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.

The finding of a genome-wide oscillation in transcription that gates cells into S phase and coordinates mitochondrial and metabolic functions has altered our understanding of how the cell cycle is timed and how stable cellular phenotypes are maintained. Here we present the evidence and arguments in support of the idea that everything oscillates, and the rationale for viewing the cell as an attractor from which deterministic noise can be tuned by appropriate coupling among the many feedback loops, or regulons, that make up the transcriptional-respiratory attractor cycle. The existence of this attractor also explains many of the dynamic macroscopic properties of the cell cycle and appears to be the timekeeping oscillator in both cell cycles and circadian rhythms. The path taken by this primordial oscillator in the course of differentiation or drug response may involve period-doubling behavior. Evidence for a relatively high-frequency timekeeping oscillator in yeast and mammalian cells comes from expression array analysis, and GC/MS in the case of yeast, and primarily from macroscopic measures of phase response to perturbation in the case of mammalian cells. Low-amplitude, genome-wide oscillations, a ubiquitous but often unrecognized attribute of phenotype, may be a source of seemingly intractable biological noise in microarray and proteomic studies. These oscillations in transcript and protein levels and the repeated cycles of synthesis and degradation they require, represent a high energy cost to the cell which must, from an evolutionary point of view, be recovered as essential information. We suggest that the information contained in this genome-wide oscillation is the dynamic code that organizes a stable phenotype from an otherwise passive genome.

A precisely controlled, continuously grown, aerobic yeast culture system shows an autonomous sustained respiratory oscillation (i.e. a high amplitude change in dissolved O2 levels: the residual O2 that remains after the organisms use what they require). This spontaneously organized synchronous state can be maintained for extended periods (months) and continuously monitored for intracellular redox state (by direct fluorimetric output for nicotinamide nucleotides: excitation 366 nm, emission 450 nm), and dissolved gases (O2 electrode and/or direct membrane inlet mass spectrometry for O2, CO2 and H2S, sampled on a 15s cycle). The whole culture population (~5 × 108 organisms/ml) is behaving metabolically as if it were a single cell, so that analysis for metabolic intermediates (keto and amino-acids, carboxylic acids), redox components (glutathione, cysteine, NAD(P)H and reactive O2 species) and products (acetaldehyde, acetic acid and ethanol), with sampling at frequent time intervals gives reliable information on phase relationships on the approximately 40min ultradian cycle. Lipid peroxidation levels indicate the changing levels of oxidative stress. Microarray analysis shows a genome-wide oscillation in transcription, with expression maxima at three nearly equally spaced intervals on the 40min time-base. The first temporal cluster (4,679 of 5,329 genes expressed) occurred maximally during the reductive phase, whereas the remaining 650 transcripts were detected maximally in the oxidative phase. Furthermore, when fixed samples of yeasts were analysed for DNA using flow cytometry, synchronous bursts in the initiation of DNA replication (occurring in about 8% of the total population) were shown to coincide with decreasing respiration rates. A precisely defined appearance of mitochondrial energy generation-dependent conformational changes, the machinery for protein synthesis and degradation and for mitochondrial ribosome assembly are also all locked on the ultradian clock cycle phase. This indicates the pervasive and all-embracing nature of temporal co-ordination of cellular growth and division. The major players in this yeast model system are identified as some of the most highly conserved components common to all eukaryotes. Thus a primeval, fundamental and insistent drum-beat reverberates in all eukaryotic systems, in microbes, animals and plants. The ultradian clock that co-evolved with increasing atmospheric O2 predates and underpins the circadian clock at the central core of endogenous intracellular timekeeping. It represents the prototype of all biological rhythmicity: circadian clocks evolved much more recently, almost as the icing on the cake.

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.

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.

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.

Microarray analysis from a yeast continuous synchrony culture system shows a genomewide oscillation in transcription. Maximums in transcript levels occur at three nearly equally spaced intervals in this approximately 40-min cycle of respiration and reduction. Two temporal clusters (4,679 of 5,329) are maximally expressed during the reductive phase of the cycle, whereas a third cluster (650) is maximally expressed during the respiratory phase. Transcription is organized functionally into redox-state superclusters with genes known to be important in respiration or reduction being synthesized in opposite phases of the cycle. The transcriptional cycle gates synchronous bursts in DNA replication in a constant fraction of the population at 40-min intervals. Restriction of DNA synthesis to the reductive phase of the cycle may be an evolutionarily important mechanism for reducing oxidative damage to DNA during replication.

Cultures of Saccharomyces cerevisiae grown continuously produce an autonomous oscillation in many metabolic outputs. The most conveniently measured variable, i.e., dissolved oxygen concentration, oscillates with a period of 40-55 min. Previously we have identified two compounds capable of resetting phase, acetaldehyde and hydrogen sulfide. The phase-response curves constructed for acetaldehyde show a strong (Type 0) response at 3.0 mM and a weak (Type 1) response at 1.0 mM. Ammonium sulfide phase-response curves (pulse injected at 1.0 microM and 3.0 microM) revealed that sulfide is only an effective perturbation agent when endogenous sulfide concentrations are at a maximum. Also only Type 1 phase responses were observed. When the phase-response curve for sulfite (at 3.0 M) was constructed, phase responses were at a maximum at 60 degrees, indicating the possible involvement of sulfite in cell synchronization. It is concluded that endogenously produced acetaldehyde and sulfite tune the oscillation of mitochondrial energization state whereas sulfide mediates population synchrony.

MOTIVATIONMicroarray and gene chip technology provide high throughput tools for measuring gene expression levels in a variety of circumstances, including cellular response to drug treatment, cellular growth and development, tumorigenesis, among many other processes. In order to interpret the large data sets generated in experiments, data analysis techniques that consider biological knowledge during analysis will be extremely useful. We present here results showing the application of such a tool to expression data from yeast cell cycle experiments.RESULTSOriginally developed for spectroscopic analysis, Bayesian Decomposition (BD) includes two features which make it useful for microarray data analysis: the ability to assign genes to multiple coexpression groups and the ability to encode biological knowledge into the system. Here we demonstrate the ability of the algorithm to provide insight into the yeast cell cycle, including identification of five temporal patterns tied to cell cycle phases as well as the identification of a pattern tied to an approximately 40 min cell cycle oscillator. The genes are simultaneously assigned to the patterns, including partial assignment to multiple patterns when this is required to explain the expression profile.AVAILABILITYThe application is available free to academic users under a material transfer agreement. Go to http://bioinformatics.fccc.edu/ for more details.

A reanalysis of expression arrays in yeast cells synchronized by alpha factor blockade or through the use of temperature sensitive mutants uncovered a genome wide pattern of oscillations in mRNA concentrations. Using wavelet decomposition as a signal processing technique and enhancement strategies borrowed from image processing, noise and trends in the Stanford yeast cell cycle data were partitioned away from time series profiles to uncover genome-wide oscillations in expression. These oscillations which were typically of cell cycle or half cell cycle duration, 40 and 80 minutes in the Stanford data set suggest that there are large-scale temporal structures and high frequency oscillations in mRNA levels through the cell cycle. Wavelet decomposition, which acts like a band pass filter bank, was used to determine where most of the power appeared in the decomposition. The ∼40-min oscillation is mirrored in continuous chemostat cultures. In these cultures, metabolic synchrony involving an unknown proportion of the transcriptome can be monitored by measurement of oxygen consumption and can be sustained for weeks. These 40-min oscillations are stable and precise with coefficients of variation less than 1% for both period and amplitude. The hypothesis that high and low amplitude oscillations are a ubiquitous property of the genetic regulatory circuitry was supported by the observation of period doubling bifurcations in the distribution of population doubling times in yeast.

. Wavelet analysis has been applied to yeast cell cycle expression microchip data to reveal large-scale temporal structures and ubiquitous oscillations in mRNA levels. Discrete intervals in time within the cell cycle when expression levels changed were visualized as contour maps in which points of transition in gene expression among all 6178 genes were plotted as a function of cell cycle time. Time-frequency analysis using wavelet transforms supported the direct visualization and led to the conclusion that the predominant period is not the cell cycle but a higher frequency, 40 min, submultiple of the cycle. Each of the 6178 gene expression profiles was dissected by wavelet decomposition into all permitted frequencies from the Nyquist limit to roughly twice the cell cycle length. Transitions associated with maximum up- or down-regulation of mRNA levels appear as bands at circa 40-min intervals, half the length of the cycle, through two cell cycles. More than two thirds of the genes, including many of the cyclins, showed this half-cycle periodicity. Gene expression and events within the yeast cell cycle may be regulated by an attractor whose fundamental period is an emergent property of dynamic interactions within the yeast transcriptome.

Replication synchrony within a cell population can be demonstrated by pulse-labeling followed by PCR amplification of immunoprecipitated 5-iodo-2'-deoxyuridine (IdUrd)-labeled DNA from cells of otherwise indeterminant kinetic stages. This replication synchrony-PCR approach may be valuable in understanding the dynamics of human normal tissue or solid tumor replication in situ where access for repeated sampling is severely limited. IdUrd labeling provides a sampling-time-independent method for assessing the replicative status of a cell population at the time when the label was presented. Using genes whose time of replication in S phase is already known, the presence of a cell in early or late S phase can be determined and a qualitative measure made of replication synchrony in the population. This approach was evaluated in synchronous and random cultures of Ej cells using the early replicating PGK-1 gene to identify cells in early S phase at the time of labeling and the late replicating factor IX gene to identify cells that were in late S phase. To test the feasibility of clinical application of this technique, human tumor cells from patients with advanced cancers, given IdUrd therapeutically at specified times of the day, were evaluated. In some patients, replication synchrony-PCR provided evidence of parasynchronous DNA replication in tumor cells. This technique could be appended to existing clinical studies in which BrdUrd or IdUrd is being given to patients either diagnostically or therapeutically.

BACKGROUND:Despite recent advances in the treatment of ovarian cancer, the long-term prognosis for patients with this malignancy appears to depend more on tumor prognostic factors than on treatment regimens. The traditionally used prognostic factors are often subjective and, currently, have not been sufficient to determine individual patient prognosis.METHODS:Newer techniques of quantitative cytologic testing, including flow cytometry, facilitate the objective evaluation of tumor cell heterogeneity and the identification of additional prognostic factors.RESULTS:There is good evidence, mainly from retrospective studies, that DNA ploidy is a valuable prognostic indicator in patients with both early-stage and late-stage ovarian cancer. Most of the recent flow cytometric studies have identified ploidy as an independent prognostic factor, with aneuploidy predicting a significantly shorter survival time, even in patients with borderline malignant tumors. Flow cytometric determination of cell cycle information (e.g., S-phase fraction or proliferative index) may represent additional prognostic information and may be used to predict the early tumor response to treatment.CONCLUSIONS:Although additional prospective studies are needed to establish the exact value of flow cytometric evaluation for ovarian cancer and other gynecologic malignancies, there is little doubt that the prognostic value of this information will influence clinical management of patients with these malignancies in the near future.

Large discrete arrays of chaotic attractors, coupled by diffusion, organize into asynchronous periodic spiral waves, synchronous periodic bands, turbulent fields or synchronous chaos as a function of coupling strength and array size. Self-organization of periodic spirals in both two and three dimensional arrays of nonexcitable systems appears to require the early establishment of an antipodal phase relationship between the few cells that will form the vortex. Cells within or close to the vortex maintain low z amplitude, near limit cycle trajectories, with stable, well-defined phase relationships. In periodic banding structures, initial antipodal phase seeds evolve to isochrons that form nested periodic trajectories. The likelihood that biological systems are fundamentally oscillatory and chaotic is discussed.

When large arrays of strange attractors are coupled diffusively through one of the variables, chaotic systems become periodic and form large archimedean spirals or concentric bands. This observation may have importance for many applications in the field of deterministic chaos and seems particularly relevant to the question of the formal temporal structure of the biological clock in metazoan organisms. In particular, although individual cellular oscillators, as manifested in the cell cycle, may have deep basins of attraction and appear to be more or less periodic, we suggest that cells oscillate with chaotic dynamics in the ultradian domain. Only when large aggregates of these cells are tightly coupled can a precise circadian clock emerge. For changing coupling strength or parameter values, period increase occurs through quantal or integral multiple increments of the fundamental. All calculations were implemented on a 386AT, using a Mercury MC6400 floating point processor.

Annals of the New York Academy of SciencesVolume 618, Issue 1 p. 257-276 Circadian and Ultradian Cytokinetic Rhythms of Spontaneous Human Cancera ROBERT R. KLEVECZ, ROBERT R. KLEVECZ Department of Cell Biology, Beckman Research Institute of the City of Hope, 1450 East Duarte Road, Duarte, California 91010–0269Search for more papers by this authorPATRICIA S. BRALY, PATRICIA S. BRALY Department of Reproductive Medicine, University of California at San Diego, San Diego, California 92103Search for more papers by this author ROBERT R. KLEVECZ, ROBERT R. KLEVECZ Department of Cell Biology, Beckman Research Institute of the City of Hope, 1450 East Duarte Road, Duarte, California 91010–0269Search for more papers by this authorPATRICIA S. BRALY, PATRICIA S. BRALY Department of Reproductive Medicine, University of California at San Diego, San Diego, California 92103Search for more papers by this author First published: February 1991 https://doi.org/10.1111/j.1749-6632.1991.tb27248.xCitations: 16 a This work was supported in part by Grant ROlCA49203–06 to RRK and National Institutes of Health Cancer Center Support Grant CA33572. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Citing Literature Volume618, Issue1Temporal Control of Drug DeliveryFebruary 1991Pages 257-276 RelatedInformation