Regulation of output from the plant circadian clock

Plants, like many other organisms, have endogenous biological clocks that enable them to organize their physiological, metabolic and developmental processes so that they occur at optimal times. The best studied of these biological clocks are the circadian systems that regulate daily (approximately 24 h) rhythms. At the core of the circadian system in every organism are oscillators responsible for generating circadian rhythms. These oscillators can be entrained (set) by cues from the environment, such as daily changes in light and temperature. Completing the circadian clock model are the output pathways that provide a link between the oscillator and the various biological processes whose rhythms it controls. Over the past few years there has been a tremendous increase in our understanding of the mechanisms of the oscillator and entrainment pathways in plants and many useful reviews on the subject. In this review we focus on the output pathways by which the oscillator regulates rhythmic plant processes. In the first part of the review we describe the role of the circadian system in regulation at all stages of a plant's development, from germination and growth to reproductive development as well as in multiple cellular processes. Indeed, the importance of a circadian clock for plants can be gauged by the fact that so many facets of plant development are under its control. In the second part of the review we describe what is known about the mechanisms by which the circadian system regulates these output processes.     

Systems and synthetic biology approaches in understanding biological oscillators

Background: Self-sustained oscillations are a ubiquitous and vital phenomenon in living systems. From primitive single-cellular bacteria to the most sophisticated organisms, periodicities have been observed in a broad spectrum of biological processes such as neuron firing, heart beats, cell cycles, circadian rhythms, etc. Defects in these oscillators can cause diseases from insomnia to cancer. Elucidating their fundamental mechanisms is of great significance to diseases, and yet challenging, due to the complexity and diversity of these oscillators. Results: Approaches in quantitative systems biology and synthetic biology have been most effective by simplifying the systems to contain only the most essential regulators. Here, we will review major progress that has been made in understanding biological oscillators using these approaches. The quantitative systems biology approach allows for identification of the essential components of an oscillator in an endogenous system. The synthetic biology approach makes use of the knowledge to design the simplest, de novo oscillators in both live cells and cell-free systems. These synthetic oscillators are tractable to further detailed analysis and manipulations. Conclusion: With the recent development of biological and computational tools, both approaches have made significant achievements.     

Interaction of mitotic oscillators as a source of variability of cell cycle duration

Interaction between membrane mitotic oscillators at the expense of exchange with the molecules of lipids (slow variable) and antioxidants (fast variable) was considered. Parameters of all the oscillators are equal, excluding a small noise added to the equation for lipids. These parameters are chosen in such a way that the oscillators are not far from the transition to the stable stationary state. The numerical modeling has shown that the exchange with lipids brings about the appearance of an additional limit cycle whose period is significantly greater than that of an autonomous oscillator. The addition of noise averages the behaviour of oscillators, and distribution according to cycle duration becomes broad and bimodal. Thus the exchange of the slow variable increases the dispersion of distribution of cell generation times. This conclusion seems to be true for any oscillator with similar dynamic properties.     

Localization of essential rhombomeres for respiratory rhythm generation in bullfrog tadpoles using a binary search algorithm: Rhombomere 7 is essential for the gill rhythm and suppresses lung bursts before metamorphosis

Frog metamorphosis includes transition from water breathing to air breathing but the extent to which such a momentous change in behavior requires fundamental changes in the organization of the brainstem respiratory circuit is unknown. Here, we combine a vertically mounted isolated brainstem preparation, “the Sheep Dip,” with a search algorithm used in computer science, to identify essential rhombomeres for generation of ventilatory motor bursts in metamorphosing bullfrog tadpoles. Our data suggest that rhombomere 7, which in mammals hosts the PreBötC (PreBötzinger Complex; the likely inspiratory oscillator), is essential for gill and buccal bursts. Whereas rhombomere 5, in close proximity to a brainstem region associated with the mammalian expiratory oscillator, is essential for lung bursts at both stages. Therefore, we conclude there is no rhombomeric translocation of respiratory oscillators in bullfrogs as previously suggested. In premetamorphic tadpoles, functional ablation of rhombomere 7 caused ectopic expression of precocious lung bursts, suggesting the gill oscillator suppresses an otherwise functional lung oscillator in early development. © 2013 Wiley Periodicals, Inc. Develop Neurobiol 73: 888–898, 2013     

Two coupled neural oscillators as a model of the circadian pacemaker

Pittendrigh first found that the circadian rhythm of locomotor activity in nocturnal rodents split into two components. Hoffman then reported that the splitting phenomenon was even more reproducible in the small diurnal primate Tupaia. These “splitting” experiments and many other experiments suggest that two coupled oscillators may constitute the circadian pacemaker system. Pittendrigh proposed a phenomenological two-oscillator model. Daan and Berde developed a quantitative model assuming that the interaction between the two constituent oscillators is by instantaneous resets. Their model system can simulate several qualitative features in the experimental data. As the assumption of instantaneous resets seems to be unnatural, we study two limit cycle oscillators, which are coupled continuously to each other, as a model of the circadian pacemaker. We assume the following points, (i) One oscillator in a resting state does not affect another oscillator, (ii) Two oscillators are identical, (iii) The coupling is symmetrical. By the theory of Hopf bifurcation it is found that the general two-oscillator system has two stable periodic solutions. One is the in-phase solution where the two constituent oscillators oscillate in phase synchrony. Another is the anti-phase solution where the two oscillators oscillate 180 ° out of phase. The former corresponds to a single pattern of locomotor activity and the latter corresponds to a splitting pattern. Furthermore, we study specific two-neural oscillators, which are linearly coupled to each other. By the method of secondary bifurcation we find that the model shows simultaneous stability of the two alternative phase relationships and the hysteresis phenomena found in Tupaia. A natural period of the uncoupled constituent oscillator is longer than that of the in-phase solution but it is shorter than that of the anti-phase solution. This is in agreement with the data of Tupaia.     

Two circadian timing circuits in Neurospora crassa cells share components and regulate distinct rhythmic processes

In Neurospora crassa, FRQ, WC-1, and WC-2 proteins comprise the core circadian FRQ-based oscillator that is directly responsive to light and drives daily rhythms in spore development and gene expression. However, physiological and biochemical studies have demonstrated the existence of additional oscillators in the cell that function in the absence of FRQ (collectively termed FRQ-less oscillators [FLOs]). Whether or not these represent temperature-compensated, entrainable circadian oscillators is not known. The authors previously identified an evening-peaking gene, W06H2 (now called clock-controlled gene 16 [ccg-16]), which is expressed with a robust daily rhythm in cells that lack FRQ protein, suggesting that ccg-16 is regulated by a FLO. In this study, the authors provide evidence that the FLO driving ccg-16 rhythmicity is a circadian oscillator. They find that ccg-16 rhythms are generated by a temperature-responsive, temperature-compensated circadian FLO that, similar to the FRQ-based oscillator, requires functional WC-1 and WC-2 proteins for activity. They also find that FRQ is not essential for rhythmic WC-1 protein levels, raising the possibility that this WCFLO is involved in the generation of WC-1 rhythms. The results are consistent with the presence of 2 circadian oscillators within Neurospora cells, which the authors speculate may interact with each other through the shared WC proteins.     

Synchronization in a neural network of phase oscillators with the central element

A neural network model is considered which is designed as a system of phase oscillators and contains the central oscillator and peripheral oscillators which interact via the central oscillator. The regime of partial synchronization was studied when current frequencies of the central oscillator and one group of peripheral oscillators are near to each other while current frequencies of other peripheral oscillators are far from being synchronized with the central oscillator. Approximation formulas for the average frequency of the central oscillator in the regime of partial synchronization are derived, and results of computation experiments are presented which characterize the accuracy of the approximation.     

Control of interaction strength in a network of the true slime mold by a microfabricated structure

The plasmodium of the true slime mold, Physarum polycephalum, which shows various nonlinear oscillatory phenomena, for example, in its thickness, protoplasmic streaming and concentration of intracellular chemicals, can be regarded as a collective of nonlinear oscillators. The plasmodial oscillators are interconnected by microscale tubes whose dimensions can be closely related to the strength of interaction between the oscillators. Investigation of the collective behavior of the oscillators under the conditions in which the interaction strength can be systematically controlled gives significant information on the characteristics of the system. In this study, we proposed a living model system of a coupled oscillator system in the Physarum plasmodium. We patterned the geometry and dimensions of the microscale tube structure in the plasmodium by a microfabricated structure (microstructure). As the first step, we constructed a two-oscillator system for the plasmodium that has two wells (oscillator part) and a channel (coupling part). We investigated the oscillation behavior by monitoring the thickness oscillation of the plasmodium in the microstructure with various channel widths. It was found that the oscillation behavior of two oscillators dynamically changed depending on the channel width. Based on the results of measurements of the tube dimensions and the velocity of the protoplasmic streaming in the tube, we discuss how the channel width relates to the interaction strength of the coupled oscillator system.     

Oscillator decomposition of infant fNIRS data

The functional near-infrared spectroscopy (fNIRS) can detect hemodynamic responses in the brain and the data consist of bivariate time series of oxygenated hemoglobin (oxy-Hb) and deoxygenated hemoglobin (deoxy-Hb) on each channel. In this study, we investigate oscillatory changes in infant fNIRS signals by using the oscillator decompisition method (OSC-DECOMP), which is a statistical method for extracting oscillators from time series data based on Gaussian linear state space models. OSC-DECOMP provides a natural decomposition of fNIRS data into oscillation components in a data-driven manner and does not require the arbitrary selection of band-pass filters. We analyzed 18-ch fNIRS data (3 minutes) acquired from 21 sleeping 3-month-old infants. Five to seven oscillators were extracted on most channels, and their frequency distribution had three peaks in the vicinity of 0.01-0.1 Hz, 1.6-2.4 Hz and 3.6-4.4 Hz. The first peak was considered to reflect hemodynamic changes in response to the brain activity, and the phase difference between oxy-Hb and deoxy-Hb for the associated oscillators was at approximately 230 degrees. The second peak was attributed to cardiac pulse waves and mirroring noise. Although these oscillators have close frequencies, OSC-DECOMP can separate them through estimating their different projection patterns on oxy-Hb and deoxy-Hb. The third peak was regarded as the harmonic of the second peak. By comparing the Akaike Information Criterion (AIC) of two state space models, we determined that the time series of oxy-Hb and deoxy-Hb on each channel originate from common oscillatory activity. We also utilized the result of OSC-DECOMP to investigate the frequency-specific functional connectivity. Whereas the brain oscillator exhibited functional connectivity, the pulse waves and mirroring noise oscillators showed spatially homogeneous and independent changes. OSC-DECOMP is a promising tool for data-driven extraction of oscillation components from biological time series data.     

Genetic interactions between clock mutations in Neurospora crassa: can they help us to understand complexity?

Recent work on circadian clocks in Neurospora has primarily focused on the frequency (frq) and white-collar (wc) loci. However, a number of other genes are known that affect either the period or temperature compensation of the rhythm. These include the period (no relationship to the period gene of Drosophila) genes and a number of genes that affect cellular metabolism. How these other loci fit into the circadian system is not known, and metabolic effects on the clock are typically not considered in single-oscillator models. Recent evidence has pointed to multiple oscillators in Neurospora, at least one of which is predicted to incorporate metabolic processes. Here, the Neurospora clock-affecting mutations will be reviewed and their genetic interactions discussed in the context of a more complex clock model involving two coupled oscillators: a FRQ/WC-based oscillator and a 'frq-less' oscillator that may involve metabolic components.     

Spontaneous switching of frequency-locking by periodic stimulus in oscillators of plasmodium of the true slime mold

Microfabrication technique was used to construct a model system with a living cell of plasmodium of the true slime mold, Physarum polycephalum, a living coupled oscillator system. Its parameters can be systematically controlled as in computer simulations, so that results are directly comparable to those of general mathematical models. As the first step, we investigated responses in oscillatory cells, the oscillators of the plasmodium, to periodic stimuli by temperature changes to elucidate characteristics of the cells as nonlinear systems whose internal dynamics are unknown because of their complexity. We observed that the forced oscillator of the plasmodium show 1:1, 2:1, 3:1 frequency locking inside so-called Arnold tongues regions as well as in other nonlinear systems such as chemical systems and other biological systems. In addition, we found spontaneous switching behavior from certain frequency locking states to other states, even under certain fixed parameters. This technique can be applied to more complex systems with multiple elements, such as coupled oscillator systems, and would be useful to investigate complicated phenomena in biological systems such as information processing.     

Timing and consolidation of human sleep, wakefulness, and performance by a symphony of oscillators

Daily rhythms in sleep and waking performance are generated by the interplay of multiple external and internal oscillators. These include the light-dark and social cycles, a circadian hypothalamic oscillator oscillating virtually independently of behavior, and a homeostatic oscillator driven primarily by sleep-wake behavior. Both internal oscillators contribute to variation in many aspects of sleep and wakefulness (e.g., sleep timing and duration, REM sleep, non-REM sleep, REM density, sleep spindles, slow-wave sleep, electroencephalographic oscillations during wakefulness and sleep, and performance parameters, including attention and memory). The relative contribution of the oscillators varies greatly between these variables. Sleep and performance cannot be predicted by either oscillator independently but critically depend on their phase relationship and amplitude. The homeostatic oscillator feeds back onto the central pacemaker or its outputs. Thus, the amplitude of observed circadian variation in sleep and performance depends on how long we have been asleep or awake. During entrainment to external 24-h cycles, the opposing interplay between circadian and homeostatic changes in sleep propensity consolidates sleep and wakefulness. Some physiological correlates and mediators of both the circadian process (e.g., melatonin and hypocretin rhythms) and the homeostat (e.g., EEG, slow-wave activity, and adenosine release) have been established, offering targets for the development of countermeasures for circadian sleep and performance disorders. Interindividual differences in sleep timing, duration, and morning or evening preference are associated with changes of circadian or sleep homeostatic processes or both. Molecular genetic correlates, including polymorphisms in clock genes, of some of these interindividual differences are emerging.     

Phase plane description of crayfish swimmeret oscillator

Crayfish swimmeret system shows rhythmic, coordinated behavior when the command fibers are stimulated chronically by electrical pulses, and the oscillating frequency becomes faster with increasing stimulus frequency. This behavior is organized by the distributed neural oscillators in the abdominal ganglia. We investigated the dynamics of the neural oscillators which are controlled by command fibers. Phase resetting experiment technique was used for this purpose; a temporary cessation of commanding pulses, which was regarded as suppressive perturbation for the neural oscillator, was applied to the chronically stimulated oscillator, and phase transition curves (PTCs) were measured. For the short cessation of command pulses, type 1 PTCs were obtained. With increasing cessation length, the PTC shifted downward, and finally changed into type 0. We also measured PTCs for temporarily increased stimulus frequency, which was an excitatory perturbation for the neural oscillator and increased the frequency of the oscillation transiently. For the short excitatory perturbation, the PTCs were also type 1 and shifted upward. PTCs changed their shapes from type 1 into type 0, as increasing the perturbation length. These shapes of the PTCs contain important information about the properties of the neural oscillator. Analyzing these PTCs, we present a phase plane diagram which describes the character of the command control of the neural oscillator.     

Pulse coupled oscillators and the phase resetting curve

Limit cycle oscillators that are coupled in a pulsatile manner are referred to as pulse coupled oscillators. In these oscillators, the interactions take the form of brief pulses such that the effect of one input dies out before the next is received. A phase resetting curve (PRC) keeps track of how much an input advances or delays the next spike in an oscillatory neuron depending upon where in the cycle the input is applied. PRCs can be used to predict phase locking in networks of pulse coupled oscillators. In some studies of pulse coupled oscillators, a specific form is assumed for the interactions between oscillators, but a more general approach is to formulate the problem assuming a PRC that is generated using a perturbation that approximates the input received in the real biological network. In general, this approach requires that circuit architecture and a specific firing pattern be assumed. This allows the construction of discrete maps from one event to the next. The fixed points of these maps correspond to periodic firing modes and are easier to locate and analyze for stability compared to locating and analyzing periodic modes in the original network directly. Alternatively, maps based on the PRC have been constructed that do not presuppose a firing order. Specific circuits that have been analyzed under the assumption of pulsatile coupling include one to one lockings in a periodically forced oscillator or an oscillator forced at a fixed delay after a threshold event, two bidirectionally coupled oscillators with and without delays, a unidirectional N-ring of oscillators, and N all-to-all networks.