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

A Self-Operating Time Crystal Model of the Human Brain: Can We Replace Entire Brain Hardware with a 3D Fractal Architecture of Clocks Alone?

Time crystal was conceived in the 1970s as an autonomous engine made of only clocks to explain the life-like features of a virus. Later, time crystal was extended to living cells like neurons. The brain controls most biological clocks that regenerate the living cells continuously. Most cognitive tasks and learning in the brain run by periodic clock-like oscillations. Can we integrate all cognitive tasks in terms of running clocks of the hardware? Since the existing concept of time crystal has only one clock with a singularity point, we generalize the basic idea of time crystal so that we could bond many clocks in a 3D architecture. Harvesting inside phase singularity is the key. Since clocks reset continuously in the brain–body system, during reset, other clocks take over. So, we insert clock architecture inside singularity resembling brain components bottom-up and top-down. Instead of one clock, the time crystal turns to a composite, so it is poly-time crystal. We used century-old research on brain rhythms to compile the first hardware-free pure clock reconstruction of the human brain. Similar to the global effort on connectome, a spatial reconstruction of the brain, we advocate a global effort for more intricate mapping of all brain clocks, to fill missing links with respect to the brain’s temporal map. Once made, reverse engineering the brain would remain a mere engineering challenge.

An Unstable Singularity Underlies Stochastic Phasing of the Circadian Clock in Individual Cyanobacterial Cells

The endogenous circadian clock synchronizes with environmental time by appropriately resetting its phase in response to external cues. Of note, some resetting stimuli induce attenuated oscillations of clock output, which has been observed at the population-level in several organisms and in studies of individual humans. To investigate what is happening in individual cellular clocks, we studied the unicellular cyanobacterium S. elongatus. By measuring its phase-resetting responses to temperature changes, we found that population-level arrhythmicity occurs when certain perturbations cause stochastic phases of oscillations in individual cells. Combining modeling with experiments, we related stochastic phasing to the dynamical structure of the cyanobacterial clock as an oscillator and explored the physiological relevance of the oscillator structure for accurately timed rhythmicity in changing environmental conditions. Our findings and approach can be applied to other biological oscillators.

The influence of day/night cycles on biomass yield and composition of Neochloris oleoabundans

BACKGROUND

Day/night cycles regulate the circadian clock of organisms to program daily activities. Many species of microalgae have a synchronized cell division when grown under a day/night cycle, and synchronization might influence biomass yield and composition. Therefore, the aim of this study was to study the influence of day/night cycle on biomass yield and composition of the green microalgae Neochloris oleoabundans. Hence, we compared continuous turbidostat cultures grown under continuous light with cultures grown under simulated day/night cycles.

RESULTS

Under day/night cycles, cultures were synchronized as cell division was scheduled in the night, whereas under continuous light cell division occurred randomly synchronized cultures were able to use the light 10-15% more efficiently than non-synchronized cultures. Our results indicate that the efficiency of light use varies over the cell cycle and that synchronized cell division provides a fitness benefit to microalgae. Biomass composition under day/night cycles was similar to continuous light, with the exception of starch content. The starch content was higher in cultures under continuous light, most likely because the cells never had to respire starch to cover for maintenance during dark periods. Day/night cycles were provided in a 'block' (continuous light intensity during the light period) and in a 'sine' (using a sine function to simulate light intensities from sunrise to sunset). There were no differences in biomass yield or composition between these two ways of providing light (in a 'block' or in a 'sine').

CONCLUSIONS

The biomass yield and composition of N. oleoabundans were influenced by day/night cycles. These results are important to better understand the relations between research done under continuous light conditions and with day/night cycle conditions. Our findings also imply that more research should be done under day/night cycles.

Enhanced phase resetting in the synchronized suprachiasmatic nucleus network

The suprachiasmatic nucleus (SCN) adapts to both the external light-dark (LD) cycle and seasonal changes in day length. In short photoperiods, single-cell activity patterns are tightly synchronized (i.e., in phase); in long photoperiods, these patterns are relatively dispersed, causing lower amplitude rhythms. The limit cycle oscillator has been used to describe the SCN's circadian rhythmicity and predicts that following a given perturbation, high-amplitude SCN rhythms will shift less than low-amplitude rhythms. Some studies reported, however, that phase delays are larger when animals are entrained to a short photoperiod. Because phase advances and delays are mediated by partially distinct (i.e., nonoverlapping) biochemical pathways, we investigated the effect of a 4-h phase advance of the LD cycle in mice housed in either short (LD 8:16) or long (LD 16:8) photoperiods. In vitro recordings revealed a significantly larger phase advance in the SCN of mice entrained to short as compared to long photoperiods (4.2 ± 0.3 h v. 1.4 ± 0.9 h, respectively). Surprisingly, in mice with long photoperiods, the behavioral phase shift was larger than the phase shift of the SCN (3.7 ± 0.4 h v. 1.4 ± 0.9 h, respectively). To exclude a confounding influence of running-wheel activity on the magnitude of the shifts of the SCN, we repeated the experiments in the absence of running wheels and found similar shifts in the SCN in vitro in short and long days (3.0 ± 0.5 h v. 0.4 ± 0.9 h, respectively). Interestingly, removal of the running wheel reduced the phase-shifting capacity of mice in long days, leading to similar behavioral shifts in short and long photoperiods (1.0 ± 0.1 h v. 1.0 ± 0.4 h). As the behavioral shifts in the presence of wheels were larger than the shift of the SCN, it is suggested that additional, non-SCN neuronal networks in the brain are involved in regulating the timing of behavioral activity. On the basis of the phase shifts observed in vitro, we conclude that highly synchronized SCN networks with high-amplitude rhythms show a larger phase-shifting capacity than desynchronized networks of low amplitude.

Systems biology of mammalian circadian clocks

Systems biology is a natural extension of molecular biology; it can be defined as biology after identification of key gene(s). Systems-biological research is a multistage process beginning with (a) the comprehensive identification and (b) quantitative analysis of individual system components and their networked interactions, which lead to the ability to (c) control existing systems toward the desired state and (d) design new ones based on an understanding of the underlying structure and dynamical principles. In this review, we use the mammalian circadian clock as a model system and describe the application of systems-biological approaches to fundamental problems in this model. This application has allowed the identification of transcriptional/posttranscriptional circuits, the discovery of a temperature-insensitive period-determining process, and the discovery of desynchronization of individual clock cells underlying the singularity behavior of mammalian clocks.

Systems biology of mammalian circadian clocks

Systems Biology is a natural extension of molecular biology and can be defined as biology after identification of key gene(s). Systems-biological research is hence seen as a multistage process, beginning with the comprehensive identification and quantitative analysis of individual system components and their networked interactions and leading to the ability to control existing systems toward the desired state and design new ones based on an understanding of structure and underlying dynamical principles. In this chapter, we take mammalian circadian clocks as a model system and describe systems-biological approaches, including the identification of clock-controlled genes, clock-controlled cis elements, and clock transcriptional circuits driven by functional genomics; the parameter change of clock components followed by quantitative measurement; and the dynamic and quantitative perturbation of the clock and its application to one of the fundamental but yet-unsolved questions: singularity behavior of clocks. As perspective for systems-biological investigations, we also introduce the system-level dynamical questions related to the core of clocks, including delay, nonlinearity, temperature-compensation and synchronization of mammalian circadian oscillator(s), and the system-level information problems related to clocks in the environment, including the internal representation of light change through perfect adaptation and internal representation of day length through photoperiodism in mammals.

The effect of light on the human circadian pacemaker

The periodic light-dark cycle provides the primary signal by which the human circadian pacemaker is synchronized to the 24 h day. Earlier reports that social contacts were more effective than light in the entrainment of human circadian rhythms have not been supported by more recent studies. In fact, we have found that exposure to a cyclic light stimulus can induce strong (type 0) resetting of the human circadian pacemaker, indicating that exposure to light affects the pacemaker's amplitude of oscillation as well as its phase. These findings support Winfree's long-standing prediction, based on his pioneering recognition of the importance of amplitude in the analysis of circadian clocks, that strong (type 0) resetting would prove to be a common property of circadian resetting responses to light across a wide array of species, from algae to humans. Research on humans has shown, for the first time, that the response of the circadian pacemaker to light depends not only on the timing, intensity and duration of light exposure, but also on the number of consecutive daily light exposures. Exposure to light of a critical strength at a critical phase can even drive the human circadian pacemaker to its region of singularity, akin to temporarily 'stopping' the human circadian clock. These findings have important implications for the treatment of circadian rhythm sleep disorders, because properly timed exposure to light can reset the human clock to any desired hour within one to three days.

Phase resetting and phase singularity of an insect circannual oscillator

In circadian rhythms, the shape of the phase response curves (PRCs) depends on the strength of the resetting stimulus. Weak stimuli produce Type 1 PRCs with small phase shifts and a continuous transition between phase delays and advances, whereas strong stimuli produce Type 0 PRCs with large phase shifts and a distinct break point at the transition between delays and advances. A stimulus of an intermediate strength applied close to the break point in a Type 0 PRC sometimes produces arrhythmicity. A PRC for the circannual rhythm was obtained in pupation of the varied carpet beetle, Anthrenus verbasci, by superimposing a 4-week long-day pulse (a series of long days for 4 weeks) over constant short days. The shape of this PRC closely resembles that of the Type 0 PRC. The present study shows that the PRC to 2-week long-day pulses was Type 1, and that a 4-week long-day pulse administered close to the PRC's break point induced arrhythmicity in pupation. It is, therefore, suggested that circadian and circannual oscillators share the same mode in phase resetting to the stimuli.

Circadian rhythms in Neurospora: a new measurement, the reset zone

The authors define a new feature of a circadian rhythm, the reset zone, and point out its usefulness for predictions concerning oscillator behavior. The reset zone measures the responses of a circadian system to resetting pulses. It can be easily determined from a phase transition curve (PTC), which is simply a phase response curve (PRC) replotted as new phase versus old phase (Winfree's format). The reset zone is the range of new phases seen in such a plot and has two potentially useful characteristics: its size and its midpoint. A series of experiments with Neurospora involving temperature pulses indicated that the size of the reset zone changed in a nonlinear way in response to both the duration of 40 degrees C pulses and to the magnitude of temperature change for 3-h pulses. Other existing data are replotted to show how the reset zone size varies with growth temperature and with the period of different clock mutants. Employing exclusively reset zone data within the framework of a limit cycle displacement model, an equation is formulated that predicts the relative changes in the values of state variables of the oscillator for changes in any given environmental condition, such as temperature. Examples are also drawn from other organisms, such as hamsters, Gonyalaux, Kalanchoe, and Drosophila, illustrating the usefulness of the reset zone measurement. It can be used as a numerical scale for assessing the strength of a pulse, for comparing the relative effects of a given pulse applied to different organisms or mutants, for determining the directionality of the changes in state variables produced by various types of pulses, and possibly for measuring clock amplitude.

Phase-amplitude resetting of the human circadian pacemaker via bright light: a further analysis

We present here an analysis of strong, weak, and critical bright-light resetting trials in humans, and report not only phase but also amplitude data for the first time. For this analysis, an appropriate iterative smoothing procedure for phase transition curves is introduced, in which the data are sequenced so as to minimize the perpendicular distance from the data to the smoothed fit. From these smoothed data, we create polar phase-amplitude resetting maps (PARMs) in order to fully illustrate the effects of the resetting stimuli on both circadian amplitude and phase, and thereby to determine whether these resetting results can be described by a phase-only model or whether a phase-amplitude model is required. Our results indicate that a single 5-hr episode of bright light induces weak type 1 resetting of the human circadian pacemaker. Two cycles of exposure to the same stimulus on consecutive days induce critical resetting, in which significant amplitude reduction may be observed. A three-cycle stimulus induces strong type 0 resetting with different effects on circadian amplitude, depending on the initial phase of the stimulus application. When a three-cycle stimulus is centered near the nadir of the temperature cycle, large phase shifts are achieved via amplitude suppression. However, when this stimulus is centered away from the temperature nadir, smaller phase shifts are achieved in which both small increases and small decreases in circadian amplitude are observed. These data indicate that the human circadian pacemaker is not a simple, phase-only oscillator. Instead, a full description of human circadian resetting responses to light requires analysis of both phase and amplitude data--a finding that is consistent with a phase-amplitude model of the circadian resetting mechanism.

Light pulses induce "singular" behavior and shorten the period of the circadian phototaxis rhythm in the CW15 strain of Chlamydomonas

While measuring action spectra for phase-shifting the circadian clock of Chlamydomonas, we observed that light pulses started near the phase response curve (PRC) "breakpoint" caused a reduction of the amplitude of the phototactic rhythm and two unexpected effects: (1) nonmonotonic fluence response curves (FRCs), and (2) shortening of the period of the subsequent free-running rhythm. The reduction of the rhythm's amplitude is dependent upon both the fluence and wavelength of the light pulse. The results are consistent with the amplitude being dependent upon the perceived "strength" of the stimulus, and with the nonmonotonic FRCs and reduced amplitude reflecting a light-induced change of the pacemaker's state variables to a region of the phase plane close to the "singularity." The period change that is evoked by single stimuli exhibits novel characteristics: large changes in period and a phase specificity that correlates with "singular" behavior. These period changes also appear to be a function of the stimulus strength, but indirectly; the magnitude of the period change is most strongly correlated with the magnitude of the light-induced phase shift. These results are interpreted in the context of limit cycle models of circadian clocks, and are used to suggest new tactics for measuring action spectra of light-induced clock resetting.

Light-induced suppression of endogenous circadian amplitude in humans

Winfree reported 20 years ago the intriguing finding that a light stimulus of a critical strength applied at a critical circadian phase could essentially stop the circadian clock in Drosophila pseudo-obscura by resetting the circadian oscillator close to its singularity (a phaseless position at which the amplitude of circadian oscillation is zero). Since then, similar observations of attenuated circadian amplitude in response to critical stimuli have been limited to unicells, insects and plants. Our recent demonstration that the phase of the human circadian pacemaker could be inverted using an unconventional three-cycle stimulus led us to investigate whether critically timed exposure to a more moderate stimulus could drive that oscillator towards its singularity. Here we report that exposure of humans to fewer cycles of bright light, centred around the time at which the human circadian pacemaker is most sensitive to light-induced phase shifts, can markedly attenuate endogenous circadian amplitude. In some cases this results in an apparent loss of rhythmicity, as expected to occur in the region of singularity.