Synchronization and entrainment of coupled circadian oscillators

Circadian rhythms in mammals are controlled by the neurons located in the suprachiasmatic nucleus of the hypothalamus. In physiological conditions, the system of neurons is very efficiently entrained by the 24-hour light-dark cycle. Most of the studies carried out so far emphasize the crucial role of the periodicity imposed by the light dark cycle in neuronal synchronization. Nevertheless, heterogeneity as a natural and permanent ingredient of these cellular interactions is seemingly to play a major role in these biochemical processes. In this paper we use a model that considers the neurons of the suprachiasmatic nucleus as chemically-coupled modified Goodwin oscillators, and introduce non-negligible heterogeneity in the periods of all neurons in the form of quenched noise. The system response to the light-dark cycle periodicity is studied as a function of the interneuronal coupling strength, external forcing amplitude and neuronal heterogeneity. Our results indicate that the right amount of heterogeneity helps the extended system to respond globally in a more coherent way to the external forcing. Our proposed mechanism for neuronal synchronization under external periodic forcing is based on heterogeneity-induced oscillators death, damped oscillators being more entrainable by the external forcing than the self-oscillating neurons with different periods.Comment: 17 pages, 7 figure

Pacer cell response to periodic Zeitgebers

Almost all organisms show some kind of time periodicity in their behavior. Especially in mammals the neurons of the suprachiasmatic nucleus form a biological clock regulating the activity-inactivity cycle of the animal. This clock is stimulated by the natural 24-hour light-dark cycle. In our model of this system we consider each neuron as a so called phase oscillator, coupled to other neurons for which the light-dark cycle is a Zeitgeber. To simplify the model we first take an externally stimulated single phase oscillator. The first part of the phase interval is called the active state and the remaining part is the inactive state. Without external stimulus the oscillator oscillates with its intrinsic period. An external stimulus, be it from activity of neighboring cells or the periodic daylight cycle, acts twofold, it may delay the change form active to inactive and it may advance the return to the active state. The amount of delay and advance depends on the strength of the stimulus. We use a circle map as a mathematical model for this system. This map depends on several parameters, among which the intrinsic period and phase delay and advance. In parameter space we find Arnol'd tongues where the system is in resonance with the Zeitgeber. Thus already in this simplified system we find entrainment and synchronization. Also some other phenomena from biological experiments and observations can be related to the dynamical behavior of the circle map

In Synch but Not in Step: Circadian Clock Circuits Regulating Plasticity in Daily Rhythms

The suprachiasmatic nucleus (SCN) is a network of neural oscillators that program daily rhythms in mammalian behavior and physiology. Over the last decade much has been learned about how SCN clock neurons coordinate together in time and space to form a cohesive population. Despite this insight, much remains unknown about how SCN neurons communicate with one another to produce emergent properties of the network. Here we review the current understanding of communication among SCN clock cells and highlight a collection of formal assays where changes in SCN interactions provide for plasticity in the waveform of circadian rhythms in behavior. Future studies that pair analytical behavioral assays with modern neuroscience techniques have the potential to provide deeper insight into SCN circuit mechanisms

A mathematical model of sleep-wake cycles: the role of hypocretin/orexin in homeostatic regulation and thalamic synchronization

Sleep is vital to our health and well-being. Yet, we do not have answers to such fundamental questions as “why do we sleep?” and “what are the mechanisms of sleep regulation?”. Better understanding of these issues can open new perspectives not only in basic neurophysiology but also in different pathological conditions that are going along with sleep disorders and/or disturbances of sleep, e.g. in mental or neurological diseases. A generally accepted concept that explains regulation of sleep was proposed in 1982 by Alexander Borb´ely. It postulates that sleep-wake transitions result from the interaction between a circadian and a homeostatic sleep processes. The circadian process is ascribed to a “genetic clock” in the neurons of the suprachiasmatic nucleus of the hypothalamus. The mechanisms of the homeostatic process are still unclear. In this study a novel concept of hypocretin (orexin) - based control of sleep homeostasis is presented. The neuropeptide hypocretin is a synaptic co-transmitter of neurons in the lateral hypothalamus. It was discovered in 1998 independently by two different groups, therefore, obtaining two names, hypocretin and orexin. This neuropeptide is required to maintain wakefulness. Dysfunction in the hypocretin system leads to the sleep disorder narcolepsy, which, among other symptoms, is characterized by severe disturbances of sleep-wake cycles with sudden sleep-attacks in the wake period and interruptions of the sleep phase. On the other hand injection of hypocretin promotes wakefulness and improves the performance of sleep deprived subjects. The major proposals of the present study are the following: 1) the homeostatic regulation of sleep depends on the dynamics of a neuropeptide hypocretin; 2) ongoing impulse generation of the hypocretin neurons during wakefulness is sustained by reciprocal excitatory connections with other neurons, including local glutamate interneurons; 3) the transition to a silent state (sleep) is going along with an activity-dependent weakening of the hypocretin synaptic efficacy; 4) during the silent state (sleep) synaptic efficacy recovers and firing (wakefulness) can be reinstalled due to the circadian or other input. This concept is realized in a mathematical model of sleep-wake cycles which is built up on a physiology-based, although simplified Hodgkin-Huxley-type approach. In the proposed model a hypocretin neuron is reciprocally connected with a local interneuron via excitatory glutamate synapses. The hypocretin neuron additionally releases the neuropeptide hypocretin as co-transmitter. Besides of the local glutamate interneurons hypocretin neuron excites two gap junction coupled thalamic neurons. The functionally relevant changes are introduced via activity-dependent alterations of the synaptic efficacy of hypocretin. It is decreasing with each action potential generated by the hypocretin neuron. This effect is superimposed by a slow, continuous recovery process. The decreasing synaptic efficacy during the active wake state introduces an increasing sleep pressure. Ist dissipation during the silent sleep state results from the synaptic recovery. The model data demonstrate that the proposed mechanisms can account for typical alterations of homeostatic changes in sleep and wake states, including the effects of an alarm clock, napping and sleep deprivation. In combination with a circadian input, the model mimics the experimentally demonstrated transitions between different activity states of hypothalamic and thalamic neurons. In agreement with sleep-wake cycles, the activity of hypothalamic neurons changes from silence to firing, and the activity of thalamic neurons changes from synchronized bursting to unsynchronized single-spike discharges. These simulation results support the proposed concept of state-dependent alterations of hypocretin effects as an important homeostatic process in sleep-wake regulation, although additional mechanisms may be involved

How Coupling Determines the Entrainment of Circadian Clocks

Autonomous circadian clocks drive daily rhythms in physiology and behaviour. A network of coupled neurons, the suprachiasmatic nucleus (SCN), serves as a robust self-sustained circadian pacemaker. Synchronization of this timer to the environmental light-dark cycle is crucial for an organism's fitness. In a recent theoretical and experimental study it was shown that coupling governs the entrainment range of circadian clocks. We apply the theory of coupled oscillators to analyse how diffusive and mean-field coupling affects the entrainment range of interacting cells. Mean-field coupling leads to amplitude expansion of weak oscillators and, as a result, reduces the entrainment range. We also show that coupling determines the rigidity of the synchronized SCN network, i.e. the relaxation rates upon perturbation. %(Floquet exponents). Our simulations and analytical calculations using generic oscillator models help to elucidate how coupling determines the entrainment of the SCN. Our theoretical framework helps to interpret experimental data

Emergence of Noise-Induced Oscillations in the Central Circadian Pacemaker

Computational modeling and experimentation explain how intercellular coupling and intracellular noise can generate oscillations in a mammalian neuronal network even in the absence of cell-autonomous oscillators

Bursting synchronization in networks with long-range coupling mediated by a diffusing chemical substance

Many networks of physical and biological interest are characterized by a long-range coupling mediated by a chemical which diffuses through a medium in which oscillators are embedded. We considered a one-dimensional model for this effect for which the diffusion is fast enough so as to be implemented through a coupling whose intensity decays exponentially with the lattice distance. In particular, we analyzed the bursting synchronization of neurons described by two timescales (spiking and bursting activity), and coupled through such a long-range interaction network. One of the advantages of the model is that one can pass from a local (Laplacian) type of coupling to a global (all-to-all) one by varying a single parameter in the interaction term. We characterized bursting synchronization using an order parameter which undergoes a transition as the coupling parameters are changed through a critical value. We also investigated the role of an external time-periodic signal on the bursting synchronization properties of the network. We show potential applications in the control of pathological rhythms in biological neural networks.Comment: 13 figure