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.     

The cyclic AMP control system in the development of Dictyostelium discoideum. I. Cellular dynamics.

A model for the synthesis and release of cyclic AMP in aggregating cells of Dictyostelium discoideum is developed. The model shows transitions from low level steady release of cAMP to excitable pulsatile release and then to autonomous periodic pulsatile release of cAMP as starvation proceeds. Finally, there is a transition to high level continuous release of cAMP. A detailed correspondence is drawn between these transitions and the phenomena that are observed to appear sequentially during the aggregation phase, specifically: cloud formation, relaying competence, autonomous competence, and tip activity. The only assumptions necessary to the model are that there is a autocatalytic mechanism for cAMP synthesis, a negative feedback regulation of cAMP through another variable C, and a source term for C that declines with starvation. By analogy with other systems across the phylogenetic scale, in which cAMP activates catabolic pathways and catabolites depress cAMP levels, C is tentatively identified as some measure of the level of energy-yielding catabolites in the cell and the source term for C, as a measure of the cells stored reserves. Starvation for C induces catabolism of stored reserves S through a rise in cAMP. As S, the source term for C declines, the feedback regulation through C can no longer maintain homeostosis and the control loop may be destabilised by small perturbations, i.e. it becomes excitable. A further decline in S can produce limit cycle oscillations in the catabolite-cAMP feedback loop. As S declines even further, continuous steady release of cAMP may ensue.In addition to incorporating the four developmental transitions observed during the aggregation phase as direct consequences of starvation, the model features a super-exponential emergence of relaying competence, phase shifts and acceleration of development by cAMP pulses, and a decreasing refractory period that becomes less than the period of an autonomous cell. All these features closely parallel experimental findings. Finally, the model suggests further experiments critical to an understanding of the dynamics underlying aggregation.     

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.     

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.     

Control of the cell cycle ofCandida utilis by external conditions

A mathematical model of the cell cycle ofCandida utilis in a continuous culture was formulated with respect to dilution rate. It makes it possible to express the duration of morphological stages in minutes, separately for mother cells and daughter cells. These values were compared with equivalent parameters in batch cultures. Duration of the morphological stage with buds was much longer in batch cultures as compared with the same value determined for a continuous culture according to the mathematical model. When using cultivation apparatus with a higher aeration capacity the (S + G₂) phase, i.e. the stage bearing the bud, was reduced also in the batch cultures and approached the values determined for the continuous culture by means of the mathematical model.     

Diffusion of extracellular K+ can synchronize bursting oscillations in a model islet of Langerhans.

Electrical bursting oscillations of mammalian pancreatic beta-cells are synchronous among cells within an islet. While electrical coupling among cells via gap junctions has been demonstrated, its extent and topology are unclear. The beta-cells also share an extracellular compartment in which oscillations of K+ concentration have been measured (Perez-Armendariz and Atwater, 1985). These oscillations (1-2 mM) are synchronous with the burst pattern, and apparently are caused by the oscillating voltage-dependent membrane currents: Extracellular K+ concentration (Ke) rises during the depolarized active (spiking) phase and falls during the hyperpolarized silent phase. Because raising Ke depolarizes the cell membrane by increasing the potassium reversal potential (VK), any cell in the active phase should recruit nonspiking cells into the active phase. The opposite is predicted for the silent phase. This positive feedback system might couple the cells' electrical activity and synchronize bursting. We have explored this possibility using a theoretical model for bursting of beta-cells (Sherman et al., 1988) and K+ diffusion in the extracellular space of an islet. Computer simulations demonstrate that the bursts synchronize very quickly (within one burst) without gap junctional coupling among the cells. The shape and amplitude of computed Ke oscillations resemble those seen in experiments for certain parameter ranges. The model cells synchronize with exterior cells leading, though incorporating heterogeneous cell properties can allow interior cells to lead. The model islet can also be forced to oscillate at both faster and slower frequencies using periodic pulses of higher K+ in the medium surrounding the islet. Phase plane analysis was used to understand the synchronization mechanism. The results of our model suggest that diffusion of extracellular K+ may contribute to coupling and synchronization of electrical oscillations in beta-cells within an islet.     

Direction of the sustained oscillation trajectory in the cell-product phase plane describing product inhibition on continuous fermentation systems

A criterion for the direction (clockwise or counterclockwise) of the limit cycle in the cell massproduct phase plane is developed for a product inhibition model of a continuous microbial culture. It is then hypothesized that the model will not admit clockwise oscillations.     

Oscillatory growth rate responses of S. Cerevisiae in continuous culture

The yeast S. cerevisiae was grown on dilute, chemically defined media in continuous culture with either glucose or ammonium sulfate as the growth-limiting ingredient. Changes in dilution rate or glucose concentration induced decaying oscillations in the numbers of yeast growing on ammonium sulfate-limited media. Spot checks indicated that Cell dry weight and Kjeldahl nitrogen followed the cell numbers during these oscillations. With glucose-limited media, there was no response to step changes in ammonium sulfate concentration, and dilution rate step changes gave non-oscillatory transient responses.     

Modeling the synchronization of yeast respiratory oscillations

The budding yeast Saccharomyces cerevisiae exhibits autonomous oscillations when grown aerobically in continuous culture with ethanol as the primary carbon source. A single cell model that includes the sulfate assimilation and ethanol degradation pathways recently has been developed to study these respiratory oscillations. We utilize an extended version of this single cell model to construct large cell ensembles for investigation of a proposed synchronization mechanism involving hydrogen sulfide. Ensembles with as many as 10,000 cells are used to simulate population synchronization and to compute transient number distributions from asynchronous initial cell states. Random perturbations in intracellular kinetic parameters are introduced to study the synchronization of single cells with small variations in their unsynchronized oscillation periods. The cell population model is shown to be consistent with available experimental data and to provide insights into the regulatory mechanisms responsible for the synchronization of yeast metabolic oscillations.     

Nature and significance of oscillatory behavior during solvent production by Clostridium acetobutylicum in continuous culture

The concurrent production of acids and solvents and the production of acetone during continuous culture in a product-limited chemostat indicated that the culture contained a mixture of acid- and solvent-producing cells. Periodic oscillations in the yield of end products and the specific growth rate of the culture were ob served during undisturbed continuous culture at a constant dilution rate. The increased specific growth rate was associated with an increased acid yield and an increase in the rate of cell division and the proportion of short rods. The decreased specific growth rate was as sociated with an increase in the solvent yield and a decrease in the rate of cell division, resulting in the production of elongated rods. It is proposed that the oscillatory behavior observed during continuous culture is an inherent characteristic related to the shift from primary to secondary metabolism. A major consequence of the oscillation of the specific rates of growth and division in cultures containing acid- and solvent-producing cells is that it precludes the attainment of a true steady state during continuous culture.     

Cultivation of thermophilic methanogen KN-15 on H2-CO2 under pressurized conditions

Cultivation of the thermophilic methanogen KN-15 was carried out under pressurized batch and continuous conditions. In pressurized batch culture, both the turning point at which cell growth changed from exponential to linear and the growth rate during the linear growth phase increased with the rise of total pressure of the gas phase in the fermentor. The cell concentration reached 18.5 g dry cell/l after 10 h of batch cultivation under 3.0 × 10⁵ Pa pressurized conditions. Under pressurized continuous conditions, it was also observed that the cell concentration and cell productivities increased with the rise of total pressure of the gas phase. Cell and methane productivities of 3.0 g dry cell/l/h and 1.28 mol/l/h, respectively, were achieved in 3.0 × 10⁵ Pa pressurized continuous culture. According to the results from the Monod model application, the achievable cell productivities (V_max) and the Monod type saturation constant for cell productivities (K_s^′) were 12.8 g dry cell/l/h and 9.7 × 10⁵ Pa, respectively.     

Influence of controlled glucose oscillations on a fed-batch process of recombinant Escherichia coli

The influence of glucose oscillations on cell growth and product formation of a recombinant Escherichia coli culture producing a heterologous alpha-glucosidase was studied in fed-batch cultures in a laboratory bioreactor. Glucose oscillations were created by an on/off-feeding mode in either fast cycles (1 min) or slow cycles (4 min) and compared to a process with constant glucose addition. The study indicates that glucose oscillations influence the product stability and the overgrowth of plasmid-free cells if such cultures are not performed under continuous pressure for selection of plasmid-containing cells. Although the glucose uptake capacity decreased after induction of the recombinant alpha-glucosidase in all cultures performed, the up-growth of plasmid-free cells during the production phase was strongly inhibited by fast oscillations. In contrast, plasmid-free cells grew up when constant feeding or slow cycles were applied. Our data suggest that the various feed protocols effect the specific carbon dioxide formation rate differently, with the highest production of carbon dioxide in the cultivations with fast cycles. In connection to product formation the initial alpha-glucosidase accumulation was the same in all cultures, but the stability of the product was significantly lower in the cultivation with slow cycles. Our results from laboratory experiments are discussed in relation to the mixing situation in large-scale bioreactors.     

Process-induced cell cycle oscillations in CHO cultures: Online monitoring and model-based investigation

The influence of process strategies on the dynamics of cell population heterogeneities in mammalian cell culture is still not well understood. We recently found that the progression of cells through the cell cycle causes metabolic regulations with variable productivities in antibody-producing Chimese hamster ovary (CHO) cells. On the other hand, it is so far unknown how bulk cultivation conditions, for example, variable nutrient concentrations depending on process strategies, can influence cell cycle-derived population dynamics. In this study, process-induced cell cycle synchronization was assessed in repeated-batch and fed-batch cultures. An automated flow cytometry set-up was developed to measure the cell cycle distribution online, using antibody-producing CHO DP-12 cells transduced with the cell cycle-specific fluorescent ubiquitination-based cell cycle indicator (FUCCI) system. On the basis of the population-resolved model, feeding-induced partial self-synchronization was predicted and the results were evaluated experimentally. In the repeated-batch culture, stable cell cycle oscillations were confirmed with an oscillating G1 phase distribution between 41% and 72%. Furthermore, oscillations of the cell cycle distribution were simulated and determined in a (bolus) fed-batch process with up to cells/ml. The cell cycle synchronization arose with pulse feeding only and ceased with continuous feeding. Both simulated and observed oscillations occurred at higher frequencies than those observable based on regular (e.g., daily) sample analysis, thus demonstrating the need for high-frequency online cell cycle analysis. In summary, we showed how experimental methods combined with simulations enable the improved assessment of the effects of process strategies on the dynamics of cell cycle-dependent population heterogeneities. This provides a novel approach to understand cell cycle regulations, control cell population dynamics, avoid inadvertently induced oscillations of cell cycle distributions and thus to improve process stability and efficiency.     

Factors affecting growth and product formation in plant cells grown in continuous culture

In the present work we examined the potential benefits of the continuous culture (chemostat) technique at improving biomass yields of Mentha and Dioscorea cells and product formation (diosgenin) by Dioscorea cells. In contrast to Mentha cells, Dioscorea cells were sensitive to mechanical agitation in the exponential growth phase and could only be grown in a bubble column type fermentor. Maximal biomass yield of 0.5 and 0.4 g cell dry weight g^?1sucrose were obtained for Mentha and Dioscorea cells, respectively. When the phosphate concentration during the growth phase of Dioscorea was increased, a maximal concentration of 7.8% diosgenin (of dry weight) was obtained. Productivity of diosgenin was 12 mg 1^?1 day^?1 in a two-stage continuous process as compared to 7.3 mg 1^?1 day^?1 in a batch culture.     

Modeling of Glucose-Induced cAMP Oscillations in Pancreatic β Cells: cAMP Rocks when Metabolism Rolls

Recent advances in imaging technology have revealed oscillations of cyclic adenosine monophosphate (cAMP) in insulin-secreting cells. These oscillations may be in phase with cytosolic calcium oscillations or out of phase. cAMP oscillations have previously been modeled as driven by oscillations in calcium, based on the known dependence of the enzymes that generate cAMP (adenylyl cyclase) and degrade it (phosphodiesterase). However, cAMP oscillations have also been reported to occur in the absence of calcium oscillations. Motivated by similarities between the properties of cAMP and metabolic oscillations in pancreatic β cells, we propose here that in addition to direct control by calcium, cAMP is controlled by metabolism. Specifically, we hypothesize that AMP inhibits adenylyl cyclase. We incorporate this hypothesis into the dual oscillator model for β cells, in which metabolic (glycolytic) oscillations cooperate with modulation of ion channels and metabolism by calcium. We show that the combination of oscillations in AMP and calcium in the dual oscillator model can account for the diverse oscillatory patterns that have been observed, as well as for experimental perturbations of those patterns. Predictions to further test the model are provided.     

UNDAMPED OSCILLATIONS OF PYRIDINE NUCLEOTIDE AND OXYGEN TENSION IN CHEMOSTAT CULTURES OF KLEBSIELLA AEROGENES

Klebsiella aerogenes was grown in chemostat culture with the pH controlled to ±0.01 and temperature to ±0.1°C. The oxygen tension of the culture was regulated by changing the partial pressure of oxygen in the gas phase and recorded by means of an oxygen electrode. Reduced pyridine nucleotide was monitored continuously in the culture by means of direct fluorimetry. On applying an anaerobic shock to the culture, damped oscillations in pyridine nucleotide fluorescence were obtained. Further anaerobic shocks decreased the damping and eventually gave rise to undamped oscillations of a 2–3 min period which continued for several days. These oscillations were paralleled by oscillations of the same frequency in respiration rate. The amplitude of the oscillations in the respiration rate was equivalent to only 1% of the total steady-state respiration, whereas that of pyridine nucleotide oscillations was equivalent to 10% of the total aerobic/anaerobic fluorescence response. The oscillations ceased on interrupting the glucose feed but restarted on adding excess glucose to the culture. Addition of succinate also restarted the oscillations so that they appear not to be of glycolytic origin. The frequency of oscillations varied with growth rate and conditions. Oscillations of much lower frequency were obtained under limited-oxygen and anaerobic conditions than under fully aerobic conditions. Under glucose-limited conditions, fluctuations were found in adenosine triphosphate (ATP) content which were in phase with the pyridine nucleotide oscillations, but under nitrogen-limited growth conditions no such fluctuations in ATP were observed. The primary oscillating pathway could not be identified but the mechanism would appear to be quite different from that involved in oscillations observed in yeast cells. The synchronization of oscillations and observations of negative damping could be explained by a syntalysis effect.     

Intensive DNA Replication and Metabolism during the Lag Phase in Cyanobacteria

Unlike bacteria such as Escherichia coli and Bacillus subtilis, several species of freshwater cyanobacteria are known to contain multiple chromosomal copies per cell, at all stages of their cell cycle. We have characterized the replication of multi-copy chromosomes in the cyanobacterium Synechococcus elongatus PCC 7942 (hereafter Synechococcus 7942). In Synechococcus 7942, the replication of multi-copy chromosome is asynchronous, not only among cells but also among multi-copy chromosomes. This suggests that DNA replication is not tightly coupled to cell division in Synechococcus 7942. To address this hypothesis, we analysed the relationship between DNA replication and cell doubling at various growth phases of Synechococcus 7942 cell culture. Three distinct growth phases were characterised in Synechococcus 7942 batch culture: lag phase, exponential phase, and arithmetic (linear) phase. The chromosomal copy number was significantly higher during the lag phase than during the exponential and linear phases. Likewise, DNA replication activity was higher in the lag phase cells than in the exponential and linear phase cells, and the lag phase cells were more sensitive to nalidixic acid, a DNA gyrase inhibitor, than cells in other growth phases. To elucidate physiological differences in Synechococcus 7942 during the lag phase, we analysed the metabolome at each growth phase. In addition, we assessed the accumulation of central carbon metabolites, amino acids, and DNA precursors at each phase. The results of these analyses suggest that Synechococcus 7942 cells prepare for cell division during the lag phase by initiating intensive chromosomal DNA replication and accumulating metabolites necessary for the subsequent cell division and elongation steps that occur during the exponential growth and linear phases.     

Specific monoclonal antibody productivity and the cell cycle-comparisons of batch,continuous and perfusion cultures

A selection of mouse hybridoma cell lines showed a variation of approximately two orders of magnitude in intracellular monoclonal antibody contents. The different levels directly influenced apparent specific monoclonal antibody productivity during the death phase but not during the growth phase of a batch culture. The pattern of changes in specific productivity during culture remained basically similar even though at different levels for all cell lines tested. Arresting the cells in the G₁ phase using thymidine increased the specific productivity, cell volume and intracellular antibody content but at the same time led to decreased viability. In continuous culture DNA synthesis decreased with decreasing dilution rate though without an accompanying change in cell cycle and cell size distributions. The data shows both the decrease in viability and intracellular antibody content to be important factors which influence the negative association between specific antibody productivity and growth rate. In high cell density perfusion culture, when the cell cycle was prolonged by slow growth, viability was low and dead, but not lysed, cells were retained in the system, the specific antibody productivity was nearly two fold higher than that obtained in either batch or continuous cultures. The results imply that the prolongation of G₁ phase and the increase in death rate of cells storing a large amount of antibody together cause an apparent increase in specific antibody productivity.     

Cyclic AMP and the control of aggregative phase gene expression in Dictyostelium discoideum.

The induction of aggregative phase functions and the acceleration of the onset of aggregation competence by nanomolar pulses of cyclic AMP can be mimicked by exposing developing cells to a high extracellular concentration of either cyclic AMP or cyclic GMP (5 × 10^?4M) during the first 1–2 hr of development. Pulses of cyclic AMP have previously been shown to result in oscillations of intracellular cyclic AMP concentration; we show that high extracellular concentrations of cyclic AMP and cyclic GMP cause intracellular cyclic AMP levels to increase. We describe a mutant, HM11, which has elevated levels of intracellular cyclic AMP from the beginning of development and which begins to accumulate cell-associated phosphodiesterase, an aggregative phase enzyme, within an hour of starvation. Our data suggest that the expression of aggregative phase functions is controlled by an elevation of intracellular cyclic AMP which may be either continuous or periodic.     

Fluctuations du taux d'AMP cyclique et des activites adenylate cyclase et AMP cyclique-phosphodiesterase dans les cultures synchrones d'un procaryote, Nocardia restricta

Cultures of Nocardia restricta, a prokaryote from the group of Actinomycetes, can be synchronised by diluting, in a fresh growth medium, cells already in stationary phase. The synchronisation of the cultures is monitored by examining the synchrony of DNA replication.In these synchronised cultures, the intracellular cyclic AMP level exhibits rythmic oscillations with a period equal to the generation time of the culture. There is only one peak per generation. The average ratio of maximum to minimum concentrations is at least 3.Cyclic AMP accumulates also in the medium with a step pattern. It appears in the medium during maximum production of cyclic AMP in the cell.The specific activity of adenylate cyclase (EC 4.6.1.1) measured in the 30 000 × g pellet of cell-free extracts also oscillates and correlates well with fluctuations in the cyclic AMP level. At the end of exponential growth, cyclic-AMP phosphodiesterase (EC 3.1.4.17) is detectable in the cells. The specific activity of this enzyme measured in the 30 000 × g supernatant of cell-free extracts shows also an oscillating pattern.To our knowledge it is the first time that such oscillations in the metabolism of cyclic AMP are described among prokaryotes. It is now possible to look at a link between this phenomenon and the cell cycle of the organism.