Frequency analysis of autonomously oscillating yeast cultures

Oscillations of the internal CO(2) concentration in tobacco leaves transferred to low CO(2)

Measurement of the internal CO(2) concentration (Ci) in tobacco leaves using a fast-response CO(2) exchange system showed that in the light, switching from 350 microLL(-1) to a low CO(2) concentration of 36.5 microLL(-1) (promoting high photorespiration) resulted in the Ci oscillating near the value of CO(2) compensation point (Gamma*). The oscillations are highly irregular, the range of Ci varying by 2-4 microLL(-1) in substomatal cavities with a period of a few seconds. The statistical properties of the time series became stationary after a transient of approximately 100s following transfer to low CO(2). Attractor reconstruction shows that the observed oscillations are not chaotic but exhibit stochastic behavior. The period of oscillations is consistent with the duration of photorespiratory post-illumination burst (PIB). We suggest that the observed oscillations may be due to a similar mechanism to that which leads to PIB, and may play a role in switching mitochondrial operation between oxidation of the photorespiratory glycine and of the tricarboxylic acid cycle substrates.

Observation of a chaotic multioscillatory metabolic attractor by real-time monitoring of a yeast continuous culture

We monitored a continuous culture of the yeast Saccharomyces cerevisiae by membrane-inlet mass spectrometry. This technique allows very rapid simultaneous measurements (one point every 12 s) of several dissolved gases. During our experiment, the culture exhibited a multioscillatory mode in which the dissolved oxygen and carbon dioxide records displayed periodicities of 13 h, 36 min and 4 min. The 36- and 4-min modes were not visible at all times, but returned at regular intervals during the 13-h cycle. The 4-min mode, which has not previously been described in continuous culture, can also be seen when the culture displays simpler oscillatory behavior. The data can be used to visualize a metabolic attractor of this system, i.e. the set of dissolved gas concentrations which are consistent with the multioscillatory state. Computation of the leading Lyapunov exponent reveals the dynamics on this attractor to be chaotic.

Autonomous oscillations in Saccharomyces cerevisiae during batch cultures on trehalose

We report that autonomous oscillations, which usually happen in aerobic glucose-limited continuous cultures of yeast at low dilution rate, were also observed in trehalose discontinuous cultures of Saccharomyces cerevisiae. This unexpected oscillatory behaviour was therefore examined using fast Fourier transformation of online gas measurements. This robust mathematical analysis underlined the existence of two types of oscillation. The first was found to be linked to the cell cycle because (a) the periodicity corresponded to a fraction of the generation time and (b) the oscillations were accompanied by a transient increase in the budding index, mobilization of storage carbohydrates, and fermentative activity. Moreover, these oscillations occurred in a range of specific growth rates between 0.04 and 0.15 h(-1). All these criteria were consistent with the cell-cycle-related metabolic oscillations observed in the same range of growth rates in glucose-limited continuous cultures. The second type were short-period respiratory oscillations, independent of the specific growth rate. Both types of oscillation were found to take place consecutively and/or simultaneously during batch culture on trehalose. In addition, mobilization of intracellular trehalose emerged as a key parameter for the sustainability of these autonomous oscillations as they were no longer observed in a mutant defective in neutral trehalase activity. We propose that batch culture on trehalose may be an excellent device for further investigation of the molecular mechanisms that underlie autonomous oscillations in yeast.

Dynamic modeling of microbial cell populations

Microbial cultures are comprised of heterogeneous cells that differ according to their size and intracellular concentrations of DNA, proteins and other constituents. Recent advances have been made in cell population modeling, which allow the effects of cell heterogeneity on culture dynamics and metabolite production to be predicted. If the intracellular state can be captured with a few variables, the population balance equation framework is a viable modeling approach. The cell ensemble modeling technique is better suited for the development of population models that include more detailed descriptions of cellular metabolism and/or cell-cycle progression.

Free intracellular amino acid pools during autonomous oscillations in Saccharomyces cerevisiae

In the present work dynamic changes of free intracellular amino acid pools during autonomous oscillations of Saccharomyces cerevisiae were quantified in glucose-limited continuous cultivations. At a dilution rate of D = 0.22 h(-1) cyclic changes with a period of 120 min were found for many variables such as carbon dioxide production rate, dissolved oxygen, pH, biomass content, and various metabolite concentrations. On the basis of the observed dynamic patterns, free intracellular amino acids were classified to show oscillatory, stationary, or chaotic behavior. Amino acid pools such as serine, alanine, valine, leucine, or lysine were subjected to clear oscillations with a frequency of 120 min, identical to that of other described cultivation variables, indicating that there is a direct correlation between the periodic changes of amino acid concentrations and the metabolic oscillations on the cellular level. The oscillations of these amino acids were unequally phase-delayed and had different amplitudes of oscillation. Accordingly, they exhibited different patterns in phase plane plots vs. intracellular trehalose. Despite the complex and marked metabolic changes during oscillation, selected intracellular amino acids such as histidine, threonine, isoleucine, or arginine remained about constant. Concentrations of glutamate and glutamine showed a chaotic behavior. However, the ratio of glutamate to glutamine concentration was found to be oscillatory, with a period of 60 min and a corresponding figure eight-shaped pattern in a plot vs. trehalose concentration. Considering the described diversity, it can be concluded that the observed periodic changes are neither just the consequence of low or high rates of protein biosynthesis/degradation nor correlated to changing cell volumes during oscillation. The ratio between doubling time (189 min) and period of oscillation of intracellular amino acids (120 min) was 1:6. The fact that there is a close relationship between doubling time and period of oscillation underlines that the described autonomous oscillations are cell-cycle-associated.

Effect of environment partitioning on the survival and coexistence of autocatalytic replicators

The paradigm of cubic autocatalytic replicators with decay in coupled isothermal continuous stirred tank reactors is selected as a model to study complex behavior in population dynamics of sexually reproducing species in a heterogenous environment. It is shown that, even a setup with single species in two coupled environments may have regions in parameter space that result in chaotic behavior, hence segregation in the environment causes complexity in the system dynamics. Furthermore, partitioning is found to lead to emergence phenomena exemplified by steady states not obtainable in the equivalent homogeneous system. These phenomena are illustrated through case studies involving single or multiple species. Results show that the coupled environments can host species, that would not survive should the coupling be removed.

Clock control of ultradian respiratory oscillation found during yeast continuous culture

A short-period autonomous respiratory ultradian oscillation (period approximately 40 min) occurs during aerobic Saccharomyces cerevisiae continuous culture and is most conveniently studied by monitoring dissolved O(2) concentrations. The resulting data are high quality and reveal fundamental information regarding cellular dynamics. The phase diagram and discrete fast Fourier transformation of the dissolved O(2) values revealed a square waveform with at least eight harmonic peaks. Stepwise changes in temperature revealed that the oscillation was temperature compensated at temperatures ranging from 27 to 34 degrees C when either glucose (temperature quotient [Q(10)] = 1.02) or ethanol (Q(10) = 0.82) was used as a carbon source. After alteration of the temperature beyond the temperature compensation region, phase coherence events for individual cells were quickly lost. As the cell doubling rate decreased from 15.5 to 9.2 h (a factor of 1.68), the periodicity decreased by a factor of 1.26. This indicated that there was a degree of nutrient compensation. Outside the range of dilution rates at which stable oscillation occurred, the mode of oscillation changed. The oscillation in respiratory output is therefore under clock control.

Multiple stable states and hysteresis in continuous, oscillating cultures of budding yeast

The conditions that precede the onset of autonomous oscillations in continuous yeast cultures were studied in three different types of experiments. It was found that the final state of the culture depended on the protocol used to start up the reactor. Batch cultures, switched to continuous operation at different stages of the batch growth curve, all exhibited similar dynamics-ethanol depletion followed by autonomous oscillations. Small perturbations of the distribution of states in the reactor, achieved by addition of externally grown cells, were able to quench the oscillatory dynamics. Reaching the desired operating point by slow dilution rate changes gave rise to different final states, two oscillatory states and one steady state, depending on the rate of change in dilution rate. The multiplicity of stable states at a single operating point is not explained by any current distributed model and points toward a segregated mechanism of these oscillations.