Internal synchronization of the main 0.1-Hz rhythms in the autonomic control of the cardiovascular system

Synchronization parameters of 0.1-Hz rhythms isolated from the heart rate and the oscillations of the blood volume in microcirculatory vessels were studied in 12 healthy subjects and 32 patients with acute myocardial infarction. Recordings of the electrocardiogram and the pulsogram from the distal phalanx of the index finger, as well as mechanical recording of respiration with the body in a horizontal position, were performed. In patients with myocardial infarction, the recordings were performed during the first three to five days and the third week after the infarction. Synchronization was tested by plotting phase differences and calculating the total percentage of phase synchronization. Synchronization parameters of 0.1-Hz rhythms were high in healthy subjects. In patients with acute myocardial infarction, synchronization of 0.1-Hz rhythms was considerably poorer. The data obtained suggest that the studied 0.1-Hz rhythms are two independent oscillatory processes that are synchronized in healthy subjects. However, this interaction may be disturbed in cardiovascular pathologies, e.g., myocardial infarction.     

The response of a classical Hodgkin–Huxley neuron to an inhibitory input pulse

A population of uncoupled neurons can often be brought close to synchrony by a single strong inhibitory input pulse affecting all neurons equally. This mechanism is thought to underlie some brain rhythms, in particular gamma frequency (30–80 Hz) oscillations in the hippocampus and neocortex. Here we show that synchronization by an inhibitory input pulse often fails for populations of classical Hodgkin–Huxley neurons. Our reasoning suggests that in general, synchronization by inhibitory input pulses can fail when the transition of the target neurons from rest to spiking involves a Hopf bifurcation, especially when inhibition is shunting, not hyperpolarizing. Surprisingly, synchronization is more likely to fail when the inhibitory pulse is stronger or longer-lasting. These findings have potential implications for the question which neurons participate in brain rhythms, in particular in gamma oscillations.     

Modeling circadian clocks: Roles,advantages, and limitations

Circadian rhythms are endogenous oscillations characterized by a period of about 24h. They constitute the biological rhythms with the longest period known to be generated at the molecular level. The abundance of genetic information and the complexity of the molecular circuitry make circadian clocks a system of choice for theoretical studies. Many mathematical models have been proposed to understand the molecular regulatory mechanisms that underly these circadian oscillations and to account for their dynamic properties (temperature compensation, entrainment by light dark cycles, phase shifts by light pulses, rhythm splitting, robustness to molecular noise, intercellular synchronization). The roles and advantages of modeling are discussed and illustrated using a variety of selected examples. This survey will lead to the proposal of an integrated view of the circadian system in which various aspects (interlocked feedback loops, inter-cellular coupling, and stochasticity) should be considered together to understand the design and the dynamics of circadian clocks. Some limitations of these models are commented and challenges for the future identified.     

Modeling the emergence of circadian rhythms in a clock neuron network

Circadian rhythms in pacemaker cells persist for weeks in constant darkness, while in other types of cells the molecular oscillations that underlie circadian rhythms damp rapidly under the same conditions. Although much progress has been made in understanding the biochemical and cellular basis of circadian rhythms, the mechanisms leading to damped or self-sustained oscillations remain largely unknown. There exist many mathematical models that reproduce the circadian rhythms in the case of a single cell of the Drosophila fly. However, not much is known about the mechanisms leading to coherent circadian oscillation in clock neuron networks. In this work we have implemented a model for a network of interacting clock neurons to describe the emergence (or damping) of circadian rhythms in Drosophila fly, in the absence of zeitgebers. Our model consists of an array of pacemakers that interact through the modulation of some parameters by a network feedback. The individual pacemakers are described by a well-known biochemical model for circadian oscillation, to which we have added degradation of PER protein by light and multiplicative noise. The network feedback is the PER protein level averaged over the whole network. In particular, we have investigated the effect of modulation of the parameters associated with (i) the control of net entrance of PER into the nucleus and (ii) the non-photic degradation of PER. Our results indicate that the modulation of PER entrance into the nucleus allows the synchronization of clock neurons, leading to coherent circadian oscillations under constant dark condition. On the other hand, the modulation of non-photic degradation cannot reset the phases of individual clocks subjected to intrinsic biochemical noise.     

The nature of the root clock at single cell resolution: Principles of communication and similarities with plant and animal pulsatile and circadian mechanisms

Oscillatory mechanisms are present in most life forms and regulate biological processes periodically. In multicellular organisms where more than one oscillatory mechanism is present, they are organized forming a hierarchical coordinated system even at the cellular level. Here, we focus on the Root Clock, an oscillatory mechanism located at the tip of roots that patterns the spacing of lateral organs through oscillating gene expression. We present a series of recent findings and hypotheses about the cellular mechanisms driving the oscillations, how oscillatory information is transmitted within this clock and similarities with other oscillatory systems. Next, we review principles of communication in other pulsatile mechanisms such as circadian rhythms in plants and mammals, and address the possible communication between plant circadian rhythms and the Root Clock. Finally, we advocate for the use of single-cell approaches to address cell communication, synchronization and integration of external outputs into the Root Clock system.     

Circadian rhythms of food and 1% NaCl intake, urine and electrolyte excretion, plasma renin activity and insulin concentration in adrenalectomized rats

The circadian rhythms of food and 1% NaCl intake, and urine, Na+, Cl- and K+ excretion were followed up in male Wistar rats before and one week after bilateral adrenalectomy at 4-hour intervals during two consecutive days. The circadian rhythms of plasma renin activity (PRA) and plasma immunoreactive insulin (IRI) were evaluated after decapitation of both intact and adrenalectomized rats at 08, 16 and 24 h. To all rats 1% NaCl was offered instead of drinking water. Adrenalectomy did not cause any significant phase shift in the cosine curves approximating the data collected at 4-hour intervals. The circadian rhythms showed the same relationships before and after the operation: the rhythms of food intake, K+ excretion and saline intake preceded significantly the rhythms of urine, Na+ and Cl- excretion. Adrenalectomy induced an increase in mean PRA and shifted its minimal value from 08 to 24 h. After the operation mean IRI decreased and the minimal value shifted from 16 to 24 h. It was concluded that adrenal glands do not play an important role in the synchronization of the circadian rhythms of food and 1% NaCl intake, urine and synchronization of the circadian rhythms of food and 1% NaCl intake, urine and electrolyte excretion with the illumination cycle, but play a relevant role in the synchronization of the circadian rhythms of PRA and IRI in the rat.     

A Hypothesis of Possible Physical Nature of Signals of Intracellular and Intercellular Synchronization of Protein Synthesis Rhythms

A hypothesis of physical nature of signals for intracellular and intercellular synchronization of protein synthesis rhythms is considered. Electromagnetic and acoustic waves generated during gel–sol phase transitions and oscillations of intracellular microstructures are proposed as synchronization signals, while endogenous rhythm of gel–sol transitions is their universal acceptor. Information significance of these signals in the evolution of cells and multicellular organisms is discussed.     

Effect of change in levels of motor activity and innervation on basic and secondary rhythms of rat heart beatings and respiration in ontogenesis

Changes in the heart basic rhythm, its rhythmical variations on periodograms, and level of spontaneous motor activity were studied on offspring of white rats from newborn to 3-week age at transition from the state of active wakefulness to narcosis as well as under conditions of blockade of M-cholinoreceptors with atropine. It is shown that the endogenous rhythmical activity can be regulated not only by a change in frequency of basic rhythms, but also by action on all parameters and properties of their rhythmical variations and secondary rhythms. The changes in power of the heart secondary rhythms exceed considerably the frequency oscillations of basic rhythms during blockade of cholinergic innervation or a change in the motor activity level that affects both the basic rhythm circulation and respiration and their variations—secondary rhythms. The atropine blockade of M-cholinoreceptors at the studied ages changes the heart contraction rhythm within the limits of 10% of bradycardia in newborns to tachycardia in the 3-week old animals. At the same time, power of the cardiac rhythm secondary oscillations changes several times. These data indicate that the cholinergic mechanisms play the key role in formation of the secondary rhythms and their correlation with motor activity.     

Effect of change in levels of motor activity and innervation on basic and secondary rhythms of rat heart rate and respiration in ontogenesis

Changes in the heart basic rhythm, its rhythmical variations on periodograms, and level of spontaneos motor activity were studied on offspring of white rats from newborn to 3-week age at transition from the state of active wakefulness to narcosis as well as under conditions of blockade of M-cholinoreceptors with atropine. It is shown that the endogenous rhythmical activity can be regulated not only by a change in frequency of basic rhythms, but also by action on all parameters and properties of their rhythmical variations and secondary rhythms. The changes in power of the heart secondary rhythms exceed considerably the frequency oscillations of basic rhythms during blockade of cholinergic innervation or a change in the motor activity level that affects both the basic rhythm circulation and respiration and their variations--secondary rhythms. The atropine blockade of M-cholinoreceptors at the studied ages changes the heart beating rhythm within the limits of 10% of bradicardia in newborns to tachycardia in the 3-week old animals. At the same time, power of the cardiac rhythm secondary oscillations changes several times. These data indicate that the cholinergic mechanisms play the key role in formation of the secondary rhythms and their correlation with motor activity.     

Spontaneously active cells induce state transitions in a model of olfactory cortex

The existence of neurons with intrinsic oscillations does not in itself explain the synchronization of local populations of neurons, but it is likely to pace population rhythms when the neurons are suitably coupled by chemical and/or electrical synapses. In the present study, we have investigated the role of spontaneously active cells as noisy or pacemaker units in setting global oscillations in a three-layered cortical model. The presence of a small number of noisy (spontaneously active) units induce oscillations at the network level in the range of the gamma rhythm. The number of noisy units in the network and their type (excitatory or inhibitory or excitatory and inhibitory together) determines the emergence of regular oscillations or aperiodic (chaotic) behaviour. It also determines the onset of the global behaviour. On replacing a noisy unit by a pacemaker unit, similar gamma oscillations were generated. With both noisy and pacemaker units, we found that certain characteristics of the spontaneous activity determine the delay period for the onset of global activity. Preliminary studies have been carried out with spontaneously active units having a chaotic dynamics but the results are much similar to that with a noisy burst. Different functional roles have been suggested for cortical oscillations, such as determining global functional states and specifying connectivity during development. Oscillations at different frequency bands, in particular in the gamma band (around 40 Hz), have also been associated with memory and attention. The presence of spontaneously active neurons, either with noisy or oscillatory activity, could be responsible for global oscillations in the absence of external stimuli in certain cortical areas in the mature brain.     

Impairment of Cognitive Function and Synaptic Plasticity Associated with Alteration of Information Flow in Theta and Gamma Oscillations in Melamine-Treated Rats

Changes of neural oscillations at a variety of physiological rhythms are effectively associated with cognitive performance. The present study investigated whether the directional indices of neural information flow (NIF) could be used to symbolize the synaptic plasticity impairment in hippocampal CA3-CA1 network in a rat model of melamine. Male Wistar rats were employed while melamine was administered at a dose of 300 mg/kg/day for 4 weeks. Behavior was measured by the Morris water maze(MWM)test. Local field potentials (LFPs) were recorded before long-term potentiation (LTP) induction. Generalized partial directed coherence (gPDC) and phase-amplitude coupling conditional mutual information (PAC_CMI) were used to measure the unidirectional indices in both theta and low gamma oscillations (LG, ∼30–50 Hz). Our results showed that melamine induced the cognition deficits consistent with the reduced LTP in CA1 area. Phase locking values (PLVs) showed that the synchronization between CA3 and CA1 in both theta and LG rhythms was reduced by melamine. In both theta and LG rhythms, unidirectional indices were significantly decreased in melamine treated rats while a similar variation trend was observed in LTP reduction, implying that the effects of melamine on cognitive impairment were possibly mediated via profound alterations of NIF on CA3-CA1 pathway in hippocampus. The results suggested that LFPs activities at these rhythms were most likely involved in determining the alterations of information flow in the hippocampal CA3-CA1 network, which might be associated with the alteration of synaptic transmission to some extent.     

Systems biology of cellular rhythms

Rhythms abound in biological systems, particularly at the cellular level where they originate from the feedback loops present in regulatory networks. Cellular rhythms can be investigated both by experimental and modeling approaches, and thus represent a prototypic field of research for systems biology. They have also become a major topic in synthetic biology. We review advances in the study of cellular rhythms of biochemical rather than electrical origin by considering a variety of oscillatory processes such as Ca++ oscillations, circadian rhythms, the segmentation clock, oscillations in p53 and NF-κB, synthetic oscillators, and the oscillatory dynamics of cyclin-dependent kinases driving the cell cycle. Finally we discuss the coupling between cellular rhythms and their robustness with respect to molecular noise.     

Rhythms of mammalian body temperature can sustain peripheral circadian clocks

BACKGROUND: Low-amplitude temperature oscillations can entrain the phase of circadian rhythms in several unicellular and multicellular organisms, including Neurospora and Drosophila. Because mammalian body temperature is subject to circadian variations of 1 degrees C-4 degrees C, we wished to determine whether these temperature cycles could serve as a Zeitgeber for circadian gene expression in peripheral cell types. RESULTS: In RAT1 fibroblasts cultured in vitro, circadian gene expression could be established by a square wave temperature rhythm with a (Delta)T of 4 degrees C (12 hr 37 degrees C/12 hr 33 degrees C). To examine whether natural body temperature rhythms can also affect circadian gene expression, we first measured core body temperature cycles in the peritoneal cavities of mice by radiotelemetry. We then reproduced these rhythms with high precision in the liquid medium of cultured fibroblasts for several days by means of a homemade computer-driven incubator. While these "in vivo" temperature rhythms were incapable of establishing circadian gene expression de novo, they could maintain previously induced rhythms for multiple days; by contrast, the rhythms of control cells kept at constant temperature rapidly dampened. Moreover, circadian oscillations of environmental temperature could reentrain circadian clocks in the livers of mice, probably via the changes they imposed upon both body temperature and feeding behavior. Interestingly, these changes in ambient temperature did not affect the phase of the central circadian pacemaker in the suprachiasmatic nucleus (SCN) of the hypothalamus. CONCLUSIONS: We postulate that both endogenous and environmental temperature cycles can participate in the synchronization of peripheral clocks in mammals.     

Robust circadian rhythms in organoid cultures from PERIOD2::LUCIFERASE mouse small intestine

Disruption of circadian rhythms is a risk factor for several human gastrointestinal (GI) diseases, ranging from diarrhea to ulcers to cancer. Four-dimensional tissue culture models that faithfully mimic the circadian clock of the GI epithelium would provide an invaluable tool to understand circadian regulation of GI health and disease. We hypothesized that rhythmicity of a key circadian component, PERIOD2 (PER2), would diminish along a continuum from ex vivo intestinal organoids (epithelial ‘miniguts’), nontransformed mouse small intestinal epithelial (MSIE) cells and transformed human colorectal adenocarcinoma (Caco-2) cells. Here, we show that bioluminescent jejunal explants from PERIOD2::LUCIFERASE (PER2::LUC) mice displayed robust circadian rhythms for >72 hours post-excision. Circadian rhythms in primary or passaged PER2::LUC jejunal organoids were similarly robust; they also synchronized upon serum shock and persisted beyond 2 weeks in culture. Remarkably, unshocked organoids autonomously synchronized rhythms within 12 hours of recording. The onset of this autonomous synchronization was slowed by >2 hours in the presence of the glucocorticoid receptor antagonist RU486 (20 μM). Doubling standard concentrations of the organoid growth factors EGF, Noggin and R-spondin enhanced PER2 oscillations, whereas subtraction of these factors individually at 24 hours following serum shock produced no detectable effects on PER2 oscillations. Growth factor pulses induced modest phase delays in unshocked, but not serum-shocked, organoids. Circadian oscillations of PER2::LUC bioluminescence aligned with Per2 mRNA expression upon analysis using quantitative PCR. Concordant findings of robust circadian rhythms in bioluminescent jejunal explants and organoids provide further evidence for a peripheral clock that is intrinsic to the intestinal epithelium. The rhythmic and organotypic features of organoids should offer unprecedented advantages as a resource for elucidating the role of circadian rhythms in GI stem cell dynamics, epithelial homeostasis and disease.KEY WORDS: Circadian rhythm, Intestinal organoid, PERIOD2, R-spondin, RU486     

Monitoring circadian rhythms of individual cells in plants

The circadian clock is an endogenous timing system based on the self-sustained oscillation in individual cells. These cellular circadian clocks compose a multicellular circadian system working at respective levels of tissue, organ, plant body. However, how numerous cellular clocks are coordinated within a plant has been unclear. There was little information about behavior of circadian clocks at a single-cell level due to the difficulties in monitoring circadian rhythms of individual cells in an intact plant. We developed a single-cell bioluminescence imaging system using duckweed as the plant material and succeeded in observing behavior of cellular clocks in intact plants for over a week. This imaging technique quantitatively revealed heterogeneous and independent manners of cellular clock behaviors. Furthermore, these quantitative analyses uncovered the local synchronization of cellular circadian rhythms that implied phase-attractive interactions between cellular clocks. The cell-to-cell interaction looked to be too weak to coordinate cellular clocks against their heterogeneity under constant conditions. On the other hand, under light–dark conditions, the heterogeneity of cellular clocks seemed to be corrected by cell-to-cell interactions so that cellular clocks showed a clear spatial pattern of phases at a whole plant level. Thus, it was suggested that the interactions between cellular clocks was an adaptive trait working under day–night cycles to coordinate cellular clocks in a plant body. These findings provide a novel perspective for understanding spatio-temporal architectures in the plant circadian system.     

Unique self-sustaining circadian oscillators within the brain of Drosophila melanogaster

In Drosophila circadian rhythms persist in constant darkness (DD). The small ventral Lateral Neurons (s-LN_v) mainly control the behavioral circadian rhythm in consortium with the large ventral Lateral Neurons (l-LN_v) and dorsal Lateral Neurons (LN_d). It is believed that the molecular oscillations of clock genes are the source of this persistent behavior. Indeed the s-LN_v, LN_d, Dorsal Neurons (DN)-DN₂ and DN₃ displayed self-sustained molecular oscillations in DD both at RNA and protein levels, except the DN₂ oscillates in anti-phase. In contrast, the l-LN_v and DN₁ displayed self-sustained oscillations at the RNA level, but protein oscillations quickly dampened. Having self-sustained and dampened molecular oscillators together in the DN groups suggested that they play different roles. However, all DN groups seemed to contribute together to the light-dark (LD) behavioral rhythm. The LD entrainment of LN oscillators is achieved through Rhodopsin (RH) and Cryptochrome (CRY). CRY's expression in all DN groups implicates also its role in LD entrainment of DN, like in DN₁. However, mutations in cry and glass that did not inflict LD synchronization of the DN₂, DN₃ oscillator implicate the existence of a novel photoreceptor at least in DN₃.     

Stochastic models for circadian rhythms: effect of molecular noise on periodic and chaotic behaviour

Circadian rhythms are endogenous oscillations that occur with a period close to 24 h in nearly all living organisms. These rhythms originate from the negative autoregulation of gene expression. Deterministic models based on such genetic regulatory processes account for the occurrence of circadian rhythms in constant environmental conditions (e.g., constant darkness), for entrainment of these rhythms by light-dark cycles, and for their phase-shifting by light pulses. When the numbers of protein and mRNA molecules involved in the oscillations are small, as may occur in cellular conditions, it becomes necessary to resort to stochastic simulations to assess the influence of molecular noise on circadian oscillations. We address the effect of molecular noise by considering the stochastic version of a deterministic model previously proposed for circadian oscillations of the PER and TIM proteins and their mRNAs in Drosophila. The model is based on repression of the per and tim genes by a complex between the PER and TIM proteins. Numerical simulations of the stochastic version of the model are performed by means of the Gillespie method. The predictions of the stochastic approach compare well with those of the deterministic model with respect both to sustained oscillations of the limit cycle type and to the influence of the proximity from a bifurcation point beyond which the system evolves to stable steady state. Stochastic simulations indicate that robust circadian oscillations can emerge at the cellular level even when the maximum numbers of mRNA and protein molecules involved in the oscillations are of the order of only a few tens or hundreds. The stochastic model also reproduces the evolution to a strange attractor in conditions where the deterministic PER-TIM model admits chaotic behaviour. The difference between periodic oscillations of the limit cycle type and aperiodic oscillations (i.e. chaos) persists in the presence of molecular noise, as shown by means of Poincaré sections. The progressive obliteration of periodicity observed as the number of molecules decreases can thus be distinguished from the aperiodicity originating from chaotic dynamics. As long as the numbers of molecules involved in the oscillations remain sufficiently large (of the order of a few tens or hundreds, or more), stochastic models therefore provide good agreement with the predictions of the deterministic model for circadian rhythms.