Sleep decreases neuronal activity control of microglial dynamics in mice.

Microglia, the brain-resident immune cells, are highly ramified with dynamic processes transiently contacting synapses. These contacts have been reported to be activity-dependent, but this has not been thoroughly studied yet, especially in physiological conditions. Here we investigate neuron-microglia contacts and microglia morphodynamics in mice in an activity-dependent context such as the vigilance states. We report that microglial morphodynamics and microglia-spine contacts are regulated by spontaneous and evoked neuronal activity. We also found that sleep modulates microglial morphodynamics through Cx3cr1 signaling. At the synaptic level, microglial processes are attracted towards active spines during wake, and this relationship is hindered during sleep. Finally, microglial contact increases spine activity, mainly during NREM sleep. Altogether, these results indicate that microglial function at synapses is dependent on neuronal activity and the vigilance states, providing evidence that microglia could be important for synaptic homeostasis and plasticity.

Sleep dynamics: a self-organized critical system.

In psychiatric and neurological diseases, sleep is often perturbed. Moreover, recent works on humans and animals tend to show that sleep plays a strong role in memory processes. Reciprocally, sleep dynamics following a learning task is modified [Hubert, Nature (London) 02663, 1 (2004), Peigneux, Neuron 44, 535 (2004)]. However, sleep analysis in humans and animals is often limited to the total sleep and wake duration quantification. These two parameters are not fully able to characterize the sleep dynamics. In mammals sleep presents a complex organization with an alternation of slow wave sleep (SWS) and paradoxical sleep (PS) episodes. Moreover, it has been shown recently that these sleep episodes are frequently interrupted by micro-arousal (without awakening). We present here a detailed analysis of the basal sleep properties emerging from the mechanisms underlying the vigilance states alternation in an animal model. These properties present a self-organized critical system signature and reveal the existence of two W, two SWS, and a PS structure exhibiting a criticality as met in sand piles. We propose a theoretical model of the sleep dynamics based on several interacting neuronal populations. This new model of sleep dynamics presents the same properties as experimentally observed, and explains the variability of the collected data. This experimental and theoretical study suggests that sleep dynamics shares several common features with critical systems.

Exact discrete breather compactons in nonlinear Klein-Gordon lattices.

We demonstrate the existence of exact discrete compact breather solutions in nonlinear Klein-Gordon systems, and complete the work of Tchofo Dinda and Remoissenet [Phys. Rev. E 60, 6218 (1999)], by showing that the breathers stability is related principally to the lattice boundary conditions, the coupling term, and the harmonicity parameter.

Exact discrete compactlike traveling kinks and pulses in phi(4) nonlinear lattices.

We show that by properly choosing the analytical form of a solitary wave solution of discrete phi(4) models we can calculate the parameters of the potential which allow the propagation of compact (kink and pulses) solutions. Our numerical simulations show that narrow kinks and pulses with finite extent can propagate freely, and that discrete breathers with finite but long lifetime, can emerge from their collisions. Moreover, our numerical simulations reveal that the propagation of two successive pulses at a relative distance of two lattice spacings propagate freely, i.e., without interaction.

Discrete Burridge-Knopoff model, with exact solitonic or compactlike traveling wave solution.

We have explored the dynamics of two versions of a Burridge-Knopoff model: with linear or nonlinear interactions between adjacent blocks. We have shown that by properly choosing the analytical form of the discrete solitary wave solution of the model we can calculate analytically the form of the friction function. In both cases our analytical results show that the friction force naturally presents the behavior of a simple weakening friction law first introduced qualitatively by Burridge and Knopoff [Bull. Seismol. Soc. Am. 57, 3411 (1967)] and quantitatively by Carlson and Langer [Phys. Rev. Lett. 62, 2632 (1989)]. With such a force function the discrete solitonic or compactlike wave-front solutions are exact and stable solutions. In the case of linear coupling our numerical simulations show that an irregular initial state evolves into kink pairs (large-amplitude events), that can recombine or not, plus nonlinear localized modes and small linear oscillations (small-amplitude events) that disperse with time, owing to dispersion. For nonlinear coupling one observes compactlike kink pairs or shocks, and a background of robust incoherent nonlinear oscillations (small amplitude events) that persist with time. Our results show that discreteness is a necessary ingredient to observe a rich and complex dynamical behavior. Nonlinearity allows the existence of strictly localized shocks.

Propagation failure in discrete bistable reaction-diffusion systems: theory and experiments.

Wave front propagation failure is investigated in discrete bistable reaction-diffusion systems. We present a theoretical approach including dissipative effects and leading to an analytical expression of the critical coupling beyond which front propagation can occur as a function of the nonlinearity threshold parameter. Our theoretical predictions are confirmed by numerical simulations and experimental results on an equivalent electrical diffusive lattice.

Dissipative lattice model with exact traveling discrete kink-soliton solutions: discrete breather generation and reaction diffusion regime.

We introduce a nonlinear Klein-Gordon lattice model with specific double-well on-site potential, additional constant external force and dissipation terms, which admits exact discrete kink or traveling wave fronts solutions. In the non-dissipative or conservative regime, our numerical simulations show that narrow kinks can propagate freely, and reveal that static or moving discrete breathers, with a finite but long lifetime, can emerge from kink-antikink collisions. In the general dissipative regime, the lifetime of these breathers depends on the importance of the dissipative effects. In the overdamped or diffusive regime, the general equation of motion reduces to a discrete reaction diffusion equation; our simulations show that, for a given potential shape, discrete wave fronts can travel without experiencing any propagation failure but their collisions are inelastic.