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.     

Oscillatory synthesis of glucose 1,6-bisphosphate and frequency modulation of glycolytic oscillations in skeletal muscle extracts

Oscillatory behavior of glycolysis in cell-free extracts of rat skeletal muscle involves bursts of phosphofructokinase activity, due to autocatalytic activation by fructose-1,6-P2. Glucose-1,6-P2 similarly might activate phosphofructokinase in an autocatalytic manner, because it is produced in a side reaction of phosphofructokinase and in a side reaction of phosphoglucomutase using fructose-1,6-P2. When muscle extracts were provided with 1 mM ATP and 10 mM glucose, glucose-1,6-P2 accumulated in a stepwise, but monotonic, manner to 0.7 microM in 1 h. The stepwise increases occurred during the phases when fructose-1,6-P2 was available, consistent with glucose-1,6-P2 synthesis in the phosphoglucomutase side reaction. Addition of 5-20 microM glucose-1,6-P2 increased the frequency of the oscillations in a dose-dependent manner and progressively shortened the time interval before the first burst of phosphofructokinase activity. Addition of 30 microM glucose-1,6-P2 blocked the oscillations. The peak values of the [ATP]/[ADP] ratio were then eliminated, and the average [ATP]/[ADP] ratio was reduced by half. In the presence of higher, near physiological concentrations of ATP and citrate (which reduce the activation of phosphofructokinase by glucose-1,6-P2), high physiological concentrations of glucose-1,6-P2 (50-100 microM) increased the frequency of the oscillations and did not block them. We conclude that autocatalytic activation of phosphofructokinase by fructose-1,6-P2, but not by glucose-1,6-P2, is the mechanism generating the oscillations in muscle extracts. Glucose-1,6-P2 may nevertheless play a role in facilitating the initiation of the oscillations and in modulating their frequency.     

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.     

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.     

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.     

Modulation by citrate of glycolytic oscillations in skeletal muscle extracts.

Oscillatory behavior of glycolysis in cell-free extracts of skeletal muscle involves repeated bursts of phosphofructokinase activity and associated oscillations in the [ATP]/[ADP] ratio. Addition of citrate, a potent physiological inhibitor of phosphofructokinase, decreased the frequency of the oscillations and delayed the first burst of phosphofructokinase activity in a dose-dependent manner. Citrate decreased the trigger point [ATP]/[ADP] ratio at which bursts of phosphofructokinase activity were initiated but had a much smaller effect on the average [ATP]/[ADP] ratio and did not decrease the peak values of the ratio. When oscillations were prevented by addition of fructose-2,6-P2, the decrease in the [ATP]/[ADP] ratio caused by citrate in the steady state system was similar to the decrease in the trigger point [ATP]/[ADP] ratio in the oscillatory system. The decrease in the average [ATP]/[ADP] ratio was greater in the steady state system than in the oscillating system. These results demonstrate advantages of oscillatory behavior of glycolysis in the regulation of carbohydrate utilization and the maintenance of a high [ATP]/[ADP] ratio.     

Phase synchronization and coherence resonance of stochastic calcium oscillations in coupled hepatocytes

The frequency of free cytosolic calcium concentration ([Ca(2+)]) oscillations elicited by a given agonist concentration differs between individual hepatocytes. However, in multicellular systems of rat hepatocytes and even in the intact liver, [Ca(2+)] oscillations are synchronized and highly coordinated. In this paper, we have investigated theoretically the effects of gap junction permeable to calcium and of the total Ca(2+) channel number located on endoplasmic reticulum on intercellular synchronization. Figures of ratio between mean oscillating frequency of coupled cells describe visually the process of phase-locking. By virtue of a set of phase analysis, we can observe a gradual transition from synchronous behavior to nonsynchronous behavior. Furthermore, a signal-to-noise ratio in two dimensional parameter space (coupling strength-total Ca(2+) channel number) has suggested that, coherence resonance will occur for appropriate noise and coupling.     

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.     

Evidence for phosphorylation of yeast phosphofructokinase

Radioactively labelled material from yeast cells grown in the presence of [32P]phosphate was specifically recognized by antibodies raised against yeast phosphofructokinase. Purified yeast phosphofructokinase was phosphorylated in a cyclic AMP-independent manner by a protein kinase enriched from yeast extracts. This phosphorylation occurred specifically on the beta-subunit, and 0.56 mol of phosphate/mol of subunit was incorporated. The results indicate the phosphorylation of yeast phosphofructokinase both in vivo and in vitro. Phosphofructokinase phosphorylated in vitro was more stable against proteolytic degradation compared to the non-phosphorylated enzyme.     

Allosteric activation and competitive inhibition of yeast phosphofructokinase by d-fructose.

Purified phosphofructokinase from bakers yeast is activated by D-fructose in low concentrations (up to 1 mM) and inhibited by high concentrations. The stimulatory effect of D-fructose is similar, but smaller than that of AMP. In the presence of AMP (0.4 mM or higher) D-fructose does no longer stimulate, but its inhibitory effect persists (KI = 8 mM). Its dualistic action on phosphofructokinase activity indicates that D-fructose might induce low frequency in glycolytic oscillations by direct interaction with the enzyme.     

Effects of gap junction to Ca(2+) and to IP(3) on the synchronization of intercellular calcium oscillations in hepatocytes

The frequency of free cytosolic calcium concentration ([Ca(2+)]) oscillations elicited by a given agonist concentration differs between individual hepatocytes. However, in multicellular systems of rat hepatocytes and even in the intact liver, [Ca(2+)] oscillations are synchronized and highly coordinated. In this paper, we have investigated theoretically the gap junction permeable to calcium and to IP(3) on intercellular synchronization by means of a mathematical model, respectively. It is shown that gap junction permeable to calcium and to IP(3) are effective on synchronizing calcium oscillations in coupled hepatocytes. Our theoretical results are similar either for the case of Ca(2+) acting as coordinating messenger or for the case of IP(3) as coordinating messenger. There exists an optimal coupling strength for a pair of connected hepatocytes. Appropriate coupling strength and IP(3) level can induce various harmonic locking of intercellular [Ca(2+)] oscillations. Furthermore, a phase diagram in two-dimensional parameter space of the coupling strength and IP(3) level (or the velocity of IP(3) synthesis) has been predicted, in which the synchronization region is similar to Arnol'd tongue.     

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.     

Dihydroxyacetone-induced oscillations in cytoplasmic free Ca2+ and the ATP/ADP ratio in pancreatic beta-cells at substimulatory glucose

Glucose stimulation of pancreatic beta-cells causes oscillatory influx of Ca2+, leading to pulsatile insulin secretion. We have proposed that this is due to oscillations of glycolysis and the ATP/ADP ratio, which modulate the activity of ATP-sensitive K+ channels. We show here that dihydroxyacetone, a secretagogue that feeds into glycolysis below the putative oscillator phosphofructokinase, could cause a single initial peak in cytoplasmic free Ca2+ ([Ca2+]i) but did not by itself cause repeated oscillations in [Ca2+]i in mouse pancreatic beta-cells. However, in the presence of a substimulatory concentration of glucose (4 mm), dihydroxyacetone induced [Ca2+]i oscillations. Furthermore, these oscillations correlated with oscillations in the ATP/ADP ratio, as seen previously with glucose stimulation. Insulin secretion in response to dihydroxyacetone was transient in the absence of glucose but was considerably enhanced and somewhat prolonged in the presence of a substimulatory concentration of glucose, in accordance with the enhanced [Ca2+]i response. These results are consistent with the hypothesized role of phosphofructokinase as the generator of the oscillations. Dihydroxyacetone may affect phosphofructokinase by raising the free concentration of fructose 1,6-bisphosphate to a critical level at which it activates the enzyme autocatalytically, thereby inducing the pulses of phosphofructokinase activity that cause the metabolic oscillations.     

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.     

Inward Rotating Spiral Waves in Glycolysis

We report on the first observation of inward rotating spiral waves (antispirals) in a biochemical reaction-diffusion system. Experiments are performed with extracts from yeast cells in an open spatial reactor. By increasing the protein concentration of the extract we observe a transition from outward to inward propagating waves of glycolytic activity. Numerical simulations with an allosteric model for the phosphofructokinase can reproduce these inward propagating waves over a wide range of parameters if the octameric structure of yeast phosphofructokinase is taken into account.     

The in situ assay of Candida albicans enzymes during yeast growth and germ-tube formation

Conditions are described for the preparation of permeabilized cells of Candida albicans. This method has been used for the in situ assay of enzymes in both yeast cells and germ-tube forming cells. A mixture of toluene/ethanol/Triton X-100 (1:4:0.2, by vol.) at 15% (v/v) and 8% (v/v) was optimal for the in situ assay of glucose-6-phosphate dehydrogenase in yeast and germ-tube forming cells, respectively. The concentration of toluene/ethanol/Triton X-100 required for optimal in situ activity of other enzymes was influenced by the cellular location of the enzyme, growth phase and morphology. The membrane-bound enzymes (chitin synthase, glucan synthase, ATPase), cytosolic enzymes (glucose-6-phosphate dehydrogenase, isocitrate dehydrogenase, pyruvate kinase, phosphofructokinase, alkaline phosphatase, glucosamine-6-phosphate deaminase and N-acetylglucosamine kinase) and wall enzymes (beta-glucosidase and acid phosphatase) were measured and compared to the activity obtained in cell extracts. The pattern of enzyme induction and the properties of the allosteric enzymes phosphofructokinase and pyruvate kinase were measured in situ. Pyruvate kinase in situ was homotropic for phosphoenolpyruvate with a Hill coefficient of 1.9 and a S0.5 of 0.6 mM, whereas in cell extracts, it had a Hill coefficient of 1.9 and a S0.5 of 1.0 mM. The Km for ATP was 1.6 mM in cell extracts and 1.8 mM in permeabilized cells. In situ phosphofructokinase was homotropic for fructose 6-phosphate (S0.5 of 2.3 mM, Hill coefficient of 4.0). The kinetic properties of pyruvate kinase and phosphofructokinase measured in situ or in vitro were similar for both yeast cells and germ-tube forming cells.     

Functional Modeling of the Shift in Cellular Calcium Dynamics at the Onset of Synchronization in Smooth Muscle Cells

In the present paper we address the nature of synchronization properties found in populations of mesenteric artery smooth muscle cells. We present a minimal model of the onset of synchronization in the individual smooth muscle cell that is manifested as a transition from calcium waves to whole-cell calcium oscillations. We discuss how different types of ion currents may influence both amplitude and frequency in the regime of whole-cell oscillations. The model may also explain the occurrence of mixed-mode oscillations and chaotic oscillations frequently observed in the experimental system.     

On the role of enzyme cooperativity in metabolic oscillations: analysis of the Hill coefficient in a model for glycolytic periodicities.

The role of enzyme cooperativity in the mechanism of metabolic oscillations is analyzed in a concerted allosteric model for the phosphofructokinase reaction. This model of a dimer enzyme activated by the reaction product accounts quantitatively for glycolytic periodicities observed in yeast and muscle. The Hill coefficient characteristic of enzyme-substrate interactions is determined in the model, both at the steady state and in the course of sustained oscillations. Positive cooperativity is a prerequisite for periodic behavior. A necessary condition for oscillation in a dimer K system is a Hill coefficient larger than 1.6 at the unstable stationary state. The analysis suggests that positive as well as negative effectors of phosphofructokinase inhibit glycolytic oscillations by inducing a decrease in enzyme cooperativity. The results are discussed with respect to glycolytic and other metabolic periodicities.     

Citrate oscillates in liver and pancreatic beta cell mitochondria and in INS-1 insulinoma cells

Oscillations in citric acid cycle intermediates have never been previously reported in any type of cell. Here we show that adding pyruvate to isolated mitochondria from liver, pancreatic islets, and INS-1 insulinoma cells or adding glucose to intact INS-1 cells causes sustained oscillations in citrate levels. Other citric acid cycle intermediates measured either did not oscillate or possibly oscillated with a low amplitude. In INS-1 mitochondria citrate oscillations are in phase with NAD(P) oscillations, and in intact INS-1 cells citrate oscillations parallel oscillations in ATP, suggesting that these processes are co-regulated. Oscillations have been extensively studied in the pancreatic beta cell where oscillations in glycolysis, NAD(P)/NAD(P)H and ATP/ADP ratios, plasma membrane electrical activity, calcium levels, and insulin secretion have been well documented. Because the mitochondrion is the major site of ATP synthesis and NADH oxidation and the only site of citrate synthesis, mitochondria need to be synchronized for these factors to oscillate. In suspensions of mitochondria from various organs, most of the citrate is exported from the mitochondria. In addition, citrate inhibits its own synthesis. We propose that this enables citrate itself to act as one of the cellular messengers that synchronizes mitochondria. Furthermore, because citrate is a potent inhibitor of the glycolytic enzyme phosphofructokinase, the pacemaker of glycolytic oscillations, citrate may act as a metabolic link between mitochondria and glycolysis. Citrate oscillations may coordinate oscillations in mitochondrial energy production and anaplerosis with glycolytic oscillations, which in the beta cell are known to parallel oscillations in insulin secretion.