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Cellular plasticity at the structural level and sleep at the behavioural level are both essential for memory formation. The link between the two is not well understood. A functional connection between adult neurogenesis and hippocampus-dependent memory consolidation during NREM sleep has been hypothesized but not experimentally shown. Here, we present evidence that during a three-day learning session in the Morris water maze task a genetic knockout model of adult neurogenesis (Cyclin D2−/−) showed changes in sleep macro- and microstructure. Sleep EEG analyses revealed a lower total sleep time and NREM fraction in Cyclin D2−/− mice as well as an impairment of sleep specific neuronal oscillations that are associated with memory consolidation. Better performance in the memory task was associated with specific sleep parameters in wild-type, but not in Cyclin D2−/− mice. In wild-type animals the number of proliferating cells correlated with the amount of NREM sleep. The lack of adult neurogenesis led to changes in sleep architecture and oscillations that represent the dialog between hippocampus and neocortex during sleep. We suggest that adult neurogenesis—as a key event of hippocampal plasticity—might play an important role for sleep-dependent memory consolidation and modulates learning-induced changes of sleep macro- and microstructure.

Inhibitory circuits of relaxation oscillators are often-used models for dynamics of biological networks. We present a qualitative and quantitative stability analysis of such a circuit constituted by three generic oscillators (of a Fitzhugh-Nagumo type) as its nodes coupled reciprocally. Depending on inhibitory strengths, and parameters of individual oscillators, the circuit exhibits polyrhythmicity of up to five simultaneously stable rhythms. With methods of bifurcation analysis and phase reduction, we investigate qualitative changes in stability of these circuit rhythms for a wide range of parameters. Furthermore, we quantify robustness of the rhythms maintained under random perturbations by monitoring phase diffusion in the circuit. Our findings allow us to describe how circuit dynamics relate to dynamics of individual nodes. We also find that quantitative and qualitative stability properties of polyrhythmicity do not always align.

Maintaining temporal coordination across physiological systems is crucial at the wake-sleep transition. As shown in recent studies, the degree of coordination between brain and autonomic arousal influences attention, which highlights a previously unrecognised point of potential failure in the attention system. To investigate how cortical and autonomic dynamics are linked to the attentive process we analysed electroencephalogram, electrocardiogram and skin conductance data of 39 healthy adults recorded during a 2-h resting-state oddball experiment. We related cross-correlations to fluctuation periods of cortical and autonomic signals and correlated obtained measures to event-related potentials N1 and P2, reflecting excitatory and inhibitory processes. Increasing alignment of cortical and autonomic signals and longer periods of vigilance fluctuations corresponded to a larger and earlier P2; no such relations were found for N1. We compared two groups, with (I) and without measurable (II) delay in cortico-autonomic correlations. Individuals in Group II had more stable vigilance fluctuations, larger and earlier P2 and fell asleep more frequently than individuals in Group I. Our results support the hypothesis of a link between cortico-autonomic coupling and dynamics and central inhibition. Quantifying this link could help refine classification in psychiatric disorders with attention and sleep-related symptoms, particularly in ADHD, depression, and insomnia.

Appearances of alpha waves in the sleep electrencephalogram indicate physiological, brief states of awakening that lie in between wakefulness and sleep. These microstates may also cause the loss in sleep quality experienced by individuals suffering from insomnia. To distinguish such pathological awakenings from physiological ones, differences in alpha-wave characteristics between transient awakening and wakefulness observed before the onset of sleep were studied. In polysomnographic datasets of sleep-healthy participants (n = 18) and patients with insomnia (n = 10), alpha waves were extracted from the relaxed, wake state before sleep onset, wake after sleep-onset periods and arousals of sleep. In these, alpha frequency and variability were determined as the median and standard deviation of inverse peak-to-peak intervals. Before sleep onset, patients with insomnia showed a decreased alpha variability compared with healthy participants (P

We present a method that facilitates a phase description of collective, irregular-oscillatory dynamics from unreliable multichannel recordings. The collective oscillations may be represented in each channel with fluctuating amplitude, phase offsets, and substantial amounts of measurement noise. Our method performs well under such realistic conditions, as we exemplify with collective brain rhythms in multichannel electroencephalogram recordings.

We identify and describe the key qualitative rhythmic states in various 3-cell network motifs of a multifunctional central pattern generator (CPG). Such CPGs are neural microcircuits of cells whose synergetic interactions produce multiple states with distinct phase-locked patterns of bursting activity. To study biologically plausible CPG models, we develop a suite of computational tools that reduce the problem of stability and existence of rhythmic patterns in networks to the bifurcation analysis of fixed points and invariant curves of a Poincar\'e return maps for phase lags between cells. We explore different functional possibilities for motifs involving symmetry breaking and heterogeneity. This is achieved by varying coupling properties of the synapses between the cells and studying the qualitative changes in the structure of the corresponding return maps. Our findings provide a systematic basis for understanding plausible biophysical mechanisms for the regulation of rhythmic patterns generated by various CPGs in the context of motor control such as gait-switching in locomotion. Our analysis does not require knowledge of the equations modeling the system and provides a powerful qualitative approach to studying detailed models of rhythmic behavior. Thus, our approach is applicable to a wide range of biological phenomena beyond motor control.

We introduce an invariant phase description of stochastic oscillations by generalizing the concept of standard isophases. The average isophases are constructed as sections in the state space, having a constant mean first return time. The approach allows to obtain a global phase variable of noisy oscillations, even in the cases where the phase is ill-defined in the deterministic limit. A simple numerical method for finding the isophases is illustrated for noise-induced switching between two coexisting limit cycles, and for noise-induced oscillation in an excitable system. We also discuss how to determine the isophases for experimentally observed irregular oscillations, providing a basis for a refined phase description of observed oscillatory dynamics., Comment: 4 pages

We introduce an optimal phase description of chaotic oscillations by generalizing the concept of isochrones. On chaotic attractors possessing a general phase description, we define the optimal isophases as Poincar\'e surfaces showing return times as constant as possible. The dynamics of the resultant optimal phase is maximally decoupled of the amplitude dynamics, and provides a proper description of phase resetting of chaotic oscillations. The method is illustrated with the R\"ossler and Lorenz systems., Comment: 10 Pages, 14 Figures

An effective dynamical description of a general class of stochastic phase oscillators is presented. For this, the effective phase velocity is defined either by the stochastic phase oscillators invariant probability density or its first passage times. Using the first approach the effective phase exhibits the correct frequency and invariant distribution density, whereas the second approach models the proper phase resetting curve. The discrepancy of the effective models is most pronounced for noise-induced oscillations and is related to non-monotonicity of the stochastic phase variable due to fluctuations.

We develop an effective description of noise-induced oscillations based on deterministic phase dynamics. The phase equation is constructed to exhibit correct frequency and distribution density of noise-induced oscillations. In the simplest one-dimensional case the effective phase equation is obtained analytically, whereas for more complex situations a simple method of data processing is suggested. As an application an effective coupling function is constructed that quantitatively describes periodically forced noise-induced oscillations., This paper has been withdrawn by the author due to errors in Fig. 3 and faulty conclusions drawn from Fig. 4