Single cell studies and simulation of cell-cell interactions using oscillating glycolysis in yeast cells

The observation of oscillations in the concentrations of NADH and other intermediates in glycolysis in dense yeast cell suspensions is generally believed to be the result of synchronization of such oscillations between individual cells. The synchrony is believed to be a property of cell density and the question is: does metabolism in each individual yeast cell continue to oscillate, but out of phase, in the absence of synchronization? Here we have used high-sensitivity fluorescence microscopy to measure NADH in single isolated yeast cells under conditions where we observe oscillations of glycolysis in dense cell suspensions. However, we have not been able to detect intracellular oscillations in NADH in these isolated cells, which cannot synchronize their metabolism with other cells. However, addition of acetaldehyde to a single cell as pulses with a frequency similar to the oscillations in dense cell suspensions will induce oscillations in that cell. Ethanol, another product of glycolysis, which has been proposed as a synchronizing agent of glycolysis in cells, was not able to induce oscillations when added as pulses. The experiments support the notion that the intracellular oscillations are associated with the cell density of the yeast cell suspension and mediated by acetaldehyde and perhaps also other substances.     

How yeast cells synchronize their glycolytic oscillations: a perturbation analytic treatment

Of all the lifeforms that obtain their energy from glycolysis, yeast cells are among the most basic. Under certain conditions the concentrations of the glycolytic intermediates in yeast cells can oscillate. Individual yeast cells in a suspension can synchronize their oscillations to get in phase with each other. Although the glycolytic oscillations originate in the upper part of the glycolytic chain, the signaling agent in this synchronization appears to be acetaldehyde, a membrane-permeating metabolite at the bottom of the anaerobic part of the glycolytic chain. Here we address the issue of how a metabolite remote from the pacemaking origin of the oscillation may nevertheless control the synchronization. We present a quantitative model for glycolytic oscillations and their synchronization in terms of chemical kinetics. We show that, in essence, the common acetaldehyde concentration can be modeled as a small perturbation on the "pacemaker" whose effect on the period of the oscillations of cells in the same suspension is indeed such that a synchronization develops.     

On the mechanisms of glycolytic oscillations in yeast

This work concerns the cause of glycolytic oscillations in yeast. We analyse experimental data as well as models in two distinct cases: the relaxation-like oscillations seen in yeast extracts, and the sinusoidal Hopf oscillations seen in intact yeast cells. In the case of yeast extracts, we use flux-change plots and model analyses to establish that the oscillations are driven by on/off switching of phosphofructokinase. In the case of intact yeast cells, we find that the instability leading to the appearance of oscillations is caused by the stoichiometry of the ATP-ADP-AMP system and the allosteric regulation of phosphofructokinase, whereas frequency control is distributed over the reaction network. Notably, the NAD+/NADH ratio modulates the frequency of the oscillations without affecting the instability. This is important for understanding the mutual synchronization of oscillations in the individual yeast cells, as synchronization is believed to occur via acetaldehyde, which in turn affects the frequency of oscillations by changing this ratio.     

Heterogeneity of glycolytic oscillatory behaviour in individual yeast cells

There are many examples of oscillations in biological systems and one of the most investigated is glycolytic oscillations in yeast. These oscillations have been studied since the 1950s in dense, synchronized populations and in cell-free extracts, but it has for long been unknown whether a high cell density is a requirement for oscillations to be induced, or if individual cells can oscillate also in isolation without synchronization. Here we present an experimental method and a detailed kinetic model for studying glycolytic oscillations in individual, isolated yeast cells and compare them to previously reported studies of single-cell oscillations. The importance of single-cell studies of this phenomenon and relevant future research questions are also discussed.     

From steady-state to synchronized yeast glycolytic oscillations I: model construction

An existing detailed kinetic model for the steady-state behavior of yeast glycolysis was tested for its ability to simulate dynamic behavior. Using a small subset of experimental data, the original model was adapted by adjusting its parameter values in three optimization steps. Only small adaptations to the original model were required for realistic simulation of experimental data for limit-cycle oscillations. The greatest changes were required for parameter values for the phosphofructokinase reaction. The importance of ATP for the oscillatory mechanism and NAD(H) for inter-and intra-cellular communications and synchronization was evident in the optimization steps and simulation experiments. In an accompanying paper [du Preez F et al. (2012) FEBS J279, 2823-2836], we validate the model for a wide variety of experiments on oscillatory yeast cells. The results are important for re-use of detailed kinetic models in modular modeling approaches and for approaches such as that used in the Silicon Cell initiative. DATABASE: The mathematical models described here have been submitted to the JWS Online Cellular Systems Modelling Database and can be accessed at http://jjj.biochem.sun.ac.za/database/dupreez/index.html.     

The rhythm of yeast

Although yeast are unicellular and comparatively simple organisms, they have a sense of time which is not related to reproduction cycles. The glycolytic pathway exhibits oscillatory behaviour, i.e. the metabolite concentrations oscillate around phosphofructokinase. The frequency of these oscillations is about 1 min when using intact cells. Also a yeast cell extract can oscillate, though with a lower frequency. With intact cells the macroscopic oscillations can only be observed when most of the cells oscillate in concert. Transient oscillations can be observed upon simultaneous induction; sustained oscillations require an active synchronisation mechanism. Such an active synchronisation mechanism, which involves acetaldehyde as a signalling compound, operates under certain conditions. How common these oscillations are in the absence of a synchronisation mechanism is an open question. Under aerobic conditions an oscillatory metabolism can also be observed, but with a much lower frequency than the glycolytic oscillations. The frequency is between one and several hours. These oscillations are partly related to the reproductive cycle, i.e. the budding index also oscillates; however, under some conditions they are unrelated to the reproductive cycle, i.e. the budding index is constant. These oscillations also have an active synchronisation mechanism, which involves hydrogen sulfide as a synchronising agent. Oscillations with a frequency of days can be observed with yeast colonies on plates. Here the oscillations have a synchronisation mechanism which uses ammonia as a synchronising agent.     

Parameter oscillation attenuation and mechanism exploration for continuous VHG ethanol fermentation

A bioreactor system composed of a stirred tank and three tubular bioreactors in series was established, and continuous ethanol fermentation was carried out using a general Saccharomyces cerevisiae strain and a very high gravity medium containing 280 g L(-1) glucose, supplemented with 5 g L(-1) yeast extract and 3 g L(-1) peptone. Sustainable oscillations of glucose, ethanol, and biomass were observed when the tank was operated at the dilution rate of 0.027 h(-1), which significantly affected ethanol fermentation performance of the system. After the tubular bioreactors were packed with 1/2' Intalox ceramic saddles, the oscillations were attenuated and quasi-steady states were achieved. Residence time distributions were studied for the packed bioreactors by the step input response technique using xylose as a tracer, which was added into the medium at a concentration of 20 g L(-1), indicating that the backmixing alleviation assumed for the packed tubular bioreactors could not be established, and its contribution to the oscillation attenuation could not be verified. Furthermore, the role of the packing's yeast cell immobilization in the oscillation attenuation was investigated by packing the tubular bioreactors with packings with significant difference in yeast cell immobilization effects, and the experimental results revealed that only the Intalox ceramic saddles and wood chips with moderate yeast cell immobilization effects could attenuate the oscillations, and correspondingly, improved the ethanol fermentation performance of the system, while the porous polyurethane particles with good yeast cell immobilization effect could not. And the viability analysis for the immobilized yeast cells illustrated that the extremely lower yeast cell viability within the tubular bioreactors packed with the porous polyurethane particles could be the reason for their inefficiency, while the yeast cells loosely immobilized onto the surfaces of the Intalox ceramic saddles and wood chips could be renewed during the fermentation, guaranteeing their viability and making them more efficient in attenuating the oscillations. The packing Raschig rings without yeast cell immobilization effect did not affect the oscillatory behavior of the tubular bioreactors, further supporting the role of the yeast cell immobilization in the oscillation attenuation.     

Sustained glycolytic oscillations in individual isolated yeast cells

Yeast glycolytic oscillations have been studied since the 1950s in cell-free extracts and intact cells. For intact cells, sustained oscillations have so far only been observed at the population level, i.e. for synchronized cultures at high biomass concentrations. Using optical tweezers to position yeast cells in a microfluidic chamber, we were able to observe sustained oscillations in individual isolated cells. Using a detailed kinetic model for the cellular reactions, we simulated the heterogeneity in the response of the individual cells, assuming small differences in a single internal parameter. This is the first time that sustained limit-cycle oscillations have been demonstrated in isolated yeast cells. DATABASE: The mathematical model described here has been submitted to the JWS Online Cellular Systems Modelling Database and can be accessed at http://jjj.biochem.sun.ac.za/database/gustavsson/index.html free of charge.     

Model for energy oscillations in cells

Rapid periodic pulses have been observed in yeast cell walls and these pulsations must be accompanied by coherent oscillations of energy. Such energy oscillations are likely to be a common feature in cells and we explore other consequences, either known or unknown, that may originate from chemical oscillations of small amplitude. We do not consider specific mechanisms for the energy oscillations, but here we accept their existence as a fact following from the yeast experiments. Chemical oscillators are treated as generic quantum oscillators and this model predicts that observed frequencies should have a simple volume-dependence where smaller cells exhibit higher frequencies than their larger counterparts. An extension to multicellular organisms then affords a derivation of the celebrated Kleiber law that evaluates both the numerical coefficient and the 34 exponent of mass. Calculations of activation energies and efficiencies at experimental temperatures follow. Finally, the model is applied to derive established expressions for blood flow and pulse rate. We conclude that the model reflects some common metabolic process insofar as it agrees with diverse quantitative findings while using minimal input data and without introducing free parameters.     

Is a constant low-entropy process at the root of glycolytic oscillations?

We measured temporal oscillations in thermodynamic variables such as temperature, heat flux, and cellular volume in suspensions of non-dividing yeast cells which exhibit temporal glycolytic oscillations. Oscillations in these variables have the same frequency as oscillations in the activity of intracellular metabolites, suggesting strong coupling between them. These results can be interpreted in light of a recently proposed theoretical formalism in which isentropic thermodynamic systems can display coupled oscillations in all extensive and intensive variables, reminiscent of adiabatic waves. This interpretation suggests that oscillations may be a consequence of the requirement of living cells for a constant low-entropy state while simultaneously performing biochemical transformations, i.e., remaining metabolically active. This hypothesis, which is in line with the view of the cellular interior as a highly structured and near equilibrium system where energy inputs can be low and sustain regular oscillatory regimes, calls into question the notion that metabolic processes are essentially dissipative.     

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.     

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.     

Oscillations in glycolysis: multifactorial quantitative analysis in muscle extract

A multifactorial quantitative analysis of oscillations in glycolysis was conducted in the postmicrosomal supernatant of rat muscle homogenates incubated in the presence of yeast hexokinase. Oscillations in adenine nucleotides, D-fructose 1,6-bisphosphate, triose phosphates, L-glycerol 3-phosphate, ³HOH generation from D-[5-³H]glucose, NADH and L-lactate production were documented. The occurrence of such oscillations were found to depend mainly on the balance between the consumption of ATP associated with the phosphorylation of D-glucose, as catalyzed by both yeast and muscle hexokinase, and the net production of ATP resulting from the further catabolism of D-fructose 6-phosphate, as initiated by activation of phosphofructokinase. The oscillatory pattern was suppressed in the presence of D-fructose 2,6-bisphosphate. It is proposed that the quantitative information gathered in this study may set the scene for further studies in extracts of cells other than myocytes, e. g. hepatocytes and pancreatic islet cells, in which no oscillation of glycolysis was so far observed.     

Oscillations in Yeast Observed Electrically

It has previously been demonstrated that oscillations occur in actively growing yeast cultures. These oscillations occur because yeast cells synchronize their glycolytic pathway following a saturation period. Periodic changes in the levels of intermediate metabolites in glycolysis as well as changes in pH ofthe media have been measured, that demonstrate this phenomenon. Here we observe that the conductivity of the media also changes periodically when yeast cells are cultured under similar conditions. As conductivity is easily measured, this provides a simple, more quantitative method to study these changes than those currently used. An electrical biosensor referred to as ECIS (electrical cell surface impedance sensing) was used to study the small conductivity changes (in the order of 0.1%). No significant differences in the observed periods were found in the two yeast strains or the commercially purchased yeast extract studied.     

Oscillations in Yeast Observed Electrically

It has previously been demonstrated that oscillations occur in actively growing yeast cultures. These oscillations occur because yeast cells synchronize their glycolytic pathway following a saturation period. Periodic changes in the levels of intermediate metabolites in glycolysis as well as changes in pH ofthe media have been measured, that demonstrate this phenomenon. Here we observe that the conductivity of the media also changes periodically when yeast cells are cultured under similar conditions. As conductivity is easily measured, this provides a simple, more quantitative method to study these changes than those currently used. An electrical biosensor referred to as ECIS (electrical cell surface impedance sensing) was used to study the small conductivity changes (in the order of 0.1%). No significant differences in the observed periods were found in the two yeast strains or the commercially purchased yeast extract studied.     

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.     

The age structure of populations of Saccharomyces cerevisiae

A discrete deterministic model is described for the growth of an age-structured population of yeast, Saccharomyces cerevisiae, incorporating recent information on the asymmetry of cell division and control of the cell cycle in this species. Solutions are obtained for the age structure of the population at equilibrium, and for the equilibrium distribution of relative frequency of cells through the cell cycle. The model is applied to experimental data on the changing age structure of nonequilibrium populations of yeast. The model predicts well both the transient behavior and the equilibrium structure of such populations. It is shown that the asymmetry of cell division explains (1) the excess of newly formed daughter cells in the population as compared to the frequency of older cells and (2) the damped oscillations in the frequencies of cells of different ages as demographic equilibrium is approached.     

Electrical stimulation of the energy metabolism in yeast cells using a planar Ti-Au-Electrode interface

We report on the influence of dielectric pulse injection on the energy metabolism of yeast cells with a planar interdigitated electrode interface. The energy metabolism was measured via NADH fluorescence. The application of dielectric pulses results in a distinct decrease of the fluorescence, indicating a response of the energy metabolism of the yeast cells. The reduction of the NADH signal significantly depends on the pulse parameters, i.e., amplitude and width. Furthermore, the interface is used to detect electrical changes in the cell-electrolyte system, arising from glucose-induced oscillations in yeast cells and yeast extract, by dielectric spectroscopy at 10 kHz. These dielectric investigations revealed a β₁-dispersion for the system electrolyte/yeast cells as well as for the system electrolyte/yeast extract. In agreement with control measurements we obtained a glycolytic period of 45s for yeast cells and of 11min for yeast extract.