Temperature dependency and temperature compensation in a model of yeast glycolytic oscillations

Temperature sensitivities and conditions for temperature compensation have been investigated in a model for yeast glycolytic oscillations. The model can quantitatively simulate the experimental observation that the period length of glycolytic oscillations decreases with increasing temperature. Temperature compensation is studied by using control coefficients describing the effect of rate constants on oscillatory frequencies. Temperature compensation of the oscillatory period is observed when the positive contributions to the sum of products between control coefficients and activation energies balance the corresponding sum of the negative contributions. The calculations suggest that by changing the activation energies for one or several of the processes, i.e. by mutations, it could be possible to obtain temperature compensation in the yeast glycolytic oscillator.     

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.     

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.     

The purine nucleotide cycle. Control of phosphofructokinase and glycolytic oscillations in muscle extracts.

Linked oscillations of the glycolytic pathway and the purine nucleotide cycle were studied in particle-free extracts of rat skeletal muscle. Under the conditions used, an accumulation of about 1 muM fructose diphosphate can trigger a sudden increase in phosphofructokinase activity. The activation by fructose diphosphate depends on the presence of AMP. When the AMP concentration drops, phosphofructokinase becomes inhibited, even though the fructose disphosphate concentration remains high. It is concluded that the oscillatory behavior can be of advantage for maintaining a high average [ATP]/[ADP] ratio.     

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.     

Sustained simultaneous glycolytic and insulin oscillations in beta-cells

Chemical oscillation in glycolysis induced by glucose is an universal feature in all living cells. In beta-cells this is accompanied by sustained oscillations of concentration of insulin, which helps to keep the blood glucose level within optimum limits. Experiments in this regard had shown that the glycolytic and insulin oscillations are almost consistently in phase and their time periods are very close to each other at both high and low initial concentration of glucose. Experiments have also demonstrated the dynamical transition between the states of glycolytic oscillations indicating a saturation behaviour of glucose transporters at a higher glucose flow rate. We propose a phenomenological model to understand these simultaneous oscillations and how glycolysis provides a mechanism for pulsatory insulin secretion in the light of these basic experimental issues.     

Probing glycolytic and membrane potential oscillations in Saccharomyces cerevisiae

We have investigated glycolytic oscillations under semi-anaerobic conditions in Saccharomyces cerevisiae by means of NADH fluorescence, measurements of intracellular glucose concentration, and mitochondrial membrane potential. The glucose concentration was measured using an optical nanosensor, while mitochondrial membrane potential was measured using the fluorescent dye DiOC 2(3). The results show that, as opposed to NADH and other intermediates in glycolysis, intracellular glucose is not oscillating. Furthermore, oscillations in NADH and membrane potential are inhibited by the ATP/ADP antiporter inhibitor atractyloside and high concentrations of the ATPase inhibitor N, N'-dicyclohexylcarbodiimide, suggesting that there is a strong coupling between oscillations in mitochondrial membrane potential and oscillations in NADH mediated by the ATP/ADP antiporter and possibly also other respiratory components.     

Model evaluation for glycolytic oscillations in yeast biotransformations of xenobiotics

Anaerobic glycolysis in yeast perturbed by the reduction of xenobiotic ketones is studied numerically in two models which possess the same topology but different levels of complexity. By comparing both models' predictions for concentrations and fluxes as well as steady or oscillatory temporal behavior we answer the question what phenomena require what kind of minimum model abstraction. While mean concentrations and fluxes are predicted in agreement by both models we observe different domains of oscillatory behavior in parameter space. Generic properties of the glycolytic response to ketones are discussed.     

Exploring the genetic control of glycolytic oscillations in Saccharomyces Cerevisiae

ABSTRACT: BACKGROUND: A well known example of oscillatory phenomena is the transient oscillations of glycolytic intermediates in Saccharomyces cerevisiae, their regulation being predominantly investigated by mathematical modeling. To our knowledge there has not been a genetic approach to elucidate the regulatory role of the different enzymes of the glycolytic pathway. RESULTS: We report that the laboratory strain BY4743 could also be used to investigate this oscillatory phenomenon, which traditionally has been studied using S. cerevisiae X2180. This has enabled us to employ existing isogenic deletion mutants and dissect the roles of isoforms, or subunits of key glycolytic enzymes in glycolytic oscillations. We demonstrate that deletion of TDH3 but not TDH2 and TDH1 (encoding glyceraldehyde-3-phosphate dehydrogenase: GAPDH) abolishes NADH oscillations. While deletion of each of the hexokinase (HK) encoding genes (HXK1 and HXK2) leads to oscillations that are longer lasting with lower amplitude, the effect of HXK2 deletion on the duration of the oscillations is stronger than that of HXK1. Most importantly our results show that the presence of beta (Pfk2) but not that of alpha subunits (Pfk1) of the hetero-octameric enzyme phosphofructokinase (PFK) is necessary to achieve these oscillations. Furthermore, we report that the cAMP-mediated PKA pathway (via some of its components responsible for feedback down-regulation) modulates the activity of glycoytic enzymes thus affecting oscillations. Deletion of both PDE2 (encoding a high affinity cAMP-phosphodiesterase) and IRA2 (encoding a GTPase activating protein- Ras-GAP, responsible for inactivating Ras-GTP) abolished glycolytic oscillations. CONCLUSIONS: The genetic approach to characterising the glycolytic oscillations in yeast has demonstrated differential roles of the two types of subunits of PFK, and the isoforms of GAPDH and HK. Furthermore, it has shown that PDE2 and IRA2, encoding components of the cAMP pathway responsible for negative feedback regulation of PKA, are required for glycolytic oscillations, suggesting an enticing link between these cAMP pathway components and the glycolysis pathway enzymes shown to have the greatest role in glycolytic oscillation. This study suggests that a systematic genetic approach combined with mathematical modelling can advance the study of oscillatory phenomena.     

Transduction of intracellular and intercellular dynamics in yeast glycolytic oscillations

Under certain well-defined conditions, a population of yeast cells exhibits glycolytic oscillations that synchronize through intercellular acetaldehyde. This implies that the dynamic phenomenon of the oscillation propagates within and between cells. We here develop a method to establish by which route dynamics propagate through a biological reaction network. Application of the method to yeast demonstrates how the oscillations and the synchronization signal can be transduced. That transduction is not so much through the backbone of glycolysis, as via the Gibbs energy and redox coenzyme couples (ATP/ADP, and NADH/NAD), and via both intra- and intercellular acetaldehyde.     

Metabolic pathways reconstruction by frequency and amplitude response to forced glycolytic oscillations in yeast

The hypothesis that frequency and amplitude response can be used in a complicated metabolic pathway kinetics model for optimal parameter estimation, as speculated by its successful prior usage for a mechanical oscillator and a heterogeneous chemical system, is tested here. Given the complexity of the glycolysis model of yeast chosen, this question is limited to three kinetics parameters of the 87 in the in vitro model developed in the literature. The direct application of the approach, used with the uninformed selection of operating conditions for the oscillation of external glucose concentration, led to miring the data assimilation process in local minima. Application of linear systems theory, however, identified two natural resonant frequencies that, when excited by external forced oscillations of the same frequency, result in the expression of many harmonics in the Fourier spectra, that is, information-rich experiments. A single such information-rich experiment at one of the resonant frequencies was sufficient to break away from the local minima to find the optimum kinetics parameter estimates. The resonant frequencies themselves represent oscillation modes in glycolysis akin to those previously observed. Furthermore, operation of the bioreactor with large amplitude oscillations of glucose feed (25%) leads to enhanced ethanol average yield by 1.6% at the resonant frequency.     

Fructose 2,6-bisphosphate and 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. Fructose-2,6-P2 is an even more potent activator of phosphofructokinase and is competitive with fructose-1,6-P2 in binding and kinetic studies. The possible role and effects of fructose-2,6-P2 on the oscillating system were therefore examined. When muscle extracts were provided with 1 mM ATP and 10 mM glucose, fructose-2,6-P2 slowly accumulated to 50 nM in 1 h. The nearly monotonic rise, in contrast to the 50-fold oscillations in fructose-1,6-P2, indicated no involvement of fructose-2,6-P2 in the oscillatory process. Addition of 0.5 microM fructose-2,6-P2 blocked the oscillations, and there was negligible appearance of glycolytic intermediates from fructose-1,6-P2 to phosphoenolpyruvate, although similar amounts of lactate accumulated. In the presence of 0.2 microM fructose-2,6-P2, there were small, transient accumulations of fructose-1,6-P2, suggesting aborted activations of phosphofructokinase. Oscillations were not blocked by 0.1 microM fructose-2,6-P2. The average [ATP]/[ADP] ratio in the presence of 0.2 or 0.5 microM fructose-2,6-P2 was half the value in its absence, demonstrating the advantage of the oscillatory behavior in maintaining a high energy state. In the presence of higher, near physiological levels of ATP and citrate, inhibitors which reduce the affinity of phosphofructokinase for fructose-2,6-P2, glycolytic oscillations were not blocked by 1 microM fructose-2,6-P2, its approximate concentration in vivo.     

Changes in glycolytic activity of Lactococcus lactis induced by low temperature

The effects of low-temperature stress on the glycolytic activity of the lactic acid bacterium Lactococcus lactis were studied. The maximal glycolytic activity measured at 30 degrees C increased approximately 2.5-fold following a shift from 30 to 10 degrees C for 4 h in a process that required protein synthesis. Analysis of cold adaptation of strains with genes involved in sugar metabolism disrupted showed that both the phosphoenolpyruvate-dependent sugar phosphotransferase system (PTS) subunit HPr and catabolite control protein A (CcpA) are involved in the increased acidification at low temperatures. In contrast, a strain with the PTS subunit enzyme I disrupted showed increased acidification similar to that in the wild-type strain. This indicates that the PTS is not involved in this response whereas the regulatory function of 46-seryl phosphorylated HPr [HPr(Ser-P)] probably is involved. Protein analysis showed that the production of both HPr and CcpA was induced severalfold (up to two- to threefold) upon exposure to low temperatures. The las operon, which is subject to catabolite activation by the CcpA-HPr(Ser-P) complex, was not induced upon cold shock, and no increased lactate dehydrogenase (LDH) activity was observed. Similarly, the rate-limiting enzyme of the glycolytic pathway under starvation conditions, glyceraldehyde-3-phosphate dehydrogenase (GAPDH), was not induced upon cold shock. This indicates that a factor other than LDH or GAPDH is rate determining for the increased glycolytic activity upon exposure to low temperatures. Based on their cold induction and involvement in cold adaptation of glycolysis, it is proposed that the CcpA-HPr(Ser-P) control circuit regulates this factor(s) and hence couples catabolite repression and cold shock response in a functional and mechanistic way.     

Local and global bifurcations at infinity in models of glycolytic oscillations

 We investigate two models of glycolytic oscillations. Each model consists of two coupled nonlinear ordinary differential equations. Both models are found to have a saddle point at infinity and to exhibit a saddle-node bifurcation at infinity, giving rise to a second saddle and a stable node at infinity. Depending on model parameters, a stable limit cycle may blow up to infinite period and amplitude and disappear in the bifurcation, and after the bifurcation, the stable node at infinity then attracts all trajectories. Alternatively, the stable node at infinity may coexist with either a stable sink (not at infinity) or a stable limit cycle. This limit cycle may then disappear in a heteroclinic bifurcation at infinity in which the unstable manifold from one saddle at infinity joins the stable manifold of the other saddle at infinity. These results explain prior reports for one of the models concerning parameter values for which the system does not admit any physical (bounded) behavior. Analytic results on the scaling of amplitude and period close to the bifurcations are obtained and confirmed by numerical computations. Finally, we consider more realistic modified models where all solutions are bounded and show that some of the features stemming from the bifurcations at infinity are still present. Received 4 September 1995; received in revised form 18 September 1996     

Control of glycolytic dynamics by hexose transport in Saccharomyces cerevisiae

It is becoming accepted that steady-state fluxes are not necessarily controlled by single rate-limiting steps. This leaves open the issue whether cellular dynamics are controlled by single pacemaker enzymes, as has often been proposed. This paper shows that yeast sugar transport has substantial but not complete control of the frequency of glycolytic oscillations. Addition of maltose, a competitive inhibitor of glucose transport, reduced both average glucose consumption flux and frequency of glycolytic oscillations. Assuming a single kinetic component and a symmetrical carrier, a frequency control coefficient of between 0.4 and 0.6 and an average-flux control coefficient of between 0.6 and 0.9 were calculated for hexose transport activity. In a second approach, mannose was used as the carbon and free-energy source, and the dependencies on the extracellular mannose concentration of the transport activity, of the frequency of oscillations, and of the average flux were compared. In this case the frequency control coefficient and the average-flux control coefficient of hexose transport activity amounted to 0.7 and 0.9, respectively. From these results, we conclude that 1) transport is highly important for the dynamics of glycolysis, 2) most but not all control resides in glucose transport, and 3) there should at least be one step other than transport with substantial control.     

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.