The mitotic oscillator in Physarum polycephalum

Living systems are smarter bots: Slime mold semiosis versus AI symbol manipulation

Although machines may be good at mimicking, they are not currently able, as organisms are, to act creatively. We offer an understanding of the emergent qualities of biological sign processing in terms of generalization, association, and encryption. We use slime mold as a model of minimal cognition and compare it to deep-learning video game bots, which some claim have evolved beyond their merely quantitative algorithms. We find that these discrete Turing machine bots are not able to make productive, yet unanticipated, "errors"-necessary for biological learning-which, based on the physicality of signs, their relatively similar shapes, and relative physical positions spatially and temporally, lead to emergent effects and make learning and evolution possible. In organisms, stochastic resonance at the local level can be leveraged for self-organization at the global level. We contrast all this to the symbolic processing of today's machine learning, whereby each logic node and memory state is discrete. Computer codes are produced by external operators, whereas biological symbols are evolved through an internal encryption process.

Adaptive behaviour and learning in slime moulds: the role of oscillations

The slime mould Physarum polycephalum, an aneural organism, uses information from previous experiences to adjust its behaviour, but the mechanisms by which this is accomplished remain unknown. This article examines the possible role of oscillations in learning and memory in slime moulds. Slime moulds share surprising similarities with the network of synaptic connections in animal brains. First, their topology derives from a network of interconnected, vein-like tubes in which signalling molecules are transported. Second, network motility, which generates slime mould behaviour, is driven by distinct oscillations that organize into spatio-temporal wave patterns. Likewise, neural activity in the brain is organized in a variety of oscillations characterized by different frequencies. Interestingly, the oscillating networks of slime moulds are not precursors of nervous systems but, rather, an alternative architecture. Here, we argue that comparable information-processing operations can be realized on different architectures sharing similar oscillatory properties. After describing learning abilities and oscillatory activities of P. polycephalum, we explore the relation between network oscillations and learning, and evaluate the organism's global architecture with respect to information-processing potential. We hypothesize that, as in the brain, modulation of spontaneous oscillations may sustain learning in slime mould. This article is part of the theme issue 'Basal cognition: conceptual tools and the view from the single cell'.

Biological Oscillators in Nanonetworks-Opportunities and Challenges

One of the major issues in molecular communication-based nanonetworks is the provision and maintenance of a common time knowledge. To stay true to the definition of molecular communication, biological oscillators are the potential solutions to achieve that goal as they generate oscillations through periodic fluctuations in the concentrations of molecules. Through the lens of a communication systems engineer, the scope of this survey is to explicitly classify, for the first time, existing biological oscillators based on whether they are found in nature or not, to discuss, in a tutorial fashion, the main principles that govern the oscillations in each oscillator, and to analyze oscillator parameters that are most relevant to communication engineer researchers. In addition, the survey highlights and addresses the key open research issues pertaining to several physical aspects of the oscillators and the adoption and implementation of the oscillators to nanonetworks. Moreover, key research directions are discussed.

Systems Level Modeling of the Cell Cycle Using Budding Yeast

Proteins involved in the regulation of the cell cycle are highly conserved across all eukaryotes, and so a relatively simple eukaryote such as yeast can provide insight into a variety of cell cycle perturbations including those that occur in human cancer. To date, the budding yeast Saccharomyces cerevisiae has provided the largest amount of experimental and modeling data on the progression of the cell cycle, making it a logical choice for in-depth studies of this process. Moreover, the advent of methods for collection of high-throughput genome, transcriptome, and proteome data has provided a means to collect and precisely quantify simultaneous cell cycle gene transcript and protein levels, permitting modeling of the cell cycle on the systems level. With the appropriate mathematical framework and sufficient and accurate data on cell cycle components, it should be possible to create a model of the cell cycle that not only effectively describes its operation, but can also predict responses to perturbations such as variation in protein levels and responses to external stimuli including targeted inhibition by drugs. In this review, we summarize existing data on the yeast cell cycle, proteomics technologies for quantifying cell cycle proteins, and the mathematical frameworks that can integrate this data into representative and effective models. Systems level modeling of the cell cycle will require the integration of high-quality data with the appropriate mathematical framework, which can currently be attained through the combination of dynamic modeling based on proteomics data and using yeast as a model organism.

Transformed yeast (Schizosaccharomyces pombe) overexpressing rice Tau class glutathione S-transferase (OsGSTU30 and OsGSTU41) shows enhanced resistance to hexavalent chromium

Two Tau class GSTs that are up-regulated in rice roots upon exposure to Cr(vi), showed resistance when expressed in yeast.

A quantitative model of the initiation of DNA replication in Saccharomyces cerevisiae predicts the effects of system perturbations

Background

Eukaryotic cell proliferation involves DNA replication, a tightly regulated process mediated by a multitude of protein factors. In budding yeast, the initiation of replication is facilitated by the heterohexameric origin recognition complex (ORC). ORC binds to specific origins of replication and then serves as a scaffold for the recruitment of other factors such as Cdt1, Cdc6, the Mcm2-7 complex, Cdc45 and the Dbf4-Cdc7 kinase complex. While many of the mechanisms controlling these associations are well documented, mathematical models are needed to explore the network’s dynamic behaviour. We have developed an ordinary differential equation-based model of the protein-protein interaction network describing replication initiation.

Results

The model was validated against quantified levels of protein factors over a range of cell cycle timepoints. Using chromatin extracts from synchronized Saccharomyces cerevisiae cell cultures, we were able to monitor the in vivo fluctuations of several of the aforementioned proteins, with additional data obtained from the literature. The model behaviour conforms to perturbation trials previously reported in the literature, and accurately predicts the results of our own knockdown experiments. Furthermore, we successfully incorporated our replication initiation model into an established model of the entire yeast cell cycle, thus providing a comprehensive description of these processes.

Conclusions

This study establishes a robust model of the processes driving DNA replication initiation. The model was validated against observed cell concentrations of the driving factors, and characterizes the interactions between factors implicated in eukaryotic DNA replication. Finally, this model can serve as a guide in efforts to generate a comprehensive model of the mammalian cell cycle in order to explore cancer-related phenotypes.

Modeling the cell cycle: why do certain circuits oscillate?

Computational modeling and the theory of nonlinear dynamical systems allow one to not simply describe the events of the cell cycle, but also to understand why these events occur, just as the theory of gravitation allows one to understand why cannonballs fly in parabolic arcs. The simplest examples of the eukaryotic cell cycle operate like autonomous oscillators. Here, we present the basic theory of oscillatory biochemical circuits in the context of the Xenopus embryonic cell cycle. We examine Boolean models, delay differential equation models, and especially ordinary differential equation (ODE) models. For ODE models, we explore what it takes to get oscillations out of two simple types of circuits (negative feedback loops and coupled positive and negative feedback loops). Finally, we review the procedures of linear stability analysis, which allow one to determine whether a given ODE model and a particular set of kinetic parameters will produce oscillations.

Quantitative site-specific phosphorylation dynamics of human protein kinases during mitotic progression

Reversible protein phosphorylation is a key regulatory mechanism of mitotic progression. Importantly, protein kinases themselves are also regulated by phosphorylation-dephosphorylation processes; hence, phosphorylation dynamics of kinases hold a wealth of information about phosphorylation networks. Here, we investigated the site-specific phosphorylation dynamics of human kinases during mitosis using synchronization of HeLa suspension cells, kinase enrichment, and high resolution mass spectrometry. In biological triplicate analyses, we identified 206 protein kinases and more than 900 protein kinase phosphorylation sites, including 61 phosphorylation sites on activation segments, and quantified their relative abundances across three specific mitotic stages. Around 25% of the kinase phosphorylation site ratios were found to be changed by at least 50% during mitotic progression. Further network analysis of jointly regulated kinase groups suggested that Cyclin-dependent kinase- and mitogen-activated kinase-centered interaction networks are coordinately down- and up-regulated in late mitosis, respectively. Importantly, our data cover most of the already known mitotic kinases and, moreover, identify attractive candidates for future studies of phosphorylation-based mitotic signaling. Thus, the results of this study provide a valuable resource for cell biologists and provide insight into the system properties of the mitotic phosphokinome.

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.

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.

The Ups and Downs of Modeling the Cell Cycle

We discuss the impact of mathematical modeling on our understanding of the cell cycle. Although existing, detailed models confirm that the known interactions in the cell cycle can produce oscillations and predict behaviors such as hysteresis, they contain many parameters and are poorly constrained by data which are almost all qualitative. Questions about the basic architecture of the oscillator may be more amenable to modeling approaches that ignore molecular details. These include asking how the various elaborations of the basic oscillator affect the robustness of the system and how cells monitor their size and use this information to control the cell cycle.

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.

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.

Modeling temperature compensation in chemical and biological oscillators

All physicochemical and biological oscillators maintain a balance between destabilizing reactions (as, for example, intrinsic autocatalytic or amplifying reactions) and stabilizing processes. These two groups of processes tend to influence the period in opposite directions and may lead to temperature compensation whenever their overall influence balances. This principle of "antagonistic balance" has been tested for several chemical and biological oscillators. The Goodwin negative feedback oscillator appears of particular interest for modeling the circadian clocks in Neurospora and Drosophila and their temperature compensation. Remarkably, the Goodwin oscillator not only gives qualitative, correct phase response curves for temperature steps and temperature pulses, but also simulates the temperature behavior of Neurospora frq and Drosophila per mutants almost quantitatively. The Goodwin oscillator predicts that circadian periods are strongly dependent on the turnover of the clock mRNA or clock protein. A more rapid turnover of clock mRNA or clock protein results, in short, a slower turnover in longer period lengths.

How proteolysis drives the cell cycle

Oscillations in the activity of cyclin-dependent kinases (CDKs) promote progression through the eukaryotic cell cycle. This review examines how proteolysis regulates CDK activity-by degrading CDK activators or inhibitors-and also how proteolysis may directly trigger the transition from metaphase to anaphase. Proteolysis during the cell cycle is mediated by two distinct ubiquitin-conjugation pathways. One pathway, requiring CDC34, initiates DNA replication by degrading a CDK inhibitor. The second pathway, involving a large protein complex called the anaphase-promoting complex or cyclosome, initiates chromosome segregation and exit from mitosis by degrading anaphase inhibitors and mitotic cyclins. Proteolysis therefore drives cell cycle progression not only by regulating CDK activity, but by directly influencing chromosome and spindle dynamics.

Theoretical dynamics of the cyclin B-MPF system: a possible role for p13suc1

In dividing cells, entry into mitosis is caused by maturation promoting factor (MPF), which is formed autocatalytically by activation of a complex of p34cdc2 and cyclin B. This biochemical system may oscillate, causing repeated mitosis. It is shown mathematically that the oscillatory tendency would be enhanced by a cofactor which binds to MPF and inhibits its autocatalytic action. A candidate for such a cofactor is the suc1 gene product p13, which binds to p34cdc2/cyclin B complex and inhibits MPF-induced MPF activation. At a steady rate of cyclin biosynthesis, with small amounts converted to MPF, p13suc1 would have to be titrated by MPF before autocatalysis could begin. This would have three possibly important effects: (1) it would determine the 'threshold' cyclin accumulation (and hence the corresponding time-delay) for MPF activation; (2) it would cause the accumulation of a backlog of MPF precursor (tyrosine-phosphorylated p34cdc2/cyclin B) sufficient to produce a substantial MPF pulse when MPF autocatalysis begins; (3) it would give the autocatalysis a high reaction order, which tends to destabilize the steady state, promote autonomous oscillations, and enhance the triggering property (excitability) of the system. The MPF pulse generated by this system may be essential for the proper triggering of the events of M phase, including the cyclin degradation which inactivates MPF at the end of M phase. This model offers explanations for several puzzling effects of p13suc1, including the fact that p13suc1, though an inhibitor of MPF activation, is nevertheless necessary for mitosis.

Hypothesis: the central oscillator of the circadian clock is a controlled chaotic attractor

Controlled chaos may be important for the generation of rhythmic behaviour in living systems. A model is proposed in which the central circadian oscillator is a chaotic attractor. Whereas a limit cycle mechanism (previously invoked to explain circadian clocks as well as ultradian clocks and cell division cycles) can provide only a single stable periodic orbit, a chaotic attractor can generate rich dynamic behaviour. Control by feedback makes accessible a selected stabilized orbit; this can be chosen so as to optimize system performance. Such a system can accommodate a wide variety of requirements, e.g. that a single clock mutation can affect both period and temperature compensation, and the generation of higher periods from an ultradian oscillator. Simultaneous operation of more than one clock (with differing periods) may require a high-dimension chaotic attractor. Attractive features of such a model include versatility of period selection (e.g. as in the per mutants of Drosophila) and the use of control elements of the type already well known in metabolic circuitry.

The cell division cycle: a physiologically plausible dynamic model can exhibit chaotic solutions

A mitotic oscillator with one slowly increasing variable (tau L of the order of hours) and one rapidly increasing variable (tau R of the order of minutes) modulated by a timer (ultradian clock) gives an auto-oscillating solution: cells divide when this relaxation oscillator reaches a critical threshold to initiate a rapid phase of the limit cycle. Increasing values of the velocity constant in the slow equation give quasi-periodic, chaotic and periodic solutions. Thus dispersed and quantized cell cycle times are consequences of a chaotic trajectory and have a purely deterministic basis. This model of the dispersion of cell cycle times contrasts with many previous ones in which cell cycle variability is a consequence of stochastic properties inherent in a sequence of many thousands of reactions or the random nature of a key transition step.

A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase

A minimal model for the mitotic oscillator is presented. The model, built on recent experimental advances, is based on the cascade of post-translational modification that modulates the activity of cdc2 kinase during the cell cycle. The model pertains to the situation encountered in early amphibian embryos, where the accumulation of cyclin suffices to trigger the onset of mitosis. In the first cycle of the bicyclic cascade model, cyclin promotes the activation of cdc2 kinase through reversible dephosphorylation, and in the second cycle, cdc2 kinase activates a cyclin protease by reversible phosphorylation. That cyclin activates cdc2 kinase while the kinase triggers the degradation of cyclin has suggested that oscillations may originate from such a negative feedback loop [Félix, M. A., Labbé, J. C., Dorée, M., Hunt, T. & Karsenti, E. (1990) Nature (London) 346, 379-382]. This conjecture is corroborated by the model, which indicates that sustained oscillations of the limit cycle type can arise in the cascade, provided that a threshold exists in the activation of cdc2 kinase by cyclin and in the activation of cyclin proteolysis by cdc2 kinase. The analysis shows how miototic oscillations may readily arise from time lags associated with these thresholds and from the delayed negative feedback provided by cdc2-induced cyclin degradation. A mechanism for the origin of the thresholds is proposed in terms of the phenomenon of zero-order ultrasensitivity previously described for biochemical systems regulated by covalent modification.

Quantized cell cycle times: interaction between a relaxation oscillator and ultradian clock pulses

Control of the timing of cell division is considered to result from a relaxation cell cycle oscillator: this has one slow and one rapid component and obeys a system of two ordinary differential equations. Interactions of the slow component with an ultradian oscillator leads to quantization of cell cycle times when the free parameters of the cell cycle oscillator are chosen close to its bifurcation point. This model fits the experimental results previously reported.

Regulation of mitosis onset and thymidine kinase activity during the cell cycle of Physarum polycephalum plasmodia: effect of fluorodeoxyuridine

The effects of fluorodeoxyuridine were investigated during three events of the cell cycle: S-phase, mitosis, and the cyclic synthesis of thymidine kinase in the synchronous plasmodium of the myxomycete Physarum. DNA synthesis was inhibited, and there was limited action on other macromolecular syntheses. When DNA synthesis was slowed down, onset of the following increase of thymidine kinase synthesis occurred at approximately the same time as in the control, but mitosis was blocked in a very early prophase stage and metaphase was never observed. These effects were suppressed when the action of fluorodeoxyuridine was prevented by the addition of thymidine to the medium. In agreement with the action of aphidicolin and hydroxyurea, these observations show that: 1) perturbation of the S-phase does not prevent the nuclei from entering a very early prophase stage, but it does prevent them from proceeding through metaphase; 2) blockage of DNA synthesis does not perturb the normal timing of the triggering of thymidine kinase synthesis; and 3) the signal that triggers the arrest of thymidine kinase synthesis is postmitotic and does not require extensive DNA synthesis. In contrast with hydroxyurea and aphidicolin, in the presence of fluorodeoxyuridine metaphase was not observed. Thus, the triggering of thymidine kinase synthesis is unambiguously dissociated from metaphase and postmitotic events. Because synthesis of thymidine kinase remains under the control of temperature shifts from 22 to 32 degrees C, a simple model of the cell cycle involving two regulatory pathways could account for the triggering of thymidine kinase synthesis, early prophase stage, and metaphase.

The cell cycle can occur in starfish oocytes and embryos without the production of transferable MPF (maturation-promoting factor)

All cells undergoing the transition from interphase to metaphase have been postulated to contain a "maturation-promoting factor" (MPF) capable of causing meiotic maturation when injected into immature oocytes. We have shown in an accompanying paper (A. Picard, M. C. Harricane, J. C. Labbe, and M. Doreé, 1988, Dev. Biol. 128, 121-128) that the basic oscillator driving the cell cycle still operates in maturing starfish oocytes and fertilized eggs in the absence of germinal vesicle (GV) material. Under such conditions of enucleation, we now show, however, that MPF activity cannot be detected after hormonal stimulation of prophase-arrested oocytes in Astropecten or after the normal time of second meiotic cleavage in Marthasterias. In contrast, cell cycles occur with the production of transferable MPF activity in embryos from which both pronuclei have been removed after fertilization. Reinjection of the entire contents of a GV after the normal time of second meiotic cleavage restores the ability of cytoplasm to induce meiotic maturation in immature recipient oocytes after transfer. Transduction of the hormonal stimulus at the level of the plasma membrane, stimulation of the phosphorylation of cytoplasmic proteins, and activation of a cycling Ca2+- and cyclic nucleotide-independent histone kinase still occur in the absence of GV material. Since previous studies have demonstrated that the presence of GV material in the recipient oocytes is absolutely required in starfish for the amplification of microinjected MPF (Kishimoto et al., 1981; Picard and Doree, 1984), we propose that some unidentified component of the GV is required, at least after the normal time of second meiotic cleavage in donor oocytes and at any time in recipient oocytes, for the successful transfer of MPF activity in starfish.

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.

Cell growth, cell division and cell size homeostasis in Swiss 3T3 cells

By separating large and small 3T3 cells we show here that cell growth (in volume) after stimulation from quiescence is not 'autocatalytic'. Rather, large cells grow significantly more slowly, in relative terms, than small cells. It follows that 3T3 cells do not require a size control mechanism operating at the level of division timing in order to achieve cell size homeostasis.

Cell cycle dynamics of an M-phase-specific cytoplasmic factor in Xenopus laevis oocytes and eggs

We have examined the regulation of maturation-promoting factor (MPF) activity in the mitotic and meiotic cell cycles of Xenopus laevis eggs and oocytes. To this end, we developed a method for the small scale extraction of eggs and oocytes and measured MPF activity in extracts by a dilution end point assay. We find that in oocytes, MPF activity appears before germinal vesicle breakdown and then disappears rapidly at the end of the first meiotic cycle. In the second meiotic cycle, MPF reappears before second metaphase, when maturation arrests. Thus, MPF cycling coincides with the abbreviated cycles of meiosis. When oocytes are induced to mature by low levels of injected MPF, cycloheximide does not prevent the appearance of MPF at high levels in the first cycle. This amplification indicates that an MPF precursor is present in the oocyte and activated by posttranslational means, triggered by the low level of injected MPF. Furthermore, MPF disappears approximately on time in such oocytes, indicating that the agent for MPF inactivation is also activated by posttranslational means. However, in the absence of protein synthesis, MPF never reappears in the second meiotic cycle. Upon fertilization or artificial activation of normal eggs, MPF disappears from the cytoplasm within 8 min. For a period thereafter, the inactivating agent remains able to destroy large amounts of MPF injected into the egg. It loses activity just as endogenous MPF appears at prophase of the first mitotic cycle. The repeated reciprocal cycling of MPF and the inactivating agent during cleavage stages is unaffected by colchicine and nocodazole and therefore does not require the effective completion of spindle formation, mitosis, or cytokinesis. However, MPF appearance is blocked by cycloheximide applied before mitosis; and MPF disappearance is blocked by cytostatic factor. In all these respects, MPF and the inactivating agent seem to be tightly linked to, and perhaps participate in, the cell cycle oscillator previously described for cleaving eggs of Xenopus laevis (Hara, K., P. Tydeman, and M. Kirschner, 1980, Proc. Natl. Acad. Sci. USA, 77:462-466).

Control mechanisms of the cell cycle: role of the spatial arrangement of spindle components in the timing of mitotic events

To characterize the control mechanisms for mitosis, we studied the relationship between the spatial organization of microtubules in the mitotic spindle and the timing of mitotic events. Spindles of altered geometry were produced in sea urchin eggs by two methods: (a) early prometaphase spindles were cut into half spindles by micromanipulation or (b) mercaptoethanol was used to indirectly induce the formation of spindles with only one pole. Cells with monopolar spindles produced by either method required an average of 3 X longer than control cells to traverse mitosis. By the time the control cells started their next mitosis, the experimental cells were usually just finishing the original mitosis. In all cases, only the time from nuclear envelope breakdown to the start of telophase was prolonged. Once the cells entered telophase, events leading to the next mitosis proceeded with normal timing. Once prolonged, the cell cycle never resynchronized with the controls. Several types of control experiments showed that were not an artifact of the experimental techniques. These results show that the spatial arrangement of spindle components plays an important role in the mechanisms that control the timing of mitotic events and the timing of the cell cycle as a whole.

A new method for examining the complexity and relationships of "timers" in developing systems

Simple methods are developed for analyzing the rate-limiting pathways, or "developmental timers," for consecutive stages in a developing system. Two conditions are first defined for short and long timing to a developmental stage. Shifts are then performed at time intervals from short to long and long to short conditions. The total time to the stage (time under first condition plus time under second condition) is scored and plotted as a function of the time of shift, resulting in two plots, one for shifts from the short to long condition, and the other for shifts from the long to short condition. Each plot is then analyzed for the number of components, slopes of components, absolute times of origins and termini of components, and discontinuities between components. This information is then used (1) to distinguish between single- and multiple-component timers, (2) to assess the sensitivity of each timer component to the change in the environmental condition employed in the method, including reversibility, (3) to test for the addition of a new timer component under long conditions, and (4) to test for an identity change of a timer component between short and long conditions. These interpretations in turn provide a minimum estimate of the complexity of the rate-limiting pathway to a developmental stage, temporally define major transition points between timer components, and provide some insight into the nature of timer components. By characterizing the rate-limiting pathway from the origin of a developmental program for each consecutive stage in that program, distinctions can also be made between single, parallel, sequential, and branching timer relationships. From these interpretations, a detailed temporal "map" of the rate-limiting program can be generated for any developmental system in which consecutive stages can be reproducibly monitored with time.

Oscillatory activity of maturation promoting factor (MPF) in extracts of Rana pipiens eggs

Dejellied Rana pipiens eggs were crushed by centrifugation and clear extracts were prepared by further centrifugation at 150,000 X G for 2 h. The extracts were kept at 0 degrees C for 2 to 3 weeks. At intervals during the storage period, 80-nl aliquots were injected into ovarian oocytes to assay maturation promoting factor (MPF). In most cases, MPF activity disappeared from the extracts on day 3 or 4, but reappeared on the following days and persisted 2 or 3 days at high levels before disappearing again. The cycle of MPF activity in extracts was repeated fairly regularly a few times during storage of the extracts. The average period of the oscillation was 5.05 + 1.25 days. If a single extract was assayed by oocytes from different frogs, all the assays exhibited exactly the same patterns of changes in MPF activity during storage of the extract. This indicates that the oscillations in MPF activity observed during storage of the extracts reflect changes in MPF activity intrinsic to the extracts, rather than fluctuations in the sensitivity of recipient oocytes to MPF. The reappearance of MPF activity in stored extracts was sensitive to Ca and dependent on Mg ions. The MPF activity that recurred periodically in cold-stored extracts was indistinguishable from that contained in fresh extracts, since oocytes induced to mature by the recurring MPF activity had chromosomes condensed to meiotic metaphase and were capable of cleavage when injected with a sperm suspension. The oscillatory behavior of MPF activity observed in this study may be comprehended on a conceptual basis by aid of a kinetic model.

Timing mechanisms in early embryonic development

Embryological development takes place in four dimensions and requires the existence of time measuring processes within the embryo. Evidence is accumulating that suggests that the emergence of many events during early embryonic development is controlled by timing mechanisms or developmental clocks. The purpose of this work is to review recent studies on developmental timing with speculations about underlying possible mechanisms. It is an attractive idea that the development of an embryo is timed by a single clock set in motion at fertilization, but this seems not feasible. The clock mechanism which determines the time of initiation of cellular differentiation may be independent of that for the timing of morphogenesis. The clock mechanism for cellular differentiation may be closely associated with the cycles of DNA replication, while the clock which counts the time to onset of early morphogenetic events is found in the cytoplasm. These ideas can provide a framework which may help to organize existing observations and to stimulate new experimental approaches to the problem.

On the distribution of cell cycle generation times

The problem of whether the cell cycle is a deterministic or probabilistic process is widely discussed in the current literature (P. Nurse, Nature, 286, pp. 9-10, 1980). In this report the question of fluctuations of cell cycle period is treated in the limits of the membrane model of cell division regulation. The parametric analysis of the equations set both for normal and tumour cells is carried out. We describe the bifurcation parameters in the neighbourhood of which the system can amplify the small fluctuations. The presence of white noise in parameters describing the lipids and antioxidants influxes into membrane is examined by methods of Marcovian processes and also by direct stochastic computer simulation. The equation for the distribution function of generation times is obtained and the increase of dispersion and mean cycle time during the changes of those parameters which would be connected with cell culture density is calculated. The influence of parameter fluctuations upon the cycle period for both normal and tumour cells is compared in the framework of model assumptions. The ratio of dispersion of generation time distribution to mean period value for an ensemble of tumour cells is shown to be several times greater than that for normal ones. In the discussion the problem of the presence of a premitotical (G02) resting state and of the possibility of its experimental detection is considered.

Clocked cell cycle clocks

The cell division cycle of both mammalian cells and microorganisms, which apparently has both deterministic and probabilistic features, is a clock of sorts in that the sequence of events that comprise it measures time under a given set of environmental conditions. The cell division cycle may itself be regulated by a programmable clock that, under certain conditions, can generate circadian periodicities by interaction with a circadian pacemaker. These clocks must insert time segments into the cell division cycle in order to generate the observed variability in cellular generation times.

Mapping the mitotic clock by phase perturbation

In synchronized V79 cells perturbed by serum, heat shock, or ionizing radiation at half-hour intervals through a modal 8.5-hour cell cycle, phase-response curves show a characteristic biphasic pattern of advances and delays in subsequent cell divisions. These observations, together with previous observations of quantizement of generation times in this an other cell lines have led us to consider a model incorporating, in the simplest case, a two-component oscillator with two threshold crossings required per cell cycle. By assuming that oscillator variables respond in a simple way to the experimental perturbations, for example, by first order destruction due to heat shock, a map of the qualitative features of the oscillator can be obtained by matching simulated with experimental phase response curves. Random fluctuations in oscillator variables about a fixed trajectory lead to subthreshold oscillations and result in a distribution of generation times which is roughly a negative exponential, but quantized within this exponential envelope. The extent of the random fluctuations can be determined from comparison with data on desynchronization of a cell population after mitotic selection. The same parameters which correctly simulate phase response and the desynchronization data also give good agreement with generation time distribution data.