Oscillatory metabolism of Saccharomyces cerevisiae: an overview of mechanisms and models

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1 Biotechnology Advances 21 (2003) Research review Oscillatory metabolism of Saccharomyces cerevisiae: an overview of mechanisms and models Pratap R. Patnaik * Institute of Microbial Technology, Sector 39-A, Chandigarh , India Received 31 January 2003; accepted 4 February 2003 Abstract The budding yeast Saccharomyces cerevisiae displays steady oscillations in continuous cultures under certain conditions. Oscillatory responses are important both metabolically and in process applications. Although much information has become available, a definitive theory to explain and model these oscillations is yet to be formulated. Models of oscillatory cultivation have focussed primarily either on intracellular reactions or on transport processes coupled to substantially lumped intracellular kinetics. This review discusses the development of the models and the directions they provide for a comprehensive model of oscillatory metabolism. D 2003 Elsevier Science Inc. All rights reserved. Keywords: Saccharomyces cerevisiae; Oscillatory metabolism; Continuous culture 1. Introduction Oscillatory phenomena are widespread in biological systems. Among the well-known and widely studied oscillatory processes are those of calcium waves (Bootman et al., 2001), yeast glycolysis (Richard et al., 1996; Teusink et al., 2000), the circadian rhythm (Turek, 1998) and the cell cycle (Mori and Johnson, 2000; Tyson and Novak, 2001). More recently known, but less studied, are the autonomous metabolic oscillations seen in continuous aerobic cultures of some yeasts, notably Saccharomyces cerevisiae (Chen and McDonald, 1990; Keulers et al., 1996a; Satroudinov et al., 1992). These oscillations occur in different carbon sources (glucose, ethanol or acetaldehyde) and are manifested through the oxygen uptake rate, CO 2 evolution rate, dissolved oxygen tension and the concen- * Fax: / address: pratap@imtech.res.in (P.R. Patnaik) /03/$ - see front matter D 2003 Elsevier Science Inc. All rights reserved. doi: /s (03)

2 184 P.R. Patnaik / Biotechnology Advances 21 (2003) trations of the carbon source, the product (ethanol), acetate, ATP, storage carbohydrate and ph (Chen and McDonald, 1990; Jones and Kompala, 1999; Keulers et al., 1996a; Sohn and Kuriyama, 2001). Fig. 1 displays a typical set of profiles. They differ from the possibly better known circadian oscillations in being of shorter time periods (a few minutes to a few hours), self-sustaining and arising spontaneously under specific conditions. The importance of such ultradian oscillations lies both in serving as a vehicle to study cellular control mechanisms and to optimize industrial fermentations, where oscillations are usually undesirable. From the perspective of both molecular genetics and industrial fermentation, S. cerevisiae is a good organism for at least three reasons: (1) there is detailed biochemical, physiological and genetic information available; (2) noninvasive methods of measurement Fig. 1. Typical profiles of some measurable variables in oscillating continuous cultures of S. cerevisiae. Changes in the patterns of oscillations arise because the dilution rate was changed from 0.13 to 0.15 h 1 at 100 h and then to h 1 at 200 h. Reproduced from Jones and Kompala (1999) with permission of Elsevier Science n 1999.

3 P.R. Patnaik / Biotechnology Advances 21 (2003) are possible in continuous cultures; and (3) it generates important industrial products (Goldbeter, 1996; Lloyd, 1998). While many researchers have identified the conditions that generate or suppress oscillations, and some have also studied different kinds of oscillations, the molecular basis of these oscillations, their relations to the operating conditions (such as dilution rate, agitation speed, ph and temperature) and their quantitative prediction are still the subjects of continuing investigations. 2. Types of oscillations and models There appears to be two kinds of ultradian oscillations in continuous cultures of S. cerevisiae, as measured through the ethanol concentration (Keulers et al., 1996b), dissolved oxygen (Murray et al., 2001) and CO 2 production rate (Keulers et al., 1996a,b). The first type occurs when the cell cycle is synchronized and is related to events at well-defined stages of the cycle. During these oscillations, the cell doubling time is around 10 h, the period of oscillation is ca. 100 min and it depends on the dilution rate (Beuse et al., 1998; Chen and McDonald, 1990; Parulekar et al., 1986). They have been interpreted in terms of the asynchronous budding pattern of S. cerevisiae (Bellgardt, 1994; Chen and McDonald, 1990; Hjortso, 1996), which results in segregated synchronous Fig. 2. Schematic diagram of a possible mechanism for the asymmetric budding cycle of yeast. Reproduced from Bellgardt (1994) with permission of Elsevier Science n 1994.

4 186 P.R. Patnaik / Biotechnology Advances 21 (2003) populations. Fig. 2 is a schematic depiction of the sequence of events in this process. The second type of oscillations occurs when there is no observable cell cycle synchronization, and, as expected, they do not depend on the dilution rate; synchronicity here seems then to be driven metabolically (Keulers et al., 1996a; Satroudinov et al., 1992). These oscillations are of shorter time periods, less than half that of the first kind. Apart from dissolved oxygen, key metabolites also respond differently in the two situations. When cell cycle synchrony is absent, oscillation is independent of storage carbohydrates and the acetate concentration oscillates 180 jc out of phase with ethanol (Duboc et al., 1996; Keulers et al., 1996a), whereas these fermentation products oscillate in phase when the cell cycle is synchronized (Bellgardt, 1994; Beuse et al., 1999). Understanding of the mechanisms that trigger or avoid metabolic oscillations should be translated to workable models that can be used to engineer suitable strains (Zhang et al., 1996) and/or to optimize bioreactor performance (Patnaik, 2001a, 2003; Shi and Shimizu, 1992). This seems to be presently a weak area for several reasons: (1) it is not always easy to generate quantitative data appropriate for modeling, especially when off-line assays are involved (Schugerl, 2001); (2) difficulties in capturing detailed biochemical and physiological information in suitably lumped models that are neither too gross nor too complex (Wiechert, 2002); and (3) combining intracellular kinetics with both intra- and extracellular transport process requires multidisciplinary understanding, which has so far been limited. Owing to these difficulties, principally the third one, quantitative descriptions of oscillating cultures have focussed predominantly either in detail on intracellular phenomena or on macroscopically observed variables such as cell mass concentration, substrate concentration and budding density combined with lumped descriptions of processes inside the cells. The models proposed by Teusink et al. (2000), Wolf et al. (2001) and Reijenga et al. (2002) are of the first kind, i.e. they portray oscillations arising from intracellular kinetics without externally driven transport effects. Of these, Teusink et al. s work pertains to glycolytic oscillations, but it is based on information similar to that used by metabolic models, that is, the involvement of PFK and acetaldehyde in the relative rates of utilization of glucose and ethanol and the synchronization of cell populations (Goldbeter, 1996; Heinrich and Schuster, 1996; Richard et al., 1996). Nevertheless, it is important to stress that glycolytic oscillations are different from metabolic oscillations (Beuse et al., 1999; Murray et al., 2001; Wang et al., 2001) in terms of the biochemistry as well as macroscopic regulators. For instance, control of glucose inflow is a crucial factor in glycolytic oscillations (Richard et al., 1996; Teusink et al., 1996, 2000), whereas ultradian metabolic oscillations can occur even in cultures grown on ethanol (Keulers et al., 1996b; Satroudinov et al., 1992) or acetaldehyde (Keulers and Kuriyama, 1998) alone. 3. Mechanistic models and engineering models Wolf et al. s (2001) model was constructed on the basis of three pathways sulfate assimilation, ethanol degradation and respiration. Hydrogen sulfide plays a pivotal role in the promotion of cell synchrony through inhibition of respiration (Marzulf, 1997; Murray et al., 2001; Sohn et al., 2000) and in sulfate assimilation by transforming O-acetylho-

5 P.R. Patnaik / Biotechnology Advances 21 (2003) moserine to cysteine. The presence of cysteine causes the eruption of oscillations by repressing sulfate assimilation (Marzulf, 1997; Ono et al., 1999; Sohn and Kuriyama, 2001). H 2 S is formed by sulfite reductase through a complex mechanism in which the uptake and assimilation of sulfate play a vital role (Sohn and Kuriyama, 2001). The central question that Wolf et al. addressed was whether cysteine, which is formed by the reaction of H 2 SwithO-acetylhomoserine, regulates sulfate uptake in such a way as to generate oscillations. Their model indicated that feedback inhibition of sulfate uptake at high concentrations of cysteine was a major source of the oscillations reported by other studies (Marzulf, 1997; Ono et al., 1999; Sohn and Kuriyama, 2001). Intracellular diffusion of H 2 S also leads to inhibition of respiration and causes significant shifts in respiratory oscillations (Murray et al., 2001; Sohn et al., 2000). This is thought to occur via reversible binding with mitochondrial cytochrome c oxidase (Grieshaber and Volkel, 1998; Marzulf, 1997), resulting in cyclic energization and de-energization of mitochondria (Lloyd et al., 2002). In addition to dissolved H 2 S, respiratory oscillations also depend on dissolved oxygen (Keulers et al., 1996a; Sohn et al., 2000), glutathione (Murray et al., 1998, 1999) and acetaldehyde (Keulers and Kuriyama, 1998). Since all these compounds help population synchronization, there is a strong possibility of crosstalk among them, but the mechanism(s) of communication is unclear. The problem is further compounded by the fact that ethanol metabolism is linked to sulfate assimilation through sulfite and redox balance (Murray et al., 1999; Sohn et al., 2000). Integrating so many complex and interacting processes (see the reaction networks in Fig. 3) into a tractable model requires judicious lumping and simplifying assumptions. Wolf et al. (2001), for instance, lumped the reduction equivalents NADH, NADPH and FADH 2 into one moiety and likewise for the intermediates of the citrate cycle. Oxidative phosphorylation was described by the minimal model even though more elaborate versions are available (Heinrich and Schuster, 1996). In spite of this simplification, their model contained 13 differential equations and 27 parameters, thus underlining the difficulty of translating biochemical information in a viable mathematical model. Perhaps recognizing this difficulty, Reijenga et al. (2002) preferred a simpler model comprising nine differential equations, adapted from Goldbeter and Lefever s (1972) PFK model for glycolysis. The focus of this study was, however, on metabolic control analysis rather than a mechanistic interpretation. The second class of models that have combined macroscopically measurable (extracellular) variables with lumped approximations of intracellular kinetics include those of Parulekar et al. (1986), Strassle et al. (1988), Chen and McDonald (1990), Martegani et al. (1990), Bellgardt (1994), Beuse et al. (1998) and Jones and Kompala (1999). Many of these engineering models (as contrasted with the biochemical models described before) are based on a central concept of feedback as a cause of oscillations. Proponents of the feedback theory (Martegani et al., 1990; Parulekar et al., 1986; Porro et al., 1988) explain that when sufficient (but not excess) glucose is available, there is aerobic fermentation of glucose, with poor cell growth, high ethanol production and rapid consumption of glucose and dissolved oxygen. Below a critical dilution rate, the supply of glucose becomes insufficient to replenish its consumption; then both glucose and ethanol (the product) become limiting substrates, and oxidative metabolism sets in (Kappeli, 1986). This is

6 188 P.R. Patnaik / Biotechnology Advances 21 (2003) Fig. 3. Reaction scheme used by Wolf et al. (2001) to model metabolic oscillations in S. cerevisiae. The following abbreviations are used: sul = sulfate ions; aps = adenylyl sulfate; pap = 3-phosphoadenylyl sulfate; hyd = hydrogen sulfide; cys = cysteine; eth = ethanol; aco = acetyl-coa; S 1, S 2 = intermediates of the citric acid cycle; oxy = oxygen; C 1,C 2 = protein complexes involved in oxidative phosphorylation; A 3 =ATP; A 2 = ADP; N 1 = NAD(P) + ;N 2 = NAD(P)H; oah = O-acetylhomoserine. The cytosolic and mitochondrial compartments are characterized by the superscripts c and m, respectively. Reproduced with permission of the Federation of European Biochemical Societies n accompanied by reduced consumption of glucose, low production of ethanol and large biomass production. This enables glucose concentration to rise again, thereby shifting the metabolism to the fermentative pathway, and the cycle is repeated. While this may be a plausible theory, it does not explain why oscillations occur even when glucose is not supplied and the substrate is purely ethanol or acetaldehyde (Keulers et al., 1996b; Keulers and Kuriyama, 1998). The role of population synchronization as a factor in the generation of oscillations has engaged the attention of engineering models as much as biochemical models. Porro et al. (1988) and Martegani et al. (1990) defined two critical cell sizes, one for budding ( P s ) and the other for cell division ( P m ), and interpreted oscillatory behavior by connecting P m / P s with the nutritional condition of the broth, glucose being a good nutrient and ethanol poor. However, this concept does not accommodate either the observed oscillations on nonglucose media or the effect of nutrient feed rate compensation (Murray et al., 2001). More elaborate population distribution models proposed later have tried to capture more features but at the cost of increased complexity. Cazzador et al. s (1990) model

7 P.R. Patnaik / Biotechnology Advances 21 (2003) includes both structure (within the cells) and segregation (of cells in the broth), and it is based on Martegani et al. s (1990) concept of P m /P s and on the observation that cells at the start of the DNA synthesis S phase utilize carbohydrates and secrete ethanol (Bellgardt, 1994). This model requires at least 30 differential equations. Strassle et al. s (1988) model is even more complex and requires nearly 100 groups of cells of different masses and nearly 500 differential equations to reproduce experimental data. In view of these difficulties, Bellgardt (1994) preferred a distribution for the cell age rather than the cell mass. Although less complex than the models of Strassle et al. (1988) and Cazzador et al. (1990), it has other weaknesses such as empirical selection of the best distribution, absence of explicit consideration of intracellular processes and strong sensitivity to the starting conditions. Whereas all these workers considered just two classes of cells mother cells and daughter cells Grover and Woldringh (1995) and Beuse et al. (1998) went further. The former presented a detailed genealogical population model with g parent and ( g +1) daughter classes. Beuse et al. (1998) chose the minimum value of g = 1 as adequate. Understandably, both models are quite complex, but they still fail to predict some observations such as oscillations of time period 50 min at a dilution rate of 0.08 h 1 (Satroudinov et al., 1992), which are too long for glycolytic oscillations and too short for synchronous growth. 4. Concluding remarks After 30 years of research, a definitive explanation of the mechanism(s) of oscillatory metabolism of S. cerevisiae in continuous cultures does not seem to have been reached, even though there has been considerable progress in understanding the contributing processes. This may not be surprising since many factors, some inside the cells and some external to them, interact in the initiation, maintenance or annihilation of oscillations. Within the cells, a number of biochemical pathways are involved in the occurrence or absence of metabolic oscillations: the ethanol assimilation pathway (Keulers and Kuriyama, 1998), the glutathione redox cycling pathway (Murray et al., 1999), the sulfate assimilation pathway (Sohn and Kuriyama, 2001) and the mitochondrial respiratory chain (Sohn et al., 2000). None of these can alone explain the spectrum of observed behavior, so there is a strong possibility of crosstalk among the pathways (Murray et al., 2001). Although population synchronization seems to be at the core of oscillatory metabolism, neither its control features nor its position in the cause-and-effect sequence is fully established. Hydrogen sulfide (Sohn et al., 2000), acetaldehyde (Keulers and Kuriyama, 1998) and glutathione (Murray et al., 1999) have all been shown to control oscillations, so it is possible that a dual or triad synchronization mechanism exists (Murray et al., 2001). Even if synchrony is required for oscillations to occur, there are indications that it should be partial and not complete (Chen and McDonald, 1990; Munch et al., 1992). Jones and Kompala (1999) raised a fundamental question when they postulated that cell synchrony is not a cause of oscillations, but the result of dynamic competition between three metabolic pathways glucose fermentation, ethanol oxidation and glucose oxidation. Oscillatory responses were attributed to shifts among these pathways. However, their

8 190 P.R. Patnaik / Biotechnology Advances 21 (2003) cybernetic model is not without weaknesses. The lack of identification of key enzymes exercising cybernetic control in each pathway and the possibility of different cybernetic formulations with different objective functions (Patnaik, 2001b) reduce the credibility of their model. In the light of these complexities, attempts to model oscillatory fermentations have inevitably had to lump many details, both inside and outside the cells. This has led to broadly two classes of models: those that focus predominantly on intracellular processes (Reijenga et al., 2002; Teusink et al., 2000; Wolf et al., 2001) and those that combine rather substantial lumping inside the cells with phenomenological descriptions of mixing, cell growth and differentiation and transport across the cell wall (Bellgardt, 1994; Beuse et al., 1998; Cazzador et al., 1990; Jones and Kompala, 1999). This scenario leaves open the question of how much lumping is optimal, i.e. what is the best balance between metabolic detail and transport descriptions. This issue is of more than academic interest because in industrial bioreactors, there are physiological variations among the cells, both with time and spatially at any time (Larsson et al., 1996; Liden, 2002). Since control of dilution rate and mixing (Meyer and Beyler, 1984) alter the occurrence and the nature of oscillations, and models accommodating structure as well as segregation have turned out to be too complex for easy automation, it is important to address the issue of optimal complexity in an industrial context. Acknowledgements Thankful appreciation is expressed to Dr. A.K. Bachhawat for helpful discussions and a critical examination of this manuscript. References Bellgardt K-H. Analysis of synchronous growth of baker s yeast: parts I and II. J Biotechnol 1994;35:19 33, Beuse M, Bartling R, Kopmann A, Diekmann H, Thoma M. Effect of dilution rate on the mode of oscillation in continuous cultures of Saccharomyces cerevisiae. J Biotechnol 1998;61: Beuse M, Kopmann A, Diekmann H, Thoma M. Oxygen, ph value and carbon source induced changes of the mode of oscillation in synchronous continuous culture of Saccharomyces cerevisiae. Biotechnol Bioeng 1999;63: Bootman MD, Collins TJ, Peppiatt CM, Prothero LS, MacKenzie L, DeSmet P, et al. Calcium signaling an overview. Semin Cell Dev Biol 2001;12:3 10. Cazzador L, Mariani L, Martegani E, Alberghina L. Structured segregated models and analysis of self-oscillating yeast continuous cultures. Bioprocess Eng 1990;5: Chen C-I, McDonald KA. Oscillatory behavior of Saccharomyces cerevisiae in continuous culture, I and II. Biotechnol Prog 1990;36:19 27, Duboc Ph, Marison I, von Stockar U. Physiology of Saccharomyces cerevisiae during cell cycle oscillations. J Biotechnol 1996;51: Goldbeter A. Biochemical oscillations and cellular rhythms. Cambridge: Cambridge Univ. Press; Goldbeter A, Lefever R. Dissipative structures for an allosteric model. Application to glycolytic oscillations. Biophys J 1972;12:

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