Determination of the Ks values during the growth of Alcaligenes eutrophus on phenol, 2,4-dichlorophenoxyacetic acid and fructose

The determination of the K_S values presented here is based on the estimation of the stationary substrate concentrations in continuous cultivation experiments. The separation of biomass from the suspension was performed by an ultrafiltration step which succeeded within one second. The decay of substrate concentration during sampling was calculated to amount to less than 6% of the stationary substrate concentration at relevant growth rates. The K_S values derived from these reduced substrate concentrations deviated by only 10% from the theoretical values at a biomass concentration of about 1 g/1. Thus relevant kinetic parameters can be calculated from the data obtained by this procedure. Values of 11, 59 and 14 μM were obtained with 2,4-dichlorophenoxyacetic acid (2,4-D), phenol and fructose, respectively. Similar K_S values were derived with 2,4-D and fructose by using a respirationbased determination for reasons of comparison. With phenol this value was only 7 μM which is as cribed to a physiological background.     

Modelling and simulation of steady-state phenol degradation in a pulsed plate bioreactor with immobilised cells of Nocardia hydrocarbonoxydans

A novel bioreactor called pulsed plate bioreactor (PPBR) with cell immobilised glass particles in the interplate spaces was used for continuous aerobic biodegradation of phenol present in wastewater. A mathematical model consisting of mass balance equations and accounting for simultaneous external film mass transfer, internal diffusion and reaction is presented to describe the steady-state degradation of phenol by Nocardia hydrocarbonoxydans (Nch.) in this bioreactor. The growth of Nch. on phenol was found to follow Haldane substrate inhibition model. The biokinetic parameters at a temperature of 30 ± 1 °C and pH at 7.0 ± 0.1 are μ _m = 0.5397 h⁻¹, K _S = 6.445 mg/L and K _I = 855.7 mg/L. The mathematical model was able to predict the reactor performance, with a maximum error of 2% between the predicted and experimental percentage degradations of phenol. The biofilm internal diffusion rate was found to be the slowest step in biodegradation of phenol in a PPBR.     

The adsorption of Fusarium flocciferum spores on celite particles and their use in the degradation of phenol

Summary Spores of Fusarium flocciferum were inserted in porous celite beads. The effects of bead size, adsorption time course, washing cycle and spore concentration on spore loading were investigated. Cell loadings up to 50% (dry weight/beads) were obtained. The degradation of phenol using adsorbed cells was studied in batch experiments. The immobilized cell system was shown to efficiently degrade high concentrations of the substrate (up to 2.0 g/l) and to remain active for more than 2 motths. The oxygen uptake rate of free and immobilized cells was determined at various concentrations of phenol. The kinetic constants K _s=85 mg/l, K _i=345 mg/l and SMI=170 mg/l were estimated from the experimental data by linearization of the Haldane function for the free cells. The uptake rates exhibited by the confined cells were lower (30%) than those obtained for free cells and no significant differences were found for phenol concentrations between 150 and 1200 mg/l.     

Kinetics of phenol oxidation by washed cells

The uptake of phenol by pure cultures of Pseudomonas putida growing on phenol in continuous culture has been studied. The purpose of the experiments was to determine the kinetic parameters governing uptake of phenol by organisms growing on phenol in the high-conversion range by measuring uptake rates per unit biomass per unit time at various phenol concentrations. The microorganisms used were taken from a chemostat at residence times of 8, 5.25, 3.85, 3.2, 3, and 2.7h. The Monod–Haldane model and modifications of it were applied to the data and the best kinetic parameters were determined by nonlinear least-squares techniques. The best model was a two-parameters simplification of Monod–Haldane in which μ = K₁S/(K₂ + S²). The value of K₁ was found to increase monotonically with the value of phenol concentration in the original chemostat with an apparent induction “threshold” of 0.1 mg/L.     

Kinetic behavior of heterogeneous populations in completely mixed reactors

The kinetic behavior of heterogeneous microbial populations was studied in a continuous flow completely mixed reactor operated at various dilution rates. Glucose was used as the growth-limiting nutrient. The physiological growth parameters for cells harvested from continuous flow reactors were determined using batch experiments. It, was found that the growth parameters, maximum growth rate (μ_m), saturation constant (k_s), and cell yield (Y) vary for each dilution rate, and cannot be considered as precise constants in depicting the kinetic behavior of heterogeneous populations. In addition, it was found that the yield coefficients obtained from batch experiments were always lower than those obtained from continuous flow experiments. Levels of substrate and biological solids calculated for different dilution rates using growth constants from batch experiments did not agree with the experimental values observed in steady-state experiments. However, when the yield values from, the continuous flow experiments were used in conjunction with batch values for μ_m and k_s the theoretical and experimental dilute-out curves agreed fairly closely (within the range needed for engineering prediction) until the culture began to wash out of the unit. In general, the data substantiated the use of the single phase relationship between growth rate and substrate concentration described by the Monod equation, μ = μ_mS/(k_s + s).     

Phenol degradation by a psychrotrophic strain of Pseudomonas putida

Summary Cell growth and phenol degradation kinetics were studied at 10°C for a psychrotrophic bacterium, Pseudomonas putida Q5. The batch studies were conducted for initial phenol concentrations, S_o, ranging from 14 to 1000 mg/1. The experimental data for 14<=S_o<=200 mg/1 were fitted by non-linear regression to the integrated Haldane substrate inhibition growth rate model. The values of the kinetic parameters were found to be: _m=0.119 h^–1, K _S=5.27 mg/1 and K _I=377 mg/1. The yield factor of dry biomass from substrate consumed was Y=0.55. Compared to mesophilic pseudomonads previously studied, the psychrotrophic strain grows on and degrades phenol at rates that are ca. 65–80% lower. However, use of the psychrotrophic microorganism may still be economically advantageous for waste-water treatment processes installed in cold climatic regions, and in cases where influent waste-water temperatures exhibit seasonal variation in the range 10–30°C.Nomenclature K _S saturation constant (mg/l) - K _I substrate inhibition constant (mg/l) - specific growth rate (h^–1) - _m maximum specific growth rate without substrate inhibition (h^–1) - _max maximum achievable specific growth rate with substrate inhibition (h^–1) - S substrate (phenol) concentration (mg/l) - S_o initial substrate concentration (mg/l) - S_max substrate concentration corresponding to _max (mg/l) - t time (h) - X cell concentration, dry basis (mg DW/l) - X_f final cell concentration, dry basis (mg DW/l) - X_o initial cell concentration, dry basis (mg DW/l) - Y yield factor (mg DW cell produced/mg substrate consumed)     

Degradation of phenol and phenolic compounds by a defined denitrifying bacterial culture

Phenol, a major pollutant in several industrial waste waters is often used as a model compound for studies on biodegradation. This study investigated the anoxic degradation of phenol and other phenolic compounds by a defined mixed culture of Alcaligenes faecalis and Enterobacter species. The culture was capable of degrading high concentrations of phenol (up to 600 mg/l) under anoxic conditions in a simple minimal mineral medium at an initial cell mass of 8 mg/l. However, the lag phase in growth and phenol removal increased with increase in phenol concentration. Dissolved CO₂ was an absolute requirement for phenol degradation. In addition to nitrate, nitrite and oxygen could be used as electron acceptors. The kinetic constants, maximum specific growth rate _max; inhibition constant, K _i and saturation constant, K _s were determined to be 0.206 h^–1, 113 and 15 mg phenol/l respectively. p-Hydroxybenzoic acid was identified as an intermediate during phenol degradation. Apart from phenol, the culture utilized few other monocyclic aromatic compounds as growth substrates. The defined culture has remained stable with consistent phenol-degrading ability for more than 3 years and thus shows promise for its application in anoxic treatment of industrial waste waters containing phenolic compounds.     

Kinetics of the biodegradation of phenol in wastewaters from the chemical industry by covalently immobilized <Emphasis Type="Italic">Trichosporon cutaneum</Emphasis> cells

A simple method for the preparation of the biocatalyst with whole cells is presented, and the applicability of the technique for biodegradation of phenol in wastewater from the chemical industries using the basidomycetes yeast Trichosporon cutaneum is explored. Kinetic studies of the influence of other compounds contained in wastewater as naphthalene, benzene, toluene and pyridine indicate that apart from oil fraction, which is removed, the phenol concentration is the only major factor limiting the growth of immobilized cells. Mathematical models are applied to describe the kinetic behavior of immobilized yeast cells. From the analysis of the experimental curves was shown that the obtained values for the apparent rate parameters vary depending on the substrate concentration (μ_maxapp from 0.35 to 0.09 h⁻¹ and K _sapp from 0.037 to 0.4 g dm⁻³). The inhibitory effect of the phenol on the obtained yield coefficients was investigated too. It has been shown that covalent immobilization of T. cutaneum whole cells to plastic carrier beads is possible, and that cell viability and phenol degrading activity are maintained after the chemical modification of cell walls during the binding procedure. The results obtained indicate a possible future application of immobilized T. cutaneum for destroying phenol in industrial wastewaters.     

Analysis of pH-stat continuous cultivation and the stability of the mixed fermentation in continuous yogurt production

A pH-stat fermentor is a continuous cultivator in which the feed rate is controlled to maintain a constant pH, i.e., end-product acid concentration. This fermentor has application to the continuous cultivation of lactic acid-producing organisms in milk-based media. The equations describing the operation of this fermentor are developed. It is shown that, where the limiting substrate is the carbon and energy source, the operation of the fermentor is essentially equivalent to that of a turbidostat. In contrast to this, where the carbon and energy source is in excess and growth is limited by another substrate, pH-state fermentation is stable both in regions of substrate excess, where D = μ_max, comparable with turbidostat operation, and substrate limitation where D < μ_max, comparable with chemostat operation. These conditions are met in milk-based media. An analysis is presented, allowing the prediction of the degree of substrate limitation, cell density, and dilution rate in a pH-stat fermentor from batch-growth kinetics. This was confirmed using experimental data for the growth of Streptococcus thermophilus TS2 and Lactobacillus LB1 in skim milk. Stable simultaneous growth of two organisms in continuous culture occurs if their growth rates are determined by separate conditions, so that, at steady state, their growth rqtes are separately madeequal to the dilution rate. It is then predicted, and confirmed by experiment, that a mixed culture of S. thermophilus TS2 and L. bulgaricus LB1 in a pH-stat continuous fermentor in yogurt mix at pH 5.5 would be stable with the growth of L. bulgaricus being substrate unlimited and the fermentor operting with D = μ_max for L. bulgaricus LB1, and the growth of S. thermophilus TS2 being substrate limited so that its growth rate is equal to the existing dilution rate. Finally, it is predicted and confirmed by experiment that if the conditions are altered so that the growth of S. thermophilus TS2 is substrate unlimited the stable association is broken down, the fermentor operates with D approaching μ_max for S. thermophilus TS2, and L. bulgaricus LB1 is washed out to the level maintained by wall growth.     

Biodegradation of phenol by arthrobacter and modelling of the kinetics

The toxic effects of phenol, a common constituent of many industrial effluents, necessitates treatment of the polluted streams. Biodegradation is a popular technique and enjoys many advantages. The degradation of phenol with Arthrobacter species is studied in batch cultures and it is observed that the substrate is inhibiting. The fit of various models, including the model proposed earlier by us [17], to the experimental data is studied. The model is used to fit available data in literature, which unfortunately is very sparse. In all the cases the present model fits the data best.List of Symbols S mg/l substrate concentration - S ₀ mg/l threshold substrate concentration - K _I mg/l inhibition constant - K _m , K _s mg/l half saturation constant of growth kinetics - m, n constants - 1/h specific growth rate - _m 1/h maximal specific growth rate - X mg/l biomass concentration at time t - X ₀ mg/l initial biomass concentration Abbreviations MTCC Microbial Type Culture Collection - IMTECH Institute of Microbial Technology The cooperation of the staff of the Biosciences and Biotechnology Center, I.I.T. Madras is greatly appreciated.     

Trichloroethene and cis‐1,2‐dichloroethene concentration‐dependent toxicity model simulates anaerobic dechlorination at high concentrations: I. batch‐fed reactors

A model was developed to describe toxicity from high concentrations of chlorinated aliphatic hydrocarbons (CAHs) on reductively dechlorinating cultures under batch‐growth conditions. A reductively dechlorinating anaerobic Evanite subculture (EV‐cDCE) was fed trichloroethene (TCE) and excess electron donor to accumulate cis‐1,2‐dichloroethene (cDCE) in batch‐fed reactors. A second Point Mugu (PM) culture was also studied in the cDCE accumulating batch‐fed experiment, as well as in a time‐ and concentration‐dependent cDCE exposure experiment. Both cultures accumulated cDCE to concentrations ranging from 9,000 to 12,000 µM before cDCE production from TCE ceased. Exposure to approximately 3,000 and 6,000 µM cDCE concentrations for 5 days during continuous TCE dechlorination exhibited greater loss in activity proportional to both time and concentration of exposure than simple endogenous decay. Various inhibition models were analyzed for the two cultures, including the previously proposed Haldane inhibition model and a maximum threshold inhibition model, but neither adequately fit all experimental observations. A concentration‐dependent toxicity model is proposed, which simulated all the experimental observations well. The toxicity model incorporates CAH toxicity terms that directly increase the cell decay coefficient in proportion with CAH concentrations. We also consider previously proposed models relating toxicity to partitioning in the cell wall (K_M/B), proportional to octanol–water partitioning (K_OW) coefficients. A reanalysis of previously reported modeling of batch tests using the Haldane model of Yu and Semprini, could be fit equally well using the toxicity model presented here, combined with toxicity proportioned to cell wall partitioning. A companion paper extends the experimental analysis and our modeling approach to a completely mixed reactor and a fixed film reactor. Biotechnol. Bioeng. 2010;107: 529–539. © 2010 Wiley Periodicals, Inc.     

Substrate inhibition kinetics of <Emphasis Type="Italic">Saccharomyces cerevisiae</Emphasis> in fed-batch cultures operated at constant glucose and maltose concentration levels

Fed-batch culture is the mode of operation of choice in industrial baker’s yeast fermentation. The particular mode of culture, operated at stable glucose and maltose concentration levels, was employed in this work in order to estimate important kinetic parameters in a process mostly described in the literature as batch or continuous culture. This way, the effects of a continuously falling sugar level during a batch process were avoided and therefore the effects of various (stable) sugar levels on growth kinetics were evaluated. Comparing the kinetics of growth and the inhibition by the substrate in cultures grown on glucose, which is the preferential sugar source for Saccharomyces cerevisiae, and maltose, the most common sugar source in industrial media for baker’s yeast production, a milder inhibition effect by the substrate in maltose-grown cells was observed, as well as a higher yield coefficient. The observed sugar inhibition effect in glucostat cultures was taken into account in modeling substrate inhibition kinetics. The inhibition coefficient K _i increased with increasing sugar concentration levels, but it appeared to be unaffected by the type of substrate and almost equal for both substrates at elevated concentration levels.     

Dual-substrate inhibition kinetic studies for recombinant human interferon gamma producing Pichia pastoris

Pichia pastoris is considered as one of the prominent host extensively used as a platform for heterologous protein production. In the present study, the growth inhibition kinetics of recombinant P. pastoris expressing human interferon gamma was studied under different initial substrate concentrations of gluconate (10–100?g?L^?1) and methanol (2–50?g?L^?1) in modified FM22 medium. The highest specific growth rate of 0.0206 and 0.019?hr^?1 was observed at 60?g?L^?1 of gluconate and 10?g?L^?1 of methanol, respectively. Various three- and four-parametric Monod-variant models were chosen to analyze the inhibition kinetics. The model parameters as well as goodness of fit were estimated using nonlinear regression analysis. The three-parameter Haldane model was found to be best fit for both gluconate (R²?=?0.95) and methanol substrate (R²?=?0.96). The parameter sensitivity analysis revealed that µ_max, K_i, and K_s are the most sensitive parameters for both methanol and gluconate. Different substrate inhibition models were fitted to the growth kinetic data and the additive form of double Webb model was found to be the best to explain the growth kinetics of recombinant P. pastoris.     

Anaerobic degradation of phenol in batch and continuous cultures by a denitrifying bacterial consortium

Summary The anaerobic degradation of phenol under denitrifying conditions by a bacterial consortium was studied both in batch and continuous cultures. Anaerobic degradation was dependent on NO_f3 ^p– and concentrations up to 4 mm phenol were degraded within 2–5 days. During continuous growth in a fermenter, steady states could be maintained at eight dilution rates (D) corresponding to residence times between 12.5 and 50 h. Culture wash-out occurred at D=0.084 h^–1. The kinetic parameters obtained for anaerobic degradation of phenol under denitrifying conditions by the consortium were: maximam specific growth rate = 0.091 h^–1; saturation constant = 4.91 mg phenol/l; true growth yield = 0.57 mg dry wt/mg phenol; maintenance coefficient = 0.013 mg phenol/mg dry wt per hour. The Haldane model inhibition constant was estimated from batch culture data giving a value of 101 mg/l. The requirement of CO₂ for the anaerobic degradation of phenol with NO_f3 ^p– indicates that phenol carboxylation to 4-hydroxybenzoate was the first step of phenol degradation by this culture. 4-Hydroxybenzoate, proposed as an intermediate of phenol carboxylation under these conditions, was detected only in continuous cultures at very low growth rates (D=0.02 h^–1), but was never detected as a free intermediary metabolite either in batch or in continuous cultures. Correspondence to: N. Khoury     

Unstable steady state operations of substrate inhibited cultures by dissolved oxygen control

Microorganism kinetic growth characterized by substrate inhibition was investigated by means of a continuous stirred tank reactor equipped with a feedback controller of the medium feeding flow rate. The aerobic growth of Pseudomonas sp. OX1 with phenol as carbon/energy source was adopted as a case study to test a new control strategy using dissolved oxygen concentration as a state variable. The controller was successful in steadily operating bioconversion under intrinsically unstable conditions. A simple model of the controlled system was proposed to set the feedback controller.The specific growth rate of Pseudomonas sp. OX1 was successfully described by means of the Haldane model. The regression of the experimental data yielded μ_M = 0.26 h⁻¹, K_Ph = 5 × 10⁻³ g/L and K_I = 0.2 g/L. The biomass-to-substrate fractional yield as a function of the specific growth rate did not change moving from substrate-inhibited to substrate-deficient state. The data was modelled according to the Pirt model: m = 1.7 × 10⁻² g/(g h), . The specific growth rates calculated for batch and continuous growth were compared.     

Multi-substrate growth kinetics of Pseudomonas putida for phenol removal

The biodegradation of phenol by a pure culture of Pseudomonas putida was investigated in a continuously fed stirred-tank reactor, under aerobic conditions. The dilution rate was varied between 0.0174 h⁻¹ and 0.278 h⁻¹, covering a wide range of dissolved oxygen and the inhibition region of phenol. Through non-linear analysis of the data, a dual-substrate growth kinetics, Haldane kinetics for phenol and Monod kinetics for oxygen, was derived with high correlation coefficients. Respective biokinetic parameters were evaluated as μ_m = 0.569 h⁻¹, K _p = 18.539 mg/l, K _i = 99.374 mg/l, K _o = 0.048 mg/l, Y _x/p = 0.521 g microorganism/g phenol and Y _x/o = 0.338 g microorganism/g oxygen, being in good agreement with other studies in the literature. Maintenance factors for both phenol and oxygen were calculated for the first time for P. putida while the saturation coefficient for oxygen, K _o, was genuinely evaluated from the constructed model, not imported or adapted from other studies as reported in the literature. All pertinent biokinetic parameters for P. putida have been calculated from continuous system data, which are most appropriate for use in continuous bioprocess applications. Received: 29 July 1996 / Received revision: 18 November 1996 / Accepted: 23 November 1996     

Degradation of 4-chlorophenol by enriched mixed cultures utilizing phenol and glucose as added growth substrate

Two mixed cultures, phenol-oxidizing (PO) and glucose-oxidizing (GO), were cultivated in two parallel chemostat reactors. The PO culture was enriched on phenol, and the GO culture was enriched on glucose. Batch biodegradation experiments were conducted to examine the degradation of 4-chlorophenol (4-CP) under various substrate conditions. The results indicate that in the absence of added growth substrate, 4-CP transformation by PO culture was complete at S _c ^o /X _o (initial 4-CP concentration/initial biomass concentration) 0.27 and that by GO culture was complete at S _c ^o /X _o = 0.09. In the presence of 5–500 mg phenol/l, the phenol dosage required to achieve the complete transformation of 4-CP was 60 mg/l at S _c ^o /X _o = 1, increasing to 120 mg/l at S _c ^o /X _o = 2, and to 180 mg/l at S _c ^o /X _o = 5. As glucose was added to the GO culture at a concentration of over 5–500 mg chemical oxygen demand (COD)/l, 4-CP was not completely transformed at S _c ^o /X _o = 5 [S _c ^o = 50 mg/l, X _o = 10 mg/l volatile suspended solids (VSS)]. These two cultures in utilizing added growth substrate were easily switched between glucose and phenol. Overall, the capacity of PO culture to degrade 4-CP, expressed as T _c (4-CP mass consumed /biomass inactivated, having unit of mg 4-CP/mg VSS), was 0.15–0.80, which compares with T _c values of 0.05–0.26 for GO culture. This work shows that adding phenol as a growth substrate is preferable over adding glucose, as it enhances 4-CP transformation, but a final choice should take into account both degradation efficiency and the risk of phenol toxicity.     

Growth kinetics of EDTA biodegradation by Burkholderia cepacia

A pure culture of an EDTA-degrading strain was isolated from the Taiwan environment. It was identified as Burkholderia cepacia, an aerobic bacterium, elliptically shaped with a length of 5–15 m. The degradation assay showed that the degradation efficiency of Fe-EDTA by B. cepacia was approximately 91%. Evaluation of kinetic parameters showed that Fe-EDTA degradation followed substrate inhibition kinetics. This is evident from the decrease in specific growth rate with an increase in the initial substrate concentration greater than 500 mg/l. To estimate the kinetic parameters – _max, K_S and K_I, five substrate–inhibition models were used. From the results of non-linear regression, the value of _max ranged from 0.150 to 0.206 d^–1, K_S from 74 to 87 mg/l, and K_I from 890 to 2289 mg/l. The five models were found to underestimate the maximum specific growth rate by 1.5–3.7. Therefore, predictions based on these models would result in lower predicted value than those from the experimental kinetic data.     

Effect of carbon:nitrogen ratio on kinetics of phenol biodegradation byAcinetobacter johnsonii in saturated sand

In polluted soil or ground water, inorganic nutrients such as nitrogen may be limiting, so that Monod kinetics for carbon limitation may not describe microbial growth and contaminant biodegradation rates. To test this hypothesis we measured¹⁴CO₂ evolved by a pure culture ofAcinetobacter johnsonii degrading 120 µg¹⁴C-phenol per ml in saturated sand with molar carbon:nitrogen (CN) ratios ranging from 1.5 to 560. We fit kinetics models to the data using non-linear least squares regression. Phenol disappearance and population growth were also measured at CN1.5 and CN560.After a 5- to 10-hour lag period, most of the¹⁴CO₂ evolution curves at all CN ratios displayed a sigmoidal shape, suggesting that the microbial populations grew. As CN ratio increased, the initial rate of¹⁴CO₂ evolution decreased. Cell growth and phenol consumption occurred at both CN1.5 and CN560, and showed the same trends as the¹⁴CO₂ data. A kinetics model assuming population growth limited by a single substrate best fit the¹⁴CO₂ evolution data for CN1.5. At intermediate to high CN ratios, the data were best fit by a model originally formulated to describe no-growth metabolism of one substrate coupled with microbial growth on a second substrate. We suggest that this dual-substrate model describes linear growth on phenol while nitrogen is available and first-order metabolism of phenol without growth after nitrogen is depleted.     

The ferrous iron oxidation kinetics of Thiobacillus ferrooxidans in continuous cultures

The oxidation and growth kinetics of ferrous iron with Thiobacillus ferrooxidans in continuous cultures was examined at several total iron concentrations. On-line off-gas analyses of O₂ and CO₂ were used to measure the oxygen and carbon dioxide consumption rates in the culture. Off-line respiration measurements in a biological oxygen monitor (BOM) were used to measure directly the maximum specific oxygen consumption rate, qO₂,max, of cells grown in continuous culture. It was shown that these reproducibly measured values of qO₂,max vary with the dilution rate. The biomass-specific oxygen consumption rate, qO₂, is dependent on the ratio of the ferric and ferrous iron concentrations in the culture. The oxidation kinetics was accurately described with a rate equation for competitive ferric iron inhibition, using the value of qO₂,max measured in the BOM. Accordingly, only the kinetic constant Ks/K _i needed to be fitted from the measurements. A new method was introduced to determine the steady-state kinetics of a cell suspension in a batch culture that only takes a few hours. The batch culture was set up by terminating the feeding of a continuous culture at its steady state. The kinetic constant K _s/K _i determined in this batch culture agreed with the value determined in continuous cultures at various steady states. Received: 8 February 1999 / Accepted: 17 February 1999