Glucose is the major source for energy production. It is converted to pyruvate via the glycolysis pathway, leading to production of ATP coupled with generation of intermediates and reducing power in the form of NADH for other biosynthetic pathways (Figure 1). When glucose-starved Saccharomyces cerevisiae cells are incubated with glucose in the presence of the respiration inhibitor cyanide, transient oscillations of levels of relevant glycolytic metabolites can occur. These include levels of nicotinamide adenine dinucleotide (NAD) which can be seen to oscillate between the oxidized (NAD⁺) and reduced forms (NADH), as well as other glycolytic intermediates, including glucose-6-phosphate, fructose-6-phosphate and fructose 1,6-bisphosphate [1]. Glycolytic oscillations are accompanied by oscillations in mitochondrial membrane potential (Δψ _m ) [2]. This phenomenon has been observed for over 40 years [3] and is known as glycolytic oscillations [4]. These oscillations are not limited to S. cerevisiae, as they have been observed in Saccharomyces carlsbergensis[5], muscle extracts [6], and pancreatic β-cells [7]. Glycolytic oscillations are an example of oscillatory phenomena, with others including waves of cAMP in Dictyostelium[8], circadian rhythms [9], oscillations of Ca²⁺ levels [10] and the cell cycle [11].

Different factors have been shown to control the oscillations. These include temperature [12], cell density [13] and plasma membrane H⁺ ATPase and mitochondrial ATP-ase [14]. It is believed that either acetaldehyde or ethanol acts as a synchronization mediator [15, 16] although the evidence for the role of ethanol had been disputed [15–17]. The controller of the oscillations (the so called “oscillophore”) has attracted a lot of attention but has yet to be fully established. The contributions of each element of the glycolytic pathway have been studied with mathematical models of yeast glycolytic oscillations [18–20]. Of the different glycolytic enzymes, phosphofructokinase (PFK), with its allosteric regulation (it is inhibited by ATP while AMP and fructose 1,6-bisphosphate reversing the inhibition) has been shown to have the greatest control over the oscillations. A role for the hexokinases has also been demonstrated [21]. In contrast, there is evidence that each glycolytic enzyme plays a role in controlling the oscillatory phenomenon – this is described as “distributed control” [22]. Both theories have been put forward as a result of analysis of the mathematical models that have been developed to explain the regulation of yeast glycolytic oscillations [17, 20].

To our knowledge there has not been previously an attempt to investigate the yeast glycolytic oscillations at genetic level. This could be due to the fact that until now, the oscillations have only been observed in the diploid S. cerevisiae strain X2180. This strain has never been used to generate targeted deletion mutants; therefore, the potential effects of deletion or over-expression of glycolytic genes have, until now, remained unknown. In contrast, almost complete collections of isogenic deletion mutants are available in the BY4743 sequenced standard laboratory genetic background [23].

In this study, we have demonstrated that glycolytic oscillations can be observed in the diploid S. cerevisiae strain BY4743. We have subsequently used the genetic resources available in this genetic background to investigate the effects of deletion of different glycolytic enzymes encoding genes on the NADH-mediated glycolytic oscillations in the respective mutants. We have observed differential roles of the two subunit types of the phosphofructokinase, as well as the different isoforms of the hexokinase and the glyceraldehyde-3-phosphate dehydrogenase. We have used this experimental data to evaluate via parameter sensitivity analysis and representative simulations the mathematical model of yeast glycolytic oscillations developed by Wolf et al. [18]. Furthermore we have provided evidence for a role of the cAMP signal transduction pathway in modulating glycolytic oscillations.

This study reports the results of the first genetic investigation of the pattern of oscillations of intracellular NADH of single deletion mutants in key components of the glycolysis pathway in S. cerevisiae. It has become possible because of the genetic resources available when using the sequenced genetic background strain BY4743, which as our study shows (Figure 2) displays an NADH oscillatory pattern identical to that of strain X2180 used in previously reported experiments.

One of the most significant results of this study is the genetic evidence of the differential roles of the two subunits of phosphofructokinase (PFK) in glycolytic oscillations. Previously, mathematical modelling which has demonstrated that the phosphofructokinase, with its allosteric regulation, has the greatest control over the oscillations has not discriminated between the two types of subunits that constitute this enzyme. Lack of PFK activity in vivo is only observed in double pfk1 pfk2 deletion mutants. In contrast, single deletion mutants (pfk1 and pfk2) can grow on glucose, although there is no in vitro detectable PFK activity in these mutants [31]. Arvanitidis and Heinisch [50] demonstrated that each of the phosphofructokinase subunits can serve catalytic as well as regulatory functions. However, while the homomeric nature of the PFK enzyme supports growth on glucose, strains that have only one of the Pfk subunits have other different phenotypes. For example Rodicio et al. [51] have shown that only the pfk2 deletion mutant is temperature sensitive for growth at 37°C, sensitive to caffeine and Congo red. The pfk1 deletion mutant on the other hand is more resistant to caffeine compared to the wild type. And in the current study we show further phenotypic differences between the two types of deletion mutants. Firstly, the pfk2 but not pfk1 deletion mutant is deficient in NADH-mediated glycolytic oscillations. Secondly, pfk2 and not pfk1 mutant does not display the characteristic NADH “spike” after glucose addition (Figure 3b), an observation which will be the subject of further investigations.

The specific role of Pfk2 in glycolytic oscillations could be due to the fact that it is the subunit which contains binding sites for fructose 6-phosphate [52], as previous studies have shown that yeast extracts fed with the PFK substrate fructose 6-phosphate can exhibit oscillations, whereas extracts fed with fructose 1–6 bisphosphate cannot [29]. On the other hand, the differential role of the two subunits of PFK could also be due to the differences in their associations with the cAMP pathway, which as this study shows is responsible for modulating the enzyme activities of the glycolytic enzymes in such a way that the system becomes unstable and starts to oscillate. Unlike PFK1, PFK2 is involved in genetic interactions with PDE2 and IRA2, the components of the cAMP pathway which affect NADH oscillatory activity (Figure 10). Pde2 and Ira2 are both responsible for feedback down-regulation of the cAMP-mediated activity of PKA [49]; hence deletion in either encoding gene causes constitutive activation of the cAMP pathway. The exact mechanism by which the cAMP-PKA pathway affects glycolytic oscillations is currently unknown, but it could be hypothesized that it might be via phosphorylation of Pfk2 by PKA, as Pfk2 (but not Pfk1) has been shown to physically interact with Tpk1. However, the fact that the pattern of glycolytic oscillations of the tpk1 Δ mutant is wild type suggests that Tpk1-mediated phosphorylation of Pfk2 does not contribute to its role in glycolytic oscillations. However, it cannot be ruled out that in the absence of Tpk1, another PKA isoform (Tpk2 or Tpk3) is capable of phosphorylating Pfk2.

Deletion of each of the hexokinases encoding genes leads to oscillations that are longer lasting with lower amplitude (Figure 3a), which agrees with earlier reports which have shown that reduced hexokinase activity results in lower flow of glucose into the glycolytic pathway [53]. Our study however, shows that the effect of HXK2 deletion on the duration of the oscillations is stronger than that of HXK1. Although the deletion mutant for GLK1 whose product is also known to phosphorylate glucose at the C6 position was not investigated, we predict that its deletion would yield results comparable to those of HXK1, as both GLK1 and HXK1 are repressed when grown on a fermentable medium using glucose as a carbon source [54]. Interestingly, the transcript abundances of both HXK1 and GLK1 have been reported to increase, whilst those of HXK2 and PFK2 decrease respectively, upon the diauxic shift [55], the transition known to be regulated by the cAMP signal transduction pathway. And remarkably, HXK2 (but not HXK1), and PFK2 (but not PFK1) have been found to interact genetically with PDE2 and IRA2, deletions of which affect glycolytic oscillations (Figure 10). We therefore like to speculate that because of the role of the cAMP pathway in this oscillatory phenomenon, the glycolytic enzymes encoded by genes found to be genetically associated with PDE2 and IRA2 have the strongest regulatory role in glycolytic oscillations.

Deletion of TDH1 and TDH2 genes has little effect on glycolytic oscillations (Figure 3c). Deletion of TDH3 however leads to a loss of oscillations. These isoforms are growth-phase specific: Tdh1 is present in stationary phase cells, while Tdh2p and Tdh3p are present in exponentially growing cells [33]. The observation that deletion of TDH3 and not that of TDH2, affects oscillations could now be explained by the fact that expression of TDH3 contributes around 60% of glyceraldehyde-3-phosphate dehydrogenase activity [32]. As demonstrated by our simulations of the GAPDH reaction in the Wolf model of glycolysis (Figure 9), glycolytic oscillations are maintained but affected in amplitude and period upon 50% reduction of the GAPDH activity in the forward reaction, and further decrease to 30% abolished them almost completely.

The question regarding effects of deletion of ENO2 and CDC19 (PYK1) in glycolytic oscillations remains as the corresponding mutants were not available to test in the current study. It could be hypothesised that their transcripts’ down-regulation upon the diauxic shift [55] suggests a role in glycolytic oscillations since a similar correlation exists for PFK2. And although there might be an enticing link between transcript down-regulation upon the diauxic shift of genes such as HXK2 and PFK2[55] and their role in glycolytic oscillations, this relationship is not as straightforward. Our study shows that deletion of both HXK1 and HXK2 affects glycolytic oscillations, however their transcript levels respond in a contrasting manner to the diauxic transition: HXK1 is up-regulated, whilst HXK2 is down-regulated. Moreover, deletion of TDH3 abolishes glycolytic oscillations completely although neither this gene, nor the remaining two (TDH1,2) are subject to differential regulation of transcription upon the diauxic shift.

Previously, Reijenga et al. [56] and Madsen et al. [30] reported the control coefficients of enzymatic steps on the amplitude and frequency of oscillations, providing a measure of the effect that changes in enzyme activity produce on these characteristics. The deletion mutations in the present investigation represent large perturbations of the glycolysis pathway components whereas parameter sensitivities refer to changes in individual reaction parameters. This type of analysis has enabled us to distinguish between forward and reverse reaction parameters in reversible reactions, and between rate and inhibition constants for the lumped HK-PFK reaction. It has identified r1ki1, the inhibition constant for the combined HK-PFK reaction, as the most sensitive parameter. Moreover, as our experimental evidence demonstrated it is the deletion of PFK2, HXK1 and HXK2 that produce the greatest effect on glycolytic oscillations. Deletion of PFK1 on the other hand does not significantly affect glycolytic oscillations showing that the components of the lumped HK-PFK reaction have specific properties. More precise models will be needed that differentiate between the different isoforms or subunit components of glycolytic enzymes. Oscillatory parameter sensitivity analysis is a useful technique to identify crucial parameters for the control of biological rhythms and investigate their robustness. It has been applied to several other types of oscillating systems, such as circadian rhythms [28, 57], NF-κB signalling pathways [58] and calcium dynamics [59].

Interestingly, the forward constant for the lumped HK-PFK reaction (r1k1) is not as sensitive as the inhibition constant. This suggests that the reverse feedback by ATP on PFK is potentially the most important controller of the oscillations which is in agreement with results obtained in yeast extract experiments by Madsen et al. [30]. So not only have we identified the role of the beta subunit (Pfk2) of phosphofructokinase in glycolytic oscillations (as deletion of PFK2 abolishes them completely), we have confirmed that the negative feedback of Pfk2 by ATP is a key regulatory factor in glycolytic oscillations.

The choice of the glycolysis model that we used in the current analysis might seem debatable. In light of the report by Madsen et al. [30] who argued firstly that there are two types of oscillations, namely relaxation type observed in cell free extracts and harmonic (sinusoidal) oscillations observed in intact cells, and secondly that the Wolf model is not applicable for oscillations in intact cells. However, it appears that the type of oscillations is not strictly coupled to the whole cells or cell extracts, but rather to how far the system is removed from the Hopf bifurcation. Close to this point the oscillations are harmonic, independent of whether they are observed in cell extracts or whole cells. Further from this point, the behaviour can move away from harmonic oscillations. This is for instance shown in Nielsen et al. [60], where cell free extract oscillations move from harmonic to complex and relaxation type of oscillations dependent on the distance from the Hopf bifurcation point. Furthermore, P. Richard [61] reports that the shape of the glycolytic oscillations varies from sinusoidal to relaxation depending on the rate of glucose addition.

This study demonstrated that r7k, the rate constant for the ATP-ase reaction, is also a highly sensitive parameter (Figures 6 and 7). Recently, Kloster and Olsen [62] investigated the role of intracellular ATPase activity using specific inhibitors for the three types of ATPases, namely F₀F₁ ATPase, Pma1 and vacuolar ATPase, and showed that both inhibiting and stimulating ATPase activity suppress glycolytic oscillations. Further support of the role of ATPase in glycolytic oscillations comes from the recent study of Ytting et al. (2012) [63]. However, the latter study uses a GAL1 promoter replacement pma1 mutant and does not present data for its isogenic wild type parental strain. Instead the report shows as supplementary data the results of an alternative wild type strain (a derivative of W303) with a NADH oscillatory pattern which is very far from comparable to X2180 and that of BY4743 shown in our study. There are different ATP-ase encoding genes in the yeast genome; however none of the respective viable deletion mutants were included in our analysis. Given the well established role of the genetic background as a modifier of different phenotypes, we propose that in future studies it would be of interest to investigate the role of the different ATP-ases further by analysing the NADH-mediated oscillations in the standard BY4743 genetic background.

This study has for the first time provided genetic evidence for the differential roles of the two types of subunits of PFK, and the isoforms of GAPDH and HK in glycolytic oscillation in the yeast S. cerevisiae. Importantly it shows genetic evidence that PDE2 and IRA2, which encode 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 with a key role in glycolytic oscillation. We demonstrate that a systematic genetic approach combined with mathematical modelling can advance the study of oscillatory phenomena.