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

Universality of stable multi-cluster periodic solutions in a population model of the cell cycle with negative feedback

We study a population model where cells in one part of the cell cycle may affect the progress of cells in another part. If the influence, or feedback, from one part to another is negative, simulations of the model almost always result in multiple temporal clusters formed by groups of cells. We study regions in parameter space where periodic 'k-cyclic' solutions are stable. The regions of stability coincide with sub-triangles on which certain events occur in a fixed order. For boundary sub-triangles with order 'rs1', we prove that the k-cyclic periodic solution is asymptotically stable if the index of the sub-triangle is relatively prime with respect to the number of clusters k and neutrally stable otherwise. For negative linear feedback, we prove that the interior of the parameter set is covered by stable sub-triangles, i.e. a stable k-cyclic solution always exists for some k. We observe numerically that the result also holds for many forms of nonlinear feedback, but may break down in extreme cases.

Omics analysis reveals mechanism underlying metabolic oscillation during continuous very-high-gravity ethanol fermentation by Saccharomyces cerevisiae

During continuous very-high-gravity (VHG) ethanol fermentation with Saccharomyces cerevisiae, the process exhibits sustained oscillation in residual glucose, ethanol, and biomass, raising a question: how do yeast cells respond to this phenomenon? In this study, the oscillatory behavior of yeast cells was characterized through transcriptome and metabolome analysis for one complete oscillatory period. By analyzing the accumulation of 26 intracellular metabolites and the expression of 90 genes related to central carbon metabolism and stress response, we confirmed that the process oscillation was attributed to intracellular metabolic oscillation with phase difference, and the expression of HXK1, HXT1,2,4, and PFK1 was significantly different from other genes in the Embden-Meyerhof-Parnas pathway, indicating that glucose transport and phosphorylation could be key nodes for regulating the intracellular metabolism under oscillatory conditions. Moreover, the expression of stress response genes was triggered and affected predominately by ethanol inhibition in yeast cells. This progress not only contributes to the understanding of mechanisms underlying the process oscillation observed for continuous VHG ethanol fermentation, but also provides insights for understanding unsteady state that might develop in other continuous fermentation processes operated under VHG conditions to increase product titers for robust production.

Self-Synchronized Oscillatory Metabolism of Clostridium pasteurianum in Continuous Culture

By monitoring the real-time gas production (CO2 and H2) and redox potential at high sampling frequency in continuous culture of Clostridium pasteurianum on glycerol as sole carbohydrate, the self-synchronized oscillatory metabolism was revealed and studied. The oscillations in CO2 and H2 production were in sync with each other and with both redox potential and glycerol in the continuous stirred tank reactor (CSTR). There is strong evidence that the mechanism for this is in the regulation of the oxidative pathway of glycerol metabolism, including glycolysis, and points toward complex, concerted cycles of enzyme inhibition and activation by pathway intermediates and/or redox equivalents. The importance of understanding such an “oscillatory metabolism” is for developing a stable and highly productive industrial fermentation process for butanol production, as unstable oscillations are unproductive. It is shown that the oscillatory metabolism can be eradicated and reinstated and that the period of oscillations can be altered by modification of the operating parameters. Synchronized oscillatory metabolism impacted the product profile such that it lowered the selectivity for butanol and increased the selectivity for ethanol. This elucidates a possible cause for the variability in the product profile of C. pasteurianum that has been reported in many previous studies.

Oscillatory behaviour control in a continuous culture under double-substrate limitation

The paper discusses the possibility of using a mixture of two growth limiting substrates to induce or eliminate self-sustained oscillations in a continuous culture process. The proportion of both substrates in the mixture is treated as a new control variable. The presented approach is based on the assumption that the oscillatory behaviour occurs for selected substrates in some range of dilution rates. Because a double-substrate limitation may occur, the analysis is performed for two fundamental substrate utilization patterns: simultaneous consumption and diauxic growth. By using model simulations and bifurcation analysis, we show that an appropriate proportion of two substrates in the mixture allows for the control of the oscillatory behaviour.

Characterizing the in vivo role of trehalose in Saccharomyces cerevisiae using the AGT1 transporter

Trehalose is a highly stable, nonreducing disaccharide of glucose. A large body of research exists implicating trehalose in a variety of cellular phenomena, notably response to stresses of various kinds. However, in very few cases has the role of trehalose been examined directly in vivo. Here, we describe the development and characterization of a system in Saccharomyces cerevisiae that allows us to manipulate intracellular trehalose concentrations independently of the biosynthetic enzymes and independently of any applied stress. We found that many physiological roles heretofore ascribed to intracellular trehalose, including heat resistance, are not due to the presence of trehalose per se. We also found that many of the metabolic and growth defects associated with mutations in the trehalose biosynthesis pathway are not abolished by providing abundant intracellular trehalose. Instead, we made the observation that intracellular accumulation of trehalose or maltose (another disaccharide of glucose) is growth-inhibitory in a carbon source-specific manner. We conclude that the physiological role of the trehalose pathway is fundamentally metabolic: i.e., more complex than simply the consequence of increased concentrations of the sugar and its attendant physical properties (with the exception of the companion paper where Tapia et al. [Tapia H, et al. (2015) Proc Natl Acad Sci USA, 10.1073/pnas.1506415112] demonstrate a direct role for trehalose in protecting cells against desiccation).

Noise-induced dispersion and breakup of clusters in cell cycle dynamics

We study the effects of random perturbations on collective dynamics of a large ensemble of interacting cells in a model of the cell division cycle. We consider a parameter region for which the unperturbed model possesses asymptotically stable two-cluster periodic solutions. Two biologically motivated forms of random perturbations are considered: bounded variations in growth rate and asymmetric division. We compare the effects of these two dispersive mechanisms with additive Gaussian white noise perturbations. We observe three distinct phases of the response to noise in the model. First, for weak noise there is a linear relationship between the applied noise strength and the dispersion of the clusters. Second, for moderate noise strengths the clusters begin to mix, i.e. individual cells move between clusters, yet the population distribution clearly continues to maintain a two-cluster structure. Third, for strong noise the clusters are destroyed and the population is characterized by a uniform distribution. The second and third phases are separated by an order-disorder phase transition that has the characteristics of a Hopf bifurcation. Furthermore, we show that for the cell cycle model studied, the effects of bounded random perturbations are virtually indistinguishable from those induced by additive Gaussian noise, after appropriate scaling of the variance of noise strength. We then use the model to predict the strength of coupling among the cells from experimental data. In particular, we show that coupling must be rather strong to account for the observed clustering of cells given experimentally estimated noise variance.

Cell cycle dynamics: clustering is universal in negative feedback systems

We study a model of cell cycle ensemble dynamics with cell-cell feedback in which cells in one fixed phase of the cycle S (Signaling) produce chemical agents that affect the growth and development rate of cells that are in another phase R (Responsive). For this type of system there are special periodic solutions that we call k-cyclic or clustered. Biologically, a k-cyclic solution represents k cohorts of synchronized cells spaced nearly evenly around the cell cycle. We show, under very general nonlinear feedback, that for a fixed k the stability of the k-cyclic solutions can be characterized completely in parameter space, a 2 dimensional triangle T. We show that T is naturally partitioned into k(2) sub-triangles on each of which the k-cyclic solutions all have the same stability type. For negative feedback we observe that while the synchronous solution (k = 1) is unstable, regions of stability of k ≥ 2 clustered solutions seem to occupy all of T. We also observe bi-stability or multi-stability for many parameter values in negative feedback systems. Thus in systems with negative feedback we should expect to observe cyclic solutions for some k. This is in contrast to the case of positive feedback, where we observe that the only asymptotically stable periodic orbit is the synchronous solution.

Cell cycle dynamics in a response/signalling feedback system with a gap

We consider a dynamical model of cell cycles of n cells in a culture in which cells in one specific phase (S for signalling) of the cell cycle produce chemical agents that influence the growth/cell cycle progression of cells in another phase (R for responsive). In the case that the feedback is negative, it is known that subpopulations of cells tend to become clustered in the cell cycle; while for a positive feedback, all the cells tend to become synchronized. In this paper, we suppose that there is a gap between the two phases. The gap can be thought of as modelling the physical reality of a time delay in the production and action of the signalling agents. We completely analyse the dynamics of this system when the cells are arranged into two cell cycle clusters. We also consider the stability of certain important periodic solutions in which clusters of cells have a cyclic arrangement and there are just enough clusters to allow interactions between them. We find that the inclusion of a small gap does not greatly alter the global dynamics of the system; there are still large open sets of parameters for which clustered solutions are stable. Thus, we add to the evidence that clustering can be a robust phenomenon in biological systems. However, the gap does effect the system by enhancing the stability of the stable clustered solutions. We explain this phenomenon in terms of contraction rates (Floquet exponents) in various invariant subspaces of the system. We conclude that in systems for which these models are reasonable, a delay in signalling is advantageous to the emergence of clustering.

Impact of osmotic stress and ethanol inhibition in yeast cells on process oscillation associated with continuous very-high-gravity ethanol fermentation

BACKGROUND

VHG fermentation is a promising process engineering strategy aiming at improving ethanol titer, and thus saving energy consumption for ethanol distillation and distillage treatment. However, sustained process oscillation was observed during continuous VHG ethanol fermentation, which significantly affected ethanol fermentation performance of the system.

RESULTS

Sustained process oscillation was investigated in continuous VHG ethanol fermentation, and stresses exerted on yeast cells by osmotic pressure from unfermented sugars and ethanol inhibition developed within the fermentation system were postulated to be major factors triggering this phenomenon. In this article, steady state was established for continuous ethanol fermentation with LG medium containing 120 g/L glucose, and then 160 g/L non-fermentable xylose was supplemented into the LG medium to simulate the osmotic stress on yeast cells under the VHG fermentation condition, but the fermentation process was still at steady state, indicating that the impact of osmotic stress on yeast cells was not the main reason for the process oscillation. However, when 30 g/L ethanol was supplemented into the LG medium to simulate the ethanol inhibition in yeast cells under the VHG fermentation condition, process oscillation was triggered, which was augmented with extended oscillation period and exaggerated oscillation amplitude as ethanol supplementation was increased to 50 g/L, but the process oscillation was gradually attenuated when the ethanol supplementations were stopped, and the steady state was restored. Furthermore, gas stripping was incorporated into the continuous VHG fermentation system to in situ remove ethanol produced by Saccharomyces cerevisiae, and the process oscillation was also attenuated, but restored after the gas stripping was interrupted.

CONCLUSIONS

Experimental results indicated that ethanol inhibition rather than osmotic stress on yeast cells is one of the main factors triggering the process oscillation under the VHG fermentation condition, and in the meantime gas stripping was validated to be an effective strategy for attenuating the process oscillation.

The yin and yang of yeast transcription: elements of a global feedback system between metabolism and chromatin

When grown in continuous culture, budding yeast cells tend to synchronize their respiratory activity to form a stable oscillation that percolates throughout cellular physiology and involves the majority of the protein-coding transcriptome. Oscillations in batch culture and at single cell level support the idea that these dynamics constitute a general growth principle. The precise molecular mechanisms and biological functions of the oscillation remain elusive. Fourier analysis of transcriptome time series datasets from two different oscillation periods (0.7 h and 5 h) reveals seven distinct co-expression clusters common to both systems (34% of all yeast ORF), which consolidate into two superclusters when correlated with a compilation of 1,327 unrelated transcriptome datasets. These superclusters encode for cell growth and anabolism during the phase of high, and mitochondrial growth, catabolism and stress response during the phase of low oxygen uptake. The promoters of each cluster are characterized by different nucleotide contents, promoter nucleosome configurations, and dependence on ATP-dependent nucleosome remodeling complexes. We show that the ATP:ADP ratio oscillates, compatible with alternating metabolic activity of the two superclusters and differential feedback on their transcription via activating (RSC) and repressive (Isw2) types of promoter structure remodeling. We propose a novel feedback mechanism, where the energetic state of the cell, reflected in the ATP:ADP ratio, gates the transcription of large, but functionally coherent groups of genes via differential effects of ATP-dependent nucleosome remodeling machineries. Besides providing a mechanistic hypothesis for the delayed negative feedback that results in the oscillatory phenotype, this mechanism may underpin the continuous adaptation of growth to environmental conditions.

Calcium participates in feedback regulation of the oscillating ROP1 Rho GTPase in pollen tubes

Biological oscillation occurs at various levels, from cellular signaling to organismal behaviors. Mathematical modeling has allowed a quantitative understanding of slow oscillators requiring changes in gene expression (e.g., circadian rhythms), but few theoretical studies have focused on the rapid oscillation of cellular signaling. The tobacco pollen tube, which exhibits growth bursts every 80 s or so, is an excellent system for investigating signaling oscillation. Pollen tube growth is controlled by a tip-localized ROP1 GTPase, whose activity oscillates in a phase about 90 degrees ahead of growth. We constructed a mathematical model of ROP1 activity oscillation consisting of interlinking positive and negative feedback loops involving F-actin and calcium, ROP1-signaling targets that oscillate in a phase about 20 degrees and 110 degrees behind ROP1 activity, respectively. The model simulates the observed changes in ROP1 activity caused by F-actin disruption and predicts a role for calcium in the negative feedback regulation of the ROP1 activity. Our experimental data strongly support this role of calcium in tip growth. Thus, our findings provide insight into the mechanism of pollen tube growth and the oscillation of cellular signaling.

Systems biology of microbial communities

Microbes exist naturally in a wide range of environments in communities where their interactions are significant, spanning the extremes of high acidity and high temperature environments to soil and the ocean. We present a practical discussion of three different approaches for modeling microbial communities: rate equations, individual-based modeling, and population dynamics. We illustrate the approaches with detailed examples. Each approach is best fit to different levels of system representation, and they have different needs for detailed biological input. Thus, this set of approaches is able to address the operation and function of microbial communities on a wide range of organizational levels.

mRNA stability and the unfolding of gene expression in the long-period yeast metabolic cycle

Background

In yeast, genome-wide periodic patterns associated with energy-metabolic oscillations have been shown recently for both short (approx. 40 min) and long (approx. 300 min) periods.

Results

The dynamical regulation due to mRNA stability is found to be an important aspect of the genome-wide coordination of the long-period yeast metabolic cycle. It is shown that for periodic genes, arranged in classes according either to expression profile or to function, the pulses of mRNA abundance have phase and width which are directly proportional to the corresponding turnover rates.

Conclusion

The cascade of events occurring during the yeast metabolic cycle (and their correlation with mRNA turnover) reflects to a large extent the gene expression program observable in other dynamical contexts such as the response to stresses/stimuli.

Oscillatory phosphorylation of yeast Fus3 MAP kinase controls periodic gene expression and morphogenesis

Signal-transduction networks can display complex dynamic behavior such as oscillations in the activity of key components [1-6], but it is often unclear whether such dynamic complexity is actually important for the network's regulatory functions [7, 8]. Here, we found that the mitogen-activated protein kinase (MAPK) Fus3, a key regulator of the yeast mating-pheromone response, undergoes sustained oscillations in its phosphorylation and activation state during continuous pheromone exposure. These MAPK activity oscillations led to corresponding oscillations in mating-gene expression. Oscillations in MAPK activity and gene expression required the negative regulator of G protein signaling Sst2 and partially required the MAPK phosphatase Msg5. Peaks in Fus3 activation correlated with periodic rounds of cell morphogenesis, with each peak preceding the formation of an additional mating projection. Preventing projection formation did not eliminate MAPK oscillation, but preventing MAPK oscillation blocked the formation of additional projections. A mathematical model was developed that reproduced several features of the observed oscillatory dynamics. These observations demonstrate a role for MAPK activity oscillation in driving a periodic downstream response and explain how the pheromone signaling pathway, previously thought to desensitize after 1-3 hr, controls morphology changes that continue for a much longer time.

Ethanol fermentation technologies from sugar and starch feedstocks

This article critically reviews some ethanol fermentation technologies from sugar and starch feedstocks, particularly those key aspects that have been neglected or misunderstood. Compared with Saccharomyces cerevisiae, the ethanol yield and productivity of Zymomonas mobilis are higher, because less biomass is produced and a higher metabolic rate of glucose is maintained through its special Entner-Doudoroff pathway. However, due to its specific substrate spectrum as well as the undesirability of its biomass to be used as animal feed, this species cannot readily replace S. cerevisiae in ethanol production. The steady state kinetic models developed for continuous ethanol fermentations show some discrepancies, making them unsuitable for predicting and optimizing the industrial processes. The dynamic behavior of the continuous ethanol fermentation under high gravity or very high gravity conditions has been neglected, which needs to be addressed in order to further increase the final ethanol concentration and save the energy consumption. Ethanol is a typical primary metabolite whose production is tightly coupled with the growth of yeast cells, indicating yeast must be produced as a co-product. Technically, the immobilization of yeast cells by supporting materials, particularly by gel entrapments, is not desirable for ethanol production, because not only is the growth of the yeast cells restrained, but also the slowly growing yeast cells are difficult to be removed from the systems. Moreover, the additional cost from the consumption of the supporting materials, the potential contamination of some supporting materials to the quality of the co-product animal feed, and the difficulty in the microbial contamination control all make the immobilized yeast cells economically unacceptable. In contrast, the self-immobilization of yeast cells through their flocculation can effectively overcome these drawbacks.

Hybrid filtering of feed stream noise from oscillating yeast cultures by combined Kalman and neural network configurations

Large continuous flow bioreactors are often under the influence of noise in the feed stream(s). Prior removal of noise is done by filters based either on specific algorithms or on artificial intelligence. Neither method is perfect. Hybrid filters combine both methods and thereby capitalize on their strengths while minimizing their weaknesses. In this study, a number of hybrid models have been compared for their ability to recover nearly noise-free stable oscillations of continuous flow Saccharomyces cerevisiae cultures from aberrant behavior caused by noise in the feed stream. Each hybrid filter had a different neural network in conjunction with an extended Kalman filter (EKF). The choice of the best configuration depended on the performance index. All hybrid filters were superior to both the EKF and purely neural filters. Along with previous studies of monotonic fermentations, the present results establish the suitability of hybrid neural filters for noise-affected bioreactors.

Hybrid filtering to rescue stable oscillations from noise-induced chaos in continuous cultures of budding yeast

In large-scale fermentations with oscillating microbial cultures, noise is commonly present in the feed stream(s). As this can destabilize the oscillations and even generate chaotic behavior, noise filters are employed. Here three types of filters were compared by applying them to a noise-affected continuous culture of Saccharomyces cerevisiae with chaotic oscillations. The aim was to restore the original noise-free stable oscillations. An extended Kalman filter was found to be the least efficient, a neural filter was better and a combined hybrid filter was the best. In addition, better filtering of noise was achieved in the dilution rate than in the oxygen mass transfer coefficient. These results suggest the use of hybrid filters with the dilution rate as the manipulated variable for bioreactor control.

Oscillatory ROP GTPase activation leads the oscillatory polarized growth of pollen tubes

Oscillation regulates a wide variety of processes ranging from chemotaxis in Dictyostelium through segmentation in vertebrate development to circadian rhythms. Most studies on the molecular mechanisms underlying oscillation have focused on processes requiring a rhythmic change in gene expression, which usually exhibit a periodicity of >10 min. Mechanisms that control oscillation with shorter periods (<10 min), presumably independent of gene expression changes, are poorly understood. Oscillatory pollen tube tip growth provides an excellent model to investigate such mechanisms. It is well established that ROP1, a Rho-like GTPase from plants, plays an essential role in polarized tip growth in pollen tubes. In this article, we demonstrate that tip-localized ROP1 GTPase activity oscillates in the same frequency with growth oscillation, and leads growth both spatially and temporally. Tip growth requires the coordinate action of two ROP1 downstream pathways that promote the accumulation of tip-localized Ca2+ and actin microfilaments (F-actin), respectively. We show that the ROP1 activity oscillates in a similar phase with the apical F-actin but apparently ahead of tip-localized Ca2+. Furthermore, our observations support the hypothesis that the oscillation of tip-localized ROP activity and ROP-dependent tip growth in pollen tubes is modulated by the two temporally coordinated downstream pathways, an early F-actin assembly pathway and a delayed Ca2+ gradient-forming pathway. To our knowledge, our report is the first to demonstrate the oscillation of Rho GTPase signaling, which may be a common mechanism underlying the oscillation of actin-dependent processes such as polar growth, cell movement, and chemotaxis.

Autonomous oscillations in Saccharomyces cerevisiae during batch cultures on trehalose

We report that autonomous oscillations, which usually happen in aerobic glucose-limited continuous cultures of yeast at low dilution rate, were also observed in trehalose discontinuous cultures of Saccharomyces cerevisiae. This unexpected oscillatory behaviour was therefore examined using fast Fourier transformation of online gas measurements. This robust mathematical analysis underlined the existence of two types of oscillation. The first was found to be linked to the cell cycle because (a) the periodicity corresponded to a fraction of the generation time and (b) the oscillations were accompanied by a transient increase in the budding index, mobilization of storage carbohydrates, and fermentative activity. Moreover, these oscillations occurred in a range of specific growth rates between 0.04 and 0.15 h(-1). All these criteria were consistent with the cell-cycle-related metabolic oscillations observed in the same range of growth rates in glucose-limited continuous cultures. The second type were short-period respiratory oscillations, independent of the specific growth rate. Both types of oscillation were found to take place consecutively and/or simultaneously during batch culture on trehalose. In addition, mobilization of intracellular trehalose emerged as a key parameter for the sustainability of these autonomous oscillations as they were no longer observed in a mutant defective in neutral trehalase activity. We propose that batch culture on trehalose may be an excellent device for further investigation of the molecular mechanisms that underlie autonomous oscillations in yeast.

Parameter oscillations in a very high gravity medium continuous ethanol fermentation and their attenuation on a multistage packed column bioreactor system

The quasi-steady-states, marked by small fluctuations of residual glucose, ethanol, and biomass concentrations, and sustainable oscillations marked by big fluctuations of these monitored fermentation parameters were observed during the continuous ethanol fermentation of Saccharomyces cerevisiae when very high gravity media were fed and correspondingly high ethanol concentrations reached. A high ethanol concentration was shown to be one of the main factors that incited these oscillations, although the residual glucose level affected the patterns of these oscillations to some extent. The lag response of S. cerevisiae to high ethanol stress that causes the shifts of morphology, viability loss, and death of yeast cells is assumed to be one of the probable mechanisms behind these oscillations. It was predicted that the longer the delay of this response was, the longer the oscillation periods would be, which was validated by the experimental data and the comparison with the oscillatory behaviors reported for the ethanologen bacterium, Zymomonas mobilis. Furthermore, three tubular bioreactors in series were arranged to follow a stirred tank bioreactor to attenuate these oscillations. However, exaggerated oscillations were observed for the residual glucose, ethanol, and biomass concentrations measured in the broth from these tubular bioreactors. After the tubular reactors were packed with Intalox ceramic saddle packing, these oscillations were effectively attenuated and quasi-steady-states were observed during which there were very small fluctuations of residual glucose, ethanol, and biomass within the entire experimental run.