Oscillatory behavior of Saccharomyces cerevisiae in continuous culture: I. Effects of pH and nitrogen levels

The appearance of sustained oscillations in bioreactor variables (biomass and nutrient concentrations) in continuous cultures of Saccharomyces cerevisiae indicates the complex nature of microbial systems, the inadequacy of current growth kinetic models, and the difficulties which may arise in bioprocess control and optimization. In this study we investigate continuous bioreactor behavior over a range of operating conditions (dilution rate, feed glucose concentration, feed ammonium concentration, dissolved oxygen, and pH) to determine the process requirements which lead to oscillatory behavior. We present new results which indicate that high feed ammonium concentrations may eliminate oscillations and that under oscillatory conditions ammonium levels are generally low and oscillatory as well. The effects of pH are complex and oscillations were only observed at pH values 5.5 and 6.5; no oscillations were observed at a pH of 4.5. Under our nominal operating conditions (feed glucose concentration 10 g/L, dilution rate 0.145 h(-1), feed ammonium concentration 0.0303M, dissolved oxygen level 50%, pH 5.5, and T = 30 degrees C) we found two possible final bioreactor states depending on the transient used to reach the nominal operating conditions. One of the states was oscillatory and characteristic of oxidative metabolism and the other was nonoscillatory and fermentative.     

Oscillations in continuous cultures of budding yeast: a segregated parameter analysis

Sustained oscillations have been observed in continuous cultures of Saccharomyces cerevisiae. These oscillations appear spontaneously under aerobic conditions and may constitute a severe limitation for process control. We have found that oscillations arise only in a well defined range of dilution rates and dissolved oxygen values. The period of the oscillations is related, but not equal, to the mass doubling time, and shows a relation ship with both the parent cells and daughter cells generation times. At high dilution rates two oscillatory regimens, with different periods, are observed. The analysis of the budding index shows a marked degree of synchronization of the culture, however significant differences, both in phase and in amplitude, are ob served if the budding index of parent cells and of daughter cells are considered separately. The complex changes of the cell population are clearly demonstrated by the continuous and periodic modification of both cell volume distributions and protein distributions. Ethanol is always accumulated before the drop of dissolved oxygen concentration and one of the peaks of budding index. We propose a model that explains the insurgence of these oscillation as a consequence of changes in cell cycle parameters due to alternate growth in glucose and in ethanol.     

Taxol production in bioreactors: Kinetics of biomass accumulation, nutrient uptake, and taxol production by cell suspensions of Taxus baccata

The kinetics of biomass accumulation, nutrient uptake and taxol production of Taxus baccata cell suspensions were examined in three bioreactor configurations, viz. 250-mL Erienmeyerflasks, 1-L working volume pneumatically mixed (PMB), and stirred tank (STB) bioreactors. Qualitatively similar kinetics were observed in all three bioreactor types. Biomass accumulation and specific nutrient uptake rates exhibited biphasic characteristics. Carbohydrate uptake and biomass accumulation substantially ceased when phosphate was depleted from the medium. Phosphate was identified as a possible growth-limiting nutrient. Taxol accumulated exclusively in the second phase of growth. A maximum taxol concentration of 1.5 mg/L was obtained in the PMB which was fivefold greater than that obtained in the Erienmeyer flasks and the STB, but the relative kinetics of taxol production was the same in all three reactor types. Biomass yields were calculated from the kinetic data and a stoichiometry for biomass formation was evaluated. The similarity of kinetics in the three bioreactor configurations suggests that taxol production by T. baccata cell suspensions is amenable to scateup. (c) 1995 John Wiley & Sons, Inc.     

Cybernetic model of the growth dynamics of Saccharomyces cerevisiae in batch and continuous cultures.

Growth of Saccharomyces cerevisiae on glucose in aerobic batch culture follows the well-documented diauxic pattern of completely fermenting glucose to ethanol during the first exponential growth phase, followed by an intermediate lag phase and a second exponential growth phase consuming ethanol. In continuous cultures over a range of intermediate dilution rates, the yeast bioreactor exhibits sustained oscillations in all the measured concentrations, such as cell mass, glucose, ethanol, and dissolved oxygen, the amounts of intracellular storage carbohydrates, such as glycogen and trehalose, the fraction of budded cells as well as the culture pH. We present here a structured, unsegregated model for the yeast growth dynamics developed from the 'cybernetic' modeling framework, to simulate the dynamic competition between all the available metabolic pathways. This cybernetic model accurately predicts all the key experimentally observed aspects: (i) in batch cultures, duration of the intermediate lag phase, sequential production and consumption of ethanol, and the dynamics of the gaseous exchange rates of oxygen and carbon dioxide; and (ii) in continuous cultures, the spontaneous generation of oscillations as well as the variations in period and amplitude of oscillations when the dilution rate or agitatin rate are changed.     

Continuous ethanol production from Jerusalem artichoke tubers. I. Use of free cells of Kluyveromyces marxianus

The Continuous fermentation of Jerusalem artichoke juice to ethanol by free cells of Kluyveromyces marxianus UCD (FST) 55-82 has been studied in a continuous-stirred-tank bioreactor at 35 degrees C and pH 4.6. A maximum yield of 90% of the theoretical was obtained at a dilution rate of 0.05 h(-1). About 95% of the sugars were utilized at dilution rates lower than 0.15 h(-1). Volumetric ethanol productivity and volumetric biomass productivity reached maximum values of 7 g ETOH/L/h and 0.6 g dry wt/L/h, respectively, at a dilution rate of 0.2 h(-1). The maintenance energy coefficient for K. marxianus culture was found to be 0.46 g sugar/g biomass/h/ Oscillatory behavior was following a change in dilution rate from a previous steady state and from batch to continuous culture. Values of specific ethanol production rate and specific sugar uptake were found to increase almost linearly with the increase of the dilution rate. The maximum specific ethanol production rate and maximum specific sugar uptake rate were found to be 2.6 g ethanol/g/ cell/h and 7.9 sugars/g cell/h, respectively. Washout occurred at a dilution rate of 0.41 h(-1).     

稀释速率对高浓度酒精连续发酵过程振荡行为的影响

在一搅拌罐和三段管式反应器组成的组合反应器系统中,使用葡萄糖浓度为280g/L,添加5g/L酵母膏和3g/L蛋白胨的底物,在总稀释速率分别为0.032h^-1,0.024h^-1,0.017h^-1,0.012h^-1和0.006h^-1的条件下,考察了稀释速率对高浓度酒精发酵系统振荡行为的影响。结果表明,振荡行为在特定的稀释速率条件下呈现,进而基于数学上的分岔理论,分析了振荡行为发生的可能性及对应的稀释速率范围,并与实验结果进行了比较,在此基础上,讨论了振荡行为对酒精发酵过程的影响。     

Kinetics of phenol oxidation by Candida tropicalis: effects of oxygen supply rate and nutrients on phenol inhibition

The kinetics of phenol degradation was estimated in a fed-batch reactor system. Effects of oxygen and nutrient excess or limitation as well as the presence of several essential ions on the phenol- and oxygen-specific uptake rates achieved simultaneously in a bioreactor were shown.Candida tropicalis was grown on phenol as the only carbon and energy source. Applying the best fit of polynomial function, the maximum specific uptake rates of phenol and oxygen, the critical concentrations of phenol, the half-saturation constants and inhibition constants were determined. Linear relationship between specific phenol uptake rate and the exogenous respiration rate was found regardless of the kind and presence of essential nutrients. At oxygen limitation both the phenol uptake rate and the cell affinity to phenol decreased more strongly compared with those under nutrient limitation. Oxygen in excess resulted in a significant increase of cell tolerance toward phenol. The presence of essential nutrients increased the specific phenol degradation rate and led to complete phenol oxidation.     

Ammonium uptake in carrot cell structures is influenced by pH-dependent cell aggregation

Semicontinuously grown wild carrot ( Daucus carota L.) cells were used in an investigation of the effect of culture medium pH on ammonium uptake in suspension cultures as a first step in exploring the relationship between pH and anthocyanin biosynthesis. In contrast to published data showing decreasing uptake rates with decreasing culture medium pH, ammonium-limited, semicontinuous carrot cell cultures showed a 25% greater ammonium uptake rate at pH 4.5 than at pH 5.5. When cells that had been grown semicontinuously in medium with a pH of 4.5 or 5.5 were grown in batch cultures at pH 4.5, 5.5 or 6.5 the ammonium uptake rates were those of the semicontinuous cultures, indicating that the pH of the batch culture medium had no effect on ammonium uptake rates over 7 days. The cell culture was composed of very small aggregates when it was grown semicontinuously in medium at pH 4.5, but was composed of large aggregates when it was grown semicontinuously in medium at pH 5.5. The aggregation/disaggregation of the cells was pH dependent, as changing the pH of the semicontinuous culture medium altered the extent of the aggregation. We conclude that the change in culture medium pH caused the cells to aggregate or disaggregate which in turn decreased or increased the rate of ammonium uptake from the medium.     

Continuous ethanol production from Jerusalem artichoke tubers. II. Use of immobilized cells of Kluyveromyces marxianus

Kluyveromyces marxianus UCD (FST) 55-82 cells were immobilized in Na alginate beads and used in a packed-bed bioreactor system for the continuous production of ethanol from the extract of Jerusalem artichoke tubers. Volumetric ethanol productivities of 104 and 80 g ethanol/ L/h were obtained at 80 and 92% sugar utilization, respectively. The maximum volumetric ethanol productivity of the immobilized cell bioreactor system was found to be 15 times higher than that of an ordinary-stirred-tank (CST) bioreactor using cells of K. marxianus. The immobilized cell bioreactor system was operated continuously at a constant dilution rate of 0.66 h(-1) for 12 days resulting in only an 8% loss of the original immobilized cell activity, which corresponds to an estimated half-life of ca. 72 days. The maximum specific ethanol productivity and maximum specific sugar uptake rate of the immobilized cells were found to be 0.55 g ethanol/g/biomass/h and 1.21 g sugars/g biomass/h, respectively.     

Induction and elimination of oscillations in continuous cultures of Saccharomyces cerevisiae

Continuous cultures of Saccharomyces cerevisiae are known to exhibit oscillatory behavior in the oxidative region. Important findings of a series of experiments conducted to identify the causes for initiation of and the means for elimination of oscillations in these cultures are reported in this paper. These oscillations are seen to be connected to the growth kinetics of the microorganism and are induced at very low glucose concentrations and at dissolved oxygen (DO) levels that are neither high nor low (DO values between 20 and 78% air saturation at a dilution rate of 0.2 h(-1) and pH of 5.5 at 30 degrees C). The oscillatory behavior is encountered over a range of dilution rates (0.09-0.25 h(-1) at 30 degrees C for pH = 5.5 and DO = 50% air saturation). The oscillations can be eliminated by raising the DO level above a critical value or by lowering the DO level below a critical value.     

Relationship between outer membrane protein and lipopolysaccharide profiles and serotypes of enterotoxigenic Escherichia coli isolated in Brazil

Abstract When the yeast Saccharomyces cerevisiae was grown under aerobic continuous culture conditions with a medium containing ethanol as carbon source, an autonomous sustained metabolic oscillation appeared. This oscillation was observed in rates and concentrations of various parameters such as, ethanol, oxygen uptake rate, carbon dioxide evolution rate, NaOH addition rate for pH control, acetate, and intracellular pH. No changes were observed in concentrations of stock carbohydrates. Intracellular pH changes were out of phase with oxygen uptake rate, which was reverse of the results with glucose-based oscillation. These results suggested that changes in glycolytic flux and intracellular pH were not regulating the oscillation. Analysis suggested that one of the oscillatory regulation points was located in the ethanol assimilation pathway.     

Parameter oscillations in a very high gravity medium continuous ethanol fermentation and their attenuation on a multistage packed column bioreactor system

The quasi-steady-states, marked by small fluctuations of residual glucose, ethanol, and biomass concentrations, and sustainable oscillations marked by big fluctuations of these monitored fermentation parameters were observed during the continuous ethanol fermentation of Saccharomyces cerevisiae when very high gravity media were fed and correspondingly high ethanol concentrations reached. A high ethanol concentration was shown to be one of the main factors that incited these oscillations, although the residual glucose level affected the patterns of these oscillations to some extent. The lag response of S. cerevisiae to high ethanol stress that causes the shifts of morphology, viability loss, and death of yeast cells is assumed to be one of the probable mechanisms behind these oscillations. It was predicted that the longer the delay of this response was, the longer the oscillation periods would be, which was validated by the experimental data and the comparison with the oscillatory behaviors reported for the ethanologen bacterium, Zymomonas mobilis. Furthermore, three tubular bioreactors in series were arranged to follow a stirred tank bioreactor to attenuate these oscillations. However, exaggerated oscillations were observed for the residual glucose, ethanol, and biomass concentrations measured in the broth from these tubular bioreactors. After the tubular reactors were packed with Intalox ceramic saddle packing, these oscillations were effectively attenuated and quasi-steady-states were observed during which there were very small fluctuations of residual glucose, ethanol, and biomass within the entire experimental run.     

初始条件对高浓度乙醇连续发酵过程的影响及振荡行为提高发酵效率的机理分析

前期实验在稀释速率为0.027h-1的高浓度乙醇连续发酵过程中,发现了一种长周期、宽振幅的参数振荡现象。本实验进一步考察了不同稀释速率下的连续发酵过程,发现在稀释速率为0.04h-1条件下,也能出现类似的振荡现象;在稀释速率为0.027h-1或0.04h-1的条件下,改变系统的初始状态可以得到振荡和稳态两种不同的发酵过程。比较振荡和稳态过程的实验数据后,发现在稀释速率为0.04h-1的条件下,与稳态过程相比,振荡过程的平均残糖浓度降低了14.8%,平均乙醇浓度提高了12.6%,平均设备生产强度提高了12.3%。进一步分析表明:与稳态过程相比,振荡过程动力学行为不仅存在滞后,而且在相同残糖和乙醇浓度条件下,所对应的平均比生长速率提高了53.8%。     

Twenty-four-well plate miniature bioreactor high-throughput system: assessment for microbial cultivations

High-throughput (HT) miniature bioreactor (MBR) systems are becoming increasingly important to rapidly perform clonal selection, strain improvement screening, and culture media and process optimization. This study documents the initial assessment of a 24-well plate MBR system, Micro (micro)-24, for Saccharomyces cerevisiae, Escherichia coli, and Pichia pastoris cultivations. MBR batch cultivations for S. cerevisiae demonstrated comparable growth to a 20-L stirred tank bioreactor fermentation by off-line metabolite and biomass analyses. High inter-well reproducibility was observed for process parameters such as on-line temperature, pH and dissolved oxygen. E. coli and P. pastoris strains were also tested in this MBR system under conditions of rapidly increasing oxygen uptake rates (OUR) and at high cell densities, thus requiring the utilization of gas blending for dissolved oxygen and pH control. The E. coli batch fermentations challenged the dissolved oxygen and pH control loop as demonstrated by process excursions below the control set-point during the exponential growth phase on dextrose. For P. pastoris fermentations, the micro-24 was capable of controlling dissolved oxygen, pH, and temperature under batch and fed-batch conditions with subsequent substrate shot feeds and supported biomass levels of 278 g/L wet cell weight (wcw). The average oxygen mass transfer coefficient per non-sparged well were measured at 32.6 +/- 2.4, 46.5 +/- 4.6, 51.6 +/- 3.7, and 56.1 +/- 1.6 h(-1) at the operating conditions of 500, 600, 700, and 800 rpm shaking speed, respectively. The mixing times measured for the agitation settings 500 and 800 rpm were below 5 and 1 s, respectively.     

A MODEL APPROACH FOR SIZE-SELECTIVE COMPETITION OF MARINE PHYTOPLANKTON FOR FLUCTUATING NITRATE AND AMMONIUM1

Phytoplankton size-selective competition for fluctuating nutrients was studied with the use of a numerical model, which describes nitrate and ammonium uptake, nitrate reduction to ammonium, and growth as a function of cell she under fluctuating nitrogen limitation. The only size-dependent parameter in the model was the cell nutrient quota. Related to this, the cell surface area per biomass was negatively correlated to cell volume, and the vacuole volume per biomass ratio was positively correlated to cell volume. Simulations showed an inverse correlation between the maximum specific growth rate and cell size under steady-state conditions. With nitrate as the limiting nitrogen source, nitrogen quotas were always higher than with ammonium at the same specific growth rate. Net passive transport of ammonium due to unspecific diffusion of ammonia across the plasma membrane decreased the affinity for ammonium, whereas the affinity for nitrate was not influenced. Transient state-specific ammonium uptake was not dependent on cell size. However, small algae always have the highest specific growth rate in ammonium-controlled systems according to our model. Transient state nitrate uptake rate was positively correlated to cell size because larger algae have a higher vacuole volume per biomass, in which nitrate can be stored. Despite their lower maximum growth rate, larger algae became dominant during simulations under fluctuating nitrate supply when amplitude of and the period between nitrate pulses were high enough. Results from model simulations were qualitatively validated by earlier observations that large diatoms become dominant under fluctuating conditions when nitrate is the main nitrogen source.     

Growth, metabolic, and antibody production kinetics of hybridoma cell culture: 2. Effects of serum concentration, dissolved oxygen concentration, and medium pH in a batch reactor.

The effects of serum, dissolved oxygen (DO) concentration, and medium pH on hybridoma cell physiology were examined in a controlled batch bioreactor using a murine hybridoma cell line (167.4G5.3). The effect of serum was also studied for a second murine hybridoma cell line (S3H5/gamma 2bA). Cell growth, viability, cell density, carbohydrate and amino acid metabolism, respiration and energy production rates, and antibody production rates were studied. Cell growth was enhanced and cell death was decreased by increasing the serum level. The growth rates followed a Monod-type model with serum being the limiting component. Specific glucose, glutamine, and oxygen uptake rates and specific lactate and ammonia production rates did not change with serum concentrations. Amino acid metabolism was slightly influenced by the serum level. Cell growth rates were not influenced by DO between 20% and 80% air saturation, while the specific death rates were lowest at 20-50% air saturation. Glucose and glutamine uptake rates increased at DO above 10% and below 5% air saturation. Cell growth rate was optimal at pH 7.2. Glucose and glutamine uptake rates, as well as lactate and ammonia production rates, increased above pH 7.2. Metabolic rates for glutamine and ammonia were also higher below pH 7.2. The consumption or production rates of amino acids followed the glutamine consumption very closely. Cell-specific oxygen uptake rate was insensitive to the levels of serum, DO, and pH. Theoretical calculations based on experimentally determined uptake rates indicated that the ATP production rates did not change significantly with serum and DO while it increased continually with increasing pH. The oxidative phosphorylation accounted for about 60% of total energy production. This contribution, however, increased at low pH values to 76%. The specific antibody production rate was not growth associated and was independent of serum and DO concentrations and medium pH above 7.20. A 2-fold increase in specific antibody production rates was observed at pH values below 7.2. Higher concentrations of antibody were obtained at high serum levels, between 20% and 40% DO, and at pH 7.20 due to higher viable cell numbers obtained.     

Growth kinetics of vitis vinifera cell suspension cultures: I. Shake flask cultures

Vitis vinifera cell suspension cultures carried out in shake flasks were closely examined for biomass growth and cell division in relation to carbohydrate, NH(4), NO(3)PO(4), and dissolved oxygen (DO)consumption. After inoculation, the oxygen uptake rate of the cultures measured on-tine was observed to increase continuously to a maximum value of 3.8 mmol O(2)L(-1)h(-1) at day 7 when cell division ceased and dissolved oxygen reached its lowest level of 17% air saturation. During this first phase of growth, the specific oxygen uptake rate remained constant at approximately 0.6 mmol 02 O(2) g(-1) dw h(-1)or approximately 2.2 mumol O(2), (10(6) cells)(-1) h(-1) whereas dry biomass concentration increased exponentially from 1.5 to 6.0 g dw L(-1). Thereafter, dry biomass concentration increased linearly to approximately 14 g dw L(-1) at day 14 following nitrate and carbohydrate uptake. During this second phase of growth, the biomass wet-to-dry weight ratio was found to increase in an inverse relationship with the estimated osmotic pressure of the culture medium. This corresponded to inflection points in the dry and wet biomass concentration and packed cell volume curves. Furthermore, growth and nutrient uptake results suggest that extracellular ammonium or phosphate ion availability may limit cell division. These findings indicate that cell division and biomass production of plant cell cultures may not always be completely associated, which suggests important new avenues to improve their productivity. (c) 1995 John Wiley & Sons, Inc.     

Involvement of a cell size control mechanism in the induction and maintenance of oscillations in continuous cultures of budding yeast

Spontaneous oscillations occur in glucose-limited continuous cultures of Saccharomyces cerevisiae under aerobic conditions. The oscillatory behavior is detectable as a periodic change of many bioparameters such as dissolved oxygen, ethanol production, biomass concentration, as well as cellular content of storage carbohydrates and is associated to a marked synchronization of the yeast population. These oscillations may be related to a periodic accumulation of ethanol produced by yeast in the culture medium.The addition of ethanol to oscillating yeast cultures supports this hypothesis: indeed, no effect was observed if ethanol was added when already present in the medium, while a marked phase oscillation shift was obtained when ethanol was added at any other time. Moreover, the addition of ethanol to a nonoscillating culture triggers new oscillations. An accurate analysis performed at the level of nonoscillating yeast populations perturbed by addition of ethanol showed that both the growth rate and the protein content required for cell division increased in the presence of mixed substrate (i.e., ethanol plus limiting glucose). A marked synchronization of the yeast population occurred when the added ethanol was exhausted and the culture resumed growth only on limiting glucose. A decrease of protein content required for cell division was also apparent. These experimental findings support a new model for spontaneous oscillations in yeast cultures in which the alternative growth on limiting glucose and limiting glucose plus ethanol modifies the critical protein content required for cell division.     

Large-scale (20 l) culture of surface-immobilized Catharanthus roseus cells.

Surface-immobilized C. roseus cell cultures were grown in a 20-l modified airlift bioreactor operated at 0.51 vvm (kLa approximately 8 h-1) under various gassing regimes [air, 2% (v/v) and 5% CO2]. Extracellular ammonium, phosphate, and nitrate ions as well as carbohydrate uptake and pH value of the medium were monitored together with on-line dissolved oxygen concentration, conductivity of the medium, and carbon dioxide production rate (CPR) of the cultures. Cultures supplemented with 2% CO2 showed higher nitrate (5.0-7.0 mM d-1) and carbohydrate (3.3 g l-1 d-1) uptake rates and biomass production (mu approximately 0.24 d-1, yield approximately 0.33 g dw g CHO-1 and 7.4 g dw L-1) as compared to air (3.6 mM d-1, 2.1 g l-1 d-1; 0.20 d-1, 0.25 g dw g CHO-1 and 5 g dw l-1) and 5% CO2 (2.0-3.6 mM d-1, 2.0 g l-1 d-1; 0.11 d-1, 0.20 g dw g CHO-1 and 5 g dw l-1) cultures and as reported previously for suspension cultures. In addition, air and 5% CO2 cultures displayed incomplete carbohydrate uptake and, more important, phosphate and ammonium ion release into the medium at the end, which was ascribed to loss of viability. This was not observed for 2% CO2 immobilized bioreactor as well as shake flask control suspension cultures, which suggests that sparged C. roseus surface-immobilized cell cultures require 2% CO2 supplementation of the gas phase for both maximum growth and retained viability. The maximum CPRs of all cultures were in the same range (2.1-2.8 mM CO2 l-1 h-1). However, the estimated maximum specific CO2 production rates of 2% CO2 and 5% CO2 immobilized cultures (0.6 mM g dw-1 h-1) were lower than those found for air-sparged immobilized cultures (1.0-1.3 mM g dw-1 h-1). These rates are significantly higher than those reported in the literature for C. roseus cell suspension cultures performed in bioreactors gassed with air (approximately 0.2-0.55 mM g dw-1 h-1).     

Continuous photoautotrophic cultures of the eukaryotic alga Chlorella vulgaris can exhibit stable oscillatory dynamics

Sustained oscillations in cell concentration, average per cell DNA content, and average cell size were found in continuous photoautotrophic cultures of Chlorella vulgaris at low dilution rates (0.1/day). The period of oscillation was approximately 10 days. DNA histograms determined by flow cytometry exhibited reproducible pattern through consecutive oscillations. At the maximum cell concentration during an oscillation, the DNA histograms showed that the majority of the cells were not replicating their chromosomes, and most of the culture was comprised of single cells in G0/G1 phase. The cells then initiated DNA replication; however, because of the long generation time, the cell concentration decreased to a minimum, and at the same time the average per cell DNA content reached its maximum value. At this point the cells began to divide, and the cell concentration increased until it reached its maximum value at the beginning of the next oscillation. Calculations based on the supplied nutrients and comparison to biomass generation showed that the oscillatory behavior in continuous photoautotrophic cultures of C. vulgaris was not due to nutrient limitation, but most likely was due to the secretion of compounds that alter cell cycle kinetics. The oscillatory behavior disappeared when the dilution rate was increased to 0.3/day and the culture reached a stable steady state.