Quantized generation time in mammalian cells as an expression of the cellular clock

Multimodal distribution of transient time of predator extinction in a three-species food chain

The transient dynamics capture the time history in the behavior of a system before reaching an attractor. This paper deals with the statistics of transient dynamics in a classic tri-trophic food chain with bistability. The species of the food chain model either coexist or undergo a partial extinction with predator death after a transient time depending upon the initial population density. The distribution of transient time to predator extinction shows interesting patterns of inhomogeneity and anisotropy in the basin of the predator-free state. More precisely, the distribution shows a multimodal character when the initial points are located near a basin boundary and a unimodal character when chosen from a location far away from the boundary. The distribution is also anisotropic because the number of modes depends on the direction of the local of initial points. We define two new metrics, viz., homogeneity index and local isotropic index, to characterize the distinctive features of the distribution. We explain the origin of such multimodal distributions and try to present their ecological implications.

A mathematical model for cell cycle control: graded response or quantized response

Cell cycle is an important and complex biological system. A lot of efforts have been put in understanding cell cycle arrest for its vital role in clinical therapies. The cell-cycle-arrest outcomes upon stimulation are complicated. The response could be stringent or relaxed, and graded or quantized. A model fully addressing various cell-cycle-arrest outcomes is to be developed. Here, we developed a mathematical model of cell cycle control incorporating distinct characteristics of various cell-cycle-arrest outcomes. The model can simulate two typical properties of cell cycle arrest, quantized and graded. We also characterized the inheritable quiescence and refractory state, which were crucial in long-term response of the population. Then, we monitored cells respond to multiple stimulations, and the results indicated that cells responded to stimulations with small interval did not induce significantly sustained cell cycle arrest as the existence of refractory state. Our work will benefit fundamental research and make efforts to predicting outcomes of clinical therapeutics.

A new ultradian rhythm in mammalian cell dry mass observed by holography

We have discovered a new 4 h ultradian rhythm that occurs during the interphase of the cell cycle in a wide range of individual mammalian cells, including both primary and transformed cells. The rhythm was detected by holographic lens-free microscopy that follows the histories of the dry mass of thousands of single live cells simultaneously, each at a resolution of five minutes. It was vital that the rhythm was observed in inherently heterogeneous cell populations, thus eliminating synchronization and labeling bias. The rhythm is independent of circadian rhythm, and is temperature-compensated. We show that the amplitude of the fundamental frequency provides a way to quantify the effects of, chemical reagents on cells, thus shedding light on its mechanism. The rhythm is suppressed by proteostasis disruptors and is detected only in proliferating cells, suggesting that it represents a massive degradation and re-synthesis of protein every 4 h in growing cells.

Establishment of fast-growing serum-free immortalised cells from Chinese hamster lung tissues for biopharmaceutical production

Chinese hamster (Cricetulus griseus) ovary-derived Chinese hamster ovary (CHO) cells are the most commonly used mammalian hosts for the industrial production of recombinant therapeutics because of their ability to fold, assemble, and perform post-translational modifications, such as glycosylation, on proteins. They are also valuable for their ability to grow in serum-free suspension cultures. In this study, we established a cell line derived from lung tissue of Chinese hamsters, named Chinese hamster lung (CHL)-YN cells. The biosafety of CHL-YN cells was confirmed by in vitro sterility testing, mycoplasma detection, and reverse transcriptase assays. One of the key characteristics of CHL-YN cells was their doubling time of 8.1 h in chemically defined culture medium; thus, they proliferate much faster than conventional CHO cells and general mammalian cells. Transgenes could be introduced into CHL-YN cells with high efficiency. Finally, between 50% to > 100% of the amount of glycosylated immunoglobulin G (IgG)1 produced by CHO-K1 cells was produced by CHL-YN cells over a shorter period of time. In summary, fast-growing CHL-YN cells are a unique cell line for producing recombinant proteins.

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.

Quantitative Studies for Cell-Division Cycle Control

The cell-division cycle (CDC) is driven by cyclin-dependent kinases (CDKs). Mathematical models based on molecular networks, as revealed by molecular and genetic studies, have reproduced the oscillatory behavior of CDK activity. Thus, one basic system for representing the CDC is a biochemical oscillator (CDK oscillator). However, genetically clonal cells divide with marked variability in their total duration of a single CDC round, exhibiting non-Gaussian statistical distributions. Therefore, the CDK oscillator model does not account for the statistical nature of cell-cycle control. Herein, we review quantitative studies of the statistical properties of the CDC. Over the past 70 years, studies have shown that the CDC is driven by a cluster of molecular oscillators. The CDK oscillator is coupled to transcriptional and mitochondrial metabolic oscillators, which cause deterministic chaotic dynamics for the CDC. Recent studies in animal embryos have raised the possibility that the dynamics of molecular oscillators underlying CDC control are affected by allometric volume scaling among the cellular compartments. Considering these studies, we discuss the idea that a cluster of molecular oscillators embedded in different cellular compartments coordinates cellular physiology and geometry for successful cell divisions.

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.

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.

Automated live cell imaging systems reveal dynamic cell behavior

Automated time-lapsed microscopy provides unique research opportunities to visualize cells and subcellular components in experiments with time-dependent parameters. As accessibility to these systems is increasing, we review here their use in cell science with a focus on stem cell research. Although the use of time-lapsed imaging to answer biological questions dates back nearly 150 years, only recently have the use of an environmentally controlled chamber and robotic stage controllers allowed for high-throughput continuous imaging over long periods at the cell and subcellular levels. Numerous automated imaging systems are now available from both companies that specialize in live cell imaging and from major microscope manufacturers. We discuss the key components of robots used for time-lapsed live microscopic imaging, and the unique data that can be obtained from image analysis. We show how automated features enhance experimentation by providing examples of uniquely quantified proliferation and migration live cell imaging data. In addition to providing an efficient system that drastically reduces man-hours and consumes fewer laboratory resources, this technology greatly enhances cell science by providing a unique dataset of temporal changes in cell activity.

Optimizing periodicity and polymodality in noise-induced genetic oscillators

Many cellular functions are based on the rhythmic organization of biological processes into self-repeating cascades of events. Some of these periodic processes, such as the cell cycles of several species, exhibit conspicuous irregularities in the form of period skippings, which lead to polymodal distributions of cycle lengths. A recently proposed mechanism that accounts for this quantized behavior is the stabilization of a Hopf-unstable state by molecular noise. Here we investigate the effect of varying noise in a model system, namely an excitable activator-repressor genetic circuit, that displays this noise-induced stabilization effect. Our results show that an optimal noise level enhances the regularity (coherence) of the cycles, in a form of coherence resonance. Similar noise levels also optimize the multimodal nature of the cycle lengths. Together, these results illustrate how molecular noise within a minimal gene regulatory motif confers robust generation of polymodal patterns of periodicity.

A genetic timer through noise-induced stabilization of an unstable state

Stochastic fluctuations affect the dynamics of biological systems. Typically, such noise causes perturbations that can permit genetic circuits to escape stable states, triggering, for example, phenotypic switching. In contrast, studies have shown that noise can surprisingly also generate new states, which exist solely in the presence of fluctuations. In those instances noise is supplied externally to the dynamical system. Here, we present a mechanism in which noise intrinsic to a simple genetic circuit effectively stabilizes a deterministically unstable state. Furthermore, this noise-induced stabilization represents a unique mechanism for a genetic timer. Specifically, we analyzed the effect of noise intrinsic to a prototypical two-component gene-circuit architecture composed of interacting positive and negative feedback loops. Genetic circuits with this topology are common in biology and typically regulate cell cycles and circadian clocks. These systems can undergo a variety of bifurcations in response to parameter changes. Simulations show that near one such bifurcation, noise induces oscillations around an unstable spiral point and thus effectively stabilizes this unstable fixed point. Because of the periodicity of these oscillations, the lifetime of the noise-dependent stabilization exhibits a polymodal distribution with multiple, well defined, and regularly spaced peaks. Therefore, the noise-induced stabilization presented here constitutes a minimal mechanism for a genetic circuit to function as a timer that could be used in the engineering of synthetic circuits.

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: the cell is an oscillator, the cell cycle a developmental process

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.

Computational analysis of mammalian cell division gated by a circadian clock: quantized cell cycles and cell size control

Cell cycle and circadian rhythms are conserved from cyanobacteria to humans with robust cyclic features. Recently, molecular links between these two cyclic processes have been discovered. Core clock transcription factors, Bmal1 and Clock (Clk), directly regulate Wee1 kinase, which inhibits entry into the mitosis. We investigate the effect of this connection on the timing of mammalian cell cycle processes with computational modeling tools. We connect a minimal model of circadian rhythms, which consists of transcription-translation feedback loops, with a modified mammalian cell cycle model from Novak and Tyson (2004). As we vary the mass doubling time (MDT) of the cell cycle, stochastic simulations reveal quantized cell cycles when the activity of Wee1 is influenced by clock components. The quantized cell cycles disappear in the absence of coupling or when the strength of this link is reduced. More intriguingly, our simulations indicate that the circadian clock triggers critical size control in the mammalian cell cycle. A periodic brake on the cell cycle progress via Wee1 enforces size control when the MDT is quite different from the circadian period. No size control is observed in the absence of coupling. The issue of size control in the mammalian system is debatable, whereas it is well established in yeast. It is possible that the size control is more readily observed in cell lines that contain circadian rhythms, since not all cell types have a circadian clock. This would be analogous to an ultradian clock intertwined with quantized cell cycles (and possibly cell size control) in yeast. We present the first coupled model between the mammalian cell cycle and circadian rhythms that reveals quantized cell cycles and cell size control influenced by the clock.

The genetic basis of the circadian clock: identification of frq and FRQ as clock components in Neurospora

Genetic approaches to the identification of clock components have succeeded in two model systems, Neurospora and Drosophila. In each organism, genes identified through screens for clock-affecting mutations (frq in Neurospora, per in Drosophila) have subsequently been shown to have characteristics of central clock components: (1) mutations in each gene can affect period length and temperature compensation, two canonical characteristics of circadian systems; (2) each gene regulates the timing of its own transcription in a circadian manner; and (3) in the case of frq, constitutively elevated expression will set the phase of the clock on release into normal conditions. Despite clear genetic and molecular similarities, however, the two genes are neither molecular nor temporal homologues. The timing of peak expression is distinct in the two genes, frq expression peaking after dawn and per expression peaking near midnight. Also, although expression of per from a constitutive promoter can rescue rhythmicity in a fly lacking the gene, constitutive expression of frq will not rescue rhythmicity in Neurospora frq-null strains, and in fact causes arrhythmicity when expressed in a wild-type strain. These data suggest that frq is and/or encodes a state variable of the circadian oscillator. Recent molecular genetic analyses of frq have shed light on the origin of temperature compensation and strongly suggest that this property is built into the oscillatory feedback loop rather than appended to it. It seems plausible that clocks are adjusted and reset through adjustments in central clock components such as frq, and, by extension, per.

Quantized cycling time in artificial gene networks induced by noise and intercell communication

We propose a mechanism for the quantized cycling time based on the interplay of cell-to-cell communication and stochasticity, by investigating a model of coupled genetic oscillators with known topology. In addition, we discuss how inhomogeneity can be used to enhance such quantizing effects, while the degree of variability obtained can be controlled using the noise intensity or adequate system parameters.

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.

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.

Cell population dynamics modulate the rates of tissue growth processes

The development and testing of a discrete model describing the dynamic process of tissue growth in three-dimensional scaffolds is presented. The model considers populations of cells that execute persistent random walks on the computational grid, collide, and proliferate until they reach confluence. To isolate the effect of population dynamics on tissue growth, the model assumes that nutrient and growth factor concentrations remain constant in space and time. Simulations start either by distributing the seed cells uniformly and randomly throughout the scaffold, or from an initial condition designed to simulate the migration and cell proliferation phase of wound healing. Simulations with uniform seeding show that cell migration enhances tissue growth by counterbalancing the adverse effects of contact inhibition. This beneficial effect, however, diminishes and disappears completely for large migration speeds. By contrast, simulations with the "wound" seeding mode show a continual enhancement of tissue regeneration rates with increasing cell migration speeds. We conclude that cell locomotory parameters and the spatial distribution of seed cells can have profound effects on the dynamics of the process and, consequently, on the pattern and rates of tissue growth. These results can guide the design of experiments for testing the effectiveness of biomimetic modifications for stimulating tissue growth.

Midblastula transition (MBT) of the cell cycles in the yolk and pigment granule-free translucent blastomeres obtained from centrifuged Xenopus embryos

We obtained translucent blastomeres free of yolk and pigment granules from Xenopus embryos which had been centrifuged at the beginning of the 8-cell stage with cellular integrity. They divided synchronously regardless of their cell size until they had decreased to 37.5 microm in radius; those smaller than this critical size, however, divided asynchronously with cell cycle times inversely proportional to the square of the cell radius after midblastula transition (MBT). The length of the S phase was determined as the time during which nuclear DNA fluorescence increased in Hoechst-stained blastomeres. When the cell cycle time exceeded 45 min, S and M phases were lengthened; when the cell cycle times exceeded 70 min, the G2 phase appeared; and after cell cycle times became longer than 150 min, the G1 phase appeared. Lengths of G1, S and M phases increased linearly with increasing cell cycle time. Enhanced green fluorescent protein (EGFP)-tagged proliferating cell nuclear antigen (PCNA) expressed in the blastomeres appeared in the S phase nucleus, but suddenly dispersed into the cytoplasm at the M phase. The system developed in this study is useful for examining the cell cycle behavior of the cell cycle-regulating molecules in living Xenopus blastomeres by fluorescence microscopy in real time.

A genomewide oscillation in transcription gates DNA replication and cell cycle

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.

Circadian gene expression in mammalian fibroblasts revealed by real-time luminescence reporting: temperature compensation and damping

Mammalian cells such as rat-1 fibroblasts have been shown to exhibit daily oscillations in the expression of several gene transcripts in culture. After induction, these oscillations persist with a period of approximately 24 h for several days. This characteristic suggests that the oscillations are controlled by a circadian clock, but the crucial criterion of temperature compensation has not been demonstrated for rat-1 fibroblasts. We have developed an automated assay of circadian expression of the mPer1 promoter in rat-1 fibroblasts that have been stably transfected with a luciferase reporter. Using this cell culture-based in vitro luminescent reporter assay, we found that the daily oscillation of mPer1 promoter activity in rat-1 cells is temperature compensated over the range of 28.5-36.5 degrees C. This finding means that these oscillations are bona fide circadian rhythms. Moreover, the circadian clock of these homeothermic mammalian cells not only is temperature compensated but also is overcompensated such that it runs faster at cooler temperatures (Q10 of 0.85-0.88). The oscillations in rat-1 fibroblasts damp more rapidly at cooler temperatures, and damping is not due to cells becoming unhealthy because a second stimulus will reinitiate a robust rhythm. These data show that rat-1 cell cultures that are stably transfected with luminescence reporters are an excellent model system for studying circadian clocks at the cellular level in mammals.

Tuning the cell cycle: a model based on averaging

The ability of intercellular communication and the basement membrane to revert the phenotypic behaviour of malignant cells suggests that such cells can be tuned to behave more benignly. In addition, the large variation in cell doubling times observed in tumour cells poses the question of whether or not cell doubling times, and hence, patient survival, can be lengthened by therapeutic intervention. In both cases, the understanding may be enhanced by obtaining a parsimonious and tractable model of the cell cycle which behaves appropriately and suggests a philosophical framework for addressing these complex issues. We introduce a simple two-dimensional model based on averaging cyclin and maturation promotion factor over a fast oscillating subsystem that exhibits the basic features of cellular division, and discuss the ramifications of the model.

Genome wide oscillations in expression. Wavelet analysis of time series data from yeast expression arrays uncovers the dynamic architecture of phenotype

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 approximately 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.

Independence of circadian timing from cell division in cyanobacteria

In the cyanobacterium Synechococcus elongatus, cell division is regulated by a circadian clock. Deletion of the circadian clock gene, kaiC, abolishes rhythms of gene expression and cell division timing. Overexpression of the ftsZ gene halted cell division but not growth, causing cells to grow as filaments without dividing. The nondividing filamentous cells still exhibited robust circadian rhythms of gene expression. This result indicates that the circadian timing system is independent of rhythmic cell division and, together with other results, suggests that the cyanobacterial circadian system is stable and well sustained under a wide range of intracellular conditions.

Transition of the blastomere cell cycle from cell size-independent to size-dependent control at the midblastula stage in Xenopus laevis

Dissociated animal cap blastomeres of Xenopus laevis blastulae were cultured at a low Ca level (1 microM) from 9th to 18th cell cycle at 22 +/- 1 degrees C and observed by a time-lapse video recorder. Blastomeres cleaved unequally to increase variability in cell size as cell cycles progressed, but synchronously at a constant cell cycle time of about 30 min up to the 12th cleavage in diploid cells, and up to the 13th cleavage in haploid cells, regardless of their cell sizes. Thereafter, blastomeres cleaved asynchronously at varying cell cycle times in proportion to the inverse square of their radii. The transition from the cell size-independent to -dependent cell cycles occurred at the critical cell radius, 37.5 microm for the diploid and 27.9 microm for the haploid. While the protein synthesis inhibitor, cycloheximide (CHX) lengthened cell cycle times two- to six-fold, epidermal growth factor (EGF) had no significant effect on the cell cycle. CHX-treated blastomeres synchronously cleaved at a constant cell cycle time of 60 min up to the 12th cleavage. Thereafter, cell cycle times became variable in proportion to the inverse square of radii in the presence of CHX at 0.10-0.14 microg/ml, but to the inverse cube of radii at 0.18 microg/ml. The critical cell size of CHX-treated blastomeres for the transition from cell size-independent to -dependent cell cycles remained the same as that of untreated blastomeres. Frequency distributions of cell cycle times of synchronous cell cycles were monomodal with the peak at 30 min, except for CHX-treated blastomeres with the peak at 60 min. In contrast, frequency distributions of asynchronous cell cycles were polymodal with peaks at multiples of a unit time of 30-35 min. To explain these results, we propose that blastomere cytoplasm has 30-min cycles that repeatedly produce mitosis promoting factor (MPF) in a quantity proportional to the cell surface area. MPF is neutralized when it titrates a nuclear inhibitor present in a quantity proportional to the genome size, and sequestered in the nucleus. When the total amount of MPF produced exceeds the threshold required to titrate all of the inhibitor, mitosis is initiated.

Circadian and ultradian clock-controlled rhythms in unicellular microorganisms

The time structure of a biological system is at least as intricate as its spatial structure. Whereas we have detailed information about the latter, our understanding of the former is still rudimentary. As techniques for monitoring intracellular processes continuously in single cells become more refined, it becomes increasingly evident that periodic behaviour abounds in all time domains. Circadian timekeeping dominates in natural environments. Here the free-running period is about 24 h. Circadian rhythms in eukaryotes and prokaryotes allow predictive matching of intracellular states with environmental changes during the daily cycles. Unicellular organisms provide excellent systems for the study of these phenomena, which pervade all higher life forms. Intracellular timekeeping is essential. The presence of a temperature-compensated oscillator provides such a timer. The coupled outputs (epigenetic oscillations) of this ultradian clock constitute a special class of ultradian rhythm. These are undamped and endogenously driven by a device which shows biochemical properties characteristic of transcriptional and translational elements. Energy-yielding processes, protein turnover, motility and the timing of the cell-division cycle processes are all controlled by the ultradian clock. Different periods characterize different species, and this indicates a genetic determinant. Periods range from 30 min to 4 h. Mechanisms of clock control are being elucidated; it is becoming evident that many different control circuits can provide these functions.

The occurrence and functions of ultradian rhythms

Ultradian oscillations with periods between 5 min and 4 h have been described in cell-free extracts, single-celled eukaryotes, cultured cells and embryos. Whereas some of these potentially oscillatory systems (e.g. glycolysis) may only exhibit this type of behaviour rarely if at all in vivo, other ultradian oscillators in lower eukaryotes are rhythms and probably have timekeeping functions. Rhythms with ultradian periods of 10 min to 20 h in oxygen consumption and carbon dioxide production have also been studied in endotherm animals: these rhythms may be modified by variations of environmental parameters and by circadian and infradian synchronizers. Interspecies and interstrain differences strongly suggest that these rhythms are endogenous and have a genetic origin. We suggest that the temporal organization of biochemical and physiological processes facilitates optimization of thermodynamic maintenance of the organism within the random fluctuations of its physicochemical environment and contributes to genetic selection.

The cellular mechanism of circadian rhythms--a view on evidence, hypotheses and problems

A stable period length is a characteristic property of circadian oscillations. The question about whether higher frequency oscillators (0.5-8 hr) contribute to or establish the stable circadian periodicity cannot be answered at present. A sequential coupling of quantal subcycles appears possible on the basis of known "ultradian" oscillations. There is, however, no supporting evidence for such a concept. Phase response curves of the circadian clock derived from various perturbing pulses allow qualitative conclusions concerning the perturbed clock process. Deductions from computer simulations also allow conclusions about the phase of this oscillatory process. The distinction between processes (a) essential to the clock mechanism, (b) maintaining and controlling the clock (inputs) and (c) depending on the clock (outputs) on the basis of "oscillatory" and "change of psi or tau after perturbation" seems to be useful but not stringent. Protein synthesis may be an essential or input process. Oscillatory changes of this process may be due to periodic translational control or RNA-supply. Circadian changes in protein concentration and/or activity may depend on periodic synthesis, proteolysis, covalent modifications or aggregations. Specific essential proteins have not been identified conclusively. The large overlap between the group of agents and treatments that phase shift the clock and the group that induces stress proteins suggest that the latter may play a role in the controlling (input) or essential domain. The role of membranes in the clock mechanism is not clear: concepts assuming an essential function are based on circumstantial evidence. The membrane potential as well as Ca2+ may be involved in either input or essential function. Ca(2+)-calmodulin may also be important as concluded from inhibitor experiments. It is tempting to assume that a calmodulin-dependent kinase is part of a periodic protein phosphorylation process, yet it is not clear whether the periodic protein phosphorylation that has been observed is essential or is just another output process.

Variance within homogeneous phytoplankton populations, I: Theoretical framework for interpreting histograms

A framework is presented for interpreting frequency distributions of volume or fluorescence as measured by a flow cytometer on homogeneous phytoplankton populations. The framework, based on both laboratory experience and theoretical concepts, is illustrated with the use of a simulation model. Asynchronous, synchronous, and phased populations were simulated, with constant and variable growth patterns over the cell cycle. Though simulations produced a wide variety of histogram shapes, including multimodal distributions, the primary difference between asynchronous and synchronous/phased distributions lies in their temporal variation. Histograms that are constant in time indicate asynchronous populations; when populations are not asynchronous, their histogram shapes vary with a periodicity on the same time scale as the cell cycle. A probability density function for the case of asynchronous populations with a constant growth rate is derived. When fitted to simulated histograms this two-parameter density function yields estimates of the two parameters: mean and variance of cell volume (or mass) at age 0.

Effect of changing the light/dark schedule, the time of onset of the light or dark period, or the daylength, on rhythms of epidermal cell proliferation

Rhythms of labeling and mitotic indices were studied in the hindlimb epidermis of the anuran tadpole Rana pipiens under different light/dark (LD) cycles and daylengths in order to examine the role of the various parameters of the lighting regimen in setting the periods of the rhythms and the timing of the cell proliferation peaks. Altering the time of, or inverting, the 12 h light period on a 24 h day resulted in phase shifting of basically bimodal circadian rhythms with peaks in the light and dark. Thus the cell proliferation rhythms were entrained to the LD cycle. These rhythms also entrained to noncircadian schedules since they lengthened on a 15L:15D cycle and shortened on a 9L:9D cycle, although the bimodal characteristic of a peak in the light and a peak in the dark remained. Studies of 18L:6D and 6L:18D cycles in which either the time of onset of light or dark was changed relative to the 12L:12D control indicated that the onset of dark may regulate the timing of the labeling index peaks while the onset of light may determine the time of occurrence of mitotic index peaks. Control of the timing of labeling and mitotic index peaks by different parameters of the LD cycle suggests a mechanism for cell cycle regulation by the environmental lighting schedule. Analysis of the rhythms on all the cycles studied suggested that labeling index rhythms equal the length of, or twice the length of, the dark period. Mitotic index rhythms equal the daylength or a multiple of the length of the dark period.

Ultradian photosynchronization in Tetrahymena pyriformis GLC is related to modal cell generation time: further evidence for a common timer model

This study contains the first report of the photosynchronization of Tetrahymena in the ultradian mode of cell division. Ultradian mode cultures of T. pyriformis GLC were grown at low cell titers in a nephelostat under five different ultradian photocycles and also under constant conditions of illumination. Entrainment was achieved only when the period of the synchronizer did not exceed the nearest modal generation time observed in free-running single cells. Thus, the discrete ranges for photentrainment of ultradian rhythms in Tetrahymena were restricted to modal windows for the generation times in free-run. Cell division was found to be a function of the phase of the ultradian zeitgeber cycle. The cells did not behave as if they had been forced into synchrony by physiological shock; the synchronous populations obtained by this technique behaved like the populations commonly used in circadian studies which had been phased by a cyclic variation within the tolerance range of the organism.

Growth rate regulation and random transition. A study performed on embryonal carcinoma cell lines. I

Analyses of cell-cycle characteristics of the three embryonal carcinoma (EC) cell lines F9, PCC3 N/1 and PCC4 Azal, have been performed. The three lines reflect successive stages in early mouse embryogenesis as regards cell surface antigens and cell-cycle characteristics. In an attempt to understand changes in cell-cycle characteristics occurring during early embryogenesis, the two-random transition probability (TP) model was applied to the EC-cell system--and particularly to the F9 line. By utilizing an intraclonal heterogeneity in intermitotic times found in these EC lines, a growth-regulating point was introduced as a modification of the two-random TP model. The modified model was found to be very useful when demonstrating the cell-cycle growth kinetics of the F9 line. The model is used in an accompanying paper to extend the analysis of cell-cycle characteristics in undifferentiated EC cells.

Quasi-exponential generation time distributions from a limit cycle oscillator

In spite of the apparently random behaviour and the often exponential distribution of generation times expressed in cell populations, there is evidence for rather precise timekeeping in the cell cycle. In experiments using time-lapse video-tape microscopy, we have noted that cell generation times are often not distributed smoothly but in many cases seem to cluster at roughly 4 hr intervals. Phase shift responses following application of heat shock, ionizing radiation or serum pulses in each case show a pattern which is repeated twice in cells with an 8-9 hr modal generation time. We describe here a cell cycle model with an independent cellular clock controlling cell cycle events which accounts for the phase response data, while also reconciling the stochastic and periodic behaviour characteristic of animal cells.

Circadian oscillators, cell cycles, and singularities: light perturbations of the free-running rhythm of cell division in Euglena

The free-running circadian rhythm of cell division in the algal flagellate, Euglena gracilis (Z) was perturbed by 3-h light signals of varying intensities imposed at different circadian times (CT). Light pulses within the range of 700 to 7,500 lux were found to yield the same 'strong' (Type 0) phase response curve (PRC) comprising both advance and delay phase shifts as great as 15 h. Dark signals generated a PRC of reduced amplitude with very little, if any, phase advance being observed. Light perturbations of lower intensity, however, elicited quite different responses if applied at a quite specific circadian time: A 40- to 400-lux pulse given at approximately CT 0 (late subjective night) induced total arrhythmicity, and the culture reverted to asynchronous, exponential growth. Different degrees of arrhythmicity were induced by the same low-intensity perturbations (I*) given slightly before or after this sensitive phase point (T*), but if imposed at other circadian times, they generated normal type 0 phase resetting. The demonstration of the existence of this critical pulse (T*, I*) provides further evidence that the cell division cycle of Euglena (and presumably other microorganisms) is regulated by a circadian oscillator and, in particular, by one having limit cycle dynamics.