Exp. no. NH3 rate Biomass activity Initial TCE

0 14.4 25.3 82.7 0.29 0 1 28.5 24.1 65.8 0.31 25.3 2 41.4 24.4 57.8 0.28 16.8 3 21.8 24.5 67.3 0.33 8.4 4 23.4 47.6 154.7 0.29 5.6 5 39.8 48.3 75.6 0.54 21.4 6 33.3 49.0 152.4 0.29 6.0 7 9.9 42.0 164.6 0.23 15.5 8 12.8 42.8 189.1 0.20 26.8 9 15.0 42.5 178.8 0.20 14.3 10 13.9 25.5 93.8 0.26 4.5 11 15.0 25.3 90.2 0.27 7.1 12 24.9 25.3 88.4 0.28 8.2 13 18.0 25.3 78.5 0.31 6.3

"Units: calculated NH,, pM; NH, feed rate, pM/min; biomass, mg proteinil; specific activity, pmol NoTimin . mg protein; initial TCE, pM. and 13 TCE degradation experiments were conducted in the 4a and prior to TCE injection in 4b and 4c. In addition, the reactor over a time period of a few months. Experimental relatively slight effect on nitrite production rate of a low conditions for the experiments with TCE and one represen- TCE exposure (Fig. 4b) and the much greater effect caused tative experiment without TCE are shown in Table 1. Rep- by a higher TCE exposure (Fig. 4c) are obvious. Activity resentative nitrite concentration data and best-fit model was reduced to near zero in experiment 7, while less than curves obtained under different conditions are presented in 50% of culture activity was lost in experiment 11. This Figure 3, along with calculated ammonia curves. (Ammo- figure also illustrates the much greater error in the calcu- nia concentrations were not measured directly. Because N. lated NO,- production rates, as discussed above. In the europaea stoichiometrically convert ammonia to nitrite un- interests of clarity and simplicity, nitrite production rates der oxygen-sufficient conditions and the experiments were are not shown in subsequent figures. designed to ensure oxygen excess at all times, ammonia Figure 5 (experiment 8) accents the real-time effects of oxidation was estimated reliably from nitrite production.) the two distinct activity-decreasing mechanisms-inhibition In Figure 3a (experiment 0), it is evident that nitrite ac- and inactivation4n ammonia-oxidizing activity (Fig. 5a) cumulated at a uniform rate, verifying the quasi-steady-state and on TCE degradation (Fig. 5b). In Figure 5a, a large ammonia oxidation condition over the 4-h experimental pe- decrease in ammonia-oxidizing activity is evident immedi- riod. Because ammonia concentration was calculated by ately after TCE injection (labeled as "Initial Activity difference, the flat ammonia curve suggests that the nitro- Loss"). Occurring too rapidly to be associated with TCE gen mass balance was acceptable, that is, essentially all oxidation, this initial drop in activity results from TCE in- injected ammonia was accounted for in produced nitrite. hibition of ammonia oxidation. (The model assumes inhi- Addition of a relatively small amount of TCE (experiment bition is instantaneous upon injection of TCE. This will be 1 1,7.1 pA4 initial TCE) caused the nitrite production rate to discussed further below .) Beyond this, the progressive in- decrease slightly, as indicated by the difference in slopes of activation of AM0 causes reductions in ammonia-oxidizing the model lines in Figure 3b before and after TCE addition. activity both directly and indirectly. As TCE is oxidized, Since ammonia addition continued at a constant rate inactivation decreases the pool of active enzyme, directly throughout the experiment, Figure 3b also indicates a grad- decreasing both ammonia and TCE oxidation rates. More- ual increase in ammonia concentration within the reactor, over, decreased TCE oxidation rates cause TCE concentra- caused by the decreased ammonia oxidation rate. When tions to remain higher for longer periods of time, indirectly significantly more TCE was injected (experiment 7, 15.5 reducing ammonia oxidation rates by prolonging inhibitory pMinitial TCE), the nitrite production rate decreased much effects. These features can be seen clearly in Figure 5. more drastically (Fig. 3c). The figure shows ammonia to Without TCE inactivation of AMO, i.e., including only accumulate at a greater rate as well. inhibition effects, the dashed curve in Figure 5b (the model The effects of TCE exposure on rates of nitrite produc- curve with inactivation and recovery excluded) indicates tion, that is, culture activity, are illustrated in Figure 4 for that essentially all of the TCE would be transformed in the same experiments depicted in Figure 3. Comparison of about 80 min. In contrast, with AM0 inactivation by TCE, data points and best-fit model curves before and after TCE only about half of the TCE is transformed in the same time injection shows relative decreases in ammonia-oxidizing ac- period, causing TCE to persist at higher concentrations. tivity. The quasi-steady-state condition is apparent in Figure Similarly, the dashed curve in Figure 5a also indicates hy-

236 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 46, NO. 3, MAY 5, 1995 0.04 ,

Calculated Ammonia I la) GFE- ] I 0.00 61 I I 0.04 r I I I

0.03

0.02

0.01 I

01 I I 0.00 I I

Inject TCE

Calculated NOt Rate

,Observed O2Rate

______-

0 I 0.00 I 90 110 130 150 170 190 210 230 2.50 90 110 130 150 170 190 210 230 2.50 Time, min Time, min Figure 3. Measured nitrite concentrations (+) versus time (minutes) Figure 4. Calculated nitrite production rates (+) and nitrite production during representative experiments. Part (a) is from experiment 0 (no TCE rates estimated from observed 0, uptake rates (0)( as described in the text) added); (b) is from experiment 11 (7.1 pkf [930 ppb] initial TCE); and part versus time (minutes). (a) From Experiment 0 (no TCE added); (b) from (c) is from experiment 7 (15.5 pkf [2.0 ppm] initial TCE). TCE was experiment 11 (7.1 pkf [930 ppb] initial TCE); and (c) from experiment 7 injected at t = 170 min. Solid lines are fitted model curves. Dashed lines (15.5 pJ4 [2.0 ppm] initial TCE). TCE was injected at t = 170 minutes. indicate calculated total ammonia concentration. Solid lines are best-fit model curves. pothetical culture activity in the absence of inactivation and recovery (and in the absence of cell growth or death), i.e., may be seen semiquantitatively by comparing culture activ- at constant cellular enzyme level. Clearly, as TCE would be ities at the times, with and without inactivation, when the oxidized more rapidly if AM0 was not inactivated, inhibi- residual TCE concentration is about 12 pM. Without inac- tion would subside, enzyme levels would not diminish, and tivation, this concentration occurs at about t = 200 min, culture activity would rebound relatively quickly. However, and the culture ammonia-oxidizing activity is about 0.018 with inactivation, inhibition is prolonged and ongoing loss mMlmin, about 0.020 mMlmin less than the 0.038 mMlmin of AM0 causes a continuing activity decline. (Because am- pre-TCE rate. With inactivation, 12 pA4 of TCE is not monia would accumulate during periods of decreased activ- reached until about t = 255 min, and the culture activity is ity, the dashed curve shows that culture activity would ex- about 0.004 mMlmin, about 0.034 mMlmin less than the ceed the pre-TCE steady-state rate for a period of time.) pre-TCE rate. Therefore, the wide divergence between the dashed and If ammonia concentrations are assumed to be equal in the solid curves in Figure 5a results both from direct losses of two cases, the amounts of activity loss attributable to inhi- activity caused by enzyme inactivation and from indirect bition would be equal (because TCE concentrations are activity decreases caused by sustained inhibition from lower equal). This suggests that, for the case with inactivation, TCE oxidation rates. roughly 0.020 mMlmin of the 0.034 dlminactivity loss is It may be inferred from Figure 5a that inhibition reduces associated with inhibition and the balance (0.014 mMlmin) ammonia-oxidizing activity more severely, at least in the results from enzyme inactivation. Therefore, under the con- short term, than does inactivation. However, by causing ditions of this experiment, nearly half of the activity loss is damage to AM0 and thus hindering the ability of the bac- attributable to enzyme inactivation some 85 min after in- teria to regain activity as the TCE concentration decreases jection of TCE. Obviously, the ammonia concentration will and inhibition subsides, inactivation may become more crit- be higher in the second case because ammonia will have ical in the long term. For experiment 8 (Fig. 5), this effect been accumulating for a longer period of time. Therefore,

ELY ET AL: COMETABOLISM MODEL, PART II 237 0.05 a) Nitrite Production Inject TCE -- A

0.04 ,’ Continuing C 3J Initial ALtivity Loss /’ Activity .- am 0.02 //Decline , s 0.03 0.01 , E J 0.00 I3 0.02

0.01

0

16 TCE ( itration

14 1 cj Experiment #9 p&Ezr 12 5t . . ?i 1 04 -- c^ 10 0 90 110 130 150 170 190 210 230 250 .-3

328 Time, min c . Ohserved model - - - Without Inactivation or Recovery s86 Figure 5. Nitrite production rates (estimated from observed 0, uptake rates as described in the text) and residual TCE concentrations versus time 2 for experiment 8 (26.8 pit4 [3.5 ppm] initial was injected at t TCE).TCE 0 = 170 min. Solid lines are best-fit model curves. Dashed lines indicate 170 190 210 230 250 170 190 210 230 250 hypothetical system behavior in the absence of inactivation (and recovery) Time, min effects. Model With Model Wilhvut Rdtc Before *Ob*erved - ____ -- Reiovery Recovery TCE lnlecriun inhibition should actually comprise less, and inactivation Figure 6. Nitrite production rates (estimated from observed 0, uptake rates as described in the text) and residual TCE concentrations versus time correspondingly more, of the total activity loss than was for experiment 9 (14.3 pM [1.9 ppm] initial TCE) and experiment 4 (5.6 estimated in this brief example. The relative importance of pM [740 ppb] initial TCE).TCE was injected at t = 170 min. Solid lines the two, activity-decreasing mechanisms will depend on a are best-fit model curves. Heavy dashed lines indicate culture activity prior number of factors including ammonia and TCE concentra- to TCE injection. Light dashed lines indicate hypothetical system behavior tions, amount and rate of TCE oxidation, and the ability of in the absence of recovery effects, that is, with the recovery rate constant set equal to zero. the cells to recover. Because the model curves (solid lines) in Figure 5 include recovery effects (the dashed curves do not), they do not represent the worst case scenario, that is, Because all parameters were held constant in the dashed a situation with no cellular recovery. curves in Figure 6, the dashed curves do not represent The real-time effects of cellular recovery on ammonia- model solutions, that is, best-fit curves. Therefore, a ques- oxidizing activity and TCE degradation are indicated in Fig- tion remains regarding how well the model curves can be ure 6. Experiment 9 had a moderate initial TCE concentra- made to fit the data if recovery is excluded from the model. tion (14.3 pM) while experiment 4 had much lower initial For experiment 9, Figure 7 illustrates that, if recovery is TCE (5.6 pM). In Figure 6a, without recovery (the dashed excluded while optimizing the remaining parameters to curve, obtained by setting the recovery rate constant at zero solve the model and minimize x2, a noticeable deterioration while holding all other model parameters constant), the de- in the quality of the curve fits results. As mentioned previ- cline in ammonia-oxidizing activity caused by AM0 inac- ously 1,’ this deterioration in the curve fits may be inter- tivation is much more severe, and departure from the ob- preted statistically by the magnitude of the change in x2. As served culture behavior (i.e., with recovery) increases sig- indicated in Table 11, recovery was detected in 10 of the 12 nificantly with time. At the same time, because recovery experiments in which recovery was possible. (Recovery serves to increase the pool of active enzyme, significantly was prevented in experiment 10 because rifampicin was more TCE is transformed over the time period than would present [lo0 mg/L] to block protein synthesis.) When re- be without recovery (Fig. 6c). These effects can be seen in covery was excluded while solving the model for the ten Figure 6b and d also, but they are less obvious, especially experiments in which recovery had been detected, eight of for the TCE data, This may be because the initial TCE the ten showed a statistically significant deterioration in concentration was low enough that it would nearly all de- model goodness-of-fit (data not shown), with statistical sig- grade either with or without recovery. nificance defined by Ax2 3 1.0.20

238 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 46, NO. 3, MAY 5, 1995 Because little energy is available to N. europaea from am- monia oxidation when metabolic activity is severely ham- pered, the former possibility seems more likely.

0, Electrode Experiments

Because 10 min elapsed between TCE injection and the first measurements of post-TCE nitrite concentration and 0, up- take rate, the development of TCE-related effects in the . 16 - -- ! TCE Concentration -~ reactor during this time period was not directly assessable. i To evaluate the immediate response of the bacteria to TCE 1 c) Best Fit with' Best Fa wllhout] ~ exposure, that is, to confirm that the large initial drop in 12 , Recovery ~ d) E 1 1 Recovery ~ ~~ ~ , l4 4 activity was due to inhibition of AM0 as earlier stated, several separate evaluations were conducted in which TCE was added to cell suspensions in the 0, electrode apparatus. If the initial activity drop was caused by inhibition, 0, uptake rate curves would be expected to show a nearly I! instantaneous slope change, with slight curvature in the 0 I I IJI - ,I graph thereafter as oxidation of TCE led to ongoing activity 170 190 210 230 250 170 190 210 230 250 loss. Alternatively, if the initial drop was caused by a large Time, min amount of TCE oxidation and concurrent enzyme inactiva- Be\tFilModel - Rate Before tion over the time period, the 0, electrode output would be *Ob\ervrd - - Curve TCE Injection expected to show a curvilinear and more gradually devel- Figure 7. Nitrite production rates (estimated from observed 0, uptake oping decrease in activity as TCE was oxidized. rates as described in the text) and residual TCE concentrations versus time Results from these experiments showed that, prior to for experiment 9 (14.3 pM[ 1.9 ppm] initial TCE. Panels (a) and (c) show TCE injection, 0, concentration decreased steadily with best-fit model curves with recovery included in the model; panels (b) and time, indicating a constant 0, uptake rate (data not shown). (d) show best-fit model curves with recovery excluded from the model. 0, Heavy dashed lines indicate culture activity prior to TCE injection. When TCE was injected into the electrode chamber, a change in 0, uptake rate occurred so quickly that no lag could be detected within the response time of the instrument Hydroxylamine Oxidoreductase (less than a second). In experiments having a relatively low Activity Experiments initial TCE concentration (about 500 ppb), curvature of the graph over a time period of 3 to 4 minutes after TCE in- As mentioned previously, the model implicitly assumes that jection was so slight as to be barely detectable, indicating changes in activity are attributable solely to TCE-related very slow activity loss resulting from TCE oxidation. In damage to AM0 components. To evaluate the validity of experiments with higher TCE concentrations (up to about this assumption, it was necessary to determine whether the 3.2 ppm in these experiments), more curvature was appar- consequences of TCE exposure were localized, that is, con- ent in the graphs, presumably due to higher rates of inac- fined to AM0 components, or more general, involving tivation with higher rates of TCE oxidation at higher TCE other 0,-dependent enzymes and/or electron transfer pro- concentrations. Therefore, these experiments verified that teins. For this reason, hydrazine-dependent 0, uptake rates inhibition of AMO, rather than inactivation, was the pre- were measured in some experiments along with ammonia- dominate cause of the large initial drop in ammonia- dependent 0, uptake, as described in the Experimental sec- oxidizing activity observed in the reactor experiments, and tion. Several measurements were performed in experiments that it occurred nearly instantaneously as assumed in the 1 and 2, and several other experiments were spot-checked model. for verification. Although the initial TCE concentrations in experiments 1 and 2 were relatively high (25.3 and 16.8 pM, respectively), Figure 8 indicates that HAO-dependent Model Solution and Parameter Estimates activity, as indicated by hydrazine-dependent 0, uptake rates, did not decrease significantly even with severe loss of As shown in Table I, initial TCE liquid-phase concentra- ammonia-dependent activity. Therefore, under the condi- tions varied from 4.5 pM (590 ppb) to 26.8 pM (3.5 ppm), tions of these experiments, TCE-related cellular damage while quasi-steady-state specific activities (prior to TCE appeared to be limited predominantly to AM0 components, injection) ranged from 0.20 to 0.54 Fmol NH,/min mg as assumed in the model. Either significant damage to other protein, and biomass levels varied from 57.8 to 189 mg enzymes and electron transfer proteins did not occur, or it proteidl. Quasi-steady-state ammonia concentrations (as was repaired or otherwise compensated for as it occurred. NH,) were calculated to range from 9.9 to 41.4 pM. Be-

ELY ET AL: COMETABOLISM MODEL, PART II 239 Table 11. Summary of parameter estimates for the AMOINH,/TCE system (numbers in parentheses are 95% confidence limits).

Exp. no. K," k KI kI kinact k,,, x2 Q-statistic

1 36 0.72 16.2 17.4 0.045 0.24 24.12 0.151 (0.7C-0.82) (12.5-23.1) (13.1-30.2) (0.032-0.073) (-0.35-0.95) 2 44 0.62 9.3 9.6 0.088 0.68 10.34 0.920 (0.55-0.63) (7.2- 12.6) (7 .C- 16.6) (0.045-0.145) (-0.30-1.56) 3 36 0.89 15.9 18.4 0.052 0.00 10.11 0.985 (0.87-1.03) ( 12.2-22.9) ( 14,625.7) (0.048-0.074) ( - 0.15-0.14) 4 36 0.75 26.5 18.6 0.062 0.04 19.65 0.808 (0.73-0.87) ( 12.9-49.5) (9.630.2) (0.0500.086) ( - 0.02-0.09) 5 36 1.02 10.0 18.2 0.064 0.36 72.45 0.000 ( 1.OC- 1.15) (7.2-1 5.4) (14.1-26.1) (0.044-0.08 8) (- 0.09-0.78) 6 36 0.61 4.8 6.4 0.039 0.00 43.24 0.006 (0.60-0.69) (3.7-6.8) (5.4-8.4) (0.035-0.050) (-0.03-0.03) 7 36 1.07 4.7 5.8 0.087 0.55 48.23 0.002 (1.05-1.29) (3.4-7.1) (4.7- 10.4) (0.073-0.116) (0.14-1.01) 8 44 0.88 4.8 5.1 0.043 0.49 20.47 0.722 (0.74-0.89) (3.2-6.7) (4.1-8.9) (0.028-0.054) (-0.361.09) 9 44 0.80 14.3 7.7 0.074 0.37 56.58 0.002 (0.69-0.82) (9.9-22.1) (5.8-1 3.7) (0.0544.084) (0.19-0.50) lob 36 0.94 6.5 5.6 0.109 0.00 20.06 0.789 (0.91-1.12) (5.2-9 .O) (4.67.2) (0.1024.152) (-0.18-0.11) 11 36 0.92 10.4 9.6 0.070 0.06 41.47 0.028 (0.89-1.10) (7.8-16.1) (7.4- 16.7) (0.059-0.109) ( - 0.15-0.27) 12 36 0.68 5.2 8.4 0.070 0.21 29.98 0.225 (0.660.79) (3.2-9.0) (6.3-1 8.5) (0.052-0.100) ( - 0.08-0.54) 13 36 0.93 11.0 12.6 0.092 0.17 30.39 0.252 (0.90 L-l .10 T, (6.8"23.1 ') (8.7 L-30.3 ' ) (0.066 T-O. 135 ') (-0.02' -0.40 ') Mean - 0.83 10.7 11.0 0.069 0.26 32.85 0.376 SD - 0.15 6.3 5.3 0.021 0.23 cv - 18.0% 58.9% 48.5% 30.6% 86.2% Excluding highest and lowest data points Mean 0.83 9.8 10.9 0.068 0.25 31.32 0.355 SD 0.13 4.3 5.0 0.017 0.19 cv 15.2% 43.5% 45.8% 24.7% 76.3%

Units: K,, pM; k, pmol NO;/min . mg protein; KI, pM; k,, nmol TCEimin . mg protein; k,,,,,, pmol NO, . Lipmol TCE . min . mg protein; k,,, pmol NO; . L/mmol NO; . min . mg protein. Value used in generating lower curve in Figure 9a and c; upper curve in Figure 9b. Value used in generating upper curve in Figure 9a and c; lower curve in Figure 9b. aValues were constrained as described in the text. bExperiment conducted with rifampicin present to block protein synthesis. cause typical K,,, and k values for N. europaea have been fidence limits for K12 ranged from 1.7 to 22.7 p,A4 (mean reported to be about 40 p,A416,24 and 0.7 to 1.7 kmol/ and standard deviation of 9.2 k 6.6 W), indicating that min * mg pr~tein,~respectively, these values indicate that some noncompetitive inhibition may occur as well (data not culture activities were in general agreement with literature shown), but inhibition of AM0 by TCE is much more values and that bioreactor operating points ranged from strongly competitive than noncompetitive in nature. slightly above K,,, to about one-fourth K,,,. Estimated parameter values and 95% confidence intervals Because only five of the six model parameters are inde- for all experiments are shown in Table I1 and example en dent,^ model solution was constrained to help the pro- model curves generated from the confidence limits for ex- gram locate optimum solutions. In all optimization runs, K,,, periment 13 are shown in Figure 9. The parameter values was constrained to 40 p,A4 2 10%;all other parameters were used to generate the curves in Figure 9 are indicated in required to be greater than zero. With K,,, constrained in this Table 11. (The curves do not represent 95% confidence lim- way, a unique solution was found for each experiment, its for the model. They are meant to indicate model varia- regardless of initial estimated parameter values. Preliminary tion and reasonable boundaries of expected outcomes with optimization results showed K,, estimates to be extremely reasonable and physically possible combinations of param- large, even into the hundreds of thousands, indicating TCE eters.) Table I1 also indicates the minimum x2 and the to be a competitive inhibitor of ammonia oxidation. There- @statistic, a value used to indicate model goodness-of-fit. fore, KI, was eliminated from further consideration and K,, Q may vary from 0 to 1, with a value of 1.0 indicating was identified in modeling results as K,. Lower 95% con- perfect fit; that is, all error between model curves and ob-

240 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 46, NO. 3, MAY 5, 1995 o.04 - - Inject TCE r- __------.-- - --+-->---I------I

nl -- i - t if 11 I I 0 20 40 60 80 I00 120 140 160 180 200 220 240 Time, min

+AM0 +HA0

Figure 8. Measured AMO-dependent (+) and HAO-dependent (0) 0, uptake rates versus time. (a) From experiment 1 (25.3 pM[3.3 ppm] initial 1 TCE); (b) from experiment 2 (16.8 pM [2.2 ppm] initial TCE). TCE was 0.00 I injected at t = 170 min. Lines connect data points. 90 110 130 150 170 190 210 230 Time, min

Figure 9. Representative plots showing high and low model curves and served data is accounted for by data variance. Because x2 observed data for experiment 13 (6.3 pM [830 ppb] initial TCE). Panel (a) and Q are sensitive to nonnormally distributed data errors shows measured nitrite concentrations; panel (b) shows measured TCE concentrations; and panel (c) shows nitrite production rates (estimated (i.e., outliers), Q values as low as 0.001 are generally taken from measured 0, uptake rates as described in the text) versus time. TCE as indicating acceptable model fit. Q values approaching was injected at t = 170 min. Dashed model curves were obtained as 1.O are sometimes taken to indicate that data variances have described in the text using parameter 95% confidence limits as indicated in been estimated too large or that the data are “too good to be Table 11. true. ””Excluding the highest and lowest parameter esti- mates for each parameter yielded mean estimates with co- 1 I efficients of variation of about (15% to 45% for k, K,, k,, and kinact. (Because it was constrained as described previ- ously, mean, standard deviation, and coefficient of varia- tion were not calculated for K,,,.) Considerably more vari- ability is evident in estimated k,,, values, even after dis- carding the lowest and highest estimates. This could result from the difficulty in estimating k,,, as shown in the sen- c kl J sitivity analysis in part 1,7 or it could suggest that k,, is not where 5 is the amount of growth substrate oxidation rate constant, as was assumed during model simplification. error and d2P,ldt2and d2P21d? are the second derivatives of the PI and P, concentrations, respectively, with respect to time. (All other terms are as defined in part l.7) Using Error Associated with Modeling the appropriate values for all terms as taken from TCE degra- Unsteady-State Process as Pseudo-Steady State dation experiment 8, and using a range of typical values for An analysis was conducted to evaluate the error resulting k, and k, of lo6 to lo8 M-’s-’,’ the error resulting from from the pseudo-steady-state assumption made in deriving the pseudo-steady-state assumption is calculated to be the model. By comparing model derivation both with and 0.000002% to 0.0002%. Therefore, it appears that, in this without the pseudo-steady-state assumption (with competi- case, no appreciable error is incurred by modeling the pro- tive inhibition), it can be shown that the amount of growth cess as pseudo-steady-state. Furthermore, it appears that k, substrate specific oxidation rate error associated with incor- and k, could be four to five orders of magnitude less (i.e., rectly making the assumption would be slower) than estimated here without causing appreciable er-

ELY ET AL: COMETABOLISM MODEL, PART II 241 ror. Therefore, the approach used in the model to account and lowest data points, were about 15% to 25% for k and for enzyme inactivation and/or recovery is valid under these kinactestimates, 45% for K, and k, estimates, and 76% for conditions. k,,, estimates (Table 11). In comparing these variabilities to Although the assumption of a pseudo-steady-state condi- those obtained with simulated experimental data under var- tion did not introduce significant error in this instance, it ied experimental conditions (Table I1 of part l’), they do cannot be inferred that such would always be the case or not seem inordinately high. Analyses of simulated data in- that a traditional Michaelis-Menten or Briggs-Haldane dicated coefficients of variation of about 3% to 12% for k model could be used without question. Changes in enzyme and kinactestimates, 33% to 48% for K, and k, estimates, and level and potential differences associated with varying con- 112% for k,,, estimates, solely due to random error in one ditions, bacterial species, and/or substrates must be ac- data set and varying experimental conditions. With constant counted for. experimental conditions and differing data sets (Table I11 of part i7), coefficients of variation for k, K,, k,, and kinact estimates ranged up to about 25% whereas those for k,, DISCUSSION went as high as 121%. Therefore, the amount of variability The development, with time, of distinct, TCE-related inhi- observed in the parameter estimates is not particularly sur- bition and inactivation of AM0 activity has been shown prising and is not inordinately high, given the sensitivity of clearly in this study by experimental and modeling results. the model to data scatter. With its affinity for AM0 being about four times greater In these experiments, data error and the effects of varying than that of ammonia for AM0 (Table 11), relatively low experimental conditions appear to account for most of the concentrations of TCE can inhibit ammonia oxidation sub- variability seen in estimated parameter values. Moreover, stantially and nearly instantly. In contrast, TCE oxidation is because these experiments were conducted over an ex- relatively slow compared to ammonia oxidation, with the tended time period with about 40 batch-grown cultures, maximum specific oxidation rate for TCE being roughly some variation in culture activities was unavoidable. Cells 100 to 200 times less than the maximum specific oxidation harvested at slightly different points on their growth curves rate for ammonia (Table 11), causing inactivation of AM0 would be expected to exhibit different specific activities and to be a more gradual process. Consequently, TCE may be respond differently to conditions in the bioreactor. Even in characterized as a comparatively poor substrate for, but a the quasi-steady-state condition, variations in enzyme levels relatively potent inhibitor of, AMO. Observed bacterial ca- from experiment to experiment, undetectable by protein as- pability to initiate recovery, i.e., synthesize new enzyme, in says, could have existed due to differences in the cells’ the absence of detectable cell growth, even with TCE condition at harvesting. Differences in enzyme levels and present, is significant because it suggests that electron trans- activity would cause the model to estimate different enzyme port proteins were functioning and cell membranes were kinetic constants, thereby contributing to variation in esti- intact (allowing the cells to realize energy from ammonia mated model parameters. oxidation) and that protein synthesis components, e.g., The insensitivity of the objective function to changes in DNA, mRNA, and tRNA, were functional. These observa- k,,, at high TCE concentrations7 is another potential source tions do not support the concept that a 50% loss of culture of variability in parameter estimates. Because all model activity (for example) necessarily would be attributed to parameters affect model output jointly and model output 50% cell death (while the other 50% of cells presumably determines optimization, difficulty in estimating k,, at high continued to function at full activity), as assumed in “active TCE levels can cause at least some Variability in other pa- biomass” models. To the contrary, our results suggest that rameters as well. However, since the sensitivity analysis under appropriate conditions, the bacteria potentially could showed the objective function to be much more sensitive to oxidize TCE while concurrently coping with AM0 damage, the other model parameters, variability due to k,,, estima- and that if ammonia and TCE concentrations were con- tion difficulties is mostly confined to k,,, itself. In fact, this trolled within specific ranges to limit the rate of TCE oxi- was shown in analyses of the simulated data (Table I11 of dation (and enzyme inactivation), while maintaining a nec- part 17), where variabilities in other parameters increased essary minimum rate of ammonia oxidation (and recovery only slightly even though k,,, variability increased dramat- rate), it may be possible that TCE degradation could be ically. But difficulty in estimating k,,, at high TCE concen- sustained by a culture indefinitely. Though longer term trations adds uncertainty to individual k,,, estimates shown studies are needed for verification, this also could imply in Table 11, especially those with higher initial TCE con- that bacterial recovery capabilities could be exploited while centrations, for example, greater than about 14 or 15 pM. minimizing bacterial growth, thereby reducing sludge han- However, results from analyses of simulated experimental dling and disposal requirements. data showed that although k,,, estimates were more variable Model solution results showed acceptable goodness-of- when TCE levels were high and the recovery effect was fit, with the Q-statistic averaging about 0.38 even though sometimes missed altogether, the distribution appeared to data outliers (usually prior to TCE injection) caused rela- be approximately normal and the mean fell reasonably close tively low Q values to be obtained for experiments 5, 6, 7, to the true value (+34.7% error for the mean, + 1.5% error and 9. Coefficients of variation, after excluding the highest for the trimmed mean). Therefore, while individual k,,,

242 BIOTECHNOLOGY AND BIOENGINEERING, VOL. 46, NO. 3, MAY 5, 1995 estimates may vary at high TCE concentrations, the mean ture) for any particular enzyme/growth substrate system, determined from several comparable experiments may be any variable component of the driving force would have to expected to approximate the true value. Therefore, we con- be contained withinf,, that is, the amount of new enzyme clude that the model solution procedure estimated all pa- synthesized per growth substrate oxidized. If new enzyme rameters reasonably well. This being the case, it would synthesis in response to inhibitiodinactivation depended on seem that k,,, was not constant, as assumed in the model, a simple binary on/off response, the driving force for re- and it becomes necessary to consider other ways in which to covery would be expected to be constant, as was assumed model recovery. by assuming f, to be constant. (This does not mean that It is evident in Table I1 that most higher k,, estimates recovery would be constant, because synthesis of new en- were obtained from experiments with higher TCE concen- zyme would support faster growth substrate oxidation rates, trations (and, therefore, greater inhibition and inactivation thereby providing more energy to support faster rates of of enzyme). This apparent relationship is depicted in Figure enzyme synthesis, which in turn would support faster 10, where the dashed line indicates the mean k,,, and the growth substrate oxidation, etc. The model accounts for solid line indicates a best-fit linear model (k,,, = - 0.18 + this.) However, if cellular response was analog, perhaps 0.032 I,) based on x2 minimization. (A power curve model increasing with greater inhibitionlinactivation, the driving was evaluated as well, but improvement in the curve fit was force for recovery would not be a constant, and nor would not statistically significant.) This figure suggests that, over f,. This being the case, the apparently higher k,,, estimates the 70- to 85-min period of TCE exposure used in these obtained at higher TCE initial concentrations could indicate experiments: (1) the estimated k,,, was higher when the that cellular response to TCE effects is metered in some way initial TCE concentration was higher; and (2) there may to the severity of enzyme inhibitionhactivation. This may have been a threshold TCE initial concentration below be envisioned by considering a ‘‘desired specific activity which the k,,, would have been zero. setpoint” to be established by the concentration of growth Generally speaking, recovery may be expected to depend substrate (as on a typical Michaelis-Menten curve), that is, on two factors: (1) some driving force for recovery; and (2) that the bacteria try to regulate the amount of enzyme (in the amount of energy available to support protein synthesis. this case, AMO) in the cell according to the amount of Assuming that the cells’ ability to gain energy from ammo- growth substrate (NH,) present. When perturbed away from nia oxidation is not damaged, energy availability would the setpoint, that is, when activity is reduced by inhibition depend primarily on the amount of growth substrate oxi- and/or inactivation of enzyme, the driving force for synthe- dized to product (and on energy storage compounds in some sis of new enzyme could depend on the magnitude of the bacterial species). The model, as derived, assumed that re- perturbation. Another possibility could be a feedback inhi- covery of specific activity resulting from new enzyme syn- bition situation in which the amount of enzyme (AMO) thesis could be calculated by multiplying a term represent- would be regulated inversely by the amount of intermediate ing a drive force (k,,,) by a term indicating energy avail- product present (NH,OH); that is, a drop in NH,OH con- ability (P,). In the model derivation, k,,, was assumed centration could create a driving force for AM0 synthesis at constant and equal to kJ,/X. Because initial and final pro- a rate related to the amount of perturbation away from some tein measurements indicated that X was constant, as men- desired internal NH,OH level (Fig. 1). It also could be that tioned previously, and k, is constant (at constant tempera- the driving force for recovery depends in some way on the duration of time away from the desired operating point. Previous injury from TCE exposure also could be a factor. Since all experiments described herein were conducted with 1.20:;:: ; Best Fit Line fresh cells for essentially the same time duration, variations in recovery with time or effects of previous TCE exposure

1.00 would not have been determinable. Additional and longer term experiments will be necessary to examine these and other possible factors influencing cellular recovery.

‘= 0.40 In addition, to the above, while P, is related to the 0.20 amount of energy available to support recovery, there also is an energy penalty associated with oxidation of the non- 0.00 t- 11 growth substrate. That is, if a given amount of growth sub- -0.20 strate is oxidized to product in the absence of a nongrowth -0.40 0 5 10 15 20 25 30 substrate, a corresponding amount of energy is made avail- Initial TCE, pM able to the cell via the electron transport chain (2 mol of electrons per mole of nitrite produced). However, if non- Figure 10. Estimated k,, values obtained in experiments with differing growth substrate is present, some of it will be oxidized by initial TCE concentrations. Error bars indicate 95% confidence limits and AMO, consuming electrons that otherwise would have pro- the dashed line indicates the mean of the k,, estimates shown in Table I1 (exclusive of experiment 10). The solid line is a best-fit linear model, as vided energy for regeneration of reductant, oxidation of described in the text. growth substrate, and cell maintenance and growth (Fig. 1).

ELY ET AL: COMETABOLISM MODEL, PART I1 243 Consequently, less energy would be realized from oxidation thesis of enzyme (i.e., recovery) would cause growth sub- of the growth substrate with the nongrowth substrate present strate oxidation to occur at a faster rate, thereby supporting than with it absent. Therefore, in addition to the possibility faster enzyme synthesis, still faster oxidation of growth sub- of cellular response being analog instead of binary, poten- strate, etc., as mentioned previously. With TCE present, tial variations in the recovery “constant” with time, and enzyme would be inactivated at a rate that would depend on possible effects of previous TCE exposure, an energy pen- the TCE concentration, the growth substrate concentration, alty associated with oxidizing a nongrowth substrate may and the amount of active enzyme. Therefore, at a particular need to be taken into account. (While recovery, as mea- TCE concentration (and growth substrate concentration), sured in these experiments, would include enzyme synthesis enzyme inactivation and synthesis rates could be balanced, associated with normal enzyme turnover as well as enzyme i.e., they could be made to equal each other. Referring synthesis related to TCE exposure, the low k,,, values ob- again to Figure 5, where culture response in the absence of served at low TCE concentrations and the possible TCE inactivation (and recovery) is shown by the dashed curves, threshold suggest that enzyme synthesis associated with it is noteworthy that if cellular recovery capabilities were normal turnover was relatively small.) controlled to balance inactivation effects, system behavior The results of this study may be extendable to other would approximate that shown by the dashed lines, since monooxygenase- or dioxygenase-utilizing species, although inactivation effects would effectively be negated. By con- model parameter values could vary considerably from spe- trolling conditions to balance inactivation and recovery, cies to species and with other growth and nongrowth sub- sustainable systems could potentially allow continuous use strates. In fact, heterotrophic species using growth sub- of cells, thereby generating less sludge requiring treatment strates other than ammonia (e.g., phenol or ) may and disposal. exhibit much higher recovery capabilities, perhaps even masking inhibition and/or inactivation effects completely and supporting significant cell growth at sufficiently low CONCLUSIONS TCE levels and/or sufficiently high growth substrate levels. Inhibition, inactivation, and recovery mechanisms may be Analyses of data from TCE degradation experiments veri- similar particularly in TCE oxidation by methane-oxidizing fied model assumptions and yielded satisfactory parameter bacteria, because significant similarities exist between am- estimates. The error associated with modeling the enzyme monia-oxidizing and methane-oxidizing bacteria and be- inhibition, inactivation, and recovery process as pseudo- tween AM0 and MMO. In part 1, similar observations by steady-state was shown to be negligible. TCE was deter- researchers working with other bacterial species were mined to inhibit ammonia oxidation competitively and en- noted,7 but a complete conceptual and mathematical model, zyme inactivation was known to be proportional to TCE including potential recovery capabilities, has not been pro- oxidation. Cellular recovery capability in the presence of posed previously. This may partially be because several of TCE was shown, with recovery effects apparently increas- the referenced studies were conducted in the absence of ing with greater inhibitiodinactivation of normal metabo- growth substrate. While higher short-term TCE degradation lism. Questions remain regarding factors controlling recov- rates are achievable without growth substrate (because TCE ery and how it may best be modeled. Moreover, the long- has greater access to the enzyme), enzyme inactivation term implications of recovery capabilities in the treatment rates are higher as well. In addition, recovery processes of compounds exhibiting product toxicity requires further would be severely hampered or obviated altogether. elucidation. Further research is necessary to address these In one study with a mixed culture of methanotrophic unresolved issues and to pursue appropriate model param- bacteria in the absence of methane, the amount of TCE that eters for other nongrowth substrates as well as for other could be oxidized was shown to vary, depending on energy bacterial types. Determination of model parameters for reserves and supply. ’,*A treatment approach was proposed other species and substrate combinations should provide in which methanotrophic bacteria would be grown in one considerable insight into cometabolic capabilities and char- reactor (with methane) and exposed to TCE in another re- acteristics of enzyme/growth substratehongrowth substrate actor (without methane).3 A disadvantage with this ap- interactions among various species capable of cometabo- proach would be that cells would be used only once, re- lism. A more complete understanding and appreciation of quiring handling and disposal of potentially large quantities the relative significance of inhibition, inactivation, and re- of sludge potentially contaminated with residual TCE and/ covery mechanisms in different bacteria and with various or toxic metabolites. Moreover, cellular recovery and, per- nongrowth substrates should facilitate rational design and haps, induction of the monooxygenase enzyme would be operation of cometabolic bioremediation systems. impaired or precluded by the absence of methane. An al- ternative approach would be to develop sustainable comet- abolic treatment systems to exploit intrinsic bacterial poten- We thank Lew Semprini, Jack Istok, and Sheryl Stuart of the Department of Civil Engineering, Oregon State University, for tial to compensate for the detrimental effects of TCE come- many helpful discussions and comments. Funding for this study tabolism. Consider that if TCE were removed from such a was provided by the Office of Research and Development, U.S. system (e.g., by degradation or by some other means), syn- Environmental Protection Agency, under Agreement R8 15738

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