Generation and maintenance of synchrony in Saccharomyces cerevisiae continuous culture

Kinetic modelling of glycolytic oscillations

Glycolytic oscillations have been studied for well over 60 years, but aspects of their function, and mechanisms of regulation and synchronisation remain unclear. Glycolysis is amenable to mechanistic mathematical modelling, as its components have been well characterised, and the system can be studied at many organisational levels: in vitro reconstituted enzymes, cell free extracts, individual cells, and cell populations. In recent years, the emergence of individual cell analysis has opened new ways of studying this intriguing system.

Studying the Human Microbiota: Advances in Understanding the Fundamentals, Origin, and Evolution of Biological Timekeeping

The recently observed circadian oscillations of the intestinal microbiota underscore the profound nature of the human-microbiome relationship and its importance for health. Together with the discovery of circadian clocks in non-photosynthetic gut bacteria and circadian rhythms in anucleated cells, these findings have indicated the possibility that virtually all microorganisms may possess functional biological clocks. However, they have also raised many essential questions concerning the fundamentals of biological timekeeping, its evolution, and its origin. This narrative review provides a comprehensive overview of the recent literature in molecular chronobiology, aiming to bring together the latest evidence on the structure and mechanisms driving microbial biological clocks while pointing to potential applications of this knowledge in medicine. Moreover, it discusses the latest hypotheses regarding the evolution of timing mechanisms and describes the functions of peroxiredoxins in cells and their contribution to the cellular clockwork. The diversity of biological clocks among various human-associated microorganisms and the role of transcriptional and post-translational timekeeping mechanisms are also addressed. Finally, recent evidence on metabolic oscillators and host-microbiome communication is presented.

A Nonlinear Delay Model for Metabolic Oscillations in Yeast Cells

We introduce two time-delay models of metabolic oscillations in yeast cells. Our model tests a hypothesis that the oscillations occur as multiple pathways share a limited resource which we equate to the number of available ribosomes. We initially explore a single-protein model with a constraint equation governing the total resource available to the cell. The model is then extended to include three proteins that share a resource pool. Three approaches are considered at constant delay to numerically detect oscillations. First, we use a spectral element method to approximate the system as a discrete map and evaluate the stability of the linearized system about its equilibria by examining its eigenvalues. For the second method, we plot amplitudes of the simulation trajectories in 2D projections of the parameter space. We use a history function that is consistent with published experimental results to obtain metabolic oscillations. Finally, the spectral element method is used to convert the system to a boundary value problem whose solutions correspond to approximate periodic solutions of the system. Our results show that certain combinations of total resource available and the time delay, lead to oscillations. We observe that an oscillation region in the parameter space is between regions admitting steady states that correspond to zero and constant production. Similar behavior is found with the three-protein model where all proteins require the same production time. However, a shift in the protein production rates peaks occurs for low available resource suggesting that our model captures the shared resource pool dynamics.

An appreciation of the prescience of Don Gilbert (1930-2011): master of the theory and experimental unravelling of biochemical and cellular oscillatory dynamics

We review Don Gilbert's pioneering seminal contributions that both detailed the mathematical principles and the experimental demonstration of several of the key dynamic characteristics of life. Long before it became evident to the wider biochemical community, Gilbert proposed that cellular growth and replication necessitate autodynamic occurrence of cycles of oscillations that initiate, coordinate and terminate the processes of growth, during which all components are duplicated and become spatially re-organised in the progeny. Initiation and suppression of replication exhibit switch-like characteristics, that is, bifurcations in the values of parameters that separate static and autodynamic behaviour. His limit cycle solutions present models developed in a series of papers reported between 1974 and 1984, and these showed that most or even all of the major facets of the cell division cycle could be accommodated. That the cell division cycle may be timed by a multiple of shorter period (ultradian) rhythms, gave further credence to the central importance of oscillatory phenomena and homeodynamics as evident on multiple time scales (seconds to hours). Further application of the concepts inherent in limit cycle operation as hypothesised by Gilbert more than 50 years ago are now validated as being applicable to oscillatory transcript, metabolite and enzyme levels, cellular differentiation, senescence, cancerous states and cell death. Now, we reiterate especially for students and young colleagues, that these early achievements were even more exceptional, as his own lifetime's work on modelling was continued with experimental work in parallel with his predictions of the major current enterprises of biological research.

Instability of the steady state solution in cell cycle population structure models with feedback

We show that when cell-cell feedback is added to a model of the cell cycle for a large population of cells, then instability of the steady state solution occurs in many cases. We show this in the context of a generic agent-based ODE model. If the feedback is positive, then instability of the steady state solution is proved for all parameter values except for a small set on the boundary of parameter space. For negative feedback we prove instability for half the parameter space. We also show by example that instability in the other half may be proved on a case by case basis.

Temporal metabolic partitioning of the yeast and protist cellular networks: the cell is a global scale-invariant (fractal or self-similar) multioscillator

Britton Chance, electronics expert when a teenager, became an enthusiastic student of biological oscillations, passing on this enthusiasm to many students and colleagues, including one of us (DL). This historical essay traces BC's influence through the accumulated work of DL to DL's many collaborators. The overall temporal organization of mass-energy, information, and signaling networks in yeast in self-synchronized continuous cultures represents, until now, the most characterized example of in vivo elucidation of time structure. Continuous online monitoring of dissolved gases by direct measurement (membrane-inlet mass spectrometry, together with NAD(P)H and flavin fluorescence) gives strain-specific dynamic information from timescales of minutes to hours as does two-photon imaging. The predominantly oscillatory behavior of network components becomes evident, with spontaneously synchronized cellular respiration cycles between discrete periods of increased oxygen consumption (oxidative phase) and decreased oxygen consumption (reductive phase). This temperature-compensated ultradian clock provides coordination, linking temporally partitioned functions by direct feedback loops between the energetic and redox state of the cell and its growing ultrastructure. Multioscillatory outputs in dissolved gases with 13 h, 40 min, and 4 min periods gave statistical self-similarity in power spectral and relative dispersional analyses: i.e., complex nonlinear (chaotic) behavior and a functional scale-free (fractal) network operating simultaneously over several timescales.

A minimal "push-pull" bistability model explains oscillations between quiescent and proliferative cell states

A minimal model for oscillating between quiescent and growth/proliferation states, dependent on the availability of a central metabolic resource, is presented. From the yeast metabolic cycles, metabolic oscillations in oxygen consumption are represented as transitions between quiescent and growth states. We consider metabolic resource availability, growth rates, and switching rates (between states) to model a relaxation oscillator explaining transitions between these states. This frustrated bistability model reveals a required communication between the metabolic resource that determines oscillations and the quiescent and growth state cells. Cells in each state reflect memory, or hysteresis of their current state, and “push–pull” cells from the other state. Finally, a parsimonious argument is made for a specific central metabolite as the controller of switching between quiescence and growth states. We discuss how an oscillator built around the availability of such a metabolic resource is sufficient to generally regulate oscillations between growth and quiescence through committed transitions.

The molecular basis of metabolic cycles and their relationship to circadian rhythms

Metabolic cycles result from the partitioning of oxidative and reductive metabolism into rhythmic phases of gene expression and oscillating post-translational protein modifications. Relatively little is known about how these switches in gene expression are controlled, although recent studies have suggested that transcription itself may play a central role. This review explores the molecular basis of the metabolic and gene-expression oscillations in the yeast Saccharomyces cerevisiae, as well as how they relate to other biological time-keeping mechanisms, such as circadian rhythms.

Function of metabolic and organelle networks in crowded and organized media

(Macro)molecular crowding and the ability of the ubiquitous cytoskeleton to dynamically polymerize–depolymerize are prevalent cytoplasmic conditions in prokaryotic and eukaryotic cells. Protein interactions, enzymatic or signaling reactions - single, sequential or in complexes - whole metabolic pathways and organelles can be affected by crowding, the type and polymeric status of cytoskeletal proteins (e.g., tubulin, actin), and their imparted organization. The self-organizing capability of the cytoskeleton can orchestrate metabolic fluxes through entire pathways while its fractal organization can frame the scaling of activities in several levels of organization. The intracellular environment dynamics (e.g., biochemical reactions) is dominated by the orderly cytoskeleton and the intrinsic randomness of molecular crowding. Existing evidence underscores the inherent capacity of intracellular organization to generate emergent global behavior. Yet unknown is the relative impact on cell function provided by organelle or functional compartmentation based on transient proteins association driven by weak interactions (quinary structures) under specific environmental challenges or functional conditions (e.g., hypoxia, division, differentiation). We propose a qualitative, integrated structural–functional model of cytoplasmic organization based on a modified version of the Sierspinsky–Menger–Mandelbrot sponge, a 3D representation of a percolation cluster, and examine its capacity to accommodate established experimental facts.

Using circadian entrainment to find cryptic clocks

Three properties are most often attributed to the circadian clock: a ca. 24-h free-running rhythm, temperature compensation of the circadian rhythm, and its entrainment to zeitgeber cycles. Relatively few experiments, however, are performed under entrainment conditions. Rather, most chronobiology protocols concern constant conditions. We have turned this paradigm around and used entrainment to study the circadian clock in organisms where a free-running rhythm is weak or lacking. We describe two examples therein: Caenorhabditis elegans and Saccharomyces cerevisiae. By probing the system with zeitgeber cycles that have various structures and amplitudes, we can demonstrate the establishment of systematic entrained phase angles in these organisms. We conclude that entrainment can be utilized to discover hitherto unknown circadian clocks and we discuss the implications of using entrainment more broadly, even in model systems that show robust free-running rhythms.

Quantifying periodicity in omics data

Oscillations play a significant role in biological systems, with many examples in the fast, ultradian, circadian, circalunar, and yearly time domains. However, determining periodicity in such data can be problematic. There are a number of computational methods to identify the periodic components in large datasets, such as signal-to-noise based Fourier decomposition, Fisher's g-test and autocorrelation. However, the available methods assume a sinusoidal model and do not attempt to quantify the waveform shape and the presence of multiple periodicities, which provide vital clues in determining the underlying dynamics. Here, we developed a Fourier based measure that generates a de-noised waveform from multiple significant frequencies. This waveform is then correlated with the raw data from the respiratory oscillation found in yeast, to provide oscillation statistics including waveform metrics and multi-periods. The method is compared and contrasted to commonly used statistics. Moreover, we show the utility of the program in the analysis of noisy datasets and other high-throughput analyses, such as metabolomics and flow cytometry, respectively.

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.

Sulfur amino acids regulate translational capacity and metabolic homeostasis through modulation of tRNA thiolation

Protein translation is an energetically demanding process that must be regulated in response to changes in nutrient availability. Herein, we report that intracellular methionine and cysteine availability directly controls the thiolation status of wobble-uridine (U34) nucleotides present on lysine, glutamine, or glutamate tRNAs to regulate cellular translational capacity and metabolic homeostasis. tRNA thiolation is important for growth under nutritionally challenging environments and required for efficient translation of genes enriched in lysine, glutamine, and glutamate codons, which are enriched in proteins important for translation and growth-specific processes. tRNA thiolation is downregulated during sulfur starvation in order to decrease sulfur consumption and growth, and its absence leads to a compensatory increase in enzymes involved in methionine, cysteine, and lysine biosynthesis. Thus, tRNA thiolation enables cells to modulate translational capacity according to the availability of sulfur amino acids, establishing a functional significance for this conserved tRNA nucleotide modification in cell growth control.

Free energy rhythms in Saccharomyces cerevisiae: a dynamic perspective with implications for ribosomal biogenesis

To describe the time course of cellular systems, we integrate ideas from thermodynamics and information theory to discuss the work needed to change the state of the cell. The biological example analyzed is experimental microarray transcription level oscillations of yeast in the different phases as characterized by oxygen consumption. Surprisal analysis was applied to identify groups of transcripts that oscillate in concert and thereby to compute changes in free energy with time. Three dominant transcript groups were identified by surprisal analysis. The groups correspond to the respiratory, early, and late reductive phases. Genes involved in ribosome biogenesis peaked at the respiratory phase. The work to prepare the state is shown to be the sum of the contributions of these groups. We paid particular attention to work requirements during ribosomal building, and the correlation with ATP levels and dissolved oxygen. The suggestion that cells in the respiratory phase likely build ribosomes, an energy intensive process, in preparation for protein production during the S phase of the cell cycle is validated by an experiment. Surprisal analysis thereby provided a useful tool for determining the synchronization of transcription events and energetics in a cell in real time.

An essential role for tomato sulfite oxidase and enzymes of the sulfite network in maintaining leaf sulfite homeostasis

Little is known about the homeostasis of sulfite levels, a cytotoxic by-product of plant sulfur turnover. By employing extended dark to induce catabolic pathways, we followed key elements of the sulfite network enzymes that include adenosine-5'-phosphosulfate reductase and the sulfite scavengers sulfite oxidase (SO), sulfite reductase, UDP-sulfoquinovose synthase, and β-mercaptopyruvate sulfurtransferases. During extended dark, SO was enhanced in tomato (Solanum lycopersicum) wild-type leaves, while the other sulfite network components were down-regulated. SO RNA interference plants lacking SO activity accumulated sulfite, resulting in leaf damage and mortality. Exogenous sulfite application induced up-regulation of the sulfite scavenger activities in dark-stressed or unstressed wild-type plants, while expression of the sulfite producer, adenosine-5'-phosphosulfate reductase, was down-regulated. Unstressed or dark-stressed wild-type plants were resistant to sulfite applications, but SO RNA interference plants showed sensitivity and overaccumulation of sulfite. Hence, under extended dark stress, SO activity is necessary to cope with rising endogenous sulfite levels. However, under nonstressed conditions, the sulfite network can control sulfite levels in the absence of SO activity. The novel evidence provided by the synchronous dark-induced turnover of sulfur-containing compounds, augmented by exogenous sulfite applications, underlines the role of SO and other sulfite network components in maintaining sulfite homeostasis, where sulfite appears to act as an orchestrating signal molecule.

Dynamics of oscillatory phenotypes in Saccharomyces cerevisiae reveal a network of genome-wide transcriptional oscillators

Genetic and environmental factors are well-studied influences on phenotype; however, time is a variable that is rarely considered when studying changes in cellular phenotype. Time-resolved microarray data revealed genome-wide transcriptional oscillation in a yeast continuous culture system with ∼ 2 and ∼ 4 h periods. We mapped the global patterns of transcriptional oscillations into a 3D map to represent different cellular phenotypes of redox cycles. This map shows the dynamic nature of gene expression in that transcripts are ordered and coupled to each other through time and concentration space. Although cells differed in oscillation periods, transcripts involved in certain processes were conserved in a deterministic way. When oscillation period lengthened, the peak to trough ratio of transcripts increased and the fraction of cells in the unbudded (G0/G1) phase of the cell division cycle increased. Decreasing the glucose level in the culture medium was one way to increase the redox cycle, possibly from changes in metabolic flux. The period may be responding to lower glucose levels by increasing the fraction of cells in G1 and reducing S-phase gating so that cells can spend more time in catabolic processes. Our results support that gene transcripts are coordinated with metabolic functions and the cell division cycle.

Time-structure of the yeast metabolism in vivo

All previous studies on the yeast metabolome have yielded a plethora of information on the components, function and organisation of low molecular mass and macromolecular components involved in the cellular metabolic network. Here we emphasise that an understanding of the global dynamics of the metabolome in vivo requires elucidation of the temporal dynamics of metabolic processes on many time-scales. We illustrate this using the 40 min oscillation in respiratory activity displayed in auto-synchronous continuously grown cultures of Saccharomyces cerevisiae, where respiration cycles between a phase of increased respiration (oxidative phase) and decreased respiration (reductive phase). Thereby an ultradian clock, i.e. a timekeeping device that runs through many cycles during one day, is involved in the co-ordination of the vast majority of events and processes in yeast. Through continuous online measurements, we first show that mitochondrial and redox physiology are intertwined to produce the temporal landscape on which cellular events occur. Next we look at the higher order processes of DNA duplication and mitochondrial structure to reveal that both events are choreographed during the respiratory cycles. Furthermore, spectral analysis using the discrete Fourier transformation of high-resolution (10 Hz) time-series of NAD(P)H confirms the existence of higher frequency components of biological origin and that these follow a scale-free architecture even in stable oscillating modes. A different signal-processing approach using discrete wavelet transformations (DWT) indicates that there is a significant contribution to the overall signal from ` ~5, ~ 10 and ~ 20-minutes cycles and the amplitudes of these cycles are phase-dependent. Further investigation (derivative of Gaussian continuous wavelet transformation) reveals that the observed 20-minutes cycles are actually confined to the reductive phase and consist of two ~15-minutes cycles. Moreover, the 5 and 10-minutes cycles are restricted to the oxidative phase of the cycle. The mitochondrial origin of these signals was confirmed by pulse-injection of the cytochrome c oxidase inhibitor H(2)S. We next discuss how these multi-oscillatory states can impinge on the apparently complex reactome (represented as a phase diagram of 1,650 chemical species that show oscillatory behaviour). We conclude that biological processes can be considerably more comprehensible when dynamic in vivo time-structure is taken into account.

Clustering in cell cycle dynamics with general response/signaling feedback

Motivated by experimental and theoretical work on autonomous oscillations in yeast, we analyze ordinary differential equations models of large populations of cells with cell-cycle dependent feedback. We assume a particular type of feedback that we call responsive/signaling (RS), but do not specify a functional form of the feedback. We study the dynamics and emergent behavior of solutions, particularly temporal clustering and stability of clustered solutions. We establish the existence of certain periodic clustered solutions as well as "uniform" solutions and add to the evidence that cell-cycle dependent feedback robustly leads to cell-cycle clustering. We highlight the fundamental differences in dynamics between systems with negative and positive feedback. For positive feedback systems the most important mechanism seems to be the stability of individual isolated clusters. On the other hand we find that in negative feedback systems, clusters must interact with each other to reinforce coherence. We conclude from various details of the mathematical analysis that negative feedback is most consistent with observations in yeast experiments.

Redox regulation in respiring Saccharomyces cerevisiae

BACKGROUND

In biological systems, redox reactions are central to most cellular processes and the redox potential of the intracellular compartment dictates whether a particular reaction can or cannot occur. Indeed the widespread use of redox reactions in biological systems makes their detailed description outside the scope of one review.

SCOPE OF THE REVIEW

Here we will focus on how system-wide redox changes can alter the reaction and transcriptional landscape of Saccharomyces cerevisiae. To understand this we explore the major determinants of cellular redox potential, how these are sensed by the cell and the dynamic responses elicited.

MAJOR CONCLUSIONS

Redox regulation is a large and complex system that has the potential to rapidly and globally alter both the reaction and transcription landscapes. Although we have a basic understanding of many of the sub-systems and a partial understanding of the transcriptional control, we are far from understanding how these systems integrate to produce coherent responses. We argue that this non-linear system self-organises, and that the output in many cases is temperature-compensated oscillations that may temporally partition incompatible reactions in vivo.

GENERAL SIGNIFICANCE

Redox biochemistry impinges on most of cellular processes and has been shown to underpin ageing and many human diseases. Integrating the complexity of redox signalling and regulation is perhaps one of the most challenging areas of biology. This article is part of a Special Issue entitled Systems Biology of Microorganisms.

Identification of MET10-932 and characterization as an allele reducing hydrogen sulfide formation in wine strains of Saccharomyces cerevisiae

A vineyard isolate of the yeast Saccharomyces cerevisiae, UCD932, was identified as a strain producing little or no detectable hydrogen sulfide during wine fermentation. Genetic analysis revealed that this trait segregated as a single genetic determinant. The gene also conferred a white colony phenotype on BiGGY agar (bismuth-glucose-glycine-yeast agar), which is thought to indicate low basal levels of sulfite reductase activity. However, this isolate does not display a requirement for S-containing amino acids, indicating that the sulfate reduction pathway is fully operational. Genetic crosses against known mutations conferring white colony color on BiGGY agar identified the gene leading to reduced H(2)S formation as an allele of MET10 (MET10-932), which encodes a catalytic subunit of sulfite reductase. Sequence analysis of MET10-932 revealed several corresponding amino acid differences in relation to laboratory strain S288C. Allele differences for other genes of the sulfate reduction pathway were also detected in UCD932. The MET10 allele of UCD932 was found to be unique in comparison to the sequences of several other vineyard isolates with differing levels of production of H(2)S. Replacing the MET10 allele of high-H(2)S-producing strains with MET10-932 prevented H(2)S formation by those strains. A single mutative change, corresponding to T662K, in MET10-932 resulted in a loss of H(2)S production. The role of site 662 in sulfide reduction was further analyzed by changing the encoded amino acid at this position. A change back to threonine or to the conservative serine fully restored the H(2)S formation conferred by this allele. In addition to T662K, arginine, tryptophan, and glutamic acid substitutions similarly reduced sulfide formation.

Quantitative analysis of cellular metabolic dissipative, self-organized structures

One of the most important goals of the postgenomic era is understanding the metabolic dynamic processes and the functional structures generated by them. Extensive studies during the last three decades have shown that the dissipative self-organization of the functional enzymatic associations, the catalytic reactions produced during the metabolite channeling, the microcompartmentalization of these metabolic processes and the emergence of dissipative networks are the fundamental elements of the dynamical organization of cell metabolism. Here we present an overview of how mathematical models can be used to address the properties of dissipative metabolic structures at different organizational levels, both for individual enzymatic associations and for enzymatic networks. Recent analyses performed with dissipative metabolic networks have shown that unicellular organisms display a singular global enzymatic structure common to all living cellular organisms, which seems to be an intrinsic property of the functional metabolism as a whole. Mathematical models firmly based on experiments and their corresponding computational approaches are needed to fully grasp the molecular mechanisms of metabolic dynamical processes. They are necessary to enable the quantitative and qualitative analysis of the cellular catalytic reactions and also to help comprehend the conditions under which the structural dynamical phenomena and biological rhythms arise. Understanding the molecular mechanisms responsible for the metabolic dissipative structures is crucial for unraveling the dynamics of cellular life.

The unfolded protein response is not necessary for the G1/S transition, but it is required for chromosome maintenance in Saccharomyces cerevisiae

BACKGROUND

The unfolded protein response (UPR) is a eukaryotic signaling pathway, from the endoplasmic reticulum (ER) to the nucleus. Protein misfolding in the ER triggers the UPR. Accumulating evidence links the UPR in diverse aspects of cellular homeostasis. The UPR responds to the overall protein synthesis capacity and metabolic fluxes of the cell. Because the coupling of metabolism with cell division governs when cells start dividing, here we examined the role of UPR signaling in the timing of initiation of cell division and cell cycle progression, in the yeast Saccharomyces cerevisiae.

METHODOLOGY/PRINCIPAL FINDINGS

We report that cells lacking the ER-resident stress sensor Ire1p, which cannot trigger the UPR, nonetheless completed the G1/S transition on time. Furthermore, loss of UPR signaling neither affected the nutrient and growth rate dependence of the G1/S transition, nor the metabolic oscillations that yeast cells display in defined steady-state conditions. Remarkably, however, loss of UPR signaling led to hypersensitivity to genotoxic stress and a ten-fold increase in chromosome loss.

CONCLUSIONS/SIGNIFICANCE

Taken together, our results strongly suggest that UPR signaling is not necessary for the normal coupling of metabolism with cell division, but it has a role in genome maintenance. These results add to previous work that linked the UPR with cytokinesis in yeast. UPR signaling is conserved in all eukaryotes, and it malfunctions in a variety of diseases, including cancer. Therefore, our findings may be relevant to other systems, including humans.

Behavior of a metabolic cycling population at the single cell level as visualized by fluorescent gene expression reporters

BACKGROUND

During continuous growth in specific chemostat cultures, budding yeast undergo robust oscillations in oxygen consumption that are accompanied by highly periodic changes in transcript abundance of a majority of genes, in a phenomenon called the Yeast Metabolic Cycle (YMC). This study uses fluorescent reporters of genes specific to different YMC phases in order to visualize this phenomenon and understand the temporal regulation of gene expression at the level of individual cells within the cycling population.

METHODOLOGY

Fluorescent gene expression reporters for different phases of the YMC were constructed and stably integrated into the yeast genome. Subsequently, these reporter-expressing yeast were used to visualize YMC dynamics at the individual cell level in cultures grown in a chemostat or in a microfluidics platform under varying glucose concentrations, using fluorescence microscopy and quantitative Western blots.

CONCLUSIONS

The behavior of single cells within a metabolic cycling population was visualized using phase-specific fluorescent reporters. The reporters largely recapitulated genome-specified mRNA expression profiles. A significant fraction of the cell population appeared to exhibit basal expression of the reporters, supporting the hypothesis that there are at least two distinct subpopulations of cells within the cycling population. Although approximately half of the cycling population initiated cell division in each permissive window of the YMC, metabolic synchrony of the population was maintained. Using a microfluidics platform we observed that low glucose concentrations appear to be necessary for metabolic cycling. Lastly, we propose that there is a temporal window in the oxidative growth phase of the YMC where the cycling population segregates into at least two subpopulations, one which will enter the cell cycle and one which does not.

ODE, RDE and SDE models of cell cycle dynamics and clustering in yeast

Biologists have long observed periodic-like oxygen consumption oscillations in yeast populations under certain conditions, and several unsatisfactory explanations for this phenomenon have been proposed. These ‘autonomous oscillations’ have often appeared with periods that are nearly integer divisors of the calculated doubling time of the culture. We hypothesize that these oscillations could be caused by a form of cell cycle synchronization that we call clustering. We develop some novel ordinary differential equation models of the cell cycle. For these models, and for random and stochastic perturbations, we give both rigorous proofs and simulations showing that both positive and negative growth rate feedback within the cell cycle are possible agents that can cause clustering of populations within the cell cycle. It occurs for a variety of models and for a broad selection of parameter values. These results suggest that the clustering phenomenon is robust and is likely to be observed in nature. Since there are necessarily an integer number of clusters, clustering would lead to periodic-like behaviour with periods that are nearly integer divisors of the period of the cell cycle. Related experiments have shown conclusively that cell cycle clustering occurs in some oscillating yeast cultures.

The diversity and evolution of circadian clock proteins in fungi

Circadian rhythms are endogenous cellular patterns that associate multiple physiological and molecular functions with time. The Neurospora circadian system contains at least three oscillators: the FRQ/WC-dependent circadian oscillator (FWO), whose core components are the FRQ, WC-1, WC-2, FRH, and FWD-1 proteins; the WC-dependent circadian oscillator (WC-FLO); and one or more FRQ/ WC-independent oscillators (FLO). Little is known about the distribution of homologs of the Neurospora clock proteins or about the molecular foundations of circadian rhythms across fungi. Here, we examined 64 diverse fungal proteomes for homologs of all five Neurospora clock proteins and retraced their evolutionary history. The FRH and FWD-1 proteins were likely present in the fungal ancestor. WC-1 and WC-2 homologs are absent from the early diverging chytrids and Microsporidia but are present in all other major clades. In contrast to the deep origins of these four clock proteins FRQ homologs are taxonomically restricted within Sordariomycetes, Leotiomycetes and Dothideomycetes. The large number of FRH and FWD-1 homologs identified and their lack of concordance with the fungal species phylogeny indicate that they likely underwent multiple rounds of duplications and losses. In contrast, the FRQ, WC-1 and WC-2 proteins exhibit relatively few duplications and losses. A notable exception is the 10 FRQ-like proteins in Fusarium oxysporum, which resulted from nine duplication events. Our results suggest that the machinery required for FWO oscillator function is taxonomically restricted within Ascomycetes. Although the WC proteins are widely distributed, the functional diversity of the few non-Neurospora circadian oscillators suggests that a WC-FLO oscillator is unlikely to fully explain the observed rhythms. The contrast between the diversity of circadian oscillators and the conservation of most of their machinery is likely best explained by considering the centrality of noncircadian functions in which RNA helicase (FRH), F-box (FWD-1), WC-1 and WC-2 (light-sensing) proteins participate in fungi and eukaryotes.

Metabolic cycling in single yeast cells from unsynchronized steady-state populations limited on glucose or phosphate

Oscillations in patterns of expression of a large fraction of yeast genes are associated with the "metabolic cycle," usually seen only in prestarved, continuous cultures of yeast. We used FISH of mRNA in individual cells to test the hypothesis that these oscillations happen in single cells drawn from unsynchronized cultures growing exponentially in chemostats. Gene-expression data from synchronized cultures were used to predict coincident appearance of mRNAs from pairs of genes in the unsynchronized cells. Quantitative analysis of the FISH results shows that individual unsynchronized cells growing slowly because of glucose limitation or phosphate limitation show the predicted oscillations. We conclude that the yeast metabolic cycle is an intrinsic property of yeast metabolism and does not depend on either synchronization or external limitation of growth by the carbon source.

Ultradian metabolic cycles in yeast

Budding yeast are capable of displaying various modes of oscillatory behavior. Such cycles can occur with a period ranging from 1 min up to many hours, depending on the growth and culturing conditions used to observe them. This chapter discusses the robust oscillations in oxygen consumption exhibited by high-density yeast cell populations during continuous, glucose-limited growth in a chemostat. These ultradian metabolic cycles offer a view of the life of yeast cells under a challenging, nutrient-poor growth environment and might represent useful systems to interrogate a variety of fundamental metabolic and regulatory processes.

Metabolism control by the circadian clock and vice versa

Circadian rhythms govern a wide variety of physiological and metabolic functions in most organisms. At the heart of these regulatory pathways in mammals is the clock machinery, a remarkably coordinated transcription-translation system that relies on dynamic changes in chromatin states. Recent findings indicate that regulation also goes the other way, as specific elements of the clock can sense changes in cellular metabolism. Understanding in full detail the intimate links between cellular metabolism and the circadian clock machinery will provide not only crucial insights into system physiology but also new avenues toward pharmacological intervention of metabolic disorders.

Periodic fermentor yield and enhanced product enrichment from autonomous oscillations

Four decades of work have clearly established the existence of autonomous oscillations in budding yeast culture across a range of operational parameters and in a few strains. Autonomous oscillations impact substrate conversion to biomass and products. Relatively little work has been done to quantify yield in this case. We have analyzed the yield of autonomously oscillating systems, grown under different conditions, and demonstrate that it too oscillates. Using experimental data and mathematical models of yeast growth and division, we demonstrate strategies to increase the efficient recovery of products. The analysis makes advantage of the population structure and synchrony of the system and our ability to target production within the cell cycle. While oscillatory phenomena in culture have generally been regarded with trepidation in the engineering art of bioprocess control, our results provide further evidence that autonomously oscillating systems can be a powerful tool, rather than an obstruction.

Respiratory oscillations in yeasts

Respiratory oscillations in yeasts have been studied in three time domains with periods of (a) about a minute, (b) about 40 min, and (c) about a day. Reactive responses (damped oscillations), rhythms and temperature-compensated clocks have been described for (b) and (c), but a timekeeping clock has not yet been shown for (a). Synchronous populations reveal the time-structure that can only otherwise be studied in single organisms; this is because time-averaging through an asynchronous population conceals its fine structure. Early studies with synchronous cultures made by size selection methods indicated ultradian-clock driven oscillations in respiration, pools of adenylates, total protein, RNA synthesis and many enzyme activities (tau = 40 min in Schizosaccharomyces pombe, 30 min in Candida utilis), and more recently in self-synchronised continuous cultures of Saccharomyces cerevisiae (tau = 48 min). Most detailed understanding comes from the latter system, where continuous, noninvasive real-time monitoring (of 02 uptake, CO2 production, and NAD(P)H redox state) is combined with frequent discrete time samples (for other redox components, including H2S, GSH and cytochromes, metabolites, and mRNA levels). A redox switch lies at the heart of this ultradian clock and a plethora of outputs is optimized to a time-base that is genetically-determined and differs in different organisms. It is suggested that the entire temporal landscape of all eukaryotic organisms and the cells of higher plants and animals is constructed on this basis. A time frame for the coordination and coherence of all intracellular processes and the construction and assembly of cellular structures is provided by the ultradian clock The circadian clock matches these functions to the daily cycle of the external environment.

Real-time luminescence monitoring of cell-cycle and respiratory oscillations in yeast

The use of luciferase reporters has become a precise, noninvasive, high-throughput method for real-time monitoring of promoter activity in living cells, especially for rhythmic biological processes such as circadian rhythms. We developed a destabilized firefly luciferase as a reporter for rhythmic promoter activity in both the cell division and respiratory cycles of the budding yeast Saccharomyces cerevisiae in which real-time luminescence reporters have not been previously applied. The continuous output of light from luciferase reporters allowed us to explore the relationship between the cell division cycle and the yeast respiratory oscillation, including the observation of responses to chemicals that cause phase shifting of the respiratory oscillations. Destabilized firefly luciferase is a good reporter of cell cycle position in synchronized or partially synchronized yeast cultures, in both batch and continuous cultures. In addition, the oxygen dependence of luciferase can be used under certain conditions as a genetically encodable oxygen monitor. Finally, we use this reporter to show that there is a direct correlation between premature induction of cell division and phase resetting of the respiratory oscillation under the continuous culture conditions tested.

The scale-free dynamics of eukaryotic cells

Temporal organization of biological processes requires massively parallel processing on a synchronized time-base. We analyzed time-series data obtained from the bioenergetic oscillatory outputs of Saccharomyces cerevisiae and isolated cardiomyocytes utilizing Relative Dispersional (RDA) and Power Spectral (PSA) analyses. These analyses revealed broad frequency distributions and evidence for long-term memory in the observed dynamics. Moreover RDA and PSA showed that the bioenergetic dynamics in both systems show fractal scaling over at least 3 orders of magnitude, and that this scaling obeys an inverse power law. Therefore we conclude that in S. cerevisiae and cardiomyocytes the dynamics are scale-free in vivo. Applying RDA and PSA to data generated from an in silico model of mitochondrial function indicated that in yeast and cardiomyocytes the underlying mechanisms regulating the scale-free behavior are similar. We validated this finding in vivo using single cells, and attenuating the activity of the mitochondrial inner membrane anion channel with 4-chlorodiazepam to show that the oscillation of NAD(P)H and reactive oxygen species (ROS) can be abated in these two evolutionarily distant species. Taken together these data strongly support our hypothesis that the generation of ROS, coupled to redox cycling, driven by cytoplasmic and mitochondrial processes, are at the core of the observed rhythmicity and scale-free dynamics. We argue that the operation of scale-free bioenergetic dynamics plays a fundamental role to integrate cellular function, while providing a framework for robust, yet flexible, responses to the environment.

Evolution of the clock from yeast to man by period-doubling folds in the cellular oscillator

Analysis of genome-wide oscillations in transcription reveals that the cell is an oscillator and an attractor and that the maintenance of a stable phenotype requires that maximums in expression in clusters of transcripts must be poised at antipodal phases around the steady state-this is the dynamic architecture of phenotype. Plots of the path through concentration phase space taken by all of the transcripts of Saccharomyces cerevisiae yield a simple three-dimensional surface. How this surface might change as period lengthens or as a cell differentiates is at the center of current work. We have shown that changes in gene expression in response to mutation or perturbation by drugs occur through a folding or unfolding of the surface described by this circle of transcripts and we suggest that the path from this 40-minute oscillation to the cell cycle and circadian rhythms takes place through a series of period-two or period-three bifurcations. These foldings in the surface of the putative attractor result in an increasingly dense set of nested trajectories in the concentrations of message and protein. Evolutionary advantage might accrue to an organism that could change period by changes in just one or a few genes as day length increased from 4 hours in the prebiotic Earth, through 8 hours during the expansion of photoautotrophs, to the present 24 hours.

Collective behavior in gene regulation: metabolic clocks and cross-talking

Biological functions governed by the circadian clock are the evident result of the entrainment operated by the earth's day and night cycle on living organisms. However, the circadian clock is not unique, and cells and organisms possess many other cyclic activities. These activities are difficult to observe if carried out by single cells and the cells are not coordinated but, if they can be detected, cell-to-cell cross-talk and synchronization among cells must exist. Some of these cycles are metabolic and cell synchronization is due to small molecules acting as metabolic messengers. We propose a short survey of cellular cycles, paying special attention to metabolic cycles and cellular cross-talking, particularly when the synchronization of metabolism or, more generally, cellular functions are concerned. Questions arising from the observation of phenomena based on cell communication and from basic cellular cycles are also proposed.

Glutathione and Gts1p drive beneficial variability in the cadmium resistances of individual yeast cells

Phenotypic heterogeneity among individual cells within isogenic populations is widely documented, but its consequences are not well understood. Here, cell-to-cell variation in the stress resistance of Saccharomyces cerevisiae, particularly to cadmium, was revealed to depend on the antioxidant glutathione. Heterogeneity was decreased strikingly in gsh1 mutants. Furthermore, cells sorted according to differing reduced-glutathione (GSH) contents exhibited differing stress resistances. The vacuolar GSH-conjugate pathway of detoxification was implicated in heterogeneous Cd resistance. Metabolic oscillations (ultradian rhythms) in yeast are known to modulate single-cell redox and GSH status. Gts1p stabilizes these oscillations and was found to be required for heterogeneous Cd and hydrogen-peroxide resistance, through the same pathway as Gsh1p. Expression of GTS1 from a constitutive tet-regulated promoter suppressed oscillations and heterogeneity in GSH content, and resulted in decreased variation in stress resistance. This enabled manipulation of the degree of gene expression noise in cultures. It was shown that cells expressing Gts1p heterogeneously had a competitive advantage over more-homogeneous cell populations (with the same mean Gts1p expression), under continuous and fluctuating stress conditions. The results establish a novel molecular mechanism for single-cell heterogeneity, and demonstrate experimentally fitness advantages that depend on deterministic variation in gene expression within cell populations.

Signal processing and the design of microarray time-series experiments

Recent findings of a genome-wide oscillation involving the transcriptome of the budding yeast Saccharomyces cerevisiae suggest that the most promising path to an understanding of the cell as a dynamic system will proceed from carefully designed time-series sampling followed by the development of signal-processing methods suited to molecular biological datasets. When everything oscillates, conventional biostatistical approaches fall short in identifying functional relationships among genes and their transcripts. Worse, based as they are on steady-state assumptions, such approaches may be misleading. In this chapter, we describe the continuous gated synchrony system and the experiments leading to the concept of genome-wide oscillations, and suggest methods of analysis better suited to dissection of oscillating systems. Using a yeast continuous-culture system, the most precise and stable biological system extant, we explore analytical tools such as wavelet multiresolution decomposition, Fourier analysis, and singular value decomposition to uncover the dynamic architecture of phenotype.

Buffering of deoxyribonucleotide pool homeostasis by threonine metabolism

Synergistically interacting gene mutations reveal buffering relationships that provide growth homeostasis through their compensation of one another. This analysis in Saccharomyces cerevisiae revealed genetic modules involved in tricarboxylic acid cycle regulation (RTG1, RTG2, RTG3), threonine biosynthesis (HOM3, HOM2, HOM6, THR1, THR4), amino acid permease trafficking (LST4, LST7), and threonine catabolism (GLY1). These modules contribute to a molecular circuit that regulates threonine metabolism and buffers deficiency in deoxyribonucleotide biosynthesis. Phenotypic, genetic, and biochemical evidence for this buffering circuit was obtained through analysis of deletion mutants, titratable alleles of ribonucleotide reductase genes, and measurements of intracellular deoxyribonucleotide pool concentrations. This circuit provides experimental evidence, in eukaryotes, for the presence of a high-flux backbone of metabolism, which was previously predicted from in silico modeling of global metabolism in bacteria. This part of the high-flux backbone appears to buffer deficiency in ribonucleotide reductase by enabling a compensatory increase in de novo purine biosynthesis that provides additional rate-limiting substrates for dNTP production and DNA synthesis. Hypotheses regarding unexpected connections between these metabolic pathways were facilitated by genome-wide but also highly quantitative phenotypic assessment of interactions. Validation of these hypotheses substantiates the added benefit of quantitative phenotyping for identifying subtleties in gene interaction networks that modulate cellular phenotypes.

Role of Gts1p in regulation of energy-metabolism oscillation in continuous cultures of the yeast Saccharomyces cerevisiae

Energy-metabolism oscillation (EMO) in an aerobic chemostat culture of yeast is basically regulated by a feedback loop of redox reactions in energy metabolism and modulated by metabolism of storage carbohydrates. In this study, we investigated the role of Gts1p in the stabilization of EMO, using the GTS1-deleted transformant gts1Delta. We found that fluctuations in the redox state of the NAD co-factor and levels of redox-regulated metabolites in glycolysis, especially of ethanol, are markedly reduced in amplitude during EMO of gts1Delta, while respiration indicated by the oxygen uptake rate (OUR) and energy charge is not so affected throughout EMO in gts1Delta. Further, the transitions of the levels of OUR, NAD(+) : NADH ratio and intracellular pH between the two phases were apparently retarded compared with those in the wild-type, suggesting attenuation of EMO in gts1Delta. Furthermore, the mRNA levels of genes encoding enzymes for the synthesis of trehalose and glycogen are fairly reduced in gts1Delta, consistent with the decreased synthesis of storage carbohydrates. In addition, the level of inorganic phosphate, which is required for the reduction of NAD(+) and mainly supplied from trehalose synthesis, was decreased in the early respiro-fermentative phase in gts1Delta. Thus, we suggested that the deletion of GTS1 as a transcriptional co-activator for these genes inhibited the metabolism of storage carbohydrates, which causes attenuation of the feedback loop of dehydrogenase reactions in glycolysis with the restricted fluctuation of ethanol as a main synchronizing agent for EMO in a cell population.

Destabilization of energy-metabolism oscillation in the absence of trehalose synthesis in the chemostat culture of yeast

Energy-metabolism oscillation (EMO) in yeast is basically regulated by a feedback-loop of redox reactions and modulated by the metabolism of storage carbohydrates like glycogen and trehalose. We found that EMO of the transformant tps1Delta deleted of TPS1 encoding trehalose-6-phosphate synthase fluctuated unsteadily with a short wavelength in the absence of trehalose synthesis, while EMO was gradually destabilized with the wavelength increasing as storage in a frozen state was prolonged. During EMO, whereas the fluctuations in levels of the oxygen uptake rate, NAD(P)H and cAMP were attenuated, the glycerol level fluctuated with high amplitude and the levels of glycogen and ethanol fluctuated with similar amplitudes to those in the wild type. Thus, EMO barely operated in tps1Delta depending on the increase of glycerol synthesis as a source of inorganic phosphate in place of trehalose synthesis and fairly conserved fluctuation in the level of ethanol as a synchronizing agent.

Regulation of yeast oscillatory dynamics

When yeast cells are grown continuously at high cell density, a respiratory oscillation percolates throughout the population. Many essential cellular functions have been shown to be separated temporally during each cycle; however, the regulatory mechanisms involved in oscillatory dynamics remain to be elucidated. Through GC-MS analysis we found that the majority of metabolites show oscillatory dynamics, with 70% of the identified metabolite concentrations peaking in conjunction with NAD(P)H. Through statistical analyses of microarray data, we identified that biosynthetic events have a defined order, and this program is initiated when respiration rates are increasing. We then combined metabolic, transcriptional data and statistical analyses of transcription factor activity, identified the top oscillatory parameters, and filtered a large-scale yeast interaction network according to these parameters. The analyses and controlled experimental perturbation provided evidence that a transcriptional complex formed part of the timing circuit for biosynthetic, reductive, and cell cycle programs in the cell. This circuitry does not act in isolation because both have strong translational, proteomic, and metabolic regulatory mechanisms. Our data lead us to conclude that the regulation of the respiratory oscillation revolves around coupled subgraphs containing large numbers of proteins and metabolites, with a potential to oscillate, and no definable hierarchy, i.e., heterarchical control.

Observation of a chaotic multioscillatory metabolic attractor by real-time monitoring of a yeast continuous culture

We monitored a continuous culture of the yeast Saccharomyces cerevisiae by membrane-inlet mass spectrometry. This technique allows very rapid simultaneous measurements (one point every 12 s) of several dissolved gases. During our experiment, the culture exhibited a multioscillatory mode in which the dissolved oxygen and carbon dioxide records displayed periodicities of 13 h, 36 min and 4 min. The 36- and 4-min modes were not visible at all times, but returned at regular intervals during the 13-h cycle. The 4-min mode, which has not previously been described in continuous culture, can also be seen when the culture displays simpler oscillatory behavior. The data can be used to visualize a metabolic attractor of this system, i.e. the set of dissolved gas concentrations which are consistent with the multioscillatory state. Computation of the leading Lyapunov exponent reveals the dynamics on this attractor to be chaotic.

Reliable cell disruption in yeast

We report the results of an optical assay to determine the degree of cell wall disruption in yeast. The results indicate that cell wall disruption with glass beads yields reproducible results that can be modelled with an integral measure of time to failure that implies a decreasing failure rate. It is shown that a standard protocol results in only 60% disruption, with a relatively large coefficient of variation. The data show that the yield of total RNA harvested is proportional to the degree of cellular disruption, and that there is no loss of RNA quality with > 90% disruption. The data also show that cell disruption of a synchronous culture varies with the cell cycle. We speculate that the decreasing failure rate is related to the cell cycle phase-dependent disruptability.

Single and cell population respiratory oscillations in yeast: a 2-photon scanning laser microscopy study

Two-photon scanning laser and confocal microscopies were used to image metabolic dynamics of single or cell populations of Saccharomyces cerevisiae strain 28033. Autofluorescence of reduced nicotinamide nucleotides, and mitochondrial membrane potential (DeltaPsim), were simultaneously monitored. Spontaneous, large-scale synchronized oscillations of NAD(P)H and DeltaPsim throughout the entire population of yeasts occurred under perfusion with aerated buffer in a continuous single-layered film of organisms. These oscillations stopped in the absence of perfusion and the intracellular NAD(P)H pool became reduced. Individual mitochondria within a single yeast also showed in-phase synchronous responses with the cell population, in both tetramethylrhodamine ethyl ester (or tetramethylrhodamine methyl ester) and autofluorescence. A single, localized, laser flash also triggered mitochondrial oscillations in single cells suggesting that the mitochondrion may behave as an autonomous oscillator. We conclude that spontaneous oscillations of S. cerevisiae mitochondrial redox states and DeltaPsim occur within individual yeasts, and synchrony of populations of organisms indicates the operation of an efficient system of cell-cell interaction to produce concerted metabolic multicellular behaviour on the minute time scale in both cases.

A rapid genome-scale response of the transcriptional oscillator to perturbation reveals a period-doubling path to phenotypic change

Perturbation of the gated-synchrony system in yeast with phenelzine, an antidepressant drug used in the treatment of affective disorders in humans, leads to a rapid lengthening in the period of the genome-wide transcriptional oscillation. The effect is a concerted, genome-scale change in expression that is first seen in genes maximally expressed in the late-reductive phase of the cycle, doubling the length of the reductive phase within two cycles after treatment. Clustering of genes based on their temporal patterns of expression yielded just three super clusters whose trajectories through time could then be mapped into a simple 3D figure. In contrast to transcripts in the late-reductive phase, most transcripts do not show transients in expression relative to others in their temporal cluster but change their period in a concerted fashion. Mapping the trajectories of the transcripts into low-dimensional surfaces that can be represented by simple systems of differential equations provides a readily testable model of the dynamic architecture of phenotype. In this system, period doubling may be a preferred pathway for phenotypic change. As a practical matter, low-amplitude, genome-wide oscillations, a ubiquitous but often unrecognized attribute of phenotype, could be a source of seemingly intractable biological noise in microarray studies.

A tuneable attractor underlies yeast respiratory dynamics

Our understanding of the molecular structure and function in the budding yeast, Saccharomyces cerevisiae, surpasses that of all other eukaryotic cells. However, the fundamental properties of the complex processes and their control systems have been difficult to reconstruct from detailed dissection of their molecular components. Spontaneous oscillatory dynamics observed in self-synchronized continuous cultures is pervasive, involves much of the cellular network, and provides unique insights into integrative cell physiology. Here, in non-invasive experiments in vivo, we exploit these oscillatory dynamics to analyse the global timing of the cellular network to show the presence of a low-order chaotic component. Although robust to a wide range of environmental perturbations, the system responds and reacts to the imposition of harsh environmental conditions, in this case low pH, by dynamic re-organization of respiration, and this feeds upwards to affect cell division. These complex dynamics can be represented by a tuneable attractor that orchestrates cellular complexity and coherence to the environment.