Ca2+-dependent hyperpolarization hypothesis for mammalian sleep

The "criticality hypothesis," based on observed scale-free correlations in neural activity, posits that the brain operates at a critical point of transition between two phases. However, the validity of this hypothesis is still debated. Here, employing a commonly used model of cortical dynamics, we find that a phase of long-range order (LRO) in neural activity may be induced by memory (time nonlocality) without invoking criticality. The cortical-dynamics model contains fast and slow time scales that govern the neural and resource (memory) dynamics, respectively. When the resource dynamics are sufficiently slow, we observe an LRO phase, which manifests in avalanche size and duration probability distributions that are fit well by power laws. When the slow and fast time scales are no longer sufficiently distinct, LRO is destroyed. Since this LRO phase spans a wide range of parameters, it is robust against perturbations, unlike critical systems.

The paper considers the eighth-order proton exchange membrane (PEM) fuel-cell mathematical model and shows that it has a multi-time scale property, indicating that the dynamics of three model state space variables operate in the slow time scale and the dynamics of five state variables operate in the fast time scale. This multi-scale nature allows independent controllers to be designed in slow and fast time scales using only corresponding reduced-order slow (of dimension three) and fast (of dimension five) sub-models. The presented design facilitates the design of hybrid controllers, for example, the linear-quadratic optimal controller for the slow subsystem and the eigenvalue assignment controller for the fast subsystem. The design efficiency and its high accuracy are demonstrated via simulation on the considered PEM fuel cell model.

Duration and quality of sleep are influenced by many factors, including hormonal changes. The aim of this study was to investigate the differences between the phases of the menstrual cycle in total sleep duration and sleep stage distribution, specifically the duration of rapid eye movement (REM) phase, light, and deep sleep states and compare sleep parameters between ovulatory and anovulatory cycles. The study involved 130 women aged 20-35 (mean = 26.2 years; SD = 4.14). Ovulation was detected using luteinizing hormone (LH) urine tests. Sleep data were collected using the Fitbit Alta HR trackers, which measured total sleep time and the duration of sleep stages. Sleep parameters were analyzed separately for each of the five phases: menstrual bleeding, follicular, periovulatory, luteal, and premenstrual using repeated measures ANOVA. Differences between ovulatory and anovulatory cycles were assessed using Student's t-test. Women with the ovulatory cycle slept longer and had longer REM phases compared to women without ovulation. No statistically significant differences were observed in total sleep duration or sleep stage distribution across five phases of the menstrual cycle among women with detected ovulation. The findings suggest that ovulatory status might be associated with differences in total sleep time and REM sleep duration, whereas sleep duration and sleep stage distribution across menstrual cycle phases remain relatively constant. These results suggest that the presence of ovulation, rather than phase-specific changes during the cycle, may play a more important role in shaping sleep characteristics.

Sleep is the preferential period when epileptic spike–wave discharges appear in human epileptic patients, including genetic epileptic seizures such as Dravet syndrome with multiple mutations including SCN1A mutation and GABAA receptor γ2 subunit Gabrg2Q390X mutation in patients, which presents more severe epileptic symptoms in female patients than male patients. However, the seizure onset mechanism during sleep still remains unknown. Our previous work has shown that the sleep-like state-dependent homeostatic synaptic potentiation can trigger epileptic spike–wave discharges in one transgenic heterozygous Gabrg2+/Q390X knock-in mouse model.1 Here, using this heterozygous knock-in mouse model, we hypothesized that slow-wave oscillations themselves in vivo could trigger epileptic seizures. We found that epileptic spike–wave discharges in heterozygous Gabrg2+/Q390X knock-in mice exhibited preferential incidence during non-rapid eye movement sleep period, accompanied by motor immobility/facial myoclonus/vibrissal twitching and more frequent spike–wave discharge incidence appeared in female heterozygous knock-in mice than male heterozygous knock-in mice. Optogenetically induced slow-wave oscillations in vivo significantly increased epileptic spike–wave discharge incidence in heterozygous Gabrg2+/Q390X knock-in mice with longer duration of non-rapid eye movement sleep or quiet–wakeful states. Furthermore, suppression of slow-wave oscillation-related homeostatic synaptic potentiation by 4-(diethylamino)-benzaldehyde injection (i.p.) greatly attenuated spike–wave discharge incidence in heterozygous knock-in mice, suggesting that slow-wave oscillations in vivo did trigger seizure activity in heterozygous knock-in mice. Meanwhile, sleep spindle generation in wild-type littermates and heterozygous Gabrg2+/Q390X knock-in mice involved the slow-wave oscillation-related homeostatic synaptic potentiation that also contributed to epileptic spike–wave discharge generation in heterozygous Gabrg2+/Q390X knock-in mice. In addition, EEG spectral power of delta frequency (0.1–4 Hz) during non-rapid eye movement sleep was significantly larger in female heterozygous Gabrg2+/Q390X knock-in mice than that in male heterozygous Gabrg2+/Q390X knock-in mice, which likely contributes to the gender difference in seizure incidence during non-rapid eye movement sleep/quiet–wake states of human patients. Overall, all these results indicate that slow-wave oscillations in vivo trigger the seizure onset in heterozygous Gabrg2+/Q390X knock-in mice, preferentially during non-rapid eye movement sleep period and likely generate the sex difference in seizure incidence between male and female heterozygous Gabrg2+/Q390X knock-in mice.

Meta-equilibrium state of multi-species ambipolar diffusion and its relevance to polar mesopheric summer echoes

We examined the role of the cerebellum in patients with tremor-dominant cervical dystonia by measuring the adaptive capacity of rapid reflexive eye movements (saccades). We chose the saccade adaptation paradigm because, unlike other motor learning paradigms, the real-time modification of saccades cannot "wait" for the sensory (visual) feedback. Instead, saccades rely primarily on the internal reafference modulated by the cerebellum. The saccade adaptation happens over fast and slow timescales. The fast timescale has poor retention of learned response, while the slow timescale has strong retention. Cerebellar defects resulting in loss of function affect the fast timescale but the slow timescale of saccade adaptation is retained. In contrast, maladaptive cerebellar disorders feature the absence of both fast and slow timescales. We were able to measure both timescales using noninvasive oculography in 6 normal individuals. In contrast, both timescales were absent in 12 patients with tremor-dominant cervical dystonia. These findings are consistent with maladaptive cerebellar outflow as a putative pathophysiological basis for tremor-dominant cervical dystonia.

In this paper, we present a review about mathematical models of population and community dynamics incorporating individual behaviour. The considered models consist in coupling a game theoretic model, going on at a fast time scale and that describes the change of tactics among individuals in a population or in a community to a model going on at a slow time scale describing the effects in the long term of individual tactics on reproduction and mortality of the populations. As application, an extension of a stage-structured population with intra-individual behavioural variability is presented. Individuals can adopt three different tactics: hawk, dove and bully. We consider a stage-structured population with immature and mature individuals. A mature individual experiences the different tactics in his life and it is assumed that the game is played at a fast time scale in comparison to population dynamics. This fast part of the model is coupled to a slow part, which describes the growth of each sub-population. By use of aggregation of variables methods, we obtain a reduced system of two differential equations governing immature and total mature sub-populations at the slow time scale. The analysis of the model shows that when the cost of fightings is smaller, the proportion of hawks is larger. The total population size equilibrium shows a maximum with respect to the gain of the game.

In recent years technology development for the design of electric and hybrid-electric vehicle systems has reached a peak, due to ever increasing restrictions on fuel economy and reduced vehicle emissions. An international race among car manufacturers to bring production hybrid-electric vehicles to market has generated a great deal of interest in the scientific community. The design of these systems requires development of new simulation and optimization tools. In this paper, a description of a real-time numerical environment for Virtual Proving Grounds studies for hybrid-electric vehicles is presented. Within this environment, vehicle models are developed using a recursive multibody dynamics formulation that results in a set of Differential-Algebraic Equations (DAE), and vehicle subsystem models are created using Ordinary Differential Equations (ODE). Based on engineering knowledge of vehicle systems, two time scales are identified. The first time scale, referred to as slow time scale, contains generalized coordinates describing the mechanical vehicle system that includs the chassis, steering rack, and suspension assemblies. The second time scale, referred to as fast time scale, contains the hybrid-electric powertrain components and vehicle tires. Multirate techniques to integrate the combined set of DAE and ODE in two time scales are used to obtain computational gains that will allow solution of the system’s governing equations for state derivatives, and efficient numerical integration in real time.

Associations between sleep duration and sleep debt with insulin sensitivity and insulin secretion in the EGIR-RISC Study

Long-range effects, such as allostery, have evolved in proteins as a means of regulating function via communication between distal sites. An NMR-based perturbation mapping approach was used to more completely probe the dynamic response of the core mutation V54A in the protein eglin c by monitoring changes in picosecond to nanosecond aromatic side-chain dynamics and H/D exchange stabilities. Previous side-chain dynamics studies on this mutant were limited to methyl-bearing residues, most of which were found to rigidify on the picosecond to nanosecond time scale in the form of a contiguous "network". Here, high precision (13)C relaxation data from 13 aromatic side chains were acquired by applying canonical relaxation experiments to a newly developed carbon labeling scheme [Teilum et al. (2006) J. Am. Chem. Soc. 128, 2506-2507]. The fitting of model-free parameters yielded S (2) variability which is intermediate with respect to backbone and methyl-bearing side-chain variability and tau e values that are approximately 1 ns. Inclusion of the aromatic dynamic response results in an expanded network of dynamically coupled residues, with some aromatics showing increases in flexibility, which partially offsets the rigidification in methyl side chains. Using amide hydrogen exchange, dynamic propagation on a slower time scale was probed in response to the V54A perturbation. Surprisingly, regional stabilization (slowed exchange) 10-12 A from the site of mutation was observed despite a global destabilization of 1.5 kcal x mol (-1). Furthermore, this unlikely pocket of stabilized residues colocalizes with increases in aromatic flexibility on the faster time scale. Because the converse is also true (destabilized residues colocalize with rigidification on the fast time scale), a plausible entropy-driven mechanism is discussed for relating colocalization of opposing dynamic trends on vastly different time scales.

Aqueous hydroxyl group as the vibrational probe to access the hydrophobicity of amide derivatives

Exercise has been recommended for enhancing sleep; a claim linked to the belief that sleep need – defined by sleep duration and depth – is increased post-exercise to allow tissue recovery. Objective studies investigating exercise–sleep responses have produced mixed outcomes, and the disparity in results between studies may be due to differences in individual characteristics and/or exercise protocol, emphasising the importance of carefully controlled trials. We investigated the role of exercise on the sleep need of sedentary adults, after controlling for exercise mode, timing and duration. Twelve healthy volunteers (25.2 ± 4.0 years, 9 females, [Vdot]O2max 35.4 ± 8.8 ml· kg–1 · min–1) were randomised to no-exercise or to a bout of treadmill exercise at 45%, 55%, 65% or 75% [Vdot]O2max in a crossover design. Sleep on no-exercise and exercise nights were assessed by polysomnography. Participants spent a greater proportion of sleep in light sleep (stage 1 + stage 2) after exercise at both 65% and 75% [Vdot]O2max (P < 0.05) than the no-exercise condition. There was a trend of a reduced proportion of rapid eye movement sleep with increased exercise intensity (P = 0.067). No other changes were observed in any other sleep variables. Two findings emerged: vigorous exercise did not increase sleep need; however, this level of exercise increased light sleep.

In this study, acoustic pressure oscillations for single and coupled longitudinal acoustic modes in Solid Rocket Motor (SRM) are investigated using Multiple Time Scales (MTS) method. Two independent time scales are introduced. The oscillations occur on fast time scale whereas the amplitude and phase changes on slow time scale. Hopf bifurcation is employed to investigate the properties of the solution. The supercritical bifurcation phenomenon is observed for linearly unstable system. The amplitude of the oscillations result from equal energy gain and loss rates of longitudinal acoustic modes. The effect of linear instability and frequency of longitudinal modes on amplitude and phase of oscillations are determined for both single and coupled modes. For both cases, the maximum amplitude of oscillations decreases with the frequency of acoustic mode and linear instability of SRM. The comparison of analytical MTS results and numerical simulations demonstrate an excellent agreement.

This paper studies large deviations of a “fully coupled” finite state mean-field interacting particle system in a fast varying environment. The empirical measure of the particles evolves in the slow time scale and the random environment evolves in the fast time scale. Our main result is the path-space large deviation principle for the joint law of the empirical measure process of the particles and the occupation measure process of the fast environment. This extends previous results known for two time scale diffusions to two time scale mean-field models with jumps. Our proof is based on the method of stochastic exponentials. We characterise the rate function by studying a certain variational problem associated with an exponential martingale.

Multi-time-scale 3-D coordinated formation control for multi-underactuated AUV with uncertainties: Design and stability analysis using singular perturbation methods